Vol. 5 N.2 - Journal of Aerospace Technology and Management by Journal of Aerospace Technology and Management

Journal of aerospace technology and management

JOURNAL OF AEROSPACE TECHNOLOGY AND MANAGEMENT Vol. 5 N. 2 Apr./Jun. 2013 ISSN 1984-9648 ISSN 2175-9146 (online)

www.jatm.com.br

V.5, n. 2, apr./Jun., 2013

Journal of Aerospace Technology and Management

General Information Journal of Aerospace Technology and Management (JATM) is a techno-scientific publication serialized, published by Departamento de Ciência e Tecnologia Aeroespacial (DCTA) and aims to serve the international aerospace community. It contains articles that have been selected by an Editorial Committee composed of researchers and technologists from the scientific community. The journal is quarterly published, and its main objective is to provide an archival form of presenting scientific and technological research results related to the aerospace field, as well as promote an additional source of diffusion and interaction, providing public access to all of its contents, following the principle of making free access to research and generate a greater global exchange of knowledge. JATM is added/indexed in the following databases; SCOPUS - Elsevier; CAS - Chemical Abstracts Service; DOAJ - Directory of Open Access Journals; J-GATE - The e-journal gateway from global literature; LIVRE - Portal to Free Access Journals; GOOGLE SCHOLAR; SUMÁRIOS.ORG - Summaries of Brazilian Journals; EZB- Electronic Journals Library; ULRICHSWEB- Ulrich´s Periodicals Directory; SOCOL@R- China Educational Publications; LATINDEX-Regional Cooperative Online Information System for Scholarly Journals from Latin America, the Caribbean, Spain and Portugal; REDALYC - Red de Revistas Científicas de América Latina y el Caribe, España y Portugal; EBSCO Publishing and PERIÓDICOS CAPES. In WEB QUALIS System, JATM is classified as B4 in the Geosciences and Engineering III areas. JATM is affiliated to ABEC - Brazilian Association of Scientific Editors and all published articles contain DOI numbers attributed by CROSSREF.

Correspondence All correspondence should be sent to: Dr Ana Cristina Avelar Journal of Aerospace Technology and Management Instituto de Aeronáutica e Espaço Praça Mal. Eduardo Gomes, 50 - Vila das Acácias CEP 12228-901 São José dos Campos/ São Paulo/Brazil Contact Phone: (55) 12-3947- 6493/5122 E-mail: editor@jatm.com.br Web: http://www.jatm.com.br Published by: Departamento de Ciência e Tecnologia Aeroespacial Distributed by: Instituto de Aeronáutica e Espaço Editing, proofreading and standardization: Zeppelini Editorial Printing: RR Donnelley Edition: 500 São José dos Campos, SP, Brazil ISSN 1984-9648

JATM is supported by:

Journal of Aerospace Technology and Management Vol. 5, n.2 (Apr./Jun. 2013) – São José dos Campos: Zeppelini Editorial, 2013 Quartely issued Aerospace sciences Technologies Aerospace engineering CDU: 629.73

Historical Note: JATM was created in 2009 after the iniciative of the diretor of Instituto de Aeronáutica e Espaço (IAE), Brigadeiro Engenheiro Francisco Carlos Melo Pantoja. In order to reach the goal of becoming a journal that could represent knowledge in science and aerospace technology, JATM searched for partnerships with others institutions in the same field from the beginning. From September 2011, it has been edited by the Departamento de Ciência e Tecnologia Aeroespacial (DCTA), and it also started to be financially supported by Fundação Conrado Wessel. The copyright on all published material belongs to Departamento de Ciência e Tecnologia Aeroespacial (DCTA)

ISSN 1984-9648 ISSN 2175-9146 (online)

Journal of Aerospace Technology and Management Vol. 5 No. 2 - Apr./Jun. 2013 Editor in Chief

Executive Editor

ASSISTANT EDITOR

Ana Cristina Avelar Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil editor@jatm.com.br

Ana Marlene F. Morais Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil secretary@jatm.com.br

Roberto Gil Annes da Silva Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil roberto.gil.silva@gmail.com

Angelo Passaro Instituto de Estudos Avançados São José dos Campos/SP – Brazil

Eduardo Morgado Belo Escola de Engenharia de São Carlos São Carlos/SP – Brazil

Marco A. Sala Minucci Vale Soluções em Energia São José dos Campos/SP – Brazil

Antonio Pascoal Del’Arco Jr Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Francisco Carlos M. Pantoja Diretoria de Engenharia da Aeronáutica Rio de Janeiro/RJ – Brazil

Mischel Carmen N. Belderrain Instituto Tecnológico de Aeronáutica São José dos Campos/SP – Brazil

Carlos Antônio M. Kasemodel Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Francisco Cristovão L. Melo Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Paulo Tadeu de Melo Lourenção EMBRAER São José dos Campos/SP – Brazil

Carlos de Moura Neto Instituto Tecnológico de Aeronáutica São José dos Campos/SP – Brazil

João Marcos T. Romano Universidade Estadual de Campinas Campinas/SP – Brazil

Rita de Cássia L. Dutra Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Acoustics

Applied computation

Ceramic Materials

Marcello A. Faraco de Medeiros Escola de Engenharia de São Carlos São Carlos/SP – Brazil

José Márcio Machado Instituto de Biociências, Letras e Ciências Exatas São José do Rio Preto/SP – Brazil

José Maria Fonte Ferreira Universidade de Aveiro Aveiro – Portugal

Aerodynamics

Romis R. F. Attux Universidade Estadual de Campinas Campinas/SP – Brasil

Circuitry

SCIENTIFIC COUNCIL

ASSOCIATE EDITORS Bert Pluymers Katholieke Universiteit Leuven Leuven – Belgium

Acir Mércio Loredo Souza Universidade Federal do Rio Grande do Sul Porto Alegre/RS – Brazil João Luiz F. Azevedo Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Aerospace Meteorology Gilberto Fisch Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil Willian W. Vaughan University of Alabama Huntsville/AL – USA

Carlos Henrique Netto Lahoz Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Astrodynamics

Antonio Sergio Bezerra Sombra Universidade Federal do Ceará Fortaleza/CE – Brazil

Altamiro Susin Universidade Federal do Rio Grande do Sul Porto Alegre/RS – Brazil

Antonio F. Bertachini Instituto Nacional de Pesquisas Espaciais São José dos Campos/SP – Brazil

Raimundo Freire Universidade Federal de Campina Grande Campina Grande/PB – Brazil

Othon Cabo Winter Faculdade de Engenharia de Guaratinguetá Guaratinguetá/SP – Brazil

Composites

Edson Cocchieri Botelho Faculdade de Engenharia de Guaratinguetá Guaratinguetá/SP – Brazil Flamínio Levy Neto Universidade de Brasília Brasília/DF – Brazil

Computational fluid dynamics

Joern Sesterhenn Technische Universität Berlin Berlin – Germany John Cater University of Auckland Auckland – New Zealand Paulo Celso Greco Escola de Engenharia de São Carlos São Carlos/SP – Brazil

Defense Systems

Adam S. Cumming Defence Science and Technology Laboratory Salisbury/Wiltshire – England Wim P. C. de Klerk Netherlands Organisation for Applied Scientific Research Rijswijk/SH – Netherlands

Eletromagnetic Compatibility

Alain Azoulay École Supérieure d’Electricité Gif–Sur–Yvette – France Cynthia Junqueira Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Energetic Materials Elizabeth da Costa Mattos Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Guidance, Navigation and Control

Radars and Tracking Systems

David Murray–Smith University of Glasgow Glasgow – Scotland

Marc Lesturgie Office National d’Etudes et de Recherches Aérospatiales Palaiseau – France

Daniel Alazard Institut Supérieur de l’Aéronautique et de l’Espace Toulouse – France

Waldemar de Castro Leite Filho Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Management Systems

André Fenili Universidade Federal do ABC Santo André/SP – Brazil

Sadek Crisostomo Absi Alfaro Universidade de Brasília Brasília/DF – Brazil

Antonio Henriques de Araújo Jr Universidade Estadual do Rio de Janeiro Resende/RJ – Brazil

Structures

Metallic Materials

José Rubens G. Carneiro Pontifícia Universidade Católica de Minas Gerais Belo Horizonte – Brazil

Photonics

Álvaro Damião Instituto de Estudos Avançados São José dos Campos/SP – Brazil

Polimeric Materials Cristina Tristão de Andrade Instituto de Macromoléculas Rio de Janeiro/RJ – Brazil

Mirabel Cerqueira Rezende Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Fluid Dynamics and Turbulence

Processing of Aerospace Materials

Vassilis Theofilis Universidad Politécnica de Madrid Madrid – Spain

Robotics and Automation

Adiel Teixeira de Almeida Universidade Federal de Pernambuco Recife/PE – Brazil

José Leandro Andrade Campos Universidade de Coimbra Coimbra – Portugal

Marcos Pinotti Barbosa Universidade Federal de Minas Gerais Belo Horizonte/MG – Brazil

Hugo H. Figueroa Universidade Estadual de Campinas Campinas/SP – Brazil

Alexandre Queiroz Bracarense Universidade Federal de Minas Gerais Belo Horizonte/MG – Brazil

Propulsion and Combustion

Fernando de Souza Costa Instituto Nacional de Pesquisa Espacial São José dos Campos/SP, Brazil

Sérgio Frascino M. Almeida Instituto Tecnológico de Aeronáutica São José dos Campos/SP – Brazil

Synthesis and Characterization of Aerospace Materials

Gilson da Silva Instituto Nacional da Propriedade Industrial Rio de Janeiro/RJ – Brazil Roberto Costa Lima Instituto de Pesquisas da Marinha Rio de Janeiro/RJ – Brazil

Thermal Sciences

Márcia B. H. Mantelli Universidade Federal de Santa Catarina Florianópolis/SC – Brazil Renato Machado Cotta Universidade Federal do Rio de Janeiro Rio de Janeiro/RJ – Brazil

Vibration and Structural Dynamics Carlos Cesnik University of Michigan Ann Arbor/MI – USA

Valder Steffen Junior Universidade Federal de Uberlândia Uberlândia/MG – Brazil

Carlos Henrique Marchi Universidade Federal do Paraná Curitiba/PR – Brazil

Editorial Production Glauco da Silva Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Lucia Helena de Oliveira Depart. Ciência e Tecnologia Aeroespacial São José dos Campos/SP – Brazil

Helena Prado A.Silva Instituto de Aeronáutica e Espaço São José dos Campos/SP – Brazil

Mônica E. Rocha de Oliveira Instituto Nacional de Pesquisas Espaciais São José dos Campos/SP – Brazil

Rosilene Maria M. Costa Instituto de Estudos Avançados São José dos Campos/SP – Brazil

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, 2013

ISSN 1984-9648 | ISSN 2175-9146 (online)

CONTENTS Editorial 137 Research activities in space program: thinking paradigm Osvaldo Catsumi Imamura REVIEW ARTICLE 139 Green Propellants: Oxidizers Gilson da Silva, Simone Carvalho Rufino, Koshun Iha ORIGINAL PAPERS 145 A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations Carlos Junqueira-Junior, Joao Luiz F. Azevedo, Leonardo C. Scalabrin, Edson Basso 169 A numerical investigation of localized and steady energy addition to high speed airflows André Carlos Fraile Jr, Mauricio Antoniazzi Pinheiro Rosa 181 Large Eddy Simulation of Bluff Body Stabilized Turbulent Premixed Flame Nicolas Moisés Cruz Salvador, Márcio Teixeira de Mendonça, Wladimyr Mattos da Costa Dourado 197 Experimental Valuation Diagnostics of Hydrous Ethanol Sprays Formed by a Blurry Injector Claudia Gonçalves de Azevedo, José Carlos de Andrade, Fernando de Souza Costa 205 Effect of Fiber Optic Chromatic Dispersion on the Performance of Analog Optical Link with External Modulation Aiming at Aerospace Applications Antonio Alves Ferreira Júnior, Olympio Lucchini Coutinho, Carla de Sousa Martins, William dos Santos Fegadolli, José Antônio Justino Ribeiro, Vilson Rosa de Almeida, José Edimar Barbosa Oliveira 217 Determining the Fixed Pattern Noise of a CMOS Sensor: Improving the Sensibility of Autonomous Star Trackers Eduardo dos Santos Pereira 223 On the Determination of a Scatter Factor for Fatigue Lives Based on the Lead Crack Concept Adriano Francisco Siqueira, Carlos Antonio Reis Pereira Baptista, Loris Molent 231 Development of Polyamide 6/Compoundby Recycled Rubber Blends Using Graphitized Polyethylene or Polypropylene with Maleic Anhydride as Compatibilizer Agent Divânia Ferreira da Silva, Edcleide Maria Araújo, Tomás Jeferson Alves de Melo 241 Environmental Effects on Thermal Properties of PEI/Glass Fiber Composite Materials Edson Cocchieri Botelho, José Carlos Bravim Júnior, Michelle Leali Costa, Maria Candida Magalhaes de Faria THESIS ABSTRACTS 255 Ultrahigh Molecular Weight Polyethylene as a Base Material for Shielding Cosmic Radiation in Aerospace Applications Marlon Antonio Pereira

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, 2013

ISSN 1984-9648 | ISSN 2175-9146 (online)

255 Analytical Techniques by Via Humid and Instrumental for Characterization of Bonding Agents Used in Solid Propellants Darci Côrtes Pires 256 Synthesis, Characterization and Application of Glycidyl Azide Polymer in the Development of New Propellants to the Brazilian Aerospace Program Jairo Sciamareli 257 INSTRUCTIONS TO AUTHORS

Editorial Research activities in space program: thinking paradigm Osvaldo Catsumi Imamura1

pace Program is one of the most ancient activity initiated by the human being. The model of program management was prepared in the last century during the World War and space rush. The Brazilian Government Space Program started in the 1970s motivated by scientific needs to access environmental and space observations. This is a very interesting way to initiate a space program, however it may be the most challenging one. This includes developing some artifacts and knowledge with scientific and technological trends, consuming a lot of human skills and financial funds. Managing this kind of initiative requires future vision, planning, and discipline. John Fitzgerald Kennedy, former president of the United States, presented one interesting space program promotion in his speech at Rice University (September 12th, 1962): “We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too”. The challenge faced is to determine the objective, goals, and start designing how we have to work to carry this out. The Brazilian Government National Program for Space Activities 2012–2021 provides the following message: “This forth version […] is certainly more realistic than the previous ones, but it also has its eyes set on horizon of dreams. It is realistic, because it seeks the path of concrete and productive achievement. It dreams, because it seeks to promote strong

changes in the spirit and way in which our space activities are conducted. It is a far dream”. Bearing these two statements in mind, the paradigm we have to deal with is the promotion of academic and scientific achievements in order to produce results we can measure to keep the path to the horizon. Therefore, there are three ways to exercise the construction of a new paradigm. Firstly, sharing our scientific achievements with collective working in the same area of interest to promote deep interaction and results; secondly, activating those results to ignite technological developments for deploying new components and products; and thirdly, government-inducted nationwide programs can direct and accelerate the production of results in the scientific and technological domains. The Brazilian Geostationary Satellite for Defense and Communications (SGDC) is one opportunity to introduce catalytic effort for capacity development. Although the project orientation focuses on launching a satellite in a very short timeline, it may drive research activities on new materials, technology, and systems to review some ill conditioned problems with the aim of finding a new direction and a new challenge. Working in the environment we call space seems to be a hard work. If we imagine that we are living and thinking in a subset of space, it is possible to see that we can do more and discover new challenges and opportunities to innovate. Research in Space Program is a great road for refining our thinking paradigm to develop management skills for conducting scientific and technological activities aligned with our dreams, but producing capacity and metrics to evaluate every achievement.

1.Graduated in Electronic Engineering – Instituto Tecnológico de Aeronáutica (1978), Master in Telecommunications – University of Electro-Communications (1983) and PhD in Electrical Engineering – The University of Tokyo (1987). Currently, he is a senior researcher at Instituto de Estudos Avançados – Comando-Geral de Tecnologia Aeroespacial (Brazil), occupying the role of Deputy Technical Director. He served as Assistant professor at Instituto Tecnológico de Aeronáutica; referee of Revista Scientia (Unisinos), consultant of Fundação de Amparo à Pesquisa do Estado de São Paulo (Fapesp), Financiadora de Estudos e Projetos (FINEP), Tribunal Superior Eleitoral and United Nations. He has experience in Electrical Engineering with emphasis on signal modeling and coding, critical embedded systems, fault-tolerant systems, voice recognition, digital signal processing and digital filters, computer and processors architecture and information systems security. E-mail: catsumi@ieav.cta.br

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.137, Apr.-Jun., 2013

doi: 10.5028/jatm.v5i2.229

Green Propellants: Oxidizers Gilson da Silva1, Simone Carvalho Rufino1, Koshun Iha2

ABSTRACT: The research for low toxicity and no damage to the environment has stimulated the development of specific investigation lines in many areas. Inevitably, the criteria for safe handling, sensitivity and, above all, specific impulse (efficiencies) of propellant compositions are still superior in relation to ecological appeals. Nowadays, however, the solid or liquid propulsion, as aerospace as military, has already compounds to efficiency and eco-friendly characteristics. This study aimed at describing “green” alternatives to propulsive systems. Keywords: Propellant, Ammonium perchlorate, Ammonium dinitramide, Hydrazinium nitroformate, Hydroxyl-terminated polybutadiene, Glycidyl azide polymer.

INTRODUCTION A publication (Silva and Iha, 2012) has approached the “green propellants”, but what is its meaning? Nowadays, friendly or green compositions are looked for in many kinds of applications, such as fertilizers, building materials, energy generation, and so on. Thus, this classification (green) can be established after subjection of the compound to a thorough toxicity study. When such compound is a energetic material (green energetic materials – GEMs), it useful to search for a material with high oxygen balances and halogen and metalfree nature (Rahn, 2010). Propellants are designed to produce high temperatures and pressures in a closed chamber to accelerate projectiles, rockets, or missiles by means of the resulting propulsive force of the gas produced by its decomposition (burn). The propulsion system can be liquid, solid, or hybrid and the propellant can be divided into two major groups: homogeneous and heterogeneous propellants. In a liquid propulsion system, the mixture of liquid oxygen (LOX) and hydrogen (LH) may be used without the generation of dangerous substances, although they are unstable together and are generally stored separately, imposing complexity to the system (oxidizer and fuel propellants tanks, pressurizing system, plumbing, valves, and engine). Another liquid propulsion system can be reached with the hydrazine, which is one of the most used monopropellants, in spite of its high toxicity, volatile, and carcinogenic properties. Hydrazine is the only liquid monopropellant widely used for generation of hot gases. In the case of hydrazine, the decomposition pathway occurs in two stages: first, hydrazine is catalytically decomposed into hydrogen and ammonia in an exothermal reaction, and thereafter the latter further does the same into hydrogen and nitrogen in an endothermal

1. Instituto Nacional da Propriedade Industrial – Rio de Janeiro/RJ – Brazil 2. Instituto Tecnológico de Aeronáutica – São José dos Campos/SP – Brazil Author for correspondence: Gilson da Silva | Instituto Nacional da Propriedade Industrial | Praça Mauá, 7 – Centro | CEP 20.081-240 Rio de Janeiro/RJ – Brazil | E-mail: gilsondasilva2011@gmail.com Received: 22/01/13 | Accepted: 26/03/13

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reaction due to the high temperature generated in the first stage; secondly endothermal reduces the flame temperature and the specific impulse (Gronland et al., 2006). In a bipropellant engine, fuel and oxidizer liquids are injected, atomized, and mixed in a first zone of the combustion chamber. With regards to a hypergolic bipropellant, such as hydrazine and nitrogen tetroxide, there is an initial chemical reaction in the liquid phase when a droplet of fuel impinges with one of oxidizer. Bipropellants that are not hypergolic use some type of igniter to initiate the chemical combustion. In a bipropellant system that applies the hydrogen peroxide as the oxidizer, a catalyst may be used. Liquid bipropellants generally offer higher specific impulse than liquid monopropellants. Bipropellant systems are thus more efficient than monopropellant ones, but they tend to be more complicated because of the extra hardware components needed to make sure the proper amount of fuel is mixed with that of oxidizer. In a solid propulsion system, nitrocellulose, or nitrates of cellulose (NC), is the main constituent of a single-base (SB) solid propellant, which has stabilizers and energetic or inert plasticizers too. However, this kind of propellant is useful for small arms, cannons, howitzers, tank, aircraft, and antiaircraft weapon (Stainhauser and Klapötke, 2008). Normally, long distance shooting with large caliber cannons needing higher bullet speeds and thus more energetic propellants require double-base (DB) propellants. An useful DB propellant is composed by nitrocellulose and nitroglycerine (NG), or another liquid nitrate ester (Stainhauser and Klapötke, 2008). The DB propellant has many advantages over the SB one, for example, the latter has a greater variance in performance, since the process of SB production uses volatile solvent and its residue is retained into the SB propellant. On the other hand, the NC/NG DB can present exudation during the storage (the nitroglycerin has a tendency to migrate out of the composition, and thereby results in poorer firing accuracy due to variance in propellant strength) bringing instability to the system. Also, nitroglycerin is volatile and its resulting vapors cause sickness and headaches to humans, resulting in health problems in the manufacture, handling, and storage of any composition containing nitroglycerin (Mosher, 1978). An important heterogeneous propellant used in modern solid-rockets and missiles is the composite propellant consisting of an oxidizer, like ammonium perchlorate (AP),

and a fuel, such as aluminum. Typically, the solid rocket propellant composition comprises yet additives, like plasticizer and burning rate modifiers, and a binder, like a hydroxy-terminated polybutadiene (HTPB) and hydroxyterminated caprolactone, which holds the propellant together (Jones and Tzeng, 2005). AP is a larger oxidizer used in solid propellants for airspace and military industries. Differently from the liquid propellant, which is injected from external tank into the combustion chamber at the time of ignition, solid propellants are placed directly in it. Nevertheless, AP/aluminum solid rocket produces amounts of hydrogen chloride, aluminum oxide, and aluminum chloride, which affect the environment around rocket launch sites. A serious drawback in military applications is that the chlorine content causes yet smoke that may be detected with radar and, in the case of high air humidity, it can also be seen as a clear white smoke (Langlet et al., 1999). The concept of GEMs for defense and space applications is acquiring importance. Ammonium dinitramide (ADN) and hydrazinium nitroformate (HNF) are emerging as potential eco-friendly replacements of AP. Although ADN and HNF have less oxygen balance and, substantially, less heat of reactants formation than AP, they have a superior specific impulse, and the exhausting gas of their burning has no hydrogen chloride. Moreover, they undergo highly exothermic combustion reactions near the surface unlike nitramines, leading to efficient heat feedback to the deflagrating surface enhancing the burning rates. Both the compounds have evinced interest all over the globe. However, severe ADN hygroscopicity and higher HNF sensitivity, particularly mechanical stimuli, are causes of concern (Nair et al., 2010). Table 1 allows the comparison between the properties of AP, ADN, and HNF. The concentration of oxygen atoms within the oxidizer, represented by “oxygen balance”, is an important parameter to identify the potential of oxidizers. Oxygen balance is the amount of molecules remaining after oxidizing hydrogen, carbon, Mg, Al, etc., producing H2O, CO2, MgO2, Al2O3, among others. The positive oxygen balance means that the composition has an excess of molecules remaining after the fuel oxidation. The heat of explosion (Hexp) is determined by the difference between the heat of formation of reactants (ΔHf,r) and that of products (ΔHf,p). Then, in order to gain high Hexp, ΔHf,r is expected to be as high as possible and ΔHf,p as low as possible.

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Table 1. Physicochemical properties of the following oxidizers: ammonium perchlorate (AP), ammonium dinitramide (ADN), and hydrazinium nitroformate (HNF). Oxidizer

AP ADN HNF

ΔHf,r (MJ/kg)*

Oxygen balance (%)*

Isp (s)*

Density (g/cm3)**

-2.52 -1.22 -0.39

34.0 -4.4 25.0

160 206 265

1.9 1.8 1.9

*Kubota (2002); **Nair et al. (2010).

AMMONIUM DINITRAMIDE The ADN is one of the most important compounds to replace the AP in solid propellants or the hydrazine in a liquid monopropellant. There are many routes for ADN production, but a large-scale production consists in the use of sulfamate salts and nitrating acid (Nagamachi et al., 2009). A new type of liquid monopropellant with a dinitramide compound salt and a fuel, which can show a high specific impulse, was taught by Anflo and Wingborg (2000). In agreement with them, the taught monopropellant had low hazardous from a handling and an environmental point of view, and does not develop smoke. Such propellant should exhibit the following properties: low toxicity, low flammability, higher theoretical specific impulse (as compared to hydrazine), higher density (as compared to hydrazine), easily ignitable, by means of a controlled ignition mechanism, storable at a temperature between -10 and 70ºC, and low sensitivity. The liquid propellants comprise an oxidizer, like ADN, and a fuel (for example alcohols, aldehyde, ketones, amino acids, carboxylic acids, amines, and mixtures thereof). The high ADN hygroscopicity is a major advantage, especially when the propellants contain water. Langlet et al. (1999) taught a large-scale method of preparing dinitramide acid, HN(NO2)2, and salts thereof having the formula M+n(-N(NO2)2)n, where M is a metal cation or a nitrogen-containing cation and n=1–3. The dinitramide salt can be used as an oxidizer in solid propellants. Dinitramidic acid is prepared by nitration of a compound selected from a group consisting of NH2NO2, NH4NH2CO2, NH2SO3H, NH(SO3H)2, N(SO3H)3, and its salts with metal or organic cations, e.g. NH(SO3NH4)2, and other products formed when a common nitrating acid such as nitric or sulphuric acids or nitric acid/acetic anhydride. In agreement with them (Langlet et al., 1999), no aprotic solvent for the nitrating agent is required when nitrating

with such acids. Ammonium and potassium salts of the initial substances, and the fact that the neutralization after nitrating is carried out with NH3 and KOH, results in an advantageous preparation direct to the products ADN and potassium dinitramide (KDN) respectively. After the synthesis process, the ADN obtained in solution is crystallized in a conventional manner through the concentration, addition of a non-solvent and/or cooling, etc. The resulting crystals of crude ADN are in the form of small rods, or even of needles. However, such crystal morphology makes ADN unsuitable for formulation, because the feasibility of the compositions is greatly compromised due to the large increase in viscosity as soon as high loading rates are envisioned. In order to solve such problem, Muscatelli et al. (2011) proposed the conditioning of the crude crystals, nor on crystallization in the presence of an added chemical element that is a crystal habit modifier, like taught by Benazet et al. (2009), but on controlling the parameters of crystal growth, resulting in (quasi) spherical crystals with a selected particle size range, which can be from a few microns to several hundred ones. The parameters under issue are: the nature of the solvent, in particular its viscosity for controlling the relative speeds of transfer and integration of the atoms into the crystal; the temperature cycles for shifting the equilibrium of the solution on the solubility diagram; the presence of impurities; the agitation, etc. The method characterized in that solvent has a viscosity greater than or equal to 0.25 Pa.s, when the spontaneous nucleation is implemented. The solvent is advantageously an alcohol, for example glycerol, 1,4-butanediol or mixture of alcohols, in particular one of glycerol and 1,4-butanediol. The crystallization process according to Muscatelli et al. (2011) makes possible to obtain ADN in energetic materials with a high charge level. Gronland et al. (2006) taught a reactor for decomposition and combustion of liquid ADN-based monopropellants, such as for rocket propulsion and controlled gas generation for any

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other purpose, such as rotary power in auxiliary power units. The combustion of the ADN-based liquid propellant can be divided into a series of steps, including the decomposition of the ADN oxidizer, which eventually generates free oxygen. In the final stage, combustible components created from thermal and catalytic decomposition will be oxidized in the homogenous gas combustion by free oxygen thus generated, without requiring catalysis. Then, the ADN-based monopropellant can be regarded as being decomposed into a bipropellant, which is combusted in a final step, during which the maximum temperature is reached. The most preferred monopropellants are: stabilized compositions of ADN, water, and glycerol or/and water and methanol; in case of methanol, a composition consisting of about 64.3% of ADN, 24.3% water and 11.4% by weight of methanol (LMP-103), to which a stabilizer is added in the above mentioned amount; in case of glycerol, a composition of about 61.0% of ADN, 26.1% of water and 12.9% by weight of glycerol (LMP-101), to which composition a stabilizer is added in such amount. Roland (2007) analyzed a composite gunpowder comprising ADN and a thermoplastic elastomer (TPE) binder, which has a melting point of 60 to 90ºC and is based on an ethylene vinyl acetate (EVA) copolymer containing 9 to 30 weight% vinyl acetate and with a melt flow index greater than 100 g/ten minutes. An energetic composition, with increased performance and total absence of hydrogen chloride in the combustion products, was done by Reed and Ciaramitaro (2004). The formulation avoids the use of halogen-based oxidizers to prevent the formation of their byproducts, using ADN as a primary oxidizer. The solid propellant formulation comprises about 5 to 10 weight% of at least one energetic binder; about 20 to 35 weight% of an energetic plasticizer; about 25 to 45 weight% of ADN, about 0 to 20 weight% of particulate aluminum having a particle size of around 1 to 60 mm; and about 0 to 20 weight% of ultrafine aluminum with less than 1 mm. The use of ADN as an oxidizer can yet minimize the secondary smoke problem caused by the nucleation of HCl in AP. The energetic plasticizer is selected from those compounds, which are liquids and contain energetic moieties or groups in their chemical structures (for example: butanetriol trinitrate (BTTN), triethylene glycol

dinitrate (TEGDN), nitroglycerin, glycidyl azide polymer terminated with azide (GAP azide or GAP plasticizer), etc.). The binder is selected from those oligomers and polymers known as “energetic binders”, i.e., typically, GAP, copolymer of (bis-azidoethyl) oxetane (BAMO) with (3-nitratomethyl-3-methyl) oxetane (NMMO), called BAMO/NMMO, polyethylene glycol (PEG), hydroxyterminated polycaprolactones, hydroxy-terminated polyesters, being preferably tetrahydroxy-terminated polyalkylene oxide (PAO).

HYDRAZINIUM NITROFORMATE On one hand, HNF is a very desirable oxidizer to use in solid propellant formulations, because it is very energetic, thus providing high performance. On the other hand, the HTPB is the most applied binder in solid propellants. Unfortunately, the HNF cannot be used with this binder, because the HNF attacks its backbone, breaking down the binder chain. Pockets of gas are formed, therefore the propellant swells. In addition, due to the breakdown of the binder backbone, the material becomes soft. Thus, when a binder containing double bonds is utilized, a typical shelf life with HNF will range from 2 to 15 days at a temperature around 20 to 30ºC, in agreement with Low and Haury (1972). With the aim of solving this problem, the authors proposed using a small amount of nitroguanidine to the solid propellant formulations having unsaturated hydrocarbon binder and containing HNF, increasing the shelf life of the propellant to at least five months at ambient temperatures. The nitroguanidine should be added to the propellant during its mixing phase and will remain in the composition to prevent the undesirable reaction of the HNF with the binder. In a second publication, Low and Haury (1973) taught a propellant formulation comprising HNF and saturated polymeric hydrocarbon binder, but without nitroguanidine. In this new case, they discovered that the reticulation of the binder with a curing agent type polyisocyanate can improve the shelf life of the composition. Polymethylene polyphenylisocyanate (PAPI) provides the best result when it is presented to provide a ratio of NCO to OH from 0.95 to about 1.3 in the composition.

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Green Propellants: Oxidizers

Schöyer et al. (1990) investigated many formulations directed in particular to solid propellant combinations in the research for high-performance ones, which could be stored for a considerable time and used not only to change the position of a spacecraft that is in space, but also for launching one into space. According to their research, it could be constituted by a combination of GAP or BAMO with boron, aluminum or aluminum hydride and a compound selected from the group of HNF, nitronium perchlorate (NO2ClO4) or AP. The proportions of the components, oxidizer and fuel, in the propellant combinations were not critical. The components should be mixed prior to the reaction in such proportions that the mixing ratios were around the stoichiometric ratio to an amount of no more than 20%, calculated on the total mixture of the energetic binder (BAMO or GAP). In agreement with them, the preferred propellant combinations with HNF are: HNF – 70 to 80%, B – 10% and GAP or BAMO – 10 to 20%; or HNF – 59 to 69%, Al – 21% and GAP or BAMO – 10 to 20%. The same were based on HNF, aluminum and on an energetic binder such as GAP or BAMO, exhibiting an improvement of the specific impulse relative to conventional AP propellants of 214 m/s, with the combustion gases much more cleaner, because HNF does not include chlorine and the environment is not burned with hydrogen chloride gas. Solid propulsion systems could provide very a high specific impulse by utilizing high performance oxidizers. Many of them offer significant gains on performance, reduced or low toxicity and have desirable exhaust signature characteristics, when compared to others using traditional solid ones. However, many oxidizers suffer yet from varying degrees and forms of instability, such as photosensitivity, shock, friction and impact sensitivity, decomposition in the presence of moisture, sensitivity to pH and incompatibility (such as hypergolic reaction) to other propellant materials. A typical example of incompatibility is the reaction between HNF and curing agents used in solid propellant binder systems such as HTPB and GAP. In order to improve the compatibility of the propellant and to reduce the risks by friction sensitivity during the mixing and casting operations, Cesaroni et al. (2002) taught an oxidizer package comprising a solid oxidizer in the form of discrete pellets

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from a predetermined geometric shape, the pellets were arranged in an array with spaces amongst the pellets and a holder for maintaining them in the array to receive a binder introduced to spaces amongst the array of pellets. The binder introduced provides a support matrix to give complementary burn rates for the pellets and the support binder matrix. The pellets were produced with HNF or ADN and the composition can present yet ballistic modifiers, other additives and, additionally, ultrafine aluminum. A monopropellant used in the conventional manner for spacecraft propulsion in existing systems, whereby it is to be noted that due to the properties of the system, less strict requirements concerning storage, transport, and handling are possible, was proposed by van den Berg et al. (2004). Their research showed that solid high-energy oxidizers, such as HNF or ADN, when dissolved in water, provide a liquid monopropellant system with a specific impulse that could be equal to the specific one of the conventional monopropellant. The monopropellant can be done by the stabilization of HNF and/or ADN in water and/or a lower alkanol. Its amount in the solution is preferably between 0 and 70 weight%, whereas methanol and/or ethanol are preferred. An especially preferred system consists of 25 to 75 weight% of HNF, 5 to 50 weight% of water and 0 to 25 weight% of lower alkanol.

FINAL CONSIDERATIONS In spite of the larger use of the AP in composite propellants and the hydrazine in liquid propulsion, they demonstrated the high risk to human health and environment. ADN and HNF are emerging as potential eco-friendly replacers to the AP and hydrazine. Despite the ADN hygroscopicity and HNF higher sensitivity, they have substantially higher specific impulse than AP, reduced or low toxicity and desirable exhaust gas signature characteristics, when compared to propulsion systems using traditional solid oxidizer (AP). They also do not contain chlorine and therefore the environment is not burned with hydrogen chloride gas produced in the burn of the propellant. These are the reasons of the increasing interest around them in all over the globe.

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REFERENCES Anflo, K. and Wingborg, N., 2000, “Dinitramide based liquid mono-propellants”, World Intellectual Property Organization, WO00/50363 A1. Benazet, S., et al., 2009, “Preparation of ammonium dinitroamide (and) crystals, and crystals and energetic composites containing them”, US Patents 2009/0090441 A1. Cesaroni, A.J., et al., 2002, “Propellant system for solid fuel rocket”, US Patents 20020157557 A1. Gronland, T.A. et al., 2006, “Reactor for decomposition of ammonium dinitramide-based liquid monopropellant and process for the decomposition”, US Patents 7,137,244 B2. Jones, M.L. and Tzeng, D.D., 2005, “Solid Rocket Propellant”, US Patents 6,905,561 B2. Kubota, N., 2002, “Propellants and Explosives”, Wiley-VCH, Weinheim, Germany, pp. 59-60.

Muscatelli, F., et al., 2011, “Method for obtaining ADN crystals through crystallization in a viscous medium”, US Patents 2011/0171104 A1. Nagamachi, M.Y. et al., 2009, “ADN – The new oxidizer around the corner for an environmentally friendly smokeless propellant” Journal of Aerospace Technology and Management, Vol. 1, N. 2, pp. 153-160. Nair, U.R., et al., 2010, “Advances in high energy materials”, Defense Science Journal, Vol. 60, N. 2, pp. 137-151. Rahn, M., 2010, “Green Propellants”, Ph.D. Thesis, Royal Institute of Technology, Stockholm, Sweden. Reed, R.J. and Ciaramitaro, D.A., 2004, “High energy propellant with reduced pollution”, US Patents 6,805,760 B1. Roland, S., 2007, “Gunpowder comprising ammonium dinitramide contains ethylene-vinyl acetate thermoplastic elastomer as binder”, SE529096 C2.

Langlet, A. et al., 1999, “Method of preparing dinitramide acid and salts thereof”, US Patents 5,976,483 A.

Schöyer, H.F.R. et al., 1990, “High-performance propellant combinations for a rocket engine”, European Patent Application EP0350136 A2.

Low, G.M. and Haury, V.E., 1973, “Hydrazinium nitroformate propellant with saturated polymeric hydrocarbon binder”, US Patents 3,708,359.

Silva, G. and Iha, K., 2012, “Hypergolic systems: a review in patents”, Journal of Aerospace Technology and Management, Vol. 4, N. 4, pp. 407-412.

Low, G.M. and Haury, V.E., 1972, “Hydrazinium nitroformate propellant stabilized with nitroguanidine”, US Patents 3,658,608 A.

Stainhauser, G. and Klapötke, T.M., 2008, “Green Pyrotechnics: A chemists’ challenge”, Angewandte Chemie International Edition, Vol. 47, N. 18, pp. 3330-3347. doi:10.1002/anie.20070510.

Mosher, P.R., 1978, “Solvent-less double base propellants and method for plasticizing MTN nitrocellulose propellants without use of solvents”, US Patents 4,082,583 B1.

van den Berg, R.P. et al., 2004, “Monopropellant System”, US Patents 20040088910 A1.

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doi: 10.5028/jatm.v5i2.179

A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations Carlos Junqueira-Junior1, Joao Luiz F. Azevedo2, Leonardo C. Scalabrin3, Edson Basso2

Abstract: The present work is primarily concerned with studying the effects of artificial dissipation and of certain diffusive terms in the turbulence model formulation on the capability of representing turbulent boundary layer flows. The flows of interest in the present case are assumed to be adequately represented by the compressible Reynolds-averaged NavierStokes equations, and the Spalart-Allmaras eddy viscosity model is used for turbulence closure. The equations are discretized in the context of a general purpose, density-based, unstructured grid finite volume method. Spatial discretization is based on the Steger-Warming flux vector splitting scheme and temporal discretization uses a backward Euler point-implicit integration. The work discusses in detail the theoretical and numerical formulations of the selected model. The computational studies consider the turbulent flow over a flat plate at 0.3 freestream Mach number. The paper demonstrates that the excessive artificial dissipation automatically generated by the original spatial discretization scheme can deteriorate boundary layer predictions. Moreover, the results also show that the inclusion of Spalart-Allmaras model cross-diffusion terms is primarily important in the viscous sublayer region of the boundary layer. Finally, the paper also demonstrates how the spatial discretization scheme can be selectively modified to correctly control the artificial dissipation such that the flow simulation tool remains robust for high-speed applications at the same time that it can accurately compute turbulent boundary layers. Keywords: Computational fluid dynamics, Turbulence modeling, Flux vector splitting scheme, Artificial dissipation.

INTRODUCTION The present work is primarily interested in studying the effects of artificial dissipation and of certain diffusive terms in the turbulence model formulation on the capability of representing turbulent boundary layer flows. This interest comes from the fact that situations could arise in which one has a certain computational fluid dynamics (CFD) tool, for instance, developed elsewhere, and wants to apply this code to a particular application. It is clear that all decisions taken in the selection of the computational tool, from the choice of a specific turbulence model to numerical issues, such as the type of spatial discretization used, may have consequences on the quality of numerical results that might be obtained from the simulations. The research group, in the context of which the present effort is inserted, has recently experienced exactly this sort of situation. Therefore, an extensive study on the effects of artificial dissipation had to be performed in order to be able to correctly reproduce turbulent boundary layer flows. Similar issues with the effect of artificial dissipation terms on boundary layer flows have been previously addressed in the literature (Bigarella, 2007; Bigarella and Azevedo, 2012). However, this previous work is mostly concerned with centrally-differenced schemes and explicitly added artificial dissipation, whereas the present effort focuses on the artificial dissipation terms that arise from an upwind, flux-vector splitting-type discretization. Furthermore, the present study also addressed the decision to include, or not, some terms of the turbulence model formulation in the implemented code, since some of them, in many turbulence models, are computationally stiff and, hence, expensive. Thus,

1.Instituto Tecnológico de Aeronáutica – São José dos Campos/SP – Brazil 2.Instituto de Aeronáutica e Espaço – São José dos Campos/SP – Brazil 3.EMBRAER – São José dos Campos/SP – Brazil Author for correspondence: Carlos Junqueira-Junior | Praça Marechal Eduardo Gomes, 50 – Vila das Acácias | CEP 12.228-900 São José dos Campos/SP – Brazil | E-mail: junior.hmg@gmail.com Received: 04/10/12 | Accepted: 28/01/13

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many investigators simply do not include these troublesome terms in their implementation of such particular model. The present research group has been focusing on different aspects of CFD in the past years. For instance, the group maintains lines of work (Bigarella, 2007; Bigarella et al., 2007; Bigarella and Azevedo, 2009) aimed at creating new capabilities on numerical methods, multigrid techniques, and turbulence modeling. The study of such aspects is also a major issue in the present work. Previous effort was primarily geared towards the simulation of satellite launch vehicle (SLV) flows, which is one of the main interests of Instituto de Aeronáutica e Espaço. It resulted in a powerful Navier-Stokes solver, known as BRU3D, frequently used by the research group. Additional effort at the group has also addressed the issue of high-order methods (Wolf, 2006; Wolf and Azevedo, 2006 and 2007; Breviglieri, 2010; Breviglieri et al., 2010a and b), and successful applications of schemes such as essentially nonoscillatory (ENO) and weighted essentially nonoscillatory methods (WENO), and spectral methods have been demonstrated. Basso (1997) used preconditioning matrices to extend CFD codes for all speed applications. All these numerical technologies are applied on aeronautical and aerospace simulations, such as high lift and drag predictions, aerodynamics optimization, aeroacoustics, turbulent flows, and wind tunnel validation. The version of the BRU3D code of interest herein is a serial Navier-Stokes solver developed to simulate threedimensional (3-D) viscous turbulent flows over general aerospace configurations. The code presents different turbulent closures such as linear eddy-viscosity turbulence models, explicit algebraic Reynolds-stress models – EARSM (Wallin and Johansson, 2000; Hellsten and Laine, 2000), and Reynolds-stress models – RSM (Batten et al., 1999). A thorough study of flux computational schemes was also undertaken during the development of the code. Spatial discretization of the BRU3D code can be performed with the second-order accurate centered scheme of Jameson et al. (1981) and the Roe flux-difference splitting upwind scheme (Roe, 1981). Different artificial dissipation terms are also added for the Jameson centered spatial discretization (Jameson et al., 1981), such as the convective upwind split pressure (CUSP) scheme (Jameson, 1995a and b), scalar and matrix versions of switched seconddifference and fourth-difference models (Mavriplis, 1988; Turkel and Vatsa, 1990). The efforts of Bigarella

(Bigarella, 2007; Bigarella and Azevedo, 2009) provided extensive expertise on turbulence modeling, which is a pacing item in CFD (Chapman, 1981). On the other hand, previous work by Scalabrin and collaborators (Scalabrin, 2007; Scalabrin and Boyd, 2007; Schwartzentruber et al., 2007; Schwartzentruber et al., 2008) developed a numerical tool using upwind schemes, unstructured meshes, high-performance computing (HPC), and implicit integration for numerical simulations of weakly ionized hypersonic flows over reentry capsules. Such research has resulted in a very efficient numerical framework, called LeMANS, to simulate reentry flows over space capsules. These extreme conditions demanded the implementation of the Navier-Stokes equations coupled to nonequilibrium chemical reaction equations. The computation of these sets of equations requires very fine meshes, which makes impractical the use of serial algorithms. Therefore, message passing interface (MPI) protocols were implemented to parallelize LeMANS and, then, reduce computational costs. One should understand that high-fidelity CFD solvers have very complex algorithms and, hence, their parallelization involves advanced numerical and computational issues. Thus, a full parallel code, as LeMANS, is always welcome. Furthermore, since LeMANS already incorporates several programming issues and highspeed flow physics models, it seems to be a more suitable code for continued developments in the future. In this context, an important motivation of the present work is to take full advantage of all scientific technology concerning turbulence modeling, boundary condition, and initial condition treatment implemented in the BRU3D solver in order to extend the LeMANS code for the research group needs, more specifically, parallel turbulent flow simulations for high dissipative spatial discretization, which are strongly recommended for high-speed configurations, such as reentry flows. However, such highly dissipative methods can strongly deteriorate boundary layer flow predictions. It is clear that the challenge is to selectively modify the discretization scheme in order to correctly control the artificial dissipation such that the flow simulation tool remains robust for high-speed applications, at the same time that it can accurately compute turbulent boundary layers. Therefore, the present work selected the well-known problem of a turbulent flow over a flat plate in order to address the dissipation issues that are relevant in this case. Two major aspects are investigated, namely the problem of excessive

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The conserved variables vector, Q, the inviscid flux vector, Fe, and viscous flux vector, Fv, are given by ┌ ρ ┌ ┌ ρv 0 t │ ρu │ ρu v + pî x │( τ xi + τ xi ) î i t (2) Q =│ ρv , F e=│ ρv v + pî y , F v =│( τ yi + τ yit ) î i , │ ρw │ ρw v + pî │( τ zi + τ zi ) î i z │ t │ │ e ( β + β i ) î i (e + p) v └ └ └ i ┌ │ │ │ │ └

where ρ stands for the density, v = {u, v, w} is the velocity vector in Cartesian coordinates, p is the static pressure, τ is the viscous stress tensor, qH is the heat flux vector, e is the total energy per unit volume, and βi is given by βi = τ ij u˜ j − qHi

. (3)

The îx, îy, and îz terms are the Cartesian coordinate orthonormal vector basis. The { ̅ } terms are the averaged and weighted averaged properties. Therefore, it is very important to emphasize that field forces, such as gravity, are neglected here. Other equations are necessary in order to close the system of equations given by Eq. (2), which are called constitutive relations. The first constitutive equation presented to close the Navier-Stokes set is known as the equation of state. This equation considers the perfect gas law, and it is written as ┌ 1 p = ( γ − 1)│ e − ρ ( u 2 + v 2 + w 2 ) 2 └

┌ │ └

, (4)

in which the mean total energy per unit volume, e̅ , is given by ┌ 1 e = ρ│ei + ( u 2 + v 2 + w 2 ) 2 └

┌ │ └

The formulation used in the present work is based on the Reynolds-averaged Navier-Stokes set of equations, also known by the CFD community as RANS equations. They are obtained by filtering the Navier-Stokes set of equations. This process filters the fluctuation part of the fluid and maintains only the mean contribution. The filtered information needs to be recovered somehow. Turbulence models are applied to the RANS formulation to recover the effect of the fluctuating part. The levels of turbulence modeling are also discussed in this section. The most used filtering processes are based on the time, space, and ensemble averages. The filtering based on the time average is the most used for steady state applications and it is the one applied in the present work. For the sake of simplicity, the filtering process is not discussed in this work. The reader can find further details on the work of Bigarella (2007) and Junqueira-Junior (2012). The filtered compressible Reynolds-averaged NavierStokes equations are written in the vector form as

. (1)

┌ │ │ │ │ └

THEORETICAL FORMULATION

∂Q + ∇ · (F e − F v ) = 0 ∂t

┌ │ │ │ │ └

artificial dissipation of the upwind spatial discretization scheme, and the inclusion of numerically stiff cross-diffusionlike terms in the formulation of the turbulence model. For the present study, the Spalart-Allmaras turbulence model was selected, primarily because it is probably the most widely used turbulence closure for realistic aerospace applications at the time the study was carried out. This study considers the case of freestream Mach number equal to 0.3, because there are experimental and other independent computational results available. Moreover, since all computational codes here considered implement a compressible formulation, there are no issues with the incompressible limit at such Mach number. The paper demonstrates that the excessive artificial dissipation automatically generated by the original spatial discretization scheme can deteriorate boundary layer predictions. The paper also demonstrates how the spatial discretization scheme should be selectively modified to correctly control the artificial dissipation. Finally, the results show that the inclusion of Spalart-Allmaras model cross-diffusion terms is primarily important in the viscous sublayer region of the boundary layer.

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, (5)

and i stands for the internal energy, defined as e =C T , (6) i

in which T stands for the mean static temperature and Cv is the specific heat at constant volume. The heat flux from Eq. (2) is obtained from the Fourier law for heat conduction, and it is given by qH j = −

γµ ∂ (ei ) Pr ∂xj

, (7)

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in which γ is the ratio of specific heats and Pr is the Prandtl number. Typically, for air, it is assumed that γ = 1.4 and Pr = 0.72. Cp is the gas specific heat at constant pressure, and µ is the dynamic molecular viscosity coefficient, calculated as a function of the temperature by the Sutherland law equation (Anderson, 1991), written as T T∞

⎛ ⎥ ⎝

µ=

⎛ µ∞ ⎥ ⎝

2 3

T∞ + S T+S

, (8)

In the above equation, S = 110K, and µ∞ is the dynamic molecular viscosity coefficient of the fluid at temperature T∞. The components of the viscous stress tensor, for a Newtonian fluid, are given by

┌ │ └

┌⎛ ∂u ∂u j 2 ∂u m τij = µ│⎥ i + − δ ∂xi 3 ∂x m ij ⎝ ∂xj └

, (9)

⎛ ⎥ ⎝

in which δij stands for the Kronecker delta. All the terms marked with the superscript { }t, in Eq. (2), appear after the time filtering processes. These terms carry important turbulent information and need to be modeled. The turbulence closures are responsible for representing them. There are two major families of turbulence models for the RANS equations, the first and second order closures. The present paper focuses on the first order closures, more specifically, on the Spalart and Allmaras (1992) model, which is an one-equation closure. This model was chosen because it is, by far, the most used turbulence model for realistic aerospace applications. Furthermore, the research group has already achieved good results using it on previous applications (Bigarella, 2007; Bigarella et al., 2007; Bigarella and Azevedo, 2009). The Spalart-Allmaras turbulence closure is a partial differential equation, which models the turbulent eddy viscosity transport. The theoretical and numerical formulations of the turbulence closure are discussed in details in the forthcoming sections.

NUMERICAL FORMULATION Spatial discretization The spatial discretization used is the first aspect to be discussed in this section, starting with the finite volume formulation and followed by the flux calculations. For the

sake of simplicity, from here, all the averaged terms are written without the { ̅ } notation. Finite volume formulation The finite volume formulation is a numerical method applied to represent and evaluate partial differential equations. It is applied by the CFD community to find the solution of the RANS equations, Eq. (1). The method is obtained integrating the flow equations for each control volume within a given mesh, ⌠ ∂Q dV + ⌠ ∇ ·(F e − F v) dV = 0 ⌡Vi ∂t ⌡Vi

. (10)

Considering a cell-centered formulation, Vi is a determined cell of the given grid. After the integration, it is possible to apply the Gauss theorem over Eq. 10, resulting in ⌠ ∂Q ⌠ ⌡V ∂t dV + ⌡S (F e − F v) · dS = 0 i i

(11)

in which Si is the outward-oriented area vector and it is defined as Si = {Sx , Sy , Sz}

(12)

Considering the mean value of the conserved variables within the i-th control volume, one can write the first term of Eq. (11) as Qi =

1 ⌠ QdVi Vi ⌡Vi

. (13)

The second term of Eq. (11) can be written as the sum of all faces of a cell nf

⌠ → → → ⌡S (F e − F v)· dS = k∑=1 ( F ek − F v k ) · n k S k i

, (14)

in which the k subscript is the index of the cell face, and nf indicates the number of faces of the i-th volume. Finally, the RANS equations discretized with a finite volume approximation is given by → ∂Q i 1 nf ( → ∑ F ek − F vk ) · n→k Sk =− ∂t Vi k =1

(15)

For this formulation, the fluxes are computed at the faces of the control volume, and the conserved variables are computed in the cell.

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A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

→

F ek · n k = F en =

∂F en Q = AQ ∂Q

Sudden Smooth

(16)

where Fen is the normal flux at the k-th face, and A is the Jacobian matrix of the inviscid flux that can be diagonalized by the matrices of its eigenvectors from the left and from the right, L and R, respectively, as A = R ΛL

Change of Sign Eigenvalues

λ+

Inviscid flux calculation The inviscid fluxes are calculated using a method based on a classical flux vector splitting formulation, the Steger-Warming scheme (Steger and Warming, 1981). The formulation implemented to compute the inviscid fluxes is explained here. This method is an upwind scheme that uses the homogeneous property of the inviscid flux vectors to write

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0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01

-0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05

λ Figure 1. Sudden (Eq. 20) and smooth (Eq. 21) sign transition of a given Eigenvalue.

, (17)

and Λ is the diagonal matrix of the eigenvalues of the Jacobian matrix. The A matrix can be split into positive and negative parts as

issue a pressure switch is implemented to smoothly shift the Steger-Warming scheme into a centered one. Then, the artificial dissipation is controlled and the numerical stability is maintained as presented in

A+ = R Λ+ L

→ → F ek· n k = Fk + + Fk − = ( A+ Q k+ + A− Qk − ) k+ k−

and

A − = R Λ− L

(18)

The splitting separates the flux into two parts, the downstream and the upstream fluxes, in relation to the face orientation as → → − + − F e · n = F e+ n + F e n = ( Acl Q cl + Acr Q cr )

(19)

where the cl and cr subscripts are the cells on the left and right sides of the face. The split eigenvalues of the Jacobian matrix are given by λ± =

1 (λ ± | λ |) 2

(20)

In order to avoid sudden sign transitions, as illustrated in Fig. 1, the split eigenvalues receive a small number, ϵ, turning Eq. (20) into λ ± = 1 ( λ ± √λ 2 + ϵ 2 ) 2

. (21)

Numerical studies performed in the present paper indicated that this flux vector splitting is too dissipative and it can deteriorate the boundary layer profiles (MacCormack and Candler, 1989; Junqueira-Junior et al., 2011). To avoid such

(22)

in which Q k+= (1−w)Q cl +wQ cr and Q k− = (1−w)Q cr+wQ cl

. (23)

The switch, w, is given by w=

1 1 2 (α∇p) 2 + 1

and ∇p =

|pcl − pcr | min (pcl , pcr )

(24)

Therefore, for small ∇p, w = (1–w) = 0.5, the code runs with a centered scheme, and for larger values of ∇p, w = 0 and (1–w) = 1, the code runs with the Steger-Warming scheme. For Eq. (24), it is suggested α = 6, but some problems may require larger values (Scalabrin, 2007). The applied formulation was originally created with interest on studying flows over reentry capsules. For this particular case, with very strong shock waves, it is very common to find solutions with nonphysical numerical structures such as carbuncles (Ramalho et al., 2011). To prevent such numerical problems, artificial dissipation has necessarily to be added to the method. The dissipation was included into the split eigenvalues, Eq. (21), using the ϵ factor, which is given by:

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⎧ |→ u k |) ϵk = ⎨ 0.3(ak + → → → ⎩ 0.3(1 − | n k · m k |)(ak + |u k |)

dk > d 0 dk < d 0

(25)

where dk is the distance of the k-th face to the the nearest wall boundary, d0 is set by the user and must be smaller than the boundary layer thickness and larger than the → shock stand-off distance, mk is the normal vector of → the nearest wall, and nk is the normal vector to the k-th face. → → Equation (25) applies the term (1 - |nk ·mk |) to decrease the ϵ value at the faces parallel to the wall inside the boundary layer (Scalabrin, 2007). This artificial dissipation model has shown an important role in the prediction of boundary layer profiles, and several tests were performed in the present work with the aim of understanding its behavior (JunqueiraJunior et al., 2011). Viscous flux calculation The viscous terms are based on derivative of properties on the faces. To build the derivative terms, two volumes are created over the face where the derivative is being calculated. At the center of each new volume, the derivative is calculated using the Green-Gauss theorem. This computation is used to find the derivative at the desired face. A two-dimensional (2-D) example is used in this section to better explain the derivative calculation. Considering the two cells, S1 and S2, in Fig. 2, two new cells, S3 and S4,

Q 12 =

1 (Q + Q 2 ) 2 1

Q 23 =

1 (Q + Q 3 ) 2 2

Q 13 = Q 31 =

1 (Q + Q 3 ) 2 1

Q 34 =

1 (Q + Q 4 ) 2 3

Q 41 =

1 (Q + Q 1 ) 2 4

(26)

Using the averaged properties, Q12, Q23, Q13, Q34, and Q41, with the normal vectors, n12, n23, n13, n34, and n41, and the surface of the faces, S12, S23, S13, S34, and S41, as illustrated in Fig. 3, it is possible to calculate the derivative at the points P7 and P8 using the Green-Gauss theorem (Jawahar and Kamath, 2000), which is applied to a scalar and relates the volume integral of the gradient of its area integral over the boundary as 1 ⌠ → → ⌠ ⌡V ∇Q dV = V ⌡○S Q · n dS

(27)

S2 P4

are created using node points, P1 and P3, and cell centered points, P2 and P4, to calculate the derivative on the face 1-3. The properties at the faces are calculated using simple averages. For the example in Fig. 2, they are given by

n12

n13 n31

n34

n23 S1

n41

Q12

Q13

Q23 S3

Q41

Q34

Figure 2. 2-D example of a new volume creation.

Figure 3. 2-D example of a derivative calculation.

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A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

Considering ∇Q as a constant over the cell, Eq. 27 yields 1 ⌠→ → ○ Q · n dS ∇Q = V ⌡S

, (28)

V3 ∇ Q 3 + V4 ∇ Q 4 V3 + V4

. (29)

The derivative computation for other types of element, 2D or 3D, is straightforward. Time integration Simulations of turbulent flows can become very stiff. Such stiffness substantially limits the use of large time steps. One classical solution is the use of implicit time integration. This work applies an implicit integration based on the backward Euler method, which is given by n ⎤ ⎡ nf → → ∆ Q cl n k S k⎦ Vcl = ⎣− ∑ ( F ek − F vk ) · → ∆t k =1

n +1

= R cl

(35)

which is not true and can decrease the numerical stability of the method. Then, the true Jacobian matrices of the split fluxes were implemented in place of A± to calculate the implicit operator. Issues involving the true Jacobians matrices have a great importance in the context of numerical stability for computational methods. The reader with interest in this subject must look further in references Anderson et al. (1986) and Steger and Warming (1981), and in chapter 20 from Hirsch (1990). The viscous terms can be written in the same form as ⎡

⎤

→

⎡

→

⎤

→ − → ⎜∂ ( F v · n ) ⎜ ∆ Q = ⎜ ∂ ( F v · n ) ⎜ ∆ Q − cl cl ⎣ ⎣ ⎦k ⎦k ∂Q ∂Q ⎡ →+ → ⎤ ⎜ ∂ ( Fv · n ) ⎜ ∆ Q cl ⎣ ⎦k ∂Q

(36)

The viscous Jacobian matrices are represented by B. The splitting of these matrices is written as ⎡ ( → →)⎤ ⎜∂ F v · n ⎜ ∆ Q =B−− ∆ Q cr,k −B++ ∆ Q cl cl k k ∂Q ⎣ ⎦k

n → n nf ⎧ ⎡ ∂ ( F e · → n )⎤ ∆ Q cl n ⎜ ∆ Qn − Vcl = R cl − ∑ ⎨ ⎜ cl ∆t ∂Q k =1 ⎩ ⎣ ⎦k n ⎡∂ (→ ⎫ Fv · → n ) ⎤ ⎜ ⎜ ∆ Qn ⎬· S cl k ∂Q ⎣ ⎦k ⎭

⎡ ( → ± →) ⎤ ⎜ ∂ F e · n ⎜= A± ∂Q ⎣ ⎦

. (30)

One can linearize the residue at time n+1 as a function of properties at time n.

. (37)

(31) The true Jacobian matrices, for A± and B±, can be found in the work of Scalabrin (2007). One can write the system as

From the spatial discretization, the inviscid terms can be written as →+ → ⎤ ⎡∂ ( F ⎡ ( → →) ⎤ e · n) ⎜ ∆ Q cl + ⎜ ∂ F e · n ⎜ ∆ Q cl = ⎜ ∂Q ∂Q ⎣ ⎣ ⎦k ⎦k ⎡∂ → n )⎤ F e− · → ⎜ ( ⎜ ∆ Q cl , ∂Q ⎣ ⎦k

(32)

nf ⎡V ⎤ n ) Sk ⎜ ∆ Qcl + ⎜ cl + ∑ ( A+k+ + B+ k+ ⎣ ∆ t k =1 ⎦ ⎤ ⎡ nf n − − ⎜ ∑ Ak− − Bk− Sk ∆ Qcr,k ⎜= R n . cl ⎣ k =1 ⎦

(38)

It is, then, possible to write nf

M cl ∆ Q ncl + ∑ N k− ∆ Q ncr,k =R cln k =1

with

⎡ ( → + →) ⎤ ∂ Fe · n ⎜ ⎜ ∆ Q = A++ ∆ Q (33) cl cl k ∂Q ⎣ ⎦k and

. (34)

The formulation described assumes

in which ∇Q is the constant cell-centered gradient. Using the derivatives in the cells S3 and S4, the derivative at face 1-3 is computed using ∇ Q 13 =

⎡ ( → − →) ⎤ ⎜∂ F e · n ⎜ ∆ Q cl = A−− ∆ Q cr k ∂Q ⎣ ⎦k

151

, (39)

with nf

M cl =

Vcl ∑ + N ∆ t k =1 k

, (40)

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N k+= ( A + + B k++) S k , (41) k+ and − B k−−) S k . (42) N k−= ( A − k− As the code is an unstructured solver, this system of equations results in a sparse block matrix, where each block is a square matrix of size equal to the number of equations to be solved in each control volume. The solution of such system is typically very expensive and, depending on the size of the mesh, it is not even practical. A less expensive implicit method is applied in the present paper, the point implicit integration (Gnoffo, 2003; Venkatakrishnan, 1995; Wright, 1997). The main idea of the point implicit integration is to move all the off-diagonal terms to the right hand side and solve the resulting system iteratively, i.e., nf

M cl ∆ Q ncl +1,p = R cln −∑ N k− ∆ Q ncr,k+1,p − 1 k =1

(43)

It is assumed that ∆Qn+1,0 = 0 and four iterations are taken in the process as suggested in the literature (Wright, 1997). The sparse linear system illustrates the point implicit method: ⎡� ⎜ ⎜� ⎜ ⎜ ⎣ ⎡�

⎜ ⎜ ⎜ ⎜ ⎣

� � �

� �

⎤ ⎡ ⎤ ⎤ ⎡ ⎜ ⎜ ⎜ �⎜⎜ � ⎜ ⎜∆ Q ( n +1) ⎜= ⎜ R n ⎜ , ⎜⎜ ⎜ ⎜⎜ ⎜⎜ ⎜ ⎜ ⎜ ⎦ ⎣ ⎦ �⎦ ⎣

⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎜ ⎜ ⎜ ⎜ ⎜⎜ ⎜⎜∆ Q ( n +1) ,p ⎜= ⎜R n ⎜− ⎜ � � ⎜⎜ ⎜ ⎜⎜ ⎜ � ⎜⎜ � ⎜⎜ ⎜ ⎜ ⎦ ⎣ ⎦ ⎣ �� ⎦ ⎣

�

⎤⎡ ⎤ ⎜ ⎜⎜ ( n +1) ,p −1 ⎜ � ⎜ ⎜∆Q ⎜⎜ ⎜⎜ ⎜ ⎜ ⎦ ⎦ ⎣

MUSCL approach A first-order spatial discretization is equivalent to represent the numerical approximation of the solution as a piecewise constant. The MUSCL idea is to use a linear approximation to achieve a second-order space discretization. A linear solution is exactly resolved, which generates a truncation error of the order ∆x2. In order to represent the conservation laws, the discrete state variables express the average state within the cells. Then, the linear approximation has to average out these values (Hirsch, 1990). One can consider the Taylor linearization as a onedimensional (1-D) local representation, Fig. 4, valid in a given cell “i”, at a determined instant Q(x ) = Qi +

1 (x −x i ) δi Q+O ( ∆ x 2) ∆x

( xi −1/2<x<xi +1/2)

(45)

setting x = xi ± ∆x/2, it is possible to write Q i +1/2 = Q i + ∆1x (xi + ∆2x −xi ) δi Q = Q i + 1 δi Q 2

(46)

Q i −1/2 = Q i + ∆1x (xi − ∆2x −xi ) δi Q = Q i − 1 δi Q 2

(47)

The use of backward and forward derivatives provides Q i + 1/2 = Q i + 1 ( Q i −Q i − 1 ) 2

, (48)

Q i −1/2 = Q i − 1 ( Q i +1 −Q i ) 2

� �

Each , in the sparse matrix, is a block matrix. The time step is computed by  ∆ t = CF L → || v || + a

in order to obtain second-order extension for the inviscid fluxes calculation. This section presents the classical formulation of the MUSCL approach and an extension for unstructured grids.

, (44)

in which CFL (Azevedo, 1988) is a parameter set to ensure stability of the time integration method, l is the size of the cell and || -v || + a is the largest wave speed in the cell (Scalabrin, 2007). Second-order extension of inviscid fluxes The monotone upstream-centered scheme for conservation laws, known as MUSCL approach (van Leer, 1979), is used

(49)

One can rewrite these terms at the same faces as Q i + 1/2 (x) = Q i + 1 (Q i −Q i − 1) 2 L

R 1 Q i + 1/2 (x ) = Q i +1 − ( Q i +2 − Q i +1 ) 2

(50) .

(51)

Using limiters to treat correctly the discontinuities, the MUSCL scheme can be written as L 1 Q i + 1/2 (x ) = Q i + ψ ( r L)( Q i −Q i − 1) 2

, (52)

Q i + 1/2 (x ) = Q i +1 − 1 ψ (r L) ( Q i +2 − Q i +1 ) 2 R

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(53)

A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

i+1/2

i-1/2 i

i-1

153

i+1

i+2 i+1

Figure 4. 1-D local representation of a finite volume grid.

where r is the ratio of consecutive variations, given by r L=

Q i +1 − Q i Qi − Qi− 1

r R=

Q i +1 − Q i Q i +2 − Q i +1

(54)

and ψ(r) is a limiter function. These functions are extremely important in the context of high-order methods. However, this discussion is not in the scope of the present work. One can find further information about limiter functions in chapter 21 from Hirsch (1990). There are several limiter functions available for highorder methods of CFD applications. Two of these functions are implemented herein, the van Albada limiter (van Albada et al., 1982), given by 2 ψ (r ) = r + 2r 1+ r

(55)

and the minmod limiter (Hirsch, 1990), written as ⎧min [r , 1], r > 0 ψ (r ) = ⎨ , r≤ 0 ⎩0

(56)

The simulations performed in the present work used mainly the van Albada limiter function (Hirsch, 1990). Second-order extension for unstructured grids The MUSCL variable extrapolation for 2-D or 3-D is straightforward for structured meshes. However, it is not very simple for unstructured solvers. The approach applied here is based on the work of Batina (1990) and Bibb et al. (1997). Here, the stencils are created using only cell-centered values. The points “i” and “i+1” are, respectively, the center of the cell at the left and right of the face. The other two points, “i-1” and “i+2”, are defined by a stencil search. The search for cells “i+2” and “i-1” is limited to the ones that share at least one node with the volumes “i+1” and “i”, respectively. The selected “i+2” point is the one that has the maximum positive value of the dot product between the face normal and the normalized vector joining the face centroid

Not selected Selected Figure 5. Search for the “i + 2” point inside an unstructured grid. (Scalabrin, 2007).

to cell centroid. Using the same principle, the chosen “i-1” point is the one with the maximum negative value of the dot product. Figure 5 is extracted from Scalabrin (2007), and illustrates the search for the “i+2” point in a given mesh. It is possible to observe that, when the stencil search is applied to unstructured grids, the distance between the “i+1” and “i+2” points can be different from the distance between the “i” and “i+1” points. Therefore, a correction is applied on the limiter, as given by r L=

Q i +1 − Q i b , Qi − Qi− 1 a

r R=

Q i +1 − Q i c Q i +2 − Q i +1 a

(57)

where “a” is the distance between the “i+1” and “i” points, “b” is the distance between the “i+2” and “i+1”points, and “c” is the distance between the “i” and “i-1” points.

tUrBUlENCE ModEliNG THe SpAlART-AllMARAS TuRBulenCe Model The Spalart-Allmaras (SA) closure (Spalart and Allmaras, 1992 and 1994) is a one-equation, linear eddy-viscosity turbulence model. It solves one transport equation for the ~ . The model uses eight modified eddy viscosity coefficient, ν closure coefficients and three closure functions derived along intuitive and empirical lines, relying heavily on calibration by reference to a wide range of experimental data (Spalart

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and Allmaras, 1992 and 1994). The one equation model is originally written as 2 ∂ ˜ν ∂ (˜ν uj ) ⎛ ˜ν⎞ = cb1 S˜ ˜ν− cw1 f w ⎝ ⎠ + + ∂t ∂x j d

σ SA

∂ ⎡ ∂ ν˜ ⎤ cb2 ∂ ν˜ ∂ ν˜ (ν + ν˜ ) + ∂x j ⎣ ∂x j ⎦ σ SA ∂x k ∂x k

(58)

The kinematic eddy viscosity is defined as νt =˜ν fv1 .

(59)

The classical approximation used by the CFD community to write this single equation model in a conservative form for compressible flows consists in multiplying Eq. (59) by ρ, which yields 2 ∂ µ˜ ∂ (˜µuj ) =cb1 S˜ µ˜ − cw1 f w ρ ⎛ ν˜ ⎞ + + ⎝d ⎠ ∂t ∂x j ⎤ cb2 ∂ ν˜ ∂ ν˜ 1 ∂ ⎡(µ+ µ) ˜ ∂ ν˜ + σ SA ρ σ SA ∂x j ⎣ ∂x j ⎦ ∂x k ∂x k

(60)

The new variable to be solved is μ̃ , defined μ̃ = ρν̃ . It is very important to point here that and are not fluid properties, but flow properties. The closure coefficients and auxiliary relations are given by cb1=0.1355, cb2=0.622, cv 1=7.1, σ SA = 2 , 3 cb1 1+cb2 cw1 = 2 + σ , cw2 = 0.3, cw 3 =2.0, k =0.41 SA k

fv1=

χ , χ 3 + c3v 1

χ = ν˜ , ν

f v2 =1−

χ , 1 + χ fv1

g= r + cw 2 (r 6− r),

ν˜ f , ˜ S=S+ v2 k2d 2

¬ S= √¯¯¯ ij Ωij 2Ω¯¯¯

ν˜ ˜ Sk 2 d 2

6 ⎡ 1 + cw 3 ⎤ 6 ⎣ g6 + c6w 3 ⎦

Dq = Dt

ρq −

ρq +

in which q is the turbulent property, Pq is the production term, Sq is the destruction term, Dq is the diffusion term, and CDq is the cross-diffusion-like term. The second term in the left-hand side is the advection term, here defined as Cpq. In the context of the SA turbulent closure, these previously discussed terms are written as

∂ (ρq) ∂˜µ = , ∂t ∂t 1 ∂ ⎡(µ+˜µ ) ∂ ˜ν⎤ , DSA= σ SA ∂xj ⎣ ∂xj⎦ ˜ P SA =cb1 S µ˜ ,

SSA =cw1 f w ρ ⎛ ˜ν⎞⎠ , C SA=

⎝d

b2 ρ ∂ ˜ν ∂˜ν CD SA= σcSA ∂xk ∂x k

∂ (µ ˜ uj )

∂xj

ρq

(62)

(65)

The SA turbulence model has been extensively used by the CFD community for 3D compressible flow with very good agreement to experimental data for many relevant applications (Spalart and Allmaras, 1992 and 1994; Bigarella, 2007; Bigarella and Azevedo 2009).

2 ⌠ ∂ µ˜ ⌠ ⎡ ⎤ ⌠⎡ ˜ 1 ^ ⎛ ν˜ ⎞ ⎤ ⌡V ∂t dV+⌡V ∇·⎣v µ˜ − σ SA µ ∇ µ˜ ⎦ dV−⌡V ⎣cb1 S µ˜ −cw 1 f w ρ ⎝d ⎠ ⎦ dV i

⌠ ⎡ cb2 ∂ ν˜ ∂ ν˜ ⎤ ρ dV=0 ∂x k ∂x k ⎦ Vi ⎣σ SA

−⌡

ρq +

(64)

Numerical implementation In order to discretize the SA turbulence model equation in a finite volume context, it is necessary to integrate Eq. (64), yielding

in which d is the distance from the closest surface and Ω stands for the terms present in the anti-symmetric part of the mean velocity gradient field. In general terms, turbulence is modeled by transport equations in order to represent turbulent properties being carried by the mean flow. These transport equations have advection, diffusion, source, production, and destruction terms, such as the ones indicated in Eq. 63: ρ

∂ (ρq) +∇ ∙ (ρqv) =Pρq −Sρq +Dρq+CD ρq ∂t

(61)

, 1

f w =g

or using the definition of total derivative:

(63)

(66)

Using the mean property definition Qi =

1 ⌠ QdVi Vi ⌡Vi

(67)

and the Green-Gauss theorem, it is possible to rewrite the finite volume equation ∂ µ˜ i 1 ⌠ ⎛ 1 µ^ ∇ µ˜ ⎞ ·dS − ⎡c S˜ µ˜ −c f ρ ⎛ ˜ν⎞ 2⎤ v µ˜ − σ SA + w1 w ⎝ ⎠ ⎣ b1 ∂t Vi ⌡S i ⎝ d⎠ ⎦ cb2 ∂ ν˜ ∂ ν˜ ⎤ ⎡ + ρ =0 . ⎣σ SA ∂x k ∂x k ⎦

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(68)

A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

The production, Pi, destruction, Si, and the cross-diffusion, CDi, terms are considered constant in the i-th volume. Summation over the faces forming the i-th volume needs to be performed in order to calculate the surface integral, nf

⎤ 1 ⌠ ⎛v˜µ − 1 µ^ ∇ µ˜ ⎞ ·dS≡ 1 ⎡ ∑ v˜µ·Sk − 1 ∑ (µ ^ σ SA k=1 ∇ µ˜ )·S k⎦ σ SA ⎠ Vi ⌡Si ⎝ Vi ⎣ k=1

. (69)

The Sk term is the outward facing normal area vector. Hence, Eq. (69) can be written as nf ∂ µ˜ i 1 ⎡ nf ∑ v µ˜ ·S k − σ 1 ∑ (µ^ ∇ µ˜ )· S k⎤ − + SA ⎦ ∂t Vi ⎣ k =1 k =1 ⎡ c S˜ µ˜ −c f ρ ⎛ ν˜ ⎞ 2⎤ + ⎡ cb2 ρ ∂ ν˜ ∂ ν˜ ⎤ =0 w1 w ⎝ d ⎠ ⎦ ⎣σ SA ∂x k ∂x k ⎦ ⎣ b1

155

for up to the wall, it is usually required that the first point off the wall be located so as to satisfy y+≤1 (Bigarella, 2007). However, obviously, it is not possible to know τw value before achieving the solution of the simulations. Then, in the present work, the position of the first point off the wall is determined using an empirical approximation (Bigarella, 2007; van der Burg et al., 2000): y=5.893 y+ L ReL−0 . 9

(75)

(70)

where y+ is the desired value set by the user, and ReL is the Reynolds number based on the reference length, L.

(71)

BOUNDARY CONDITIONS

After the operations, the SA equation is written as ∂ µ˜ i =− RHS t ∂t

where the residue is nf

1⎡ ∑ v µ˜ · S k − σ 1 ∑ ( µ^ ∇µ˜ )·S k ⎤ − SA k =1 (72) ⎦ Vi ⎣ k =1 2 ⎡c S˜ µ˜ − c f ρ ⎛ ˜ν ⎞ ⎤ − ⎡ cb2 ρ ∂ ˜ν ∂ ˜ν ⎤ . w1 w ⎝ ⎠ ⎣ b1 d ⎦ ⎣ σ SA ∂x k ∂x k ⎦

RHS t =

It is important to point out here that this formulation needs property values on the cell faces to compute the summation terms and property values on the cell centers for the computation of the source terms.

The boundary conditions are implemented using ghost cells. The solver creates the ghost cells to hold properties that satisfy the correct flux calculation at the boundaries. The implementation assigns properties that satisfy the Euler boundary conditions to calculate the inviscid fluxes, and properties that satisfy the Navier-Stokes boundary conditions for calculating the viscous fluxes. Therefore, the ghost volumes store two different types of fluxes for the correct computation of the RANS equations. Inviscid boundary conditions

Mesh requirements for turbulent simulations Turbulent simulations require that a sufficiently refined mesh at the wall is provided. In particular, the parameter typically used to measure such refinement is denoted y+, which is the dimensionless distance from the point to the nearest wall (Tennekes and Lumley, 1972). Schlichting (1978) defines y+ as a Reynolds number based on the friction velocity, y +=

uτ y ν

, (73)

in which y is the distance to the nearest wall, and uτ is the friction velocity, written as u τ= √¯τρw¬ .

(74)

Here, τw is the wall shear stress. For the correct solution of wall-bounded turbulent flows, with turbulence models solved

Wall and symmetry boundary conditions Ghost cells are applied for the implementation of boundary conditions. The ghost cells hold the properties in the same manner to calculate the inviscid fluxes at the wall and at the symmetry boundaries. Mass and energy fluxes should yield zero, and the momentum flux is equal to the pressure flux. This is accomplished by setting the normal velocity component to the boundary face zero. To simplify, the properties at the left side of the boundary face, which is the interior domain, are rotated to the face coordinates using Q rot cl =R Q cl

(76)

As the left side of the boundary is the interior domain, the right side of the boundary is the ghost cell. In the present section, the turbulent variable from the SpalartAllmaras model is included in the Q vector, which now is written as

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Junqueira-Junior, C., Azevedo, J.L.F., Scalabrin, L.C. and Basso, E.

Q= [ ρ

ρu

In Eq. (76), ⎡1 ⎜0 R= ⎜⎜ 0 ⎜0 ⎜0 ⎣0

ρv

ρw

µ˜ ]

(77)

0 nx tx rx 0 0

0 ny ty ry 0 0

0 nz tz rz 0 0

0 0 0 0 1 0

0 0 0 0 0 1

Ri ,

(78)

→ →→ and the n , t , r vectors define the face-based reference frame. The properties at the ghost cells are set to = − ρ cl u rot cl,n

ρ cr u rot cr, t = ρ cl

u rot cl, t

, ,

rot (79) ρ cr u rot , cr,r = ρ cl u cl,r

e i cr= e i cl

µ˜ cr = µ˜ cl

One can write in the matrix form as Q rot =W Q rot , (80) cr

=Ri +int =vnint + γ −2 1

a int

(84)

→→ in which vn is the normal velocity component given by vn= v · n . The subscripts ∞ and int represent the property at the freestream and in the interior domain, respectively. The normal velocity component and the speed of the sound at the boundary face can be written as + vnf = Riint

af =

ρ cr= ρ cl , ρ cr u rot cr,n

invariants are derived from the characteristic relations for the Euler equations. The formulation at the boundary is given by Ri − = Ri −∞ = vn∞ − γ −2 1 a ∞

is the rotation matrix given by, ⎡ ⎜ ⎜ ⎜ ⎜ ⎜ ⎣

156

γ−1 4

+ 2

Ri −∞

Ri +int + Ri −∞

(85)

in which the f subscript represents the property at the farfield computational surface. It is possible to write the velocity for a subsonic exit, 0 < vn int / aint < 1, using the tangential velocity components of the interior and the definition of normal velocity. uf =u int + (vnf −vn int )· nx , v f =v int + (vnf −vn int )· ny wf =w int + (vnf −vn int )· nz

, .

(86)

in which W is the inviscid wall matrix given by 0 −1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

The other properties are given by

⎡ ⎜ ⎜ ⎜ ⎜ ⎜ ⎣

⎡1 ⎜0 ⎜0 W= ⎜ ⎜0 ⎜0 ⎣0

Therefore, the boundary condition can be written as −1 Q cr=R

WRQ cl

(81)

pf =

(82)

0 0 0 0 1 0

0 0 0 0 0 1

(83)

⎡

0 rx ry rz 0 0

⎣

0 tx ty tz 0 0

⎜ ⎜ ⎜ ⎜ ⎜

0 nx ny nz 0 0

ρ f a 2f γ

1 γ−1

pf 1 ef = + ρ f ( u 2f + v f2 + w f2 ) (γ−1) 2 µ˜ f =˜µint .

(87)

For a subsonic entrance boundary, -1 < vn int / aint < 0, one should extrapolate the freestream properties as

in which the R-1 matrix is given by ⎡1 ⎜0 ⎜0 −1 =⎜ ⎜0 ⎜0 ⎣0

γ ⎛ ρ int a 2f ⎞ ρ f = ⎝ γp ⎠ int

u f =u ∞+(v nf +v n ∞ )· nx , v f =v ∞+(v nf +v n ∞ )· ny

, w f =w ∞+(v nf +v n ∞ )· nz , 1

It returns the properties to the Cartesian coordinate frame. Nonreflecting farfield boundary condition The concept of Riemann invariants (Long et al., 1991; Bigarella, 2007) is implemented to achieve a nonreflecting farfield boundary condition at subsonic speeds. These

⎛ ρ γ∞ a 2f ⎞ γ − 1 ρ f = ⎝ γp ∞ ⎠

(88)

ρ f a 2f , γ pf ef = + 1 ρ f (u 2f +v f2+w f2 ) ( γ−1) 2 µ˜ f = µ˜ ∞ .

pf =

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(89)

A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

For supersonic flows, it is not necessary to use the concept of Riemann invariants, because information propagates in only one direction in inviscid supersonic flows. Therefore, zeroth-order extrapolation is used for it yields a cheaper computation. Hence, for a supersonic exit boundary, vn int / aint > 1, the properties are extrapolated from the interior of the domain as Qf = Qint = Qcl

(90)

(91)

The freestream properties are previously provided by the user. Ghost cells One can obtain the properties at the boundary face using the Riemann invariants. However, in order to obtain the boundary conditions these properties need to be computed in the ghost cells. It is possible to use an average to calculate the properties in the ghost volume as Qgh = Qcr = 2Qf - Qint

(92)

⎛ ∂p⎞ = 0 ⎝∂n ⎠wall

(95)

one can use the equation ⎛ ∂p⎞ = T ⎛ ∂ρ ⎞ + ρ wall wall ⎝∂n ⎠ ⎝∂n ⎠wall wall

⎛∂T ⎞ ⎝∂n ⎠

wall

(96)

Riemann invariants are derived for farfield boundary conditions. It is strongly recommended to avoid their use for other flow situations, such as entrance and exit boundary conditions for internal flow cases (Bigarella, 2007). The implementation has shown to be very sensitive when the farfield boundary is set close to solid walls. vISCouS BoundARy CondITIonS For adiabatic boundary condition, it should be assumed that the heat conduction through the boundary face yields zero, qH wall·n = 0, hence (93) ∇T wall ·n = 0 . Therefore, one can state that .

⎛ ∂ρ ⎞ = 0 . ⎝ ∂n ⎠wall

(97)

Thus, it is possible to extrapolate the density from the interior

ρ cr = ρ cl

(98)

The Cartesian components of the wall velocity, uwall, vwall and wwall, are set by the user. It is possible to use these velocity components and the average procedure to calculate the velocity components, ucr , vcr and wcr , in the ghost cells. u cr = 2 u wall − u cl , v cr = 2 v wall − v cl w cr = 2 w wall − w cl

(99)

, .

The ghost cell conservative properties are obtained as

in which the subscript gh stands for ghost cell.

T cr =T wall =T cl

In order to satisfy wall pressure condition (Schilichting, 1978),

and then write

On the other hand, for an entrance boundary, vn int / aint < -1, the properties are extrapolated from the freestream as Qf = Q∞

157

(94)

ρucr = ρ cr u cr , ρvcr = ρ cr v cr , ρwcr = ρ cr w cr , 2 2 e cr = (C v )cr T cr+ 12 ρ cr (u 2cr +v cr + w cr ) µ˜ cr = −˜µ cl .

(100)

The turbulent property in the ghost cell is set to –µ˜ cl in order to force µ˜ wall = 0. Symmetry, nonreflecting farfield, and zeroth-order extrapolation boundary conditions use the same procedures applied on the computation of the corresponding inviscid boundary conditions. IMplICIT BoundARy CondITIonS Implicit boundary conditions are necessary in order to obtain a truly implicit time-marching method. The use of explicit boundary conditions can substantially limit the stability of the numerical method in the marching procedure for the solution convergence.

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158

Basic implicit formulation A simplified form of the implicit equation, Eq. (38), is written in this section in order to detail the implementation of implicit boundary conditions for flux vector splitting schemes:

⎡ Vcl ⎤ + A + + B k++ ) Sk ∆Q cl + ⎣ ∆ t ( k+ ⎦ ( A −k − −B k−− ) Sk ] ∆Q cr,k =R cln .

(101)

]

In such equation, the repeated k index in the second term in left hand side of the equation indicates summation over all the k faces of the control volume. Equation (101) is written only to present the relation between an internal cell, cl, and a boundary cell, cr, k. In the original formulation, Eq. (38), the cl-th cell has contributions from other faces, which may or may not be boundaries. As presented in the beginning of this section, the ghost cells hold different values for inviscid and viscous calculations. Hence, using the splitting definition, presented in section numerical formulation, Eq. (101) can be written as ⎤ ⎡ Vcl + + − ⎣ ∆ t + (A k + +B k + ) Sk ⎦ ∆Q cl + A k − Sk ∆ Q cr,k,inv − − B k − Sk ∆ Q cr,k,visc =R cln .

F k, inv, wall = F k, inv, sym =

−1 −1

W W

, .

(106)

The matrices are applied to ∆Q for the implicit boundary condition according to Eq. (104). It is possible to use the identity matrix to represent the zeroth-order extrapolation as given by F k,inv= [ I ] .

(107)

For the purpose of developing the implicit boundary condition, the farfield variables are considered constant. Hence, ∆Q at a farfield boundary is given by ∆ Q cr,k = 0

(108)

which implies in , (109)

Fk,inv = 0

where 0 stands for the zero matrix.

(102)

(103)

Viscous boundary conditions The viscous Jacobians are created using primitive variables. Therefore, the implementation of implicit viscous matrices is performed using primitive variables. They are applied directly at the calculation of the Jacobians matrices as

∆ Q cr,k,visc = Fk,visc ∆ Q cl .

(104)

V= [ ρ

The contributions of the boundary face can be expressed in terms of the internal cell corrections as

Hence, Eq. (102), can be rewritten as ⎡Vcl ⎤ + − − + n ⎣ ∆ t +(A k + + A k − F k,inv−B k − F k,visc + B k + ) Sk ⎦ ∆Q cl =R cl

ν˜ ]

(110)

. (105)

The adiabatic wall implicit boundary condition is calculated using

The viscous Jacobians are calculated using primitive variables, and the corrections are set for the primitive variables and applied directly at the calculation of the viscous Jacobians. The matrix B+k already includes the contribution from the boundary. The A+k , A–k , B+k and B–k are presented in the work of Scalabrin (2007). –

⎡0 ⎜0 ⎜0 F k,visc = ⎜ ⎜0 ⎜0 ⎣0

0 −1 0 0 0 0

0 0 −1 0 0 0

0 0 0 −1 0 0

0 0 0 0 1 0

0 0 0 0 0 −1

⎡ ⎜ ⎜ ⎜ ⎜ ⎜ ⎣

∆ Q cr,k,inv = Fk,inv ∆ Q cl

(111)

–

Inviscid boundary conditions The matrix for an inviscid wall or for a symmetry boundary is the same presented in Eq. (82),

The same procedure used for the inviscid zeroth-order extrapolation is used here, hence F k,visc = [ I ]

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. (112)

A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

The viscous farfield matrix is the same one used for the inviscid farfield boundary condition, which is given by F k,visc = Fk,inv =0

(113)

cf =

1 2

τw ρ ∞ u 2∞

(115)

is compared to experimental data (Coles and Hirst, 1969), and to the analytical formulation (von Karman, 1934) given by

in which 0 stands for the zero matrix.

− 1

cfvon Karman (Re x ) = 0 .025 Re x

FloW SiMUlatioN rESUltS aNd diSCUSSioN

⎧ y +< 5 viscous sublayer u+= y + ⎨ 1 + + ln (y+)+5.5 ⎩30 < y <300 log-law region u = 0.41

. (114)

The distribution of the local skin friction coefficient, cf , which is written as

(116)

Farfield

2 1

Farfield

Symmetry

Wall 3

Symmetry 4

Figure 6. Domain used for the zero-pressure-gradient flow over a flat plate.

(a) 3

2 1 0

(b) 3 2 Y

The test case used in this work is the simulation of turbulent subsonic flow over a flat plate geometry in absence of streamwise pressure gradients. The work studies the addition of different levels of artificial dissipation, at different distances of the wall, in an attempt to fully understand the effects of the high dissipative upwind spatial discretization over turbulent dimensionless boundary layer profiles and over the friction coefficient. All results are compared to analytical and experimental data. The Mach number at the freestream condition is set to M∞ = 0.3, and the Reynolds number based on 1 m long flat plate is 7.2 million. Therefore, the flow can be considered as a turbulent compressible flow. The computational domain covers a 3 m high and 7 m long region. The wall flat plate is located between 3< x <4. As illustrated in Fig. 6, the applied boundary conditions are as follows: in the lower portion of the computational domain, symmetry is used between the entry and the flat plate, and between the trailing edge and the outlet; an adiabatic wall is assumed over the flat plate surface; and farfield Riemann-type boundary conditions are used for all the other boundaries. The simulations are performed using two grids, one with 60,000 cells and another with 210,000 cells, as illustrated in Fig. 7. Both meshes have y+ = 0.5 at the first grid point off the wall, but the mesh with 210,000 cells has more points near to the wall. The dimensionless boundary layer profiles obtained by the simulations are compared to the analytical formulation given by the law of wall (Schilichting, 1978), which is written by

159

1 0

Figure 7. Visualization of the meshes used in the zeropressure-gradient flow over a flat plate. (a) Mesh with 60,000 volumes; (b) Mesh with 210,000 volumes.

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Junqueira-Junior, C., Azevedo, J.L.F., Scalabrin, L.C. and Basso, E.

where Re x is local Reynolds number based on a distance from the current position to a reference point, and is given by Re x =

ρU∞ x µ

, (117)

in which U∞ is the freestream velocity and x is the distance to a reference position. The upwind Steger-Warming (Steger and Warming, 1981) scheme is too dissipative and, therefore, implementing a turbulence closure to treat the turbulent flows is not enough to provide accurate results. The dissipative terms, present in the spatial discretization and in the turbulence model equations, need to be carefully treated. The effects of the spatial discretization on the results are analyzed by forcing the switch term, Eq. (24), to the classical Steger-Warming scheme, w = 0, and to the centered scheme, w = 0.5. The artificial dissipation term, Eq. (25), and the Spalart-Allmaras cross-diffusion-like term, Eq. (65), are added in different quantities and at different positions of the boundary layer profile in order to study their influence on the skin friction coefficient and on the dimensionless boundary layer.

Table 1 presents the validation studies performed for this test case. It enumerates the simulations and indicates the chosen spatial discretization; the distance, d0, for the artificial dissipation; the amount of artificial dissipation at a given region; the choice of the turbulence model; and the choice of the cross-diffusion-like term. The first three simulations are an introductory study of the numerical issues concerned in this work, and the results are illustrated in Fig. 8. Simulation No. 0 is performed without any turbulence modeling. It provides an underestimated cf distribution over the flat plate and a boundary layer profile completely different from the analytical turbulent one. For case No. 1, as an initial approximation, the cross-diffusion like term of the SA equation, the most expensive source term, is not included in the formulation and the inviscid flux is calculated using the original scheme of the code, as presented in Eqs. (23) and (24). The results with the turbulent model have shown to be better than those without any turbulence model. The boundary layer profile matches the analytical results at the viscous sublayer, however the excessive artificial dissipation, provided from the spatial discretization, deteriorates the

Table 1. Zero-pressure-gradient flow over flat plate simulations. Case No

Switch

ϵk at (dk < do)

ϵk at (dk >do)

0 1 2 3 4 5

w=0 w=0 w=0.5 w=0.5 w=0.5 w=0.5

0.0 0.0 0.0 0.0 0.0 0.0

---------0.001 0.1

0.3 (ak + |uk|) 0.3 (ak + |uk|) ---0.001 0.1

off on on on on on

on off off off off off

w=0.5

0.0

→

off

7 8

w=0.5 w=0.5

0.0 y+ ≈ 7500

→

on on

w=0.5

→

11 12 13 14 15 16 17 18 19

on on on on on on on on on

on on on on on (dk >do) on (dk < do) on (dk < do) on (dk < do) on (dk < do)

→

0.001 n x (ax+ |ux|) →

0.1 n x (ax+ |ux|) ----

→

0.001 n x (ax+ |ux|) 0.1 n x (ax+ |ux|) ----

0.0

y+ ≈ 750

0.01 n x (ax+ |ux|)

0.0

w=0.5

y+ ≈ 750

0.1 n x (ax+ |ux|)

w=0.5 w=0.5 w=0.5 w=0.5 w=0.5 w=0.5 w=0.5 w=0.5 w=0.5

y+ ≈ 750 y+ ≈ 750 y+ ≈ 750 y+ ≈ 750 y+ ≈ 5 y+ ≈ 5 y+ ≈ 5 y+ ≈ 5 y+ ≈ 5

0.1 n x (ax+ |ux|) 0.1 (ak + |uk|) 0.3 (ak + |uk|) 0.5 (ak + |uk|) 0.5 (ak + |uk|) 0.001 0.001 0.001 0.001 0.001

0.1 n x (ax+ |ux|) 0.1 (ak + |uk|) 0.3 (ak + |uk|) 0.5 (ak + |uk|) 0.7 (ak + |uk|) 0.0 0.3 (ak + |uk|) 1.0 (ak + |uk|) 1.25 (ak + |uk|) 1.5 (ak + |uk|)

→

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A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

boundary layer profile at the log-law zone. The skin friction distribution is still underestimated, which indicates that the computation of shear-stress tensor, τw , at least at the wall, is not correct. Simulation No. 2 uses the centered scheme without any artificial dissipation. The results present the same shortcomings as the previous ones discussed here. However, the results for test case No. 2 have shown to be closer to the analytical data. The solution of a nonlinear partial differential equation, spatially discretized without the addition of artificial dissipation, is numerically unstable (Lomax et al., 2001), due to the frequency cascade phenomenon. Test case No. 2 achieved convergence of the solution because it provides a very simple geometry and due to the presence of the viscous fluxes, which are dissipative by nature. The numerical solver set up, which uses the centered scheme without the addition of artificial dissipation, is unstable and cannot be used for complex configurations. 40 35 30

Simulations including test cases No. 3 to No. 19 are performed using the centered scheme. Artificial dissipation is added to the formulation in different quantities, and at different locations within the boundary layer profile. The local error is measured as the difference between the analytical, and is given by err(%)=100 ∗

25 20 15 10

15 10

0.008 0.006

10 15 25 40 65 100 200 y+

0.008

No. 0 No. 1 No. 2 Cf=0.025*Re (x) ^(1/7) Experimental

0.007

No. 3 No. 4 No. 5 No. 6

0.007 0.006

Cf=0.025*Re (x) ^(1/7) Experimental

0.005

No. 3 No. 4 No. 5 No. 6 Log-law Sublayer

0.004

0.004 0.003

0.003

0.002

0.001

(118)

Figures 9 and 10 present the results and errors for simulations No. 3, 4, 5 and 6, using the SA model without the crossdiffusion-like term. These figures illustrate that the addition of artificial dissipation, in the flow direction, does not affect substantially the boundary layer profile. As with simulation No. 1, the results are in good agreement with the analytical ones at the sublayer zone and overpredicted the log-law zone by about 20% of the analytical value.

No. 0 No. 1 No. 2 Log-law Sublayer

|LeM AN S −Analytical | . Analytical

161

1e+06 2e+06

3e+06 Re (x)

4e+06 5e+06 6e+0

Figure 8. Comparison of the dimensionless turbulent boundary layer and skin friction coefficient to analytical and experimental data (Coles and Hirst, 1969) for simulations 0, 1, and 2.

1e+06

2e+06 3e+06 4e+06 Re (x)

5e+06

6e+0

Figure 9. Comparison of the dimensionless turbulent boundary layer and skin friction coefficient to analytical and experimental data (Coles and Hirst, 1969) for simulations 3, 4, 5, and 6.

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162

The cf distributions are underestimated and presented nonphysical oscillations. The CD terms are implemented to test the full SA turbulent equation. Simulations No. 7, 8, 9 and 10 are performed to study the effects of the cross-diffusionlike terms and of the artificial dissipation on the results. These simulations use a centered scheme and the artificial dissipation in the flow direction in different quantities and positions off the wall. Figures 11 and 12 demonstrate that the numerical oscillations, discussed in the previous simulations without the CD terms, are no longer present in the skin friction coefficient distribution along the flat plate. However, the shape of the boundary layer profile in the log-law zone is very different from the analytical one, with errors superior to 100% of the analytical value. Once again, the addition of artificial dissipation in the

flow direction does not significantly affect the boundary layer profile. Simulations No. 11, 12, 13 and 14 are carried out using a centered scheme with artificial dissipation added in all directions, in different quantities and positions of the boundary layer profile. Figures 13 and 14 illustrate that this simple modification significantly affects the results. The simulation results with 系 < 0.3 (ak+|uk|) have the same behavior as the other simulations presented so far, a good agreement of the sublayer region with analytical data, overpredicted log-law boundary layer, and an underestimated cf distribution. The simulations with 系 > 0.3 (ak+|uk|) have shown good agreement of the skin friction coefficient with the analytical and experimental data, and an underestimated boundary layer profile. From the results, it is clear that the addition of artificial dissipation improves the boundary layer results

(a)

40 u+

Error %

24 22

No. 3 No. 4 No. 5 No. 6 130

18 30

80 y+

10 0

200

10 15 25 40 65 100 200 y+

0.006

Cf=0.025*Re (x) ^(1/7) Experimental

0.005

No. 7 No. 8 No. 9 No. 10

0.007

No. 3 No. 4 No. 5 No. 6

0.004

0.003

0.002

0.001

6 5

0.008

(b)

Error %

30 20

No. 7 No. 8 No. 9 No. 10 Log-law Sublayer

0 0

Figure 10. Boundary layer error distribution for simulations 3, 4, 5, and 6. (a) Error in the log region; (b) Error in the viscous sublayer.

1e+06

2e+06 3e+06 4e+06 Re (x)

5e+06

6e+0

Figure 11. Comparison of the dimensionless turbulent boundary layer and skin friction coefficient to analytical and experimental data (Coles and Hirst, 1969) for simulations 7, 8, 9, and 10.

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A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

at the log-law zone, but it deteriorates the viscous sublayer. The implementation of the cross-diffusion-like terms eliminates the numerical oscillations of the cf distribution, but shifts the log-law region of the boundary layer. Using this information, simulations No. 15 to No. 19 are performed using a centered scheme with the addition of artificial dissipation in log-law region and of the CD terms only in the viscous sublayer region of the boundary layer profile. These simulations are performed in order to take advantage of the CD terms near the wall and the artificial dissipation at the log-law zone. The best results are achieved when the diffusion term, ϵ, is switched off below the viscous sublayer and the CD terms are added only in the viscous sublayer region, as seen in Figs. 15 to 17. Comparing all results, simulations No. 18 and 19 have the best agreement with

the analytical and experimental data, with errors of ≈ 5% for the log-law zone of the boundary layer profile and for the skin friction coefficient distribution over the flat plate. These simulations are carried out using the mesh illustrated in Fig. 7(b). Results are accurate and correspond to aerospace industry needs. On the other hand, the sublayer solutions presented maximum error of ≈10% for the simulations No. 18 and 19. These sublayer errors are not excellent but plausible, since there is good agreement of the log-law zone and the c f distribution with the literature. Therefore, results with good agreement with analytical (von Karman, 1934) and experimental (Coles and Hirst, 1969) data are achieved when one controls the artificial dissipation in the log-law zone, using 1.25 (a k+|u k|) < ϵ < 1.5 (a k+|u k|), and turn off the cross-diffusion-like-terms above the sublayer zone.

160

140

30 (b)

5 0

10 15 25 40 65 100 200 y+ No. 11 No. 12 No. 13 No. 14

0.006

9 8

Cf=0.025*Re (x) ^(1/7) Experimental

0.005 0.004 0.003

0.002

0.001

0.007

0.008

No. 7 No. 8 No. 9 No. 10

Error %

20 10

No. 7 No. 8 No. 9 No. 10 200 130

25 15

100

No. 11 No. 12 No. 13 No. 14 Log-law Sublayer

Error %

(a) 180

120

163

Figure 12. Boundary layer errors for simulations 7, 8, 9, and 10. (a) Error in the log region; (b) Error in the viscous sublayer.

1e+06

2e+06 3e+06 4e+06 Re (x)

5e+06

6e+0

Figure 13. Comparison of the dimensionless turbulent boundary layer and skin friction coefficient to analytical and experimental data (Coles and Hirst, 1969) for simulations 11, 12, 13, and 14. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.145-168, Apr.-Jun., 2013

Junqueira-Junior, C., Azevedo, J.L.F., Scalabrin, L.C. and Basso, E.

164

(a) 140

120

20 15

Error %

100 80 60

No. 11 No. 12 No. 13 No. 14 130

20 0

50 (b)

80 y+

200

25 50 100

250 500 100

0.005 0.004 0.003

0.002

0.001

Error %

Cf=0.025*Re (x) ^(1/7) Experimental

0.006

(c)

20 10 1e+06

2e+06 3e+06 4e+06 Re (x)

5e+06

1e+06

2e+06 3e+06 4e+06 Re (x)

5e+06

6e+0

Figure 15. Comparison of the dimensionless turbulent boundary layer and skin friction coefficient to analytical and experimental data (Coles and hirst, 1969) for simulations 15, 16, and 17.

No. 11 No. 12 No. 13 No. 14

40 30

No. 15 No. 16 No. 17

0.007

100 90 80 70 60 50

0.008

No. 11 No. 12 No. 13 No. 14

Error %

No. 15 No. 16 No. 17 Log-law Sublayer

6e+0

Figure 14. Boundary layer and skin friction coefficient error distribution of simulations 11, 12, 13, and 14. (a) Error in the boundary layer log region; (b) Error in the viscous sublayer; (c) Error in the skin friction coefficient.

CoNClUdiNG rEMarKS The present work presents results obtained in the study of the effects of artificial dissipation terms on the ability of correctly capturing turbulent boundary

layer flows. The paper presents the details of the theoretical and numerical formulations used. The Reynolds-averaged Navier-Stokes equations are used to represent the flows of interest here. Turbulent effects are modeled using the oneequation Spalart-Allmaras eddy-viscosity turbulent model. The work also addresses the inclusion of numerically-stiff cross-diffusion-like (CD) terms in the formulation of the selected turbulence model. The work performed included the implementation of the Spalart-Allmaras turbulence closure in the LeMANS code, a parallel CFD code developed to simulate laminar reentry flows. This code uses a spatial discretization based on the Steger-Warming flux vector splitting scheme, which turned out to be very dissipative for boundary layer flow applications. Flat plate zero-pressure-gradient flow simulations are performed to evaluate the behavior of the dimensionless boundary layer profile and to compare with analytical and

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.145-168, Apr.-Jun., 2013

A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

7 6

Error %

15 10

5 4 3

5 0

25 50 100

0.008

No. 18 No. 19 Log-law Sublayer

2 1 0 30

250 500 100

No. 18 No. 19

0.007

100

(b)

Cf=0.025*Re (x) ^(1/7) Experimental

0.006

250

No. 18 No. 19 500

100

No. 18 No. 19

13 12

Error %

0.005 0.004 0.003

11 10 9

0.002

0.001

(a)

165

1e+06

2e+06 3e+06 4e+06 Re (x)

5e+06 6e+0

experimental data. The very dissipative spatial discretization can deteriorate the boundary layer profile and the distribution of the local skin friction coefficient. Therefore, the effort is undertaken in order to adapt the numerical scheme for turbulent applications. The switch term is changed to force the upwind scheme to a centered one in boundary layer regions. Different artificial dissipation terms are added to improve the numerical stability of the method, shift the shape of the boundary layer, and change the distribution of the local skin friction coefficient. The cross-diffusion-like terms of the turbulent equation have also shown to possess an important role on the results. The study has shown that it is possible to achieve good results for turbulent flows using a discretization based on the Steger-Warming flux vector splitting scheme, provided that an appropriate control of the intrinsic artificial dissipation terms is implemented. The artificial dissipation must be correctly applied only in the

Error %

Figure 16. Comparison of the dimensionless turbulent boundary layer and skin friction coefficient to analytical and experimental data (Coles and Hirst, 1969) for simulations 18 and 19.

50 45 40 35 30 25 20 15 10 5 0

1 (c)

No. 18 No. 19

1e+06

2e+06 3e+06 4e+06 Re (x)

5e+06

6e+0

Figure 17. Boundary layer and skin friction coefficient error distribution of simulations 18 and 19. (a) Error in the boundary layer log region; (b) Error in the viscous sublayer; (c) Error in the skin friction coefficient.

log-law zone, and the cross-diffusion-like terms only in the viscous sub-layer region. In the context of validating the code for turbulent flows application, it is possible to state that good results were achieved for the 2D flat plate flow simulation using

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spatial discretization based on the Steger-Warming scheme. However, the good agreement is dependent upon the addition of artificial dissipation and CD terms at the correct position in the boundary layer profile. In the present work, these modifications are explicitly performed to provide good results for a predefined local Reynolds number. It is very important to adapt the switches in the computational implementation of the numerical scheme in order to add artificial dissipation in the correct position in the boundary layer profile. Similarly, the cross-diffusion-like terms must be switched on only in the sublayer region. Hence, the turbulence model implementation must be performed in such a way that the code could automatically recognize the correct position in the dimensionless boundary layer profile and switch on/off the CD terms and the artificial dissipation. This can certainly be accomplished using an appropriate scaling of boundary layer quantities and the normalized distance to the wall, which is already computed by the turbulence model. However, these are implementation issues, which are beyond the scope of

the present work. Clearly, such implementations would be necessary in order to handle more complex configurations. More complex applications, in the sense, for instance, of treating flows with more obvious compressibility effects, are not an issue, since the turbulence model and the present CFD tool were both originally developed for compressible flows.

ACKNOWLEDGMENTS The authors would like to acknowledge Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, which partially supported the project under the Research Grants No. 312064/2006-3 and No. 471592/2011-0. Further partial support was provided by Fundação Coordenação de Aperfeiçoamento Pessoal de Nível Superior, CAPES, through a Ph.D. scholarship to the first author, and it is also gratefully acknowledged.

REFERENCES Anderson, J.D., 1991, “Fundamentals of Aerodynamics”, McGraw-Hill International Editions, New York, NY, USA. Anderson, W.K., Thomas, J.L. and van Leer, B., 1986, “A Comparison Of Finite Volume Flux Vector Splittings For The Euler Equations”, AIAA Journal, Vol. 24, No. 9, pp. 1453-1460.

Bigarella, E.D.V. and Azevedo, J.L.F., 2009, “Turbulence Modeling for Aerospace Applications, Turbulence”, Vol. 6 of Coleção Cadernos de Turbulência, Chapter 4, ABCM, Rio de Janeiro, RJ, 1st ed., pp. 215296 (in Portuguese, original title is Modelagem de Turbulência para Aplicações Aeroespaciais).

Azevedo, J.L.F., 1988, “Transonic Aeroelastic Analysis Of Launch Vehicle Configurations”, Ph.D. Thesis, Stanford University, Stanford, California, USA.

Bigarella, E.D.V. and Azevedo, J.L.F., 2012, “A Study Of Convective Flux Schemes For Aerospace Flows”, Journal of the Brazilian Society for Mechanical Sciences and Engineering, Vol. 34, No. 3, pp. 314-329.

Basso, E., 1997, “Numerical Analysis of Cascade Flow Problems for All Speed Regimes”, Master’s Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil (in Portuguese, original title is Análise Numérica de Escoamentos em Grades Lineares de Perfis para Vários Regimes de Velocidade).

Bigarella, E.D.V., Azevedo, J.L.F. and Scalabrin, L.C., 2007, “Centered and Upwind Multigrid Turbulent Flow Simulations of Launch Vehicle Configurations”, Journal of Spacecraft and Rockets, Vol. 44, No. 1, pp. 52-65.

Batina, J., 1990, “Three-Dimensional Flux-Split Euler Schemes Involving Unstructured Dynamic Meshes”, AIAA Paper No. 90-1649, 21st AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference, Seattle, WA. Batten, P., Craft, T.J., Leschziner, M.A. and Loyau, H., 1999, “Reynolds-Stress-Transport Modeling for Compressible Aerodynamics Applications”, AIAA Journal, Vol. 37, No. 7, pp. 785-797. Bibb, K.L., Peraire, J. and Riley, C.J., 1997, “Hypersonic Flow Computations On Unstructured Meshes”, AIAA Paper No. 97-0625. Bigarella, E.D.V., 2007, “Advanced Turbulence Modeling for Complex Aerospace Applications”, Ph.D. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil.

Breviglieri, C., 2010, “High-Order Unstructured Spectral Finite Volume Method for Aerodynamic Applications”, Master’s Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil. Breviglieri, C., Azevedo, J.L.F. and Basso, E., 2010a, “An Unstructured Grid Implementation Of High-Order Spectral Finite Volume Schemes”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 32, No. 5 (Special Issue), pp. 419-433. Breviglieri, C., Azevedo, J.L.F., Basso, E. and Souza, M.A.F., 2010b, “Implicit High-Order Spectral Finite Volume Method For Inviscid Compressible Flows”, AIAA Journal, Vol. 48, No. 10, pp. 2365-2376. Chapman, D., 1981, “Trends and Pacing Items in Computational Aerodynamics, Seventh International Conference on Numerical

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.145-168, Apr.-Jun., 2013

A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

Methods in Fluid Dynamics”, edited by W. Reynolds and R. MacCormack, Lecture Notes in Physics, Vol. 141, Springer, Heidelberg, pp. 1–11. Coles, D.E. and Hirst, E.A., 1969, “Computation Of Turbulent Boundary Layers”, Proceedings of the 1968 U.S. Air Force Office of Scientific Research-Internal Flow Program-Stanford Conference, Vol. 2, Stanford University Press, Palo Alto, CA, USA.

167

Roe, P.L., 1981, “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes”, Journal of Computational Physics, Vol. 43, No. 2, pp. 357-372. Scalabrin, L.C., 2007, “Numerical Simulation of Weakly Ionized Hypersonic Flow Over Reentry Capsules”, Ph.D. Thesis, University of Michigan, Ann Arbor, Michigan, USA.

Gnoffo, P.A., 2003, “Computational Aerothermodynamics In Aeroassist Applications”, Journal of Spacecraft and Rockets, Vol. 40, No. 3, pp. 305-312.

Scalabrin, L.C. and Boyd, I.D., 2007, “Numerical Simulations of the FIRE-II Convective and Radiative Heating Rates”, AIAA Paper No. 2007-4044.

Hellsten, A. and Laine, S., 2000, “Explicit Algebraic Reynolds-Stress Modelling In Decelerating And Separating Flows”, AIAA Paper No. 2000-2313.

Schlichting, H., 1978, “Boundary-Layer Theory”, 7th ed., McGraw Hill, New York, NY, USA.

Hirsch, C., 1990, “Numerical Computation of Internal and External Flows, Vol. II: Computational Methods for Inviscid and Viscous Flows”, Wiley, New York, USA.

Schwartzentruber, T.E., Scalabrin, L.C. and Boyd, I.D., 2007, “A Modular Particle-Continuum Numerical Method For Hypersonic NonEquilibrium Gas Flows”, Journal of Computational Physics, Vol. 225, No. 1, pp. 1159-1174.

Jameson, A., 1995a, “Analysis And Design Of Numerical Schemes For Gas Dynamics 1 – Artificial Diffusion, Upwind Biasing, Limiters And Their Effect On Accuracy And Multigrid Convergence”, International Journal of Computational Dynamics, Vol. 4, No. 3-4, pp. 171-218.

Schwartzentruber, T.E., Scalabrin, L.C. and Boyd, I.D., 2008, “Hybrid Particle-Continuum Simulations Of Non-Equilibrium Hypersonic BluntBody Flowfields”, Journal of Thermophysics and Heat Transfer, Vol. 22, No. 1, pp. 29-37.

Jameson, A., 1995b, “Analysis And Design Of Numerical Schemes For Gas Dynamics 2 – Artificial Diffusion And Discrete Shock Structure”, International Journal of Computational Dynamics, Vol. 5, No. 1-2, pp. 1-38.

Spalart, P.R. and Allmaras, S.R., 1992, “A One-Equation Turbulence Model For Aerodynamic Flows”, AIAA Paper No. 92-0439.

Jameson, A., Schmidt, W. and Turkel, E., 1981, “Numerical Solution Of The Euler Equations By Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes”, AIAA Paper No. 81-1259. Jawahar, P. and Kamath, H., 2000, “A High Resolution Procedure For Euler And Navier-Stokes Computation On Unstructured Grids”, Journal of Computational Physics, Vol. 164, No. 1, pp. 165-203. Junqueira-Junior, C.A., 2012, “A Study On The Extension Of An Upwind Parallel Solver For Turbulent Flow Applications”, Master’s Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, São Paulo, Brazil. Junqueira-Junior, C.A., Azevedo, J.L.F., Basso, E. and Scalabrin, L., 2011, “Study Of Robust And Efficient Turbulence Closures For Aerospace Applications”, 32nd Iberian Latin American Congress on Computational Methods in Engineering, Ouro Preto, Minas Gerais, Brazil. Lomax, H., Pulliam, T.H. and Zingg, D.W., 2001, “Fundamentals of Computation Fluid Dynamics”, Springer, New York, USA. Long, L.N., Khan, M. and Sharp, H.T. 1991, “A Massively Parallel Three-Dimensional Euler/Navier-Stokes Method”, AIAA Journal, Vol. 29, No. 5, pp. 657-666. MacCormack, R.W. and Candler, G.V., 1989, “The Solution of the Navier Stokes Equations Using Gauss-Seidel Line Relaxation”, Computer and Fluids, Vol. 17, No. 1, pp. 135-150. Mavriplis, D.J., 1988, “Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes”, AIAA Journal, Vol. 28, No. 2, pp. 213-221. Ramalho, M.V.C., Azevedo, J.H.A. and Azevedo, J.L.F., 2011, “Further Investigation into the Origin of the Carbuncle Phenomenon in Aerodynamic Simulations”, AIAA Paper No. 2011-1184, 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, USA.

Spalart, P.R. and Allmaras, S.R., 1994, “A One-Equation Turbulence Model For Aerodynamic Flows”, La Recherche Aerospatiale, Vol. 1, No. 1, pp. 5-21. Steger, J.L. and Warming, R.F., 1981, “Flux Vector Splitting of the Inviscid Gasdynamic Equations with Application to the FiniteDifference Method”, Journal of Computational Physics, Vol. 40, No. 2, pp. 263-293. Tennekes, H. and Lumley, J.L., 1972, “A First Course In Turbulence”, The MIT Press, Cambridge, MA, USA. Turkel, E. and Vatsa, V.N., 1990, “Effect of Artificial Viscosity on Three-Dimensional Flow Solutions”, AIAA Journal, Vol. 32, No. 1, pp. 39-45. van Albada, G.D., 1982, van Leer, B. and Roberts, W.W., 1982, “A Comparative Study of Computational Methods in Cosmic Gas Dynamics”, Astronomy and Astrophysics, Vol. 108, No. 1, pp. 76-84. van der Burg, J.W. 2000, “Turnaround Time And Accuracy Evaluation Of Viscous Flow Computations On Hybrid Grids”, Technical Report NLRTP-2000-228, Amsterdam, The Netherlands. van Leer, B., 1979, “Towards the Ultimate Conservative Difference Scheme. V. A Second-Order Sequel to Godunov’s Method”, Journal of Computational Physics, Vol. 32, No. 1, pp. 101-136. Venkatakrishnan, V., 1995, “Implicit Schemes and Parallel Computing in Unstructured Grid CFD”, VKI Lecture Series, Rhode-Saint-Genèse, Belgium. von Karman, T., 1934, “Turbulence and Skin Friction”, Journal of the Aeronautical Sciences, Vol. 1, No. 1, pp. 1-20. Wallin, S. and Johansson, A.V., 2000, “An Explicit Algebraic Reynolds Stress Model For Incompressible And Compressible Turbulent Flows”, Journal of Fluid Mechanics, Vol. 403, pp. 89-132. Wolf, W.R., 2006, “Simulation of Compressible Aerodynamic Flows Using Unstructured Grid, High-Order, Non-Oscillatory Schemes”, Master’s Thesis, Instituto Tecnológico de Aeronáutica, São José

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Junqueira-Junior, C., Azevedo, J.L.F., Scalabrin, L.C. and Basso, E.

dos Campos, SP, Brazil (in Portuguese, original title is Simulação de Escoamentos Aerodinâmicos Compressíveis Utilizando Esquemas Não Oscilatórios de Alta Ordem de Precisão em Malhas Não Estruturadas).

Wolf, W.R. and Azevedo, J.L.F., 2007, “High-Order ENO and WENO Schemes for Unstructured Grids”, International Journal for Numerical Methods in Fluids, Vol. 55, No. 10, pp. 917-943.

Wolf, W.R. and Azevedo, J.L.F., 2006, “High-Order Unstructured Essentially Nonoscillatory and Weighted Essentially Nonoscillatory Schemes for Aerodynamic Flows”, AIAA Journal, Vol. 44, No. 10, pp. 2295-2310.

Wright, M.J., 1997, “A Family of Data Parallel Relaxation Methods for the Navier-Stokes Equations”, Ph.D. Thesis, University of Minnesota, Minneapolis, MN, USA.

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doi: 10.5028/jatm.v5i2.207

A Numerical Investigation of Localized and Steady Energy Addition to High Speed Airflows André Carlos Fraile Jr1, Mauricio Antoniazzi Pinheiro Rosa1

ABSTRACT: This work presents a numerical analysis of the gas dynamic problem of localized and steady energy addition to uniform high-speed airflows. Firstly, the general effects caused by a localized energy deposition on the flow were investigated, then an extensive parametric analysis concerning the effects of energy deposition rate and dispersion for different free stream flow speeds was performed. As a general result, localized and steady energy deposition generates compression waves and constant property flow stream tube downstream to the source. The parametric analysis results have shown that either increasing the rate or decreasing dispersion in the orthogonal direction to the flow of the deposited energy has the effect of enhancing property flow changes, which is even more pronounced for lower flow speeds. In contrast, energy dispersion in the flow direction has presented very little effect on the flow changes. The results of this numerical analysis should be very helpful in studies of energy addition applications in hypersonic. KEYWORDS: High speed flow, Energy addition, Flow control, Numerical analysis.

INTRODUCTION The need of aerospace vehicles for high speeds discloses a series of aerodynamics problems, such as large pressure drag forces and strong shock waves. It is known that, for a blunt body at supersonic speeds, a physical spike placed at its nose modifies the structure of the strong shock wave, which can reduce wave drag in an effective way, although this structure also requires an undesirable additional cooling system (Riggins et al., 1999, Riggins and Nelson, 1999, Knight, 2003). Another way to control high speed flows, which has also been considered for the reduction of aerodynamic drag of aerospace vehicles, corresponds to energy deposition in a small region of the airflow upstream to the vehicle. This is similarly capable of modifying the properties and path of the fluid elements and consequently of reducing the strength of the vehicle shock wave by modifying its shape (Riggins et al., 1999, Riggins and Nelson, 1999, Knight, 2003). Besides this application, energetic techniques for high-speed flow control have been recently widely studied with several other purposes, such as inlet mass capture increase by scramjet engines operating at off design speeds, attitude control of supersonic vehicles, scramjet isolator shortening, among others. Deposition of energy to airflows has been experimentally accomplished by several different means, such as plasma arcs, laser pulse, microwave, electron beam, glow discharges, and so on (Oliveira, 2008c). This work is part of some development activities that are being carried out at the Institute for Advanced Studies (IEAv) regarding high-speed airflow control. The advance of

1.Instituto de Estudos Avançados – São José dos Campos/SP – Brazil Author for correspondence: André Carlos Fraile Jr | Instituto de Estudos Avançados – Divisão de Aerotermodinâmica e Hipersônica | Trevo Coronel Aviador José Alberto Albano do Amarante, 1 | CEP 12.228-001 São José dos Campos/SP – Brazil | E-mail: fraile@ieav.cta.br Received: 03/12/12 | Accepted: 10/04/13

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into account a two-dimensional representation in space by considering axial symmetry. The physical (computational) domain, also shown in Fig, 1, contains a cylindrical volumetric heat source representing a localized steady energy deposition in a supersonic uniform airflow. This cylindrical heat source is aligned with the flow. The Navier-Stokes equations (Eq. 1), with a volumetric source term representing the energy addition, were used in this work (FLUENT INC., 2006, Fraile Jr., 2011): ⎧ дρ ⎜ дt + · (ρv) = 0 ⎜ ⎜ ⎨ д (ρv) + · (ρvv) = − p + · ( = τ) ⎜ дt ⎜ д ⎜ τ · v)] + Q (ρE) + · [v (ρE + p)] = · [k T + ( = ⎩ дt ∆

(1)

∆

experimental studies previously performed at the IEAv, with respect to the addition of laser energy pulses to investigate vehicle drag and heat transfer (Minnuci et al., 2005, Oliveira, 2008a, 2008b, 2008c, Salvador et al., 2005, 2007, 2008), has shown the need of numerical analyses to obtain a better understanding of the phenomena generally observed and also to support new experiments. Therefore, in this work, which focused on understanding the properties of an energized flow without the presence of bodies, it is presented a numerical investigation of a localized steady energy addition to highspeed airflows, by varying the energy deposition rate and the spatial dispersion for different free stream airflow speeds (Fraile Jr., 2011). While this subject has already been studied, this paper presents a series of results showing airflow variables — such as velocity, density, pressure, and temperature — when several conditions were modified, and these results can provide information to another ongoing numerical study at IEAv related to wave drag reduction of blunt bodies in supersonic flows using energy addition. Herein, energy addition to high-speed flows is studied from thermodynamics and gas dynamics standpoints by considering that the energy addition effectively represents the direct energy transfer to the air translational (thermal) mode. Therefore, no plasma effects are considered and localized energy addition to the flow is simply treated as a volumetric heat source.

∆

170

where ρ is the flow density, p is the pressure,v is the velocity, τ represents the influence of viscosity on momentum and energy equations, k is the thermal conductivity, E is the energy per mass unit, and Q is the energy source term (per time and volume unit). Also, a small region of the domain receives energy and the term Q is the mathematical way employed to deposit energy to the airflow. The tensor τ can be written as in Eq. 2 (FLUENT INC., 2006, Fraile Jr., 2011):

∆

The schematic shown in Fig. 1 represents the numerical problem treated in this work. The analysis performed takes

∆

τ =µ

vT −

2 3

∆

METHODOLOGY

·vI

where µ is the molecular viscosity and I is the unit tensor. The gas is considered ideal, therefore it can be written as in Eq. 3:

pressure far field

p = ρ RT pressure far field

pressure outlet

M∞

(2)

(3)

where R is the gas constant. The energy per mass can be defined as Eq. 4 (FLUENT INC., 2006; Fraile Jr., 2011):

source axis Figure 1. Physical (computational) domain employed for calculation of a steady heat source in a supersonic flow.

2 E=h− p + v ρ 2

where dh = cpdT .

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A Numerical Investigation of Localized and Steady Energy Addition to High Speed Airflows

The numerical solution to this problem is obtained by using the Fluent® solver (FLUENT INC., 2006) for the Navier-Stokes equations, with the conditions of laminar flow and ideal gas, in a square grid that is well suitable for the geometry shown in Fig. 1. Since the numerical domain is axisymmetric, the Navier-Stokes equations are solved in cylindrical coordinates (FLUENT INC., 2006, Tannehill et al., 1997). The equations are discretized in accordance with an implicit method and a first order upwind spatial scheme. A “pressurebased” numerical method is used with an algorithm of coupling between the pressure and velocity named “coupled”, for which the equations of continuity and momentum are solved simultaneously, and then the other ones of the model are solved separately. The boundary conditions employed to solve the problem are also presented in Fig. 1. The addition of energy to the flow in a region of the computational domain is modeled through a user-defined function (UDF), which is an available tool of the solver. The steady-state solution for the problem is sought since only steady energy depositions in the flow are considered (FLUENT INC., 2006). The supersonic free stream flows from left to right with a static pressure of p∞ = 1,0x105 Pa and a temperature of T∞ = 300K. While it is intended to use the results of this work for better understanding the effects of energy addition on supersonic airflow, they have been also used to study the effects of energy addition on blunt body wave drag reduction. This fact justifies some of the variables used herein, like the heat source dimensions, which have the same magnitude (millimeters) of those used in shock tunnels, and also of the heat power presented in the following sections, which have been used in recent works at the IEAv.

RESULTS AND DISCUSSION This section presents the results concerning the modification of a uniform flow due to the presence of an energy source confined to a small flow region in order to understand how the source affects the flow properties. General characteristics of the flow with localized steady energy addition In order to identify the key changes of the properties of a uniform flow caused by the addition of energy to a small

171

region in space, the physical domain shown in Fig. 1 is used to perform numerical calculations. It is considered that energy is steadily deposited uniformly in a small cylindrical region (length l0 = 1.0 mm and radius r0 = 0.5 mm), which is centered at the origin of the reference axes, with total power of 471 W, in a uniform Mach 4 free stream flow. The square grid used in all calculations is 20 cells/mm, which has yielded good accuracy results. The data used to validate this grid will be presented in this section after some basic effects of energy addition to the airflow have been discussed. The results corresponding to the scalar fields of the flow properties, such as pressure (p), temperature (T), density (ρ), as well as the flow movement quantities such as Mach number (M), axial (Vx) and radial velocities (Vy) are presented in Fig. 2. Figure 3 presents the outcomes for the flow variables along the symmetry axis (lower boundary in Fig. 1) and in a cross-sectional plane downstream to the heat source perpendicular to the free stream flow direction (right-hand boundary in Fig. 1). As can be seen in the scalar fields of Fig. 2 and in the plots of Fig. 3, inside the heat source the flow is heated up with the effect of compressing the flow and diverting some part obliquely with respect to the symmetry axis. The localized energy deposition in the flow generates compression waves that propagate radially with the local sound speed and axially with the flow one. Inside the heat source, the flow density increases only slightly while the Mach number is reduced mainly because of the increase in temperature. The results in Fig. 3 show that there are two distinct flow regions around the symmetry axis downstream to the source: one just behind it, of about six source radius length, where all flow properties change considerably while the flow expands (pressure and density are reduced) and accelerates accompanied by a certain reduction in the temperature; and the other region following the first one, where flow properties are basically constants along the source axis, i.e. the pressure returns to the free stream value while the other flow variables reach values that are different from the free stream ones, even for distances far downstream from the source. Actually, this latter region, as can be observed in Figs. 2 and 3b, is characterized by a long constant property stream tube, aligned to the symmetry axis, of about the same source radius. Also, the wave fronts propagate radially in both regions, but only in the second one the flow between the constant property stream tube and the wave fronts is very close to the free stream one. As can be noticed, in the constant

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8 4 0

-8

-4

12 16 x/r0

-8

-4

8 4 -8

-4

(e)

-8

12 16 x/r0

12 8

(d)

-4

Vy(m/s) 160 131 102 73 42 14 -15

4 4

4.00 3.75 3.50 3.25 3.00 2.75 2.50

y/r0

12 16 x/r0

Vx(m/s) 1460 1431 1402 1373 1343 1314 1285

16 y/r0

-8

4 0

(c)

1.49 1.32 1.14 0.97 0.80 0.62 0.45

782 710 639 567 495 423 352 280

ρ (kg/m3)

16 y/r0

y/r0

(b)

T (K)

y/r0

(a)

p (Pa) 2.5x10+05 2.2x10+05 1.9x10+05 1.7x10+05 1.4x10+05 8.0x10+05

-8

-4

12 16 x/r0 (f)

12 16 x/r0

Figure 2. Scalar fields for a Mach 4 free stream and a 471 W heat source, of: (a) pressure; (b) temperature; (c) density; (d) Mach; (e) axial velocity; and (f) radial velocity.

property stream tube, the temperature has doubled whereas the Mach number and density have reduced about 30 and 50%, respectively, of their free stream values. However, it should be noted that the laminar model used in this work does not take into account diffusion and convection effects in flows far from walls, therefore it behaves as an inviscid one that justifies the later results. On the other hand, in real life flows are always at least somewhat turbulent, thus it is expected that the influence of the source on the flow — in terms of the distance from the source that all flow properties return to their free stream values — is smaller than for laminar ones. The results shown in this work were obtained with a square grid of 20 cells/mm (each millimeter along the source

axis or the direction perpendicular to it is divided into 20 parts), which can be validated through comparison with others of different resolutions. Figure 4 presents some flow variables (pressure, temperature, Mach number, and density) along the source symmetry axis when the resolution of the square grid is modified. Even with the 10 cells/mm mesh, it is already possible to capture the main effects discussed herein, and it is also clear that the use of more refined meshes provides more accurate results. Therefore, it was chosen the 20 cells/mm mesh, instead of the higher resolution one, because this yields enough accurate results, for the present purpose, without being so computationally costly.

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A Numerical Investigation of Localized and Steady Energy Addition to High Speed Airflows

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Figure 3. Normalized flow properties for a Mach 4 free stream and a 471 W heat source, along the (a) lower (symmetry axis) and (b) right-hand boundaries of the domain in Fig. 1.

In order to show that the boundary condition of free stream near the energy source is not affecting the results, it is possible to analyze the airflow when the distance between the source center and the left pressure far field boundary shown in Fig. 1 is increased. Figure 5 presents the pressure distribution along the symmetry axis for a Mach 4 free stream and a 471 W heat source when it is centered in the same position of all results of this paper, x/r0 = 0, and when it is centered 12 units of r0 away from its original position. When the pressure distribution for x/r0 = 12 is graphically shifted 12 units to the left along the x/r0 axis (Fig. 5b), both distributions are approximately coincident, which indicates that the far field boundary condition is not affecting the solution. The same analysis was performed for other flow properties (temperature, density, and Mach number) and they showed the same behavior presented in Fig. 5.

In the next sections, the effects of energy deposition rate and dispersion as well as the free stream velocity in supersonic flows are analyzed based on the fluid behavior nearby, inside the source and also in both regions downstream to the source mentioned before, which actually are of more interest for practical applications.

Effects of energy deposition rate (heat source power) When the effects of energy addition to high speed flows are analyzed, it is also of interest to study how the rate of energy deposition changes the flow properties. Figure 6 presents results of the flow properties along the symmetry axis whereas Fig. 7 shows results in a downstream perpendicular plane to the symmetry axis for three different values of energy deposition rate (heat source power).

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Fraile Jr, A.C. and Rosa, M.A.P.

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Figure 5. Pressure along the symmetry axis (Mach 4 free stream and 471 W) for different source center positions: (a) original distributions; (b) distribution when source center in x/r0=12 is shifted 12 units of x/r0 to the left. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.169-180, Apr.-Jun., 2013

A Numerical Investigation of Localized and Steady Energy Addition to High Speed Airflows

(a)

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It is observed in Fig. 6 that the higher the heat source power the more pronounced the effects on the flow properties, as previously discussed. In other words, increasing the source power, the pressure, temperature, and density also increase inside the heat source, making the flow compression higher and consequently diverting more flow obliquely to the symmetry axis. Furthermore, by increasing the source power, the expansion of the flow is more pronounced (higher variable changes) in the region immediately downstream to the source, although its length is not much affected by the source power for the same free stream velocity. Considering the effects on the flow for distances beyond the downstream expanding region, that is, where the pressure along the symmetry axis has already basically returned to its free stream value, it can be inferred from Figs. 6 and 7 that by increasing the power the axial length

of the first region behind the source, where the flow properties are still changing, is not much affected (Fig. 6). The changes in temperature, Mach number and density get more pronounced inside the flow stream tube (Figs. 6 and 7), the radius of the stream tube gets only slightly bigger (Fig. 7), and the wave fronts get stronger and slightly faster (Figs. 7a and d). Effect of free stream flow speed Another aspect to be considered in this study is the effect of the free stream flow speed on the flow properties with localized steady energy addition to the flow. Figures 8 and 9 show their results along, respectively, the symmetry axis and the right-hand boundary in Fig. 1, corresponding to three values for M∞ (for the same free stream sound speed) and 471 W power added to the flow.

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1.30

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Figure 7. Change of flow properties (M∞= 4.0) along the cross section plane at the right-hand boundary as a function of power: (a) p/p∞; (b) T/T∞ ; (c) M/M∞; (d) ρ/ρ∞.

The results in Fig. 8 confirm the trend already observed that the most significant variations of the flow properties occur basically inside the heat source and in a small distance downstream from it. Also, in Fig. 8, it can be seen that the expansion region is elongated for higher Mach numbers, due to the increase in the flow speed, which corresponds to the transport of changes in flow property to greater distances from the source before reaching almost constant values. When the free stream Mach number is higher, due to an increase in the free stream speed, the fluid residence time inside the heat source decreases and so does the rate of temperature change inside the source (lower peak) resulting in smaller alterations to the other flow properties not only inside the source but also downstream of it. For instance (Fig. 8), the Mach number and density reductions

in the flow stream tube for M∞=7 are about 10% smaller than for M∞=4. Therefore, the higher the free stream velocity the higher should be the rate of energy addition to the flow to keep its property percent changes in the stream tube. Still, as observed in Fig. 9, the stream tube radius is basically not affected by the free stream velocity. However, as shown in Figs. 9a and c, the wave fronts reach the right-hand boundary in Fig. 1 at lower coordinates for higher free stream Mach numbers. This happens mainly because of the higher free stream flow velocity, since the local sound speed is basically the same for all cases. As a consequence, the diverted flow angle is smaller for higher free stream flow velocity. It is also interesting to mention that the strength of the wave fronts is not very affected by the free stream velocity, as can be seen in Fig. 9a.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.169-180, Apr.-Jun., 2013

A Numerical Investigation of Localized and Steady Energy Addition to High Speed Airflows

3.0

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0.3

-4

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Figure 8. Flow properties (471 W heat source) along the symmetry axis as a function of free stream flow velocity: (a) p/p∞; (b) T/T∞ ; (c) M/M∞ ; (d) ρ/ρ∞.

Effects of energy deposition dispersion (heat source size) This section presents the overall results of a study about the effects of the energy deposition dispersion on a supersonic flow. This will be treated here by considering different heat source sizes, that is, by varying the radius (r) and length (l) of the cylindrical source, taking as reference the heat source used in the previous sections (l0=1.0 mm and r0=0.5 mm; 471 W total power). For the sake of clarity, the cylindrical source size (length and radius) will be written in the normalized form (l/l0×r/r0). Four different cases have been considered: the reference source (1×1); the double length (2×1); the double radius (1×2); and the double length and radius (2×2). In terms of the source volumetric heat rate, considering that the reference source is q0, then the others are q0/2, q0/4 and q0/8, respectively.

Figures 10 and 11 show the flow property results along, respectively, the symmetry axis and the right-hand boundary in Fig. 1, corresponding to the four cases mentioned for a Mach 4 free stream and 471 W source total power. As can be observed in these figures, the source length has very little effect on the main aspects of the flow behavior, although it seems that as the volumetric heat rate gets higher (reducing source radius), the source length begins to show some influence on the flow. On the other hand, the source radius has major effects on the flow behavior, for example, decreasing the source radius: the compression inside the source increases; the expanding region behind the source gets shorter but still about six times the source radius; the differences between the constant flow properties inside the flow stream tube and their respective free stream ones get even bigger; the

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1.15

2.2

(a)

1.10

T/T∞

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1.00

M∞= 4.0 M∞= 5.5 M∞= 7.0

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1.05

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1.2

y/r0

(d)

1.1 1.0

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ρ/ρ∞

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1.6 1.2

(c)

1.00

0.85 0.75 0

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0.9 0.8 0.7

M∞= 4.0 M∞= 5.5 M∞= 7.0

0.80 0.70

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1.8

1.05

0.90

(b)

2.0

M∞= 4.0 M∞= 5.5 M∞= 7.0

0.6 0.5 14

0.4

y/r0

Figure 9. Flow properties (471 W heat source) along the cross-sectional plane at the right-hand boundary in Fig. 1 as a function of free stream flow velocity: (a) p/p∞ ; (b) T/T∞ ; (c) M/M∞ ; (d) ρ/ρ∞ .

flow stream tube radius is still about the source radius; and the wave fronts gain in strength but with unchangeable wave speed. In conclusion, energy deposition dispersion in the flow direction (x-direction) has little effect on the flow, except for small radial dispersion whereas dispersion in the radial direction (y-direction) has major impact on the flow.

COMMENTS AND CONCLUSIONS This work has shown the effects on the flow structure of a localized and steady energy addition to uniform supersonic airflows, based only on thermodynamics and gas dynamics standpoints. The knowledge obtained here about the highspeed flow changes due to localized energy addition certainly

will be of great importance for the subsequent studies related to the applications of energetics in hypersonics at the IEAv. The results presented here show that a localized energy source in a uniform high-speed airflow can modify its path lines at oblique angles, generating compression wave fronts whose strength increases with the rate of energy deposition and also with the reduction in radial dispersion. Free stream velocity as well as axial dispersion has shown little effect on the wave front strength, although the oblique wave angle gets smaller for higher free stream speeds. The results have shown that the flow downstream to the heat source may be separated into two distinct regions: one just behind it, which is characterized by considerable flow property variations; and the other, that follows the first one, where the flow properties are basically constants but different from those of the free stream one, with the exception of the pressure that returns to its original value.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.169-180, Apr.-Jun., 2013

A Numerical Investigation of Localized and Steady Energy Addition to High Speed Airflows

3.0

(a)

2.5

2.0

1.5

1.2

0.5 -4

0.8 -4

1.1

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16 x/r0

(d)

1x1 2x1 1x2 2x2

0.9 0.8 0.7 0.6

0.7

0.5

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1x1 2x1 1x2 2x2

(c)

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1.0

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M/M∞

2.8

1x1 2x1 1x2 2x2

179

0.4 -4

12 16 x/r0

0.3

-4

16 x/r0

Figure 10. Flow properties (M∞ = 4,0) along the symmetry axis of the energy source as a function of source geometry: (a) p/p∞ ; (b) T/T∞ ; (c) M/M∞ ; (d) ρ/ρ∞ .

Actually, this latter region is characterized by a long constant flow property stream tube aligned to the symmetry axis, of about the same source radius, with lower density and Mach number and higher temperature than their respective free stream values. Between these two regions and the wave fronts, the flow remains very close to the free stream one. The outcomes have also shown that either increasing energy deposition rate, or reducing free stream speed as well as decreasing radial dispersion, has the effect of increasing the changes in the flow properties inside the source and in both mentioned regions around the symmetry axis. In contrast, axial dispersion has presented little effect on the flow, mainly when the radial dispersion is comparable or higher than the axial one. Another important parameter is the first region length, which increases substantially by increasing the

free stream speed or source radius. Another interesting result is that for a fixed free stream speed, the length of this region is always given by a fixed number of source radius, for instance, for a Mach 4 free stream, this region length is approximately six times the source radius. Also, it is important to mention that the constant property stream tube radius has always approximately the source radius and is not much affected by source power, free stream speed, or axial dispersion. It could be observed that the source radius (radial dispersion) has a major effect on the flow properties, whereas its length (axial dispersion) has a negligible one. Therefore, highly focused energy deposition, mainly in the radial direction, will always need less energy deposition rate. As the free stream speed increases, higher energy addition rate, or lower radial dispersion, is required to achieve about the same relative flow changes.

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1.15 1.10

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1x1 2x1 1x2 2x2

y/r0

0.8 0.7

1x1 2x1 1x2 2x2

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0.4

y/r0

Figure 11. Flow properties (M∞ = 4,0) in a cross-sectional plane at the right-hand boundary in Fig. 1 as a function of source geometry: (a) p/p∞ ; (b) T/T∞ ; (c) M/M∞ ; (d) ρ/ρ∞.

REFERENCES FLUENT INC., 2006, “FLUENT 6.3 User’s Guide”, Retrieved in May 03, 2013, from http://cdlab2.fluid.tuwien.ac.at/LEHRE/TURB/ Fluent.Inc/fluent6.3.26/help/html/ug/main_pre.htm Fraile Jr., A.C., 2011, “Um estudo numérico da redução de arrasto em corpos rombudos por adição de energia em escoamentos de altas velocidades” (In Portuguese), Thesis, Instituto Tecnológico de Aeronáutica, 128 p. Knight, D., 2003, “Survey of Aerodynamic Flow Control at High Speed by Energy Deposition”, 41st AIAA Aerospace Sciences Meeting and Exhibit, 19 p. Minucci, M.A.S. et al., 2005, “Laser-supported directed-energy ‘airspike’ in hypersonic flow”, Journal of Spacecraft and Rockets, Vol. 42, No. 1, pp. 51-57. Oliveira, A.C. et al., 2008a, “Bow shock wave mitigation by laserplasma energy addition in hypersonic flow”, Journal of Spacecraft and Rockets, Vol. 45, No. 5, pp. 921-927. Oliveira, A.C. et al., 2008b, “Drag Reduction by Laser-Plasma Energy Addition in Hypersonic Flow”, Fifth International Symposium on Beamed Energy Propulsion, Vol. 997, pp. 379-389. Oliveira, A.C., 2008c, “Investigação experimental da adição de

energia por laser em escoamento hipersônico de baixa densidade” (In Portuguese), Thesis, Instituto Nacional de Pesquisas Espaciais, 202 p. Riggins, D.W. et al., 1999, “Blunt-body wave drag reduction using focused energy deposition”, AIAA Journal, Vol. 37, No. 4, pp. 460-467. Riggins, D.W., Nelson, H.F., 1999, “Hypersonic flow control using upstream focused energy deposition”, Aerospace Sciences Meeting & Exhibit, 37, Reno. Salvador, I.I. et al., 2005, “Experimental Analysis of Heat Flux to a Blunt Body in Hypersonic Flow with Upstream Laser Energy Deposition Preliminary Results”, 4th International Symposium on Beamed Energy Propulsion, Vol. 830, pp. 163-171. Salvador, I.I. et al., 2007, “Surface Heat Flux and Pressure Distribution on a Hypersonic Blunt Body with DEAS”, Fifth International Symposium on Beamed Energy Propulsion, Vol. 997, pp. 367-37. Salvador, I.I. et al., 2008, “Experimental Analysis of Heat Flux to a Blunt Body in Hypersonic Flow with Upstream Laser Energy Deposition”, Fifth International Symposium on Beamed Energy Propulsion, Vol. 997, pp. 379-389. Tannehill, J.C. et al., 1997, “Computational fluid mechanics and heat transfer”, Taylor and Francis, London, England, 792 p.

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doi: 10.5028/jatm.v5i2.245

Large Eddy Simulation of Bluff Body Stabilized Turbulent Premixed Flame Nicolas Moisés Cruz Salvador1, Márcio Teixeira de Mendonça2, Wladimyr Mattos da Costa Dourado2

Abstract: A turbulent reacting flow in a channel with an obstacle was simulated computationally with large eddy simulation turbulence modeling and the Xi turbulent combustion model for premixed flame. The numerical model was implemented in the open source software OpenFoam. Both inert flow and reactive flow simulations were performed. In the inert flow, comparisons with velocity profile and recirculation vortex zone were performed as well as an analysis of the energy spectrum obtained numerically. The simulation with reacting flow considered a pre-mixture of propane (C3H8) and air such that the equivalence ratio was equal to 0.65, with a theoretical adiabatic flame temperature of 1,800 K. The computational results were compared to experimental ones available in the literature. The equivalence ratio, inlet flow velocity, pressure, flame-holder shape and size, fuel type and turbulence intensity were taken from an experimental set up. The results shown in the present simulations are in good agreement with the experimental data. Keywords: Computational fluid dynamics, Reacting flow, Large eddy simulation, Combustion modeling.

INTRODUCTION In turbulent reactive flow simulations, computational models have achieved a great development in recent years with the improvement of computer power. This development allowed more accurate solution of problems such as the instability caused by the turbulence in combustion chambers of rocket engines, gas turbines, turbojet afterburners, ramjets and scramjets. These models have been used to study bluff body stabilized flames, which allow combustion devices to operate at very high free stream velocities. Advanced afterburner design methods have been discussed by Lovett et al. (2004), who outlined the fundamental combustion sciences and engineering challenges that need to be addressed. Among other problems, Lovett et al. (2004) highlighted the requirements for flame stabilization and combustion dynamics. These authors discuss the need for advanced design methodologies and tools, and they stress the limitations of existing computational models to capture the physics of those phenomena. In turbulent combustion, the behavior of the turbulent flame front is predominantly dictated by the turbulence (Peters, 2000). Combustion instability is also directly related to turbulence (Weller, Marooney and Gosman, 1990). Therefore, it becomes mandatory in numerical simulations to use turbulence models that reproduce these dynamic processes, which are mainly produced by large scale turbulence. Many researchers have used Reynolds Averaged Navier Stokes (RANS) and eddy viscosity turbulence models to simulate reactive flows behind bluff bodies. However, important discrepancies were observed due to shortcomings in the RANS methodology, especially in complex flows with circular obstacle (Saghafian et al.,

1.Instituto Nacional de Pesquisas Espaciais – São José dos Campos/SP – Brazil 2.Instituto de Aeronáutica e Espaço – São José dos Campos/SP – Brazil Author for correspondence: Marcio Teixeira de Mendonça | Instituto de Aeronáutica e Espaço | Praça Marechal Eduardo Gomes, 50 – Vila das Acácias | CEP 12.228-904 São José dos Campos/SP – Brazil | E-mail: marciomtm@iae.cta.br Received: 22/06/12 | Accepted: 13/12/12

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Salvador N.M.C., Mendonça M.T. and Dourado W.M.C.

2003; Frendi, Skarath and Tosh, 2004) and triangular one (Bai and Fuchs, 1994; Dourado, 2003; Eriksson, 2007). Significant differences in results were found for the turbulent velocity, integral length scale and turbulent viscosity distribution between RANS models. These differences affect the computation of flame front diffusion, which is underpredicted. The Kelvin-Helmholtz effects behind the obstacle are not captured well and the length of the recirculation zone as well as the turbulent flame speed are not recovered. Experimental studies were conducted by Sjunesson, Henriksson and Lofstrom (1992) and Sjunnesson, Olovsson and Sjoblom (1991) at Volvo (Sweden). The Volvo test rig had an equilateral triangular bluff body with a blockage of 33% and a Reynolds number (Re) based on the inlet velocity and two times the channel height of 204,000. For this Re, the Strouhal number (St) observed was 0.417. The premixed gases were air and propane at equivalence ratios of 0.65 and 0.85. The Damköhler number (Da) was 10 and the Karlovitz number (Ka) was 4. The resulting flame for these conditions was on the thickened-wrinkled flame regime of the Borghi diagram rather than in the wrinkled flame regime. Sanquer (1998) also presented experimental results for premixed flame stabilized by a triangular prismatic bluff body at the University of Poitier (France). The blockage in his experiments was also 33% for a Re in the range of 6,690 to 23,150, much lower than the Re on the Volvo experiments. The St for the lower Re experiment was 0.276. Therefore, the vortex shedding characteristics and the turbulent scales (integral and Kolmogorov) were significantly different from the Volvo experiment. Sanquer’s results will be discussed and compared to the present numerical simulations on the following sections. Specifically, the present simulations correspond to Sanquer’s experiment that falls on the Borghi diagram where Da<1 and Ka>1 corresponding to the thin-wrinkled flame region. These and other experimental results (Cheng, 1984, Cheng, Shepherd and Gokalp, 1989, Cheng and Shepherd, 1991, Kiel et al., 2007, Chaudhuri et al., 2011) describe the interaction between the turbulent structures and the flame. Numerical simulations of turbulent combustion must rely on models that are able to capture the complex turbulent vortical structures and this explains why results obtained with RANS models are less accurate. In order to improve numerical simulations, turbulent combustion models can be ported from RANS models to Large Eddy Simulation (LES) models, which are known to capture the large scale turbulent structures. This approach does not always result in more accurate

simulations. It is necessary to identify those models that have the best results and show greater potential for future improvements when used in LES. A number of investigators have used LES to simulate reactive flows with bluff body flame holders. Porumbel and Menon (2006), Akula, Sadiki, and Janicka (2006), Ge et al. (2007), Park and Ko (2011) and Manickam et al. (2012) simulated the Volvo experiment (Sjunnesson, Olovsson and Sjoblom, 1991). Porumbel and Menon (2006) have simulated bluff body flows with the Linear Eddy Mixing (LEM) LES based on the model proposed by Kerstein (1989) and developed into a sub-grid model by Menon et al. (1993) for premixed combustion. They discussed the differences between their model and the Eddy Breakup model (LES-EBU) and which of the two is best to represent the physics of the reacting flow behind an obstacle besides the ability to resolve the turbulent eddies that wrinkle the flame front. This model is specially adequate for high turbulent intensities where the chemical time is considered infinitely small, corresponding to a Da much greater than 1. Their conclusions were confirmed by experimental results presented by Chaudhuri et al. (2011). Akula, Sadiki, and Janicka (2006) also performed LES simulations with a flame surface density formulation adapted from Boger and Veynante (2000). This model includes the resolved progress variable in the transport equations and the flame wrinkling model avoids unrealistic detachment of the flame from the flame holder. The compressible model presented by Tabor and Weller (2004), along with a similar progress variable approach, is also able to capture the flame wrinkling and thus capture the physics as proposed by Porumbel and Menon (2006). The model of Tabor and Weller (2004) is used in the present simulations. Park and Ko (2011) used a dynamic sub-grid scale combustion model based on the G-equation that describes the flame front propagation (Peters, 2000). The G-equation is a model for the chemical species conservation equations. In this model, a new LES dynamic sub-grid combustion model is introduced along with a new turbulent flame speed model based on the sub-grid turbulent diffusivity. These models are intended to better represent the flame characteristics. Park and Ko (2011) present comparisons between non-reacting and reacting flows and discuss the effect of chemical reaction on the development of the wake behind the triangular bluff body. They show that their model is able to capture the stabilization of the Karman vortex street

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.181-196, Apr.-Jun., 2013

Large Eddy Simulation of Bluff Body Stabilized Turbulent Premixed Flame

behind the obstacle due to combustion. The results for the dynamic model show better agreement with experimental results when compared with the Smagorinsky model. The unsteady flow field was captured with good accuracy and the temperature and reaction rate profiles are well capture by both models, showing that the two combustion models tested are reasonable for the simulation of pre-mixed combustion behind a bluff body. Manickam et al. (2012) used an algebraic flame surface wrinkling (AFSW) reaction model based on the progress variable approach. Inert and reacting cases were analysed and compared with experimental results and with another well validated turbulent flame speed closure model denominated Turbulent Flame Speed Closure (TFC) (Zimont and Lipatnikov, 1995). For the non-reacting test case, they found a shedding frequency equal to 122Hz, while the experimental measured frequency was 110Hz. The comparisons for the mean flow variables and root mean square axial and normal velocity components were in good agreement with the experiments. In spite the fact that the recirculation zone length was well captured, the rms velocity distributions were underpredicted in this zone. Manickam et al. (2012) presented a detailed discussion on the influence of grid refinement and three subgrid scale models on the results and concluded that a coarse grid is too dissipative. Contrary to what might be expected, the grid refinement has a weak influence on the computation of the St, showing that at least the large scale structures were captured by a course grid LES simulation. The St dependence on the grid was also not observed for the reactive case, independently of the reaction model. The three sub-grid scale models tested were the Smagorinsky (SM), the dynamic Smagorinsky (DS) and the sub-grid scale kinetic energy (KSGS). They showed that the performances of the three different models are more or less equivalent. Flame Surface Density (FSD) models rely on geometric parameters of the flame front to evaluate its progress. In this case, the laminar flamelet model used in RANS has been adapted to LES by considering a locally laminar flame wrinkled by turbulence. The amount of wrinkling (Σ) is measured by the flame surface area per unit volume (Boger and Veynante, 2000). Transport equations for the progress variable and for the wrinkling variable are solved to describe the evolution of the flame since the wrinkling increases the burning rate. Similar to the Σ variable, Weller (1993) proposed a model based on the density of wrinkling (Ξ), which is the flame

183

area per unit area resolved in the mean direction of propagation. Weller (1993) originally developed this model for RANS and later Tabor and Weller (2004) adapted the model for LES. The advantage of using Ξ is that it should be easier to model the transport terms as discussed in Weller (1993), Weller et al. (1998) and Tabor and Weller (2004). This model is used in the present study and will be discussed in detail on the following sections. In the present study, the SM and dynamic sub-grid models for turbulence were used. For the combustion model, the flame surface wrinkling (Ξ) formulation, developed by Tabor and Weller (2004), was used. The objective of the study was to investigate the performance of a turbulent combustion model when applied to the simulation of pre-mixed turbulent flames behind a triangular obstacle. The review of the literature shows that such type of performance investigation has been conducted previously, with results compared to the Volvo experiment, which has a Da in the range of 10 and a Ka of 4, corresponding to a thickened, wrinkle flame. The present investigation considered an experiment which has a Da of 4.5 and a Ka of 1.3; on the range of thin, wrinkled flame, previous investigations found in the open literature did not consider LES simulations in this combustion regime, and the thinner flame thickness poses a more severe test for the turbulent combustion model. The Re for the simulation was 6,690, lower than the Re on the Volvo experiment, which was 204,000 and thus have a significant different flow dynamics. The chosen reactive LES model was evaluated by comparing results with experimental ones obtained by Sanquer (1998), which have not been analyzed before with other LES numerical models.

PROBLEM FORMULATION In order to account for turbulence and combustion, the reactive flow governing equations are filtered using the LES concept, and the combustion process is accounted for by following the flame front. Therefore, it is necessary to define the filtering and a variable to account for the regions of burned and unburned gases. In this section, the formulation derived by Weller (1993) and Tabor and Weller (2004) is presented. Preliminary definitions In premixed flames, a reaction wave propagates from the burned to fresh gases. The progress variable c, that identifies

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Salvador N.M.C., Mendonça M.T. and Dourado W.M.C.

this propagation, varies between 0 for fresh gas and 1 for burned gas. The transitions between these values describe the flame front. A progress variable c can be defined based on the normalized temperature (T) or on the reactant mass fraction (Y). Using the temperature, it results in:

T − Tu Tb − Tu

(1)

Where b subscript stands for burned gas and u subscript, for fresh unburned gas. The flame front propagation is modelled by solving a transport equation for the density-weighted mean reaction regress variable denoted by b, where b = 1 - c.

ψ = bψu ,

(6)

where b (x, t) is the probability of the point (x, t) being in the unburned gas. b = ∫ G ( x − x ʹ )l( x ʹ ,t)d 3 x ʹ .

(7)

In compressible flow, there is density (ρ) variation, and . b ρψ be written: the product ρψ =can

ρψ = b ρψ . .

(8)

Where the subscript u indicates the unburned gases. In LES, it is assumed that the dependent variables can be divided into grid scale (GS) and sub-grid scale (SGS) components, such that, for any given dependent variable, it results in:

ψ = ψ +ψ ʹ

ρψu = ρψ~u Defining a density-weight average phase, we can obtain: ρψ = ρψ~ . u

ρψ = b ρψ~u

ψ = G * ψ ∫ G ( x' , Δ)ψ( x' ,t)d 3 x'

(9)

From Eq. 8 in Eq. 9, results in:

(2)

Where

.in the unburned

(10)

(3)

Introducing a conditional filter (Tabor and Weller, 2004), with an indicator function l, results in:

Filtered continuity equation The governing equations will be written in a coordinate system placed at the flame surface, such that n⊥ and n|| are the unity vectors pointing the normal x⊥ and parallel x|| directions to the flame surface. The metrics of this coordinate system are h⊥ and h|| . This coordinate system is used in order to include the conditional filter based on the progress variable b. The filtered continuity equation reads (Tabor and Weller, 2004):

⎧1 if ( x , t) l ( x , t) = ⎨ ⎩0

  ∂ρ + ∇ ⋅ ρU = ρ (U − U I ) ⋅ n⊥ Σ. . ∂t

Here, D is the computational domain with boundaries ∂D, t is the time and x, the coordinate directions. The kernel G=G(x, ∆) is any function of x and of the filter width ∆. G has the properties ∫D G(x)d3x=1, lim∆→0 G(x,∆)=δ(x)

(4)

(11)

is in the unburned gas region otherwise. For a tensor ψ of any rank, one may define ψ =the ʹ, tI )= ψU G * phase(lψ ) = ∫ G ( xWhere − x ʹ)l ( xU ( x ʹ+, tv)adn3⊥x,ʹUI . is the full velocity on an interface D UI = U +and va n⊥the , UI weighted value of ψ at any point. consisting of the movement due to advection term U + va n⊥ ., UI advance of the interface relative to U the I = flow

ψ = G * (lψ ) = ∫ G ( x − x ʹ)l ( x ʹ, t)ψ ( x ʹ, t)d 3 x ʹ

In the transformed coordinates for ( x⊥ , x|| ):

(5)

Introducing the combustion progress variable b as a GS indicator function, we can obtain:

Σ = G ⊥ ( x⊥ − x⊥ , I )∫∫ G||( x|| − x||ʹ ) | ℑ | d 2 x|| .

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(12)

Large Eddy Simulation of Bluff Body Stabilized Turbulent Premixed Flame

2 x||ʹ Where | ℑ | drepresents the Jacobian of the transformation. 2 | ℑ | d x||ʹ is the area element on the surface interface. Σ

is interpreted as the amount of interface for the filtered component, the flame surface density.

185

The final continuity equation reads:

~ ~ ~ ∂ρ b + ∇ ⋅ (b ρ U u ) = − ρ u S u Ξ | ∇b | ∂t

(20)

where Su is the laminar flame speed. ⎧ ⎨ ⎩

The surface filtering operation

is defined as:



1 1 ψ = ∫ G ( x − x ʹ)ψ ( x ʹ)δ (( x ʹ − x ) ⋅ n⊥ ) d 3 x ʹ . . ΣD h⊥

(13)

Filtered momentum and energy equations Conditionally filtering the momentum equation gives: ~ ∂b ρ u U u ~ ~ +∇⋅(b ρ uUu ⊗ U u ) = −∇b p u ∂t

From Eq. 10 in Eq. 11, results in:

 ∂bρ u ~ + ∇ ⋅ bρ uU u = − ρ v a Σ. . (14) ∂t This surface filtering operation applied to n⊥ results in:  1 n⊥ = G⊥ ( x⊥ − x⊥ , I ) ∫∫ G|| ( x|| − x '|| ) n⊥ ( x⊥ , I | , x '|| ) | ℑ | d 2 x||ʹ .. (15) Σ  1 . n⊥ =can Gbe x⊥ − x⊥ , Ito ) ∫∫the G|| ( GS x|| − with x '|| ) n⊥the ( x⊥ ,nI | , xdirection ' ) | ℑ | d 2 xof||ʹ the ⊥ ( related f || Σ

(21) ⎡    ⎤ ⎢ ⎥ +∇ ⋅ b(S u − B u )}+ ( pI − S) ⋅ n⊥ − ( ρva U ) Σ .. ⎢ ⎥ ⎣ ⎦

{

Where p is the pressure, Su is the laminar flame speed, Σ is the flame surface density, S = λ∇ ⋅ UI + 2 μ is the stress 1 tensor and = (∇U + ∇U T ) is the symmetric part of the 2 strain tensor. The terms in brackets represent the effect of the interface on the momentum balance.

interface:  nf n⊥ = Ξ

. (16)

Where Ξ represents the total sub-grid surface area by the smoothed surface area in the n f direction: Ξ=

Σ 1 = . .  | G⊥ ( x⊥ − x⊥,I ) G|| ( x|| − x'|| )n⊥ ( x⊥,I , x'|| ) | ℑ | d 2 x||ʹ | ∫∫ n⊥

(17) Or: Ξ=

Σ | ∇b | Ξ=

Where

.. (18)

Σ . | ∇b | represents

Bu represents the SGS stress tensor. ~ ~ B u = (ρU ⊗ U )u − ρuU u ⊗ U u

. .

(22)

This term requires modeling. The filtered energy equation is: ∂ (bρ u e~u ) ~ + ∇ ⋅ (b ρ u e~uU u ) = ∂t ~ − (bρ u ∇ ⋅ U u + bρ uπ u ) + (bS u ⋅ Du + bρ uε u ) (23) ⎡   ⎤ + ∇ ⋅ b(h u − bu ) + ⎢( ρe v a ) − h ⋅ n⊥ ⎥ Σ . ⎢ ⎥ ⎣ ⎦

the area of the GS surface. Where

Combining the burned and unburned gases into the weighted total density results in:

ρ = ρ u b + ρ c (1 − b)

. .

~ Such that ρ b = ρ u b .

(19)

~ ρ uπ u = ( p∇ ⋅ U )u + p u ∇ ⋅U u , ,

(24)

and

ρ uε u = ( S ⋅ D)u + S u Du , ,

(25)

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Salvador N.M.C., Mendonça M.T. and Dourado W.M.C.

⋅ D)u + S u Du , represent the SGS pressure dilatation π and dissipationρ uε u = ( Swhere (Tabor and Weller, 2004). The total energy at the interface is C ρ k 3/2 , ε= e (31) presented in brackets. Δ

Turbulence model In the present study, three turbulence models available in OpenFoam were used. These turbulence models are described by Fureby et al. (1997). First, the Smagorinsky classical model is presented:

τ ij −

δ ij 3

⎛ ∂u~i

τ kk = −υt ρ ⎜⎜

⎝ ∂x j

~ δ ~ = −2 ρ υ sgs ( S ij − ij S kk ) 3

∂u~j

2 ∂u~ ⎞ − δ ij k ⎟ ∂xi 3 ∂xk ⎟⎠

(26)

and

2 kI − 2v k dev(D) 3

(32)

The third turbulence model is the dynamic one-equation model that used the Germano identity, following Ghosal et al. 1995, considering a scaling law and homogeneous flow. The kinetic energy equation is: ∂k ∂ρ u~i k ∂vk ∇k + − = − ρ BL − ε , , (33) ∂t ∂ui ∂ui

~ ~ ~ 1 ⎛ ∂u~ ∂u ⎞ ) 2 S . viscocity and S ij = ⎜ i + j ⎟ C s Δsub-grid Where υ sgs = is (the 2 ⎜⎝ ∂x j ∂xi ⎟⎠ is the strain tensor.

where L is the Germano identity (Ghosal et al., 1995): L = T − B with:

~ υ sgs = (C s Δ ) 2 S . .

L = (u ⊗ u − u ⊗ u ),

(27)

T = (u ⊗ u − u ⊗ u ),

(34)

The constant Cs is equal to 0.18.

B = (u ⊗ u − u ⊗ u ) .

The second turbulence model is the one-equation model ~ 1 1 ~ ~ and . with sub-grid kinetic energy k =proposed ( uYoshizawa ρ τ kk = by k uk − uk uk ) 2 2 Horiuti (1985) and given by:

Subgrid combustion model Models for the SGS stress tensor, flux vectors, dissipation and filtered reaction rates are used to close the governing equations. The models for the SGS stress tensor and flux vectors are the standard ones used in LES, since they do not depend on reacting flow data. A flamelet model with conditional filtering for LES is used to derive the transport equations. This model considers conditions of the Klimov-Williams criterion (Ka=1) in the Borghi diagram (Borghi and Destriau, 1998). Instead of using the flame propagation speed in terms of the laminar flame area per unit volume Σ and the degree of wrinkling of the flame at a point in the domain, the present model (Weller, 1993) uses the flame surface density and a wrinkling surface function Ξ . The function Ξ is the average flame area per unit volume divided by the projected area in the mean direction of propagation. In the flamelet regime, turbulent motions are slow and do not affect the flame structure. The disturbance velocity u´ considers how a rotation speed of the larger turbulent motion wrinkles the flame surface front (Veynante, 2006). In the reaction zone, the characteristic scales for the reaction processes are below the filter, so that, in reacting LES, a proper treatment (modeling)

(

)

~ 1 1 k = ρ τ kk = uk uk − u~k u~k . . 2 2

where the operation above.

stands for

(28)

a~ in the product uk uk

The sub-filter stress is: ⎛~

τ ij = −2 ρC v Δ k ⎜⎜ S ij − ⎝

δ ij ~ ⎞ 2 3

S kk ⎟⎟ + ρkδ ij ⎠ 3

. , (29)

and turbulent viscosity is: vsgs = ρ Ck Δ k

To close the system of equations, the transport equation for the kinetic energy is used. ∂k ∂ρ u~i k ∂vk ∇k + − = − ρD : B − ε ∂t ∂ui ∂ui

. (30)

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Large Eddy Simulation of Bluff Body Stabilized Turbulent Premixed Flame

of the reaction zone is needed. In other words, equations for the geometric variables b and Ξ are needed.

∂Ξ  + Us ⋅ ∇Ξ = GΞ − R(Ξ − 1) + max [(σ s − σ t ),0 ] Ξ , , (39) ∂t

ρu

.. (35)

σs =

~ ∇b

, 1)S uvelocity Ξn f − D of where U uc =is( the−slip minus burned ~ the~unburned b (1 − b ) ~ ~ ρc ~ gas U uc = U u − U c . .

This is similar to the properties of laminar flame for LES:

~ ρ ∇b ~ U uc = ( u − 1)S u Ξn f − D ~ ~ ρc b (1 − b )

, (40)

 T 1 || ∇ U I + ∇ U I || 2

(41)

The models for G and R, which accounts for the interaction between turbulence and flame, are: G=R

(36)

Ξ eq − 1 Ξ eq

(42)

and

where

is the diffusion coefficient of the sub-grid, and n f = ∇b / | ∇b | is the flame normal direction.

From Eq. 20, one arrives at the final equation for b (Tabor and Weller, 2004): ~ ~ ∂ρ b ~~ + ∇ ⋅ ( ρUb ) − ∇ ⋅ ( ρ D ∇b ) = − ρu S u Ξ | ∇b |. ∂t

⎧ ⎨ ⎩

T Sub-grid scale model for b 1 σ = || ∇ U t + ∇ U t || t In Eq. 20, the right hand side needs a SGS model, which 2 ~ ~ ~ ~ is based on the conditional filter of unburned gas velocity U u .= U + (1 − b )U uc . and This term is modeled using:

~ ~ ~ ~ U u = U + (1 − b )U uc

187

∗ 0.28 Ξ eq − 1 τη Ξ eq∗

, , (43)

where Ξ eq∗ = 1 + 0.62

uʹ Re η Su

(44)

, ,

(37) Ξ eq = 1 + 2(1 − b )(Ξ eq∗ − 1).

(45)

Sub-grid scale modeled equation for Ξ uʹ where Re From the transport equation for the sub-grid flame u´ is the intensity of Ξ eq∗area = 1 + 0.62 τη is, the Kolmogorov time, Su uʹ ∗ density Σ , proposed by Weller (1993), an equation for Ξ is turbulence in the Ξ eq sub-grid = 1 + 0.62and Re η , is, the Kolmogorov Su Reynolds number. obtained from the relation Ξ = Σ / | ∇b | and the resolved unburned gas volume fraction b (Tabor and Weller, 2004): Finally, an equation for the laminar flame speed (Tabor and Weller, 2004) is needed. A proposed transport       ∂Ξ  + U ⋅ ∇Ξ = −Ξn⊥ ⋅ ∇U I ⋅ n⊥ + Ξn f ⋅ ∇U t ⋅ n f (38) equation is: ∂t   ∇ | ∇b |     .  + (U∂tΞ− + U IU) ⋅⋅ ∇Ξ = −Ξ Ξn ⋅ ∇ U ⋅ n f ⋅ ∇U t ⋅ n f ⊥ I n⊥ + Ξ       | b | ∇ (S 0 − S u ) ∂S u  ∂Ξ ∂t . . (46) + U s ⋅ ∇S u = −σ s S u + σ s S u∞ 0u + U ⋅ ∇Ξ = −Ξn⊥ ⋅ ∇U I ⋅ n⊥ + Ξn f ⋅ ∇U t ⋅ n f   ∇ | ∇b | ∂t (S u − S u∞ ) ∂t . effective velocity of the flame isU the surface-filtered where(U t − Ξ I )⋅  + b | | ∇b |. ∇ |∇ is the localΞ instantaneous velocity of flame surface. and + (U t − U I )⋅ | ∇b | The convective velocity of the laminar flame0 is the ∂S u  ∞ (S u − S u ) U . + ⋅ ∇ S u =the −σ superscripts The proposed model for Eq. 38 considers wrinkling . And 0 and ∞ filtered surface speed s s Su + σ s Su   ∂t (S u0 − S u∞ ) ∂Ξ ∂Ξ [ ] + U ⋅ ∇ Ξ = GΞ − R (Ξ − 1 ) + max (σ − σ ),0 Ξ , +generation Us ⋅ ∇Ξ = GΞs −and R(Ξremoval − 1) + max [(σ s − σ, t such ),0 ] Ξthat and stand for the value of unstrained flame speed and the value s , (Tabor t ∂t ∂t Weller, 2004): at equilibrium, respectively.

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Salvador N.M.C., Mendonça M.T. and Dourado W.M.C.

The present investigation uses OpenFoam, an open source C++ collection of libraries for transport equations. The model equations are solved numerically based on a cell centered unstructured finite volume scheme. The solution is based on a segregated approach. For time integration, a first order explicit Euler method is used. For spatial discretization, second and third order Total Variation Diminishing (TVD) schemes are used. The PISO algorithm (pressure-implicit split-operator) is used to solve the pressure-velocity coupling. The discretization method is the standard Gauss finite volume integration. The combustion solver called Xifoam, available on OpenFoam, was used. This premixed turbulent combustion model is described in the previous section – Preliminary definitions (Weller et al., 1998; Tabor and Weller, 2004). Both reactive and non-reactive cases were run on a SGI Altix XE 1300 cluster with Intel x86 64 processors, running SUSE Linux Enterprise Server version 10. The cluster has 144 cores with 432 GB, DDR3, 1066 MHz RAM. For the non-reactive cases running with 64 cores, the average seconds per iteration computational time for a simulation using SM was 1.47 seconds. The clock time was about 12h52m. For the reactive case running with 136 cores, the average seconds per iteration for a simulation using the dynamic model was 8.04 seconds. InITIAl And BoundARy CondITIonS The geometry of the channel with a bluff body flame holder is presented in Fig. 1. It consists of a channel 0.600 m long, 0.160 m wide and 0.0288 m tall. The Re based on the inlet velocity and twice the channel height (R e = U axe 2h /ν ) is 6,690. The obstacle used as flame holder is an equilateral triangular cross section obstacle whose backside is located 0.160 m from the entrance. The obstacle blockage is 33% of the total area and corresponds to the r-65 test case in Sanquer’s experiment (Sanquer, 1998). First, only inert simulations are considered with an initial temperature of 300K. At the outflow boundary, a pressure wave transmissivity boundary condition is used for pressure (Candel, 1992). A uniform velocity profile is imposed at the entrance with a speed of Uaxe=3.1 m/s to match the experimental value. On top of the uniform average velocity profile at the inlet, a fluctuation is added using a

routine available on OpenFoam that mimics the turbulent statistical properties. This procedure is necessary since the inlet turbulence determines the flow behavior on the domain, as discussed by Tabor and Baba-Ahmadi (2010). The flow is considered periodic in the spanwise direction. A wall function is used in the channel walls, as shown schematically in Fig. 2 (Jayatilleke, 1969). For reacting flows, propane (C3H8) premixed with air is considered. The mixture is ignited behind the obstacle in the recirculation zone to achieve a proper performance and avoid flame blow off. The ignition point is located at 0.05m behind the obstacle in the center of the recirculation zone. A combustion time of 3ms was used before collecting data to avoid numerical transients and allow time to achieve stable combustion behavior. The imposed initial flame speed was 0.256 m/s and the initial condition for the regress variable was b=1. Mixture Air-Propane

y 0

0.6 0.00288

0.0095 x

0.16

Bluff-body Window

0.16

Unit: m

Figure 1. Scheme of Sanquer’s experiment.

Impose velocity profile

Wall

Obstacle

Wall function

Wall channel

H = 2h

NUMEriCal ModEl

188

Exit conditions

Figure 2. Schematic boundary conditions. turbulent velocity profile at the channel entrance, walls and obstacle.

Figure 3. Grid structure around the obstacle.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.181-196, Apr.-Jun., 2013

Large Eddy Simulation of Bluff Body Stabilized Turbulent Premixed Flame

rESUltS In this section, the performance of the turbulent combustion models presented in problem formulation section and available on OpenFoam is assessed for the flow conditions considered by Sanquer (1998). First, results are presented in terms of frequencies fq and Strouhal numbers (St=fqd/Uaxe) of the vortex emission frequency behind the obstacle, where d is the obstacle height and Uaxe is the maxim velocity at the channel entrance. The size of the average recirculation zone Xr is also compared. Next, the energy spectrum is analysed in order to verify the adequacy of the computational grid and

to compare the inertial range against the -5/3 turbulence decay rate for both inert and reactive cases (Pope, 2000). Then, streamwise and normal velocity profiles are compared to the experimental results in the recirculation zone and downstream of the recirculation zone. Finally, the progress variable and temperature profiles are presented. The recirculation zone and the energy spectra are determined through the velocity data after the simulation reaches the stationary periodic state. Once the length of the recirculation zone Xr is determined, one can calculate the St to compare it with experimental results. To determine the values of the energy spectrum, the Fast Fourier Transform (FFT) of the oscillatory instantaneous velocity is taken. This information is used to determine if the simulation captures the large turbulent scales and models the sub-grid scales correctly. IneRT flow CASe First, inert flow results are presented. Table 1 presents the frequencies, St and recirculation zone length for the present

Ux(m/s)

The grid used in the present study is composed of 388,355 volumes for two-dimensional simulations and 2,300,000 volumes for three-dimensional simulations. Figure 3 shows the grid topology around the obstacle. Lower grid densities were tested but it was not possible to recover the recirculation zone size obtained by Sanquer (1998). The adequacy of the grid was also tested through the turbulent decay rate, which should follow the Kolmogorov -5/3 decay, as discussed in the next section. A detailed study of grid requirement using grid quality assessment techniques was presented by Manickam et al. (2012). They simulated the Volvo experiment using LES and a flame surface wrinkling reaction model based on the progress variable, similar to the model used in this investigation. Their finest grid size has 2.4 million cells, close to the grid size used in the present investigation. Their intermediate and fine grids were able to recover all relevant experimental results for mean and turbulent quantities as well as the St. Nevertheless, even the fine grid presented lower quality near the flamelet region. Considering that the Volvo experiment has a Re much larger than the Sanquer’s experiment, it is safe to say that the fine grid for the Volvo higher Re should capture all the relevant structures for the Sanquer’s lower Re experiment and will allow the necessary level of accuracy for the sub-grid scale model. The instantaneous velocity was monitored in order to establish the time for which the flow can be considered periodic stationary. Figure 4 shows the history of longitudinal velocity. As can be seen, the transition lasts 0.18 seconds, so the flow can be considered periodic stationary beyond that.

189

6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

0.05

0.1

0.15

0.2 0.25 t(s)

0.3

0.35

0.4

Figure 4. Evolution of velocity component Ux.

table 1. Comparison of numerical large Eddy Simulation (lES) and Reynolds averaged Navier Stokes (RaNS) results with experimental results.

Experimental – Sanquer (1998) LES (current work) RANS – Dourado (2003)

fq [Hz]

fqd/U

∆Xr [m]

Xr/d

0.276

0.0204

2.12

93.5

0.284

0.023

2.42

0.2694

0.0222

2.31

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Salvador N.M.C., Mendonça M.T. and Dourado W.M.C.

LES simulation and for RANS simulations performed by Dourado (2003). The results show good agreement with those obtained experimentally. The length of the recirculation zone based on the evolution of the average velocity Ux was determined taking the average values along the X axis downstream of the obstacle. Figure 5 shows the profile of the average velocity used to define the recirculation zone as shown schematically in Fig. 6. The length of the recirculation zone found in the present simulation is 0.023m, while the length found by Sanquer (1998) is 0.0204m, and a simulation based on a RANS model (Dourado, 2003) gives 0.0222m. The recirculation zone length differs approximately 11.5% from the experimental value. To determine the vortex emission frequency, a temporal Fourier analysis was used (Dourado, 2003). For the numerical simulation using LES, a value of 93.5Hz was found, as shown in Fig. 7, while the experimental result was fq = 89Hz. These values correspond to a St=0.284 for the simulation and St=0.276 from the experiment with a difference of only 3%. The RANS model gives fq=87 Hz and St=0.2694, with 2.39% difference in the St to the experimental result in this inert case. For the three-dimensional simulations, the energy spectrum shown in Figs. 8 through 11 has the -5/3 energy decay rate expected for large Re turbulent flows. Figures 8 and 9 are the spectrum for the streamwise velocity component at X/Xr=1.4, in two different distances from the channel centerline, y/h=0.1 and y/h=0.41, respectively. Figures 10 and 11 are spectrum at those two same positions, but for the normal velocity component. On the energy spectrum in Figs. 9 and 11, peaks at about 80Hz can be identified. These peaks correspond to the large scale vortex shedding frequency measured above the channel centerline. At the centerline on Figs. 8 and 10, the peaks seem to be at 100Hz but the spectrum is not conclusive. Filtered longitudinal Ux and normal Uy component velocity profiles at X/Xr=0.8 and X/Xr=1.4 are shown in Figs. 12 to 15. Figure 12 shows the longitudinal velocity profiles in the normal direction obtained in the simulation at X/Xr=0.8. The results are in good agreement with the experimental results, but the dynamic model overpredicts the velocities in the region behind the obstacle and does not show the reverse flow in the recirculation zone. Downstream of the recirculation zone at X/Xr=1.4 (Fig. 13), the longitudinal velocity distributions are also close to the experimental results, even for the dynamic model, which now shows

a moderate underprediction. The results obtained with the SM and one equation models are more accurate. The normal velocity component is underpredicted by all models in the regions behind the obstacle (y/h<0.6; Fig. 14), with the dynamic model showing the worse results. Approaching the upper wall (y/h greater than 0.6) the turbulence models give better predictions, but the Smagorinsky model gives results a little higher than the experiments. Never the less, the results are within the limits of the experimental error.

1 LES Xi Experimental

0.8 0.6 U/Uaxe

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0.4 0.2 0 -0.2 -0.4 -0.6 0.5

1 X/Xr

Figure 5. profile of the average velocity

1.5

u in the recirculation zone.

Uaxe

<u>

X 0 -Ur

Figure 6. Schematic representation of the velocity distribution (Sanquer, 1998).

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Large Eddy Simulation of Bluff Body Stabilized Turbulent Premixed Flame

Further downstream at X/Xr=1.4 (Fig.15), the turbulence models show a better performance, but the dynamic model captures an upwash velocity profile where the other models and the experimental results show a downwash normal velocity distribution. This error occurs in the region behind the obstacle, but approaching the upper wall, all models show improved results. Further investigations are underway to clarify this dynamic model behavior.

ReACTIve CASe For the reactive flow, pre-mixed propane (C3H8) and air with an equivalence ratio equal 0.65 is considered and compared to Sanquer (1998) results. The energy spectrum of the spanwise fluctuation velocity kinetic energy for the reactive case is shown in Fig. 16. The velocity time series was taken at X/X r=1 and y/h=0. As in the inert case, the simulation recovers

1.2

10-1

10-2 Spectrum (Ek/(U'x)2

0.8 A 0.6 0.4 0.2

f(max)=93.5 Hz

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-5/3

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Figure 9. Energy spectrum of the longitudinal velocity components Ux at X/Xr=1.4, y/h=0.41. three-dimensional simulation.

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10-2

-5/3

10-4

180

Figure 7. Frequency spectrum identifying the vortex emissions frequency.

Spectrum (Ek/(U'x)2

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191

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Figure 8. Energy spectrum of the longitudinal velocity components Ux at X/Xr=1.4, y/h=0. three-dimensional simulation.

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101 102 Frequency (Hz)

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Figure 10. Energy spectrum of the normal velocity components Uy at X/Xr=1.4, y/h=0. three-dimensional simulation. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.181-196, Apr.-Jun., 2013

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192

0.05

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Figure 14. Inert case. One equation, dynamic and Smagorinsky models. Mean normal velocity profile Uy at X/Xr=0.8.

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Figure 11. Energy spectrum of the normal velocity components Uy at X/Xr=1.4, y/h=0.41. three-dimensional simulation.

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Figure 15. Inert case. One equation, dynamic and Smagorinsky models. Mean normal velocity profile Uy at X/Xr=1.4.

y/h 10-2

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

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<Ux>/Uaxe

Figure 12. Inert case. One equation, dynamic and Smagorinsky models. Mean longitudinal velocity profile Ux at X/Xr=0.8.

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y/h Figure 13. Inert case. One equation, dynamic and Smagorinsky models. Mean longitudinal velocity profile Ux at X/Xr=1.4.

the -5/3 decay rate. A peak on the energy spectrum can be observed at 94Hz, which is close to the experimental value of 89Hz observed by Sanquer (1998).

102 Frequency (Hz)

103

Figure 16. Energy spectrum of the normal velocity component at X/Xr=1 and y/h=0.

Streamwise and normal velocity profiles at two different positions in the streamwise direction (X/Xr=0.8 and X/Xr=1.4) are presented in Figs. 17 through 20. Again,

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X/Xr=0.8

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LES XI-DynamicOneEq

0.2

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y/h Figure 17. Mean longitudinal velocity profile Ux at X/Xr=0.8. Reactive case.

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LES XI-DynamicOneEq

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y/h Figure 18. Mean longitudinal velocity profile Ux at X/Xr=1.4. Reactive case.

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LES XI-DynamicOneEq

0.2

0.4

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y/h Figure 19. Mean normal velocity profile Uy at X/Xr=0.8. Reactive case.

X/Xr=1.4

0.1 <Uy>/Uaxe

dynamic, one equation and Smagorinsky SGS model results are presented. The streamwise velocity distribution at X/Xr=0.8 is very close to the experimental observed velocity distribution for all the three models, as shown in Fig. 17. At X/Xr=1.4, the results for the streamwise velocity also compare very well with the experiments, as shown in Fig. 18, but the one equation model overpredicts the velocity distribution. The values of the normal velocity component at X/Xr=0.8 are presented in Fig. 19. The one equation and the Smagorinsky models are in good agreement with the experimental results in the region behind the obstacle (y/h<0.4), while the dynamic model underpredicts the experimental results. Away from the central region, approaching the upper wall, the trend is reversed and the dynamic model shows better results than the Smagorinsky and one equation models. These results are not conclusive to which turbulence model is more suitable for the reactive case simulation. This same behavior is also observed for the normal velocity component at X/Xr=1.4 (Fig. 20), with different turbulent models performing better or worse at different regions of the flow domain, but all models capturing the general trends of the experimentally observed velocity distributions. The progress variable computed by the dynamic model is presented in Figs. 21 and 22 and compared to the experimental distribution. The simulation captures the general behavior of the progress variable quite well. Despite the fact that the simulation overpredicts the progress variable inside the flame zone, the flame front at c=0.05 around y/h=0.6 matches the experimental value in X/Xr=0.35 and underpredicts for X/ Xr=1.4. Also, Sanquer (1998) states that the experimental results seem to be displaced to the left. For the 3-D reactive case, a value of 1,750K was obtained for the flame average temperature with the dynamic model. The theoretical adiabatic flame temperature for a equivalence ratio of 0.65 corresponds to 1,750K for this fuel. Figures 23 and 24 show the temperature distribution in the normal direction with a profile corresponding to a premixed flame. The vorticity distribution in the inert and reactive cases can be compared with the help of Figs. 25 and 26. These figures show the flow structure in the (x, y) cut at the center of the channel. As in Park’s discussion (Park and Ko 2011), the chemical reaction has a stabilizing effect on the vortex shedding.

<Ux>/Uaxe

Large Eddy Simulation of Bluff Body Stabilized Turbulent Premixed Flame

-0.1

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LES XI-DynamicOneEq

0.2

0.4

0.6

0.8

y/h Figure 20. Mean normal velocity profile Uy at X/Xr=1.4. Reactive case.

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194

X/Xr=0.35 0.8 0.7

Experimental LES-XI-Smagorinsky

0.6 <C>

0.5 0.4 0.3 0.2

Figure 24. temperature contours behind the bluff body.

0.1 0

0.2

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y/h

0.6

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Figure 21. profile of the progress variable at X/Xr=0.35.

X/Xr=1.4

Experimental LES-XI-Smagorinsky

0.8

Figure 25. Inert flow spanwise vorticity.

<C>

0.6 0.4 0.2 0

0.2

0.4

y/h

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0.8

Figure 22. profile of the progress variable at X/Xr=1.4. Figure 26. Reactive flow spanwise vorticity.

The inert case clearly shows the Karman vortex street behind the bluff body, while in the reactive case the characteristic alternating vortex structure starts further downstream with a much weaker strength. The vorticity near the bluff body has a stretched topology on the reactive case and the wake spreading is lower than the wake spreading of the inert case, which is in agreement with the behavior described by Park and Ko (2011).

X/Xr=0.8

1800 1600

LES-XI-Smagorinsky

1400

<T>

1200 1000 800 600 400 200 0

0.2

0.4

y/h

0.6

0.8

Figure 23. Mean temperature profile at X/Xr=0.8.

CoNClUSioNS Results from numerical simulations of inert and reactive flows were compared to experimental results obtained by Sanquer

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(1998). Smagorinsky, one equation and dynamic LES models were used and the reaction was simulated using the Ξ density of wrinkling model. The experiments are in the thin, wrinkled flame regime with a Re of 6,690, a Da of 4.5 and a Ka of 1.3. For the inert flow case, the simulations using LES good results were obtained for the St, with an error of the order of 3%. The size of the recirculation bubble is close to the size observed experimentally but the margin of error is larger, around 12%. But these values are not absolute values since the experimental results also have a margin of error. The energy decay on the inertial range was correctly captured at -5/3. As far as the velocity distribution is concerned, the streamwise velocity component shows good agreement with the experimental values, but the normal velocity components are somewhat off, in part as a consequence of the over-predicted recirculation zone length. The results for the reactive flow case show similar performance with the inert case. The energy decay rate in the inertial range was correctly captured and the vortex sheading frequency was close to the experimental value. The progress variable and the correct behavior considering the stabilization

195

of the vortex sheading behind the obstacle for the reactive case were captured by the simulation. Again, on the reactive case, the velocity distribution was somewhat off from the experimental measurements. Regarding the velocity profile, it is still interesting to observe that the SM gives a better result than the dynamic model used in these simulations. The results may be improved by tailoring the dynamic turbulent model coefficients. In general, the results for all three models are relatively similar and the differences between these models are small. Therefore, since the dynamic model has a higher computational cost, it may be worthwhile to use the Smagorinsky or the one equation model.

ACKNOWLEDGMENTS The authors would like to thank the Instituto de Aeronáutica e Espaço for the use of their computational facilities in the Laboratory of Liquid Propulsion and Brazilian Government CAPES for the financial support.

REFERENCES Akula, R.A., Sadiki, A. and Janicka, J., 2006, “Large Eddy Simulation of Bluff Body Stabilized Flame by Using Flame Surface Density Approach”. Proceedings of the European Conference on Computational Fluid Dynamics. ECCOMAS CFD. Bai, X.S. and Fuchs, L., 1994, “Modeling of turbulent reactive flows past a bluff body: Assessment of accuracy and efficiency”. Computers & Fluids, Vol. 23, No. 3, pp. 507-521. Borghi, R. and Destriau, M., 1998, “Combustion and Flames: chemical and physical principles”. Éditions TECHNIP. Boger, M. and Veynante, D., 2000, “Large eddy simulations of a turbulent premixed V-shape flame”. In: Advances in Turbulence VIII, Proceedings of the Eighth European Turbulence Conference, Barcelona, pp. 449-452. Candel, S., 1992, “Combustion instabilities coupled by pressure waves and their active control”. Symposium (International) on Combustion, Vol. 24, No 1, pp. 1277-1296. Chaudhuri, S., Kostka, S., Tuttle, S.G., Renfro, M.W. and Cetegen, B.M., 2011, “Blow off mechanism of two dimensional bluff body stabilized turbulent premixed flames in a prototypical combustor”. Combustion and Flame, Vol. 158, No 7, pp. 1358-1371. Cheng, R.K., 1984, “Conditional sampling of turbulence intensities and Reynolds stress in premixed turbulent flames”. Combustion Science and Technology, Vol. 41, pp.109-142.

Cheng, R.K., Shepherd, I.G. and Gokalp, I., 1989, “A comparison of the velocity and scalar spectra in premixed turbulent flames”. Combustion and Flame, Vol.78, No 2, pp. 205-221. Cheng, R.K. and Shepherd, I.G., 1991, “The influence of burner geometry on premixed turbulent flame propagation”. Combustion and Flame, Vol. 85, No 1-2, pp. 7-26. Dourado, W.M.C., 2003, “Desenvolvimento de um método numérico em malhas não estruturadas híbridas para escoamentos turbulentos em baixo número de Mach: aplicação em chama propagando-se livremente e esteiras inertes e reativas”. Tese (Doutorado), Instituto Tecnológico de Aeronáutica, São José dos Campos. Eriksson, P., 2007, “The Zimont TFC model applied to premixed bluff body stabilized combustion using four different RANS turbulence models”. Proceedings of ASME GT2007, ASME Turbo Expo 2007, Vol. 2, pp. 353-361, Montreal. Frendi, A., Skarath, G. and Tosh, A., 2004, “Prediction of noise radiated by flow over a smooth square cylinder”. Proceedings of the 10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK. Fureby, C., Tabor, G., Weller, H.G. and Gosman, A.D., 1997, “A comparative study of subgrid scale models in homogeneous isotropic turbulence”. Physics of fluids, Vol. 9, No 5, pp. 1416-1429. Ge, H.W., Zhu, M., Chen, Y. and Gutheil, E., 2007, “Hybrid unsteady RANS and PDF method for turbulent non-reactive and reactive flows”. Flow, Turbulence and Combustion. Vol. 78, No 2, pp. 91-109.

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Ghosal, S., Lund, T., Moin, P. and Akselvoll, K., 1995, “A dynamic localization model for large-eddy simulation of turbulent flows”. Journal of Fluid Mechanics, Vol. 286, pp. 229-255. Jayatilleke, C., 1969, “The influence of prandtl number and surface roughness on the resistance of the laminar sublayer to momentum and heat transfer”. Prog. Heat Mass Transfer, Vol. 1, pp. 193-321. Kerstein, A.R., 1989, “Linear-eddy modeling of turbulent transport II. Application to shear layer mixing”, Combustion and Flame, Vol. 75, No 3-4, pp. 397-413. Kiel, B., Garwick, L.K., Gord, J.G., Miller, J. and Lynch, A., 2007, “A detailed investigation of bluff body stabilized flames”. AIAA 2007168, Proceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit 8 - 11 January 2007, Reno, Nevada. Lovett, J.A., Brogan, T.P., Philippona, D.S., Keil, B.V. and Thompson, T.V., 2004, “Development Needs for Advanced Afterburner Designs”, Proceedings of the 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Fort Lauderdale, Florida. Manickam, B., Franke, J., Muppala, S.P. and Dinkelacker, F., 2012, “Large-eddy Simulation of Triangular-stabilized Lean Premixed Turbulent Flames: Quality and Error Assessment”. Flow, Turbulence and Combustion. Vol. 88, No 4, pp. 563-596. Menon, S., McMurtry, P.A. and Kerstein, A.R., 1993, “A linear eddy mixing model for large eddy simulation of turbulent combustion”, In: Galperin, B. and Orszag, S. (Eds.), “Large Eddy Simulation of Complex Engineering and Geophysical Flows”, Cambridge University Press, Cambridge, pp. 287-314. Park, N.S. and Ko, S.C., 2011, “Large eddy simulation of turbulent premixed combustion flow around bluff body”. Journal of Mechanical Science and Technology, Vol. 25, No 9, pp. 2227-2235. Peters, N., 2000, “Turbulent Combustion”, Cambridge University Press, Cambridge. Pope, S.B., 2000, “Turbulent Flows”. Cambridge University Press, Cambridge.

Models”, Ph.D. Thesis, Université de Poitiers, Potiers. Saghafian, M., Stansby, P.K., Saidi M.S. and Apsley, D.D., 2003, “Simulation of turbulent flows around a circular cylinder using nonlinear eddy viscosity modelling: steady and oscillatory ambient flows”. Journal of Fluids and Structures, Vol. 17, No 8, pp. 1213-1236. Sjunesson, A., Henriksson, R. and Lofstrom, C., 1992, “Cars measurements and visualization of reacting flows in bluff body stabilized flame”. AIAA-92-3650. Sjunnesson, A., Olovsson, S. and Sjoblom, B., 1991, “Volvo Flygmotor internal report”, VFA9370-308. Tabor, G. and Weller, H.G., 2004, “Large eddy simulation of premixed turbulent combustion using Xi flame surface wrinkling model”. Flow, Turbulence and Combustion, Vol. 72, pp. 1-28. Tabor, G.R. and Baba-Ahmadi, M.H., 2010, “Inlet conditions for large eddy simulation: a review”. Computers & Fluids, Vol. 39, No 4, pp. 553-567. Veynante, D., 2006, “Large eddy simulation of turbulent combustion”. Conference on Turbulence and Interaction, Vol. TI 2006, p. 20, Porquerolles, France. Weller, H.G., Marooney, C.J. and Gosman, A.D., 1990, “A new spectral method for calculation of the time varying area of laminar flame in homogeneous turbulence”. Proceedings of the 23rd Symposium (International) on Combustion, The Combustion Institute, Vol. Twenty-third Symposium, pp. 629-636. Weller, H.G., 1993, “The development of a new flame area combustion model using conditional averaging”. Thermo-Fluids Section Report TF 9307, Imperial College of Science, Technology and Medicine, London. Weller, H.G., Tabor, G., Gosman, A. and Fureby, C., 1998, “Application of a flame-wrinkling les combustion model to a turbulent mixing layer”, Symposium (International) on Combustion, The combustion Institute, Vol. 27, No 1, pp. 899-907.

Porumbel, I. and Menon S., 2006, “Large Eddy Simulation of Bluff Body Stabilized Premixed Flame”, AIAA 2006-152.

Yoshizawa, A. and Horiuti, K., 1985, “A statistically-derived subgridscale kinetic energy model for the large-eddy simulation of turbulence flows”. Journal of Physical Society of Japan, Vol. 54, pp. 2834-2839.

Sanquer, S., 1998, “Experimental Study of a Bluff Body Wake, in Presence of Combustion, in Fully Developed Turbulent Channel Flow. Turbulence Scales and Critical Analysis of Transport and Combustion

Zimont, V.L. and Lipatnikov, A.N., 1995, “A numerical model of premixed turbulent combustion of gases”. Chemical Physics Report, Vol. 14, No 7, pp. 993-1025.

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doi: 10.5028/jatm.v5i2.231

Experimental Valuation Diagnostics of Hydrous Ethanol Sprays Formed by a Blurry Injector Claudia Gonçalves de Azevedo1, José Carlos de Andrade1, Fernando de Souza Costa1

ABSTRACT: Concerns about the rising fuel price and environmental changes have led to the search for alternative fuels and energy sources. The interest in improving the performance of power generation, with the aim of reducing costs, increasing operating efficiency, and reducing the emissions of pollutants, has driven the scientific community to work on new burning technologies. Flameless combustion is one of the best alternative new technologies for a clean and efficient one. The burning of liquid fuels in power generation and propulsion systems depends on the effective atomization to increase the surface area of the fuel and thus to achieve high rates of mixing and evaporation. This work described the spray characteristics of hydrous ethanol in a blurry injector for applications in a flameless compact combustion chamber. The experimental results are obtained over a range of relatively low flow rates with different air-toliquid mass flow ratios. Keywords: Blurry injector, Hydrous Ethanol, Drop size, Discharge coefficients.

INTRODUCTION Spray combustion is extensively used in power generation and liquid-fueled rocket engines. In general, before burning, liquid fuels need to be dispersed in small droplets that are rapidly vaporized and mixed with the oxidizer. The atomization process increases the surface area of the fuel, aiming at making the contact area between the fuel and oxidizer higher and, therefore, its rates of mixing and fuel evaporation and in the time available for complete combustion. Effective fuel atomization is essential to minimize emissions of particulate matter (PM), carbon monoxide (CO), unburned hydrocarbons (UHC), and nitric oxides (NOx). The increasing costs of fossil fuels, environmental concerns, and stringent regulations on fuel emissions have caused a significant interest for the use of biofuels. Ethanol has become an attractive alternative fuel for: it is a renewable energy source, easily available from common biomass sources, biodegradable, contributes to sustainability and is oxygenated, thereby providing the potential to reduce pollutants emissions. Due to its combustion characteristics, it also has been considered as a low polluting liquid propellant for the combustion rocket propulsion application (Gajdeczko et al., 2000). The most typical mixing twin fluid atomization technique is the air-blast atomization. Air-blast injectors have been widely used and studied (Lefebvre, 1992a, b; Clack et al., 2004; Hoeg et al., 2008; Bolszo and McDonell, 2009; Batarseh et al., 2010). In this technique, air and liquid are supplied separately to the injector, and mixing takes place downstream of the

1.Instituto Nacional de Pesquisas Espaciais – Cachoeira Paulista/SP – Brazil Author for correspondence: Claudia Gonçalves de Azevedo | Instituto Nacional de Pesquisas Espaciais, Laboratório Associado de Combustão e Propulsão | Rodovia Presidente Dutra, km 40 | CEP 12.630-000 Cachoeira Paulista/SP – Brazil | E-mail: claudia@lcp.inpe.br Received: 11/02/13 | Accepted: 06/04/13

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Azevedo, C.G., Andrade, J.C. and Costa, F.S.

nozzle orifice, externally. The liquid discharges through a circular orifice, while the air is supplied through an annular slot around the periphery, resulting in a conical discharge pattern. The main atomization technique is shear interaction caused by high relative velocities between the air and liquid. A liquid jet is exposed to a stream of air flowing at high velocities, which impinge on the liquid jet outside the discharge orifice, producing threads and ligaments. According to Lefebvre (1989), their initial hydrodynamic instabilities are augmented by aerodynamics disturbances, so that they expand away from the nozzle and their thickness slenderizes. When the ligaments collapse, droplets are produced. According to Lorenzetto and Lefebvre (1977), the air-blast injector produces finer droplets as the supply pressure or mass flow rate of the atomizing air is higher, which also increases the power requirement of the atomizer. However, the air blast injector performs poorly with fuels of high kinematic viscosity, creating large droplets that burn in diffusion mode to result in high PM, CO, and NOx emissions. Another typical atomization technique of internal mixing type is known as effervescent atomization (Lefebvre, 1988; Lefebvre et al., 1988). A pressurized gas is injected into the bulk liquid in a mixing chamber, upstream of the discharge orifice. The injected gas forms bubbles to produce a two-phase mixture that flows through the orifice. They are expanded quickly when the mixture is exposed to a low-pressure zone at the injector exit, shattering the liquid into droplets. There have been many studies reported in the literature involving effervescent injectors over a range of air-to-liquid mass and liquid flow rates (Lörcher et al., 2005; Konstantinov et al., 2010). According to Sovani et al. (2001), compared with an air blast injector, effervescent ones present advantages like the formation of a spray with finer droplets over a wide range of operating conditions, even for less refined fuels; the injector performance is relatively insensitive to the liquid kinematic viscosity; the larger diameter of the orifice alleviates clogging problems and simplifies fabrication. Gañan-Calvo (2005) describes the flow-blurring injector, or blurry injector, a novel twin fluid atomization technique, which exploits the advantages of internal and external mixes. This injection method presents several advantages over other injectors, such as formation of a uniform spray, better atomization, high atomization efficiency, robustness, excellent fuel vaporization and mixture with air, and potential for the application in compact combustion systems that can be used

as portable power sources. Also, for a specified liquid flow rate and total energy input, the flow-blurring injector creates about 5 to 50 times more droplet surface areas than any other pneumatic injector of the “plain-jet air blast” type. Figure 1 presents the scheme of the flow-blurring injector. The flow-blurring injector consists of a fuel tube and an exit orifice both of diameter (d). The concept behind flowblurring atomization is that the air is forced through a small gap between the fuel tube exit and a coaxial orifice located H distance downstream the fuel tube. As shown in Fig. 1, when H/d < 0.25, part of the air is forced a short distance into the fuel tube and the remaining produces shear layer as it leaves the injector orifice enhancing the atomization process. The back flow of air at the tip of the fuel tube results in a twophase turbulent flow passing through a positive pressure field. This mixture undergoes sudden decrease in pressure, while exiting through the injector orifice. Due to the significant pressure decrease, air bubbles in the two-phase flow expand and shatter the liquid into fine droplets. The flow-blurring injector is capable of producing internal and external mixes of the two phases simultaneously, providing then superiority over other injectors.

Fuel Inlet d

Atomizing Air

Spray

Figure 1. Scheme of the flow-blurring injector (Dent, 2012).

Combustion experiments by Simmons et al. (2008) demonstrated that the flow-blurring injector has the ability to effectively atomize high-viscosity vegetable oil. Furthermore, the fuel supply tube diameter of the injector could alleviate problems of clogging while incurring a lowpressure drop. Panchasara et al. (2009) experimentally compared a flow-blurring with a commercial air blast

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.197-204, Apr.-Jun., 2013

Experimental Valuation Diagnostics of Hydrous Ethanol Sprays Formed By a Blurry Injector

injector, using kerosene and diesel burning in a swirl stabilized combustor operated at atmospheric conditions, and verified that for such fuel and atomizing air flow rates, the flow-blurring injector produced three to five times lower NOx and CO emissions as compared to the air blast injector. Reduction in emissions was attributed to improved fuel atomization that resulted in a decrease in the mean droplet size for the flow-blurring injector. Sadasivuni and Agrawal (2009) used the flow-blurring injector in a compact combustion system with a counter flow heat exchanger. The volumetric energy density of the system was substantially higher than that of the concepts previously developed. Heat release rate of up to 460 W was achieved in a combustor volume of 2.0 cm3. The combustion system produced clean, compact, quiet, distributed, and attached flat flame. No soot or coking problems were experienced during or after combustor operation on kerosene fuel. Simmons and Agrawal (2010) used laser sheet visualization and a phase Doppler particle analyzer to obtain the spray characteristics of a flow-blurring injector, operating with a configuration where H/D=0.23 and using as working fluids water and air. The authors also compared the performance of such injector with that of an air blast and from the results, they concluded that the flow-blurring injector can effectively atomize liquids at relatively low air-to-liquid mass ratio (ALR) compared to the air-blast injector, while reducing the pressure drop penalty in the atomizing air line. Rapid fuel vaporization and mixing with oxidizer are key requirements for liquid-fueled small-scale combustion systems. Thus, the optimization of combustion systems is very attractive, since the use of non-renewable liquid hydrocarbon fuels is responsible for most of the energy production and pollutants emissions. Therefore, improvements in the design and operation of this equipment are essential for current environmental and energy requirements. The flow-blurring injector is effective in generating a fine spray for liquid fuels in mesoscale systems to promote vaporization. Therefore, this work presents the characterization of hydrous ethanol sprays formed by a blurry injector with a divergent exit. The liquid and air mass flow rates were measured experimentally and, since lower flow rates and pressures were adopted, the injector will be considered for applications in a flameless compact combustion chamber. Flameless combustion is a homogeneous low temperature

199

burning process leading to strongly reduced pollutant emissions and higher efficiency compared to the traditional processes (Wünning and Wünning, 1997). Experiments are conducted for different liquid and air mass flow rates at ambient conditions of temperature and pressure.

EXPEriMENtal SEtUP BluRRy InJeCToR Figure 2 shows the injector developed that will be possibly used in a flameless compact combustor. The blurry injector consisted of a central liquid tube (d = 0.5 mm) and a coaxial atomizing air passage with 6 mm inner diameter. The two-phase mixture exits through the orifice of diameter (d=0.5 mm) in the discharge plate located, such that H=0.125 mm. As discussed, this geometry creates a turbulent mixing between the air and liquid phases at the tip of the liquid supply tube to produce a fine spray.

6 mm

1 mm 0.125 mm

60º

0.5 mm

0.1 mm

Figure 2. Schematic representation of the blurry injector.

Test bench Compressed air was used as the atomizing gas and was supplied from a high-pressure cylinder, controlled by a needle valve, and measured by a calibrated flow meter with an uncertainty of ± 1.5 standard liters per minute (slpm). The flow rates of hydrous ethanol were measured by rotameters, with the uncertainty in the measurements being ± 2%. Supply pressure in the fuel and atomizing air lines were measured using pressure transducers at locations depicted in Fig. 3. The average droplet diameters and size distribution of the spray were measured using a laser diffraction system

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Azevedo, C.G., Andrade, J.C. and Costa, F.S.

Air

Hydrous Ethanol tank

Injector

Laser System

Valve on/off

Press transducer

Manometer

Mass flow meter

Needle valve

Figure 3. Schematic representation of the test bench.

(Malvern Spraytec®) at atmospheric conditions. The operating principle of this system is the laser scattering produced by the droplets. The laser diffraction system can measure droplet diameters from 0.1 to 2,000 μm with accuracy of ± 1% of full scale (specified by the manufacturer). It could measure the droplet size and distribution of sprays with obscurations up to 95% and calculates spray average properties along a sight line across the spray. The laser measurements were taken 50 mm downstream of the injector exit, where the spray drop size was constant further downstream. The centre of the spray was positioned at the laser beam centre, so it could be fully covered by the laser beam. Table 1 shows the properties of the hydrous ethanol. Density ρ, surface tension σ, and dynamic viscosity ν were determined by measurement in laboratory. table 1. properties liquid fuel at 95 kpa. Surface tension, σ (n/m)

density, ρ (kg/m3)

dynamic viscosity, ν (ns/m2)

0.024*

806.7**

0.00124**

*measured at 299.15 K; **measured at 298.15 K.

rESUltS aNd diSCUSSioN Initially, the liquid flow rate was kept constant and the airflow rate was varied to obtain the variation in ALR in the injector. Then, the liquid flow rate was varied for different values of airflow rate. Air density was calculated considering the supply pressure and temperature of the atomizing air. pReSSuRe dATA Figure 4 shows the pressure in the atomizing air line and the pressure in the hydrous ethanol one for different air flow rates. The pressure measured was effectively that drop in the line because the injector was open to the room. It can be seen in Fig. 4 that the air and liquid pressures in the injector increase with air flow rate being higher. The air pressure ranged from 1.02 and 2.88 bar for air flow rate from 0.082 to 0.24 g/s, and the liquid pressure varied between 0.94 to 2.34 bar for air flow rate from 0.082 to 0.24 g/s. The pressure is higher when there is an increase of both air and hydrous ethanol mass flow rates.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.197-204, Apr.-Jun., 2013

2.5

2.0

2.0 Liquid pressure [bar]

Air pressure [bar]

Experimental Valuation Diagnostics of Hydrous Ethanol Sprays Formed By a Blurry Injector

1.5

1.0

liquid flow rate, g/s 0.08

0.5

0.0 0.00

0.42

(a)

0.06

0.12 0.18 Air flow rate [g/s]

0.24

1.5

1.0

liquid flow rate, g/s 0.08

0.5

0.30

201

0.42

(b)

0.0 0.00

0.06

0.12 0.18 Air flow rate [g/s]

0.24

0.30

Figure 4. air and liquid pressures.

dISCHARge CoeffICIenT The discharge coefficient is the ratio between the experimental mass flow rate and the maximum theoretical mass flow rate of the liquid in the injector. It is given by Eq. 1 (Delmeé, 1983): cd =

ml A√2ρl∆Pl

(1)

where cd is the discharge coefficient of the liquid; ml the experimental liquid mass flow rate, kg/s; A is the total

3.5 3.0

liquid flow rate, g/s 0.08

2.5

0.17 0.25 0.33

ALR [-]

AIR-To-lIquId MASS flow RATIoS The ALR for the operational conditions are depicted in Fig. 5. To obtain the plots in Fig. 5 the liquid flow rate was initially kept constant and the air flow rate was varied over a range to obtain the variation in ALR. The liquid flow rate was then varied and the entire procedure was repeated for different values of air flow rate. It is observed in Fig. 5 that for a given liquid flow rate an increase in the air one leads to an increase in ALR. The data in Fig. 5 also show an increase in ALR with a decrease in the liquid flow rate. The reason for the increase in ALR can be attributed to the fact that with the decrease in the area occupied by the liquid due to the decrease in its flow rate the area available for air flow increases, doing the same in the air flow rate. For the liquid flow rates analyzed, it was verified that the air flow rate varied between 0.082 and 0.24 g/s and the ALR was seen changing from 0.21 to 2.88.

2.0

0.42

1.5 1.0 0.5 0.0 0.00

0.06

0.12 0.18 Air flow rate [g/s]

0.24

0.30

alR: air-to-liquid mass ratio.

Figure 5. air-to-liquid mass flow ratio.

cross-sectional area of the discharge orifices, m2; ∆Pl is the pressure difference of the liquid flow across the nozzle, Pa; and ρl is the density of the liquid, kg/m3. At each test condition, the discharge coefficient was determined by substituting into Eq. 1 the measured values of liquid flow rate and pressure drop across the injector, along with injector flow area and liquid density. Figure 6 shows the typical curve of the discharge coefficients versus ALR. It is seen in Fig. 6 that for a given liquid flow rate the discharge coefficient decreases with an increase in ALR. Lefebvre (1983) has defined the discharge coefficient to be a measure of the extent to which the liquid flowing through the final discharge orifice

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Azevedo, C.G., Andrade, J.C. and Costa, F.S.

0.18

Discharge coefficient [-]

0.16

liquid flow rate, g/s 0.08 0.17 0.25 0.33 0.42

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00

0.0

0.5

1.0

1.5 2.0 ALR [-]

2.5

3.0

3.5

alR: air-to-liquid mass ratio.

Figure 6. Discharge coefficient versus air-to-liquid mass ratio.

makes full use of the available flow area. Therefore, the discharge coefficient depends on the amount of flow area available for the liquid phase. As ALR increases, the flow area available for liquid decreases and Cd is inferior. The rate of change in discharge coefficient decreases with an increase in ALR, which is responsible for a slower rate of decrease in the liquid flow rate at higher values of ALR as seen in Fig. 6. The values of discharge coefficient shown in Fig. 6 vary from 0.022 and 0.157 over the entire operating range. dRopleT dIAMeTeR dATA Different characteristic diameters can be obtained to represent a spray. In this work, the Sauter mean diameter (SMD)

and the mass median diameter (MMD) were obtained with aid of the laser system. The SMD is the droplet size that possesses a volume-to-surface-area ratio proportional to that of the entire spray, and MMD is the drop diameter such that 50% of the total mass of spray consists of droplets of smaller diameter. Figure 7 illustrates the effect of ALR on the SMD and MMD at different liquid mass flow rates for hydrous ethanol. The results show that the droplet size is strongly influenced by the ALR. The data presented in Fig. 7 conclude that the droplet size decreases with an increase in ALR for a given liquid flow rate. It is verified that a decrease in liquid mass flow rate causes a decreasing in the mean drop size. The higher the ALR is, the higher the air flux will be, and then a larger smashing energy can be provided for liquid atomization. It can be speculated that this decrease in the droplet diameter value is due to two effects. First, the increase in ALR increases the air flow rate and the effective area occupied by air, decreasing the effective area occupied by liquid and liquid flow rate through the injector orifice. Increase in air flow area is beneficial to atomization, because it reduces the area available for the liquid flow, i.e. it squeezes the liquid into thinner films and ligaments as it flows through the injector orifice. Secondly, the increase in ALR is accompanied by one in exit velocities and turbulence inside the injector, resulting in improved atomization. Figure 8 illustrates the effects of atomizing air velocity on SMD and MMD at different liquid mass flow rates for hydrous ethanol. Table 2 shows the ranges of ALR, air velocity, SMD, and MMD measured.

24 22

liquid flow rate, g/s

0.08 0.17 0.25 0.33

18 16

0.08 0.17 0.25 0.33

MMD [µm]

SMD [µm]

liquid flow rate, g/s

0.0

0.5

1.0

2.0 1.5 ALR [-]

2.5

3.0

3.5

0.0

0.5

1.0

2.0 1.5 ALR [-]

SMD: Sauter mean diameter; MMD: mass median diameter; alR: air-to-liquid mass ratio.

Figure 7. Influence of air-to-liquid mass ratio on Sauter mean and mass median diameters. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.197-204, Apr.-Jun., 2013

2.5

3.0

3.5

Experimental Valuation Diagnostics of Hydrous Ethanol Sprays Formed By a Blurry Injector

203

table 2. Ranges of air-to-liquid mass ratio, air velocity and average diameters. liquid mass flow rate (g/s)

AlR (-)

Air velocity (m/s)

SMd (µm)

MMd (µm)

0.08

1.04–2.82

176.96–304.49

10.37–6.59

14.53–7.97

0.17

0.52–1.40

181.37–309.27

10.71–7.20

14.27–9.17

0.25

0.35–0.93

185.04–313.30

11.75–8.97

16.27–12.13

0.33

0.26–0.70

188.27–316.82

14.17–10.41

21.37–14.40

SMD: Sauter mean diameter; MMD: mass median diameter; alR: air-to-liquid mass ratio.

24 22

0.08

0.17 0.25

0.33

MMD [µm]

SMD [µm]

liquid flow rate, g/s 0.08 0.17 0.25 0.33

liquid flow rate, g/s

14 12

10 8

8 6 4 160

200

240 280 320 Air velocity [m/s]

360

400

4 160

220

280

340

400

Air velocity [m/s]

SMD: Sauter mean diameter; MMD: mass median diameter.

Figure 8. Influence of air velocity on Sauter mean and mass median diameters.

Cumulative (%)

100

Particle Diameter (µm)

ALR

Dx(10)

Dx(50)

Dx(90)

0.26

8.39

21.03

44.51

0.35

7.20

16.27

32.66

0.51

5.92

13.75

30.36

0.68

5.16

12.22

27.19

0.76 1.02

4.88 4.19

11.10 10.11

22.84 22.46

2.82

3.65

7.97

15.50

100

1000

Figure 9. Cumulative drop size distributions. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.197-204, Apr.-Jun., 2013

204

Azevedo, C.G., Andrade, J.C. and Costa, F.S.

Figure 9 depicts the effects of ALR on cumulative drop size distributions and on representative diameters, Dx10, Dx50 and Dx90, i.e. the drop diameters such that 10, 50 and 90% of total liquid volume are in drops of smaller diameter. The particle size distribution at a low ALR depicts the presence of larger droplets compared to the case of higher ALR, where the percentage of smaller size droplets have increased significantly, reflecting an improved atomization at higher ALR. As expected, it was verified that an increase in ALR leads to a decrease in droplet diameters, since the increase in air flow results in better atomization.

CONCLUSIONS A blurry injector has been developed for applications in a compact flameless combustion chamber, and the spray characteristics were obtained for injection of hydrous ethanol. The discharge coefficient is seen to decrease with an increase in ALR, which is attributed to the decrease in an available area for liquid flow with increasing air flow. The average droplet diameters decreased significantly with increasing ALR and air velocity. Air and liquid injection pressures were higher, approximately, linearly with increasing air flow rates.

REFERENCES Batarseh, F.Z., Roisman, I.V. and Tropea, C., 2010, “Characterization of a spray generated by an airblast atomizer with prefilmer”, Atomization and Sprays, Vol. 20, No 10, pp. 887-903. Bolszo, C.D. and McDonell, V.G., 2009, “Evaluation of plain-jet air blast atomization and evaporation of alternative fuels in a small gas turbine engine application”, Atomization and Sprays, Vol. 19, No 8, pp. 771-785. Clack, H. L., Koshland, C. P., Lucas, D. and Sawyer, R. F., 2004, “Development of an air-blast atomizer for independent control of droplet size and spray density”, Atomization and Sprays, Vol. 14, No 3, pp. 265-288. Delmeé G.J., 1983, “Manual de Medição de Vazão”, São Paulo, Editora Edgard Blucher, 474 p. Dent, T.J., 2012, “Mesoscale power generation incorporating heatrecirculation, porous inert media, and thermoelectric modules”, Ph.D. Thesis, University of Alabama, Alabama, USA. Gajdeczko, B.F., Luff, J., Dryer, F.L. and Lavid, M., 2000, “Laser Ignition of Liquid Oxygen/Ethanol Propellants”, Twenty-Eighth Symposium (International) on Combustion, Abstracts of Work in Progress Poster Presentations (No. 2-B20), The Combustion Institute, Pittsburgh, PA, 244 p. Gañán-Calvo, A.M., 2005, “Enhanced Liquid Atomization: From FlowFocusing to Flow-Blurring”, Applied Physics, Letters 86. Hoeg, D.P., Wang, Z., Friedman, P. D. and Laoulache, R. N., 2008, “Investigation of a coaxial air-blast atomizer using particle image velocimetry and computational fluid dynamics”, Atomization and Sprays, Vol. 18, No 8, pp. 739-759. Konstantinov, D., Marsh, R., Bowen, P. and Crayford, A., 2010, “Effervescent atomization for industrial energy–technology review”, Atomization and Sprays, Vol. 20, pp. 525-552.

Lefebvre, A.H., 1989, “Atomization and Sprays”, Hemisphere, New York. Lefebvre, A.H., 1992a, “Energy consideration in twin-fluid atomization”, Journal of Engineering for Gas Turbine, Vol. 114, pp. 89-96. Lefebvre, A.H., 1992b, “Twin Fluid Atomization: Factors Influencing Mean Drop Size”, Atomization and Sprays, Vol. 2, No 2, pp. 101-119. Lefebvre, A.H. et al., 1988, “Spray characteristics of aerated-liquid pressure atomizers”, Journal of Propulsion and Power, Vol. 4, pp. 293-298. Lörcher, M., Schmidt, F. and Mewes, D., 2005, Effervescent atomization of liquids, Atomization and Sprays, Vol. 15, pp. 145-168. Lorenzetto, G.E. and Lefebvre, A.H., 1977, “Measurements of Drop Size on a Plain-Jet Airblast Atomizer”, AIAA Journal, Vol. 15, Issue 7, pp. 1006-1010. Panchasara, H.V., Sequera, D.E., Schreiber, W.C. and Agrawal, A.K., 2009, “Emissions Reductions in Diesel and Kerosene Flames Using a Novel Fuel Injector”, Journal of Propulsion and Power, Vol. 25, No. 4, pp. 984-987. Sadasivuni, V. and Agrawal, A.K., 2009, “A novel meso-scale Combustion System for Operation with Liquid Fuels”, Proceedings of the Combustion Institute, Vol. 32, pp. 3155-3162. Simmons, B. and Agrawal, A.K., 2010, “Spray Characterization of a Flow-Blurring Atomizer”, Atomization and Sprays, Vol. 20, pp. 821-835. Simmons, B.M., Panchasara, H.V. and Agrawal, A.K., 2008, “Effect of fuel injection concept on combustion performance of liquid fuels”, Proceedings of 2008 Technical Meeting of the Central States Section of The Combustion Institute, Combustion Institute, Pittsburgh.

Lefebvre, A.H., 1983, “Gas Turbine Combustion”, Hemisphere, Washington, D.C.

Sovani, S.D., Sojka, P.E. and Lefebvre, A.H., 2001, “Effervescent atomization”, Progress in Energy and Combustion Science, Vol. 27, pp. 483-521.

Lefebvre, A.H., 1988, “A novel method of atomization with potential gas turbine applications”, Defense Sciences Journal, Vol. 38, pp. 353-362.

Wünning, J.A. and Wünning, J.G., 1997, “Flameless Oxidation to Reduce Thermal No-formation”, Progress in Energy and Combustion Science, Vol. 23, Issue 1, pp. 81-94.

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doi: 10.5028/jatm.v5i2.201

Effect of Fiber Optic Chromatic Dispersion on the Performance of Analog Optical Link with External Modulation Aiming at Aerospace Applications Antonio Alves Ferreira Júnior1, Olympio Lucchini Coutinho2, Carla de Sousa Martins3, William dos Santos Fegadolli2, José Antônio Justino Ribeiro1, Vilson Rosa de Almeida4, José Edimar Barbosa Oliveira2

Abstract: This paper addresses the subject of fiber optic chromatic dispersion effect on the performance of analog optical link with dual-drive electro-optic Mach-Zehnder modulator, aiming at aerospace applications. Thus, a direct detection link model that emphasizes both the modulator electronic drive and the dispersion characteristic of a linear optical fiber is discussed. Furthermore, a mathematical approach yielding a rather insightful analysis of the link performance for either optical double or single sideband modulation formats is fully discussed. It is worthwhile to point out that such modeling has the special feature of relying on a uniform nomenclature, which enables one to quickly retrieve a wide range of known results regarding optical fiber link performance that are already available on an ample literature. The model usefulness is illustrated by predicting the performance dependence of a direct detection fiber optic link with respect to the radiofrequency and link length. Results of numerical simulations for a link that comprises commercial optoelectronic components with potential for practical application on electronic warfare field were also provided. Keywords: Dual-drive Mach-Zehnder modulator, Analog fiber optic link, Fiber optic chromatic dispersion, Optical single sideband modulation, Optical double sideband modulation.

INTRODUCTION Due to the increasing evidence that radio-overfiber technology will be playing a major role in global interconnectivity, many efforts have been directed toward researches and development on the field of fiber optic link. A great deal of emphasis continues to be driven by important military and commercial demands, which aim at previously unachievable performance on the subjects of radiofrequency (RF) and microwave signal processing, radio-over-fiber, and antenna-remoting (Yao, 2012a, 2012b). Nowadays, analog photonic links have attracted significant interest in many applications, such as phased array antennas, radar systems, broadband cable-television (CATV) networks, ROF access wireless communications, and so on (Capmany et al., 2013; Yao, 2012c; Zhang et al., 2012a, 2012b; Wu et al., 2011). Aiming at aerospace applications, the remote radar antenna could be placed at a distance of several kilometers from the central office, and the generated radar signals could be distributed to other antennas for tracking an aircraft, or to other central offices (Oliveira et al., 1999; Coutinho et al., 2011; Lim et al., 2009). This versatility is very interesting because human resources and equipments can be allocated in a safety and controlled place, while the remote radar antenna is

1.Instituto Nacional de Telecomunicações – Santa Rita do Sapucaí/MG – Brazil 2.Instituto Tecnológico de Aeronáutica – São José dos Campos/SP – Brazil 3.Instituto de Pesquisas da Marinha – Rio de Janeiro/RJ – Brazil 4.Instituto de Estudos Avançados – São José dos Campos/SP – Brazil Author for correspondence: Antonio Alves Ferreira Júnior | Instituto Nacional de Telecomunicações | Avenida João de Camargo, 510 | CEP 37.540.000 Santa Rita do Sapucaí/MG – Brazil | E-mail: antonioa@inatel.br Received: 20/11/12 | Accepted: 09/04/13

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206

Ferreira Júnior, A.A., Coutinho, O.L., Martins, C.S., Fegadolli, W.D.S., Ribeiro, J.A.J., Almeida, V.R. and Oliveira, J.E.B.

located at field, as suggested in Fig. 1a. A central office that is connected to a large number of base stations via optical fiber may be used in a high capacity metropolitan optical fiber network to distribute data signals from various communications systems to users or to another optical fiber network area, as illustrated in Fig. 1b (Yao, 2012b; Lim et al., 2010). At the input end of such links, an optical laser diode generates a carrier at a desired optical wavelength, and a dualdrive electro-optic Mach-Zehnder modulator (DD-MZM) imposes an analog RF signal (e.g. radar signal) on the optical carrier. This signal is applied to an optical fiber link, whereas at the output end of the link a photodetector (PD) is employed to recover the analog RF signal from its optical carrier, and then processed by a RF front-end and delivered to a load (e.g. remote radar antenna). It is worthwhile to point out that the DD-MZM plays an important role in the link for it enables the wideband implementation of either optical

Fiber optic link

Central office: - Human resources - Radar signal generator - Video monitoring - Dara acquisition, processing and control Electrical signals Optical signals

Fiber optic link Central office (a)

Remote radar antenna

users

High capacity metropolitan optical fiber network

users Local area optical fiber network

base stations

STATEMENT OF THE PROBLEM A typical schematic representation of the IM/DD link with a transmitter, an optical channel, and a receiver is illustrated in Fig. 2a. In Fig. 2b an external electro-optic modulator electronic driver is emphasized. At the input of the fiber optic link, a continuous wave from a distributed feedback single-mode laser diode (DFB-LD) generates an optical carrier at a desired wavelength/frequency with a complex optical field given by Yariv and Yeh (2007), as seen in Eq. 1:

E o (t ) = 2ξPo (t )e

To/from trunk network

base stations

single sideband (OSSB) or optical double sideband (ODSB) modulation formats. This publication is concerned with the effect of fiber optic chromatic dispersion on the performance of links that operate based on external intensity modulation and direct detection techniques, called IM/DD optical links configuration. Assuming a balanced 50/50 splitting ratio of the DD-MZM Y-junctions, a rigorous analysis of the chromatic dispersion effect on the performance of the analog link was provided by Corral et al. (2001). However, the expressions are in the form of infinite series. Such drawback is overcome in Cheng et al. (2005), where an analytical model, in which the modulation indexes of the two DD-MZM drives can be unbalanced, yields a closed-form expression for the power at the output of the detector. Nevertheless, fabrication tolerances make a balanced DD-MZM particularly difficult to achieve, hence practical modulators have a finite extinction rate. Therefore, a general model that allows the study of all these cases will be very helpful for the system design.

base stations

users

users (b) Figure 1. Fiber optic links (a) connecting a central office and the remote radar antenna aiming at aerospace applications, and (b) for data system communications.

j[ωot+φo]

(1)

where ωo is the mean optical frequency, ϕo is an arbitrary initial optical phase, Po(t) is the optical power, and ξ (ohms per square meter) is a constant that depends on both the laser beam effective cross-section and the optical wave impedance. The present publication relies on the often used approach in the analysis of IM/DD optical links according to which the laser average power and its phase are time invariant (Corral et al., 2001; Cheng et al., 2005). In Fig. 2b one should notice that the optical power delivered by the laser diode reaches the input Y-junction of the integrated z-cut LiNbO3 DD-MZM, and then it is divided into two parcels according to a splitting ratio, determined

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.205-216, Apr.-Jun., 2013

Effect of Fiber Optic Chromatic Dispersion on the Performance of Analog Optical Link with External Modulation Aiming at Aerospace Applications

Transmitter

Optical channel

Eo(t)

Electrooptic modulator

EMZM(t)

Ef(t)

(t)

Dispersive optical fiber

Eo(t)

y r1

r2 EMZM(t) 1 - r2

v2(t) Eo(t)

θ1

(90º or 180º)

vg(t)

z-cut LiNbO3

1 - r1

0º Hybrid coupler

(a)

Electrical signals Opticalsignals

RF data electrodes

Receiver Remote radar Photodetector antenna

Laser

207

EMZM(t)

DD-MZM

Optical waveguides

(a)

θ2

v1(t)

RF data electrodes

(b) v1(t)

Figure 2. Overall architecture of the IM/DD analog fiber optic link, where (a) shows the transmitter, optical channel and receiver, and (b) presents the external electro-optic modulator with the electronic driver.

by the Y-junction power transmission coefficient r1 (Lin et al., 2008). The simplified view of an integrated DD-MZM is illustrated in Fig. 3 (Morant et al., 2011; Janner et al., 2008), where (A) shows the top view in which the optical waveguides are properly positioned with respect to the RF modulation field pattern, and (B) presents the cross-section view. Once a MZM’s configuration is specified, as shown in Fig. 3, its performance dependence on substrate orientation and geometry of electrodes can be predicted through the variation of the optical phase factor. Using a standard perturbation analysis, such variation turns into Eq. 2 (Kitano and Oliveira, 2000):

, TM ΔβTE = op

+∞ +∞



∫ ∫E

∗

(x, z) ⋅ [− εii εjjrijkE k(m) (x, z)]ETE,TM(x, z)dxdz 

TE , TM

−∞ −∞

ωo2 με0 , TM 2βTE op

+∞ +∞

∫∫



(2)



∗ ETE , TM (x, z) . E TE , TM (x, z) dxdz

−∞ −∞

where βopTE,TM and ETE,TM are the unperturbed optical phase factor and electric field for TE or TM modes, respectively; Ek(m) is the RF modulation electric field; rijk and εii are the components of the electro-optic tensor and electric permittivity of LiNbO3, respectively. Equation 2 shows that as a consequence of the electro-optic effect, a RF signal can be used to control the phase of the optical field associated with each optical power parcels as they propagate through the

v2(t)

z-cut LiNbO3 Optical waveguides

(b)

Figure 3. Simplified integrated dual-drive electro-optic MachZehnder modulator (DD-MZM) scheme with a z-cut LiNbO3 substrate using an optical transverse magnetic (TM) mode, where (a) is the top view showing transmission coefficients of the Y-junctions, and (b) demonstrates the cross-section view.

distinct arms of the DD-MZM. It is worthwhile to point out that in the configuration selected in Fig. 3 the optical guided mode has TM polarization, since it enables the use of the strongest LiNbO3 electro-optic coefficient, namely r33. The RF signal, henceforth named modulation signal, must generate an electric field with both a temporal and a spatial pattern adequately distributed in order to reach some key performance requirements, such as low RF power consumption and wide RF bandwidth (Kitano and Oliveira, 2000; Oliveira and Ribeiro, 2000). A great deal of such control may be achieved through the drive electronics, by properly choosing the phase shift (θ1) and the bias (θ2) of the electrical signal applied to the modulator electrodes, as indicated in Fig. 2b. According to Fig. 2, the instantaneous values of the modulating signals applied to the lower and upper electrodes of MZM, are as in Eqs. 3a and 3b:

v1 (t ) = V1 cos(ω RF t + θ1 )

(3a)

v 2 (t ) = V2 cos (ω RF t )

(3b)

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.205-216, Apr.-Jun., 2013

Ferreira Júnior, A.A., Coutinho, O.L., Martins, C.S., Fegadolli, W.D.S., Ribeiro, J.A.J., Almeida, V.R. and Oliveira, J.E.B.

208

where V1 and V2 are the amplitudes of signals in the lower and upper arms, ωRF is the angular frequency of the RF signal, and θ1 is the phase difference between the signals. The optical phase variations introduced in the arms of the modulator through linear electro-optic effect are given by Eq. 4:

φ1 (t ) =

π v1 (t ) = m1 cos (ω RF t + θ1 ) Vπ

(4a)

v 2 (t ) = V2 cos (ω RF t )

φ b (t ) =

(4b)

π Vb = θ 2 Vπ

(4c)

where Vπ is the MZM half-wave switching voltage that can be calculated using Eq. 2, and θ2 is the phase variation due to the voltage bias applied to the proper access. The coefficients m1 and m2 are the modulation indexes due to their signals in the lower and upper arms, which are given, respectively, by Eqs. 5a and 5b: m1 =

πV1 Vπ

(5a)

m2 =

πV2 Vπ

(5b)

with electric field given by Eq. 6 feeds a spool of standard single-mode optical fiber (SSMF) with a step-index profile, circular dielectric waveguide and length L, as illustrated in Fig. 4a. This simplified representation has n1 and n2 as the refractive indexes of the core and cladding with radius a and b, respectively (Yariv and Yeh, 2007). As an example, typical values of core and cladding diameters of a commercial fiber is 8.2 and 125 µm, respectively (Corning®, 2002). For instance, in the fiber modeling, a fused silica glass SSMF operating at 1,550 nm wavelength is considered to be linear with constant loss α(ω) (dB per kilometer), whereas the phase factor β(ω) (radians per meter) exhibits dependence with respect to the frequency deviation and chromatic dispersion. The optical field signal is affected by the attenuation and the phase factors after propagates through an optical fiber with length L, as shown in Fig. 4a. In order to achieve different values for the chromatic dispersion parameter, optical fibers with index profiles as illustrated in Fig. 4b are often used to this purpose, like the nonzerodispersion shifted (NZ-DSF) and the zero-dispersion shifted (DSF) (Agrawal, 2002; Li and Nolan, 2008). In the model of fiber optic propagation characteristics, one should bear in mind the presence of three phenomena in the fiber channel, which are different in nature, occur

SSMF step-index profile cladding

Based on the schematic representation illustrated in Fig. 3a and taking into account the splitting ratio of the output Y-junction r2, it can be shown that the optical electrical field at the output of the DD-MZM has a complex form given by Eq. 6:

{

E MZM (t ) = E o e jωot r1 r2 e j[m1cos(ωRF t+θ1)+ θ2] + +

(1 − r1 )(1 − r2 )e

jm2cos(ωRF t )

}

core

2a 2b

L α (ω),β (ω),

e jωot

n2 cross-section view

(a) NZ-DSF index profile

DSF index profile

center core ring core

(6)

where Eo=√(2ξPo). It should be pointed out that Eq. 6 applies to DD-MZM with both arbitrary splitting ratio and modulation signals. Such general situation often occurs in the real world, either at the fabrication stage of the modulator or in field applications. The optical signal at the output of the modulator

e jωote − [ (ω) + jβ (ω)] L

center core

trench core

(b) Figure 4. (a) A simplified representation of a step-index profile standard single-mode optical fiber (SSMF) with circular dielectric waveguide, and the optical signal affected by the attenuation and phase factors after being propagated through an optical fiber with length L; (b) Index profiles often used to nonzero-dispersion shifted (NZ-DSF) and the zerodispersion shifted (DSF) optical fibers.

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Effect of Fiber Optic Chromatic Dispersion on the Performance of Analog Optical Link with External Modulation Aiming at Aerospace Applications

simultaneously, and influence each other, namely: noise, filtering, and Kerr nonlinearity (Essiambre et al., 2010). This publication is mainly concerned with the filtering phenomenon that stems from the chromatic dispersion of the fiber, including waveguide and material (Winzer and Essiambre, 2006). In order to understand these characteristics, for a SSMF we will use the Fig. 5 with the results that were published in Essiambre et al. (2010) and Li and Nolan (2008). Regarding SSMF attenuation, as see in Fig. 5a (Essiambre et al., 2010), the 1,550 nm transmission window has the lowest attenuation value, around 0.2 dB/km, compared with the 1,310 nm transmission one, which is around 0.35 dB/km. However, the SSMF chromatic dispersion value, red line in Fig. 5b (Li and Nolan, 2008), at 1,550 nm is around 17 ps/nm.km, while the 1,310 nm has zero-dispersion. The green and purple lines refer to NZ-DSF and DSF, respectively, where some types of index profiles for these fibers were presented in Fig. 4b.

O-band

E-band

0.4

OH absorptíon

0.35 0.3 0.25 0.2

S-band C-band L-band U-band

yle

ígh

Allwave SSMF

sca

EDFA

tte

rin

0.15 1200 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700 Wavelength (nm)

(a)

0.5

Attenuation (all fiber types)

SMF

10 3-8

0.4 0.3

0 Low water peak fiber

0.2 0.1 1100

EDFA band

NZ-DSF

-10

DSF

Dispersion (ps/nm.km)

Attenuation (dB/km)

0.6

1300

1400

1500

1600

1 β(ω) = β0 (ωo ) + β1 (ωo )(ω − ωo ) + β2 (ωo )(ω − ωo )2 + 2 (7) 1 + β3 (ωo )(ω − ωo )3 +  6

β 2 (ω o ) = −

-20 1200

The 1,550 nm window (C-band) is widely used for long-haul transmission system and the advance in research of erbiumdoped fibers amplifiers (EDFA) made possible the use of this device in wavelength-division multiplexing (WDM) systems. However, the DSF were not suitable for WDM, because the nonlinear effect of four-wave mixing (FWM) is the strongest when the dispersion is zero. Certain amount of dispersion is desirable to reduce the FWM effect, being the NZ-DSF proposed. Some techniques to design optical fibers have been developed to achieve a desired value for the chromatic dispersion parameter (Li and Nolan, 2008). All the optical signal spectral components will propagate through the fiber optic with different velocities, and the phase of each component will be changed by chromatic dispersion. Bearing in mind that an exact functional form is rarely known, its expansion in Taylor series around the carrier frequency ωo as Agrawal (2002) performed is useful (Eq. 7):

The high order terms were not considered. The four ones on the right side shows distinct dependence about the frequency deviation. The first term is constant and related to phase velocity of optical carrier, the second varies linearly, and β1(ωo) determines the group velocity that is related to the group delay. The third has a quadratic dependence and it is related to the derivative of group velocity with respect to the frequency. The interesting here is on β2(ωo) coefficient related to the fiber chromatic dispersion parameter D(λ), the optical carrier wavelength (λo), and the speed of light (c) in vacuum, according to Eq. 8 (Agrawal, 2002):

In absfrare orp d tío n

Fiber loss coefficient (dB/km)

0.5 0.45

209

1700

Wavelength (nm)

(b) Figure 5. Spectral dependence of fiber optic characteristics, where (a) is the behavior of attenuation factor (Essiambre et al., 2010), and (b) is its chromatic dispersion parameter for three types of fiber: standard single-mode optical fiber – SSMF (red), nonzero-dispersion shifted – NZ-DSF (green) and the zerodispersion shifted – DSF (purple) (Li and Nolan, 2008).

D (λ )λ2o 2 πc

(8)

While the phase factor β(ω) presents dependence with respect to the frequency, the chromatic dispersion parameter D(λ) has it with optical wavelength and can be modeled by a Taylor’s series expansion around the operation wavelength (Wandel and Kristensen, 2006). However, a practical insightful expression can be seen as in Eq. 9 (Corning®, 2002):

D (λ ) =

S0 4

⎛ λ4 ⎜λ − o ⎜ λ3 ⎝

⎞ ⎟ ⎟ ⎠

(9)

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.205-216, Apr.-Jun., 2013

Ferreira Júnior, A.A., Coutinho, O.L., Martins, C.S., Fegadolli, W.D.S., Ribeiro, J.A.J., Almeida, V.R. and Oliveira, J.E.B.

210

where S0 is the zero-dispersion slope and a typical value is less than 0.092 ps/nm2.km (Corning®, 2002), λ is the operation wavelength (nm), and λo is the zero-dispersion wavelength (nm). The β3(ωo) parameter in Eq. 7 can be obtained from the high order derivatives of phase factor, or it is defined as the derivative of β2(ωo) with respect to the frequency. It contributes to the calculation of the dispersion slope S(λ), which has dependence with optical wavelength, as Eq. 10 (Winzer and Essiambre, 2006):

S (λ ) =

(10)

At the output end of the SSMF, a square law PD transforms the photon stream into a RF electric current. When introducing the concept of PD responsivity, it can be shown that the electrical photocurrent is proportional to the incident average optical power, hence it is also to the magnitude of the optical Poynting vector. Assuming a uniform power distribution over the fiber cross section, the time dependent RF current is as in Eq. 11:

E f (t )E ∗f (t ) 2ξ

+ n(t )

(11)

where ℜ is the PD responsivity, ξ (ohms per square meter) is a constant that depends on both the fiber effective cross-section and the optical wave impedance, and Ef (t) is the optical electrical field at the fiber link output according to Fig. 2a. The n(t) accounts for PD additive noises sources, such as thermal and shot noises (Lim et al., 2009; Yariv and Yeh, 2007). However, the noise subject will not be addressed in this publication. As will be shown later, Eq. 11 reveals that by applying the fiber output to the PD, beating signals between the optical spectral components will generate harmonics of the original RF modulating signal. The characteristics of these depend on both the fiber optic chromatic dispersion and the modulation format, which will be used to estimate the performance of the link. OPTICAL FIBER LINK MODEL As previously stated, the present study is concerned with links based on DD-MZM having a 50/50 splitting ratio. Hence, using Eq. 6, the output electrical field in the complex form turns out to be expressed as Eq. 12:

E o jω ot ⎡ +∞ n e j J n (m1)e jn(ωRFt +θ1)e jθ2 + ⎢ 2 ⎣n= −∞ +∞ ⎤ j n J n (m 2 )e jn ωRF t ⎥ + n= −∞ ⎦

∑

(12)

where Jn(.) represents the first kind Bessel’s function with order n. By rewriting Eq. 12 in Eqs. 13 and 14:

E MZM (t ) =

d [D(λ )] = ⎛⎜ 4π3c ⎞⎟β 2 + ⎛⎜ 2π2c ⎞⎟ β 3 dλ ⎝ λ ⎠ ⎝ λ ⎠

i(t ) = ℜ

E MZM (t ) =

[

E o jωot +∞ e a ne jn ωRF t 2 n = −∞

∑

(13)

]

a n = j n J n (m1)e j (nθ1+θ2) + J n (m 2)

(14)

It is readily seen that the optical field at the DD-MZM output indeed consists of an infinite series of optical spectral components, i.e. an optical carrier component at ωo and an infinite number of sidebands, with frequencies ω = ωo ± nωRF and amplitude an. A small-signal analysis was performed in Ferreira Júnior et al. (2012), which enables one to identify the requirement that should be satisfied by the DD-MZM drive electronics in order to provide certain modulation formats. For example, single sideband (OSSB), double sideband (ODSB), and carrier suppressed (OCS) optical modulation formats can be obtained when the pair of parameters (θ1,θ2) obeys the following constraint: (π/2, ±π/2), (π, ±π/2), and (π, π), respectively. In order to further develop the analysis of the link, one should analyze again Eq. 13. Taking into account the linear nature of the fiber optic and bearing in mind the spectral composition of the optical field at the output of the DD-MZM, we tackled the effect of the chromatic dispersion with the help of Eq. 7. Thus, we have obtained the following expression for the phase factor of an optical spectral component with frequency equal to ω = ω o ±nω RF (Eq. 15):

1 β (ωo ± nωRF ) = β0 (ωo ) ± β1(ωo )nωRF + β2 (ωo )(nωRF )2 2 1 3 ± β3 (ωo)(nωRF ) +  6 (15) Using this result in combination with Maxwell’s equations, we undertook the time domain analysis of the propagation of the optical field given by Eq. 13 along a linear SSMF. The expression obtained for the output electrical field after propagation through a fiber with length L is given by Eq. 16:

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.205-216, Apr.-Jun., 2013

Effect of Fiber Optic Chromatic Dispersion on the Performance of Analog Optical Link with External Modulation Aiming at Aerospace Applications

− αdB L 20

E f (t ) = 10

j 1 (nωRF )2 β2 (ω o)L E o jωot +∞ e an e jnωRFte 2 (16) 2 n= −∞

∑

Once more, we remember the linear characteristics of the fiber optics under consideration. Therefore, it might be possible to benefit from standard techniques developed for frequency domain analysis of system. First, we took the Fourier’s transform of Eq. 16 from a linear system, and after some mathematical manipulations, we obtained Eq. 17 for the electrical field in the frequency domain: − αdBL 20 πE

E f (ω) = 10

+∞

∑

n = −∞

a nδ(ω − nω RF )e

j 1 (n ω RF)2 β2 (ωo )L 2

(17)

where δ represents the Dirac’s delta function. Therefore, we must be able to use the model to predict dependence on frequency of such current. To this aim, we first remember that the convolution theorem can be applied to rewrite the time domain expression of the PD current, as given by Eq. 11 in the frequency domain, as Eq. 18:

I (ω) = ℜ

E f (ω)

∗ E ∗f

(ω)

4πξ

(18)

spectral components of the PD current was rather cumbersome and yielded little physical insight, except when one assumed a small signal approximation. It is worth to remember such complexity mostly stems from the fact that the coefficient aN+kak* involves the product of Bessel’s function, as it is readily seen in Eq. 14. However, a few years ago such drawback was overcome through the application of Graf ’s addition theorem for Bessel’s functions (Cheng et al., 2005; Chi and Yao, 2008). In order to be able to take advantage of such theorem in the analysis presented in this publication, we have used Eq. 14 to calculate aN+kak* and then substituted the obtained result into Eq. 20. After some mathematical manipulations we obtained expressions for I(NωRF) and for the detected DC current (N=0), which besides allowing the retrieving of previous results, it also includes a few parameters such as the fiber attenuation, PD responsivity and laser output power. These were not explicitly accounted for in previous publications. Such expressions are given, respectively, by Eqs. 22 and 23:

I (Nω RF ) = 10

I (ω) = 2 π

+∞

N = −∞

I (Nω RF )

− α dB L = 10 10

φ = Nω2RF β 2 (ωo )L

ℜPo j e 4

Nφ +∞ 2

∑ a N+k a k e

k = −∞

∑ J N+k (m2 )J k (m 2)e jkφ +

(20)

(22)

k = −∞

⎡ ⎛ ⎤ φ+π ⎞ +∞ j ⎢N ⎜θ 1 + ⎟ +θ 2 ⎠ 2⎥⎦ ⎣ ⎝

∑ J N+k (m1)J k (m 2 )e jk(φ+θ ) + 1

k = −∞ ⎡ ⎛ φ+π ⎞ ⎤ ⎟ − θ2⎥ + ∞ ⎣ ⎝ 2 ⎠ ⎦

j ⎢N ⎜

− α dB L = 10 10

⎫ ⎪

∑ J N+k (m2 )J k (m1)e jk(φ−θ ) ⎬ 1

⎪⎭

k = −∞

I (0 ) jk φ

⎛ φ +π⎞ + ∞ ⎟ ⎝ 2 ⎠

jN ⎜

(19)

∗

ℜPo 4

∑

∑ I (Nω )δ(ω − Nω )

−αdB L 10

⎧⎪ jN ⎛⎜ θ1 + φ+π⎞⎟ + ∞ 2 ⎠ ⎝ J N+k (m1)J k (m1)e jkφ + ⎨e k = −∞ ⎪⎩ +e

where the mathematical symbol * denotes convolution. Then, Eqs. 19, 20 and 21 were obtained for the RF current Fourier’s transform, under the condition n=N+k:

211

+∞

ℜPo 4

∑ [J

k = −∞

2 k

(m1 ) + J k2 (m2 ) +

(23)

+ 2 J k (m1 )J k (m2 ) cos (kθ1 + θ 2 )]

(21)

Equation 19 was achieved without introducing any approximation and is in perfect agreement with results published by many authors (Corral et al., 2001; Cheng et al., 2005). Until a few years ago, using such formulas to predict the

Furthermore, Eqs. 6 and 22 enable to quickly retrieve previous results with DD-MZM having infinite extinction ratio (r1 = r2 = 0.5), and when the modulation indexes are equal (m1 = m2 = m). Since the intention was to compare our predictions with previous publications, Graf ’s addition

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.205-216, Apr.-Jun., 2013

212

Ferreira Júnior, A.A., Coutinho, O.L., Martins, C.S., Fegadolli, W.D.S., Ribeiro, J.A.J., Almeida, V.R. and Oliveira, J.E.B.

theorem was applied for Bessel’s functions (Abramowitz and Stegun, 1965) to Eq. 22, under the assumption that the modulation indexes are equal, resulting in Eq. 24:

I (Nω RF ) = 10

− α dB L 10

[

ℜPo . 4

]

⎧⎪ jN (θ + π ) ⎡ ⎛ φ ⎞⎤ 1 + e jNπ J N ⎢2 m sin ⎜ ⎟⎥ + ⎨e ⎪⎩ ⎝ 2 ⎠⎦ ⎣ ⎡ ⎛θ ⎤ ⎞ j ⎢ N ⎜ 1 + π ⎟ + θ 2⎥ ⎠ ⎣ ⎝ 2 ⎦

(24)

⎡ ⎛ φ + θ1 J N ⎢2 m sin ⎜⎜ ⎝ 2 ⎣

⎞⎤ +e ⎟⎟⎥ + ⎠⎦ ⎡ ⎛ θ1 ⎤ ⎞ ⎫ j ⎢ N ⎜ + π ⎟ −θ 2⎥ ⎡ ⎛ φ − θ1 ⎞ ⎤ ⎪ 2 ⎠ ⎦ J +e ⎣ ⎝ m 2 sin ⎜ ⎟ N⎢ ⎜ 2 ⎟⎥ ⎬ ⎝ ⎠⎦ ⎪ ⎣ ⎭ In this publication, the modeling of the analog fiber optic link is synthesized by Eq. 24. It enables the frequency domain analysis of how the fiber optic chromatic dispersion affects the link performance which employ DD-MZM. The ϕ parameter, which is given in Eq. 21, takes into account the harmonic order, RF, chromatic dispersion, and fiber optic length. The optical modulation format can be specified by properly selecting the parameters θ1 and θ2. This article follows the approach adopted in Cheng et al. (2005), and the two situations addressed are obtained when either θ1 = π (ODSB) or θ1 = π/2 (OSSB), with θ2 = π/2 for both cases. Usually, the performance of the fiber link is evaluated in terms of the RF power delivered to output load (RL), and the average power of the harmonic with order N is (Eq. 25):

PRL (Nω RF

) = 1 I (Nω RF 2

)

(25)

In order to compare the exact analytical model, Eqs. 24 and 25, with a particular case of small-signal approximation (m << 1), which is widely discussed in the literature (Lim et al., 2010), the detected RF fundamental (N = 1) power is (Eq. 26):

PRL (ω RF

⎛ −α dB L ⎜ 10 5 m2 P 2 ℜ 2 R o L )= ⎜ 8 ⎜ ⎜ ⎝

⎞ 2 2 ⎟ ⎛ πLDf RF λo ⎟ cos 2 ⎜ ⎜ c ⎟ ⎝ ⎟ ⎠

⎞ ⎟ ⎟ (26) ⎠

Impedance matching networks are often used at the DD-MZM input and PD output to provide the maximum signal power transfer, due to the frequency response of these

devices. In this work, all the impedances were considered purely resistive and matched. In Eq. 26, the modulation index (m) is related to signal power (PRF) and impedance (Zg) of the RF source, and to the DD-MZM input impedance (ZMZM). The RF power delivered to the load (PRL) is related to the PD output impedance (Coutinho et al., 2005). NUMERICAL RESULTS AND DISCUSSION The numerical simulations were developed by using commercial components with parameters specified in Table 1. To validate our model, first of all we developed our simulations with exactly the same link parameters used in Cheng et al. (2005) and they were presented in Ferreira Júnior et al. (2012). Figure 6a shows the normalized RF fundamental power for 10 GHz frequency in function of fiber optic length, for both exact and small-signal approximations, using the ODSB modulation: (θ1 , θ2) = (π , π/2). It is observed that the results are in perfect agreement and the modeling presented can recover previous simulations (Lim et al., 2010). However, if the modulation index increases, i.e. large-signal condition, the small-signal approximation moves away from the exact analysis as shown in Fig. 6b. It can be seen that the increases in a RF power do not improve the performance of the link. In order to observe the fiber optic length (L) in which the RF power is minimum, this periodic variation, under the condition

Table 1. Typical values of parameters used in the simulation Parameter description

Symbol

Value

RF source impedance

50 Ω

RF load impedance

50 Ω

RF power applied to DD-MZM

PRF

1 mW

Laser optical power

1 mW

Laser wavelength

λo

1,550 nm

DD-MZM half-wave voltage

Vπ

DD-MZM input impedance

ZMZM

50 Ω

SSMF fiber attenuation @ 1,550 nm (Corning®, 2002)

αdB

0.2 dB/km

SSMF fiber chromatic dispersion @ 1,550 nm (Corning®, 2002)

17 ps/nm.km

Speed of light in vacuum

3x108 m/s

ℜ

0.5 A/W

PD responsivity

RF: radiofrequency; DD-MZM: dual-drive electro-optic Mach-Zehnder modulator; SSMF: standard single-mode optical fiber; PD: photodetector.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.205-216, Apr.-Jun., 2013

Effect of Fiber Optic Chromatic Dispersion on the Performance of Analog Optical Link with External Modulation Aiming at Aerospace Applications

with low and equal modulation indexes (m1 = m2 = m << 1) and fundamental RF frequency (N = 1), can be predicted by Eq. 27:

Lp =

(2 p + 1) c 2 2 2 Df RF λo

(27)

where p = 0, 1, 2, etc. The dispersion effect exhibits a cyclic behavior and the period length is determined by Eq. 28:

ΔL =

c 2 2 Df RF λo

(28)

Relative detected RF to DC power, dB

Exact analysis Small-signal approximation

-10 -20 -30 -40 -50 -60 -70

80 100 120 140 160 180 200 220 240 Fiber optic lenght (L), km

(a)

Similar results were presented considering only the first minimum point (Gliese et al., 1996). The influence of chirp effect in the fiber length in which the RF power is minimum was observed in Smith et al. (1997). Based on Eqs. 6 and 22, the authors have been investigating the chirp modeling of DD-MZM as a function of both the splitting ratio and modulation indexes, and the results will be published elsewhere. For instance, the relative detected RF fundamental power to DC level versus RF, with fiber optic length (L) equals 40 km, for ODSB push-pull (m1 = m2 = m, θ1 = π, θ2 = π/2), single-arm (m2 = 0, θ1 = π, θ2 = +π/2 and −π/2), and OSSB (m1 = m2 = m, θ1 = π/2, θ2 = π/2) modulations are presented in Fig. 7. It is observed in Fig. 7 that the analytical formulation presented in this paper is in agreement with experimental results obtained by Han et al. (2003), which the expressions are in infinite series form. For a single-arm ODSB modulation, the frequency that the detected power is minimized could be changed by adjusting the bias parameter θ2. The dependence of the fundamental RF power for the ODSB modulation is strongly affected by the chromatic dispersion and the power is minimized in approximately 10 GHz. This is the so-called notch filter like behavior. For OSSB modulation, the link exhibits the special feature of RF fundamental power displaying very low sensitivity with respect to both the fiber length and the RF. Such unique feature has been

-10

-20

-10

Relative detected RF to DC power, dB

-30 -40 -50 -60 -70

Exact analysis Small-signal approximation 0

80 100 120 140 160 180 200 220 240 Fiber optic lenght (L), km

(b)

-20 -30 -40 -50 -60

Push-pull Single-arm (+θ2)

-70 -80

Single-arm (–θ2)

-90 -100

Figure 6. Detected radiofrequency (RF) fundamental (N = 1) power normalized to the direct current (DC) level versus fiber length, for exact and small-signal approximations, under conditions: (a) small- (m = 0.2), and (b) large-signals (m = 1.2). The RF is equal to 10 GHz and uses optical double sideband (ODSB) modulation (θ1, θ2) = (π, π/2).

213

OSSB 0

6 7 8 9 10 11 12 13 14 15 Frequency (fRF), GHz

Figure 7. Detected fundamental radiofrequency – RF (N = 1) power normalized to the direct current (DC) level versus frequency for optical double sideband (ODSB) push-pull and single-arm, and optical single sideband (OSSB) modulations, with θ2 = π/2, L = 40 km.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.205-216, Apr.-Jun., 2013

Ferreira Júnior, A.A., Coutinho, O.L., Martins, C.S., Fegadolli, W.D.S., Ribeiro, J.A.J., Almeida, V.R. and Oliveira, J.E.B.

5 0 Relative detected RF to DC power, dB

widely exploited in practical applications on the subject of microwave photonics, as in aerospace and long-haul fiber optical telecommunications (Urick et al., 2011). It is important to point out that the principle of energy conservation is obeyed, i.e. in this analysis the fundamental RF power (N = 1) is minimized in a specific RF for the ODSB modulation (θ1, θ2) = (π, π/2), according to Fig. 7. The energy is transferred to the harmonics of superior orders (N = 2, 3,…) and DC level (N = 0). The summation of RF power of all spectral components is the same for each value of RF (or fiber optic length). Figure 8 shows the detected RF power versus RF for N = 0, 1, 2, with fiber optic length (L) equals to 40 km. In order to be able to better illustrate the effect of the chromatic dispersion in the RF fundamental (N = 1) power, it is convenient to analyze its dependence with respect to the length of the fiber. To this aim we first tackled the ODSB modulation (θ1, θ2) = (π, π/2), and the results are shown in Fig. 9. As can be seen, irrespective of the RF, the chromatic dispersion results in a periodic variation of the RF power as the fiber length increases. The position along the fiber at which the RF power is minimized depends on the RF. For example, when the RF is 20 GHz, the first minimum occurs at approximately 10 km, whereas for a 10 GHz frequency this is nearly 36 km. Using Eqs. 27 and 28 allows one to calculate the fiber length in which the RF power is minimum.

-10 -20 -30 -40 -50 -60 -70

N=0 N=1 N=2

-80 -90

-100

6 7 8 9 10 11 12 13 14 15 Frequency (fRF), GHz

Figure 8. Detected radiofrequency (RF) power normalized to the direct current (DC) level versus frequency, with N = 0 (DC), N = 1 (fundamental) and N = 2 (second harmonic), for optical double sideband (ODSB) modulation (θ1, θ2) = (π, π/2) with L = 40 km.

0 Relative detected RF to DC power, dB

214

-10 -20 -30 -40 -50 -60 -70

f1 = 10 GHz

-80

f2 = 15 GHz

-90

CONCLUSION

-100

f3 = 20 GHz 0

Fiber Optic length (L), km

This publication presented a very comprehensive analytical model that enables the analysis of the effect of fiber optic chromatic dispersion in the performance of analog fiber optic link with DD-MZM. The model besides relaying on parameters that suits experimental researchers, also allows one to retrieve important results widely available in the literature. Using some commercial components and devices, we performed numerical simulations that yielded results, which seem to be of practical interest. The authors are working towards designing, implementing, and characterizing fiber link based on the model developed.

Figure 9. Detected radiofrequency (RF) fundamental (N = 1) power normalized to the direct current (DC) level versus fiber optic length, with RF as a parameter for optical double sideband (ODSB) modulation (θ1, θ2) = (π, π/2).

ACKNOWLEDGMENTS To the Electronic Warfare Laboratory at the Instituto Tecnológico de Aeronáutica (ITA) and the Instituto Nacional de Telecomunicações (INATEL) for their support in this research.

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Effect of Fiber Optic Chromatic Dispersion on the Performance of Analog Optical Link with External Modulation Aiming at Aerospace Applications

215

REFERENCES Abramowitz, M. and Stegun, I., 1965, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables”, Dover Publications, New York.

Kitano, C. and Oliveira, J.E.B., 2000, “Dispositivos à Óptica Integrada para Aplicações em Telecomunicações”, Revista Telecomunicações, Vol. 3, No. 2, pp. 27-38.

Agrawal, G.P., 2002, “Fiber-Optic Communication 3rd edition, John Wiley & Sons, New York.

Li, M.J. and Nolan, D.A., 2008, “Optical Transmission Fiber Design Evolution”, Journal of Lightwave Technology, Vol. 26, No. 9, pp. 10791092. doi:10.1109/JLT.2008.922150.

Systems”,

Capmany, J. et al., 2013, “Microwave Photonic Signal Processing”, Journal of Lightwave Technology, Vol. 31, No. 4, pp. 571-586. doi:10.1109/JLT.2012.2222348. Cheng, L. et al., 2005, “An Exact Analytical Model for Dispersive Transmission in Microwave Fiber-Optic Links Using Mach-Zehnder External Modulator”, IEEE Photonics Technology Letters, Vol. 17, No. 7, pp. 1525-1527. doi:10.1109/LPT.2005.848563. Chi, H. and Yao, J., 2008, “Power Distribution of Phase-Modulated Microwave Signals in a Dispersive Fiber-Optic Link”, IEEE Photonics Technology Letters, Vol. 20, No. 4, pp. 315-317. doi:10.1109/ LPT.2007.915653. Corning®, 2002, “SMF-28™ Optical Fiber Product Information”. Retrieved in April 29, 2013, from http://www.photonics.byu.edu/ FiberOpticConnectors.parts/images/smf28.pdf. Corral, J.L. et al., 2001, “General expressions for IM/DD dispersive analog optical links with external modulation or optical up-conversion in Mach-Zehnder electrooptical modulator”, IEEE Transactions on Microwave Theory and Techniques, Vol. 49, No. 10, pp. 1968-1976. doi:10.1109/22.954816. Coutinho, O.L. et al., 2005, “Analysis of analog fiber optical links based on DSB+C and SSB+C modulation techniques”, In: International Conference on Microwave and Optoelectronics – SBMO/IEEE MTT-S, pp. 439-443. doi:10.1109/IMOC.2005.1580038. Coutinho, O.L. et al., 2011, “Uso de redes de comunicações ópticas para transmissão e distribuição de emissores radar”, In: Simpósio de Aplicações Operacionais em Áreas de Defesa – XIII SIGE, São José dos Campos, SP, Brazil. Essiambre, R.J. et al., 2010, “Capacity limits of optical fiber networks”, Journal of Lightwave Technology, Vol. 28, No. 4, pp. 662701. doi:10.1109/JLT.2009.2039464. Ferreira Júnior, A.A. et al., 2012, “Effect of fiber optic chromatic dispersion on the performance of analog optical link with dual-drive MachZehnder modulator”, In: Simpósio de Aplicações Operacionais em Área de Defesa – XIV SIGE, pp. 119-126, São José dos Campos, SP, Brazil. Gliese, U. et al., 1996, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links”, IEEE Transactions on Microwave Theory and Techniques, Vol. 44, No. 10, pp. 1716-1724. doi:10.1109/22.538964. Han, J. et al., 2003, “Reduction of fiber chromatic dispersion effects in fiber-wireless and photonic time-stretching system using polymer modulators”, Journal of Lightwave Technology, Vol. 21, No. 6, pp. 1504-1509. doi:10.1109/JLT.2003.812155. Janner, D. et al., 2008, “Waveguide electro-optic modulation in micro-engineered LiNbO3”, Journal of Optics A, No. 10, pp. 01-06. doi:10.1088/1464-4258/10/10/104003.

Lim, C. et al., 2010, “Fiber-Wireless Networks and Subsystem Technologies”, Journal of Lightwave Technology, Vol. 28, No. 4, pp. 390-405. doi:10.1109/JLT.2009.2031423. Lim, W. et al., 2009, “Analytical time-domain model for radio over free space optical military communication systems under turbulence channels”, In: IEEE Military Communications Conference – MILCOM 2009, Paper 901734, pp. 1-5. doi:10.1109/MILCOM.2009.5379930. Lin, C. et al., 2008, “Impact of nonlinear transfer function and imperfect ratio of MZM on optical up-conversion employing double sideband with carrier suppression modulation”, Journal of Lightwave Technology, Vol. 26, No. 15, pp. 2449-2459. doi:10.1109/JLT.2008.927160. Morant, M. et al., 2011, “Dual-drive LiNbO3 interferometric MachZehnder architecture with extended linear regime for high peak-toaverage OFDM-based communication systems”, Optics Express, Vol. 19, No. 26, pp. 450-456. doi:10.1364/OE.19.00B452. Oliveira, J.E.B. et al., 1999, “Trends in photonics applied to electronic warfare at Brazilian airforce”, In: International Microwave and Optoelectronics Conference – SBMO/IEEE MTT-S, pp. 599-602, Rio de Janeiro, RJ, Brazil. doi:10.1109/IMOC.1999.866252. Oliveira, J.E.B. and Ribeiro, J.A.J., 2000, “Interfaces para enlaces de fibra óptica de alta velocidade”, Revista Telecomunicações, Vol. 3, No. 2, pp. 65-75. Smith, G.H. et al., 1997, “Overcoming Chromatic-Dispersion Effects in Fiber-Wireless Systems Incorporating External Modulators”, IEEE Transactions on Microwave Theory and Techniques, Vol. 45, No. 8, pp. 1410-1415. doi:10.1109/22.618444. Urick, V.J. et al., 2011, “Long-Haul Analog Photonics”, Journal of Lightwave Technology, Vol. 29, No. 8, pp. 1182-1205. doi:10.1109/ JLT.2011.2119292. Wandel, M. and Kristensen, P., 2006, “Fiber designs for high figure of merit and high slope dispersion compensating fibers”, Journal of Optical and Fiber Communications Research, Vol. 3, No. 1, pp. 25-60. doi:10.1007/s10297-005-0061-1. Winzer, P.J. and Essiambre, R.J., 2006, “Advanced Optical Modulation Formats”, Proceedings of the IEEE, Vol. 94, No. 5, pp. 952-985. doi:10.1109/JPROC.2006.873438. Wu, P.Y. et al., 2011, “An upconverted phase-modulated fiber optical CATV transport system”, Journal of Lightwave Technology, Vol. 29, No. 16, pp. 2422-2427. doi:10.1109/JLT.2011.2160330. Yao, J., 2012a, “A tutorial on microwave photonics I”, IEEE Photonics Society Newsletter, Vol. 26, No. 2, pp. 4-12. Yao, J., 2012b, “A tutorial on microwave photonics II”, IEEE Photonics Society Newsletter, Vol. 26, No. 3, pp. 5-12.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.205-216, Apr.-Jun., 2013

216

Ferreira Júnior, A.A., Coutinho, O.L., Martins, C.S., Fegadolli, W.D.S., Ribeiro, J.A.J., Almeida, V.R. and Oliveira, J.E.B.

Yao, J., 2012c, “Microwave Photonics,” In: IEEE International Workshop on Electromagnetics, Applications and Student Innovation – iWEM, pp. 1-2. doi:10.1109/iWEM.2012.6320333.

link with compensation of the dispersion-induced power fading”,

Yariv, A. and Yeh, P., 2007, “Photonics: Optical Electronics in Modern Communications”, 6th edition, Oxford University Press, New York.

Zhang, G. et al., 2012b, “Postcompensation for nonlinearity of Mach-

Zhang, H. et al., 2012a, “Polarization-modulated analog photonic

808. doi:10.1364/OL.37.000806.

Optics Letters, Vol. 37, No. 5, pp. 866-868. doi:10.1364/ OL.37.000866.

Zehnder modulator in radio-over-fiber system based on second-order optical sideband processing”, Optics Letters, Vol. 37, No. 5, pp. 806-

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doi: 10.5028/jatm.v5i2.206

Determining the Fixed Pattern Noise of a CMOS Sensor: Improving the Sensibility of Autonomous Star Trackers Eduardo dos Santos Pereira1

ABSTRACT: Autonomous star trackers are optical-electronic devices used for attitude determination of artificial satellites, having as a reference for this computation the positions of stars. There is one autonomous star tracker in development at the Aerospace Electronics Division of the Brazilian National Institute for Space Research. The autonomous star tracker imager is a complementary metal-oxide-semiconductor active pixel sensor, consisting of an integrated circuit with an array of them. Each pixel has a photodetector and an active amplifier. Since it has many amplifiers, the active pixel sensor has an additional fixed pattern noise, therefore its characterization is different from the traditional method used for the charge coupled devices. With this experiment, it was observed that the mean value per columns of fixed pattern noise is ~100% greater than the mean value of the pixel one. Taking into account this result, modeling the pixel fixed pattern noise will not be important to improve the autonomous star tracker sensibility. Furthermore, the random noise value was less than 1% of the fixed pattern noise range data, being possible to estimate it. In this work, we presented the fixed pattern noise new parametric model, which has a good agreement when compared with the experimental data. It was calculated Pearson’s product-moment correlation coefficient between the model and the observed data, in order to quantify the model accuracy and it was obtained 99% for flat field and 79% for dark current. KEYWORDS: Star trackers, Aerospace systems, Attitude determination, Spacecraft, Applied astronomy.

INTRODUCTION Autonomous star trackers (AST) are optoelectronic instruments used for attitude determination of a satellite by observing stars (Liebe, 1995, Liu et al., 2011). The precision of attitude determination depends on the accuracy of the AST image registration. Thus, the calibration of a fixed pattern noise (FPN) of the AST image sensor has an important role. The FPN is a variation in the output pixel values, under uniform illumination, due to device and interconnection mismatches across an image sensor. In the case of complementary metaloxide-semiconductor (CMOS) sensors, passive and active pixel (PPS and APS), there are several amplifiers in which some are shared by pixels and others are not. Thereby, in order to determine the FPN, it is necessary to take into account not only the pixel noise, but also that of the column (Gamal et al., 1998, Bigas et al., 2006). On the other hand, Schöberl et al. (2009) showed that it is possible to model the FPN as a function of the image acquisition integration time, with a nonlinear parametric model. However, for that model, it is necessary to find a set of parameters for each pixel, and for a 6 MPixel sensor 75 Mbytes are required to save those data. Another issue presented by Schöberl et al. (2009) is concerning the fact of assuming dark current as a constant for each pixel as the model of Pillman et al. (2006) for describing the FPN with a linear algorithm. However, these authors also presumed that the segmented linear and quadratic models have a better characterization of the FPN than a pure linear one. In this work, we were mainly interested in determining and modeling the FPN of the CMOS used in the AST. This

1.Instituto Nacional de Pesquisas Espaciais – São José dos Campos/SP – Brazil Author for correspondence: Eduardo dos Santos Pereira | Instituto Nacional de Pesquisas Espaciais, Divisão de Eletrônica Aeroespacial | Avenida dos Astronautas, 1.758 – Jardim da Granja | CEP 12.227-010 – São José dos Campos/SP – Brazil | E-mail: eduardopereira@dea.inpe.br Received: 30/11/12 | Accepted: 25/03/13

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Pereira, E.S.

where W is the vector direction of stars into the AST reference frame, which is given by Eq. 3 (Xing et al., 2006 and Liu et al., 2011):

aUtoNoMoUS Star SENSor The AST consists of a pinhole imaging system that measures the direction vector of a star in its own reference frame (Zenick, 2003, Xing et al., 2006, Liu et al., 2011). Firstly, the stars into the field of view (FOV) are registered by the CMOS APS, secondly they are recognized by a pattern recognition routine. Finally, the stars are compared with an internal catalog and the attitude matrix of the AST is calculated. In Fig. 1 a simplified block diagram of AST functionality is presented. For the calculus of AST attitude matrix, M, it is necessary to know a vector direction, v, of the star in an inertial frame. The value of v is obtained from the right ascension, α, and declination, δ, from a master catalog, as Eq. 1:

⎡-(x-x0) 1 -(y-y0) 2 2 √(x-x0) (y-y0) +f ⎣ f 2

⎡

procedure would allow us to perform a data correction before starting the process of pattern recognition from stars. Such review will improve the sensibility of the AST and therefore reduce errors on the satellite attitude determination.

⎣

218

n L = 1 ∑ ai||Mvi - Wi||2 2 i=1

(4)

where a’i are the weights and n is the number of observations. This equation is also called Wahba’s problem (Wahba, 1965).

⎣

(1)

θij

⎡ | ⎣

⎡

Then, a new catalog is generated. The attitude matrix should satisfy (Eq. 2): ,

(3)

where x0 and y0 represent the intersection points of the focal plane and the optical axis; x and y are the observed star locations on the detector plane and ƒ is the focal length of the AST camera. In Fig. 2 an illustration of the AST reference, o, and inertial frames, O’, is presented. Usually, the matrix M can be estimated by minimizing the least-square error (Eq. 4):

⎡vx ⎡cos(α) cos(δ) v = | vy = | sin(α) cos(δ) | . ⎣vz ⎣ sin(δ)

W = Mv

, ,

Lens system

y o (x0, y0)

(2)

O’ Yn

Pinhole Lens Xn

Image Field of View

Active Pixel CMOS Imager

Pattern Recognition Software

Processor

Figure 2. Star tracker measurement. the O represents the inertial referential frame and O’ is the autonomous star trackers referential frame. adapted from liu et al. (2011).

EStiMatioN aNd ModEliNG tHE FiXEd PattErN NoiSE

Star Catalog Attitude Estimation (x, y, z)

Figure 1. Simplified block diagram of a star tracker. adapted from Zenick (2003).

To estimate the FPN, we started considering the method described by Gamal et al. (1998). Thus, from the sample of images, the FPN is determined by column and pixel, which are in Eqs. 5 and 6, respectively:

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.217-222, Apr.-Jun., 2013

Determining the Fixed Pattern Noise of a CMOS Sensor: Improving the Sensibility of Autonomous Star Trackers

N Yj = 1 ∑ Fij , , N i=1

(5)

Xij = Fij - Yj

(6)

, ,

where Fij is an average estimator that is obtained from a sample of AST images, and N is the number of columns of the images. Fij is determined as follows: • obtain a sample of k images from the AST; • in order to reduce the random noise, the mean value of the sample should be calculated; • from the result of the image, the average value of all pixels is found; • Fij is determined through the subtraction from the mean image of the average value of all their pixels, each at a time. The variances, by column and pixel, are presented in Eqs. 7 and 8: 2 1 M ∑ Y M - 1 j=1 j

σ Y2 = σ x2 =

, ,

N M 2 1 ∑ ∑ X M(N - 1) i=1 j=1 ij

(7) . .

(8)

Furthermore, we consider the normalized root mean square error (NRMSE) for each image of the sample in order to determine the predominance of the random error. Therefore, this allows us to know if it is possible to make a FPN correction. In the present case, a residual value of each image, Rijk, was obtained by subtracting the average value of all the pixels, each at a time, from the image k. The NRMSE of FPN by columns and pixels is in Eqs. 9 and 10: k Crms =

Pkrms =

1 max(Yj) -min(Yj) 1 max(Xj) -min(Xj)

1 N 1 N k ∑ N ∑ Rij - Yj N j=1 i=1

219

and based on the work of Schöberl et al. (2009), we considered a fit of the FPN columns as a function also of the integration time as Eq. 12: Ffpn(x,τ) = fc(x)gc(τ)

(12)

where τ represents the integration time, and gc(τ)=b0+b1τ+b2τ2 and ai, bi are parameters to be determined. However, in the work of Schöberl et al. (2009), the set of parameters found were for each individual pixel. Herein, we are more interested in modeling the column FPN using only one function for all columns and integration time range. In order to determine ai, bi, we minimize the least-square error as in Eq. 13: J (a, b) = 1 ∑ ∑ ||Yjl - Ffpn (a, b, xj, τl)|| 2 l j

, (13)

where a=[a0, a1, a2, a3], b=[b0, b1,b2], and Yjl are the FPN columns given by Eq. 13 for l different integration times. In order to quantify the model fit accuracy, using Eq. 12 and setting the best fit parameters to compare with the experimental data, we have considered Pearson’s product-moment correlation coefficient (Press et al., 1993), as seen in Eq. 14:

ρ=

∑ ∑ (Yjl - Y) (Ffpn, jl - Ffpn) j

∑ ∑ (Yjl - Y)2 l j

∑ ∑ (Ffpn, jl - Ffpn)2 l j

, (14)

being Y the mean value of Yjl , Ffpn, jl is given by Eq. 12 for xj, τl and Ffpn is the mean value of Ffpn, jl.

RESULTS

(9)

1 M N k 1 N k- X ∑ ∑ Rij - N ∑ Rij ij MN i=1 j=1 i=1

. . (10)

In this work, we modeled the FPN columns tendency as a third-order polynomial function (Eq. 11), fc(x) = a0 + a1x + a2x2 + a3x3 , (11)

We collect the images sample under dark and flat field illuminations. In both cases, we consider 100, 200, 300 and 400 msec. of integration time. For the flat field it was used an integrating sphere, which is a device for measuring optical radiation. For more details see the technical manual (http:// www.photonicsonline.com/doc.mvc/A-Guide-to-IntegratingSphere-Radiometry-and-0001). The mean value of the FPN per column is ~100 greater than that of the pixel FPN. Thus, the modeling of pixel FPN will not be important to improve the

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Pereira, E.S.

AST sensibility. Taking into account these results, in this work we focused our attention on the column FPN modeling. Figure 3 shows the total FPN estimated, Fij, in (A) and the pixel one, in (B). It is noteworthy that the value of the pixel FPN is the Fij subtracted from the column FPN. These results are for 200 msec of integration time. It is also possible to observe vertical lines in the image in A, which are the FPN column, and their values are plotted in Fig. 4. The highlighted line in Fig. 3 is a defective column in our APS. This column is not considered for the FPN analyses. Figures 4 and 5 show the FPN per columns for dark current (flat field), the continuous line is the polynomial modeling of the column FPN, given by Eq. 11. In these cases, the vector of parameters that provide us a better fit is presented in Table 1. In Figs. 6 and 7 the normalized root mean square error of FPN per column estimated for each image of the sample for dark current and flat field is represented. In both cases, the integration time was 200 msec. These figures represent the general behavior of the random noise from image to image, when compared to the FPN range amplitude. In general, the random noise, or error of FPN, has a value lower than 1% with respect to FPN range amplitude. The Figs. 8 and 9 demonstrate the last-square fit of the Eq. 12 for dark current and flat field, respectively. The set of best fit parameters are given in Table 2. Pearson’s product-moment correlation coefficients, given by Eq. 14, were obtained for dark current (0.7947) and flat field (0.9995). These results show that we had a good agreement with the modeling fit when compared with the experimental data. This means that we have 99.95% of accuracy in modeling the flat field column FPN and 79,47% of accuracy in the dark current model for the column FPN.

For this work, a software tool, called FPNAnalyser© was developed for analyzing and modeling the FPN. This program was based on all the theories about FPN determination presented here. The first tab of the Graphical Using Interface of FPNAnalyser© is shown in Fig. 10. It will be released as an table 1. Best fit parameters set for modeling fixed pattern noise columns. a0

Dark current Flat field

81.9

8.5x10-3

-1.1x10-4

2.0x10-7

168.0

5.5x10-2

-3.5x10-4

4.3x10-7

the column fixed pattern noise (FpN) has different behaviors when the dark current FpN is compared to the flat field one. as the FpN is distinct for each sensor, we expect different sets of parameters for varied complementary metaloxide-semiconductor sensors.

92 90

Model Data

88 86 84 fc

220

82 80 78 76 0

100

200 300 Column

400

500

the continuous line is the polynomial modeling.

Figure 4. Column fixed pattern noise for dark current and 200 msec of integration time.

174 172

170

168 fc

166 164 162 160 158 1560

the bright column to the right is the defective of the apS, which is not being taking into account for the fixed pattern noise modeling.

Figure 3. high brightness and contrast image of dark current for 200 msec of integration time. total fixed pattern noise estimation (a) and pixel fixed pattern noise (B).

100

200 300 Column

Model Data 400 500

the continuous line is the polynomial modeling.

Figure 5. Column fixed pattern noise for flat field and 200 msec of integration time.

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Determining the Fixed Pattern Noise of a CMOS Sensor: Improving the Sensibility of Autonomous Star Trackers

0.07

1.96

0.06

1.92 1.90

k Cτms

0.04

1.88

0.03

2.0 2.1 2.2 2.3 2.4 2.5 2.6

20 25 k Image

500

Figure 6. Normalized root mean square error for dark current and 200 msec of integration time.

400

300

200

Column

log

0.01

100

the integrating time, τ, is in msec. this surface was obtained using Eq. 13. the scattered points are experimental data.

Figure 8. least-square fit of the fixed pattern noise column considering dark current.

0.09 0.08 0.07 0.06

2.3

0.05 0.04

k Cτms

2.2 2.1

100

15 20 k Image

200 300 Column

400

2.4 2.5 2.2 2.3 (τ) 2.1 g lo 10 500 2.0

2.6

log10 (Ffpn)

2.4

1.938 1.932 1.926 1.920 1.914 1.908 1.902 1.896

(τ)

0.02

0.03 0.02 0.01 0.000

log10 (F ) fpn

1.94

0.05

0.000

221

2.40 2.36 2.32 2.28 2.24 2.20 2.16 2.12

the integrating time, τ, is in msec. this surface was obtained using Eq. 13. the scattered points are experimental data.

Figure 7. Normalized root mean square error for flat field and 200 msec of integration time.

Figure 9. least-square fit of the fixed pattern noise column considering flat field.

Figure 10. Graphic using interface of the FpNanalyser© software. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.217-222, Apr.-Jun., 2013

222

Pereira, E.S.

Table 2. Set of best fit parameters for fixed pattern noise columns models as a functional of integration time. a0

Dark current

7.3

1.0x10-3

-1.1x10-5

2.3x10-8

11.2

9.7x10-5

-3.3x10-6

Flat field

-5.2

-1.3x10-3

8.3x10-5

-1.0x10-8

-10.7

-1.0x10-1

-2.9x10-6

open source under the general GNU license version 3 (see http://www.gnu.org/licenses/gpl-3.0.txt for more details).

DISCUSSION AND CONCLUSION It was presented a general concept of AST and a way to evaluate the FPN of CMOS APS used as the AST image. The determination of the FPN is important to achieve not only higher precision of observations of greater magnitude stars (less bright stars), but also to perform corrections of the brightness of low magnitude stars. The attitude determination depends on the precision of stellar identification, therefore the FPN correction leads to a better knowledge of this attitude. With this experiment, it was observed that the mean value per FPN columns is greater than that of the pixel FPN. Thus, it is relevant only the FPN column for doing the APS image correction. Also, we showed that the parametric model of FPN columns, as function of columns and integration time, had a good agreement with experimental data. This fact was quantified by Pearson’s

product-moment correlation coefficient. We obtained 99.95% of accuracy for flat field and a 79.47% for dark current. We strongly suggest future works including the development and implementation of the correction algorithm of FPN columns for the AST. The greatest contribution of this work is the applied methodology, since it was widely detailed in a single paper, i.e., a FPN correction analysis for an AST image. Another point is that we have developed a software tool that could be used not only for modeling the FPN, but also to trace strategies for doing an automatic image correction by an embedded system into the AST image.

ACKNOWLEDGEMENTS Eduardo S. Pereira would like to thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ) for their financial support (process: 382477/2012), Instituto Nacional de Pesquisas Espaciais (INPE) for their technical support, and Regla Duthit Somoza and Marcio A. A. Fialho for their constructive opinions.

REFERENCES Bigas, M., Cabruja, E., Forest, J., Salvi, J., 2006, “Review of CMOS image sensors”, Microelectronics Journal, Vol. 37, pp. 433-451. Gamal, A.E., Fowler, B., Min, H., Liu, X., 1998, “Modeling and estimation of FPN components in CMOS image sensors”, International Society for Optics and Photonics, Vol. 3301, pp. 168-177. Liebe, C.C., 1995, “Star trackers for attitude determination”, Aerospace and Electronic Systems Magazine, Institute of Electrical and Electronics Engineers, Vol. 10, pp. 10-16. Liu, H.B., Wang, J., Tan, J., Yang, J., Jia, H., Li, X., 2011, “Autonomous on-orbit calibration of a star tracker camera”, Optical Engineering, Vol. 50, pp. 023604. Pillman, B., Guidash, R., Kelly, S., 2006, “Fixed pattern noise removal in CMOS imagers across various operational conditions”, US Patent 7,092,017.

Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1993, “Numerical Recipes in FORTRAN; The Art of Scientific Computing”, Cambridge University Press, New York, NY, USA, 973 p. Schöberl, M., Senel, C., Fößel, S., Bloss, H., Kaup, A., 2009. “Nonlinear Dark Current Fixed Pattern Noise Compensation for Variable Frame Rate Moving Picture Cameras”, 17th European Signal Processing Conference (EUSIPCO), Vol. 1, Glasgow, Scotland, pp. 268-272. Wahba, G., 1965, “A least squares estimate of satellite attitude”, SIAM Review, Vol. 7, pp. 409-409. Xing, F., Dong, Y., You, Z., 2006, “Laboratory calibration of star tracker with brightness independent star identification strategy”, Optical Engineering, Vol. 45, pp. 063604-063604-9. Zenick, R., 2003, “Lightweight, low-power coarse star tracker”, Proceedings of the AIAA/USU Conference on Small Satellites, Mission Lessons, SSC03-X-7, Vol. 1, Logan, Utah, pp. 01-14.

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doi: 10.5028/jatm.v5i2.219

On the Determination of a Scatter Factor for Fatigue Lives Based on the Lead Crack Concept Adriano Francisco Siqueira1, Carlos Antonio Reis Pereira Baptista1, Loris Molent2

ABSTRACT: The lead crack concept is adopted as the basis for a new fatigue lifeing method using the safe life philosophy. As part of its management strategy, a full-scale fatigue test is conducted to identify high-risk locations in the airframe, and for each item the time for retirement or structural repair is dictated by the safe life limit. A scatter factor is defined to account for the scatter in the material fatigue performance. The fatigue life variation of any given region of aircraft metallic structures is assumed to primarily correlate to the distribution of the equivalent pre-crack size of the fatigue crack initiators. By assuming that the sizes of these crack initiators are independent from each other, the present paper estimates the scatter factor by calculating safe life limit based on known growth characteristics of critical cracks. KEYWORDS: Fatigue crack propagation, Aluminum alloys, Scatter factor, Airframe.

INTRODUCTION This paper describes a new fatigue lifeing method, which uses the lead crack concept (Molent, Barter and Wanhill, 2011) within the safe life (SL) philosophy framework. The lead crack initiates upon entry into service and leads to failure first in any given airframe location. As part of the SL management strategy, a full-scale fatigue test (FSFT) is conducted under representative loading in order to identify high-risk locations in the airframe, and for each item a safety-by-inspection schedule is defined or the time for retirement or structural repair is dictated by the SL limit (SLL). A scatter factor (SF) is established to account for the scatter in the material fatigue performance and the specific acceptable cumulative probability of failure. The FSFT is normally conducted for a period representing the desired service life times the SF. However, it is known that the current SF determination methods have an empirical basis. On the other hand, the fatigue life variation of any given region of aircraft metallic structures appears to correlate primarily to the distribution of what is known as the equivalent pre-crack size (EPS) of the fatigue crack initiators (for a certain material, spectrum, and stress level). The EPS is a measure of the crack-like effectiveness of the initiating discontinuity. Only one example of a production induced initial discontinuity was considered, namely pits induced through chemical etching, which is a common production material degreasing process. By assuming that the sizes of these crack initiators are independent from each other, the present paper intended to estimate the “true” SF of a critical location by calculating the SL based on known growth characteristics of critical cracks.

1.Universidade de São Paulo (EEL/USP) – Lorena/SP – Brazil 2.Visiting Fellow, Universidade de São Paulo (EEL/USP) – Lorena/SP – Brazil Author for correspondence: Carlos Antonio Reis Pereira Baptista | Universidade de São Paulo, Escola de Engenharia de Lorena | CEP 12.602-810 Lorena/SP – Brazil | E-mail: baptista@demar.eel.usp.br Received: 17/12/12 | Accepted: 18/04/13

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THE LEAD CRACK CONCEPT A fatigue lifeing framework using a lead crack concept has been developed by the Defence Science and Technology Organisation (DSTO) for metallic primary airframe components (Molent, Barter and Wanhill, 2011). Many observations at the DSTO and by other researchers have shown that approximately exponential fatigue crack growth (FCG) is a common occurrence for naturallyinitiating lead cracks (i.e. those leading to first failure) in test specimens, components, and airframe structures subjected to variable amplitude load histories. Lead crack characteristics The lead cracks start to grow shortly after testing begins or the aircraft has been introduced into service. They are subject to several conditions and grow approximately exponentially with time, i.e. FCG may be represented by an equation of the form a = a0eλN, where a is the crack size at time N, a0 is the initial crack size (or EPS), and λ is a growth rate parameter that includes the geometrical factor β. The conditions are the following: • Little error is made when assessing the EPS of the fatigue-initiating discontinuity. An underestimate or overestimate of the discontinuity effectiveness will cause a small temporary departure from an exponential trend near the commencement of FCG. • The crack does not grow into an area with significant thickness change, particularly if the crack length/depth is small compared to the specimen or component thicknesses or widths. • The crack is not unloaded, either by the cracked area losing stiffness and shedding load to other sites of the specimen, component or structure; or because it grows primarily under bending loads and it approaches a neutral axis or develops away from an externally induced stress concentration, such as a pin-loaded hole in a multi-pin loaded joint. • The crack does not find a significantly changing stress field by growing into or away from an area containing residual stresses. • FCG is not retarded by infrequent very high loads (usually in excess of 1.2 times the peak load in the load history). • The small fraction of FCG life influenced by quasi-static fracture close to final failure is ignored.

Within the bounds of these conditions, observations from the DSTO about the formation, growth, and failure of lead cracks have led to various deductions (Molent, Barter and Wanhill, 2011), including: • For a given material, spectrum and item, the λ parameter of the exponential equation, i.e. the slope of the crack growth curve shown in Fig. 1, is approximately a constant. • Typical initial discontinuity sizes of AA7050-T7451 are approximately equivalent to a 0.01 mm deep fatigue crack (Molent, Sun and Green, 2006; Molent and Barter, 2007). In other words, this is a good starting point for FCG assessment (Fig. 1). This value is below the smallest initial flaw/crack size — the equivalent initial flaw size (EIFS) — usually assumed in the damage tolerant method (USAF, 1974). • The metallic materials used in highly stressed areas of a high-performance aircraft have typical critical crack depths of about 10 mm (Molent, Sun and Green, 2006; Molent and Barter, 2007). Equivalent full life As mentioned, it is usual to conduct a FSFT for a specified period representing a multiple of the required service life and then to perform a residual strength test – RST (Molent et al., 2009a; 2009b). If the test article survives the residual strength loading, typically the equivalent service hours (ESH) achieved at the end of the test will be divided by a SF to result in the SL. However, this may be a lower bound SL, as in many cases the FSFT may have been capable of sustaining further fatigue cycling and would still have survived RST. The lead crack concept provides simple means of estimating the elapsed ESH when the test article would have just met the RST criterion (i.e. equivalent full life) as illustrated in Fig. 1. For illustration, assume that the FCG data shown in Fig. 1 represent the termination of a FSFT, when a nondestructive inspection (NDI) detectable crack (aNDI) was found in a principle component at approximately 5,000 ESH. The critical crack size under the RST conditions can be determined through conventional fracture mechanics (aRST). The lead crack concept can then be used to extrapolate from aNDI to aRST, estimating an equivalent full life of approximately 7,000 ESH, as seen in Fig. 1. Thus, by using the lead crack concept, an optimal SL can be achieved, even if limited FSFT cycling has occurred. This technique has already been used at the DSTO (see for example Molent et al., 2009b).

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On the Determination of a Scatter Factor for Fatigue Lives Based on the Lead Crack Concept

equIvAlenT pRe-CRACK SIze Production aircraft components and structures often have many sources of surface or near-surface discontinuities capable of initiating fatigue cracking. These include various forms of machining damage (e.g. scratches, grooves, burrs, small tears, and nicks), etch pits from surface treatments (e.g. pickling, pre-anodising), porosity (especially in thick aluminum alloy plate and castings), and in the case of aluminum and steels, constituent particles that may themselves be cracked. The procedure for predicting the lead crack depth at any given life and location in the airframe and subsequently calculating its SL depends on an accurate measure of the crack-like effectiveness of the initial discontinuities for the locations and areas to be assessed, as what is known as the EPS or a0. The EPS is a recent development, and its values for some defect types are approximations to a physical measurement of the initiating flaw or discontinuity derived via back projection to time zero from experimental FCG data. Therefore, it should not be compared to the more traditional EIFS concept (Molent, Sun and Green, 2006). The fatigue life variation of any given region of metallic structure appears to correlate primarily to the distribution of the EPS of these fatigue initiators for a given material, spectrum, and stress level (Pell, Molent and Green, 2004).

225

A previous investigation into fatigue crack defect types and EPS in commercial 7050-series aluminum alloy subjected to various F/A-18 aircraft spectra loading considered over 360 cracks in full-scale structural components and coupon test specimens. Note that this is the EPS distribution for the discontinuities present at lead cracks, i.e. not the EPS distribution for say, all etch pits initiated cracks in one specimen. The defect descriptions and EPS results were obtained from quantitative fractography (QF) data. Comparisons between the coupon specimen and the test article specimen from EPS distributions with same surface conditions verified that the former are representative of typical flaw sizes in service aircraft for each surface finish considered. It was also noted that the log-normal distribution approximates well the EPS population, i.e. the a0 values (Molent, Sun and Green, 2006). Taking into account the lead crack exponential growth behavior and assuming that the a0 population follows the log-normal distribution, then the life to grow a crack to a given size, N, must follow the normal distribution. This is not in accordance with the hypothesis assumed in a recent work (Underhill and DuQesnay, 2008), which N follows the log-normal distribution. However, this apparent inconsistency can be explained by the fact that when

In-service Crack Depth 10

Critical (RST) Crack Depth (mm)

NDI detectable crack depth 1

0.1 Equivalent full life

Service life at crack detection 0.01 0

1000

2000

3000

4000 5000 6000 Equivalent Service Hours

7000

8000

9000

10000

Figure 1. Schematic of the lead crack growth showing the crack depth versus time history for blocks of loading, the limit of crack detection (nondestructive inspection), and the critical crack depth for the required residual strength – RSt (critical RSt). J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.223-230, Apr.-Jun., 2013

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a normal distribution (μ, σ) has an arithmetic mean μ that is much higher than its arithmetic standard deviation σ, which is the case of the typical airframe fatigue lifetimes involved, the distribution tends to look log-normal.

of a “true” SF by calculating SLL based on known growth characteristics of critical cracks.

DEVELOPMENT BACKGROUND ON SCATTER FACTORS The SLL corresponds to the maximum life of each location, while maintaining an acceptable safety level. For example, DEFSTAN 00-970 defines the SLL of an item as the life at which the weakest example only retains the required standard of strength, deformation, stiffness, or mechanical function under 80% of the design ultimate load (British Ministry of Defence, 1983). A SF is defined to account for scatter in the material fatigue performance and build-quality variations (British Ministry of Defence, 1983). The SF is a factor that the test demonstrated fatigue life must be reduced by to ensure that the failure probability does not exceed a specified level. A large number of fatigue scatter estimates for aluminium alloy aircraft structures is available in literature (Hoffman and Hoffman, 2001; Forgues, 1996; Parish, 1965; Stagg, 1969; Benoy, 1981; Cardrick and Mew, 1999; Impellizzeri, 1966; Young and Ekvall, 1981; Cardrick, 2008). It was verified that some of the differences found in the fatigue scatter estimates may be related to the varied structural details tested, the different surface treatments of batches of material that were tested, the introduction of artificial crack starters, surface residual stresses and whether the cracks were surface or subsurface initiated. As many of the results quoted are total lives (FCG was not investigated), therefore the individual effects of these influencing factors are masked or unclear. Moreover, care needs to be exercised with the figures presented in the literature to determine whether the scatter estimate relates to individual items or whole components. An important consideration here is the area effect. Some results determined through small coupon testing may not reveal the lead crack, because the probability of having a discontinuity at the optimum locations to grow a lead crack is much reduced compared to the whole component. Therefore, the current SF determination methods appear to have a weak basis. The present paper intended to contribute to the estimation

In this work, it is assumed that the major contributor to the scatter in the fatigue performance of monolithic metallic structure like airframes is governed by variability in the metal fatigue resistance and manufacturing quality. These features can be quantified through the variability in: the initial discontinuity that leads to fatigue cracking; time to crack initiation; variations in local stress concentration due to manufacturing tolerances; fit-up or residual stresses; the fracture toughness, and the FCG rate. Except for the latter, these items define the aircraft build quality from a fatigue perspective. Indeed, specifically for monolithic structures, the effects of fit-up or residual stresses are minimal. It is known (e.g. from White, Molent and Barter, 2005) that the most significant variable for a given loading is the initiating discontinuity. Furthermore, for lead cracks, the initiation periods are negligible and conservatively ignored in the following analysis (note that fretting induced cracking is an exception to this). Also, modern aircraft like the F/A-18 are built to exacting standards and close tolerance so that for a specific location the variability of a local stress concentration between aircraft is negligible. It was also shown by White, Molent and Barter (2005) that variation in fracture toughness had little effect on the probability of failure. In this paper, the EPS relevant to etched aluminium alloy 7050-T7451 surfaces from F/A-18 Hornet test airframes (Molent, Sun and Green, 2006) were considered. Many aircraft components are chemically etched prior to the application of a corrosive preventative treatment (e.g. anodised or ionvapour deposited pure aluminium). The etching produces pitting that readily initiates the growth of cracks. The individual EPS values from the crack leading to failure in representative full-scale tests are determined through using back-extrapolation of the FCG data (i.e. crack depth versus load blocks or flight hours) obtained through QF. Generally, the extrapolation from the first identified fracture surface progression mark to the start of fatigue was less than 0.1 mm. For the initial discontinuity types considered by Molent, Sun and Green (2006), it was shown that the EPS distribution was

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On the Determination of a Scatter Factor for Fatigue Lives Based on the Lead Crack Concept

a0 ~ log normal (μ0 , σ02) = log normal (-4.428, 0.957 2)

. (1)

The starting point for the method is that every crack nucleated under fatigue conditions shows the potential to be the lead one of a certain item, and only one is identified in post-mortem analysis. Let us now assume that the number M of nucleated cracks, which possibly develop into a lead crack in a given component, follows Poisson’s distribution, i.e. M is a random variable with a mean value equals to µ. The approximation of the number of initial cracks in a given component by a punctual Poisson’s process also can be justified by the assumed hypothesis that the small initial discontinuities are randomly introduced in that location, and they are not due to a systematic factor. By using the known EPS distribution, a critical value for a0 is defined as the initial crack size having a determined probability of occurrence among the M nucleated cracks, which possibly

develop into a lead crack. Thus, the probability that none of the M initial cracks in a certain location have an a0 > a0c (where a0c is the critical value of a0) is determined as follows: assuming that the initial cracks are independent from each other (hypothesis of the independence of a0), and considering M as a random variable modeled by Poisson’s process, the required probability is calculated according to Gumbel (2004), conditioned to the occurrence of a specific M value. This is shown by Eq. 2: ∞

P(None a0>a0c) = Σ P(None a0>a0c/M=i). P(M=i) = i=0

∞

Σ exp(-ip)

i=0

(2)

exp(-μ)μi i!

where p is the probability that one initial crack has a0>a0c, and p is calculated as shown.

Mean=-4.428 SD=0.957 n=97

Frequency

20 15 10 5 0

-6

-5

-4 ln (EPS)

-3

-6

Figure 2. Normal distribution of the ln (equivalent pre-crack size – EpS) of 97 cracks in test articles (Molent, Sun and Green, 2006). 99.9 99

Percent

independent of spectra and stress levels. Only the etched-out pit EPS distribution from 97 cracks examined from full-scale test articles were considered in the present analysis. Knowing the critical crack size acr (e.g. from fracture mechanics considerations or test) and using the exponential growth equation, the fatigue lifetime Nv is determined, corresponding to the number of blocks/flight hours for a lead crack to grow from a0 to acr. The SL is the fatigue lifetime divided by SF, i.e.: SL = Nv/SF. Generally, more than one fatigue prone area will exist and each will have its own SL, which can be estimated. For the purpose of this paper, the slope of the crack growth curve, λ, assumed to be a constant for a given part location/material. Therefore, the problem of fatigue scatter is reduced to the a0 (EPS) distribution. The keystone is that the initial discontinuity size can be assumed as an independent random variable. A fundamental hypothesis of the present work is that the EPS is derived from small (submillimeter) discontinuities introduced randomly during the processes of material and component productions. The histogram with normal natural logarithm distribution of the EPS from the 97 cracks in the test articles is shown in Fig. 2. These data were tested for the hypothesis that a0 follows the log-normal distribution. The obtained results, shown in Fig. 3, present a p-value corresponding to 0.623, meaning that there is no evidence to refute this hypothesis based on the collected data. Therefore, it is assumed in this paper that a0 follows the distribution given by Eq. 1:

227

95 90 80 70 60 50 40 30 20 10 5

Log normal 95%CI n=97 AD=0.285 p-value=0.623

1 0.1

0.001

0.010 EPS

0.100

1.000

Figure 3. probability plot of the equivalent pre-crack size (EpS) of the 97 cracks from test articles.

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Siqueira, A.F., Baptista, C.A.R.P. and Molent, L.

By developing Eq. 2, we obtain Eq. 3: P(None a0>a0c) = exp(-μ) Σ exp(exp(-p)μ-μ)

∞ i=0

(exp(-p)μ)i = i!

(3)

Thus, from a preestablished level of confidence (for instance, 0.999), a critical value of a0 can be determined (i.e. the a0c meaning that, in 0.1% of the situations, the a0 of a crack initiated in a critical location will be higher than a0c). Therefore, for the probability of none of the initial cracks have a0 > a0c we choose the value P(None a0 > a0c) = 0.999. Then, from Eq. 3, we have ln(0.999) = exp(-p)µ-µ, or as in Eq. 4: exp(-p)=

μ + ln (0.999) . . μ

(4)

μ . . μ + log(0.999)

Nv . . Next

a0c=0.707 mm

0.6

(5)

With the calculated value for p and using the log-normal distribution shown in Fig. 3, the a0c value was determined. With this a0c and taking the appropriate λ for the considered critical location, we grow a0c to acrit to provide Next, which is a SL estimation corresponding to this critical initial crack size. Thus, the “true” SF for the established probability is given by Eq. 6: SF =

0.8 0.7

The expression for p calculus is from Eq. 5: p = ln

have a0c = 0.707 mm. For the adopted confidence level, it is expected that, for each 1,000 parts presenting this behavior (i.e., having µ = 100), one, in average, will show a0 > a0c. This is illustrated in Fig. 4, which shows a simulation of the maximum a0 values for 1,000 similar parts. In the numerical example it will be considered the growth of a typical crack from a F/A-18 full scale fatigue test as shown by Molent and Barter (2010), with a0 = 0.011 mm, λ = 0.0004 and equivalent RST = 16,000 flight hours. Table 1 shows the calculated a0c, SL and “true” SF values corresponding to several µ values ranging from 1 to 1,000. Therefore, if the average number of nucleated cracks in the considered critical location is µ = 100,

Maximum a0 of each part (mm)

228

(6)

NUMEriCal EXaMPlE In order to run a numerical example, it must be recognized that critical locations (or parts) having the same EPS distribution can show distinct amounts of nucleated cracks. In other words, although the EPS distribution is location independent for a given material/manufacturing process, the mean number of nucleated cracks, µ, that possibly develop into a lead crack is assumed to be location dependant, due to the spectrum/stress/environmental history of each site. Considering the EPS distribution of the 97 cracks from test articles (Fig. 3) and a 0.999 confidence level, the a0c value depends exclusively on µ. For instance, if the average number of nucleated cracks in a given critical location is µ = 100, we

0.5 0.4 0.3 0.2 0.1 0.0

100 200 300 400 500 600 700 800 900 1000 Number of parts

Figure 4. a computer simulation of the maximum a0 values for each of 1,000 similar parts.

table 1. Calculated a0c, safe life (Sl), and “true” scatter factor (SF) values corresponding to several µ ones ranging from 1 to 10,000 for confidence level of 0.999 μ

a0c (mm)

Sl (flight Hours)

0.2297

9,433.79

1.782

0.3099

8,685.38

1.936

0.3534

8,357.19

2.012

0.3699

8,242.74

2.040

0.4194

7,929.05

2.121

100

0.7071

6,622.98

2.539

1,000

1.1285

5,454.14

3.083

10,000

1.9534

4,387.27

3.832

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On the Determination of a Scatter Factor for Fatigue Lives Based on the Lead Crack Concept

then for a 0.999 confidence level the “true” SF to be applied to the equivalent RST is 2.539. It is interesting to observe that, by plotting the “true” SF against the natural logarithm of µ, a linear relationship is obtained, as observed in Fig. 5. Another important point is that, because the way it was defined, the SF does not depend on the growth rate parameter λ. In other words, even distinct loading spectra or crack geometry may eventually present the same “true” SF, if

3.5 Scatter Factor

µ and EPS distributions are similar. This can be verified by the relationship given by Eq. 7:

SF =

1 10 ln a0 λ

1 10 ln a0c λ

10 a0 (7)

10 a0c

CONCLUSIONS

4 3 2.5 2 1.5 1 0.5 0

229

ln (μ)

Figure 5. Plot of the “true” scatter factor estimation against the natural logarithm of µ showing a linear fashion.

By assuming that the scatter in a material’s fatigue performance is mainly governed by equivalent crack-like size distribution of initiating discontinuities, the present paper illustrated a method of estimating a “true” SF, with a confidence level and average number µ of nucleated cracks in an aluminium alloy 7050-T7451 critical airframe location. The presented results illustrate how the developed method makes note that, even for similar parts, the average initial crack size for a given confidence level increases with the number of nucleated cracks, and thus so does the “true” SF. Therefore, the adoption of a SF for a given part should also take into account the average number of nucleated cracks.

REFERENCES Benoy, M.B., 1981, “Fatigue life variability in civil aircraft”, Proceedings of the 11th ICAF Symposium, Noordwijkerhout, Netherlands. British Ministry of Defence, 1983, “Design and airworthiness requirements for service aircraft”, v. 1, Aeroplanes of Defence Standard 00-970, Issues 1 to 5. Cardrick, A.W. and Mew, A.B., 1999, “Scatter considerations in the interpretation of major fatigue tests”, Proceedings ICAF Symposium, Seattle, USA. Cardrick, A., 2008, “Interpretation of the F/A-18 Bulkhead Tests”, Farnborough. Forgues, S., 1996, “Study of material and usage variability for probabilistic analyses and scatter factor determination”, RDADSD-123, Bombardier Inc.

Molent, L. and Barter, S.A., 2007, “A comparison of crack growth behavior in several full-scale airframe fatigue tests”, International Journal of Fatigue, Vol. 29, pp. 1090-1099. Molent, L. and Barter, S.A., 2010, “The lead fatigue crack concept for aircraft structural integrity”, Procedia Engineering, Vol. 2, pp. 363-377. Molent, L., Barter, S.A. and Wanhill, R.J.H., 2011, “The lead crack fatigue lifeing framework”, International Journal of Fatigue, Vol. 33, pp. 323-331. Molent, L., Barter, S., White, P. and Dixon, B., 2009a, “Damage tolerance demonstration testing for the Australian F/A-18”, International Journal of Fatigue, Vol. 31, pp. 1031-1038.

Gumbel, E.J., 2004, “Statistic of extremes”, New York, Dover Publications.

Molent, L., Dixon, B., Barter, S., White, P., Mills, T., Maxfield, K., Swanton, G. and Main, B., 2009b, “Enhanced teardown of ex-service F/A-18A/B/C/D centre fuselages”, Proceedings ICAF, Rotterdam.

Hoffman, M.E. and Hoffman, P.C., 2001, “Corrosion and fatigue research: structural issues and relevance to naval aviation”, International Journal of Fatigue, Vol. 23, S1-S10.

Molent, L., Sun, Q. and Green, A.J., 2006, “Characterization of equivalent initial flaw sizes in 7050 aluminum alloy”, Fatigue & Fracture of Engineering Materials & Structures, Vol. 29, pp. 916-937.

Impellizzeri, L.F., 1966, “Development of a scatter factor applicable to aircraft fatigue life”, Structural Fatigue in Aircraft, ASTM CTP 404, American Society for Testing Materials, p. 136.

Parish, H.E., 1965, “Fatigue test results and analysis of 42 provost wings”, Reports and Memoranda No. 3474, Aeronautical Research Council.

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Pell, R.A., Molent, L. and Green, A.J., 2004, “The fractographical comparison of F/A-18 aluminum alloy 7050-T7451 bulkhead representative coupons tested under two fatigue load spectra at several test levels”, DSTO-TR-1547, Melbourne, Australia.

United States Air Force – USAF, 1974, “Military specification airplane damage tolerance requirements”, MIL-A-83444, United States Military Standard.

Stagg, A.M., 1969, “Scatter in fatigue: elements and sections from aircraft structures”, CP No. 1357, Her Majesty’s Stationary Office.

White, P., Molent, L. and Barter, S., 2005, “Interpreting fatigue test results using a probabilistic fracture approach”, International Journal of Fatigue, Vol. 27/7, pp. 752-767.

Underhill, P.R. and DuQuesnay, D.L., 2008, “The effect of dynamic loading on the fatigue scatter factor for Al 7050”, International Journal of Fatigue, Vol. 30, pp. 614-622.

Young, L. and Ekvall, J.C., 1981, “Reliability of fatigue testing”, Statistical Analysis of Fatigue Data, ASTM STP 744, American Society for Testing and Materials, pp. 55-74.

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doi: 10.5028/jatm.v5i2.164

Development of Polyamide 6/Compound by Recycled Rubber Blends Using Graphitized Polyethylene or Polypropylene with Maleic Anhydride as Compatibilizer Agent Divânia Ferreira da Silva1, Edcleide Maria Araújo1, Tomás Jeferson Alves de Melo1

Abstract: The toughening of polyamide 6 is desirable for many applications and may be obtained by adding a phase to the elastomeric matrix. However, this leads to a loss in its rigidity characteristics. Therefore, this study aimed at developing blends of polyamide 6/compound by recycled rubber (SBR-R), with the addition of compatibilizer graphitized polyethylene and polypropylene with maleic anhydride method by mixing in the molten state in order to obtain a balance between stiffness and toughness. The systems were prepared in several compositions, and their rheological properties and spectroscopy in the Fourier transform infrared were studied by means of rheological curves obtained in an internal mixer of Haake Buchler. The results obtained with the rheological study and Fourier transform infrared showed that mixtures of polyamide 6/graphitized polyethylene with maleic anhydride presented the best results compared to those of polyamide 6/ graphitized polypropylene with maleic anhydride, probably indicating reaction between the components. Thus, it was chosen graphitized polypropylene with maleic anhydride as a compatibilizing agent for carrying out other characterizations. Blends of polyamide 6/compound by recycled rubber/ graphitized polypropylene with maleic anhydride and their properties were analyzed by means of mechanical tests (tensile and impact), dynamic mechanical thermal analysis, differential scanning calorimetry, and scanning electron microscopy. The impact strength and elastic modulus of the blends compatibilized reduced somewhat when compared to polyamide 6. Therefore, these results indicate a good prospect of application of industrial waste, minimizing the negative effect on the environment and adding value to a disposable material. Keywords: Polymers blends, Polyamide 6, Recycled rubber, Compatibilizers.

INTRODUCTION Blending polymers with different molecular structures or mechanical properties have recently become a useful route in developing new, high-performance polymeric materials. Improved mechanical properties, processibility, barrier behavior, and electrical properties can be achieved through such technology. Choosing suitable polymers is the primary task in the preparation of polymer blends; however, more attention has been paid to control the morphology of blends, which has been found to have a great impact on the properties of polymer blends. Actually, most polymers used in blends are immiscible or partially miscible due to their high molecular weight and unfavorable interactions, resulting in the multiphase morphology. For binary polymer blends, when the content of one component is much lower than the other one, the minor usually forms droplet in the matrix of the major component, which is usually known as the sea island morphology (Yu et al., 2010). Since last century, the development of polymeric materials has expanded greatly, which can be seen in our daily lives, through the composition of numerous utilities. With the development of new technologies, polymerization produced a series of new polymers. However, in some situations, rather than synthesizing a new polymer material, the search was directed to the study of physical mixtures of polymers, in other words, polymer blends. These consist of a mixture of two or more polymers and/or copolymers (Utracki, 2000).

1.Universidade Federal de Campina Grande – Campina Grande/PB – Brazil Author for correspondence: Divânia Ferreira da Silva | Departamento de Engenharia de Materiais | Universidade Federal de Campina Grande | Rua Aprígio Veloso, 882 – Bodocongo | CEP 58.109-970 Campina Grande/PB – Brazil | E-mail: divaniaf@yahoo.com.br Received: 02/10/12 | Accepted: 13/01/13

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The blends of polymers with different physical properties can help improving the properties of the material through the contribution of each system component. Among the advantages of the blends, we can mention the ease of adjusting the properties of plastics usage needs. They are primarily important for generating mechanical, chemical, or unwanted barriers and improving the processibility of high-performance polymers (Vossen, 2009). For example, the application of some polymers is limited by the low impact on performance under room temperature conditions. This situation gets worse, especially when using in temperatures below 0ºC (Newman, 1978). One way around this limitation is to prepare polymer blends, in which the dispersed phase is an elastomer, and it is then classified as an immiscible blend. The blends with this feature have a high interfacial tension and weak adhesion between the continuous and dispersed phases. Studies have been directed to assess the shape, size, and distribution of the dispersed phase domains, relating them to macroscopic properties of the resulting material. The small amounts addition of a third component to the miscible blend can change the dispersion and interfacial energies between the phases, acting as a compatibilizer agent. These are generally block copolymers or grafted and can cause a decrease in size of the dispersed phase, modifying the toughness of the blends (Maglio and Palumbo, 1984). The interfaces at the nano scale are fundamental to the macroscopic physical properties of binary polymer blends, for example, morphology, mechanical strength, fracture toughness, thermal stability, and surface wetting. The interface property is intimately connected to an adhesion at the interface and interfacial tensions, which quantify miscibility and compatibilization capabilities. The characterization and understanding of the interfacial properties of phase-separated blends on a microscopic level are of great importance, both from practical as well theoretical points of view. On a larger length scale, one can envisage the blend material as an ensemble of interfaces. The structure and thermodynamics of these interfaces determine many practically important properties of the blend (Ramya et al., 2012). Among the several polymer matrices, polyamide 6 – PA6 (also known as nylon 6) was chosen as an engineering polymer, providing some advantages such as dimensional stability, good impact strength without notch, excellent chemical resistance, high melting temperature, among many

others. Aiming at improving its performance, it has been used with toughening of polyamide-based elastomer materials (Fornes et al., 2001). The styrene-butadiene copolymer (SBR) is considered a general-purpose elastomer. It has some properties as reasonable aging resistance, good abrasion resistance, and good resistance to sea water (Anjos, 2007). These materials have good aging stability when protected by additives. About 50% of car tires are made from various types of SBR. The styrene/butadiene ratio influences the properties of the polymer, with high styrene content, and the rubbers are harder and less rubbery (Obrecht et al., 2012). Bassani et al. studied blends of nylon-6 with acrylonitrile/ EPDM/styrene (AES) using a series of methyl methacrylate maleic anhydride (MMA-MA) copolymers, at the same time that compatibilizing agents were being prepared. The MA units in the copolymers are capable to react with the nylon-6 end groups. The MMA-MA copolymer has a potential to form in situ copolymers at the blend interface during melt processing as indicated by torque rheometry tests. This study focused on the effects of functionality and concentration of the reactive MA units of the compatibilizer on the their blends’ mechanical properties. The results show that incorporation of the MMA-MA copolymer significantly improves the impact strength of nylon-6/AES blends. The blend containing 1.3 wt% of MA in the copolymer is supertough at room temperature, and it remains tough at subzero temperatures. The aerospace industry is characterized by always making use of the latest technology, and recently its evolution is connected to the advent of research and knowledge related to new materials, as for example, polymer blends, leading to the appearance of new applications for new products before reserved for traditional materials such as steel, bronze, or brass. The polymer blends have the ability to meet some requirements like reduced weight without loss of strength and stiffness, and for this reason it is gaining prominence, and wide acceptance in structural projects. Still, many companies are producing aircraft with polymer blends, and these can be used in internal and external components, landing gear, structural parts, leading edges etc. The blends stand out when compared to other materials for presenting some advantages, such as higher values of impact resistance and service temperature, low moisture absorption, low processing costs, transport, and storage (Oliveira and Botelho, 2007).

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Besides the described advantages, the polymer blends do not permanently harden and can be repeatedly reheated and shaped, have high fatigue strength, ease in carrying out repairs, and especially greater possibility of recycling waste contributing to eliminate or minimize the environmental impact. This shows mechanical properties equal or superior to those shown by the conventionally used thermosetting composites in aerospace (Oliveira and Botelho, 2007). The market for polymer blends has grown steadily over the past decades, being the largest ones: automotive, electrical and electronics, packaging, construction, and aviation industries (Fiegenbaum, 2007). Although it is known that the polymer blends are economically viable alternatives for obtaining new materials, many polymers, when mixed, form immiscible blends and/or present incompatible properties unsuitable for use in the aircraft industry. The final ones of an immiscible polymer blend are influenced by their morphology, which in turn is very complex and depends on many factors, such as: composition, thermal and rheological properties of the components, processing conditions, among others (Fiegenbaum, 2007). This study aimed at developing blends of polyamide 6/compound by recycled rubber (SBR-R), with the addition of a compatibilizer.

MATERIALS AND METHODS Materials A PA6 was used, Technyl C216, molecular weight (10.500 g/mol), viscosity index (VI=134 mL/g) in the form of pellets, supplied by Rhodia (São Paulo, Brazil). Waste rubber (SBR-R) was used from the shoes industry São Paulo Alpargatas SA, located in Campina Grande, Paraíba. These compounds consist of a mixture of SBR as a main component, fillers, additives of processing, curing agents, stabilizers, and other types of rubber. The residues were used as powder with a particle size of 425 μm passed in 35-mesh sieve. The used compatibilizers were: PE-g-MA, Polybond 3009, with melt flow index of 5 g/10 min. and grafted with 1% by weight of MA; and polypropylene (PP-g-MA), Polybond 3200, with melt flow index of 110 g/10 min. grafted with 0.2 wt% MA both supplied by Crompton (São Paulo, Brazil).

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Preparation of polymers blends Before each processing step of the PA6 and compatibilizers, they were dried in vacuum oven at 80°C for 48 hours. The binary blends were prepared in the proportions of: PA6/SBR 90/10, 80/20, 70/30, and 60/40. Ternary mixtures were done in: PA6/SBR/compatilizers 87.5/7.5/5.0; 77.5/17.5/5.0; 67.5/27.5/5.0, and 57.5/37.5/5.0 using a internal mixer of Haake Buchler. Subsequently, the following compositions were chosen: 90/10; 80/20; 87.5/7.5/5; 77.5/17.5/5 to be processed by simultaneous extrusion of all the components in a twin screw extruder modular co-rotating ZSK-18K from Coperion with a 240°C temperature at all zones, 300 rpm speed, and feed rate of 4 kg/h. Also, the PA6 was extruded under the same conditions of the blends as reference. These compositions were chosen with lower levels of SBR-R, because they are in powder form and the polyamide and compatibilizer as granules were blended and introduced simultaneously into the extruder. Higher concentrations of SBR-R could compromise the homogeneity of the mixture. CHARACTERIZATION OF MIXTURES Torque rheometry tests were carried out in an internal mixer RHEOMIX 600 (Haake Büchler) coupled to a Torque Rheometer Haake System 90 of Büchler, operating with roller type rotors, rotating at 60 rpm at a temperature of 240°C for 20 minutes in air atmosphere. The total mass within the mixing chamber was kept constant at 55 g for all compositions. Rheological curves were obtained from the following materials: PA6, SBR, PE-g-MA, PP-g-MA binary and ternary blends. The Fourier transform infrared (FTIR) spectroscopy was used to characterize binary and ternary blends with 5 wt% PE-g-MA and PP-g-MA in a SPECTRUM 400 spectrometer from PerkinElmer with a scan of 4,000 to 650 cm-¹. FTIR analyzes were performed on films made of blends. The tensile tests were conducted on specimens injected, according to the American Society for Testing and Materials (ASTM) D638 using a universal testing machine model AG-Is 100KN from Shimadzu, with loading speed of 50 mm/min. The tests were conducted at room temperature and the results were analyzed from an average of five specimens. Impact tests were performed on specimens notched Izod type according to ASTM D256, on a CEAST instrument brand model Resil 5.5, operating at 2.75 J hammer and the

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Silva, D.F., Araújo, E.M. and Melo, T.J.A.

RESULTS AND DISCUSSION Torque rheometry and spectroscopy of the Fourier transform infrared Figures 1 to 4 present the variation curves of torque versus time of pure polymers, and the blends with and without compatibilizer. Figure 1 illustrates the torque curves for pure polymers used in this work. It can be observed that after three minutes of the beginning of the process, the torque tends to be practically constant with small oscillations around a

mean value. This behavior indicates viscosity stability to the process used conditions, in other words speed of 60 rpm and temperature of 240°C. The high-density PE grafted with MA had the highest torque compared to other polymers and, therefore, higher viscosity under these conditions. Figure 2

Torque (N.m)

conclusions were analyzed based on a weighted average of five specimens. The dynamic mechanical thermal analysis (DMTA) was performed on a DMTA equipment from TA Instruments Explorer brand, model Q 800. The request mode dynamicmechanical bending was used at one point, suitable for the type Izod specimens applied in the tests. The heating rate was 10°C/min. and it had a frequency of 1 Hz in a temperature range from -100 to 150°C. Thermal analysis using differential scanning calorimetry (DSC) was performed on DSC Q20 machine from TA Instruments, under the following conditions: heating from room temperature to 300°C at a rate of 10°C/min. under nitrogen atmosphere. The amount of sample employed was 5 mg. The scanning electron microscopy (SEM) analysis was performed on fracture surface of the specimens subjected to impact test in a SEM, Shimadzu SSX-550 Superscan, at a voltage of 15 kV, under high vacuum, and the surfaces fracture of notched specimens coated with gold.

PA6 SBR PA6/SBR (90/10) PA6/SBR (80/20) PA6/SBR (70/30) PA6/SBR (60/40)

10 Time (min)

Figure 2. Torque curves of the binary blends.

Torque (N.m)

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PA6/SBR-R/PE-g-MA (87.5/7.5/5) PA6/SBR-R/PE-g-MA (77.5/17.5/5) PA6/SBR-R/PE-g-MA (67.5/27.5/5) PA6/SBR-R/PE-g-MA (57.5/37.5/5)

10 Time (min)

Figure 3. Torque curves of the polyamide 6/SBR-R/PE-g-MA blends.

10 PA6/SBR-R/PP-g-MA (87.5/7.5/5) PA6 SBR PE-g-MA

Torque (N.m)

PP-g-MA

10 Time (min)

Figure 1. Torque curves of pure polymers.

PA6/SBR-R/PP-g-MA (77.5/17.5/5) PA6/SBR-R/PP-g-MA (67.5/27.5/5)

PA6/SBR-R/PP-g-MA (57.5/37.5/5)

10 Time (min)

Figure 4. Torque curves of the polyamide 6/SBR-R/PP-g-MA blends.

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Development of Polyamide 6/Compound by Recycled Rubber Blends Using Graphitized Polyethylene or Polypropylene...

blend torque (PA6/SBR-R/PE-g-MA) was greater than that of PA6/SBR-R/PP-g-MA blends, which indicate that PE-g-MA is more reactive with PA6 compatibilizer than the PP-g-MA. Figures 5 to 7 present the FTIR spectra of PA6/SBR-R binary blends containing 10, 20, and 30% by weight of SBR and PA6/SBR-R/compatibilizer ternary blends containing 5 wt% of the PE- and PP-g-MA compatibilizers. It is possible to observe that the characteristic bands of PA6 were not modified by the presence of SBR and not by increasing its share in the binary blends and the presence of PE-g-MA and PP-g-MA in the ternary blends, showing that their chemical groups were not affected. The profiles of the spectra remain with predominant features of the polyamide, which has a band above 3,000 cm-1 as a characteristic NH stretch of bending and other bands near 1,700 cm-1 referring to carbonyl groups (C=O). The presence of SBR-R does not cause significant changes in the polyamide spectrum, therefore this compound

0.4 Absorbance (u.a)

shows the torque rheometry curves for binary blends of PA6/SBR (90/10, 80/20, 70/30, 60/40). It can be observed that such values of the blends increase with a superior percentage of the added SBR, implying an increase of viscosity, probably because the SBR is acting as a load. Figures 3 and 4 show the torque rheometry curves of ternary blends (PA6/SBR/PE-g-MA) varying the content of SBR and let remaining constant at 5% (by weight) the content of compatibilizer PE- and PP-g-MA. It was found that the torque values of the blends PA6/SBR/PE-g-MA (67.5/27.5/5) and (57.5/37.5/5) with higher percentages of SBR-R were superior when compared with others, which show that increasing percentage of SBR-R in the blend involves a higher increase in viscosity and torque with the addition of PE-g-MA than with PP-g-MA, indicating possible bigger reactions of this compatibilizer. When the PE-g-MA is added to the blend of PA6/SBR-R, here is an increase in torque. According to Roeder et al. (2002), Jiang et al. (2003), and Bassani et al. (2005), anhydride groups of PE-g-MA react with the amine terminal ones of PA6 forming the imide group and resulting in a copolymer in situ at the interface. The reaction between the anhydride groups of PE-g-MA and amine terminal ones of PA6 involves the formation of water as a byproduct, which can lead to degradation of the PA6 chains by hydrolysis. However, Fig. 3 shows that the torque of the blends and PA6/SBR-R/ PE and PP-g-MA were constant, which is an indication of degradation nonoccurrence. One explanation for this behavior is that the PE-g-PP and MA-g-MA has only 1% MA, which would not be sufficient to induce degradation. If we compare the torque curves in function of time (Figs. 3 and 4) of the compatibilized blends, one may see that the

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PA6 SBR PE-g-MA PA6/SBR/PE-g-MA (87.5/7.5/5) PA6/SBR/PE-g-MA (77.5/17.5/5) PA6/SBR/PE-g-MA (67.5/27.5/5)

C =O 0.2

0.0

4000

(C H 2)5

N -H

3500

3000 2500 2000 Wavenumber (cm-1)

1500

1000

Figure 6. Fourier transform infrared spectra of ternary blends with PE-g-MA.

PA6 PP-g-MA PE-g-MA PA6/SBR (90/10) PA6/SBR (80/20) PA6/SBR (70/30)

0.3

(CH2)5

C=O

0.2

N-H 0.1 0.0 4000

3500

3000 2500 2000 Wavenunber (cm-¹)

PA6 SBR PP-g-MA PA6/SBR/PP-g-MA (87.5/7.5/5) PA6/SBR/PP-g-MA (77.5/17.5/5) PA6/SBR/PP-g-MA (67.5/27.5/5)

0.4

1500

1000

Figure 5. Fourier transform infrared spectra of binary blends.

Absorbance (u.a)

0.4

0.2

0.0 4000

N-H

3500

(CH 2)5

C=O

3000 2500 2000 Wavenumber (cm-1)

1500

1000

Figure 7. Fourier transform infrared spectra of ternary blends with PP-g-MA.

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does not cause alterations in the chemical structure of the polymer after processing. From these results, it seems that the molecular weight of the rubbery phase is not an important parameter in this SBR-R concentration. One possible explanation for this behavior is that at this SBR concentration the percolation condition is reached for both molecular weights. The band increases with the SBR-R concentration correspond to the stretching molecular vibrations. This is an important band for it allows determination of the rubbery phase content in the blend. Mechanical tests under tensile and impact In Table 1 and Figs. 8 to 10, it is possible to check the results of the mechanical properties of tensile and impact PA6, binary (PA6/SBR-R) and ternary (PA6/SBR-R/PE-g-MA) blends with 5% of PE-g-MA weight. Selected compositions were only 90/10% and 80/20%, they were chosen with lower levels of SBR-R, because it is in powder form and polyamide and compatibilizer are as granules were blended and introduced simultaneously into the extruder. Higher concentrations of SBR-R could compromise the homogeneity of the mixture.

It is observed in Table 1 and Figs. 8 to 10 that the impact strength, elastic modulus, and maximum stress in the flow of compatibilized blends somewhat reduced when compared with the PA6 values. However, when one considers that the incorporation of recycled material cross-linked in amounts of up to 20% by weight in PA6, this reduction is acceptable because it does not compromise the properties and significantly contributes to cost reduction of the final compound.

Elastic modulus (MPa)

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1000 500

PA6

90/10

80/20

PA6/SBR-R

87.5/7.5/5

77.5/17.5/5

PA6/SBR-R/PE-g-MA

Figure 9. Elastic modulus of polyamide 6 and of binary and ternary blends.

Maximum tension (MPa)

Impact strength (J/m)

1500

70 60 50 40 30 20 10 0

2000

PA6

90/10

80/20

PA6/SBR-R

87.5/7.5/5

50 40 30 20 10 0

77.5/17.5/5

PA6

PA6/SBR-R/PE-g-MA

Figure 8. Impact strength of polyamide 6 and of binary and ternary blends.

90/10

80/20

PA6/SBR-R

87.5/7.5/5

77.5/17.5/5

PA6/SBR-R/PE-g-MA

Figure 10. Maximum tension of polyamide 6 and of binary and ternary blends.

Table 1. Mechanical properties of polyamide 6 and of binary and ternary blends. Compositions

PA6 PA6/SBR-R 90/10 PA6/SBR-R 80/20 PA6/SBR-R/PE-g-MA (87.5/7.5/5) PA6/SBR-R/PE-g-MA (77.5/17.5/5)

E (MPa)

MT (MPa)

Tenacity* (J)

2,080±13.4 2,157±44.7 2,042±30.1 1,864±57.7 1,845±37.8

54.2±0.3 49.9±0.3 41.6±0.3 45.5±1.6 39.5±0.3

94.1±4.1 26.5±11.2 14.9±5.2 32.3±5.4 18.4±8.1

E: elastic modulus; MT: maximum tension, IS: impact strength; *calculated by area under the curve of tension-deformation.

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IS (J/m)

51.9±11.8 41.2± 3.6 35.9±6.1 48.0±6.7 40.1±4.4

Development of Polyamide 6/Compound by Recycled Rubber Blends Using Graphitized Polyethylene or Polypropylene...

Dynamic mechanical thermal analysis Through DMTA, one can estimate changes in molecular relaxations that occur in polymeric materials in a wide temperature range. Knowledge of these changes allows relating molecular parameters and mechanical properties of polymers. Figure 11(a) shows the values of tanδ and the storage modulus (E’) of PA6 and binary and ternary blends with 5% by weight of PE-g-MA in function of temperature, respectively. It was observed that the PA6 presents two peaks at approximately -7 and 61°C. The first transition may be related to β relaxation and the other would be the very Tg, assigned to the α relaxation. For the binary and ternary blends, there was displacement of the peaks to about -10 ºC and the relaxation of displacement α of PA6 to larger values. In Fig. 11(b), it was observed that the peak height of the storage modulus seen after the Tg peak of PA6, which

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appeared to 25°C, may be related to the elastic modulus of the blend. Therefore, the higher, greater is the stored energy and higher elastic modulus of the material. Thus, as the amount of rubber increased, the greater the height and intensity of the peaks and elastic modulus, as also seen in Fig. 9, for the elastic modulus. Differential scanning calorimetry Figure 12(a)-heating and (b)- cooling presents the DSC curves of the blends of PA6 and PA6/SBR-R with 10 and 20 wt% of SBR-R ternary and with 5 wt% of the compatibilizer PE-g-MA. It is noted that the present PA6 melting temperature (Tm) at approximately 224°C and its crystallization starts at about 195°C. The melting enthalpy (DHm) for PA6 is approximately 191 J/g. In the ternary blends peak melting and crystallization compatibilizing agent for the PE-g-MA are observed, in which the crystalline melting temperature (a)

(a) PA6 PA6/SBR-R (80/20) PA6/SBR-R (90/10) PA6/SBR-R/PE-g-MA (87.5/7.5/5) PA6/SBR-R/PE-g-MA (77.5/17.5/5)

61.6°C 83.7°C 96.6°C

Endo

- 7.04°C

tan δ

125°C PA6 PA6/SBR-R (90/10) PA6/SBR-R (80/20) PA6/SBR-R/PE-g-MA (87.5/7.5/5) PA6/SBR-R/PE-g-MA (77.5/17.5/5)

50 -100

-50

Temperature (°C)

100

150

150 200 Temperature (°C)

250

(b) PA6 PA6/SBR-R (90/10) PA6/SBR-R (80/20) PA6/SB/PE-g-MA (87.5/7.5/5) PA6/SB/PE-g-MA (77.5/17.5/5)

(b)

195°C

Endo

PA6 PA6/SBR-R (80/20) PA6/SBR-R (90/10) PA6/SBR-R/PE-g-MA (87.5/7.5/5) PA6/SBR-R/PE-g-MA (77.5/17.5/5)

E' (GPa)

100

224°C

110°C

-100

-50

100

Temperature (°C)

150

Figure 11. tanδ and E’ curves a function of temperature for the polyamide 6 and binary (PA6/SBR-R) and ternary (PA6/SBR-R/PE-g-MA) blends.

100

150 200 Temperature (°C)

250

Figure 12. Differential scanning calorimetry curves of polyamide 6, binary (polyamide 6/SBR-R) and ternary (polyamide 6/SBR-R/PE-g-MA) blends: (a) Heating; (b) cooling.

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(Tm) is approximately 125°C and the crystallization ones (Tc) is approximately 110°C. In all curves, the peaks crystallization of PA6 in both binary and ternary blends indicated that the compatibilizer is not directly influencing the crystallinity of PA6. Scanning electron microscopy In Figs. 13 to 17 the SEM photomicrographs of PA6 and binary and ternary blends with 5% by weight of PE-g-MA and increases of 100 and 2,000 X are shown. These photomicrographs were obtained from the fracture surface of the specimens of PA6 and of binary and ternary blends subjected to Izod impact testing. In Fig. 13 there is a regular morphology with a ductile fracture aspect which is characteristic of PA6. In Figs. 14 to 17, it can be observed poor adhesion between the phases, probably due to poor interfacial interaction between these, indicating the immiscibility of the system and also due to this weak interaction interfacial voids exist between the domains and the matrix

rubber, which decrease with the addition of compatibilizing agent percentage in the blend. The addition of the compatibilizing agent to the blend stimulated a better interfacial adhesion between the domains and the matrix and size of the fields altered in relation to binary blends. The morphology appears with some degree

Empty

Figure 15. Scanning electron microscopy micrograph of polyamide 6/SBR-R of the blend (80/20).

Rubber phase

Figure 13. Scanning electron microscopy micrograph of polyamide 6.

Rubber phase

Figure 16. Scanning electron microscopy micrograph of the blend polyamide 6/SBR-R/PE-g-MA (87.5/7.5/5).

Rubber phase

Empty

Figure 14. Scanning electron microscopy micrograph of polyamide 6/SBR-R of the blend (90/10).

Figure 17. Scanning electron microscopy micrograph of the blend of polyamide 6/SBR-R/PE-g-MA (77.5/17.5/5).

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of co-continuity for the addition of the compatibilizing agent causes a refinement of the co-continuous structure, which can be explained by the reduction in interfacial tension, stabilizing interface and preventing coalescence (Oliveira, 2009). However, the introduction of this was not enough to significantly improve the mechanical properties of the blend PA6/compound by recycled rubber. It can be attributed to the quantity or type of compatibilizing agent used. Therefore, it was observed that the morphology presented by binary and ternary blends rubber particles has not been homogeneously distributed, the average distance between the particles is not uniform and, in certain regions of the fracture surface of the particles, almost touch and in other regions, their distance is greater. The main feature observed for this material, however, was the relative lack of compatibility particle/matrix. We observed particles torn and totally broken matrix interfaces. These two aspects are evidences of a low interfacial adhesion.

CONCLUSIONS Blends of PA6/compound recycled rubber (SBR) were produced. In rheological, it was found that the addition of the

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compatibilizer PE-g-MA showed higher torque values both for the binary mixtures and for the ternary ones. This result may indicate a higher efficiency of PE-g-MA with respect to the PP-g-MA compatibilizer. The impact resistance and elastic modulus of the compatibilized blends reduced somewhat when compared to PA6. Also, the impact resistance of the compatibilized blends increased as compared to noncompatibilized ones. The addition of the compatibilizing agent was not sufficient to provide significant differences in the mechanical properties. Even so, the blends of PA6/ compound recycled rubber are a good alternative for recycling the SBR-R, resulting in a new material with specific properties.

ACKNOWLEDGMENTS The authors thank Programa de Pós-graduação em Ciência e Engenharia de Materiais (PPGCEMat), Rhodia/SP, Crompton/SP, São Paulo Alpargatas/PB and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for their support.

REFERENCES Anjos, M.R.O., 2007, “Avaliação do emprego de borrachas SBR utilizadas em solas de calçados pretos de uso da marinha no Brasil”, 93f, Dissertação (Mestrado em Ciências em Engenharia Metalúrgica e de Materiais), Universidade Federal do Rio de Janeiro. Bassani, A., Hage Jr., E., Persan, L. A., Machado, A. V. and Covas, J. A. - 2002, “Propriedades Mecânicas de Blendas de Nylon-6/ Acrilonitrila-EPDM-Estireno (AES) Compatibilizadas com Copolímero Acrílico Reativo (MMA-MA)”, Polímeros, Vol. 12, No. 2. Bassani, A., Hage Jr., E. and Persan, L. A., et al., 2005, “Evolução da Morfologia de Fases de Blendas PA6/AES em Extrusora de Dupla Rosca e Moldagem por Injeção”, Polímeros Ciência e Tecnologia, Vol. 15, p. 176. Fiegenbaum, F., 2007, “Estudo da Compatibilização das blendas PP/ PA6 e PA6/EPR”, 79f. Dissertação (Mestrado em Engenharia Química), Universidade Federal do Rio Grande do Sul, Rio Grande do Sul. Fornes T. D., Yoon, P. J., Keskkula, H. and Paul, D. R., 2001, “Nylon 6 nanocomposites: The effect of matrix molecular weight”, Polymer, Vol. 42, No. 25, pp. 9929-9940.

Jiang, C., Filippi, S. and Magagnini, P., “Reactive compatibilizer precursors for LDPE/PA6 blends II: maleic anhydride grafted polyethylenes”, Polymer, Vol. 44, p. 2411. Maglio, G. and Palumbo, R., 1984, “The role of interfacial agents in polymer blends”. Polymer Blends, Processing, Morphology and Properties. New York, Plenum Press, Vol. 2, p. 41. Newman, S., 1978, Rubber modification of plastics, In: Paul, D.R. and Newman, S. “Polymer Blend”, New York, Academic Press, Vol. 2., p. 63. Obrecht, W., 2012, “Rubber, 4. Emulsion Rubbers”, Ullmann’s Encyclopedia of Industrial Chemistry. Oliveira, A.D., 2009, “Dispersão seletiva de argila montmorilonita em blendas poliméricas de PA6/ABS”, Dissertação (Mestrado em Ciência e Engenharia de Materiais), Programa de Pós-Graduação em Ciência e Engenharia de Materiais (PPG-CEM/UFSCar), São Carlos, Brazil. Oliveira, G.H. and Botelho, E.C., 2007, “Avaliação da Resistência à Fadiga do Compósito de Fibras de Carbono/PEI com Aplicações na Indústria Aeroespacial”, Proceedings from IX CECEMM, Florianópolis, Brazil.

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Silva, D.F., Araújo, E.M. and Melo, T.J.A.

Ramya P., Ranganathaiah C., Williams J. F., 2012, “Experimental determination of interface widths in binary polymer blends from free volume measurements”, Polymer, Vol. 53, pp. 4539-4546. Roeder, J., Oliveira, R. V. B., Gonçalves, M. C., Soldi, V. and Pires, A. T. N., 2002, “Compatibility effect on the thermal degradation behaviour of polypropylene blends with polyamide 6, ethylene propylene diene copolymer and polyurethane”, Polymer Testing, Vol. 21, p. 815. Utracki, L.A., 2000, “Polymer blends”, Rapra Review Reports, Vol. 11, No. 3.

Vossen, C.A., 2009, “Nanocompósitos de ABS/PA e Argila Organofílica”, 88f. Dissertação (Mestrado em Engenharia metalúrgica e de materiais), Escola Politécnica da Universidade de São Paulo, Brazil. Obrecht W., Lambert J., Happ M., Oppenheimer-Stix C., Dunn J. and Krüger R., 2012, “Rubber, 4. Emulsion Rubbers” in Ullmann’s Encyclopedia of Industrial Chemistry. Yu W., Zhou W. and Zhou C., 2010, “Linear viscoelasticity of polymer blends with co-continuous morphology”, Polymer, Vol. 51, pp. 2091-2098.

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doi: 10.5028/jatm.v5i2/193

Environmental Effects on Thermal Properties of PEI/Glass Fiber Composite Materials Edson Cocchieri Botelho1, José Carlos Bravim Júnior1, Michelle Leali Costa1, Maria Candida Magalhaes de Faria1

ABSTRACT: The aim of this study was to investigate the effects of hygrothermal exposure, ultraviolet (UV) radiation, salt spray and thermal shock aging on the thermomechanical behavior of glass fiber reinforced by poly (ether-imide) (PEI) composites. Dynamic mechanical (DMA) and Thermomechanical (TMA) analyses have been performed on the aged PEI composites after being submitted to the climatic chambers. Additional techniques have been used to characterize the laminates, such as optical microscopy and infrared spectroscopy (FT-IR) in order to evaluate possible structural changes in these materials. Slight changes were observed both in glass transition temperature and in thermal expansion coefficient as a result from the environmental conditioning used (hygrothermal, salt spray, UV radiation and thermal shock conditioning). Thus, when exposed to these conditions, PEI/glass fiber laminates maintain its compromise with the performance component. KEYWORDS: Thermoplastic composites, Environmental conditioning, Glass transition temperature, PEI/glass fiber.

INTRODUCTION Lightweight composite materials are currently finding extensive use in a wide range of load-bearing engineering applications due to its low density and its high performance in terms of strength and stiffness, besides high cost competitive market. These factors place it in a position to replace the traditional metallic materials already used in the sectors of interest of new technologies such as civil, naval, automotive and aerospace principally (Diaz and Rubio, 2003; Botelho et al., 2003). With the constant necessity of the development of lightweight structures, the advancements of science and technology in several areas has contributed to the improvement of aviation parts. Structural components of aircraft for civilian and military purposes, such as flaps, rudders, fairings, aileron, fuel tanks, elevator, tail cone and others that were previously made o f metal alloys are recently being manufactured in laminated structures of advanced polymeric composites (Kim and Ye, 2005). Currently, several companies are already introducing these parts in their aircraft, among which may be cited as Airbus, Boeing and Embraer (Botelho and Rezende, 2000). Thermoplastic composite materials have several advantages over traditional thermoset composites in the manufacture of lightweight structures, among them the fact that these materials can be reprocessable, have good costeffectiveness and solidify in a short time compared with slow curing of the thermoset resins, which facilitate their use (Botelho et al., 2003). Between the thermoplastic matrix, the poly (ether-imide) (PEI) is a polymer of high performance

1. Faculdade de Engenharia de Guaratinguetá – Guaratinguetá/SP – Brazil Author for correspondence: Edson Cocchieri Botelho | Departamento de Materiais e Tecnologia/FEG | Avenida Ariberto Pereira da Cunha, 333 – Pedregulho | CEP 12.516-410 Guaratinguetá/SP – Brazil | E-mail: ebotelho@feg.unesp.br Received: 22/11/12 | Accepted: 06/03/13

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with good properties, such as strength and stiffness at elevated temperatures, good electrical properties, ample chemical resistance, besides low cost. Furthermore, its glass transition temperature Tg is high compared to other engineering polymers and can be used in aeronautical applications (Oliveira et al., 2009; Zenasni et al., 2006; Viña et al., 2008; Chevali et al., 2010). Fiber-reinforced thermoplastic composites in outdoor applications encounter ambient moisture, variation of temperature, salinity and ultraviolet (UV) radiation in addition to stress and temperature, which affects mechanical properties (White and Shyichuk, 2007). These materials are used for long periods of time on airplanes, so it is necessary to know exactly which influence of such factors ensure its safe operation, preserving their properties for the period desired (Yakimets et al., 2004). When these composite materiais are subjected to distinct and repetitive ranges of temperature, the heating and cooling processes can generate interlaminar stresses, causing defects in the microstructure or delamination of their laminas, and in this cases can occur mechanical deformations of thermal origin (thermal fatigue) (Boualem and Sereir, 2011; Chawla, 2001; Costa et al., 2012; Botelho et al., 2005; Hufenbach et al., 2011; Ramanujam et al., 2008). In this context, a better prediction of the long-term durability of composite materials with organic matrix is essential. In particular, the study of the coupled effects of mechanical cyclic loads, of temperature variations and of a more or less oxidative environment on the damage of these materials remains to be made. When composite laminates with long continuous fibers are subjected to temperature variations, the mismatch of thermal expansion coefficients of fibers and matrix as well as the difference of ply orientation in the lay up are such that local stresses appear, which can take part in the degradation of the laminate. When these thermal variations are cyclic, they induce, at the ply level, cyclic stress variations which can be compared, at this scale, to a fatigue phenomenon. Various types of damage similar to those observed in mechanical fatigue result from these cyclic stresses, like transverse matrix cracking, fiber/matrix debonding and delamination. Few works deal with the long-term behavior of composites subjected to thermal chock condition (Boualem and Sereir, 2011; Chawla, 2001; Costa et al., 2012; Botelho et al., 2005; Hufenbach et al., 2011; Ramanujam et al., 2008). Concerning moisture influence, this can penetrate into the composite structure by diffusive and/or capillaries

processes in accordance with the second Fick’s law. It is commonly assumed that water diffuses into the amorphous regions of the polymer where hydrolysis should occur at a rate which depends upon the crystallinity and the initial content of end-groups. In particular, the increase of humidity decreases the mechanical properties of some materials and it is aggravated when combined with high temperatures (Jedidi et al., 2006; Kellogg et al., 2003; Costa et al., 2010; Ray, 2006; Botelho and Rezende, 2010). Moisture absorption may induce severe mechanical and physicochemical changes in polymer matrix or fiber/matrix interphase: polymer chains can undergo a reversible plasticization process, which lowers the glass transition temperature, be subjected to irreversible hydrolysis (Jedidi et al., 2006) and the fiber/matrix interphase can be damaged due to the coupling with internal stresses, for instance. The moisture diffusion process is highly dependent on the temperature and relative humidity (Jedidi et al., 2006; Kellogg et al., 2003; Costa et al., 2010; Ray, 2006; Botelho and Rezende, 2010). In the case of incidence of UV radiation, it is known that energy is comparable to the covalent bonds in the polymers, thus photo-oxidative reactions may occur and cause degradation in the polymeric matrix, crosslinking among other effects which affects the mechanical resistance of the laminate (White and Shyichuk, 2007; Yakimets et al., 2004). Also, it is important to understand the behavior of composite materials concerning its exposition in sea water. In the seawater environment, a composite structure is subjected to moisture absorption and fatigue wave loading. Composite materials are known to exhibit some degree of degradation due to moisture absorption. Several studies have examined the mechanical performance of polymeric composites in seawater (Boualem and Sereir, 2011). By comparing cycles to failure as a function of stress amplitude, some concluded seawater exposure gives degradation in performance, while others observed very little degradation (Boualem and Sereir, 2011; Chawla, 2001; Costa et al., 2012; Botelho et al., 2005; Hufenbach et al., 2011; Ramanujam et al., 2008). Few have, however, studied the effect of seawater exposure on thermoplastic composites, which may change, even when there is no significant seawater induced degradation. The effect of moisture on delamination cracking resistance is critical to the durability of composite materials in seawater environment because delamination crack growth has been identified as the most dominant failure mechanism (Boualem and Sereir,

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2011; Chawla, 2001; Costa et al., 2012; Botelho et al., 2005; Hufenbach et al., 2011; Ramanujam et al., 2008). So, in addition to mechanical properties (tensile, compression, shear etc.), it is important that the maximum service temperature be verified making sure the aircraft flight envelope, based on knowledge of Tg and melting temperature (Tm). In this study, moisture, UV radiation, salinity and temperature influences on thermal properties of PEI/glass fiber laminate have been investigated. The effects of environment on this thermoplastic composite were studied by Dynamical Mechanical Analyses (DMA) and Thermomechanical Analyses (TMA). Additional techniques have been used to characterize the laminates, such as optical microscopy and FT-IR (infrared spectroscopy) in order to evaluate possible structural changes in these materials.

EXPERIMENTAL Materials The material used in this work is a composite laminated with glass fiber fabric reinforcement and PEI thermoplastic matrix, supplied by the Ten Cate Advanced Composites (Dutch company). Its configuration consists of a laminate with around 2.0 mm of nominal thickness and woven made in 8 Hardness Satin (HS) configuration. Environmental conditioning In order to check the mass gain per unit of time on these laminates, the specimens (in triplicate) remained for 60 days at temperature of 80°C with a relative humidity of 90% in climatic chamber. The hygrothermal exposure is based on ASTM D5229/D5229M-04 for composite materials. The samples were dried for 48 hours in a vacuum oven at 60°C in order to remove all the moisture present before to be subjected to hygrothermal chamber. The mass control allowed knowing the material moisture absorbing by the Eq. 1. M=

M u-Ms . 100 (1) Ms

Where M is the mass percentage; Mu, the wet mass and Ms is the dry mass.

243

In the conditioning by thermal shock, it was used a chamber with a hot zone (upper) and a cold zone (lower) interconnected by a vertical lift, which remained for 30 minutes for each step. This chamber was programmed to operate during 1,800 cycles in temperature range from -50 to +80°C in order to simulate the flight envelope of the aircraft (Yakimets et al., 2004; Boualem and Sereir, 2011). The conditioning methodology by UV exposure was conducted according to ASTM 4329-99 standard. The system used consists of UVB-313 lamps emitting radiation during 8 hours at 60°C with an intensity of 0.76 W/(m2nm), alternating with 4 hours of water condensation coming from vapor generated at 50°C. Samples were used in order to set the time intervals of 200, 600 and 1,200 hours. During exposure, the samples were photographed to check the degradation of the material up to 1,200 hours of exposure. In order to evaluate if UV radiation generated a degradation process in PEI/glass fiber, FT-IR analyses were used in this work. The equipment utilized was a Spectrum One of Perkin-Elmer and the parameters were: analyzed range of 4,000 to 400 cm-1, resolution of 4 cm-1 and gain of 20 scanning. The specimens were analyzed according to the reflective technique (UATR), in which only the surface of the specimen is evaluated. The coupons submitted to salt spray climatic chamber remained exposed for 15 days, following the ASTM B117-03 standard. The salt solution was prepared with 1 kg of NaCl in 19 L of distilled water, and the final pH was around 7. The chamber test temperature was set in 47°C, the solution, in 35°C and the pressure was 1 kgf/cm². Thermal and morphological evaluation Optical microscopy was used to evaluate the structural quality of the laminates as received and also after the environmental conditionings (hygrothermal, thermal shock and salt spray conditionings), generating information about the quality of the processing. It was used an optical microscope with a Zeiss stereoscopic magnifier. The ultrasonic inspection was performed by using the pulse-echo method, immersing the specimen in a water bath. The results were provided in A-scan graph, which can detect discontinuities in the composites, e.g. resin-rich regions, voids or cracks. The inspection was carried out with an equipment model MUIS32 from MATEC. The range of probe can be varied from 2.25 to 10 MHz. In this research, the 10 MHz probe was more suitable due to the easiest

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assessment to identify the defects. A-scan graph aided to calibrate the patterns of a typical structural composite peaks (reference-without defects) and the difference between the reference peak and the other peaks is referred as attenuation signal. The intensity of the attenuation signals can inform what type of defect might occur. Each point of the laminate creates an A-scan signal, after scanning the entirely laminate. The referred map shows the background echo produced by the A-scan, which can show any flaws along the thickness. DMA tests were conducted in a bending loading mode, by the DMA equipment, model DMS 6100 from Seiko – SII Nanotechnology on samples with thickness of 2.0 mm, width of 12.0 mm and length of 50 mm. All measurements were performed with frequency of 1Hz, N2 atmosphere (20 mL/min) and heating rate of 3°C/min, in the temperature range from 30 to 210°C. This experiment was used in order to determine the Tg. TMA was conducted in order to determine Tg (ASTM E1545) and also thermal expansion coefficient (ASTM E831) for all conditioning studied in the composite PEI/glass fiber. For the TMA tests, it was used N2 atmosphere (20 mL/min) and heating rate of 3°C/min in the temperature range from 30 to 210°C. All TMA tests have been carried out in TMA SS 6100 equipment, EXSTAR6000 model, version 6.2U, from SII Nanotechnology.

According to the results found, the maximum moisture content absorbed by the specimens was 0.18%, determined after around 25 days — showed in Fig. 1 as (hours)1/2. Water is only absorbed by the amorphous part of the thermoplastic matrix (Botelho and Rezende, 2010). However, in composite materials reinforced by glass fiber, the surface treatment of the fiber can absorb the moisture, increasing the weight gain promoted by moisture, inside of composite. Therefore, as explained before, in this work, it was not found significant differences between the neat matrix (Botelho and Rezende, 2010) and the results obtained from PEI/glass fiber laminate. Note that the absorption rate was nearly constant during the first two weeks, about 0.01% by mass gain. After this period, the composite reaches a state called pseudo-equilibrium with the amount of water maintained practically constant. This behavior is explained by the fact that the free water penetrates the matrix by the concentration gradient with the continuous exposure. After the conditioning period, the amount of moisture in the composite did not vary significantly. Figure 2 shows representative optical micrographs of the composite submitted to the hygrothermal conditioning (Fig. 2b). The rate of moisture diffusion is controlled by the diffusivity. It is a strong function of temperature and a weak function of relative humidity. Moisture can potentially cause debonding at the fiber/matrix interface not only through chemical attack and reaction, but also through mechanical-chemical effects such as osmotic pressure. The mechanism of attack at the interface is

RESULTS

0.20 Moisture Gain (%)

Moisture absorption Figure 1 displays the weight gain curves of the PEI/ glass fiber laminates after being submitted to hygrothermal conditioning at 80°C and 90 RH. The composite weight gain has been normalized according to Eq. 1. The results of three composite specimens are shown in the plot. The reproducibility of the uptake curve is fairly good among different specimens. The uptake curves of the composite obey the Fick’s law, with the weight gain initially increasing linearly with respect to (time)1/2 and gradually leveling off. Furthermore, the normalized composite weight gain is very close to that of the neat matrix, as can be observed in the literature (Yakimets et al., 2004; Boualem and Sereir, 2011).

0.25

0.15 0.10 0.05 0.00

30 Time (h½)

Figure 1. Moisture absorption curve for poly (ether-imide) (PEI)/glass fiber composites.

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decisively governed by the chemistry, structure, morphology, and modes of failure at that interface (Boualem and Sereir, 2011; Chawla, 2001; Costa et al., 2012; Botelho et al., 2005; Hufenbach et al., 2011; Ramanujam et al., 2008).

(a)

245

Figure 3 depicted the A-scan ultrasound results for the PEI/glass fiber specimens after being submitted to hygrothermal conditioning. From these results, for specimens subjected to hygrothermal conditioning, there is a small

(b)

Figure 2. Microscopy of the composite poly (ether-imide) (pEI)/glass fiber. (a) Unweathered hygrothermal conditioning; (b) after hygrothermal conditioning.

(a)

(b)

Figure 3. a-scan ultrasound results for poly (ether-imide) (pEI)/glass fibers composites. (a) Unweathered hygrothermal conditioning; (b) after being hygrothermally weathered. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.241-254, Apr.-Jun., 2013

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change of the reference peaks, in which a decrease lower than 10% in the bottom echo signal can be observed. This small change is not enough to indicate modification in the structure of the laminate, confirming the optical microscopy results. ulTRAvIoleT degRAdATIon Surfaces of all specimens exposed to UV radiation exhibited a distinct change in color from yellow to dark yellow during early stages of the exposure. The discoloration established that photo-oxidation resulted in the formation of chromophoric chemical species, which were absorbed in the visible range of light. Minor changes in surface roughness were also visible for all specimens exposed to UV radiation. Exposure to water vapor condensation did not result in any visible changes in specimen morphology. According to the literature (Botelho and Rezende, 2010), further details regarding the physical processes that

govern material degradation can be revealed by examination of the specimens under an optical microscope (OM). Therefore, in this work, no changes in morphology — using OM — were observed for either the specimen surface or edge, for specimens exposed to UV radiation (Fig. 4). Also, it was observed that the fibers were more exposed after the radiation process. This behavior is expected since it was happen degradation of the matrix during the UV conditioning. In Fig. 5, the FT-IR spectra for the unconditioned specimens and that one submitted to UV radiation conditioning for different times of exposure are depicted. Analyzing the samples before and after conditioning by UV radiation, small changes can be observed in the chemical structures of the material. In this study, up to 200 hours of exposure, the principal absorption is in the region of 3,300 cm-1, corresponding to stretching (v) hydroxyl group (-OH); beyond the range 3,300–3,600 cm-1, it

(a)

(b)

(c)

(d)

Figure 4. Optical microscopy results for poly (ether-imide) (pEI)/glass fiber composites after being submitted to ultraviolet radiation. (a) 0 hours; (b) 200 hours; (c) 600 hours; (d) 1,200 hours. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.241-254, Apr.-Jun., 2013

Environmental Effects on Thermal Properties of PEI/Glass Fiber Composite Materials

corresponds to the stretching amine (NH). At 600 hours of exposure, it is observed, in addition to the aforementioned events, the band of 2,950 cm-1, which shows a small change, indicating an elongation of aliphatic CH groups. As for the maximum interval conditioning (1,200 hours), there were small changes, indicating that the compound undergoes degradation (but probably not significant to modify their structural application) in incidence of radiation. effeCTS of THeRMAl SHoCK CondITIonIng Figure 6 shows the optical micrographs of PEI/glass fiber specimens after being submitted up to 1,000 thermal cycles. Concerning thermal fatigue process, it is expected that the porous generate failures or delaminations process during the thermal cycling. As can be observed in this work, this behavior was not verified by means of OM for either the specimen surface or edge, after being exposed to thermal

% Transmittance

100 95 90 85 80 75 70 65 60 55

cycling condition. This behavior confirms that the cycling number used was not enough to generate thermal fatigue in the composite. In this study, the amount of porosity was not considered, since this behavior depends on the analyzed region of the specimen. Figure 7 depicts the A-scan ultrasound results for the PEI/glass fiber specimens after being submitted to thermal cycle conditioning. From these results, significant changes in the peaks were not observed, indicating that probably there are no significant differences in thermal expansion coefficients between the layers. effeCTS of AgIng on THe THeRMAl BeHAvIoR: dynAMICAl MeCHAnICAl AnAlySeS And THeRMoMeCHAnICAl AnAlySeS Figures 8 to 10 show the dynamic-mechanical behavior of PEI/glass fiber composite as received and after being

(b)

100 95 % Transmittance

% Transmittance

100 (a) 95 90 85 80 75 70 65 60 55 50 45 40 35 4500 4000 3500 3000 2500 2000 1500 1000 500 cm-1

247

90 85 80 75 70 65 60 4500 4000 3500 3000 2500 2000 1500 1000 500 cm-1

(c)

Reference Conditioned

4500 4000 3500 3000 2500 2000 1500 1000 500 cm-1 Figure 5. Infrared spectroscopy (Ft-IR) results of the samples subjected to ultraviolet radiation. (a) 200 hours; (b) 600 hours; (c) 1,200 hours. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.241-254, Apr.-Jun., 2013

Botelho, E.C., Bravim Júnior, J.C., Costa, M.L. and Faria, M.C.M

248

(a)

(b)

Figure 6. Optical microscopy of poly (ether-imide) (pEI)/glass fiber laminates. (a) Unweathered thermal shock conditioning; (b) after thermal shock conditioning.

(a)

(b)

Figure 7. a-scan ultrasound results for poly (ether-imide) (pEI)/glass fibers composites. (a) Unweathered thermal shock conditioning; (b) after thermal shock conditioning.

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submitted to hygrothermal and salt spray conditioning, UV exposition and thermal shock, respectively. Figures 11 to 13 present the TMA curves for all conditioning studied in this work. The method of determining the Tg in the DMA can be a manner for disagreement, as at least five ways are in current use. Depending on the industry standards or background of the operator, the peak or onset of the tan delta curve, the onset of the E’ drop, or onset or peak of the E” curve may be used. The values obtained from these methods can differ up to 25°C from one another on the same run. In addition, a 10–20°C difference from Differencial Scaning Cromatography (DSC) or TMA is also seen in many materials. Differences as great as 25°C have been reported. In practice, it is important to specify exactly how the Tg should be determined (Menard, 2008). According to Table 1, the Tg values obtained by DMA (peak of tan d) are lower than the values of Tg measured by TMA, in the order of 20°C.

1.8

(a)

(b)

1.6 1.4

E’’ [GPa]

E’ [GPa]

As can be observed in Fig. 8 and also in Table 1, the hygrothermally aged glass fiber reinforced specimen did not show significant decrease in the magnitude of the relaxation peak (Tg), since the samples subjected to hygrothermal conditioning had a reduction of only 3.7% compared to the unweathered sample values; and this decrease for sample subjected to saline conditioning was only 2.7% (Tg obtained from onset E’ drop values). Similar behaviors were observed when Tg was obtained from E’’ and tan δ. The phenomenon of decrease in the Tg temperature for the hygrothermally aged glass fiber reinforced sample is related to plasticization, which induces an increase in the amorphous chain mobility but, since for PEI/glass fiber composite the absorbed moisture content was very low, this effect was not so pronounced. In the characteristic plot of the storage modulus (Fig. 8a), hygrothermally and salt spray aged glass fiber reinforced samples had a lower storage modulus compared to unweathered specimen, but it was observed only around

2.0

4 2

1.2 1.0 0.8 0.6

100 150 200 Temperature (ºC)

tan δ

249

0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

250

0.4 0.2 0

100 150 Temperature (ºC)

(c)

100 150 Temperature (ºC)

200

250

Hygrothermal Reference Salt-Spray

250

Figure 8. Dynamic mechanical analysis (DMa) curves of the poly (ether-imide) (pEI)/glass fibers composite after being conditioned in salt spray and hygrothermal chamber. (a) E’; (b) E’’; (c) tan δ. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.241-254, Apr.-Jun., 2013

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5% of decrease of this property. This behavior is probably related to the plasticizing effect promoted by the moisture absorption. Also, it was observed a second peak in Fig. 8c, probably related to the beginning of plasticizing effect. Figure 9 and Table 1 show the results of DMA for the samples submitted to the UV exposure. As can be seen, the Tg value increases as the time of exposure to the UV radiation

increases. As can be observed from this result, the Tg value obtained from the onset of E’ was 164°C for the unweathered specimen. After being submitted to UV radiation during 200, 600 and 1,200 hours, the PEI/glass fiber laminate increases the Tg values in 1.89, 2.31 (table shows the contrary) and 4.98%, respectively. This increase in Tg after exposure to UV condensation indicates that the PEI matrix underwent

table 1. Dynamic mechanical analysis (DMa) and thermomechanical analysis (tMa) results obtained from aged poly (ether-imide) (pEI)/glass fiber laminate. Conditioning

Tg (onset e’ drop – dMA) (°C)

Tg (peak of tan δ – dMA) (°C)

Tg (TMA) (°C)

α x 10-6 (°C-1)

Reference

164±0.8

184±0.8

204±2.3

16±0.5

Hygrothermal

167±0.7

186±1.7

206±1.2

19±1.5

Salt spray

164±0.3

183±0.2

202±0.5

37±0.5

UV – 200 hours

169±0.8

185±0.9

204±1.4

38±3.6

UV – 600 hours

167±0.8

185±0.6

206±0.4

35±1.3

UV – 1200 hours

173±0.5

186±0.4

216±0.5

27±3.8

Thermal shock

170±0.3

183±0.2

183±0.5

26±3.0

Tg: glass transition temperature.

(a)

8 E’’ [GPa]

E’ [GPa]

6 4 2 0

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Figure 9. Dynamic mechanical analysis (DMa) curves of the poly (ether-imide) (pEI)/glass fiber composite after being submitted to ultraviolet (UV) radiation. (a) E’; (b) E’’; (c) tan δ. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.241-254, Apr.-Jun., 2013

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hydrolysis and irreversible crosslink process, but very slightly, confirming the FT-IR results. However, since this process was significant only for specimens submitted to UV radiation after 1,200 hours, higher periods are necessary to confirm this result. The measurement of Tg, among other reasons, presents scatter because the glass transition is actually defined as a temperature range within large range molecular motion is activated by the temperature increase. The problem is more complex in the case of wet polymer samples with high Tg values, because the samples lose moisture to a significant extent in the glass transition region, where the molecular mobility and the moisture diffusion are enhanced. Thus, probably there is a gradient of moisture concentration through the samples in the Tg region, and a corresponding distribution of temperature dependent of the molecular relaxation times (Costa et al., 2005).

The moisture level leads to different changes in Tg depending on the particular characteristics of molecular structures and matrix/fiber interface interactions of the matrix system. The different behavior of the samples studied (samples submitted to the hygrothermal conditioning and samples submitted to the UV radiation and humidity) and changes in the distribution of relaxation times associated with the α-transition (Tg) could not have been caused only by the plasticization effect, because the both specimens were submitted to the humidity conditioning before the DMA tests. When Tg variations and FT-IR results are compared, initial breaks of chains apparently occur, with a maximum of reticulation in 600 hours, and some breaks of chains happen in 1200 hours, when the E’ results are evaluated. Figure 10 and Table 1 present the DMA results obtained for PEI/glass fiber composite after being exposed to thermal

2.5

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Figure 10. Dynamic mechanical analysis (DMa) curves of the poly (ether-imide) (pEI)/glass fiber composite after being submitted to thermal shock conditioning. (a) E’; (b) E’’; (c) tan δ. J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.241-254, Apr.-Jun., 2013

Botelho, E.C., Bravim Júnior, J.C., Costa, M.L. and Faria, M.C.M

Reference UV 200

1600

UV 600 UV 1200

1200 TMA (mm)

shock chamber during 1,000 cycles. In this case, it is observed that the Tg value, as determined by onset of E’, increases slightly in only 3.54% in the sample after being submitted to thermal cycling (170°C), due probably to the reticulation process of the matrix. Since there is no evidence that this conditioning generates thermal fatigue, as showed from OM experiments, these results were expected. Figures 11 to 13 and Table 1 present the results obtained from TMA experiments. As can be observed, the Tg tendency values were similar to those found by using DMA experiments with exception of thermal shock sample. Also from TMA experiments, it was observed that the values of thermal expansion coefficient change as a function of the kind of conditioning to which the sample was submitted. The polymeric matrices used in composite present positive and high thermal expansion coefficient (typically higher than the steel alloy and aluminum). However, because of their polar groups, these matrices may both absorb moisture and expand, or release moisture and shrink. These expansions and contractions dimensional per unit length are called hygroscopic deformation, and in many cases are directly proportional to the amount of water that the matrix absorbs or releases. Thus, it can be seen that all α values obtained after the conditioning increased, indicating that the system PEI/fiberglass expanded by moisture absorption.

800 400 0 0

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Figure 12. thermomechanical analysis (tMa) curves of the poly (ether-imide) (pEI)/glass fiber composite for conditioning in ultraviolet radiation and reference state.

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Figure 13. thermomechanical analysis (tMa) curves of the poly (ether-imide) (pEI)/glass fiber composite for shock thermal conditioning and reference state.

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Figure 11. thermomechanical analysis (tMa) curves of the poly (ether-imide) (pEI)/glass fiber composite for saline and hygrothermal conditionings and reference state.

From the results of this research work, it was found that the material absorbed about 0.18% of moisture, which is considered low when compared to other composites used in aeronautical applications found in the literature, and the absorption rate was constant during the first two weeks of hygrothermal exposure. The hygrothermal conditioning does not show significant evidence that the plasticizing effects

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.241-254, Apr.-Jun., 2013

Environmental Effects on Thermal Properties of PEI/Glass Fiber Composite Materials

resulted in decrease of properties of PEI/glass fiber laminates. Similar observation can be attributed to the salt spray conditioning effects on thermal properties of PEI/glass fiber, since Tg was not significantly affected by this conditioning. The specimens submitted to UV radiation presented small changes in the chemical structures of the material, indicating that the compound undergoes degradation, but this behavior was not so appreciable to indicate decreases of thermal properties. The increase of Tg after UV condensation exposure during 1,200 hours indicates an irreversible crosslink process, but very slight. The thermal shock conditioning promotes slight increase in the Tg value, but the cycling number used was not enough

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to generate thermal fatigue in the composite. According to this work, it was not observed significant differences before and after shock conditioned specimens on thermal properties to disqualify this composite when applied in aeronautical field, when changes of the temperature are evaluated.

ACKNOWLEDGMENTS The authors acknowledge the financial support received from FAPESP and are also grateful to Ten Cate Company for supplying the material.

REFERENCES Botelho, E.C. et al., 2005, “Processing and Hygrothermal Effects on Viscoelastic Behavior of Glass Fiber/Epoxy Composites”, Journal of Materials Science, Vol. 40, No 14, pp. 3615-3623. Botelho, E.C. et al., 2003, “Mechanical Behavior of Carbon Fiber Reinforced Polyamide Composites”, Composites Science and Technology, Vol. 63, No 13, pp. 1843-1855. Botelho, E.C. and Rezende, M.C., 2010, “Evaluation by Free Vibration Method of Moisture Absorption Effects in Polyamide/Carbon Fiber Laminates”, Journal of Thermoplastic Composite Materials, Vol. 23, No 2, pp. 207-225. Botelho, E.C. and Rezende, M.C., 2000, “O uso de Compósitos Estruturais na Indústria Aeroespacial”, Polímeros, Vol. 10, No 2, pp. e4-e10. Boualem, N. and Sereir, Z., 2011, “Accelerated aging of unidirectional hybrid composites under the long-term elevated temperature and moisture concentration”, Theoretical and Applied Fracture Mechanics, Vol. 55, No 1, pp. 68-75. Chawla, N.E.A, 2001, “Thermal-shock behavior of a Nicalon-fiberreinforced hybrid glass-ceramic composite”. Composites Science and Technology, Vol. 61, No 13, pp. 1923-1930. Chevali, V.S. et al., 2010, “Effect of environmental weathering on flexural creep behavior of long fiber-reinforced thermoplastic composites”, Polymer Degradation and Stability, Vol. 95, pp. 2628-2640. Costa, A.A. et al., 2012, “The effect of thermal cycles on the mechanical properties of fiber-metal laminates”, Materials & Design, Vol. 42, pp. 434-440. Costa, A.P. et al., 2010, “Influence of environmental conditioning on the shear behavior of poly (phenylene sulfide)/glass fiber composites”, Journal of Applied Polymer Science, Vol. 118, No 1, pp. 180-187. Costa, M.L. et al., 2005, “Hygrothermal Effects on Dynamic Mechanical Analysis and Fracture Behavior of Polymeric Composites”, Materials Research, Vol. 8, No 3, pp. 335-340.

Diaz, J. and Rubio, L., 2003, “Developments to manufacture structural aeronautical parts in carbon fibre reinforced thermoplastic materials”, Journal of Materials Processing Technology, Vol. 143-144, pp. 342-346. Hufenbach, W. et al., 2011, “The effect of temperature on mechanical properties and failure behaviour of hybrid yarn textilereinforced thermoplastics”, Materials & Design, Vol. 32, No 8-9, pp. 4278-4288. Jedidi, J. et al., 2006, “Accelerated hygrothermal cyclical tests for carbon/epoxy laminates”. Composites Part A: Applied Science and Manufacturing, Vol. 37, No 4, pp. 636-645. Kellogg, K.G. et al., 2003, “Influence of moisture and reducedtemperature thermal cycles on the izod notch toughness of a pultruded glass-fiber composite”, International Journal of Offshore and Polar Engineering, Vol. 13, No. 3, pp. 232-239. Kim, K.Y. and Ye, L., 2005, “Influence of Matrix and Interface on Transverse Mechanical Properties of CF-PEI Thermoplastic Composites at Elevated Temperatures”, Journal of Reinforced Plastics & Composites, Vol. 24, No 4, pp. 429-445. Menard, K.P., 2008, “Dynamic Mechanical Analysis: a practical introduction”, CRC Press, Taylor & Francis Group, USA, 218p. Oliveira, G.H. et al., 2009, “Influência da Temperatura no Desempenho Mecânico de Compósitos PEI/Fibras de Vidro”, Polímeros: Ciência e Tecnologia, Vol. 19, No 4, pp. 305-312. Ramanujam, N. et al., 2008, “Interlaminar fatigue growth of crossply composites under thermal cycles”, Composite Structure, Vol. 85, pp.175-187. Ray, B.C., 2006, “Temperature effect during humid ageing on interfaces of glass and carbon fibers reinforced epoxy composites”, Journal of Colloid and Interface Science, Vol. 298, No 1, pp.111-117.

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Botelho, E.C., Bravim Júnior, J.C., Costa, M.L. and Faria, M.C.M

Viña, J. et al., 2008, “Wear Behavior of a Glass Fiber-Reinforced PEI Composite”, Journal of Thermoplastic Composite Materials, Vol. 21, No 3, pp. 279-286.

Yakimets, I. et al., 2004, “Effect of photo-oxidation cracks on behaviour of thick polypropylene samples”, Polymer Degradation and Stability, Vol. 86, No 1, pp. 59-67.

White, J.R. and Shyichuk, A.V., 2007, “Effect of stabilizer on scission and crosslinking rate changes during photo-oxidation of polypropylene”, Polymer Degradation and Stability, Vol. 92, No 11, pp. 2095-2101.

Zenasni, R. et al., 2006, “Effect of Hygrothermomechanical Aging on the Interlaminar Fracture Behavior of Woven Fabric Fiber/PEI Composite Materials”, Journal of Thermoplastic Composite Materials, Vol. 19, No 4, pp. 385-398.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.241-254, Apr.-Jun., 2013

Thesis abstracts This section presents the abstract of most recent Master or PhD thesis related to aerospace technology and management

Information System (SPENVIS) site, assessing, in particular, the

Ultrahigh Molecular Weight Polyethylene as a Base Material for Shielding Cosmic Radiation in Aerospace Applications

secondary radiation produced by shielding slabs of ultra-high molecular weight polyethylene (pure and with cadmium chloride)

Marlon Antonio Pereira Instituto de Estudos Avançados; São José dos Campos/SP – Brazil marlon@ieav.cta.br

subjected to the fluency of a typical trapped cosmic radiation incidence on a low Earth orbit satellite. The energy spectrum and fluency of this radiation were also obtained from a SPENVIS calculation of a low Earth orbit mission in an orbit similar to

Thesis submitted for Masters in Sciences and Technologies Spatial at Instituto Tecnológico de Aeronáutica, in 2013.

a sino-Brazilian series satellite of China-Brazil Earth Resources

ADVISORS: Doctors Odair Lelis Gonçalez and Deborah Dibbern Brunelli

radiation sources, the samples were characterized according

KEYWORDS: Shielding, Polyethylene, Ultra-high molecular weight polyethylene, Cosmic radiation, Thermal neutrons.

1,408 keV; dose deposition curve for

ABSTRACT: Materials with high content of hydrogen and composed by low atomic mass elements have good properties of shielding against the effects of cosmic rays because they are less effective than the heavy ones, with high nuclear masses in the generation of secondary radiation. Among these materials, besides aluminum, polyethylene has been used as a reference and as basis for composites applied in structures and shielding of ionizing radiation for aerospace applications. In this work, ultra-high molecular weight polyethylene, pure and 10% doped by mass with cadmium chloride, was evaluated with respect to its shielding properties for cosmic radiation existing in a low Earth orbit. Considering the high cost and the difficulties to obtain radiation sources with the composition and energy of the cosmic radiation at space and in the Earth atmosphere, at altitudes of high operational ceiling flights, the methodology used in this evaluation was performing irradiation experiments with conventional radioactive sources under controlled conditions and at simple geometries, and then computational simulation for isotropic fluxes of high energy particles. Narrow beam transmission experiments and measurements of secondary radiation production (electrons, gamma radiation, and thermal neutrons) were performed with a 241Am-Be radioactive neutron

of thermal neutrons and of internal cascades of secondary

Satellite (CBERS) series. In the energy area of conventional to their: gamma total attenuation coefficients from 59 to Co gamma-rays; fast

neutron transmission coefficient; generation and self-absorption

source and a set of conventional sources of gamma radiation, in order to certify the shielding microscopic description (materials and cross sections) and effectiveness (transmission coefficients). Based on this description, Monte Carlo simulations were performed on free programs, with performance and reliability widely recognized (Geant4). These were provided by the European Space Agency in the Space Environment

electrons; and gamma-rays by nuclear interactions of fast neutrons source with shielding material nuclei. The samples employed in the experiments were cylindrical plates of 6.5 cm in diameter and 0.60 g/ cm2 thickness, manufactured by hot compression molding. The experimental results were compared with their corresponding values calculated from cross sections of the main interactions of monoenergetic gammas and fast neutrons, with the atoms of the shielding materials and their nuclei. The main effects of the additive (cadmium chloride) in the polyethylene base are the most effective removal of gamma radiation and of secondary electrons with energies below 200 keV, and the reduction of the thermal neutron albedo and of the thermal neutrons transmission by a factor that can reach up to four, depending on the thickness of shielding. However, for dose reduction due to primary cosmic radiation, these results were not significant, since the largest contribution to the dose is due to high energy ionizing particles transmitted and to secondary radiation produced in shielding with energies above 1 MeV.

Analytical Techniques by Via Humid and Instrumental for Characterization of Bonding Agents Used in Solid Propellants Darci Côrtes Pires Instituto de Aeronáutica e Espaço; São José dos Campos/SP – Brazil darcidcp@iae.cta.br Thesis submitted for PhD degree in Mechanical and Aeronautical Engineering, in 2012.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.255-256, Apr.-Jun., 2013

256

Thesis abstracts

ADVISORS: Doctors Rita de Cássia Lazzarini Dutra and Koshun Iha KEYWORDS: Propellants, Characterization, Quantification, FT-IR, Analysis by wet, Thermal analysis. ABSTRACT: In the open literature, there are few studies on the synthesis and characterization of the bonding agents and their application in industry composite solid propellants. These additives are considered strategic in the formulations, and most of the publications are found as patents. Thus, taking as basis the proper characterization

Synthesis, Characterization and Application of Glycidyl Azide Polymer in the Development of New Propellants to the Brazilian Aerospace Program Jairo Sciamareli Instituto de Aeronáutica e Espaço; São José dos Campos/SP – Brazil; jairojs@iae.cta.br Thesis submitted for PhD degree in Mechanical and Aeronautical Engineering, in 2012.

of the bonding agents is the starting point for choosing a

ADVISOR: Doctor Koshun Iha

particular formulation of propellant in order to test and

KEYWORDS: Synthesis, Chemistry, Polymer, Characterization, Glycidyl azide polymer, Energetic polymer.

verify the effect on mechanical and ballistic properties of the composite. Three types were studied, aziridine, amine, and hydantoin by different techniques, ranging from wet and instrumental. The main methodologies developed for their characterization and quantification include new method, which characterized ring opening characteristic of agents aziridine by means of differential scanning calorimetry, wet, and spectroscopy of the mid-infrared. This method is important in the study of changes of chemical structure, aging of these compounds and characterization of novel binding agents with two or three rings open synthesized with starting materials, easily found in the domestic market, such as 12-hydroxystearic acid. The products obtained are reacted with NCO giving a polyurethane resin similarly to the hydroxyl polybutadiene (HTPB). Also, monitoring the reaction by the mid-infrared spectrometer shows that changes occur only in the reaction with formaldehyde, among three types of aldehydes studied, therefore the formation of the product 1,3-bis-(hydroxymethyl) 5,5-dimethylhydantoin in the presence of water. The indication of the NIR analytical bands of the amine bonding agent for quantitative studies in order to determine the equivalent weight of TEPA, with good precision, and agreement with the corresponding data cited in the literature, and the methodology developed being validated by DSC and potentiometry were also included. Data molecular weights are calculated of TEPA from the developed methodology for the determination of equivalent weight. They contribute to a new line of research in the Division of Chemistry of Instituto de Aeronáutica e Espaço, and to the characterization and quantification of bonding agents used in propellants.

ABSTRACT: In recent years it has been constant the search for new materials that could be used in propellants. It has been sought, among other features, for those more energetic, with greater thermal stability or chemistry, less aggressive to the environment, with lower cost, easier handling, and that allow for better performance of rockets, missiles and explosives. Glycidyl azide polymer (GAP) satisfies this expectation. The presence of azide groups brings to the product positive heat formation, 975 kJ/kg at 293 K, which is important because the energetic performance of propellant is proportional to the enthalpy of reactants formation. This work aimed at allowing Brazil to be at the forefront of research of new propellants, seeking to possess production capacity, characterization and application of glycidyl azide polymer in new formulations. It also allowed us to be into the energetic propellant components research. Synthesis processes were conducted using three different catalysts in three varied proportions. The products obtained were characterized by volumetric (hydroxyl index) and instrumental analyses (FT-IR and thermal analysis). Sample that used SnCl4 as catalyst and relationship monomer/catalyst 20:1 was chosen to repeat its synthesis process for five times, and each of these products has been subjected to the same analyses to ensure that the properties were repetitive. The glycidyl azide polymer obtained was used in a process for the production of polyurethanes with isocyanates, TDI and IPDI, and specimens obtained tested for evaluating mechanical properties. According to the analysis performed, we can say that the process for the production and characterization of glycidyl azide polymer have been fully achieved and has similar features to the product produced abroad.

J. Aerosp. Technol. Manag., São José dos Campos, Vol.5, No 2, pp.255-256, Apr.-Jun., 2013

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The Journal of Aerospace Technology and Management (JATM) is the official publication of the Departamento de Ciência e Tecnologia Aeroespacial (DCTA), in São José dos Campos, São Paulo State, Brazil. The journal is quarterly published (March, June, September, and December) and is devoted to research and management on different aspects of aerospace technologies. The authors are solely responsible for the contents of their contribution. It is assumed that they have the necessary authority for publication. When submitting the contribution, authors should classify it according to the area selected from the following topics:

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MANUSCRIPT CATEGORIES Editorial: Any researcher may write the editorial on the invitation of the Editor in Chief. Editorials should cover broad aspects of Aerospace Technology. Such manuscripts are not submitted to peer review. Review articles: These should cover subjects that are relevant to the scope of the journal. Authors should bear in mind that they are expected to have expertise in the reviewed field. The article may be of any length required for the concise presentation of the subject. Original papers: These articles should report results of the scientific research. The article may be of any length required for the concise presentation and discussion of the data, but succinct papers are favored in terms of impact as well as in readability. Communications: They should report previous results of ongoing research and should not exceed eight pages. Thesis abstracts: The journal welcomes recent Masters and PhD thesis abstracts for publication. Such contribution will not be submitted to peer review.

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Clark, J.A., 1986, “Private Communication”, University of Michigan, Ann Harbor. EMBRAPA, 1999, “Politics of R&D”, Retrieved in May 8, 2010, from http://www.embrapa.br/publicacoes/institucionais/ polPD.pdf. Silva, L.H.M., 1988, “New Integral Formulation for Problems in Mechanics” (In Portuguese), Ph.D. Thesis, Federal University of Santa Catarina, Florianópolis, S.C., Brazil, 223p. Sparrow, E.M., 1980a, “Forced Convection Heat Transfer in a Duct Having Spanwise-Periodic Rectangular Protuberances”, Numerical Heat Transfer, Vol. 3, pp. 149-167. Sparrow, E.M., 1980b, “Fluid-to-Fluid Conjugate Heat Transfer for a Vertical Pipe-Internal and External Natural Convection”, ASME Journal of Heat Transfer, Vol. 102, pp. 402-407. Tables: Tables should be constructed using the table feature in the word processor or using a spreadsheet program, such as Microsoft Excel. They should be numbered in order of appearance in the text, using Arabic numerals. Each table should have a title and an explanatory legend, if necessary. All tables must be referenced and mentioned in the text as “Table” and succinctly described in the text. Under no circumstances should a table repeat data that are presented in an illustration. Statistical measures of variation (i.e., standard deviation or standard error) should be identified, and decimal places in tabular data should be restricted to those with mathematical and statistical significance. Authors should take notice of the limitations set by the size and layout of the journal. Therefore, large tables should be avoided. Figures: All illustrations, line graphs, charts, schemes, photographs, and graphs should be referred as “Figure” and submitted with good definition. Number figures consecutively using Arabic numerals in order of appearance. References should be made in the text to each figure using the abbreviated form “Fig.”, except if they are mentioned in the beginning of the sentences. Captions should be descriptive and should allow the examination of the figures, without reference to text. The size of the figures (including frame) should be 8 cm (one column) or 17 cm (two columns) wide, with maximal height smaller than 22 cm. Equations: Type them on individual lines, identifying them by Arabic numerals enclosed in parenthesis. References should be made in the text to each equation using the abbreviated form “Eq.”, except in the beginning of the sentences, where the form “Equation” should be used.

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