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Journal of Aerospace Technology and Management J. Aerosp. Technol. Manag. Vol. 3, Nº. 1, Jan – Apr., 2011

Editor in Chief

Executive Editor

Francisco Cristovão Lourenço de Melo Institute of Aeronautics and Space São José dos Campos - Brazil editor@jatm.com.br

Ana Marlene Freitas de Morais Institute of Aeronautics and Space São José dos Campos- Brazil secretary@jatm.com.br

ASSOCIATE EDITORS Adriana Medeiros Gama - Institute of Aeronautics and Space - São José dos Campos - Brazil Ana Cristina Avelar - Institute of Aeronautics and Space - São José dos Campos - Brazil André Fenili - Universidade Federal do ABC- São Paulo - Brazil Angelo Pássaro - Institute for Advanced Studies - São José dos Campos - Brazil Antonio Fernando Bertachini - National Institute for Space Research - São José dos Campos - Brazil Antonio Pascoal Del’Arco Jr.- Institute of Aeronautics and Space - São José dos Campos - Brazil Carlos de Moura Neto - Technological Institute of Aeronautics - São José dos Campos - Brazil Cynthia C. Martins Junqueira - Institute of Aeronautics and Space - São José dos Campos - Brazil Eduardo Morgado Belo - University of São Paulo - São Carlos - Brazil Elizabeth da Costa Mattos - Institute of Aeronautics and Space - São José dos Campos - Brazil Flaminio Levy Neto - Federal University of Brasília - Brasília - Brazil Gilberto Fisch - Institute of Aeronautics and Space - São José dos Campos - Brazil João Luiz F. Azevedo - Institute of Aeronautics and Space - São José dos Campos - Brazil José Márcio Machado- Univ. Estadual Paulista - São José do Rio Preto - Brazil José Roberto de França Arruda - State Universiy of Campinas- Campinas - Brazil Marcos Pinotti Barbosa - Federal University of Minas Gerais- Belo Horizonte - Brazil Mischel Carmen N. Belderrain- Technological Institute of Aeronautics - São José dos Campos - Brazil Paulo Tadeu de Melo Lourenção - Embraer - São José dos Campos - Brazil Valder Steffen Junior - Federal University of Uberlândia - Uberlândia - Brazil Waldemar de Castro Leite - Institute of Aeronautics and Space - São José dos Campos - Brazil

Editorial Production Ana Cristina C. Sant’Anna Glauco da Silva Helena Prado A. Silva Márcia M. E. Robles Fracasso

J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 1-4, Jan-Apr., 2011

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Editorial Board

Editorial Board Acir Mércio Loredo Souza - Federal University of Rio Grande do Sul - Porto Alegre - Brazil Adam S. Cumming - Defence Science and Technology Laborator - Fort Halstead - UK Adrian R. Wittwer - National University of the Northeast - Resistencia - Argentine Alain Azoulay - Superior School of Eletricity - Paris - France Alexandre Queiroz Bracarense - Federal University of Minas Gerais- Belo Horizonte - Brazil Antonio Henriques de Araujo Jr - State University of Rio de Janeiro - Rio de Janeiro - Brazil Antonio Sérgio Bezerra Sombra - Federal University of Ceará - Fortaleza - Brazil Bert Pluymers - Catolic University of Leuven - Leuven - Belgium Carlos Eduardo S. Cesnik - University of Michigan - Ann Arbor - USA Carlos Henrique Marchi - Federal University of Paraná - Curitiba - Brazil Charles Casemiro Cavalcante - Federal University of Ceará - Fortaleza - Brazil Cosme Roberto Moreira da Silva - University of Brasília - Brasília - Brazil Edson Aparecida de A. Querido Oliveira - University of Taubaté - Taubaté - Brazil Edson Cocchieri Botelho - Univ. Estadual Paulista - Guaratinguetá - Brazil Fabrice Burel - National Institute of Applied Sciences - Lion - France Fernando Luiz Bastian - Federal University of Rio de Janeiro - Rio de Janeiro - Brazil Francisco Souza - Federal University of Uberlândia - Uberlândia - Brazil Frederic Plourde - Superior National School of Mechanics and Aerotechnics - Poitiers - France Gerson Marinucci - Institute for Nuclear and Energy Research São Paulo - Brazil Gilson da Silva - National Industrial Property Institute - Rio de Janeiro - Brazil Hazin Ali Al Quresh - Federal University of Santa Catarina - Florianópolis - Brazil Hugo P. Simão - Princeton University - Princeton - USA João Amato Neto - University of São Paulo - São Paulo - Brazil Joern Sesterhenn - University of Munich - Munich - Germany Johannes Quaas - Max Planck Institute for Meteorology - Hamburg - Germany John Cater - The University of Auckland - Auckland - New Zealand Jorge Carlos Narciso Dutra Institute of Aeronautics and Space - São José dos Campos - Brazil José Alberto Cuminato - São Carlos School of Engineering - São Carlos - Brazil José Ângelo Gregolin - Federal University of São Carlos - São Carlos - Brazil José Atílio Fritz Rocco - Technological Institute of Aeronautics - São José dos Campos - Brazil José Carlos Góis - University of Coimbra - Coimbra - Portugal José Leandro Andrade Campos - University of Coimbra - Coimbra - Portugal José Maria Fonte Ferreira - University of Aveiro - Aveiro - Portugal José Rubens G. Carneiro - Pontifícia Univers. Católica de Minas Gerais- Belo Horizonte- Brazil Juno Gallego - Univ. Estadual Paulista - Ilha Solteira - Brazil Ligia M. Souto Vieira - Technological Institute of Aeronautics - São José dos Campos - Brazil Luis Fernando Figueira da Silva - Pontifical Catholic University - Rio de Janeiro - Brazil Luiz Antonio Pessan - Federal University of São Carlos - São Carlos - Brazil Márcia Barbosa Henriques Mantelli - University of Santa Catarina - Florianópolis - Brazil Maurizio Ferrante - Federal University of São Carlos - São Carlos - Brazil Michael Gaster - University of London - London - UK Mirabel Cerqueira Resende - Institute of Aeronautics and Space - São José dos Campos - Brazil Nicolau A.S. Rodrigues - Institute for Advanced Studies - São José dos Campos - Brazil Paulo Celso Greco - São Carlos School of Engineering - São Carlos - Brazil Paulo Varoto - São Carlos School of Engineering - São Carlos - Brazil Rita de Cássia L. Dutra - Institute of Aeronautics and Space - São José dos Campos - Brazil Roberto Costa Lima - Naval Research Institute - Rio de Janeiro - Brazil Roberto Roma Vasconcelos - Institute of Aeronautics and Space - São José dos Campos - Brazil Samuel Machado Leal da Silva - Army Technological Center - Rio de Janeiro - Brazil Selma Shin Shimizu Melnikoff - University of São Paulo - São Paulo- Brazil Tessaleno Devezas - University of Beira Interior - Covilha - Portugal Ulrich Teipel - University of Nuremberg - Nuremberg - Germany Vassilis Theofilis - Polytechnic University of Madrid - Madrid - Spain Vinicius André R.Henriques -Institute of Aeronautics and Space - São José dos Campos - Brazil Wim P. C. de Klerk - TNO Defence - Rijswijk - The Netherlands 2

J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 1-4, Jan-Apr., 2011


ISSN 1984-9648 ISSN 2175-9146 (online)

Journal of Aerospace Technology and Management Vol. 03, N. 01, Jan. - Apr., 2011

CONTENTS

Editorial 5

A short history of the academic activities at the Brazilian National Institute for Space Research Antonio Fernando Bertachini de Almeida Prado

Technical Papers 13

The use of molecular spectra simulation for diagnostics of reactive flows Angelo Passaro, Dermeval Carinhana Jr, Enizete Aparecida Gonçalves, Marcio Moreira da Silva, Ana Paula Lasmar Guimarães, Nancy Mieko Abe, Alberto Monteiro dos Santos

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Computation of multiple limit cycles in nonlinear control systems – a describing function approach Alexandro Garro Brito

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Entropy variation in isothermal fluid flow considering real gas effects Maurício Guimarães da Silva, Paulo Afonso Pinto de Oliveira

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A multilayer model to simulate rocket exhaust clouds Davidson Martins Moreira, Leonardo Barboza Trindade, Gilberto Fisch, Marcelo Romero de Moraes, Rodrigo Martins Dorado, Roberto Lage Guedes

53 On reduction of longest accessibility gap in LEO sun-synchronous satellite missions Hossein Bonyan Khamseh, M. Navabi 59

Experimental measurements and numerical simulation of permittivity and permeability of Teflon in X band Adriano Luiz de Paula, Mirabel Cerqueira Rezende, Joaquim José Barroso

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Synthesis of 2,4,6-triamino-1,3,5-trinitrobenzene Gilson da Silva, Elizabeth da Costa Mattos

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Measurements in an outdoor facility and numerical simulation of the radar cross section of targets at 10 GHz Guilherme G. Peixoto, Mauro Angelo Alves, Alberto José de Faro Orlando, Mirabel Cerqueira Rezende

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Orbit determination modeling analysis by GPS including perturbations due to geopotential coefficients of high degree and order, solar radiation pressure and luni-solar attraction Paula C. P. M. Pardal, Rodolpho Vilhena de Moraes, Helio K. Kuga

87

Aerodynamic study of sounding rocket flows using Chimera and patched multiblock meshes João Alves de Oliveira Neto, Edson Basso, João Luiz F. Azevedo

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Thesis abstract 99

Widely linear processing in antenna array: purpose, evaluation and hardware implementation Adilson Walter Chinatto Junior

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Study of the influence of different types of environmental conditionings on the mechanical properties of carbon/epoxy composites José Antonio Peixoto Cunha

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Analysis of the wind profile in the surface boundary layer and meteorological systems at the Alcântara Launching Center Carlos Alberto Ferreira Gisler.

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High-order unstructured spectral finite volume method for aerodynamic applications Carlos Breviglieri Junior

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Nonlinear turbulent transonic flow phenomena influence on aeroelastic stability analysis Hugo Stefanio de Almeida.

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Automation of H-infinity controller design and its observer-based realization Fausto de Oliveira Ramos

103 Instructions to the Authors

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J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 1-4, Jan-Apr., 2011


Antonio Fernando Bertachini de Almeida Prado President of the Council of Graduate Studies at INPE São José dos Campos – Brazil bertaquini@inpe.br

Editorial A short history of the academic activities at the Brazilian National Institute for Space Research

The Brazilian National Institute for Space Research (INPE, acronym in Portuguese) is an institute in charge of activities related to space, which include not only Science, but also Aerospace Engineering, covering the development of the Brazilian satellites. The majority of the facilities are located in São José dos Campos (SP), but it also has activities in Santa Maria (RS), Natal (RN), Belém (PA), São Luís (MA), Cachoeira Paulista (SP), Eusébio (CE), Atibaia (SP), São Paulo (SP), Cuiabá (MT), Brasília (DF), and San Martino da Serra (RS). The Institute will complete 50 years in August 2011, and many important achievements in the space field were made in these five decades. Although the INPE is not a dedicated academic institution, it has a strong and large graduate school, which offers courses at the master and doctoral levels. This academic structure is very important for the Institute, and graduate students are involved in several important research projects organized by the institution. The main goal of the present text is to show some details about this activity. But, first of all, it is important to take a look at the Institute itself. As can be seen in its official website (www.inpe.br), its mission is to foster science and technology in Earth and space context and be able to offer products and regular services in benefit of the country. The strategic goals to achieve this mission are to: •

extend and consolidate competences in technical-scientific excellence and innovation in the space and tropical environment in order to respond to national challenges;

develop, in the worldwide sphere, scientific and technological leadership in space and tropical environment scope emphasizing Brazilian specificities;

extend and consolidate competences in weather forecasting and global climate change;

consolidate the INPE’s performance as a unique institution in the segment of satellites and space technologies development;

promote industrial policy for the space sector oriented towards the growth and sustainability of its space activities, and, additionally, oriented towards the technological-basis industrial development;

strengthen positive actions along the national and international institutions;

provide a sufficient infrastructure;

establish a new human resource policy to the INPE, based on strategic management of competences;

identify and implement a management and institutional pattern, in conformity with the specificities and challenges that have been presented to the INPE.

The Graduate school located in INPE contributes towards all of these strategic goals, but before going in more details about it, let us first recall some of the important milestones of the Institute in those 50 years of existence. To do this, some of the main facts related to INPE’s history are shown in the following paragraphs.

THE FIRST DECADE (1961 to 1970) In 1961, a presidential decree created the Organization Group of the National Space Activities Commission (GOCNAE, acronym in Portuguese). This organization is considered as the creation of INPE, and it is the reason why we consider J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 5-12, Jan. - Apr., 2011

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2011 as the year that INPE makes its 50 years of existence. Then, in 1963, GOCNAE became the National Commission of Space Activities (CNAE, acronym in Portuguese). In the following year, 1964, the Aeronautics Ministry established the Workgroup of Space Studies and Projects (GTEPE, acronym in Portuguese). Some real activities started in the space field in 1965, when the first campaigns for launching INPE work-loaded probing rockets, from “Barreira do Inferno” Launching Center (Natal, in Rio Grande do Norte), took place. In 1966, the Meteorology by Satellite (MESA) program began, which consisted on the reception of meteorological images. After that, in 1967, the first library started working at INPE and, in 1968, the graduate school was created, as a major step in the development of space related activities in the country. In 1969, the activities started in remote sensing. The project SACI started in 1970, with the purpose of studying the use of satellites in education.

THE SECOND DECADE (1971 to 1980) In 1971, the CNAE no longer existed and the INPE was created, associated with the National Council for Scientific and Technological Development (CNPq, acronym in Portuguese). In this same year, the Brazilian Commission of Space Activities (COBAE) was originated. In 1972 and 1973, we had the implementation of the remote sensing satellite data reception station in Cuiabá (MT). Also, in 1973, INPE received the first images of the American satellite LANSAT-1. The first important mark of the second part of this decade was in 1978, when the first edition of the Brazilian Remote Sensing Symposium was organized. Later on, in 1979, a major step in the Brazilian aerospace engineering was made, with the creation of the Complete Brazilian Space Mission (MECB). It was established that INPE would develop data collecting and remote sensing satellites, and CTA would develop the satellite launching vehicle and the implementation of a Brazilian launching center. In 1980, the Mackenzie Radioastronomy and Astrophysics Center (CRAAM) transfer to INPE occurred, which is a fact that impacted in the graduate school activities in INPE, as will be further detailed.

THE THIRD DECADE (1981 to 1990) Starting this decade, in 1982, we had the first scientific expedition to Antarctica. There was also a large investment in infrastructure for the MECB: the Integration and Tests Laboratory (1983 to 1987) and the Satellite Tracking and Control Center (1987 to 1989). Another mark of 1982 was the realization of the first Brazilian Colloquium of Orbital Dynamics (CBDO). In 1985, the Science and Technology Ministry was created and INPE passed over to the MCT, as an autonomous organ. For the second half of this decade, there was the creation of the Associated Laboratories – Plasma, Sensors and Materials, Computing and Applied Mathematics and Combustion and Propulsion, all of them in 1986. In this same year, we had the beginning of the burned land monitoring program. In 1987, there was the inauguration of the Integration and Tests Laboratory. Then, in 1988, the cooperation agreement was executed between Brazil and China, aiming at the development of satellites (CBERS-1 and CBERS-2). In 1989, the Brazilian Special Science and Technology Bureau (SCT) was created as an organ integrating the Republic’s Presidency. In the same year, there was the start-up of the PRODES – Project Brazilian Amazonian Forest Monitoring by Satellites, with annual data survey about data on the deforestation of Legal Amazonia. In 1990, the INPE was denominated National Institute for Space Research and integrated to the SCT/PR Republic’s Presidency Science and Technology Bureau’s basic structure.

THE FOURTH DECADE (1991 to 2000) In 1992, SCT became the Science and Technology Ministry (MCT), and INPE was integrated to it in the condition of a specific organ. Then, in 1993, there was a very important milestone in the history of INPE, since it was the year that SCD-1, the first data collecting Brazilian satellite, wholly developed by INPE, was launched from Cape Canaveral, in Florida, USA. In the folowing year, 1994, INPE created the Weather Forecast and Climatic Studies Center (CPTEC). In this same year, the Brazilian Space Agency was created to replace COBAE. In 1995, MCT’s Regulatory Structure was created and INPE came to integrate it, in the quality of a Singular Specific Organ.

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For the second part of this decade, we also had very important events. Starting in 1998, when there was the launching of the satellite SCD-2, also from the American base in Cape Canaveral, Florida. The CBERS-1 – Earth Resources ChineseBrazilian Satellite was launched from a base in China, in 1999.

THE FIFTH DECADE (2001 TO 2010) For the fifth decade of the the INPE history, we can start in 2002, when there was the execution of a new cooperation agreement between Brazil and China for the development of Satellites CBERS-3 and CBERS-4. 2003 was also a year full of activities, with the launching of the Satellite CBERS-2, from the Chinese base. Also, the SCD-1 completed ten years in orbit and SCD-2 completed five years. The Amazonian monitoring system gained a digital image classification, which was made available on the Internet. In 2004, there was the introduction of the images divulgation from CBERS, with a catalog made available on the internet. Also, nation-wide Thunderbolt Monitoring Network was available on the Internet. In this same year, INPE Supercomputer placed Brazil among the eight countries with high processing capacity in weather and climate numerical forecast. In 2005, the Amazonian Deforestation Real Time Detection Program Data (DETER) was available on the Internet. In this period, INPE also reached the number of 100.000 CBERS images distributed; thus, becoming the largest world CBERS image distributor. Another mark of this year is the fact that the Integration and Tests Laboratory totalized 1,000 clients served. In the second half of this decade, starting in 2006, free CBERS image catalog is extended to whole South America. In addition to that, the United States also received images from CBERS. In 2007, the satellite CBERS2-B was launched again from China. In the following year, we had the creation of the Center of Science of the Earth’s System. In 2009, INPE reached the number of one million satellite images distributed, 70% from CBERS and 30% from LANDSAT. Finally, in 2010, we had the beginning of services of the most powerful supercomputer in South Hemisphere to perform climate and meteorological research.

MAJOR ASPECTS OF THE ACADEMIC ACTIVITIES HISTORY AT INPE The Graduate Courses at INPE were gradually introduced, starting from 1968, with the purpose of training highly qualified human resources in the Institute areas of activities, because of the lack or inadequacy of institutions that generate knowledge in these areas in Brazil. The Institute offers, nowadays, the following graduate courses: Astrophysics, Space Engineering and Technology (divided in four subdivisions: Space Mechanics and Control, Combustion and Propulsion, Sciences and Technology of Materials and Sensors and Engineering, and Management of Space Systems), Space Geophysics, Applied Computing, Meteorology, Remote Sensing, and Earth System Science. Graduate courses are regulated by the Council of Graduate Studies, which is composed by representatives of all courses. In addition, each course has its own rules, which is made by a local Council elected by the professors that belong to that course. Now, we can address the history and goals of every individual course.

Astrophysics The Astrophysics graduate courses at INPE were conceived to generate M.Sc. and Doctoral staff prepared to face the challenges of astrophysical research at INPE and, more generally, all over Brazil. The research activities carried at this course and by the Astrophysics Division of INPE (DAS) are: •

theoretical studies and observations in stellar astrophysics, extragalactic astrophysics, cosmology, and extrasolar planets;

observations and phenomenological analysis of the cosmic microwave background radiation, as well as cosmic Xand gamma-ray sources;

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solar studies, including solar flares, their propagation effects in the interplanetary environment, solar-terrestrial phenomena, and their relation to space weather;

studies in gravitational waves astrophysics, to support these researches, INPE is leading the efforts to build and operate the first gravitational waves observatory in Brazil;

various studies in radioastronomy: quasars, radio galaxies, stars and star-forming regions, both in continuum and spectral lines.

Following the INPE’s tradition, DAS and the Astrophysics Course strongly support the development of astronomical instrumentation in all areas. Their scientists are deeply involved in the design, production and operation of radio interferometers, gravitational wave detectors, satellites, microwave receivers, infrared detectors, besides other components and parts of the instrumentation.

Space Engineering and Technology The Space Engineering and Technology Graduate Course came from a concentration area of the Space Science Course. With the name of Space Science, the course started in 1968, with a concentration in “Combustion” at the master’s level and a concentration in “Astrogeophysics” at the master and doctoral levels. In 1972, the Engineering field was established to concentrate the area of “Orbital Mechanics” at the Master level. In 1974, the area started offering also a doctoral degree. In 1980, the Graduate Course in Space Science added the areas of concentration in Astronomy and Solar Physics at the Masters and doctoral levels, as a result of the mentioned transfer before the Center for Radio Astronomy and Astrophysics Mackenzie (CRAAM) from the National Observatory (ON) to INPE, as a result of a determination of the Board of CNPq. Thus, the name of the Graduate Course in Space Science existed from 1968 until 1993. At its meeting on April 18, 1996, the Technical Advisory Group (JWG) of CAPES authorized the split of the Graduate Course in Space Science, transforming their areas of concentration in independent courses, with retroactive effect from January 1, 1994. Thus, the designation “Graduate Course in Space Technology and Engineering”, with concentration areas in Combustion and Propulsion and Space Mechanics and Control formally came into existence in January, 1994, although it was in effect since 1987. In December, 2001, a new concentration area in Science and Technology of Materials and Sensors was created, starting its activities in 2002. The objective of the course is to improve staff-level Master and Doctoral in the areas of Orbital Dynamics, Guidance and Control, Structure and Thermal Control, Combustion and Propulsion of Space Vehicles, Engineering and Management Systems and Space Science, and Technology of Materials and Sensors for space applications, as a source of human resources to be used at the INPE, in other research institutions or in the industry and education. General Characteristics of the areas of concentration in the Space Engineering and Technology course The graduate course in Space Mechanics and Control works mainly in the Division of Space Mechanics and Control (DMC) at INPE, located in São José dos Campos, Brazil. It accounts with a specialized library with more than 30,000 books and 1,500 subscriptions to scientific journals, laboratories, and other facilities. It concentrates studies in the field of orbital dynamics, control of spacecrafts and structures and thermal control of satellites. Among its research topics, activities like the orbit determination and maneuvers of satellites, design of space vehicles, studies regarding thermal control and structures are developed. The area of concentration in Combustion and Propulsion works at the Laboratory of Combustion and Propulsion (LCP) at INPE, located in Cachoeira Paulista, São Paulo. INPE Cachoeira Paulista occupies an area of 480 acres, containing an extensive green area with eucalyptus plantations, orchards and lakes. It has excellent sports and leisure, as well as catering to students. It is located halfway between Rio and São Paulo, equivalent to less than three hours of each city and is situated near the spa towns of Southern Minas Gerais, near the Northern coast of São Paulo and the Southern one of Rio de Janeiro. The infrastructure available to the students includes six buildings with total area of

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approximately 1,500 square meters, including specialized library, office and research building, chemical laboratory, mechanical workshop, bank for altitude simulation tests – BTSA (Latin America only), and bank of tests in atmospheric conditions (BTCA). The experimental and computational capabilities are perfectly suited to the development of both the Master and Doctoral research, and technical work of all kinds in their projects. The library of the LCP/INPE has direct contact with other libraries and provides the most comprehensive collections in the specialized area of combustion and propulsion. The area of concentration in Science and Technology of Materials and Sensors works in the Associated Laboratory of Sensors and Materials (LAS), Special Technologies Center (CTE), INPE, located in São José dos Campos, São Paulo. The LAS has several laboratories and the following research lines: •

Environmental Technologies: Research and development of sensors of environmental parameters; special ceramics – zircon, alumina e alumina-zircon; nanoparticle systems (nanopowders) and nanostructures ceramics; research and development on modification of surfaces and interfaces;

Condensed Matter Physics: Strongly correlated electronic systems; superconductivity; critical phenomena and phase transition; disordered systems; crystal growth modeling; optical and transport properties in semiconductors; electronic structure of semiconductor nanostructures and spintronics;

Solar Cells: Study and characterization of solar cells for space applications; monitoring of the solar cell experiment flying on INPE’s Data Collecting Satellite (SCD-2) and study of albedo radiation through the data collected from this experiment; research and development of radiometer sensors for meteorological data platforms; development of techniques to obtain porous silicon;

Material Technologies: Molecular beam epitaxy of IV-VI semiconductor compounds and alloys with europium; structural, electrical, optical, and magnetic properties of nanostructures of IV-VI compounds and respective alloys with europium; growth of bulk crystals of Groups IV-VI (PbSnTe) and II-VI (HgCdTe) semiconductor alloys; solidification of alloys in microgravity environment;

Diamond and Related Materials: Growth of thin and self-sustained diamond films by chemical vapor deposition (CVD) on different substrates and surfaces; in situ characterization during diamond growth; optical characterization of synthetic diamond film; development and industrialization of devices based on synthetic diamond; modeling of diamond growth and graphic visualization; growth of boron doped diamond films for electrochemical applications; deposition of molybdenum disulfide thin films for tribological applications; deposition and characterization of diamond like carbon (DLC) for space applications; research and development on modification of surfaces and interfaces;

Plasma immersion ion implantation (PIII): Surface treatment of materials by ion implantation using PIII technique.

Besides specific growth and sample preparation systems of each research group, several equipments for materials characterization and some facilities are installed in LAS/INPE: scanning electron microscope JEOL with the capability of energy dispersive X-ray analysis; high resolution X-ray diffractometer Philips X’Pert MRD; powder X-ray diffractometer Philips PW1840; Micro-Raman spectrometer Renishaw 2000; profilemeter Tencor Alpha Step 500; temperature dependent Hall effect and resistivity measurement system (10-450K); automated system to measure current and capacitance versus voltage curves; infrared Fourier transform spectrometer Perkin Elmer FTIR 1600 (2000 a 22000 nm); spectrophotometer Hitachi U3501 (185 a 3200 nm); equipment for mechanical tests; solar cells characterization bench; bench for photoacoustic and photothermic techniques; electron beam evaporator system Edwards Auto 306; clean room for photolithography and micromachining in silicon; and equipment for plasma etching. The area of concentration in Management and Engineering of Space Systems is taught at the master and doctoral levels in different divisions of INPE, São José dos Campos, Brazil. This area is responsible for the design, development, assembly and integration of the satellites made by INPE. The lines of scientific and technological research and development are: design, specification, architecture and management of space systems, on-board systems for space missions, ground system for space missions, quality control of space missions, and modeling and simulation of space systems.

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Space Geophysics The Masters and Ph.D. in Space Geophysics from INPE aims at training graduate personnel, preferably in the areas of physics and engineering sciences, enabling them to act in areas of education, research and applications at universities, research institutes, companies, and government teams in subjects involving the direct knowledge of science or technology associated with or resulting from the development of space research. Subjects covered are magnetospheric and heliospheric physics, ionospheric physics, geomagnetism, atmospheric chemistry, airglow, atmospheric electricity and atmospheric electrodynamics, and atmospheric physics. Most of these areas are strongly connected to the science of space weather. As a consequence of the Institute’s purpose, the graduate course in Space Geophysics (GES) at INPE started in 1968 under the name of “Space Sciences - Astrogeophysics”. The designation “Graduate Course in Space Geophysics” formally came into existence in January, 1994. Since 2004, the Graduation Course in Space Geophysics has two new concentration areas: Solar-Terrestrial Environment Sciences (AST) and Atmospheric Sciences (ATM). The GES course is a member of the “Excelence Program” of the Brazilian Ministry of Education, ranking in the top 20% of all graduate programs in Brazil.

Applied Computing The graduate program in Applied Computing in the strict sense of the INPE aims at contributing to technological development and scientific level, generating knowledge, and training researchers with multidisciplinary knowledge and skills needed in information technology, extraction information, and computational modeling, which meet the current needs of the research and development in Science and Space Technologies, in line with the institutional mission of INPE.

Meteorology Meteorology is the science that studies the weather and climate. Its goal is the understanding of physical and chemical processes that determine the atmosphere state in various spatial and temporal scales, ranging from local turbulence to the global atmospheric and oceanic circulation. The progress in knowledge of this science is of vital importance for the development of the country, especially in the agricultural, energy, and environment conservation. The graduate course in Meteorology from INPE, Brazil’s oldest in the field, is part of the activities of the Center for Weather Forecasting and Climate Studies (CPTEC). Its goal is to train staff at master and doctoral levels. It is within the mission of the CPTEC: “To provide the country with state of the art in weather forecasting and climate and have the scientific and technological capacity to continuously improve these forecasts, for the benefit of society.” CPTEC center is the most advanced numerical weather prediction and climate in Latin America, providing weather forecasts for short and medium term with high precision, since early 1995. CPTEC places Brazil in the first world of weather forecasts and the excellence of its work is recognized in countries with advanced technology. CPTEC mastered the techniques of numerical modeling of the atmosphere and oceans, with highly complex models used to predict future conditions in the atmosphere and oceans. It operates in a global atmospheric model with a resolution of 63 km, and a regional model with a resolution of 20 km. Featuring highly skilled professionals, CPTEC uses supercomputers capable of processing billions of arithmetic operations per second. The combination of knowledge and technology makes the reliability achieved in numerical weather prediction and climate to have the same level of forecast centers in more developed countries. Its team is highly trained in the finest institutions in the country and abroad, and CPTEC is constantly investing in training and upgrading its employees to generate new scientific knowledge and develop technology for applications in various areas of meteorology.

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Editorial

CPTEC has offered scientific, technical and logistics capabilities for its students that is unparalleled in Latin America. It has a unique computational park, which features the supercomputer NEC-SX6-32 with a processing capacity of approximately 0.8 TFLOPS, considered one of the most advanced supercomputing systems in the world, and global and regional atmospheric models for weather and climate. Leads field experiments in the Amazon (Large-Scale Biosphere-Atmosphere Experiment in Amazonia - LBA), in Pantanal (IPE), experiment low level jet (LLJ), predictability of extreme weather events on the coastal range (Serra do Mar) and in environmental projects, among others. The Faculty is composed mostly by PhD researchers from CPTEC with high scientific productivity. The students have the best libraries in Latin America and updated knowledge in these areas, containing a collection of more than 31,000 books and 1,500 periodicals, online access to the contents of many libraries worldwide and access to electronic versions of major publications in atmospheric sciences. CPTEC combines research and development activities with advanced technological operational weather forecasting and climate to provide students, with an unparalleled work environment of advanced academic and professional training. The teaching activities and student research can be developed equally in São José dos Campos and Cachoeira Paulista. It also has modern appeal of telecommunications (video conference), allowing students to attend classes in São José dos Campos and Cachoeira Paulista, simultaneously. The Course accepts students with undergraduate or graduate degrees in meteorology, physics, engineering, mathematics, oceanography, and related fields.

Remote Sensing Brazil, due to its continental dimensions, is one of the countries that can benefit from the use of remote sensing research and monitoring of natural resources renewable and nonrenewable. Since 1969, INPE collects and analyzes remote sensing data obtained by aircrafts (cameras, imagers, radars, and so on) and/or orbital platforms (LANDSAT, SPOT, SPACE SHUTTLE, NOAA, ERS, JERS, RADARSAT, etc.), researching, developing and applying methodologies to the study of the natural resources of the country. Foreseeing the great need to prepare researchers specialized in the analysis and interpretation of remote sensing data, INPE created in 1972 the Graduate Course in Remote Sensing at Master level. In 1998, the Doctoral program was created. The Course includes basic compulsory and optional subjects. The application and selection procedures are based on curriculum vitae analysis, examinations of proficiency in foreign language (English), basic mathematics, and physics. As soon as the required subjects are completed, a research proposal has to be presented by the Master student. The Doctoral student is submitted to a qualification examination and, if approved, a research proposal must also be presented. The final academic step is the Master Dissertation or the Doctoral Thesis presentations.

Earth System Science Earth System Science seeks to understand the dynamics of natural and social systems complex interaction. It explores the interactions of natural components, such as oceans, soil and vegetation with the atmosphere, as well as their interactions at the levels of biodiversity, biogeophysics and chemistry with human systems and dynamics (institutions, policies, culture, economy, demographics, etc.). The Center for Earth System Science (CCST) of the INPE aims to create interdisciplinary knowledge for national development, which integrates concern about equity and the preservation of planetary life-sustaining systems. It conducts studies to evaluate impacts of global and regional environmental changes on social, economic, and environmental systems, especially those bearing on national development and quality of life. By means of modeling tools and analysis of environmental data, it develops technologies for monitoring, mitigating and adapting environmental changes. The Doctoral program in Earth System Science (PG-CST) provides high-level training in the above areas of research, enhancing human capacity to find practical solutions to global, regional and local environmental problems of importance to Brazil and South America. It offers to the students broad access to INPE’s facilities in support of advanced research and teaching. The program seeks to facilitate the process of finding financial assistance for doctoral students through national education-oriented agencies, such as CAPES, CNPq and FAPESP, among others.

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Antonio Fernando Bertachini de Almeida Prado

THE GRADUATE SCHOOL TODAY Some details of the Graduate School at INPE can be seen from the statistics obtained from its history, in particular from the recent year of 2010. To have an idea of the size of the graduate school, we can mention that, by the end of 2010, the number of permanent professors was 201, and the number of participant professors was 58, making a total of 259. Regarding students, at the same time, we had 189 students enrolled in a master program, 293 enrolled in a doctoral program and 108 students registered in singles classes, making a total of 590 students. As far as quality is concerned, we can say that the courses had a good result in the latest evaluation performed by CAPES. Table 1 shows the result of the last two evaluations. Those grades are good enough to place INPE as one of the best graduate schools in the country. The number of graduates from INPE is also an important factor, and it is shown in Table 2. Table 2 shows the number of graduations made by INPE by every Course in the period from 2006 to 2010. From there, we can see that 53 master and 21 doctoral degrees were given by INPE in 2010. Since we had a total of 1,624 master and 435 doctoral degrees given by INPE until 2009, the new historic totals are 1,677 master and 456 doctoral degrees awarded. Table 1: Results from CAPES evaluation in the last two periods

Program Astrophysics Applied Computing Engineering and Space Technology Space Geophysics Meteorology Remote Sensing Earth System Science

Previous (2007) Master Doctor 4 4 4 4 5 5 6 6 6 6 6 6 -

Now (2010) Master Doctor 3 3 5 5 5 5 6 6 6 6 7 7 5 5

Table 2: Graduations by INPE in the last five years

Program Astrophysics Applied Computation Earth’s Science Science and Tec. of Materials and Sensors Combustion and Propulsion Space Mechanics and Control Eng. and Management in Space System Space Geophysics Meteorology Remote Sensing Total Total M and D M: Master; D: Doctor.

2006 M D 5 1 9 11 --4 6 5 -3 4 --4 2 8 1 19 4 57 29 86

2007 M D 1 2 20 10 --9 1 3 -3 ---1 4 10 3 20 7 67 27 94

2008 M D 6 1 16 10 --3 4 -1 6 3 --5 6 12 8 18 8 66 41 107

2009 M D 4 3 15 13 --5 6 7 1 13 9 --7 7 15 10 22 4 88 53 141

2010 M D 2 3 8 2 --6 4 1 -3 ---7 3 11 5 15 4 53 21 74

To conclude this text, we can say that the INPE reaches its 50 anniversary having a long list of important achievements in space related fields. In particular, the Graduate school that exists inside INPE has made large steps in the progress of space engineering and sciences in Brazil.

ACKNOWLEDGEMENTS The author thanks the staff members of the Secretaria de Pós-Graduação for the numbers collected, and the Academic Coordinators of all Courses for helping in the description of their activities. 12

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doi: 10.5028/jatm.2011.03019610

Angelo Passaro Instituto de Estudos Avançados São José dos Campos – Brazil angelo@ieav.cta.br

Dermeval Carinhana Jr* Instituto de Estudos Avançados São José dos Campos – Brazil dcarinhana@ieav.cta.br

Enizete Aparecida Gonçalves Instituto Nacional de Pesquisas Espaciais São José dos Campos – Brazil enizeteaparecida@ibest.com.br

Marcio Moreira da Silva Instituto de Estudos Avançados São José dos Campos – Brazil mmsmarcio@hotmail.com

Ana Paula Lasmar Guimarães Universidade Estadual Paulista Guaratinguetá – Brazil ana_paula_lg@hotmail.com

Nancy Mieko Abe

The use of molecular spectra simulation for diagnostics of reactive flows Abstract: The C2* radical is used as a system probe tool to the reactive flow diagnostic, and it was chosen due to its large occurrence in plasma and combustion in aeronautics and aerospace applications. The rotational temperatures of C2* species were determined by the comparison between experimental and theoretical data. The simulation code was developed by the authors, using C++ language and the object oriented paradigm, and it includes a set of new tools that increase the efficacy of the C2* probe to determine the rotational temperature of the system. A brute force approach for the determination of spectral parameters was adopted in this version of the computer code. The statistical parameter c2 was used as an objective criterion to determine the better match of experimental and synthesized spectra. The results showed that the program works even with low-quality experimental data, typically collected from in situ airborne compact apparatus. The technique was applied to flames of a Bunsen burner, and the rotational temperature of ca. 2100 K was calculated. Keywords: Optical emission spectra, Computerized simulation, Combustion control, Computer programs, Rotational spectra.

Instituto de Estudos Avançados São José dos Campos – Brazil nancy@ieav.cta.br

Alberto Monteiro dos Santos Instituto de Estudos Avançados São José dos Campos – Brazil alberto@ieav.cta.br *author for correspondence

INTRODUCTION Combustion processes and plasma formation are inherent phenomena of the aerospace technology. Operation of propulsion artifacts, like gas turbine and rocket engine, and shock-wave formation, as observed in hypersonic flight and re-entrance procedures, are the most common examples of this association. In general, both systems constitute a high-temperature environment, with electrons and ionized species produced by a complex chemistry and a time-varying turbulent flow field (Zel’dovich and Raizer, 2002). The measurement of any basic system data, such as temperature and concentration of major species and intermediated radicals and flow velocities, requires the employment of specific diagnostic techniques. For some kinds of combustion systems, which includes aeronautic and aerospace applications, the use of conventional probes, such as thermocouples and gas analyzers, for combustion diagnostic is not possible or can cause structural Received: 26/11/10 Accepted: 01/02/11

problem and aerodynamic instability, disturbing the system (Gregory, 2005). In these cases, the reliability of measurements is affected by the high-temperature observed in these flames and by perturbations in the flow stability caused by probe insertion. As alternative, these systems can be monitored by using nonintrusive methods, especially those based on optical properties, i.e., in the absorption or emission of radiation of the system (Docquier and Candel, 2002). Among them, the natural or spontaneous emission spectroscopy of radical species shows some remarkable advantages, as it only needs a simple, low-cost, and compact experimental apparatus. These features point to the use of the emission spectroscopy as an important and powerful tool to support active control of combustion processes, where a real time and in situ system monitoring is required (Ballester and Garcia-Armingol, 2010). Emission of flames is due to chemical reactions that produce intermediate chemical species, like, for example, free radicals in excited states. The radiation emission of these radicals is known as chemiluminescence. In hydrocarbon fuel flames, the most intense emissions are associated with C2*, CH* e OH* species (Durie, 1952; Kane and Broida, 1953). The asterisk denotes the electronic state associated

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with each molecule. Apart from spectroscopic constants and experimental factors, the intensity of radical emission spectra is related to the system temperature. This relation is expressed by the Boltzmann´s equation, which is given by: I

= CS J' J"Ȝ - 4 exp

(- ) E J'

(1)

kT

where SJ´J” is the line strength of a transition from the upper (J´) to the lower (J”) rotational state of the excited species; EJ´ is the rotational energy of the upper rovibrational level; C is a proportionality constant related to experimental factors, like detector and diffraction grating responses, which attenuate or maximize the emission signal; l is the line wavelength associated with the transition; and k is the Boltzmann factor (Herzberg, 1950). Thus, the challenge of combustion diagnosis is to establish a consistent relation between microscopic features of the system, spontaneous emission of chemical species generated by fuel burning, and macroscopic property, e.g., its kinetics temperature, which is the most common temperature concept adopted to characterize a flame. Considering that the emission spectrum follows the Boltzmann distribution given by Eq. 1, a plot of the natural logarithm of line intensities versus the energy term shows a straight line whose slope is the inverse of the rotational temperature. In some cases, the rotational temperature of the intermediate species of hot gases is very close to the kinetic temperature, because the translational and rotational energies of a molecule equilibrate within a trajectory of a few mean free path length by collisional processes with other species (Lapworth, 1974). In nonequilibrium systems, as in hypersonic flows (Fujita et al., 2002; Ivanov et al., 2008; Tsuboi; Matsumoto, 2006), supersonic combustion (Do et al., 2008), or plasmas generated by spacecraft during reentry (Blackwell et al., 1997), the various forms of energy are not in equilibrium, and there is not one temperature value able to describe all physical chemistry processes in course (Reif et al., 1973). In these cases, rotational temperature is useful to provide information about chemical reactivity of the medium and produced thermal energy (Acquaviva, 2004). A direct and simple method to determine the rotational temperature is the comparison of experimental spectra with a synthetic one. The latter can be computed by applying Eq. 1 to each rotational transition belonging to a specific natural emission band. The final spectrum profile is synthesized by the convolution of every spectral line using, for example, a Gaussian-type function. Most of the emitted chemiluminescent is due to intermediated radicals, generally diatomic molecules. Herein, the calculations are relatively simple, as the spectroscopy parameters are well-known experimentally. However, there are some mathematical aspects, as the number of points chosen for 14

theoretical calculation, which can generate nondesirable artifacts, as spectral line losses. The aim of this paper is to present molecular spectra simulation as a combustion and plasma diagnostic tool. The species chosen as probe for rotational temperature determination was the C2* excited radical. This intermediated reaction product is largely present in all combustion processes containing fossil fuel. It is also present in plasmas formed by high-temperature exposure and ion irradiation of carbonic composites, which are materials with several aerospace applications (Arepalli et al., 2000; Paulmier et al., 2001).

SPECTRA SIMULATION The computer code for spectra simulation used in this paper was developed by the authors using the C++ language and the object oriented paradigm, and it follows the procedure presented in Pellerin et al. (1996) and Acquaviva (2004) to synthesize the spectra. The computer code allows the visualization of the experimental spectra and of the theoretical one, of the computed emission lines, of both wavelength and intensity, and of the relative contribution of branches P, Q, and R for each C2* band. The comparison of theoretical and experimental spectra can be done by visual inspection, with both spectra superposed in one graph and showing the discrepancy between them for each wavelength in a second plot. The theoretical spectrum curves are obtained following the steps: (i) calculation of the spectral lines position; (ii) determination of its relative intensities and finally (iii) application of a Gaussian-type broadening factor. The first step is carried out using spectroscopic data taken from literature (Pellerin et al., 1996). The two latter steps are dependent of the rotational temperature and total spectral resolution, respectively. The spectra simulator allows the computation of a single spectrum from the temperature and resolution, and the solution of the inverse problem, determining an optimum pair (temperature, resolution) that minimizes differences between the simulated and experimental spectra. A brute force approach is adopted in this version of the computer code. A range for these two parameters is defined by the user, as well as the variation step of each of them. The implementation explores the multicore characteristic of the modern processors in order to determine both temperature and resolution in a very short time. The number of computer cores is detected automatically by the computer program and an adequate number of threads is launched, parallelizing coarse grain computations. From these data, synthesized spectra for each pair combination,

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The use of molecular spectra simulation for diagnostics of reactive flows

with commercial, low-cost, and compact spectrometers. These characteristics present special importance regarding the acquisition of data from aeronautics and aerospace applications. In most cases, the payload weight is a critical limiting variable, and the use of compact spectrometers of low-resolution is an interesting choice for in situ airborne diagnostic of plasma or combustion (Gord and Fiechtner, 2001; Knight et al., 2000).

1.0 (a)

0-0 band

0.8 I (a.u.)

temperature/resolution, is iteratively computed. Basically, each set of input data in the ranges defined by the user is used to simulate a spectrum. Every synthesized spectrum is compared with the experimental one to choose the synthesized spectrum that better matches the experimental one. The quality of each synthesized spectrum is defined by comparison with the experimental one, using the chi-squared statistical parameter (c2) as a figure of merit. The computer code adopts the full wavelength range as default, but this can be a bad choice if several bands are under consideration or if the contribution of other radicals is important in the experimental spectrum. The user can define a particular range of wavelength, for instance, a region where only a given band of a molecule contributes appreciably to the spectra, as basis for the chi-squared computation in order to reduce the influence of these factors and improve the parameter determination. These tools are fundamental to reduce the error usually associated in literature with the determination of temperature. Although a detailed description of the tools implemented in our computer code is out of the scope of this work, some few special characteristics are presented when needed in the Results section.

0.6 0.4

1-1 band

0.2 0.0 510 511 512 513 514 515 516 517 Ȝ (nm) 1.0 (b)

SPECTRA ACQUISITION

RESULTS AND DISCUSSION Typical experimental C2* emission spectra acquired with three instrumental resolutions, 0.061, 0.096  and 0.13 nm are presented in Fig. 1. These resolutions are easily obtained

0-0 band

I (u.a.)

0.6 0.4

1-1 band

0.2 0.0 510 511 512 513 514 515 516 517 Ȝ (nm) 1.0 (c)

0-0 band

0.8 I (u.a.)

Bunsen-type flames were investigated to illustrate employment and capability of the theoretical simulation to obtain the temperature related to the experimental spectra. The fuel burned was liquefied petroleum gas (LPG). The optical system consisted on a TRIAX 550 (Jobin Yvon) monochromator of 0.5 m focal length (f), equipped with a 1.200 lines.mm-1 diffraction grating, with blaze at 500 nm. The instrumental resolutions (Dlinst) resulting were 0.061, 0.095, and 0.13 nm, for exit slit apertures of 30, 60 and 90  µm, respectively. These values were calculated from the measurement of the full width at half maximum (FWHM) of the emission line at 546 nm of a low-pressure discharge Hg lamp. Three C2* spectra were acquired in the same experimental conditions for each instrumental resolution. Flame radiation was collected by a fiber optic bundle connected to the spectrometer light entrance. Emission signal was detected by a Hamamatsu R928P phototube, with 950 V as work voltage. Spectra were obtained in the 502 to 518 nm range, which corresponds to the d3Πg → a3Πu electronic transition, known as Swan band (Gaydon, 1957). All spectra were measured at the region corresponding to the end of the inner flame cone.

0.8

0.6 0.4

1-1 band

0.2 0.0 510 511 512 513 514 515 516 517 Ȝ (nm) Figure 1: Emission spectrum of the Swan band of the C2* radical. Measured instrumental resolution were: (a) 0.061 nm, (b) 0.095 nm and (c) 0.13 nm.

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The spectra were normalized with respect to the bandhead of the 0-0 vibrational band. The use of different instrumental resolutions provides spectra with remarkable differences. Characteristic intense peaks are observed at ca. 516.6 and 513.0 nm, corresponding to the band-heads of 0-0 and 1-1 vibrational bands, respectively. In the present paper, only the peaks of 0-0 band between 513.5 -516 nm were used in the determination of temperature. This range contains an appreciable quantity of “thermometric peaks”, i.e., peaks whose relative intensities are more sensitive to changes in the rotational temperature (Carinhana, 2006). However, the degradation of spectrum profiles caused by peak broadening is stronger in this region. In the following subsections, we illustrate the use of the simulation tool to aid the temperature determination for the case of higher resolution spectra (0.061 nm).

The next step is the optimized values determination of the simulation parameters. In fact, as previously explained, a brute force approach is used to solve an inverse problem. For that, a range of Trot and of Dl, and the number of steps for each of them, is defined by the user. The program computes a sequence of spectra for each (Trot, Dlspec) pair, and also calculates the respective value of c2 comparing the synthesized spectra with the experimental one. These results are expressed graphically as a family of curves of c2 versus Trot for each value of Dlspec. The optimized parameters of the theoretical spectrum are given by the Table 1:

Trot  and Dlspec calculated from experimental spectra. Temperature uncertainties corresponds to the standard deviation of the measurements

Dlinst (nm) 0.061 0.095 0.13

Trot (K)

Dlspec (nm)

2113 (77) 2173 (34) 2616 (77)

0.069(2) 0.0961(16) 0.1451(31)

A - Procedure for the rotational temperature determination The first issue for temperature determination is the choice of initial values of the rotational temperature (Trot) and of the spectral resolution (Dlspec), which will be used as input data for computing the theoretical spectra. The initial input data were set as Trot = 1850 K and Dlinst = 0.061 nm. The chosen temperature corresponds to the temperature for Bunsen-type flames at the investigated region, determined by McPherson and Henderson (1927). The initial value of spectral resolution was assumed to be equal to the instrumental resolution determined with the Hg lamp.

Intensity (A.U.)

1e+003 800 600 400 200 0 512.5 513.5 514.5 515.5 516.5 517.5 Wavelength

One of the tools implemented in the simulator allows a wavelength adjustment in order to match both experimental and synthesized spectra in a region between two defined peaks. This process is done to correct these deviations, improving the procedure taken in the next step to determine the temperature. To carry out the matching, the correspondence of two known pair of peaks of experimental and theoretical spectra, defined by the user, is set in a specific graphic window. In this example, a match was accomplished choosing as reference peaks the band-head of the 0-0 and 1-1 bands, that is, the limits of the region of interest regarding the 0-0 band (Fig. 3). Apparently, a reasonable match between both spectra is shown. Nevertheless, some remarkable differences in the peak intensities can be observed. 16

Figure 2: Experimental spectrum with instrumental resolution of 0.061 nm superimposed to a synthesized spectrum computed with rotational temperature of 1850 K and spectral resolution of 0.061 nm. 1e+003 Intensity (A.U.)

Figure 2 shows the experimental spectrum overlapped with the synthesized one. It can be noticed differences in the wavelength of corresponding peaks in the experimental and synthesized spectra. These differences can be explained by small deviations in spectral calibration of the experimental apparatus.

800 600 400 200 0

512.5 513.5 514.5 515.5 516.5 517.5 Wavelength (nm)

Figure 3: Experimental spectrum with instrumental resolution of 0.061  nm superimposed to a synthesized spectrum computed with rotational temperature of 1850  K and spectral resolution of 0.061  nm after the matching operation.

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The use of molecular spectra simulation for diagnostics of reactive flows

With respect to Fig. 4, the testing range of Dl was arbitrarily assigned as 0.061 ± 0.01 nm, i.e., ca. 15% for lower and upper values. A similar criterion was adopted for the Trot range, which was chosen as 1,850 ± 270 K. The number of steps for both ranges was 32. Of course, these were not good choices because it is not certain that the family of curves have reached a minimum. The optimized temperature can be out of the chosen range. Figure 5 shows a new set of curves obtained for 2000 ≤ Trot ≤ 2,700 K and 0.061 ≤ Dlspec ≤ 0.081 nm. From this family of curves, the minimum of c2 corresponds to the pair Trot  =  2113  K and Dlspec  =  0.069  nm. Note that the determined rotational temperature was considerably higher than the original input data. The same procedure was applied to determine the temperature associated with the other experimental spectra. Values of Trot and Dlspec presented in Table 1 correspond to the mean values computed from the set of spectra acquired for each instrumental resolution. The errors, presented inside the parenthesis, correspond to the standard deviation.

for low-pressure Hg lamp, and that Dlinst is given by the peak profile of atomic lines (Griem, 1997). However, for atmospheric LPG flames, the Doppler and the collisional 0.4 0.313 Chi-Squared

best spectra match, i.e., by the point where the minimum value of c2 is observed. Examples of these calculated curves are shown in Figs. 4 and 5.

0.225 0.138 0.05

1550.0

1700.0

1850.0

200.0

2150.0

Temperatures Figure 4: c2 versus Trot curves used in optimization procedure of spectral parameters. Each one corresponds to a value of Dlspec between 0.05 and 0.07 nm. The minimum value of c2 corresponds to the pair Trot = 2120 K and Dlspec = 0.07 nm.

0.24

Here, it is important to say that instrumental resolution (Dlinst) is not the unique contribution to the peak profile of the emission spectra. There are physical-chemistry phenomena, like Doppler Effect and collisional processes involving the chemical species present in the system, which also cause line broadening of the spectrum (Gaydon, 1957; Griem, 1997). As both factors are mainly dependent on the temperature and pressure of the system, respectively, it can be accepted that they are negligible Table 2:

Trot and Dlspec calculated from experimental spectra with nominal resolution of 0.13 nm (lower resolution)

Trot (K) Dlspec (nm)

Spectrum 1 2555 0.146

Spectrum 2 2592 0.141

Spectrum 3 2814 0.146

0.16 0.12 0.08 0.04 2000.0 2140.0 2280.0 2420.0 2560.0 2700.0 Temperatures

Figure 5: Final c versus Trot curves used in optimization procedure of spectral parameters. The minimum value of c2 corresponds to the pair Trot = 2,113 K and Dlspec = 0.069 nm. 2

1e+003 Intensity (A.U.)

Figure 6 shows the spectrum synthesized with the parameters presented in Table 1 for Dlinst 0.061  nm superposed to one of the experimental spectra. Figure 7 shows the deviation between the same experimental spectrum and the synthesized spectra referring to Figs. 2, 3, and 6. The deviation graph is other of the tools implemented in the computational program, and it is very useful in the superposing spectra evaluation. The optimum synthesized spectrum is in very good agreement with the experimental one. Only small differences are observed in the region between 513.2 and 516 nm, distributed around zero, i.e., in the region of the thermometric peaks.

Chi-Squared

0.2

800 600 400 200 0 512.0 513.0 514.0 515.0 516.0 517.0 0.04 Wavelength (nm)

Figure 6: Final synthesized spectrum overlapped with an experimental one. Trot  =  2,113  K and Dlspec = 0.069 nm.

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broadening show appreciable influence. Thus, the spectral resolution of C2* emission spectra is expected to be larger than the Dlinst. In all cases, the results regarding Dlspec  were consistent with the expected behavior: all of them were higher than the Dlinst. The temperature obtained from the spectra with nominal resolution of 0.061 and 0.095  nm agrees, considering the standard deviation.

400

Differences

300 200 100 0 -1e+002 -2e+002

The difference observed in temperature between the computed and the original input data (1850 K) is not related to the computer code response, but to the deactivation processes of the C2* radical. In fact, C2* radical rotational temperatures have been described in literature as being higher than the theoretical equilibrium flame temperature (Gaydon and Wolfhard, 1970). This means that the rotational degrees of freedom are not in equilibrium and Boltzmann-Maxwell distribution of velocities is not strictly followed. The average number of collisions in the excited state is not sufficient to establish a rotational distribution equivalent to the temperature associated with the translational, or kinetic, mode. The emission spectra, therefore, correspond to a description of the rotationally excited states of the C2* species. This feature of C2* radical is useful to describe the physical chemistry processes of reactive flows with the presence of organic reactants (Rond et al., 2007). In these systems, the nonequilibrium situation produces a strong radiative emission from the excited species, and this radical can be used as a probe to indicate the temporal evolution of rotational temperature.

Wavelength (nm)

(a)

B - Limits of the proposed approach As already stated, the temperature determination by spectra simulation is based on the comparison of experimental and computed spectra profiles. The analyzed range of wavelengths has to contain an appreciable quantity of peaks, whose relative intensities are more sensitive to changes in the rotational temperature. As the resolution decreases (greater values of Dlspec), a degradation of spectrum profiles caused by peak broadening is expected, reducing the elements for the pair determination (Trot,  Dlspec). In this case, the determination of the temperature can be a problem.

Differences

100

50

0

-5e+001

-1e+002

Wavelength (nm)

(b)

Spectra with 0.13 nm instrumental resolution are examples of cases where the spectra broadening results in a lack of thermometric peaks (Fig. 8b). Table 1 shows that the rotational temperature obtained for the spectra acquired with Dlinst  =  0.13  nm is much higher than the value presented in other cases. The computer code was able to reproduce consistently the temperature and Dlspec even for this set of experimental spectra, resulting in a rotational temperature above 2,600 K with a standard deviation of the same magnitude as the other cases.

Differences

100

50

0

-5e+001

-1e+002

Wavelength (nm)

(c) Figure 7: Deviation between synthesized spectrum and the experimental one: (a) original data – 1,850  K; (b) after spectra matching - 1,850 K; and (c) optimized spectrum – 2,113  K. Note that the amplitude of the deviation between the spectra decreases systematically from (a) to (c). 18

A simple procedure was performed to test the former result consistency: the experimental spectra were compared with the simulated ones with Trot of 2,150 K as input data. This value corresponds to the average Trot presented in Table 1 computed from the other two more resolved spectra. The superposed spectra in Figs. 8a and 8b suggest that the experimental one with larger nominal resolution do not present the same Trot of

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The use of molecular spectra simulation for diagnostics of reactive flows

the others, because the synthesized spectrum is systematically below the experimental in the region of interest, from 513.2 to 517 nm. The temperature determined for each spectrum, in this case, is presented in Table 2, which can indicate that the mixture of oxygen and LPG was not anymore stable when these spectra were acquired.

Environment”, Spectrochimica Acta Part a-Molecular and Biomolecular Spectroscopy, Vol. 60, No. 8-9, pp. 20792086. doi:10.1016/j.saa.2003.10.040

The use of C2* molecular emission spectroscopy allied with spectra simulation for reactive flows diagnostic was presented. The presented methodology was able to determine consistently the temperature for C2* spectra acquired within a large range of spectral resolution, including low-quality spectrum data. The developed computational program allows a quick determination of the C2* rotational temperature associated with the 0-0 band. A brute force approach to solve the inverse problem, allied to a C2* spectra simulator, which explores the multicore capability of the modern computers, proved to be a good strategy for determining the optimum pair (Trot, Dlspec). The time frame to obtain the optimum pair is compatible with the spectrum acquisition time, making this one useful tool to flame diagnostics in laboratory. This has remarkable importance for aeronautics and aerospace applications, where the use of light and compact spectrometers of low-resolution can reduce the payload weight. The computed values of C2* rotational temperatures, considering the higher resolution spectra, were ca. 2150 K for a Bunsen burner flame. This value is ca. 6% higher than the one reported in literature, which indicates, as expected, that the Bunsen-type flames are not completely in equilibrium state.

512.0

513.0

514.0

515.0

516.0

517.0

516.0

517.0

Wavelength (nm) 100

50

0

-5e+001

-1e+002

Wavelength (nm)

(a) 1e+003

800

600

400

200

0 512.0

513.0

514.0

515.0

Wavelength (nm) 100

Differences

Angelo Passaro wishes to thank the financial support of the Brazilian National Council for Research and Development (CNPq), under grant: 310768/2009-8.

400

0

Nowadays, the computer code computes up to five Swan bands, but the determination of the rotational temperature is based only on the thermometric peaks of the 0-0 band. New tools to explore the additional bands are under development.

ACKNOWLEDGMENTS

600

200

Differences

CONCLUSIONS

800

Intensity (A.U.)

Additional tests have to be carried out in order to determine the actual limitations of the proposed approach.

Intensity (A.U.)

1e+003

50

0

-5e+001

-1e+002

REFERENCES Acquaviva, S., 2004, “Simulation of Emission Molecular Spectra by a Semi-Automatic Programme Package: The Case of C-2 and CN Diatomic Molecules Emitting During Laser Ablation of a Graphite Target in Nitrogen

(b)

Wavelength (nm)

Figure 8: Comparison of synthesized and experimental spectra for two different set of input parameters : (a) Trot  =  2,150  K and (b) Trot = 2,616  K. The same Dl = 0.145 nm is used in both cases.

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Passaro, A. et al.

Arepalli, S., Nikolaev, P., Holmes, W. and Scott, C. D., 2000, “Diagnostics of Laser-Produced Plume under Carbon Nanotube Growth Conditions”, Applied Physics A-Materials Science & Processing, Vol. 70, No. 2, pp. 125-133. doi: 10.1007/s003390050024 Ballester, J., García-Armingol, T., 2010, “Diagnostic Techniques for the Monitoring and Control of Practical Flames”, Progress in Energy and Combustion Science, Vol. 36, No. 4, pp. 375-411. doi: 10.1016/j. pecs.2009.11.005 Blackwell, H. E.; Scott, C.D.; Arepalli, S., 1997, “Measured Nonequilibrium Temperatures in a Blunt Body Shock Layer in Arc Jet Nitrogen Flow”, 32nd  Thermophysics Conference, AIAA. Carinhana Junior, D., 2006, “Determination of Flame Temperature by Emission Spectroscopy” (In Portuguese), Ph.D. Thesis, State University of Campinas, Campinas, SP, Brazil, 129p. Do, H., Mungal, M. G. and Cappelli, M. A., 2008, “Jet Flame Ignition in a Supersonic Crossflow Using a Pulsed Nonequilibrium Plasma Discharge”, IEEE Transactions on Plasma Science, Vol. 36, No. 6, pp. 2918-2923. Docquier, N., Candel. S., 2002, “Combustion Control and Sensors: A Review”, Progress in Energy and Combustion Science, Vol. 28, No. 2, pp. 107-150. Durie, R. A., 1952, “The Excitation and Intensity Distribution of CH Bands in Flames”, Proceedings of the Physical Society of London Section A, Vol. 65, No. 386, pp. 125-128. Fujita, K., Sato, S., Abe, T. and Ebinuma, Y., 2002, “Experimental Investigation of Air Radiation from Behind a Strong Shock Wave”, Journal of Thermophysics and Heat Transfer, Vol. 16, No. 1, pp.77-82. Gaydon, A. G., Wolfhard, H. G., 1970, “Flames”, Ed. Chapman and Hall, London, Great Britain, 401 p. Gaydon, A. G., 1957, “The Spectroscopy of Flames”, Ed. Chapman and Hall, London, Great Britain, 279p. Gord, J. R., Fiechtner, G. J., 2001, “Emerging Combustion Diagnostics”, 39th AIAA Aerospace Sciences Meeting & Exhibit, Reno, USA, pp. A01-16608. Gregory, O.J., You, T., 2005, “Ceramic Temperature Sensors for Harsh Environments”, IEEE Sensors Journal, Vol. 5, No. 5, pp 833-838. Griem, H. R., 1997, “Principles of Plasma Spectroscopy”, Cambridge University Press. 20

Herzberg, G., 1950, “Molecular Spectra and Molecular Structure - i. Spectra of Diatomic Molecules”, 2nd ed., Ed. Van Nostrand Reinhold Company, New York, Brazil, 658 p. Ivanov, V. V. et al., 2008, “Spectroscopic Investigations of Longitudinal Discharge in Supersonic Flow of Air with Injection of Propane into the Discharge Zone”, High Temperature, Vol. 46, No. 1, pp. 3-10. Kane, W. R., Broida, H. P., 1953, “Rotational Temperatures of Oh in Diluted Flames”, Journal of Chemical Physics, Vol. 21, No. 2, pp. 347-354. doi:10.1063/1.1698883 Knight, A. K. et al., 2000, “Characterization of LaserInduced Breakdown Spectroscopy (Libs) for Application to Space Exploration”, Applied Spectroscopy, Vol. 54, No. 3, pp. 331-340. Lapworth, K. C., 1974, “Spectroscopic TemperatureMeasurements in High-Temperature Gases and Plasmas”, Journal of Physics E-Scientific Instruments, Vol. 7, No. 6, pp. 413-420. McPherson, W., Henderson, W. E., 1927, “A Course in General Chemistry”. 3rd ed., Ed. Ginn and Company, Boston, USA, 559 p. Paulmier, T. et al., 2001, “Physico-Chemical Behavior of Carbon Materials under High Temperature and Ion Irradiation”, Applied Surface Science, Vol. 180, No. 3-4, pp. 227-245. Pellerin, S. et al., 1996, “Application of the (O,O) Swan Band Spectrum for Temperature Measurements”, Journal of Physics D-Applied Physics, Vol. 29, No. 11, pp. 2850-2865. Reif, I., Fassel, V. A. and Kniseley, R. N., 1973, “Spectroscopic Flame Temperature-Measurements and Their Physical Significance .1. Theoretical Concepts Critical Review”, Spectrochimica Acta Part B-Atomic Spectroscopy, Vol. B 28, No. 3, pp. 105-123. Rond, C. et al., 2007, “Radiation Measurements in a Shock Tube, for Titan Mixtures”, Journal of Thermophysics and Heat Transfer, Vol. 21, No. 3, pp. 638-646. Tsuboi, N., Matsumoto, Y., 2006, “Interaction between Shock Wave and Boundary Layer in Nonequilibrium Hypersonic Rarefied Flow (5th Report, Nonequilibrium of Rotational Temperature in Flow over Flat Plate)”, Jsme International Journal Series B-Fluids and Thermal Engineering, Vol. 49, No. 3, pp. 771-779. Zel’dovich, Y. B., Raizer, Y. P., 2002, “Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena”, Ed. Dover Publications, Mineola, USA, 916 p.

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doi: 10.5028/jatm.2011.03017010

Alexandro Garro Brito* Institute of Aeronautics and Space São José dos Campos – Brazil alegbrito2@gmail.com *author for correspondence

Computation of multiple limit cycles in nonlinear control systems – a describing function approach Abstract: Limit cycles play an important role in nonlinear systems, provided that many control loops with common nonlinearities like relay, hysteresis, and saturation can present them. Thus, a proper description of this nonlinear phenomenon is highly desirable. A strategy for the linearized analysis is the describing function method, which is a frequency domain approach that allows the limit cycle prediction and stability analysis. Some papers had discussed the method for the simplified analysis; however, they are concentrated in the prediction of only one limit cycle even for systems with multiple conditions. This paper proposes a systematic way of multiple limit cycle determination, as well as the stability analysis of each one. All theoretical/computational issues involved in the approach are also discussed. Keywords: Limit cycle, Multimodal optimization, Describing functions.

INTRODUCTION Nonlinear behavior is common in aerospace systems, where many kinds of nonlinearities can produce limit cycles or other phenomena that can affect the system overall behavior. In Dotson, Baker and Sako (2002), the limit cycle induction due to aerodynamic forces over launcher fairings and aircraft wings was discussed. Leite Filho and Bueno (2003) presented the analysis of self-sustained oscillations in actuator systems of a launch vehicle. Furthermore, Newman (1995) and Stout and Snell (2000) studied the presence of this nonlinear behavior in spacecrafts and launchers propulsion systems. Due to the limit cycle phenomenon importance in several systems, a systematic approach to predict its amplitude and frequency is necessary, and many methods based on an analytical analysis have been proposed. For predator-prey systems, a proper formulation can be derived to predict limit cycles, as seen in the works of Freedman (1990), Hofbauer and So (1994); however, it cannot be directly extended to other dynamic systems. In Nayfeh and Mook (1979), two important general methods are presented: the Lindstedt-Poincar’e and the Multiple Scales, both of them based on a linearization through power-series expansion and algebraic manipulations that can become hard in some cases.

Received: 21/05/10 Accepted: 16/08/10

In spite of extremely useful, the methods mentioned above consider that the nonlinear part can be written as a power-series, which implies that the nonlinearity must be differentiable. Obviously, this is not ever the case, mainly in nonlinear control loops where several discontinuous elements can be present. Then, alternative methods, in which the differentiability is not a requirement, should be adopted. One of the most reliable methodologies is the harmonic balance, where the input-output relation is expressed through the Fourier series (Slotine and Li, 1991). This strategy is much less restrictive than a power-series and can be applied to a wider class of nonlinear systems, including the discontinuous ones. If one is interested in an approximate result, the analysis of the Fourierseries fundamental used to be sufficient, leading to the describing function method, which is a generalization of linear frequency response for nonlinear systems (Gelb and Velde, 1968; Gibson, 1964; Slotine and Li, 1991), and it provides a graphical way to determine the limit cycle existence as well as its amplitude and frequency. In Kienitz (2005) and Somieski (2001), the describing function method was modified so that the existence of limit cycles is related to a functional minimization. Thus, one can obtain the amplitude and frequency of the limit cycle by a unimodal optimization of that functional. However, even this method cannot be directly applied if one is interested in obtaining information about multiple limit cycles of a dynamic system. This paper presents a methodology to compute all limit cycle conditions of nonlinear systems. It is based on a multimodal optimization

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Brito, A.G.

algorithm, which is able to find all the global minima of a cost-function related to the limit cycle occurrence. In spite of other methods like multimodal genetic algorithms that can lose some global minima depending on the cost function topology (Darwen and Yao, 1996), the proposed procedure was developed to guarantee that all minima are reached, even those in complex topological regions like sharp attraction basins. The theory associated with limit cycle calculation is presented, including the describing function concept and the stability analysis. In this paper, this strategy is expanded to permit the computation of multiple limit cycle conditions through the multimodal optimization algorithm presented herein. To test the methodology, some common nonlinearities are associated with simple linear systems, in order that multiple limit cycle conditions appear. Then, the algorithm is used to calculate the amplitude and frequency of the limit cycles and their stability.

LIMIT CYCLE DETERMINATION Methods for quantitative analysis of limit cycle are very useful in a lot of practical applications. Different approaches were developed along time, each one with their benefits and disadvantages. Some of them will be further discussed. Power-series expansion Take into consideration a nonlinear system governed by equations, having the following form (Eq. 1): x  f ( x  R0 ) " 0



(1)

where f is a nonlinear function. Assuming that this function can be expanded by Taylor series, it can be rewritten as in Eq. 2: N

x  ¨ F n x n " 0 

(2)

n"1

where (Eq. 3): 1 y f ( R ). n ! yt n 0 n

Fn "

(3)

There are several ways to obtain an approximate solution of Eq. 2, most of them based on a perturbation analysis around the initial condition u0. The Lindstedt-Poincar’e Method writes the solution as polynomial expansions over two independent variables related to the oscillations 22

amplitude and frequency (Nayfeh and Mook, 1979). This strategy permits that the nonlinear differential equation is converted to a number of algebraic equations; the precision of the approximate solution is strongly related to the polynomial order. This method gives uniformly valid approximations; however, the algebraic manipulation becomes complex for relatively low orders. Another technique is the method of multiple scales, in which the polynomial expansion is a function of multiple independent variables instead of only one. Though more involved, it is also able to treat the damped systems (Nayfeh and Mook, 1979). The power-series approaches – mainly the method of multiple scales – have been successfully applied in many systems where limit cycles are expected to appear. In Li et al. (2008), the bifurcations of multiple limit cycles for a rotoractive magnetic bearings were considered and an approximate solution was obtained through the mentioned method. The same ideas are also applied in Mendelowitz, Verdugo and Rand (2009), in which the limit cycles for coupled oscillators were studied. Yu and Corless (2009) performs the limit cycle computation of the Hilbert’s 16th problem – a complex system where the analysis through the multiple scales requires intensive symbolic computations. Besides very useful to analyze a huge class of nonlinear systems, the power-series methods present some drawbacks. First of all, they assume that the nonlinear function (Eq. 2) is analytic around u0, which implies that one can differentiate f (u) as much as necessary. This is true for several systems, such as the one expressed as a polynomial function (Li et al., 2008; Yu and Corless, 2009). However, it is not always true for nonlinear control loops. In these cases, the presence of nonlinear elements like saturation, backlash, and other equipments that exhibit a discontinuous profile can become the method of multiple scales impossible to apply. Moreover, the use of symbolic manipulation softwares like Maple and Mathematica is essential for multiple limit cycle computation, and the computational effort can also be relatively high even for simple nonlinear control loops. Another important disadvantage is that one cannot obtain any information about the unstable limit-cycles through these methods. It is important to notice that information about unstable oscillations are very useful in control analysis.

Harmonic balance and describing function As already emphasized, one of the powerseries methods disadvantages is related to the approximation used to express the nonlinear function f (u) in Eq. 2, which is proper for analytic functions. In those cases, where this is not a valid argument, overall in nonlinear control loops with discontinuous elements (Gibson, 1964; Siljak, 1969;

J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 21-28, Jan. - Apr., 2011


Computation of multiple limit cycles in nonlinear control systems – a describing function approach

Slotine and Li, 1991), the harmonic balance method seemed to be more appropriate (Nayfeh and Mook, 1979). It is based on the nonlinear function expansion through Fourier series, much less restrictive than Taylor’s. Collecting the harmonics of f (u) properly, the user is also able to rewrite the nonlinear equation as set in algebraic equations. The describing function analysis is a special case of the harmonic balance, in which only the fundamental contribution of the Fourier series is used (Siljak, 1969). The system can be seen in Fig. 1a, with a sinusoidal input of amplitude A and frequency ω. The output can be expanded by Fourier series as in Eq. 4, a0 h  ¨ a cos( n\ t )  bn sin( n\ t ). 2 n"1 n

y (t ) "

(4)

with coefficients given by Eq. 5 to 7:

a limit cycle. The limit cycle’s frequency and amplitude are given by the values ω = ω LC and A = ALC, where the curves intercept themselves, respectively. Asin(\t)

N(A,\)

y(t) +

A

N(A,\)

G(j,\)

B

Figure 1: Diagrams for nonlinear analysis.

The Eigenvalue Method (Somieski, 2001) is an approach that uses a persistent eigenvalue analysis of the nonlinear closed loop to find the limit cycle. To systematize the limit cycle analysis, let’s rewrite the system represented in Fig. 1 as a set of first order nonlinear equations (Eq. 11): x " Fx  f ( x , x ) 

a0 "

1 U

µ

an "

1 U

µ

1 bn " U

µ

U U

U U

U U

y (t ) d (\ t )



(5)

y (t ) cos( n\ t ) d (\ t )

y (t ) sin( n\ t ) d (\ t )





(6)

(7)

If the nonlinear element satisfies some conditions so that its output can be properly approximated by its fundamental Fourier expansion (Slotine and Li, 1991), then (Eq. 8): y (t ) ~ a1 cos(\ t )  b1 sin(\ t ) " M sin(\ t  ^ ) " „{ Me j (\ t ^ ) }

)  b1 sin(\ t ) " M sin(\ t  ^ ) " „{ Me j (\ t ^ ) }



(8)

where, ℑ represents the imaginary part of a complex number. The describing function is defined as (Eq. 9): N ( A, \ ) "

Ae j\ t

where, x is a state vector, F is a system matrix representing the linear part and f is a matrix with the nonlinearities. The nonlinear matrix f is linearized by the describing function concept yet discussed, producing (Eq. 12):

f ( x, x ) ¡ N ( A, \ ) x; N ( A, \ ) " N …  jN „ 



1

© N ¹  " ª I  „ º ( F  N… )  \ » «

(13)

which produces the eigenvalue problem (Eq. 14): (14)

(9)

which is dependent of both input frequency ω and amplitude A. Let’s consider the Fig. 1b, where G(jω) represents the linear part of the system, while N(A, ω) is the describing function of the nonlinear element. According to Nyquist criterion, self-sustained oscillation occurs in this loop if and only if (Eq. 10):

G ( j\ ) N ( A, \ ) " 1 ¡ G j \ ) "

(12)

where, N(A, ω) is the describing function of Nℜ and Nℑ are the real and imaginary parts of N(A, ω), respectively. Applying this formulation to Eq. 11 and by using the Laplace notation, one can obtain the linearized matrix for the closed loop given by (Eq. 13):

( sI  ) x " 0 

Me j (\ t ^ )

(11)

1 N ( A, \ ) 

(10)

Applying Nyquist stability criterion over (Eq. 10), one can notice that each intersection between the curves G(j ω) and −1/N(A, ω) in the Nyquist complex plane corresponds to

Note that Nℑ = 0 and F=F+Nℜ for static nonlinearities. Using this representation for the linearized nonlinear system, a limit cycle occurs if a purely complex eigenvalue pair exists for some A ≡ ALC and ω ≡ ωLC. The computation approach used in the eigenvalue method is a rigorous sweep over the A×ω space, evaluating and analyzing the eigenvalues until a purely complex pair occurs. In Somieski (2001), a frequency iteration procedure is presented for a fine calculation when a frequency dependence over F= exists. Obviously, this is not a proper way for systematic limit cycle search, because even regions without limit cycles must be researched, becoming an eigenvalue-based algorithm highly inefficient.

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Brito, A.G.

Another way to limit cycle computation was presented in Kienitz (2005), where the optimization procedure is based on singular values evaluation. The process is possible due to the following condition:

can become excessively slow without guaranteeing that every minimum will be found. Other methods based on the simulated annealing technique suffer from the same problems (Gibson, 1964).

Theorem 1 (Singular Value Condition): The complex matrix F=(A,ω) has a purely imaginary eigenvalue with magnitude ωLC, if and only if the matrix 15:

This paper proposes a mixed populational-deterministic optimization method able to find multiple minima in a safer fashion. It is based on an initial population that evolves along the attraction basins through a gradient-like procedure, and converge to the global minima gradually. During the process, many “inefficient” points (with high cost-function or close to another better-ranking point) are progressively discarded, increasing the computational speed. As it will be discussed herein, the number of parameters to be set is not as high as other methods, and their tuning is much more intuitive.

" " j\ I  ( A, \ ) 

(15)

is singular at ω = ωLC and A=ALC (Kienitz, 2005). S is singular if and only if its minimum singular value, denoted by σ (S), is null at ω = ωLC. Then, a limit cycle exists at ω = ωLC and A = ALC if the optimization problem (Eq. 16)

( ALC , \ LC ) " arg min X ( " ) 

(16) Mixed populational-deterministic multimodal algorithm

has a solution and σ (S(ALC, ωLC)) ≡ 0. The singular value method presents an important advantage: the singular values computation is easier and faster than the eigenvalues one, increasing the computational efficiency. Then, this is the preferable method for limit cycle computation.

MULTIPLE LIMIT CYCLE SEARCH There are some procedures to compute multiple limit cycle in the literature, however they are based on the analytical analysis of the nonlinear differential equation (Hofbauer and So, 1994; Li et al., 2008; Mendelowitz et al., 2009; Yu and Corless, 2009), which cannot be suitable for nonlinear control systems so that many of their nonlinearities are discontinuous. The describing function is useful in these cases, but the optimization procedure above (Eq. 16) must be modified, since it is a unimodal optimization process intended to search only one limit cycle in a search space. The objective of this section is to present an optimization algorithm able to extend the singular value method above to the multiple limit cycle computation. A first attempt would be trying to use classical multimodal optimization procedures within the cost-function (Eq. 16), but most of them are constructed to obtain all the minima in situations not much restrictive, which the attraction basins have similar aspect and are not very sharp. These issues were well discussed in Darwen and Yao (1996) study, the most common multimodal genetic methods were there discussed and compared. In their conclusions, one can note that a purely evolutionary multimodal method can lose some of the sharper attraction basins unless a high population size is used. Obviously, this is unacceptable in a multiple limit cycle search because the algorithm 24

Let’s consider J(x) a cost-function to be minimized. Therefore, the mixed populational-deterministic multimodal algorithm (MPDMA) procedure is as it can be seen in Fig. 2. Firstly, the search region should be spread out with N initial points (PopInitial), so that all possible attraction basins can be properly researched. The amount of points will depend on the search region size and the number of global minima. As an initial attempt, the user can set this value bigger than 100 times of the expected minima number. If the region size is very large (A, ω ≥ 50), we recommend a ratio bigger than 200. The next step consists in a Gradient-like procedure, where each point walks under the functional surface following the opposite direction of the local gradient vector. This is computed through an eight-sided regular polygon with a small radius Rpoly around each point, as shown in Fig. 3a; the base point xk is replaced by the vertex x1 since that it has the lowest value for the functional f(x). The Gradientlike procedure is applied over the prior population Pop(k to obtain the current population Pop(k), and over that to − 1) obtain the next one Pop(k + 1); as stressed below, this will be necessary to update Rpoly that should be initially chosen around 1% of the search region range. During the population evaluation, some points can be far from a possible minima. Because of this, a selection procedure is necessary to discard such points so that only well-ranked points remain in the optimization. This selection is performed in two steps: i) points outside of the search region are automatically discarded; ii) after the first NSel2 iterations, and for each iteration multiple of NSel1, the point neighbors are discarded to assure that each possible minimum is represented by only one point.

J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 21-28, Jan. - Apr., 2011


Computation of multiple limit cycles in nonlinear control systems – a describing function approach

A and ω (region search). The user should avoid bigger values, for the algorithm can merge two near attraction basins, losing one of them. After some iterations, the population evolution over the minima stops since that the polygon radius Rpoly is not ever sufficient to provide more precise convergence. The result is that the global minima begin to be surrounded, but the points are not able to reach them and this is reflected by the fact that the prior population (Pop(k-1)) become equal to the future one (Pop(k+1)). When this occurs, Rpoly should be decreased by a rate, so that a finer evolution is possible and the prior population (to be used in the next iteration) is taken as the mean between Pop(k) and Pop(k+1). Values for rate around 2/3 provided good results. The algorithm is finished when Rpoly is less than the precision defined by the user. NONLINEAR CONTROL SYSTEMS – MPDMA APPLICATION TO REAL EXAMPLES

Figure 2: MPDMA flowchart.

Many relatively simple nonlinear control systems can exhibit multiple limit cycles. In the describing function context, this means that all interceptions between G(jω) and −1/N(A, ω) represent limit cycles which the stability will determine the attraction or repulsion of near trajectories in the phase plane. Then, the existence of multiple limit cycles is expected in every system where these multiple intersections occur. Notice that infinite combinations between a linear and a nonlinear model can provide the conditions above and the number of examples is really huge. Only to demonstrate some situations where multiple limit cycles occur, let us suppose the following examples.

Liénard system Figure 3: Multimodal optimization algorithm. In a, the Gradient-like procedure is shown. In b, the point neighbor is discarded.

This is achieved throwing out all points inside a disc in the A×ω space, except the best one. The selection is performed as stated: firstly, all points are sorted according to their cost-function values in descending order. The first point is selected and a R-ray disc centered in this point is evaluated; all other points inside this disc are discarded. Then, the next non-discarded point is selected and the procedure is repeated. The strategy is repeated until only non-neighbors remain. Figure 3b summarizes this selection level – points inside the gray discs will be discarded except the black ones, which are the best solutions in their respective disc. The radius R should chosen between 2 and 10% of the maximum range of

A Liérnard system can be represented by the set of differential equations (Eq. 17):

¯ x " y  F ( x ) ¿  ° À ±² y "  x Á²

(17)

In this paper, we use F(x) as Eq. 18:

F ( x ) " 0.8 x  G ( x ) 

(18)

where G(x) = −4/3 x3 + 0.32 x5. In Giacomini and Neukirch (1997), an analytic method to determine the number of limit cycles of Eq. 18, and an approximate solution were presented. It showed that this system has one stable limitcycle and another unstable. Obviously, one could use a power-series expansion method to obtain the approximate solution, since that G(x) is already expanded. However, the

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Brito, A.G.

method of multiple scales becomes tedious to apply and a symbolic software is necessary. Moreover, none information about the unstable limit-cycle would be obtained. By using the method of describing function over G(x), one can apply the MPDMA procedure to obtain information about both limit-cycles. Initially, the describing function of G(x) can be obtained through the Fourier expansion, according to Eq. 4-8, producing Eq. 19:

N G ( x ) ( A) " A2 (0.2 A2  1) 

(19)

Substituting Eq. 19 into 18, we have the describing function matrix: ¬ 0.8  N G ( x ) ( A) 1¼ "­ ½ 1 0 ¾½ ­®

(20)

Figure 4 shows the contour plot for the cost (Eq.  16) (in right). There are two attraction basins related to the limit cycles. On the left, the system simulation and the approximate solutions are presented. To compute these approximations for both limit cycles, the MPDMA procedure was applied and the results are shown in Table 1. Notice that the amplitude and frequency of the limit cycles are in absolute accordance to Giacomini and Neukirch (1997).

Relay control system The relay control is widely applied; however, it can present self-sustained oscillations that influence over the system behavior, and they should be analyzed. In some cases, unstable and multiple limit cycles can be present and it is important to have consistent approaches to study each of them. Relay elements are discontinuous by definition so that a linearization procedure based upon analytical expansions becomes hard to apply. To avoid this drawback, the describing function method has been used to analyze control loops with these elements. In Fig. 5, some relay elements widely used in control applications are shown. To exemplify situations where multiple limit cycles can occur, let us consider the control loop in Fig. 1b, where the linear part can be represented by the transfer function: G ( s) "

3( s  1)2  ( s  0.1)3 ( s  10)2

(21)

According to Gibson (1964), the describing function of each relay element above is given by Eq. 22 and 23: 4M NNa ((AA))"" 4 M  a UUAA

(22)

4M 1  NNb ((AA))"" 4 M ee jj.sin .sin 1((kk // AA)) b UUAA

(23)

y

y M

M

k

X

Figure 4: Liénard system. The contour plot for the cost function (Equation 16) is in the left. In the right, the system simulation and the describing function approximate solutions (continuous lines) are presented. The internal continuous line represents the unstable limit cycle.

A

B

Figure 5: Some relay elements: (a) relay; (b) hysteresis.

The nonlinear matrix F can be obtained straightforwardly through Eq. 21 and 22 or 23 in Fig.1b, leading to: Table 1:

MPDMA application to the Liénard System (Eq.  18); 100 optimizations were performed with search region range equal to 4. The other adopted parameters were N = 250, NSel2 = 50, NSel1 = 10, Rpoly(0) =1%, R = 5%

Limit Cycle

Amplitude

Frequency

Unstable

0.9996 ± 0.0007

1.0000 ± 0.0004

Stable

2.0000 ± 0.0004

0.9998 ± 0.0008

26

¬ 0.1 0.9 0.9487 ­ -0.1 0.9487 ­ 0 ­ " 0 0 -0.1 ­ 0 0 ­ 0 ­ 0 0 0 ®

0 0 1 -10 0

T

¬0.9487 ¼ 0 ¼ ¬0 ¼ ½ ­ ½ ­ ½ 0 ½ ­0 ½ ­0.9487 ½ 0 ½  ­0 ½ .N ( A). ­ 1 ½  (24) ½ ­ ½ ­ ½ 1 ½ ­0 ½ ­ 0 ½ ­ 0 ½  10 ½¾ ­®1 ½¾ ® ¾

where N(·)(A) is each of the describing functions above.

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Computation of multiple limit cycles in nonlinear control systems – a describing function approach

The relay, as the hysteresis case, has three limit cycles, two of them stable. Their time response is presented in Figs. 6 and 7. To obtain the whole information about these nonlinear systems, the MPDMA procedure was applied. The results are summarized in Table 2. Notice that the results are in perfect accordance with the simulations in Figs. 6 and 7.

Table 2:

MPDMA applied to the relay controllers; 100 optimizations were performed with search region range equal to 40. The other adopted parameters were N = 250, NSel2 = 50, NSel1 = 10, Rpoly(0) = 1%, R = 8%

Relay element Na(A)

CONCLUSIONS This paper presented a new systematic approach intended to compute the multiple limit cycle conditions through the describing function method. Presently, this classical methodology for self-sustained oscillations analysis was applied to describe only one limit cycle, but many systems

Nb(A)

Limit cycle

Amplitude

Frequency

S

0.058 ± 0.003

8.1 ± 0.2

U

2.33 ± 0.03

0.808 ± 0.006

S

37 ± 2

0.261 ± 0.005

S

0.048 ± 0.006

2.7 ± 0.2

U

0.24 ± 0.04

1.0 ± 0.2

S

6.3 ± 0.1

0.253 ± 0.02

Stability – S: stable, U: unstable.

Figure 6: Stable limit cycles for the relay controller (Eq. 22) with M = 20 and the linear part given by Eq. 21. Top: the phase plane; bottom: the output time evolution.

Figure 7: Stable limit cycles for the hysteresis controller (Eq. 22) with M = 3.125, k = 0.02 and the linear part given by Eq. 21. Top: the phase plane; bottom: the output time evolution. J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 21-28, Jan. - Apr., 2011

27


Brito, A.G.

can present multiple conditions that conduct to oscillatory trajectories. Herein, the describing function criterion was discussed for multiple limit cycle existence and numerical analysis. The multiple limit cycle computation is based on an optimization algorithm that guides an initial population to the optimal points. In spite of its population character, the method is quite different of multimodal genetic algorithms: the points evolve following a deterministic Gradient-like procedure and the selection approach is different, as discussed during the text. The optimization algorithm was very robust and precise in all practical cases presented in the paper, and the computational cost was acceptable. Furthermore, it was able to catch all global minima even in very sharp attraction basins. This characteristic, which is difficult to achieve with other methods, is important to the multiple limit cycle detection. The main disadvantages of the proposed methodology are concerned to problems with very flat attraction basins, or which the topology presents non-differentiable regions because the Gradient-like procedure assumes differentiability condition. Despite many theoretical and practical problems have non-differentiabilities only in regions with high cost-function values, other optimization methods should be studied in cases which these issues become crucial to obtain a proper limit cycle description.

Gibson, J.E., 1964, “Nonlinear automatic control”, McGraw Hill, New York, USA. Hofbauer, J., So, J.W., 1994, “Multiple limit cycle for three dimensional lotka-volterra equations”, Applied Mathmatics Letters, Vol. 7, No. 6, pp. 65-70. Kienitz, K., 2005, “On the implementation of the eigenvalue method for limit cycle determination in nonlinear systems”, Nonlinear Systems, Vol, 45, pp. 25-30. Leite Filho, W., Bueno, M., 2003, “Analysis of limitcycle phenomenon caused by actuator’s nonlinearity”, In Proceedings of the 20th Inter. Conf. Appl. Simul. and Modeling. Li, J., Tian, Y., Zhang, W. and Miao, S., 2008, “Bifurcation of multiple limit cycles for a rotor-active magnetic bearings system with time-varying stiffness”, International Journal of Bifurcation and Chaos, Vol. 18, No. 3, pp. 755-778. Mendelowitz, L., Verdugo, A. and Rand, R., 2009, “Dynamics of three coupled limit cycle oscillators with application to artificial intelligence”, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 1, pp. 270-283. Nayfeh, A.H.,Mook, D., 1979, “Nonlinear oscillations”, Wiley, New York, USA.

REFERENCES

Newman, B., 1995, “Dynamics and control of limit cycling motions in boosting rockets”, Journal of Guidance, Control and Dynamics, Vol. 18, No. 2, pp. 280-286.

Darwen, P., Yao, X., 1996, “Every niching method has its niche: fitness sharing and implicit sharing compared”, Lecture Notes in Computer Science, Vol. 1141, pp. 398-407.

Siljak, D., 1969, “Nonlinear systems – the parameter analysis and design”, John Willey & Sons, New York, USA.

Dotson, K.W., Baker, R.L. and Sako, B.H., 2002, “Limitcycle oscillation induced by nonlinear aerodynamic forces”, American Institute of Aeronautics and Astronautics Journal, Vol. 40, No. 11, pp. 2197-2205.

Slotine, J.J., Li, W., 1991, “Applied nonlinear control”, Prentice Hall, New York, USA.

Freedman, H. I., 1990, “A model of predator-prey dynamics as modified by the action of a parasite”, Mathematical Biosciences, Vol. 99, No. 2, pp. 143-155. Gelb, A., Velde, W., 1968, “Multiple-input describing functions and nonlinear system design”, McGraw Hill, New York, USA.. Giacomini, H., Neukirch, S., 1997, “Number of limit cycles of the li´enard equation”, Physical Review E, Vol. 56, No. 4, pp. 3809-3813.

28

Somieski, G., 2001, “An eigenvalue method for calculation of stability and limit cycles in nonlinear systems”, Nonlinear Dynamics, Vol. 26, pp. 3-22. Stout, P., Snell, S., 2000, “Multiple on-off valve control for a launch vehicle tank pressurization system”, Journal of Guidance, Control and Dynamics, Vol. 23, No. 4, pp. 611-619. Yu, P., Corless, R., 2009, “Symbolic computation of limit cycles associated with hilbert’s 16th problem”, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 12, pp. 4041-4056.

J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 21-28, Jan. - Apr., 2011


doi: 10.5028/jatm.2011.03019210

Maurício Guimarães da Silva* Institute of Aeronautics and Space São José dos Campos – Brazil maugsilva09@yahoo.com.br

Paulo Afonso Pinto de Oliveira (In memoriam) Universidade Estadual Paulista Guaratinguetá – Brazil * author for correspondence

Entropy variation in isothermal fluid flow considering real gas effects Abstract: The present paper concerns on the estimative of the pressure loss and entropy variation in an isothermal fluid flow, considering real gas effects. The 1D formulation is based on the isothermal compressibility module and on the thermal expansion coefficient in order to be applicable for both gas and liquid as pure substances. It is emphasized on the simple methodology description, which establishes a relationship between the formulation adopted for ideal gas and another considering real gas effects. A computational procedure has been developed, which can be used to determine the flow properties in duct with a variable area, where real gas behavior is significant. In order to obtain quantitative results, three virial coefficients for Helium equation of state are employed to determine the percentage difference in pressure and entropy obtained from different formulations. Results are presented graphically in the form of real gas correction factors, which can be applied to perfect gas calculations. Keywords: Isothermal flow, Real gas, Entropy, Petroleum engineering.

List of Symbols a A AW B C Cp Cv f h M

!m

P pW qc

R R

S t T u U v WHe x Z α

Sound velocity Cross section Wet area Second virial coefficient Third virial coefficient Specific heat at constant pressure Specific heat at constant volume Friction coefficient Enthalpy Mach number Mass flow rate Pressure Wet perimeter Heat exchange parameter

m/s m2 m2 cm3/mole cm3/mole2 J/kgK J/kgK J/kg kg/s Pa m W/m2K

Gas constant Parameter of Equation (37) Entropy Time Temperature Velocity Internal energy Specific volume Molecular weight of helium Longitudinal coordinate Compressibility factor Angle between the horizontal and the direction of flow

J/kgK m3/Pa/kg/K J/kgK s K m/s J/kg m3/kg mole m rad

Received: 18/10/10 Accepted: 02/11/10

αP βT εP εS γ ρ µ W

Thermal expansion module Isothermal compressibility module Pressure correction factor Entropy correction factor Specific heat ratio Density Viscosity Shear stress

K-1 m2/N Pa2 kg/m3 kg/ms N/m2

!

INTRODUCTION The term “isothermal process” describes a thermodynamic process that occurs at a constant temperature. There are a lot of examples of technical analysis using isothermal process. Isothermal compression is an example to illustrate the position that isothermal process takes along other thermodynamic processes. In a real engine (compressor), the isothermicity condition cannot be fulfilled and every real thermodynamic process demands more energy than the isothermal compression. In this context, the practical importance of isothermal compression lies in its use, as a reference process to evaluate the actual compression (Oldrich and Malijesvsky, 1992). The adiabatic frictional flow assumption is appropriate to high speed flow in short ducts. For flow in long ducts, such as natural gas pipelines, the gas state approximates more closely to the isothermal one. By doing this approach, it is possible to establish a relationship among all thermodynamic quantities (White, 2005). In the flow field thermodynamic calculation of aeronautical devices, the real process is approximated to a suitable idealized one that can be mathematically

J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 29-40, Jan. - Apr., 2011

29


Silva, M.G., Oliveira, P.A.P.

described. Usually, the choice lies among isentropic, polytropic, and isothermal processes. These thermodynamic processes are also used as reference ones in the internal flow field calculation of aeronautical devices. The isentropic and polytropic processes have been discussed by many authors, including their applications to real gases (Oldrich and Malijesvsky, 1992). In contrast, the isothermal process has not received such attention. Attempts at refining the results by inserting values calculated from a virial equation of state for real gas have led to some improvement. However, these efforts particularize the solution of the flow field issue. The present paper is concerned over the estimative of the pressure loss and entropy variation in an isothermal fluid flow considering real gas effects. The formulation is based on the isothermal compressibility module and on the coefficient of thermal expansion, in order to be applicable for both gas and liquid as pure substances. The description of the simple methodology, which establishes a relationship between the formulation adopted for ideal gas and that considers the real gas effects, will be emphasized. A computational procedure has been developed, and it can be used to determine the flow properties in duct with a variable area where real gas behavior is significant. In order to obtain quantitative results, three virial coefficients for helium equation of state (Miller and Wilder, 1968; Schneider and Duffie, 1949) are employed to determine the percentage difference in pressure, and entropy between the different formulations. Results are graphically presented in the form of real gas correction factors, which can be applied to perfect gas calculations. This paper is part of a continuing effort that is being carried out at the Institute of Aeronautics and Space from the Brazilian Aerospace Technology and Science Department (DCTA/IAE, acronyms in Portuguese) to develop flow analysis methods, and design of aeronautical devices in a conceptual context.

q !

Isothermal flow is a model of compressible fluid flow whereby the flow remains at the same temperature while flowing in a conduit. In the kind of flow, heat transferred through the walls of the conduit is offset by frictional heating back into the flow. Although the flow temperature remains constant, a change in stagnation temperature occurs because of a change in the velocity. From this approximation, it is possible to demonstrate that, for ideal gas formulation, the flow is choked at mach number (M) given by " 1 /   , and not at mach number equal to one as in! the case

W

! Flow direction

CV

W

!dx

Figure 1: Differential control volume (CV).

(i) Continuity Equation

A  t

uA " 0 ; x

(1)

(ii) Momentum Equation P 4 uAu u " A RA  x x 3 x x

uA  t

W

pW ;

(2)

(iii) Energy Equation: hA  t 4 RA 3

MATHEMATICAL FORMULATION

30

of many other models, such as Fanno flow (John and Keith, 2006). This analysis is applied to the 1D fluid flow (Fig. 1). It is assumed that the fluid undergoes an isothermal process during this process. In other words, its total energy remains unchanged by the flow. The generalized form of this process includes the possibility of the presence and effect of viscosity (through µ and W ), gravity (through α– the angle between the horizontal ! and the direction of flow), pressure (P), heat exchange ( qc ) and thermal conducting terms (k). W is the shear stress due to wall friction. Equations 1, 2 and 3 show the generalized ! mathematical model.

uAh P p T "A  Au   kA x t x x x u x

2

u

W

pW 

!

qpW . cos



(3)

In order to create practical relations for engineering use, steady state flow hypothesis is adopted, and the thermal conduction and viscosity terms are neglected. This approach gives the following results: (i) Continuity Equation d uA " 0 ; dx

!

(4)

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Entropy variation in isothermal fluid flow considering real gas effects

(ii) Momentum Equation

dP d uAu " A dx dx

dh " Cp P , T  dT 

pW ;

W

 v dP P

(5)

.

(10)

Now, take into consideration the momentum Eq. 5 in

(iii) Energy Equation:

dP d uAh " Au u dx dx

v T

T

dP

W

AW 

qpW cos 

(6)

The strategy chosen in this development is to convert the dependent variable (Ď , u, h) in terms of pressure (P) and temperature (T). Thus, the equation system is reduced to two equations, whose dependent variables are pressure and temperature, and the independent one is the longitudinal coordinate (x). It is important to highlight that during this development, any constitutive relation, such as virial equation of state, was adopted, in order to generalize the applicability of the method to all pure substances.

d uAu

 w pw , and substitute it in the form Au dx " dx energy equation, considering the continuity equation, which will! result in Eq. 11:

v d d uAh 2 A " qpw   um dx cos dx

(11)

!Note that:

d uAh dh d uA dh dh " uA h " uA "m dx dx dx dx dx

Thus, from Eq. 11, mCp P , T

 dT dx

m

v T

T

v P

dv dA dP mv 2 A dx v dx m  " Q, A dx A2

Energy Equation Since

h " h @ P x  ,T x B ,

h T

dh "

dP " Cp P , T  dT 

h P

dT  P

where : Q "

it can be written as:

T

h P

dP T

 (7)

!By definition:

Considering an isothermal process:

!

" T

v P

P T

v T

Q " dS T



(8)

. Since , the first law becomes: In this expression, the isothermal condition is used: T S " U  P v . P

P

T

T

P

T

P

dT  dx

v P

T

dP dx

,

v T

v P

I "

Q m  A m

2

v2

2

v P

v

m A

2

v

v T

T T

v T



" I P , T ,

(12)

v, P

, and P

d ln A dx

T

Therefore, using Eq. 8, and, by the Maxwell relation (Wyllen and Sonntag, 1987), the result is the following (Eq. 9): " T

m A

H " Cp P , T  

Q " dU  Pdv

TdS " dU  Pdv .

h P

!

dT  H P ,T   dP dx dx

where: G "

The second law applied to the reversible process is given by:

v T

mv and u " A .

G P ,T

dh " dU  Pdv  vdP .

U P

dv " dx

,

From algebraic manipulation of the previous equation, the energy equation is obtained with pressure and temperature as dependent variables, which is:

h " U  Pv , so

h P

q pW cos



! Substituting Eq. 9 in Eq. 7, it is obtained Eq. 10:

(9)

Momentum Equation Since the cross section of the duct is a function of the longitudinal coordinate, A=A(x), it can be written:

du d mv d v " "m dx dx A dx A

J. Aerosp.Technol. Manag., SĂŁo JosĂŠ dos Campos, Vol.3, No.1, pp. 29-40, Jan. - Apr., 2011

;

31


Silva, M.G., Oliveira, P.A.P.

thus,

Therefore, by considering definitions of isothermal compressibility module and thermal expansion coefficients, it is possible to write the general equations as:

d uAu d v " m2 . dx dx A

By substituting the last equation into momentum Eq.  5 and dividing it by A, one obtains the representative equation of momentum conservation in terms of pressure and temperature, which can be seen in Eq. 13:

dP dT J P, T   K P, T  " M P, T  , dx dx where: J "

m A

K "

!

m A

M "

2

m A

2

v T

2

v

v P

(13)

1,

v P



P

32

1 v

v T



" M P ,T



 ,

(16)

where,

!K

(14)

T

P

dT  K P ,T   dP dx dx

T

T

P

,

(15)

"

!

2

m A

J "v

p W W . A

The thermal expansion coefficient describes how the size of an object changes with a change in temperature. Specifically, it measures the fractional change in size per degree change in temperature at a constant pressure. In the general case of a gas, liquid, or solid, the volumetric coefficient of thermal expansion is given by: "

J P ,T

!

P

Equations 12 and 13 represent the generalized formulation written in terms of pressure and temperature, which include heat exchange, flow with friction (wall friction), and flow in variable-area ducts influence. It is noteworthy that, up to this point, any approximation for equation of state was not used. In order to extend the applicability of the mathematical model, it is interesting to write the parameters G, H, I, J, K and M in terms of isothermal compressibility module (βT) and thermal expansion module (ιP). In gas dynamics, compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) change. Since the compressibility depends strongly on whether the process is adiabatic or isothermal, it is usually defined as: 1 v

H " Cp P , T   vK ,

Generalized flow formulation

"

" I P ,T

P

!

T

dT  H P ,T   dP dx dx

G "v 1 K

T

, and

d ln A dx

G P ,T

u2 v

1 , and

T

P

.

Critical Conditions for Generalized Flow Applying Kramer rule in the system of equations dP " dx

(Eq. 16), it will provide:

H K

I M

H K

G J

"

HM IK HJ GK

.

It is desirable, as in the isentropic case, to investigate this relationship by the choice of a convenient reference state. Since stagnation conditions are not constant, the stagnation state is not suitable for this purpose. However, the state corresponding to unity mach number (“critical condition�) is suitable, because, as Eq. 16 shows, condition there is constant for a given flow. In this case, the critical condition is obtained from the expression: HJ

GK " 0 .

(17)

Since: HJ " Cp P , T



m A



4

v

m A v T

2

v P

P

v P



 Cp P , T  T

 T

m A

2

v

v T

P

,

and

J. Aerosp.Technol. Manag., SĂŁo JosĂŠ dos Campos, Vol.3, No.1, pp. 29-40, Jan. - Apr., 2011


Entropy variation in isothermal fluid flow considering real gas effects

GK "

4

m A

v T

v

v P

P

!

T T

m A

2

v T

2

m A

v P

2

v T

P

,

1

I "1 Mv

m A

1

2

P

v

1

T " 1

1 Ƣ Real M 2

T

P

T

(21)

by substituting it in Eq. 17, it is obtained: u "v

Cp P ,T Cp P ,T



v P

 v T

T T

2



P

(18)

!It should be noted that the relationship between the specific heats at pressure and volume constant is given by Van Wyllen and Sonntag (1987, p. 284): Cp P , T



Cv P , T  " T

v T

2

P

v P

T

!The sound velocity (a), in an isothermal process, can

be written as (John and Keith, 2006, p. 45):

a"

v

Equation 21 presents an interesting mathematical format. It is possible to distinguish the “driver� terms (left side of the equation), in a dimensionless form, which represents the physical conditions necessary to obtain an isothermal flow. This term is built with the contributions of heat exchange, wall friction, area variation, and mass flow. The right side of the Eq. 21 represents the thermodynamic conditions obtained in an isothermal flow, with the “driver� conditions defined by the left side. Another important thing to note about Eq. 21 is that the variation of the parameter I / Mv , at constant temperature, can be found from the equation of state and mass flow rate. This information can be used in the control system design based on isothermal fluid flow. The simplicity of this formulation is a great attractive for conceptual design and engineering analysis.

.

T

Substituting the relations above in Eq. 18, the following equation is obtained by: u "v

Cp P , T v P



Cv P , T



"

Cp P , T v 2 Cv P , T

T



v P

Critical conditions for isothermal flow Equation 21 shows that the critical condition can be obtained from the expression:

"a

In other words, the critical condition in a generalized flow field, considering real gas effects, is given by the mach number equals to one. This value is in accordance with technical literature. Isothermal flow formulation Isothermal flow can be characterized by the relation (Eq. 19): dT "0 T

(19)

dP I M " " dx G J 

(20)

!Considering Eq. 19 and the general system (Eq. 16), it is obvious the relation: !From

2

m A

1

T

v

"0

T

(22)

Considering the concepts of sound velocity and isothermal compressibility module, the second term of the left side becomes: 1

m A

!

"

2

v

T

"1

2 Re al

"0.

m A

2

v

T

"

u2 v

T

"

2

. Then,

From that, it is obtained:

1 Re al



(23)

!Analogously to the ideal formulation (John and Keith, 2006, p. 366), Eq. 23 shows that the critical mach number for isothermal flow is not subcritical flow. It follows that because the adiabatic speed of sound is greater than the isothermal speed of sound, isothermal flow may be supercritical without being necessarily supersonic. It is important to highlight that constitutive relations are not used in this development. Thus, it is assumed that Eq. 23 is valid for all real gas or liquid formulation, for the flow process does not involve change of physical state.

this expression, it is possible to characterize isothermal flow in another, but similar, manner: IJ = MG.

Pressure drop in isothermal flow

Using the previous definitions for parameters J and G, it can be concluded that:

The most effective approach to flow problems of this type is to express ratios of the gas properties and flow

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33


Silva, M.G., Oliveira, P.A.P.

parameters between any two points in the flow stream, as function of the mach number and specific heat ratio of the gas. Using these ratios, a reference state is defined, and the ratios of the variables at any mach number to those at the reference state are tabulated. Following this reasoning, consider the case of duct with constant cross section, by applying Eq. 20:

2



(24)

Re al

!It is a common practice to assume (John and Keith, 2006, p. 291): 1 " u2 f  8

W

Re al

fdx D



(28)

In other words, it can be concluded that: dP "

dP P



Ideal

(29)

The right side of the Eq. 29 can be related to the mach number. Using the definition of βT and an isothermal process, we will have: dv "

v T

dT  P

v P

dP " T

v P

dP T

,

(30)

Re al

1 u2 2 v 1

1

2

Re al

2

dv " v 1

By substituting it in Eq. 24, it is obtained:

fdx D 

2

Re al

(31)

However, from continuity equation, one has:

dv du d " " v u

fdx D .



(32)

Thus:

Since 1 1 u2 " 2v 2 v

2

v

Re al

"

T

1 2

2

,

Re al

T

1 T

2

Re al

2

fdx D



(26)

Equation 26 establishes the relationship between the pressure drop and the parameters ‘mach number’, ‘wall friction’, and ‘thermodynamic properties of the gas’, when the longitudinal direction considered. Note that for ideal gas: 1 v

v P

" T

"

d



Ideal

(33)

Ideal

flow in ducts with variable cross section.

Re al

1

dP P

!It is easy to demonstrate that Eq. 33 can be used for

2

dP "

dP "

T

It is demonstrated that:

1 v 1 " v P P 

(27)

Substituting Eq. 27 into 26, the pressure drop formulation developed for ideal gas (John and Keith, 2006, p. 366) is recovered, which is:

34

1

Ideal

2

2

PW 4A 4 W 1 2 f " W " " u D . 2 A A D D

"

2

The expression (Eq. 26) can be written as:

W

T

"

(25)

Thus,

dP "

!

T

P W W A

dP M " " dx J 1

2 Re al

dP P

Entropy variation in isothermal flow

Since S

" S P ,T

dS "

S T

 , it can be written:

dT  P

S P

dP 

(34)

T

Using the concepts of specific heat at constant pressure and Maxwell relation: dS " Cp P , T

 dT T

v T

dP 

(35)

P

Considering an isothermal process and the definition of ÎąP, it is obtained:

J. Aerosp.Technol. Manag., SĂŁo JosĂŠ dos Campos, Vol.3, No.1, pp. 29-40, Jan. - Apr., 2011


Entropy variation in isothermal fluid flow considering real gas effects

dS "

P

vdP .

(36)

Substituting Eq. 26 in 36, it is obtained: 2

2

fdx d " D

2

Re al

where: R "

P

,

(37)

Ideal

R"

v P

" 1

TR Cv P , T  

dP P

v

v T v P

" v

the value of

(38)

T v

" 1, P

v

R

P

,

(39)

"

2

1

Ideal

2

Re al

fdx " D

d Ideal



(44)

Equation 44 can be integrated in terms of mach number, considering the friction factor f constant in the segment dx . From this result, it is possible to evaluate the pressure drop for ideal gas formulation. Thus, applying the multiplicative factor T on the last result, the drop pressure considering real gas effects is obtained. Regarding to the entropy variation, it is possible to write from Eq. 37 and 44:

can be written as:



R " R , v

,

(45)

Ideal

CORRECTION FACTORS In this section, the pressure correction factor ( P   ) and entropy correction factor ( S ) are defined. !The parameter P is calculated from !the use of Eq. 33 for ideal and real ! gases. By substituting Eq. 14 in Eq. 33, the following result is given:

T

(40)

dP P

"

Re al

P

P

T

dP P

"

(41)

which is in accordance with results from technical literature (John and Keith, 2006, p. 367).

EXAMPLE OF APPLICATION From Eq. 29 and 37, it is possible to define multiplicative correction factors that can be used in an ideal gas formulation in order to solve problems associated with the real gas formulation. However, it is important to define the concept of specific heat ratio in

P

1 " P , T

P

Ideal

where the correction factor

Note that for ideal gas: R "v

(43)

2



T

P T

(42)

P

dS dP " R P

R "v

TR ;

Re al

or

P T

P

P

P T

T

Cv P , T  "

This value is used in Eq. 44, which is:

Since v P

Re al

v

! By definition: v T



thus, the expression for specific heat ratio is given by:

T

v

!

. According to Wyllen and Sonntag (1987,

R

Cp P , T

Re al

dS " R 1

terms of p. 285):

P

!

dP P

,

(46)

Ideal

is given by: (47)

!In analogous fashion, it is defined the entropy correction factor. In accordance with Eq. 37 and 44, the entropy correction factor is given by: S

" R / R ,

(48)

In order to obtain quantitative results, an equation of state for helium, based on a three virial coefficient (Miller and Wilder, 1968; Schneider and Duffie, 1949), is employed to determine the correction factor for pressure and entropy variation. The equation used to

J. Aerosp.Technol. Manag., SĂŁo JosĂŠ dos Campos, Vol.3, No.1, pp. 29-40, Jan. - Apr., 2011

35


Silva, M.G., Oliveira, P.A.P.

represent the pressure-density-temperature relationship of real helium gas is the virial equation of state:

P " Z RT " RT 1  B T  

C T



(49)

!A

relatively large amount of experimental data on the second virial coefficient, B(T), exist for low and moderate temperatures (up to about 1,000 K). Experimental results for the third virial coefficient, C(T), are few and show a great deal of scatter. At the conditions dealt within this paper, the contribution of C(T) to the state equation is relatively small. In this context, the expression derived for the virial coefficients is given by:

B T  " b0  b1T

1

4

 b2T

3

4

 b3T

5

4



P



2

and

 b4T

7

4

, (50)



" RT 1 2 B T  3 2C T T



(53)

Considering the virial equation of state, Eq.49 and 47, the pressure correction factor ( P ) is given by:

P

"

!

1 1 2 B T  3 2C T Z







(54)

Entropy correction factor (ÎľS) Using Eq. 40 and 48, it is demonstrated that:

S

" 1

B T   T

dB T dT





2

C T   T

dC T dT



.

(55)

and

C T  " c 0  c1T

1

4

3

 c 2T

4

 c3T

5

4



(51)

The coefficients of virial equation are given in Tables 1 and 2. The units of T, B(T) and C(T) are K, cm3/mole and (cm3/mole)2, respectively. Table 1: Second virial coefficient – B(T)

Coefficient b0 b1 b2 b3 b4

T < 1300 K -13.4067 165.4459 -1357.92 5959.061 -12340.8

T > 1300 K 1.178236 -7.57134 5225.701 -188923 2460461

Table 2: Third virial coefficient â&#x20AC;&#x201C; C(T)

Coefficient c0 c1 c2 c3

T -13.7898 139.7339 8114.259 -17456.9

Pressure correction factor (ÎľP) From the Eq. 49, it is obtained: P T

!

36

" R 1

B T   T

dB T dT





2

C T   T

dC T dT



,

 (52)

RESULTS The values of B(T) and C(T) computed from Eq. 2 and 3, for real helium gas, are plotted in Figs. 2 and 3. Note that the virial coefficients are plotted in terms of [cm 3/mole], where [cm 3/mole] = W He/1000 (m 3/kg). The accuracy of these coefficients was checked by comparing the values of the resulting compressibility coefficient, Z, with those given in the tabulation of helium properties prepared by the International Union of Pure and Applied Chemistry (IUPAC). Figure 4 shows the compressibility coefficient Z, which was in very close agreement with IUPAC for all densities. Figure 5 shows the multiplicative correction factor for pressure drop. It is a common practice the use of relation (Eq. 26), in a context of ideal gas, in order to obtain the solution for isothermal flow of real gas by only using a real specific heat ratio. However, it can be noted that the specific heat ratio is not the only parameter of influence. In fact, the correction factor P must also be considered in this procedure. In this! context, although the first methodology is easy to conceive, the latter, more complete, requires the knowledge of more details about the physical properties of the pure substance. Another interesting aspect of this result is related to the value of P . When a gas undergoes a reversible process, in which ! there is heat transfer, the process frequently takes place in such a manner that a plot of log P versus v is a straight line. This is called polytropic process (Wyllen and Sonntag, 1987, p. 167), in other words:

J. Aerosp.Technol. Manag., SĂŁo JosĂŠ dos Campos, Vol.3, No.1, pp. 29-40, Jan. - Apr., 2011


Entropy variation in isothermal fluid flow considering real gas effects 12 11.5 11

B [cm 3/mol]

10.5 10 9.5 9 8.5 8 200

400

600

800

T [K]

1000

1200

1400

1600

T= 1300 K

Figure 2: Second virial coefficient – B(T). 120 110 100

C [cm 3/mol 2]

90 80 70 60 50 40 200

400

600

800

T [K]

1000

1200

1400

1600

Figure 3: Third virial coefficient – C(T).

1.11

= 10 kg/m3 = 20 kg/m3 = 30 kg/m3

1.1 1.09 1.08

Z

1.07 1.06 1.05 1.04 1.03 1.02 200

400

600

800

1000

1200

1400

1600

T [K]

Figure 4: Compressibility coefficient – Z. J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 29-40, Jan. - Apr., 2011

37


Silva, M.G., Oliveira, P.A.P. 1.11

= 10 kg/m3 = 20 kg/m3 = 30 kg/m3

1.1 1.09 1.08 1.07

P 1.06 1.05 1.04 1.03 1.02 200

400

600

800

T [K]

1000

1200

1400

1600

Figure 5: Correction factor for pressure drop.

dP P dv v

" n,



(56)

Ideal

not clear in B(T) variation (Fig. 2), this discontinuity is probably associated with the model adopted for gas equation. The fit curve coefficients for high temperature (Table 1) are not consistent when it is considered high variation in density.

where, n = 1 (one) is an ideal isothermal process. COMENTS AND CONCLUSION From Eq. 32, 33 and 52, it is possible to note that: dP P dv v

"

1 " P T

P



(57)

Re al

Thus, the pressure corrector factor εP establishes a direct comparison of ideal and real isothermal processes. Results presented in Fig. 5 can be used as a good indicative of the tolerance that must be adopted in a system specification, based on isothermal fluid flow results. Figure 6 shows the entropy correction factor, εS. It is clear that εS is more temperature sensitive than εP. Internal energy and entropy are not directly physically measurable, whereas certain of the intensive variables (e.g. T,P) are. Thus, the entropy formulation presented in this paper is an important mathematical model to know the accuracy of entropy correction factor, obtained indirectly from the 1D analysis using ideal gas formulation. Another aspect that must be considered during flow analysis of helium gas is related to the discontinuity observed at T = 1300 K. Although it is

38

The primary purpose of this investigation was to develop a method required to study the behavior of real pure substance in an isothermal fluid flow. Particular emphasis was given to develop useful procedures and techniques in order to study the general types of gas, which are encountered in aeronautical applications, such as, wind tunnel, combustors, and so on. More complicated systems can be studied, in a 1D context, with little additional difficulty. From this research, it is possible to draw several conclusions: •

The mathematical formulations developed for pressure and entropy variation, Eq. 26 and 36, respectively, can be used for different pure substances. the pressure correction factors (εP) that must be adopted in an isothermal gas flow are a function of isothermal compressibility module, βT , and static pressure. These factors establish a direct comparison of ideal and real isothermal processes (Eq. 47).

The entropy correction factor (ε S) is a function of thermal expansion module (αP), isothermal compressibility module (βT), and specific volume (v). It is given by the Eq. 48. Similar to the pressure correction factor, it depends on the state equation.

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Entropy variation in isothermal fluid flow considering real gas effects 9

= 10 kg/m3 = 20 kg/m3 = 30 kg/m3

8 7 6

%

S

5 4 3 2 1 200

400

600

800

T [K]

1000

1200

1400

1600

Figure 6: Correction factor for entropy variation.

ACKNOWLEDGMENTS The first author gratefully acknowledges the partial support for this research, which was provided by BASF – The Chemical Company. This paper is dedicated to my friend Paulo Afonso Pinto de Oliveira (In memoriam).

REFERENCES

Oldrich, J., Malijesvsky, A., 1992, “The Isothermal Change of a Real Gas”, Technology Today, No. 2, p. 56-60. Schneider, W.G., Duffie, J.A.H., 1949, “Compressibility of Gases at High Temperature. II. The Second Virial Coefficient of Helium in The Temperature range of 0oC to 600oC”, Journal of Chemical Physics, Vol. 17, No 9, p. 751. doi:10.1063/1.1747394b

John, J.G.A., Keith, T.G., 2006, “Gas Dynamics”, 3th edition, pp. 520.

Van Wyllen, G., Sonntag, R., 1987, “Fundamentos da Termodinâmica Clássica”, 2th edition, p. 320.

Miller, C.G., Wilder, S.E., 1968, “Real Helium Hypersonic Flow Parameters for Pressures and Temperatures to 3600 atm and 15,000 K”, NASA TN-D 4869.

Whyte, F.M., 2005, “Fluid Mechanics”, McGraw Hill, New York, 5th edition, p. 866.

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39


doi: 10.5028/jatm.2011.03010311

Davidson Martins Moreira* Universidade Federal do Pampa Bagé – Brazil davidson.moreira@gmail.com

Leonardo Barboza Trindade Universidade Federal do Rio Grande do Sul Porto Alegre – Brazil trindade@ct.ufrgs.br

Gilberto Fisch Institute of Aeronautics and Space São José dos Campos – Brazil gilbertofischgf@iae.cta.br

Marcelo Romero de Moraes Universidade Federal do Pampa Bagé – Brazil marcelomoraes@gmail.com

A multilayer model to simulate rocket exhaust clouds Abstract: This paper presents the MSDEF (Modelo Simulador da Dispersão de Efluentes de Foguetes, in Portuguese) model, which represents the solution for time-dependent advection-diffusion equation applying the Laplace transform considering the Atmospheric Boundary Layer as a multilayer system. This solution allows a time evolution description of the concentration field emitted from a source during a release lasting time tr , and it takes into account deposition velocity, first-order chemical reaction, gravitational settling, precipitation scavenging, and plume rise effect. This solution is suitable for describing critical events relative to accidental release of toxic, flammable, or explosive substances. A qualitative evaluation of the model to simulate rocket exhaust clouds is showed. Keywords: Alcântara Launch Center, Advection-diffusion equation, Atmospheric dispersion.

Rodrigo Martins Dorado Universidade Federal do Pampa Bagé – Brazil rdorado@bol.com.br

Roberto Lage Guedes Institute of Aeronautics and Space São José dos Campos – Brazil robertolagerl@iae.cta.br *author for correspondence

INTRODUCTION A model is an abstract idealization of a process involving one or more functions designed to simplify our description of the process. Constraints on the model include the availability and scope of the dataset; the mathematical approximation and limits of solution; and the complexity of analysis and data reduction that can be tolerated. In these considerations, we are interested in a diffusion model to provide a viable description of the transport of rocket exhaust effluents in the atmosphere. The transport of the rocket exhaust effluents is characterized by turbulent diffusion, in the atmosphere, which has not been uniquely formulated in the sense that a single basic physical model capable of explaining all the significant aspects of the transport process has not yet been proposed. The two general models are: the gradient transport model and the statistical one. Since atmospheric transport processes tend to be generally a nonstationary random process over periods of interest, and because normal meteorological data are incompatible with the statistical model, this approach is rejected in favor of the gradient transport model in the selection of an operational diffusion one. While the numerical and statistical techniques offer some vantages, especially in research investigations, the state of art of these transport techniques has not evolved Received on: 11/02/11 Accepted on: 10/03/11

to the point where they offer a viable solution to operational transport predictions rocket exhaust effluents for air quality and environmental assessments; thus, our selection offers an analytical technique for diffusion predictions (Stephens and Stewart, 1977). The burning of rocket engines during the first few seconds prior to and immediately following vehicle launches results in the formation of a large cloud of hot, buoyant exhaust products near the ground level, which subsequently rises and entrains ambient air until the temperature and density of the cloud reach an approximate equilibrium with ambient conditions. By convention, this cloud is referred to as the ground-cloud. The rocket engines also leave an exhaust trial from normal launches that extend throughout and beyond the troposphere depth. The National Aeronautics and Space Administration (NASA) has computational codes that are designed to calculate peak concentration, dosage and deposition (resulting from both gravitational settling and precipitation scavenging) downwind from normal and aborted launchings to use in mission planning activities and environmental assessments, pre-launch forecasts of the environmental effects of launch operations and post-launch environmental analysis (Bjorklund et al., 1982). Many of these models are based on the same steady-state Gaussian dispersion model concepts used by other ones. For sake of illustration, we cite the MSFC (Dumbauld et al., 1973),

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Moreira, D.M. et al

REEDM (Bjorklund et al., 1982), RTVSM (Bjorklund, 1990), and OBODM (Bjorklund et al., 1998). Recently, we take a step forward regarding the Gaussian concepts to simulate pollutant dispersion in atmosphere. The solution was obtained for a vertically inhomogeneous atmospheric boundary layer (ABL) of the time-dependent advection-diffusion equation, applying the Laplace transform, considering the ABL as a multilayer system. This technique is called advection-diffusion multilayer method (ADMM) and it is well established in the literature (Moreira et al., 2005a, b, c, d; Moreira et al., 2006). Therefore, the aim of this paper is to report the construction of a new model based on ADMM model, now called MSDEF, to simulate rocket exhaust clouds. For a better understanding, in the sequel, we briefly discuss the idea behind this method. The main feature of the ADMM approach consists on the following steps: stepwise approximation of the eddy diffusivity and wind speed; the Laplace transform application to the advection-diffusion equation in the x and t variables; semi-analytical solution of the linear ordinary equation set resulting in the Laplace transform application and construction of the pollutant concentration by the Laplace transform inversion, using the Gaussian quadrature scheme. It is important to mention that, for the first time, the ADMM model (now MSDEF) is depending on time release, deposition velocity, first-order chemical reaction, gravitational settling, and precipitation scavenging. This solution allows a time evolution description of the concentration field emitted from a source during a release lasting time tr. The model takes into account the plume rise formulation of the literature (Briggs, 1975) for convective conditions, which is included in the computational codes of the NASA. The code used by NASA is the well-know rocket exhaust effluent diffusion model (REEDM). The REEDM has been used to assess the environmental impact of Space Shuttle operation and

to support the first launches of the Space Shuttle. The dispersion models used in the REEDM code are based on Gaussian model concepts. The exhaust material, which is a mixture amongst CO, CO2, HCl and alumina, that is, the most solid propellants exhausted gases, is assumed to be uniformly distributed in the vertical and to have a bivariate Gaussian distribution in the plane of the horizon at the point of cloud stabilization. The REEDM system is operationally used at Cape Canaveral to model the behavior of rocket exhaust clouds, and to evaluate the potential threat to health from the toxic gases present in those clouds.

PHYSICAL APPROACH A tool for analysis of toxic dispersion in the USA and to support the release and evaluation of public risk is the 7.13 version of the REEDM (Bjorklund et al., 1982; Bjorklund, 1990; Bjorklund et al., 1998). Thus, this program was used as reference for modeling physics and mathematics of the problem in the development of MSDEF program. For more details about these approaches, see Bjorklund et al. (1982). The main assumption used in the REEDM on the nature and behavior of the cloud released by the rocket is that it can be initially defined as a single cloud that grows and moves, but remains the same during the formation of its ascending phase. This concept is illustrated in Fig.  1, where it can be noticed that the model is designed for REEDM concentrations from the vertical position of the stabilized cloud. The aspect “multilayer” is still used in the REEDM and relates to the partitioning of cloud stabilized in “disks” of material from the cloud, represented by different meteorological levels at different altitudes. Typical levels are 20 to 50 m deep.

Figure 1: Conceptual illustration of cloud formation (source), “cloud-rise” and atmospheric dispersion of the cloud (Nyman, 2009). 42

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A multilayer model to simulate rocket exhaust clouds

Since the cloud is defined and has reached the condition of thermal stability with the atmosphere, it is partitioned into “disks”. The position of each disk with respect to the origin (launch pad) is determined based on the cloud’s rise time through a sequence of layers, which are defined using meteorological measuring levels obtained from a radiosonde. Each layer can have a single meteorological speed and wind direction that moves the disk into the same cloud. The concept of stabilized cloud partition is illustrated in Fig. 2. The hypothesis of transport in a straight line used in the REEDM during the transport of clouds and phase dispersion ignores the possibility of wind fields, which can arise in complex mountainous terrain or may evolve during the passage of a sea breeze front or greater scale. Thus, it is recommended that the assumption of uniform wind is limited to the transport of the plume at distances that do not exceed 25 km. Therefore, the model does forecast REEDM concentration ranging from 5 to 10 km from the launch pad, so that this hypothesis is not a problem. The REEDM assumes that all chemical reactions are completed before the combustion process of the cloud’s rise. A mass fraction is assigned to each constituent and the total mass of the source (cloud) is multiplied by this fraction to determine the total mass of each chemical component in the cloud. The molecular weight of each species is used to convert the mass concentration per unit volume (mg/m3) to part per million (ppm). The REEDM makes predictions of instantaneous and average concentration in time (typically a 10-minute average). In many situations, an average of one hour is made to compute the average concentrations. A shorter average time is appropriate to expose the cloud of the rocket, because the source (cloud) typically goes on a receiver with a time scale of ten minutes before the hour.

THE MATHEMATICAL MODEL A typical problem with the advection-diffusion equation involves the solutions of problems corresponding to instantaneous and continuous sources of pollution. More precisely, considering a Cartesian coordinate system in which the x direction coincides with the one of the average wind, the time dependent advection-diffusion equation can be written as (Huang, 1979): yC yC yC y © yC ¹ y © yC ¹ y © yC ¹ K  K  S K u  vg " yt yx y z y x ª« x y x º» y y ª« y y y º» y z ª« z y z º»



(1)

Where C denotes the average concentration, Kx, Ky, Kz are Cartesian components of eddy diffusivity, u is the longitudinal wind speed, vg is the gravitational settling, and S is a source/sink term. The analytical solution of the Eq. 1 can be obtained assuming (Huang, 1979): C ( x , y , z , t ) " f ( x , y , t )C y ( x , z , t )

(2)

The function f (x,y,t) can be expressed as: f ( x, y, t ) "

© ( y  y )2 ¹ o exp ª  º . 2 2 X 2UX y « » y 1

(3)

C y ( x , z , t ) is the solution of the following equation: yC y yC y © yC y ¹ y © yC y ¹ yC y K  K  QC y  1C y u  vg " yt yx y z y x ª« x y x º» y z ª« z y z º»



(4)

Where Cy is the crosswind integrated concentration, λ represents a chemical-physical decay coefficient, and Λ is the scavenging coefficient. The decay term λ represents in situ loss associated with processes, such as chemical reaction or radioactive decay.

Figure 2: Partitioning of cloud stabilized “disks” (Nyman, 2009). J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 41-52, Jan. - Apr., 2011

43


Moreira, D.M. et al

The mathematical description of the dispersion problem represented by the Eq. 4 is well posed when it is provided by initial and boundary conditions. Indeed, it is assumed that at the beginning of the pollutantâ&#x20AC;&#x2122;s release, the dispersion region is not polluted, which means: C y ( x , z , 0) " 0

at t = 0

(5)

A source of constant emission rate Q is assumed: Q C ( 0, z , t)= ŽM(t)-M(t-t r ) Ÿž I ( z  H s ) at x = 0 u y

Cny " Cny1 Kn

n = 1, 2,...(N-1)

yCny yC y " K n1 n1 yz yz

(9a)

n = 1, 2,...(N-1)

(9b)

Both equations must be considered in order to be possible to uniquely determine the 2N arbitrary constants, appearing in the set of problems solution (Eq. 8). Now, applying the Laplace transform in Eq. 8, the result is:

(6)

d 2 Cny ( s, z , p ) dz

2

vg dCny ( s, z , p ) ( p  Q  1  sun  K x s 2 )Cny ( s, z , p ) ( K x s  un )Cny (0, z ,  " Kz dz Kz Kz



Where2 δ(z-H ) is the Dirac delta function, H the source d C y ( s, z ,Sp ) vg dCny ( s, z , p ) ( p  Q  1  sun S K x s 2 )Cny ( s, z , p ) ( K x s  un )Cny (0, z , p )  height, Ρn is2 the Heaviside function, and tr is the duration "   K dz Kz Kz of releasedz(Bianconiz and Tamponi, 1993). with the initial condition: The pollutants are also subjected to the boundary C y ( s, z , 0) " 0 at t = 0 conditions: Kz

yC y " 0 yz

at z = h

(7a)

Kz

yC y " Vd C y at z = 0 yz

Indeed, it is now possible to recast problem (4) as a set of advective-diffusive problems with constant parameters, which for a generic sub-layer reads like: yCny y Cny y Cny y 2 Cny y 2 Cny  QCny  1Cny  un  vg " K x ,n  K z ,n 2 yt yx yz y z2 yx



Q 1 e r (  )I ( z  H s ) at x = 0 u s s

(12)

and the boundary conditions:

Next, we assume that Kx, Kz as well as the wind speed u depend only on the variable z , and an averaged value is taken. The stepwise approximation is applied in problem (4) by discretization the height h into sub-layers in such manner that inside each sub-layer, average values for Kx, Kz and u are taken. At this point, it is important to remark that this procedure transforms the domain of problem (4) into a multilayered-slab in the z direction. Furthermore, this approach is quite general, and can be applied when these parameters are an arbitrary continuous function of the z variable.

(8)

for n = 1:NL, where NL denotes the number of sub-layers y and Cn , the concentration at the nth sub-layer. Besides which, two boundary conditions are imposed at z = 0 and h given by Eq. 7 together with the continuity conditions for the concentration and flux of concentration at the interfaces Namely:

44

 pt

(7b)

Where h is the height of ABL and Vd is the deposition velocity.

zn f z f zn1

(11)

source condition: C y ( 0 ,z , p)=

and

(10)

Kz

dC y ( s, z , p ) " 0 dz

at z = h

(13a)

and Kz

dC y ( s, z , p ) " Vd C y ( s, z , p ) at z = 0 dz

(13b)

`

b

y y where C ( s, z , p ) " L C ( x , z , t ); x q s; t q p , which has the solution:

1  e  Q e p R  ptr

Cny ( s, z , p ) " An e

 Rn z

 Bn e

Rn z



 Rn ( z  H s )

e

Rn ( z  H s )

a





(14)

Finally, applying the initial and boundary conditions, one obtains a linear system for the integration constants. Then, the concentration is obtained by numerically inverting the transformed concentration C by a Gaussian quadrature scheme (Stroud and Secrest, 1966): for t > tr: k Š p š m Š pj š G z G z Cny ( x , z , t ) " ¨ ai ª i º ¨ a j ª º Ž An e n  Bn e n   t  j "1  x  i "1  pi

(1  e Q Fn 

tr t

)

e

 ( z  H s ) Gn

e

( z  H s ) Gn

Ÿ ½ H z  Hs ½ ½ž





(15)

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A multilayer model to simulate rocket exhaust clouds

for tr > t : C ( x, y, z , t ) " C ( x, z , t )



Ÿ Q  ( z  Hs )Gn ( z  H )G e  e s n H z  Hs ½ Fn ž





2 y

e

, (17) 2UX y Where C y ( x , z , t ) is expressed by the previous discussed formulation.

Š p š m Š pj š G z G z C ( x , z , t ) " ¨ ai ª i º ¨ a j ª º Ž An e n  Bn e n   t  j "1  x  i "1 k

y n



 y / 2X  2

y

(16)

Therefore, after determining the stabilization time and source (multiple sources due to partitioning of the cloud), the final concentration will be the contribution from all sources, i.e.,

Where, n

Gn " 

Fn " 2

vg 2Kz

pi t

Š p p šŸ 1 Š vg š 4  pi ­  Q  1  j un ª 1  j º ½ ª º  Kz ­ t x  Pe  ½ ; 2  Kz  Ž ž 2

t

p Š p p šŸ K z ­ i  Q  1  j un ª 1  j º ½ x  Pe  ½ ­Ž t ž Š pj š ª1 º Pe  

Where Ρ is the Heaviside function and Pe " un x K x is the well known Peclet number, essentially representing the ratio between the advective transport to diffusive transport. This can be physically interpreted as the parameter whose magnitude indicates the atmospheric conditions in terms of the winds strength. Small values of this number may be related to the weak winds when the downwind diffusion becomes important and the region of interest remains close to the source, whereas large values imply moderate to strong winds when the downwind diffusion is neglected in comparison to the advection, and the region of interest extends to a larger distance from the source. The solution is valid for x > 0 and t > 0, as the quadrature scheme of Laplace inversion does not work for x = 0 and t = 0. The constants ai , aj , and pi , pj are the weights and roots of the Gaussian quadrature scheme and are tabulated in the book by Stroud and Secrest (1966), while k and m are the quadrature points. However, we are aware of the existence in the literature of more accurate methods to evaluate this integral, like the multi-precision approach (Abate and ValkĂł, 2004). The semi-analytical character of the solutions (Eq. 15) and (Eq. 16) reduces to the solution of Moreira et al. (1999), when time goes to infinity (t â&#x2020;&#x2019;â&#x2C6;&#x17E;), Pe â&#x2020;&#x2019;â&#x2C6;&#x17E; , vg= 0, Î&#x203A; = 0 and Îť = 0. In order to show time-dependent three-dimensional pollutant numerical simulations, we finalize reporting a simplified solution for this sort of problem, reliable for some physical scenarios. Indeed, we assume that the timedependent three-dimensional solution is written in terms of the time-dependent two-dimensional solution, multiplied by the steady Gaussian function in the y-direction. This procedure yields:

C ( x , y , z , t ) " ¨ Ci ( x , y , z , t ) ,

(18)

i

Where i = 1,2,3,â&#x20AC;Ś, n and n represents the nth source due to the partitioning of the cloud of pollutants released by the rocket at the stabilization time.

BOUNDARY LAYER PARAMETERIZATION In the atmospheric diffusion problems, the choice of a turbulent parameterization represents a fundamental aspect for pollutant dispersion modeling. The reliability of each model strongly depends on the way the turbulent parameters are calculated, and it is related to the current understanding of the ABL (Mangia et al., 2002). In order to calculate the three-dimensional concentration in the ground-level centerline concentration (Eq. 14), we need to know the lateral dispersion parameter Ď&#x192;y. In this paper, the lateral dispersion parameter Ď&#x192;y derived by Degrazia et al. (1998) was used. It presents the following form:

X 2y h2

"

h



dne 0.21 sin 2 2.26^ 1/ 3 Xne  Âľ U 0 (1  ne )5/ 3 ne 2

(19)

Where X is a nondimensional distance ( X " xw* uh ), w* is the convective velocity scale, and h is the ABL top. Equation 19 contains the unknown function Ψ, the molecular dissipation of turbulent velocity is a leading destruction terms in equations for the budget of second-order moments, and according to HĎ&#x2020;jstrup (1982), has the form: 1/ 2

2 2 / 3 Š Ÿ zš Š z š 1/ 3 ½  ^ " ­ª 1  º ª 0 . 75  (20) º ­Ž h    L  ½ž Where L is the length of Monin-Obukhov defined in the surface boundary layer.

In terms of the scaling parameters, the vertical eddy diffusivity can be formulated as (Degrazia et al., 1997): Kz Š zš " 0.22 ª º w* h  h



J. Aerosp.Technol. Manag., SĂŁo JosĂŠ dos Campos, Vol.3, No.1, pp. 41-52, Jan. - Apr., 2011

1/ 3

Š zš ª 1  h º

1/ 3

 Š 4z š Š 8z š Ÿ ­1  exp ª  º  0.0003exp ª º ½  h  h ž Ž

(21)

45


Moreira, D.M. et al

The micrometeorological parameters are adapted from the routine of the model AERMET / AERMOD (EPA, 2004), whose function is to calculate the parameters: u* (friction velocity), L (Monin-Obukhov length), w* (convective velocity), h (ABL height), and H (heat flux) from the sounding (including the vertical wind speed) taken in Alcântara Launch Center.

Figure 5 demonstrates the concentration time evolutions with the parameters of the reference situation for time release of 50 seconds to different values of the chemical-physical decay coefficient (λ), at downwind distance of 500 and 1000 m (typical values of λ: 10-6 to 10-2). It also shows that the concentration peak values decrease as the downwind distance increase.

NUMERICAL SIMULATIONS

a)

For sake of illustration, the sensitivity analysis on tr and λ parameters is showed. Then, the sensitivity of the groundlevel concentration to these parameters is tested. Firstly, to show an example of the application of the obtained solution (Eq. 16) (tr > t), we report in Fig. 3 the time evolution of nondimensional concentration (Cyuh / Q) at three downwind distances (x = 500, 1000 and 2000 m). The concentration was computed as a mixture of CO, CO2, HCL and Alumina, which are the residuals from the solid propellant combustion. Figure 4 shows the nondimensional ground level concentration (Cyuh / Q) as a function of the source distance with variable duration releases (tr= 50, 100, 150, ! 200 seconds) for three different times (t = 250, 500 and 750 seconds), emitted through a stack with a physical height of 10 m, in micrometeorological conditions characterized by a 2 m/s wind velocity, a 1,100 m mixing layer, w* = 2 m/s and L = -10 m.

b)

Figure 4 shows that the concentration peak values increases as the duration of the release grows longer, until it reaches a limit value, for sufficiently long durations of the release. Besides, the concentration peak values decrease with the source distance increase.

c)

!

!

Figure 3: Time evolution of nondimensional concentration at three downwind distances (x = 500, 1,000 and 2,000 m). 46

!

Figure 4: Crosswind integrated concentration as a function of the source distance for three different times (t = 250, 500 and 750 seconds) and different durations of release (tr = 50, 100, 150 and 200 seconds).

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A multilayer model to simulate rocket exhaust clouds

Also, as the downwind distance increase, the peak position changes with respect to time and the peak concentration variation between the chemical-physical decay constants increase. Figure 6 has the concentration distributions in the horizontal xy-plane at ground-level for six different times: t = 100, 500, 100, 2000, 3000 and 5000 seconds. These isolines of equal concentration corresponds to the solution tr > t. As expected, when time becomes longer, the concentrations values enter into a steady-state condition. Figure 7 shows concentration distributions in the horizontal xy-plane at ground-level for the time t = 1000 seconds and four different time release (tr = 300, 500,

a)

b)

!

800 and 950 seconds). The lines represent isolines of equal concentration. As the duration of the release becomes longer, the concentrations values enter into a steady-state condition. Comparing Fig. 6 for t = 1000 seconds with Fig. 7, this affirmative is clearly observed. Furthermore, due to lack of experimental data with rockets, we evaluated the performance of the model (tr > t, with a single source at 115 m) with the boundary layer parameterization proposed, using the well-known Copenhagen data set (Gryning et al., 1987). The Copenhagen data set is composed of tracer SF6 data from dispersion experiments carried out in Northern Copenhagen. The tracer was released without buoyancy from a tower at 115 m height, and was collected at ground-level positions in up to three crosswind arcs of tracer sampling units. The sampling units were positioned from 2 to 6 km far from the point of release. We used the values of the crosswind integrated concentrations normalized with the tracer release rate from Gryning et al. (1987). Tracer releases typically start up one hour before the tracer sampling and stop at the end of the sampling period. The site was mainly residential with a roughness length of 0.6 m. Generally, the distributed data set contains hourly mean values of concentrations and meteorological data. However, in this work, data with a greater time resolution were used. In particular, 20 minutes averaged measured concentrations and 10 minutes averaged values for meteorological data were used. In such manner, in the present work, the variables (L, u* , w *) in the Copenhagen data set are dynamical (except the variable h). For details of the experimental data, see the work of Tirabassi and Rizza (1997). The results obtained with the model are compared with the M4PUFF model (Tirabassi and Rizza, 1997), which is based on a general technique for solving the K-equation using the truncated Gram-Charlier expansion (type A) of the concentration field, and a finite set equation for the corresponding moments. Table 1 presents some performance measurements, obtained using the wellknown statistical evaluation procedure described by Hanna (1989). The statistical index FB indicates whether the predicted quantities underestimate or overestimate the observed ones. The statistical index NMSE represents the quadratic error of the predicted quantities in relation to the observed ones. The best results are indicated by values nearest 0 in NMSE, FB, and FS, and nearest 1 in COR and FA2.

!

Figure 5: Time evolution of concentration at downwind distance of 500 and 1,000 m for time release of 50 seconds and different chemical-physical decay constants.

The statistical indices point out that a good agreement is obtained between experimental data and the model.

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Moreira, D.M. et al

a)

b)

!

!

c)

d)

!

!

e)

f)

!

!

Figure 6: Concentrations distributions in the horizontal xy-plane at ground-level for six different times: t = 100, 500, 100, 2000, 3000 and 5000 seconds, for the solution tr > t. 48

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A multilayer model to simulate rocket exhaust clouds

a)

b)

! c)

! d)

!

!

Figure 7: Concentrations distributions in the horizontal xy-plane at ground-level for t = 1,000 seconds and four different times releases: tr = 300, 500, 800 and 950 seconds, for the solution t > tr.

A more detailed inspection of the Table 1 can stress that the model does a very well simulation of the observed concentrations presenting the best values for NMSE, COR (81%), and FA2 (95%).

Finally, a simulation considering a grid of 100 x 100 km in the region covered by the Alcântara Launch Center is carried out. The main points are shown in Fig. 8, with the vector wind speed and dispersion of the plume. The concentration unit is ppm.

Table 1: Statistical evaluation of model results (Copenhagen dataset)

Model MSDEF M4PUFF

NMSE 0.15 0.21

R 0.81 0.74

FA2 0.95 0.90

FB 0.18 0.10

FS 0.38 0.45

CONCLUSIONS A solution of the time-dependent advection-diffusion equation in the construction of the MSDEF has been

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Moreira, D.M. et al

! Figure 8: Topography of the region of 100 x 100 km with a resolution of 100 m showed the vector wind speed and plume generated in the simulation. The coordinate axes are in UTM. TMI represent the Tower Mobile Integration and VLS is the Satellite Launch Vehicle.

presented. This solution considers duration time release, chemical-physical decay, settling velocity, scavenging coefficient, and can be applied for describing the turbulent dispersion of many scale quantities, such as air pollution, radioactive material, heat, and so on. From the previous results, we promptly notice the aptness this model to understand the time evolution of the concentration and its dependency on the duration of the contaminant emission. In fact, this model allows us to simulate the continuous, shortterm, and instantaneous emissions. In particular, the model is suitable for an initial and rapid assessment of atmospheric dispersion under emergency conditions without sophisticated computing resources. The model can be used in different conditions of atmospheric stability, making it possible to predict or simulate the concentration in accordance with emergency plans and pre and post-launches for environmental management, 50

in situations of rocket launches in the Alcântara Launch Center. To show the solution performances in actual scenarios, a parameterization of the ABL has been introduced, and their values have been compared with experiment dataset. The analysis of the results shows a reasonably good agreement between the computed values and the experimental ones. The discrepancies with the experimental data depend not on the solution of the advection-diffusion equation but on the equation itself, which it is only a reality model. Moreover, a source of discrepancies between the predicted and measured values lies in the ABL parameterization used (i.e., vertical wind and eddy diffusivity profiles). Although models are sophisticated instruments that ultimately reflect the current state of knowledge on turbulent transport in the atmosphere, the results they provide

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A multilayer model to simulate rocket exhaust clouds

are subject to a considerable margin of error. This is due to various factors, including the uncertainty of the atmosphere intrinsic variability. Models, in fact, provide values expressed as an average, that is, a mean value obtained by the repeated performance of many experiments, whereas the measured concentrations are a single value of the sample to which the ensemble average provided by models refers. This is a general characteristic of the theory of atmospheric turbulence and is a consequence of the statistical approach used in attempting to parameterize the chaotic character of the measured data. In light of the considerations, an analytical solution is useful to evaluate the performances of sophisticated numerical dispersion models, which numerically solve the advection-diffusion equation, yielding results that can be compared not only with experimental data but, in an easy way, with the solution itself, to check numerical errors without the uncertainties presented above.

ACKOWLEDGEMENTS The authors thank the Brazilian National Council for Scientific and Technological Development (CNPq) for the partial financial support of this work through their Research Grant (PQ).

REFERENCES Abate, J., Valkó, P.P., 2004, “Multi-precision Laplace transform inversion”, International Journal for Numerical Methods in Engineering, Vol. 60, pp. 979-993. doi: 10.1002/nme.995 Bianconi, R., Tamponi, M., 1993, “A mathematical model of diffusion from a steady source of short duration in a finite mixing layer”, Atmospheric Environment, Vol. 27, No. 5, pp. 781-792. doi:10.1016/0960-1686(93)90196-6  Bjorklund, J.R., Dumbauld, J.K, Cheney, C.S. and Geary, H.V., 1982, “User’s manual for the REEDM (Rocket Exhaust Effluent Diffusion Model) compute program”, NASA contractor report 3646. NASA George C. Marshall Space Flight Center, Huntsville, AL. Bjorklund, J.R., 1990, “User instructions for the RealTime Volume Source Dispersion Model (RTVSM)”, H.E Cramer Company, Inc. Report TR-90-374-02, prepared for U.S. Army Dugway Proving Ground, Dugway, UT. Bjorklund, J.R., Bowers, J.F., Dodd, G.C. and White, J.M., 1998, “Open Burn/Open Detonation Dispersion Model (OBODM) users’ guide”, Vol. 2, Technical description.

West desert test center, US Army Dugway proving ground, Dugway, Utah. Briggs, G.A., 1975, “Plume Rise Predictions, Lectures on Air Pollution and Environmental Impact Analyses”, D.A. Haugen ed., American Meteorological Society, Boston, MA, pp. 59-111. Degrazia, G.A., Campos Velho, H.F. and Carvalho, J.C., 1997, “Nonlocal exchange coefficients for the convective boundary layer derived from spectral properties”, Contributions to Atmospheric Physics, Vol. 70, No. 1, pp. 57-64. Degrazia, G.A., Mangia, C. and Rizza U., 1998, “A comparison between different methods to estimate the lateral dispersion parameter under convective conditions”, Journal of Applied Meteorology, Vol. 37, pp. 227-231. Dumbauld, R.K., Bjorklund, J.R. and Bowers, J.F., 1973, “NASA/MSFC multilayer diffusion models and computer program for operational prediction of toxic fuel hazards”, NASA Contractor Report CR-129006, NASA George C. Marshall Space Flight Center, Huntsville, AL. EPA-454/B-03-002, 2004. User’s Guide for the AERMOD meteorological preprocessor (AERMET). Gryning, S., Holtslag, A., Irwing, J. and Silversten, B., 1987, “Applied dispersion modeling based on meteorological scaling parameters”, Atmospheric Environment, Vol. 21, pp. 79-89. Hanna, S.R., 1989, “Confidence limit for air quality models as estimated by bootstrap and jacknife resampling methods”, Atmospheric Environment, Vol. 23, pp. 13851395. Hφjstrup, J., 1982, “Velocity spectra in the unstable boundary layer”, Journal of Atmospheric Science, Vol. 39, pp. 2239-2248. Huang, C.H., 1979, “A theory of dispersion in turbulent shear flow”, Atmospheric Environment, Vol. 13, pp. 453-461. Mangia, C., Moreira, D.M., Schipa, I., Degrazia, G.A., Tirabassi, T. and Rizza, U., 2002, “Evaluation of a new eddy diffusivity parameterisation from turbulent Eulerian spectra in different stability conditions”, Atmospheric Environment, Vol. 36, pp. 67-76. Moreira, D.M., Degrazia, G.A. and Vilhena, M.T., 1999, “Dispersion from low sources in a convective boundary layer: an analytical model”, Il Nuovo Cimento, Vol. 22C, n.5, pp. 685-691.

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Moreira, D.M., Rizza, U., Vilhena, M.T. and Goulart, A.G., 2005a, “Semi-analytical model for pollution dispersion in the planetary boundary layer”, Atmospheric Environment, Vol. 39, No. 14, pp. 2689-2697. Moreira, D.M, Carvalho, J.C., Goulart, A.G. and Tirabassi, T., 2005b, “Simulation of the dispersion of pollutants using two approaches for the case of a low source in the SBL: evaluation of turbulence parameterisations”, Water, Air and Soil Pollution, Vol. 161, pp. 285-297. Moreira, D.M, Ferreira Neto, P.V. and Carvalho, J.C., 2005c, “Analytical solution of the Eulerian dispersion equation for nonstationary conditions: development and evaluation”, Environmental Modelling and Software, Vol. 20, No. 9, pp. 1159-1165. Moreira, D.M., Tirabassi, T. and Carvalho, J.C., 2005d, “Plume dispersion simulation in low wind conditions in stable and convective boundary layers”, Atmospheric Environment, Vol. 39, No. 20, pp. 3643-3650. Moreira, D.M, Vilhena, M.T., Tirabassi, T., Costa, C. and Bodmann, B., 2006, “Simulation of pollutant dispersion

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in the atmosphere by the Laplace transform: the ADMM approach”, Water, Air and Soil Pollution, Vol. 177, pp. 411-439. Moreira, D.M., Trindade, L., 2010, “Manual do Usuário do Modelo MSDEF (Modelo Simulador da Dispersão de Efluentes de Foguetes)”, Versão 1.0/2010, Relatório Técnico, CTA/IAE/ACA. 70pp. Nyman, R.L., 2009, “NASA Report: Evaluation of Taurus II Static Test Firing and Normal Launch Rocket Plume Emissions”. Stephens, J.B., Stewart, R.B., 1977, “Rocket exhaust effluent modeling for thopospheric air quality and environmental assessment”, National Aeronautics and Space Administration – NASA Technical Report. Stroud, A.H., Secrest, D., 1966, “Gaussian Quadrature Formulas”, Englewood Cliffs, N.J., Prentice Hall, Inc. Tirabassi, T., Rizza, U., 1997, “Boundary layer parameterization for a non-Gaussian puff model”, Journal of Applied Meteorology, Vol. 36, pp. 1031-1037.

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doi: 10.5028/jatm.2011.03010211

Hossein Bonyan Khamseh Shahid Beheshti University, GC Tehran − Iran h.bonyan@gmail.com

M. Navabi* Shahid Beheshti University, GC Tehran − Iran navabi.edu @gmail.com *author for correspondence

On reduction of longest accessibility gap in LEO sun-synchronous satellite missions Abstract: Accessibility gaps are inherent properties of Low Earth Orbit (LEO) sun-synchronous satellite missions. Long accessibility gaps in satellite missions imply strict in-orbit autonomy requirement, met by expensive solutions. Thus, methods to shorten accessibility gaps in satellite missions are appreciated by space mission designers. For that purpose, in this paper, ground segment site location is employed as a mechanism to reduce the longest accessibility gaps in LEO sun-synchronous missions. For a given repeatability cycle, it is shown that longitude of the ground segment does not affect the access gaps. Simulation results show that increasing the latitude of ground segment reduces the longest accessibility gaps, especially in extreme latitudes near Polar Regions. To avoid polar ground segments due to their practical difficulties, mission architectures with two co-high-latitude ground segments are proposed. Selection of longitude distance between the two cohigh-latitude ground segments is discussed to further reduce the longest accessibility gap in LEO sun-synchronous missions. To show the feasibility of the proposed approach, simulation results are included for illustration. Keywords: Ground segment location, LEO sun-synchronous satellite, Longest accessibility gap.

INTRODUCTION During the last two decades, there has been a significant increase in LEO sun-synchronous missions for various applications (Dittberner and McKnight, 1993; Anilkumar and Sudheer Reddy, 2009). Regarding nearfuture activities, Petersen (1994), in his book The road to 2015, says: “most of the new growth in commercial space appears to be in LEO missions”. An inherent characteristic of LEO missions is that the pattern of ground segment access to the satellite is made up by short and discontinuous access events (Wertz and Larson, 1999). To take account of this peculiar access pattern, in our previous papers (Bonyan Khamseh and Navabi, 2010a; 2010b) we developed two access-based metrics namely Total Accessibility Duration (TAD) and Longest Accessibility Gap (LAG). Accessibility gaps indicate requirement of autonomous operation (Chester, 2009) and in Bonyan Khamseh and Navabi (2010b) it was discussed that LAG metric is related to minimum requirement of in-orbit autonomy. To obtain LAG metric in a time-independent manner, the concept of repeatability cycle is employed. For a given repeatability cycle, it is discussed that longitude variation of a ground segment has negligible effect on LAG metric. Yet, our simulation results show that increasing the latitude of ground segment location improves LAG metric. It was Received: 10/02/11 Accepted: 05/03/11

observed that significant improvement in LAG metric is only achieved for very-high-latitude ground segments, at either Polar Regions. Still, establishment, operations and maintenance of ground segments at Polar Regions brings in practical difficulties. Thus, effectiveness of single-ground-segment architecture is questionable. To overcome this drawback, mission architectures with two ground segments are proposed and a procedure is given to select ground segments location with improved LAG metric. The contribution of this paper is to improve LAG metric for LEO sun-synchronous missions by employing ground segment site location. In this manner, single and twoground-segment architectures are studied.

NUMERICAL METHOD OF LAG DETERMINATION Accessibility gap is defined as the time gap between any two consecutive events of ground segment access to the satellite, schematically shown in Fig. 1. Thus, to obtain accessibility gaps in a given satellite mission, pattern of ground segment access to the satellite must be determined. For that purpose, position of the satellite in its orbit must be found. In our previous work (Bonyan Khamseh and Navabi, 2010b), Cowell’s differential propagation formula was employed to obtain position of the satellite. In this paper, we employ some alternative analytical

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Khamseh, H.B., Navabi, M.

Figure 1: Gaps in ground segment access to a satellite.

relationships to obtain position vector of the satellite. In this method, Lagrange planetary equations are employed with the second-degree gravitational potential function. Lagrange planetary equations can be found in references such as Capderou (2005) and are given by Eq. 1: ¯ ² ² ² ² ² ² ² ²² ° ² ² ² ² ² ² ² ² ²¹

da 1 Š yR š " 2 dt na ª yM º yR yR š 1 1  e2 Š 1 de " 2   ª º 2 e  dt na 1  e y\ yM  Š yR di 1 yR š "   cos i ª 2 2 dt na 1  e sin i  y< y\ º Š yR š 1 d< " 2 2 dt na 1  e sin i ª yi º Š 1  e2 yR cos i yR š 1 d\ "  dt na 2 1  e2 ª e ye sin i yi º 1 Š yR 1  e2 yR š dM " n  2 ª 2 a  ya dt e ye º na 

`



(1)

b

In Eq. 1, a, e, i, <, \ , M is the Keplerian set of orbital elements namely semi-major axis, eccentricity, inclination, Right Ascension of Ascending Node (RAAN), argument of perigee and mean anomaly, respectively. Also n " R3 is a the mean motion, Âľ is Earth gravitational parameter and R is perturbing Geopotential. A second-degree perturbing Geopotential takes account of J2 effect i.e. dominant perturbation of LEO region and thus is employed in this Â&#x2022; cos 1 cos t < sin 1 sin t cos i study. If we only take account a(1 < e2 ) ofÂłthe secular variations of ď ˛ sin elegant 1 cos t +relationship cos 1 sin t cos i rS (t )we = may obtainÂł an orbital elements, 1 + e cos Â&#x17E; (t ) sin iperturbing sin t for the average second-degree ÂłÂ&#x2013;gravitational function, i.e. R J 2. The procedure to obtain R J 2 is given by Capderou (2005) and the result is given by Eq. 2: R J2 " 

54

3 2

R Re2

a3 1  e



3 2 2

Š1 1š J 2 ª sin 2 i  º 3 2

(2) 

Where Re is Earthâ&#x20AC;&#x2122;s equatorial radius and J2 = 0.00108263 is a constant related to Earthâ&#x20AC;&#x2122;s oblateness. Substituting Eq. 2 in Eq. 1 and noting that y R J2 y R J2 3 sin i cos i y R J2 3e "  R J2 , " RJ R J 2, " 2 1 1 2 ya a y i ye 1 e sin 2 i  2 s y R J2 y R J2 y R J2 and " " " 0 , we obtain the following yM y\ y< analytical relationships for orbital elements of the satellite: ÂŻ ² ² ² ² ² ² ° ² ² ² ² ² ² Âą

a " 0 q a(t ) " a0 " cte e " 0 q e(t ) " e0 " cte i " 0 q i(t ) " i0 " cte 2  Ÿ Š Re š 3 <(t ) " <0  ­ cos i ½ t  t0 nJ º 2ª 2 2 ­ 2(1  e ) ½  a Ž ž 2 Ÿ  ŠR š 3 \ (t ) " \ 0  ­ nJ 2 ª e º 5 cos 2 i  1 ½ t  t0  2 2 ­ 4(1  e ) ½  a ž Ž M ( t ) " M 0  n ( t  t0 )

Where





2  ŠR š 3 n " M " n0 ­1  J 2 ª e º 3cos 2 i  1 3 ­ a   ­Ž 4(1  e2 ) 2



(3)

Âź

½½ .

With the

½ž

orbital elements determined at any time t, satellite I position, i.e. rS , may be determined in the geocentric inertial frame as: ď ˛ rS (t ) =

Â&#x2022; cos 1 cos t < sin 1 sin t cos i < cos 1 sin t < sin 1 cos t c a(1 < e2 ) Âł sin t + cos 1 cos t c Âł sin 1 cos t + cos 1 sin t cos i < sin 1(4) 1 + e cos Â&#x17E; (t ) Âł t sin i sin sin i cos t Â&#x2013;

< cos 1 sin t < sin 1 cos t cos i sin 1 sin i < sin 1 sin t + cos 1 cos t cos i < cos 1 sin i sin i cos t cos i

Â&#x2014; Â&#x2022; cos Â&#x17E; (t ) ¾³ Âľ Âł sin Â&#x17E; (t ) ÂľÂ&#x2DC; ÂłÂ&#x2013; 0

Â&#x2014; Âľ Âľ Âľ Â&#x2DC;

And Ď&#x2018;(t), i.e. satellite true anomaly, is determined from Keplerâ&#x20AC;&#x2122;s equation by iterative methods such as NewtonRaphson. In case of circular orbits, simply Ď&#x2018;(t)=M(t). With the satellite position determined at any time t, now ground segment position vector in the inertial frame must be determined. Based on WGS84 model, Fig. 2 shows a

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On reduction of longest accessibility gap in LEO sun-synchronous satellite missions

ground segment (GS) on the Earthâ&#x20AC;&#x2122;s surface in the inertial geocentric equatorial frame.

commercial communication hardware. From Eq.  7, rise/set times of the satellite with respect to a given ground segment may be determined. Duration of each accessibility gap is computed by subtracting the access termination time from next access initiation time.

LAG â&#x20AC;&#x201C; MINIMUM TIME INTERVAL TO STUDY?

rGS: ground segment position; θ: local sidereal time of ground segment (in degrees); Re: Earthâ&#x20AC;&#x2122;s equatorial radius; RĎ&#x2020;: radius of curvature in prime vertical (Polar axis); Rp: Earthâ&#x20AC;&#x2122;s polar radius; θG: Greenwich sidereal time (in degrees). Figure 2: A ground segment (GS) on the surface of oblate Earth.

At a given time t, the ground segment position vector I rGS (t ) in the inertial frame is given by:



(5)

ď&#x20AC;Ś) Rev Â&#x203A; (t e < 1 n + ¨ n + tď&#x20AC;Ś



(8)

Where Rev is integer number of full revolution in D days, and \ e " 7.2925  105 rad/sec is Earthâ&#x20AC;&#x2122;s rotation rate. For sun-synchronous orbits, we have  " 1.9965  107 rad/sec . Also, Î&#x201D;n and \ are: < 2

3 3 2 2

4(1  e )

ŠR š nJ 2 ª e º 3cos 2 i  1  a 2

Where Ď&#x2020; is ground segment latitude, Rc = RÄł + AltGS ,



ŠR š 3 \ " nJ 2 ª e º 5 cos 2 i  1 2 2 4(1  e )  a



Re

, R = 1 < (2 f < f )sin ij and f = 0.00335 is the Earth flattening factor. Also, AltGS is the altitude of ground segment above the ellipsoidal surface and θ (t) is the instantaneous angular distance between the ground segment location and the Vernal Equinox, measured in I the equatorial plane. With rGS (t ) determined, position vector of the satellite relative to the ground segment I rS _ rel _ GS (t ) is: ij

D=

¨n "

Š R cos ij cos V (t ) š ª c º I rGS (t ) " ª Rc cos ij sin V (t ) º º ª º RS sin ij  

RS = (1 < f )2 RÄł

In LEO missions, chronological distribution of the ground segment access to the satellite varies as the time interval of study is increased. This brings up an immediate drawback since, in this manner, LAG will be a time-dependent metric. Yet, after a certain simulation time, it is observed that distribution of access events repeats identically. This time interval is called repeatability cycle and is taken as the minimum time interval to obtain time-independent LAG metric. For a satellite mission with given orbit, one may obtain repeatability cycle, i.e. D, from Eq. 8:

2

I I I rS _ rel _ GS (t ) " rS (t )  rGS (t ) 

2

In Eq. 8, only integer values of D give admissible scenarios. Chronological distribution of access events is identical after each D days and, consecutively, LAG metric is determined in a time-independent manner. Thus, repeatability cycle obtained from Eq. 8 is taken as the time interval to study LAG metric.

SITE LOCATION OF GROUND SEGMENT (6)

At any given time, the satellite is accessible from the ground segment if Eq. 7 is satisfied: I I Š rS _ rel _ GS (t ) Â&#x161; rGS (t ) š J (t ) " 90  cos ÂŞ Âş v J min (7) ÂŤ rS _ rel _ GS (t )  rGS Âť  I I In Eq. 7, rS _ rel _ GS (t ) and rGS are magnitudes of rS _ rel _ GS (t ) I and rGS (t ) , respectively. Îľmin accounts for minimum ground elevation constraint, typically 5-10 degrees for

As it was discussed in the section â&#x20AC;&#x153;Numerical method of LAG determinationâ&#x20AC;?, for a mission with given orbit, LAG metric depends on the ground segment location. In this section, selection of ground segment location is employed as a mechanism to improve LAG metric.

1

Site location of single ground segment Location of a ground segment on the terrestrial surface is given by three parameters, namely longitude, latitude and

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altitude relative to the mean surface level. In this paper, effect of longitude and latitude of the ground segment on LAG metric is studied and zero altitude is assumed for all ground segment locations.

Effect of ground segment longitude Through extensive simulations for given repeatability cycles, it was observed that pattern of access to LEO sun-synchronous satellite remains constant as the location of ground segment is altered in the longitude direction. In Li and Liu (2002), it was analytically shown that the Probability Density Function (PDF) of elevation angles for a given ground segment does not depend on its longitude. Also, the same results were verified by extensive simulations in Modiri and Mohammady (2008). Consequently, selection of ground segment location to reduce LAG metric must be done in the latitude direction, only.

in Fig. 3. In access type (a), the ground segments access to the satellite do not overlap at all. In access types (b) and (c), the ground segments access to the satellite partially overlap each other. Finally, in access types (d) and (e), a ground segment access to the satellite initiates before and extends after the other ground segment access to the satellite. Regarding these five access types, single ground segment access events must be merged accordingly to obtain the network access pattern. In the next section, a case study is discussed to evaluate the effect of ground segment(s) location on LAG metric.

SIMULATION AND RESULTS To evaluate the effect of ground segment site location on LAG metric in a given LEO sun-synchronous mission, a case study is considered. Orbital parameters of our case study – called RS-Sat hereafter – are shown in Table 1.

Effect of ground segment latitude Based on the results obtained in Li and Liu (2002), the PDF of elevation angles is symmetrical for both northern and southern hemispheres. Thus, for two ground segments at latitude of ± lat, identical access patterns and LAG metrics are obtained. Due to the fact that most of the lands at the terrestrial surface reside in the northern hemisphere, one may assume that the ground segment resides in northern hemisphere. Latitude of the ground segment is changed from Equator to 90° N i.e. North Pole. Step size for latitude variation may be chosen according to the required accuracy. Here we will adopt 10 deg steps, in northward direction.

Site location of two ground segments To achieve further improvement in LAG metric, twoground-segment mission architectures are discussed in this section. We will assume co-latitude ground segments. From previous subsections, longitude of either ground segments has negligible effect on LAG metric. Thus, at constant latitude, only the relative longitude distance between the two ground segments must be selected. In two-ground-segment mission architectures, care must be taken to merge access patterns of two ground segments in order to obtain the combined network access pattern. In general, sequential access pattern of a two-ground-segment network to a satellite may take any of the five types shown 56

Figure 3: Possible sequential types of two ground segments access to a satellite. Table 1: Orbital characteristics of RS-Sat

Parameter Value Orbit altitude 655 km Eccentricity 0 Inclination 98.01 deg (sun-synchronous) Local time of ascending node 10:00 a.m.

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On reduction of longest accessibility gap in LEO sun-synchronous satellite missions

Orbital altitude of 655 km has been selected to reflect the popularity of the 600-1,000 km range for remote sensing applications (Stephens, 2002; Sandau, 2010). Similarly, local time of ascending node of 10:00 a.m. has been purposefully adopted to reflect the popularity of such architecture for imagery purposes (Stephens, 2002). From Eq. 8, repeatability cycle of RS-Sat is 10 days. Thus, simulation was carried out for a 10-day period from 1 Jan 2010 00:00:00 to 10 Jan 2010 24:00:00. Just as in the case of preceding parameters, a 10-day period reflects the upper-bound of revisit-time requirements for various remote sensing applications (Stephens, 2002).

Single ground segment scenarios In the first scenario, the ground segment resides at the Equator and the arbitrary longitude of 30° N. In subsequent scenarios, latitude of ground segment is increased in 10 deg steps. By this reasoning, location of the ground segment in the tenth scenario will be in 30° E 90° N, i.e. in the center of the arctic region. For the 10-day simulation period, LAG metric in each scenario was obtained and illustrated in Fig. 4, in which it can be readily seen that very little improvement in LAG metric is obtained as the ground segment moves from the Equator to the latitude of 50° N. At the latitude interval of 60° N–70° N, LAG metric experiences additional improvement. Significant improvement in LAG metric is achieved only in the 70° N - 90° N latitude interval, especially in the upper-bound limits, i.e. the arctic region. However, due to adverse environmental conditions and poor access to required operational resources (e.g. electricity) at affordable cost, Polar Regions are highly disadvantageous for ground segment deployment. As a result, effectiveness of single-ground-segment architecture is questionable.

Two-ground-segment scenarios To achieve further improvement in LAG metric, twoground-segment mission architectures are explored in this section. To avoid difficulties encountered in Polar Regions, we will assume 60° N as the upper latitude limit for ground segments location. Co-latitude ground segments at 60° N are considered. From previous subsections, longitude of either ground segments has negligible effect on LAG metric. In the first scenario, location of the first and second ground segment will be considered at 30° E 60° N and 40° E 60º N, respectively i.e. a 10º difference in longitude direction. In the subsequent scenarios, longitude difference will be increased in 10° steps in the eastward direction. Thus, the longitude distance between the two ground segments in jth scenario i.e. ΔL j is (Eq. 9): 

(9)

where j is the sequential number of the scenario. The 10° increment in longitude difference between the two ground segments will result in 35 scenarios. Due to circular cross section of the Earth, only 18 unique two-ground-segment scenarios are taken into account. For the 10-day repeatability cycle, simulations were carried out for the 18 described scenarios and pattern of two-ground-segment network access to RS-Sat was obtained for each scenario. Results for LAG metric for each scenario are given in Fig. 5. As it can be seen from Fig. 5, minimum LAG is experienced in the 12th scenario, in which the ground segments reside at 30° E 60° N and 150° E 60° N, i.e. 120° apart in the longitude direction. In this scenario, LAG metric is 11549 seconds, i.e. 3 hours 12 minutes and 29 seconds. At this point, it must be verified that lands 120° apart in the longitude direction actually exist at the latitude of 60° N over the Earth’s surface (for practical applications, the two ground segments must reside on land not in the seas!). If the preferred two-groundsegment architecture did not fit into the land distribution over the terrestrial surface, the scenario with second-best LAG metric would be examined, and so on.

14

It is recalled that if it was desired to achieve the same LAG metric i.e. 11549 seconds by single ground segment architecture, latitude of the ground segment would be 77.5° N somewhere in the arctic regions. This verifies the effectiveness of the two-ground-segment architecture to improve LAG metric while avoiding operational difficulties of ground segments in very-high latitudes and the arctic region.

Longest accessibility gap (Hours)

12

10

8

6

4

2

CONCLUSION 0 0

10

20

30 40 50 60 Latitude of ground segment (Deg)

70

80

90

Figure 4: Longest accessibility gap metric for RS-Sat in single ground segment scenarios.

LAG is an important metric which is related to minimum requirement of in-orbit autonomy. An analytical approach was adopted to determine the prescribed metric. Site selection of single and two ground segments to improve LAG metric

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Khamseh, H.B., Navabi, M.

Figure 5: Longest accessibility gap metric for RS-Sat in two-ground-segment scenarios.

in LEO sun-synchronous missions was discussed. Our results showed that, for single ground segment, LAG metric improves as the ground segment moves to high latitudes and Polar Regions. Also, for two-ground-segment mission architectures, the relative distance to achieve improved LAG metric was obtained. It was observed that two-groundsegment mission architectures are effective in that they offer improved LAG metric while avoiding operational difficulties of polar ground segments. By employing the procedures discussed in this paper, one may determine single and twoground-segment architectures to provide acceptable LAG metric in a given mission.

REFERENCES Anilkumar, A.K., Sudheer Reddy, D., 2009, “Statistical Conjunction Analysis and Modeling of Low-Earth-Orbit Catalogued Objects”, Journal of Spacecraft and Rockets, Vol. 46, No. 1, pp. 160-167. doi: 10.2514/1.36976. Bonyan Khamseh, H., Navabi, M., 2010a, “Development of Metrics for Ground Segment Site Location Based on Satellite Accessibility Pattern from Ground Segment”, Proceedings of the 4th Asia-Pacific Conference on Systems Engineering, Keelung, Taiwan. Bonyan Khamseh, H., Navabi, M., 2010b, “Development of Access-based Metrics for Site Location of Ground Segment in LEO Missions”, Journal of Aerospace Technology and Management, Vol. 2, No. 3, pp. 279-286. doi: 10.5028/jatm.2010.02038210. Capderou, M., 2005, “Satellites Orbits and Missions”, Springer-Verlag, Berlin, Germany, 364 p. 58

Chester, E., 2009, “Down to Earth systems engineering: The forgotten ground segment”, Acta Astronautica, Vol. 65, No 1-2, pp. 206-213. Dittberner, G., McKnight, D., 1993, “Collision Risk in Sunsynchronous Low Earth Orbit”, Advances in Space Research, Vol. 13, No. 8, pp. 187-190. doi: 10.1016/02731177(93)90589-4. Li, S.Y., Liu, C.H., 2002, “An analytical model to predict the probability density function of elevation angles for LEO satellites”, IEEE Communications Letters, Vol. 6, No. 4, pp. 138-140. Modiri, A., Mohammady, L., 2008, “Mathematical Prediction of Sun-synchronous Polar LEO Satellite Visions for Earth Stations”, Proceedings of 10th International Conference on Advanced Communication Technology, Korea, pp. 1559-1563. Petersen, J.L., 1994, “The Road to 2015: Profiles of the Future”, Waite Group Press, Corte Madera, CA, USA. Sandau, R., 2010, “Status and Trends of Small Satellite Missions for Earth Observation”, Acta Astronautica, Vol. 66, No. 1-2, pp. 1-12. Stephens, J.P., 2002, “A Novel International Partnership: The Disaster Monitoring Constellation of Small Low Cost Satellites”, Proceedings of the United Nations Regional Workshop on the Use of Space Technology for Disaster Management in Asia and the Pacific, Bangkok, Thailand. Wertz, J.R., Larson, W.J., 1999, “Space Mission Analysis and Design”, 3rd Ed., Microcosm Press, Bloomington, IN, USA, 969 p.

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doi: 10.5028/jatm.2011.03019410

Adriano Luiz de Paula* Institute of Aeronautics and Space São José dos Campos, Brazil adrianoalp@iae.cta.br

Mirabel Cerqueira Rezende Institute of Aeronautics and Space São José dos Campos, Brazil mirabelmcr@iae.cta.br

Joaquim José Barroso National Institute for Space Research São José dos Campos, Brazil barroso@plasma.inpe.br *author for correspondence

Experimental measurements and numerical simulation of permittivity and permeability of Teflon in X band Abstract: Recognizing the importance of an adequate characterization of radar absorbing materials, and consequently their development, the present study aims to contribute for the establishment and validation of experimental determination and numerical simulation of electromagnetic materials complex permittivity and permeability, using a Teflon® sample. The present paper branches out into two related topics. The first one is concerned about the implementation of a computational modeling to predict the behavior of electromagnetic materials in confined environment by using electromagnetic three-dimensional simulation. The second topic re-examines the Nicolson-Ross-Weir mathematical model to retrieve the constitutive parameters (complex permittivity and permeability) of a homogeneous sample (Teflon®), from scattering coefficient measurements. The experimental and simulated results show a good convergence that guarantees the application of the used methodologies for the characterization of different radar absorbing materials samples. Keywords: Electric permittivity, Magnetic permeability, Radar absorbing material, Computational modeling.

INTRODUCTION Knowledge of complex permittivity, ε*, and permeability, µ*, of materials proves to be of great interest in scientific and industrial applications. The measurement of ε* and µ* in the microwave frequency range finds direct application in different areas. the electromagnetic radiation effects on biological systems study in ceramic sintering, plastic welding, and remote sensing (Chung, 2007) can be mentioned as examples. In this latter case, a good understanding of the vegetation dielectric properties is vital to get useful information from the remotely sensed data for earth resources monitoring and management, because the vegetation dielectric constant has a direct effect on radar backscattering measured by microwave sensors. Concerning sectors of electronic, telecommunication, aerospace industries, and in particular in the research and development of radar absorbing materials (RAM), the knowledge of ε* and µ* allows to predict the electromagnetic properties of materials via computer simulation. Thus, the simulation is useful for supporting studies related to the RAM processing optimization, as well as its utilization for specific purposes. Computational modeling becomes relevant as long as the simulated results reproduce and anticipate experimentally Received: 06/11/10 Accepted:11/11/10

measured data. Strong interrelation between modeling and experimental contributes to ensure confidence in the computational tool developed for a given application. A purpose of computer modeling is to reconstruct experimental measurements aiming at understanding and evaluating measured parameters, and also to obtain new parameters in different contexts but consistent with the experimental interpretation. In situations in which a modal analysis turns out too complex and difficult to solve, numerical methods are widely used, such as finite element method (FEM), finite difference method (FDM), and particularly specialist tools for three-dimensional electromagnetic simulation in both time and frequency domains on volume and surface meshes, such as the CST Microwave Studio. Particularly, this tool uses, in simulations, the perfect boundary approximation (PBA) and the thin sheet technique (TST) to increase the modeling precision in comparison with the conventional software (Chung, 2001). The electromagnetic parameters can be deduced from the scattering parameters (De Paula et al.; ASTM, 2001; Nicolson and Ross, 1970; Weir, 1974; Agilent Technologies, 1985). For this, the boundaries of the material under test (MUT) are defined and afterwards the S parameters can be accurately known. The following equations relate the parameters S11 (scattering parameter related to the radiation emission from port 1 and collect in port 1) and S21 (scattering parameter related to the

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Paula, A.L., Rezende, M.C., Barroso, J.J.

radiation emission from port 1 and collect in port 2) (Fig. 1) to the reflection and transmission coefficients Γ and T, respectively. These equations allow to solve the boundary-condition problem at l = 0 (l is the line of air) and l = d (d is the sample thickness) (Fig. 1), such that the reflection coefficient can be expressed as Eq. 1 and 2 (ASTM, 2001; Nicolson and Ross, 1970): ī=K±¥k2±



(

1 = ȁ2

ȝr =

{S112(Ȧ) – S212(Ȧ)}+1 2S11(Ȧ)



(2)

The transmission coefficient is given by Eq. 3: T=

{S11(Ȧ) + S21(Ȧ)}–ī 1–{S11(Ȧ) + S21(Ȧ)}ī



(3) ছr =

From Eq. 1 and 3, auxiliary variables (x and y) are defined as follows (Eq. 4 to 7) (ASTM, 2001; Nicolson and Ross, 1970):

( (

ȝ 1+ī x= r = 1–ī ছr

y = ȝ r . İr =

2



(4)

{ ( ({ c ln 1 ȦG T

ȝr =¥[Â y

1

Ȝ

2 0

Ȝ

2 c

1

=–

2



(5)



(6)

1+ī

ȁ – ī

(

1 ȁ

(

1 Ȝ20

1

Ȝ2c

2

ʌG

1n

1



(8)

T

(

Ȝ02

1 Ȝ2c

(



(9)



(10)

Where, λ0 is the free space wavelength and λc the cutoff wavelength of the guide. Since the material is a passive medium, the signal of the square root in Eq. 1 is determined by the requirement that Re(1/Λ)>0. It is also noted that Eq. 9 and 10 can be applied for measurements using a coaxial sample holder, for which λc → ∞.

=0

Port 1

=d

V2 + V2

V1

Source



ȝr

Vin y ছr = x ¥

( [ ( ([

2

ছr Âȝr

(1)

where: K=

For measurements using a rectangular waveguide sample holder, Eq. 4 and 5 can be rewritten as Eq. 8, 9 and 10 (ASTM, 2001; Nicolson and Ross, 1970):

V1 , I 1

(7)

Z0

V2 , I 2

Port 2

V3+ Detector

V3 , I3

ZS air

Z0 air

where,

d

c = speed of the light in the free space; μr = relative permeability of material; Ɛr = relative permittivity of material; ω = angular speed. 60

Sample Figure 1: Waveguide filled with material. (Z0 is the impedance of air, ZS is the impedance of the material, Vn (n= 1, 2, 3…) is the voltage, In (n= 1, 2, 3…) is the intensity, n is the interface between the means, d is the sample thickness and l is the thickness of line of air (ASTM, 2001; Nicolson and Ross, 1970). J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 59-64, Jan. - Apr., 2011


Experimental measurements and numerical simulation of permittivity and permeability of Teflon in X band

One methodology that makes use of the scattering parameters S11 and S21 to calculate the mentioned complex parameters of samples is named Nicolson-Ross-Weir (NRW) (Nicolson and Ross, 1970; Weir, 1974). The NRW modeling is the most common used method to perform the calculation of complex permittivity and permeability of materials. This modeling has the advantage of being non-interactive (no interactive procedure is needed), as required in the Baker-Jarvis method (Baker-Jarvis et al., 1993). Besides this, the NRW modeling is applicable for coaxial line and rectangular waveguide cells. On the other side, it is known that the NRW can diverge for low-loss materials at frequencies corresponding to integer multiples of one half wavelength in the sample (Nicolson and Ross, 1970; Weir, 1974). At this particular frequency, the magnitude of the measured S11 parameter is particularly smaller (thickness resonance) and the S11 phase uncertainty becomes larger. This behavior can lead to the appearance of inaccuracy peaks on the permittivity and permeability curves. Considering the knowledge importance on the complex permittivity and permeability of materials aiming the adequate characterization of them and new developments, the present work presents a study involving measured and simulated complex permittivity and permeability of a Teflon® (polydifluoroethylene) test sample with 11.75 mm thick. Herein, the experimental complex parameters were retrieved using the NRW modeling. Simulated frequencydependent quantities were obtained by CST tool and these results are compared with experimentally measured values in the 8.2-12.4 GHz frequency range (X-band).

Teflon ·

Network analyzer HP 8510 C

S Parameters (S11 and S21)

NRW modeling

Calculation of İr and ȝr Figure 2: Flow chart of complex permittivity and permeability experimental measurements.

MATERIALS AND METHODS Experimental Measurements

Figure 3: Waveguide calibration set for X band.

In this study, the experimental methodology was performed according to the steps depicted in Fig. 2. For this, it was assembled a setup including an automatic vector network analyzer (VNA) HP8510C, which was connected as a source and measurement equipment. During calibration, standard setup values must be stored, so that when making calibration, the measured and reference values are compared to characterize measurement systematic errors (ASTM, 2001). The calibration also establishes the reference planes for the measurement test ports. Figure 3 shows the calibration X band kit used in this paper. To determine the complex permittivity and permeability, via S-parameters (S11 and S21), it was used the two-port transmission/reflection approach, with a material-undertest (Teflon® sample with 11.75 mm thick) of smooth flat faces, and filling completely the fixture cross section, being placed inside a rectangular waveguide (Fig. 4). The

Figure 4: Setup for measurements of S-parameters.

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Paula, A.L., Rezende, M.C., Barroso, J.J.

sample holder is a precision waveguide section of 140 mm length, which is provided with the calibration kit. When measuring the scattering parameters, the offset, placed between ports 1 and 2, is closed with the sample holder. The adapter of port 1 is taken as the reference plane (Fig. 4).

Teflon® sample were based on the literature (εr = 2.04-0.0j and µr = 1.0-0.0j) (ASTM, 2001).

After the S-parameters measurements, the complex parameters (ε* and µ*) were calculated according to the NRW modeling, as depicted in Fig. 2.

Based on the complex parameters from literature (ASTM, 2001) and on the scattering matrix defined in this study (Fig. 6), the MS-CST tool was used to simulate the scattering parameters S11 and S21 of the Teflon® sample. Afterwards, from the magnitude and phase values of the simulated parameters, the complex parameters were retrieved according to Fig. 5.

Numerical Simulations

RESULTS AND DISCUSSION

The numerical simulations were carried out according to flow chart presented in Fig. 5. In this case, the electromagnetic parameters were deduced from a scattering matrix defined between the sample planes (marked in red), as shown in Fig. 6. The used complex parameters for the

Measured and calculated scattering parameters of a Teflon® test sample with thickness of 11.75 mm are compared in Figs. 7 and 8. In Fig. 7, the experimental and numerical S21 parameters both coincide and they are near 0 dB level in magnitude. Experimental and numerical S21 parameters related to the inversion of phase also show

START in CST Teflon· İr= 2.04-0.0j ȝr=1.0-0.0j

S-Parameters in Magnitude and Phase S11 S21 in CST

[S

2 11

[

– S212 + 1

Use following S-Parameters S11 S21 of CST

K=

Calculate Reflection Coefficient

ī=

K (3Q– 1

Calculate Transmission Coefficient

T=

{S + S { – ī 1 –{S + S { ī

2 11

2S

11

21

11

Calculate Permeability

21

1+ ī

ȝr =

( (

ȁ(1– ī

1

Ȝ20

Calculate Permittivity

ছr =

(

1 ȁ2

1

Ȝ2c

(

1

Ȝ2c

Ȝ02

ȝr

Figure 5: Flow chart of the numerical simulation used in the complex permittivity and permeability calculation. 62

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Experimental measurements and numerical simulation of permittivity and permeability of Teflon in X band

a good agreement (Fig. 8). The scattering parameter S11 (experimental and numerical) shows a resonance at the 10.04 GHz frequency (Fig. 7), but it is also observed a slight difference in the maximum amplitude value, in which the simulated S11 resonance presents a higher attenuation value (~-55 dB) than the experimental one (~-45 dB). To understand this difference is important to mention that the simulation configuration depicted in Fig.  6 takes place in an ideal environment, where temperature, humidity, misalignment, and air gap effects are not taken into account.

A/m

A careful analysis of Fig. 8 shows that measured and simulated S11 curves in phase present any difference, where the simulated S11 curve bends downward in the frequency range of ~10.1 to ~10.7 GHz. This behavior is attributed to the actual interaction of the electromagnetic wave with the material in phase (Fig. 8), considering that the simulation takes place in an ideal environment, as already mentioned. Then, based on the NRW procedure, the S-parameters were used to determine ε* and µ*, which are given in Figs. 9 and 10, respectively. In a general way, these figures show that the agreement between measured and simulated quantities is quite satisfactory, except for the calculated ε'. These results allow to infer that the bending effect on

5-9 5-16 4-43 3-69 2-95 2-21 1-48 0-738 0

V/m 1563 1367 1172 977 781 586 391 195 0

Sample

Figure 6: Configuration modeling of electric and magnetic fields in X band rectangular waveguide. Sample planes are marked in red line. In the scale: red means a greater interaction of the electrical (A/m scale) and magnetic (V/m scale) fields with the sample (material), and green means a lower wave-sample interaction.

Thickness 11.75mm S Parameter in Phase in Degree

Sample

180 150 120 90 60 30 0 -30 -60 -90 -120 -150 -180

S11E S21E

S11S S21S

8.4 8.8 9.2 9.6 10.010.410.811.211.612.012.4 Frequency in GHz

Figure 8: Experimental and simulated parameters of S11 and S21 in phase of Teflon® with 11.75 mm thickness (E experimental and S - simulated).

Thickness 11.75mm 2.5 2.5

2 -10 -20 -30 -40

2

1.5 1.5

S11 E S21 E

S11 S S 21S

-50

഍' and ഍'' ' and "

S Parameters in Magnitude in dB

0

11

഍' measured ' measured ഍'' measured " measured ' calculated ഍' calculated " calculated ഍'' calculated

0.5 0.5 00

-0.5 -0.5

-60 8.4 8.8 9.2 9.6 10.0 10.4 10.8 11.2 11.6 12.012.4

-1 -1 88

8.5 8.5

9.5 9.5

10 10

10.5 10.5

Frequency in GHz

11 11

11.5 11.5

12 12.5 12.5 12

Frequency in GHz

Frequency in GHz

Figure 7: Experimental and simulated parameters of S11 and S21 in magnitude of Teflon® with 11.75 mm thickness (E - experimental and S - simulated).

99

Figure 9: Test sample complex permittivity ε* = εʹ ‒ jεʺ : measured (red curves) and calculated (blue curves) using the NRW modeling.

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Paula, A.L., Rezende, M.C., Barroso, J.J.

CNPq (Project no. 305478/2009-5) for the financial supports.

1.5 1.5

0.5 0.5

+ ' and + "

µ' and µ''

11

REFERENCES Agilent Technologies, “Measuring the dielectric constant of solids with the HP 8510 network analyzer”, Technical Overview 5954-1535.USA, 10p., 1985.

00

-0.5 -0.5

+µ' ' measured measured

+µ'' " measured measured

-1-1

+µ' ' calculated calculated

+µ'' " calculated calculated

-1.5 -1.5

8

8.5

9

9.5

10

10.5

11

11.5

12 12.5

Frequency in GHz

Figure 10: Test sample complex permeability μ* = μʹ - jμʺ: measured (red curves) and calculated (blue curves) using the NRW modeling.

the simulated S11 curve, which was observed in Fig. 8 (in the frequency range of ~10.1 – 10.7 GHz), is translated into a decrease of ε' and µ` at higher frequencies (Figs. 9 and 10).

American Society for Testing and Materials, “ASTM D5568-1: Standard Test Method for measuring Relative Complex permittivity and Relative Magnetic Permeability of Solid Materials at Microwave Frequencies”, West Conshohoken, PA: ASTM, 2001. Baker-Jarvis, J., Janezic, M. D., Grasvenor Jr., J. H., and Geyer, R. G., “Transmission/Reflection and ShortCircuit Line of Methods for Measuring Permittivity and Permeability”, NIST Technical Note 1355-R, Colorado, 1993, from http://whites.sdsmt.edu/classes/ee692gwmm/ additional/NIST_Tech_Note_1355-R.pdf. Chung, B. K., “Dielectric constant measurement for thin material at microwave frequency”, Progress in Electromagnetics Research,Vol., No. 75, pp. 239-252, 2007.

CONCLUSION The comparative study of the electromagnetic parameters of a Teflon® slab shows a good agreement between measured and simulated complex permittivity and permeability, which were retrieved using the NRW modeling. From these results, it is possible to conclude that the used procedure guarantees an accuracy experimental characterization of materials and their simulation. It was also noted that the tested procedure proved to be robust, and no anomalies were noticed because resonance for the 11.75-mm-thickness sample occurs above 10.04 GHz. This result overcomes a possible disadvantage of using the NRW modeling, as previously mentioned in this text.

CST MICROWAVE STUDIO. Version 3 Getting Started, Jan.2001, CST Computer B.-K Chung, “Dielectric constant measurement for thin material at microwave Simulation Technology”. De Paula, A. L., Rezende, M. C., Barroso, J. J., Pereira, J. J. and Nohara E. L., “Comparative Study of S parameters of the Teflon® obtained experimentally and by Electromagnetic Simulation”, Symposium on Operating Systems Application Areas of Defense, São José dos Campos, Brazil, 2008.

ACKNOWLEDGMENTS

Nicolson, A. M., Ross, G. F., “Measurement of the Intrinsic Properties of Materials by Time Domain Techniques”, Instrumentantion and Measurement, Vol. 19, pp.377-382, 1970. doi: 10.1109/TIM.1970.4313932 

The authors are thankful to the Aerospace Technology and Science Department (DCTA, acronym in Portuguese), Institute of Aeronautics and Space, Financiadora de Estudos e Projetos – FINEP (Project No. 1757/03) and

Weir, W.B., “Automatic Measurement of Complex Dielectric Constant and Permeability at Microwave Frequencies”, Proceedings of the IEEE, Vol. 62, pp. 3336, 1974.

64

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doi: 10.5028/jatm.2011.03010411

Gilson da Silva* National Industrial Property Institute Rio de Janeiro – Brazil gilsondasilva@uol.com.br

Elizabeth da Costa Mattos Institute of Aeronautics and Space São José dos Campos – Brazil elizabethecm@iae.cta.br *author for correspondence

Synthesis of 2,4,6-triamino-1,3,5trinitrobenzene Abstract: The 2,4,6-triamino-1,3,5-trinitrobenzene (TATB) is perhaps the most thermostable and insensitive explosive known. Its low sensibility to shock makes it suitable for military and civil applications. TATB application is done either alone or in combination with another high energetic material. This study aimed at reporting the review about many processes to produce TATB and the problems associated with them, as well as suggest techniques like Fourier Transform Infrared Spectroscopy (FT-IR) and Differential Scanning Calorimetry (DSC), which can be useful in the characterization of this energetic compound. Keywords: TATB, Fourier Transform Infrared Spectroscopy, Differential Scanning Calorimetry, Plastic-bonded explosive.

LIST OF SYMBOLS TATB HE PBX HMX RDX TCB TCTNB DCA NMP VNS DMSO ATA DATB DAP FT-IR DSC HNS PETN

2,4,6-triamino-1,3,5-trinitrobenzene high explosive plastic-bonded explosive octogen hexogen 1,3,5-trichlorobenzene 1,3,5-trichloro-2,4,6-trinitrobenzene 3,5-dichloroanisole N-methylpyrrolidinone vicarious nucleophilic substitution dimethyl-sulfoxide 4-amino-1,2,4-triazole diamino-trinitrobenzene diaminopicric acid Fourier Transform Infrared Spectroscopy Differential Scanning Calorimetry 2,2’, 4,4’, 6,6’-hexanitrostilbene pentaerythritol tetanitrate

Introduction Insensitive explosives have been receiving a great deal of attention in connection with low vulnerability. The high energy content and low sensitivity are intrinsically connected to the size, shape and defects of the crystals, as well as the molecule’s structure and compatibility with the binder. The 2,4,6-triamino-1,3,5-trinitrobenzene (TATB) is an explosive with a high melting point and thermal stability, it has been applied in situations where insensitivity to Received: 16/02/11 Accepted: 15/03/11

impact hazards is important. Other potential applications include the use of TATB as the booster or main charge explosives for down-hole oil perforation at elevated temperature surroundings (Lee, 1996). TATB is a high explosive (HE) that can be combined with plastic binder to produce a plastic-bonded explosive (PBX) composition, which is heat-resistant and highly insensitive. It is insoluble in organic solvents and has a melting point above 400oC. TATB was firstly prepared in 1888 by Jackson and Wing, in agreement with Akhavan (2004), from tribromotrinitrobenzene. It has also been prepared on a laboratory scale from 2,4,6-trinitrotoluene through selective reduction of the 4-nitro group, nitration to pentanitroaniline, and, then, ammonolysis. Among the various insensitive HEs, TATB is an attractive insensitive explosive as it satisfies the safety requirements at high temperatures, and it is resistant to accidental initiation and explosion (Boddu et al., 2010). This is perhaps the most thermoresistant insensitive explosive, and it can be used in modern warheads in the military and in deep oil well explorations. Table 1 shows its properties. Table 1: Properties of TATB (Meyer, 2007)

Characteristics Color Form Molecular weight/g.mol-1 Melting temperature/oC Decomposition temperature/oC Thermal ignition temperature/oC Crystal density at 20oC/g.cm-3 Energy of formation/kJ.kg-1 Enthalpy of formation/kJ.kg-1 Oxygen balance Nitrogen content

J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 65-72, Jan. - Apr., 2011

Yellow-brown Crystalline solid 258.1 350 350 384 1.93 -425 -597.9 -55.80% 32.60% 65


Silva, G., Mattos, E.C.

The presence of impurity and by-product of synthesis process can bring serious compatibility problems when using TATB in certain types of ordinance, as well as in the use of other HE like octogen (HMX) and hexogen (RDX). Therefore, the production process must be carefully studied and its influence, evaluated.

Synthesis TATB can be manufactured by the nitration of 1,3,5trichlorobenzene (TCB) to 1,3,5-trichloro-2,4,6trinitrobenzene (TCTNB) and the amination of TCTNB to TATB. The major impurity brought in this process is ammonium chloride, which is a by-product, and smaller amounts of tetrachlorodinitrobenzene partial amination. The presence of these amounts of ammonium chloride can produce serious compatibility problems in the use of TATB. Benziger (1977) found that TCTNB is highly resistant to hydrolysis and the presence of a sufficient amount of water during the amination of TCTNB to TATB results in a TATB product, which is essentially free of ammonium chloride. Then, Benziger (1977) developed a process comprising the nitration of TCB to TCTNB followed by amination to TATB, where, in the amination step, sufficient water can be added to the solvent for the TCTNB to rend the ammonium chloride to a semideliquescent condition. The process is conducted in toluene as a solvent, in the ratio of about ten parts toluene to one part TCTNB by weight, and in the presence of about 2.5% by weight of water in the toluene. The process described by Benziger (1977) is conducted in a Pfaudler reactor, which is capable of operating over a range of 20 to 150oC, with 0.69 MPa pressure; agitation is provided by an anchor-type blade at speeds from 20 to 200 rpm. A glass-lined, concentric tube reflux condenser, integral with the Pfaudler reactor is also used. The reactor is charged with 56.7 kg of oleum, 7.2 kg of sodium nitrate is then added at slow rate, with full agitation with the jacket cooling kept in 60 to 70oC. After finishing the NaNO3 addition, the contents of the reactor are brought to a temperature of 100oC. The reactor is charged with 2.5 kg of TCB, and the jacket temperature increased quickly to 145-155oC and kept for four hours. The contents of the reactor are cooled to 40oC and discharged in a recipient with 113 kg of crushed ice. Full agitation is provided in this step with a vacuum pump to remove the nitrous fumes. The TCTNB precipitates in the form of heavy white crystals that are pumped through the plate and frame press. The cake is washed with a lot of water until the wash water 66

gets pH 6-7, it is also dried in open trays in a forceddraft oven at 60oC, for 16 hours. The amination step is conducted with 2.7 kg of TCTNB dissolved in 27 kg of toluene, where 6.8 kg of water (2.5%) is added. After being clarified by filtration using Celite filter, the reactor system is sealed, and heating is continued until the contents are at 145oC. The jacket steam is turned off at this time and ammonia gas is added to the gas phase in the reactor, through an opening on the top of the kettle, in the ratio of 0.36 kg/h. When the NH3 overpressure reaches about 34 kPa, the reactor system is purged of residual air by venting through the reflux condenser. The system is then resealed and the reaction gone about three hours with moderate agitation, temperature at 150oC and the pressure remained at 240 to 270 kPa. The termination of the amination reaction is marked by a sharp rise in the system pressure to about 413 kPa. The NH3 flow is stopped, the system is cooled to about 60oC and vented, water is added with good agitation. The TATB can be recovered by filtration using the plate and frame press, equipped with cotton cloths backed with filter paper. The cake is washed three times with water and dried in open trays in a forced-draft oven at 100oC for 16 hours. The water addition can reduce the chlorine to 0.20%, instead of the 0.60% of Cl found in the product without the water addition. When water is present, the only change in process conditions is a moderate increase in system pressure. Benziger (1984) taught a method of making fine-grained TATB, where the energetic material shows increased sensitivity over TATB produced by previously known method, and it does not require grinding of the TATB as a final step. The method comprises the amination of TCTNB while dissolved in an emulsion of organic solvent, preferably toluene, in water. The emulsion includes a protective colloid, and is prepared with the water volume being greater than the toluene volume, so the water is the continuous phase and the toluene is the dispersed one of the emulsion. Amination is preferably conducted by introducing gaseous ammonia into the emulsion. The particle size of the product TATB is effectively controlled by the size of the toluene droplets in the emulsion. Ammonium oleate can be used as an emulsifying agent, and the emulsion is prepared in situ by the reaction between oleic acid and gaseous ammonia. The TCTNB, which will be aminated, is insoluble in water and, soluble in toluene. Then, in an emulsion consisting on toluene droplets dispersed in water, TCTNB added to the emulsion will reside in the toluene droplets and the size of the TCTNB-containing toluene droplets determines the maximum size of the TATB particles, which are

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Synthesis of 2,4,6-triamino-1,3,5-trinitrobenzene

formed upon the TCTNB amination. The method is preferably conducted using an emulsion, containing from approximately 50 to 75% by volume water, with the remainder preferably consisting on toluene. Ott and Benziger (1991) proposed the preparation of TATB from 3,5-dichloroanisole, in which the nitration of 3,5-dichloroanisole (DCA) under relatively mild conditions gave 3,5-dichloro-2,4,6-trinitroanisole in high yield, and purity followed by the ammonolysis of this latter compound to give the TATB. Another route is to first chlorinate this intermediate to give 1,3,5-trichloro-2,4,6-trinitrobenzene, which can be ammonolyzed to produce TATB. The conditions necessary to effect the introduction of the third nitro group into the trichloro compound starting material, 1,3,5-trichlorobenzene, to produce 1,3,5-trichloro-4,6-trinitrobenzene, are quite severe. An excess of 90 to 95% nitric acid (4.35:2 ratio mol) and 25 to 30% oleum (20 mol) are used at a reaction temperature of 150oC, with vigorous stirring for 2.5 hours. After quenching the mixture with water, the product was isolated in 91% yield, 89% purity. The conversion was 0.80 mole of 1,3,5-trichloro-4,6-trinitrobenzene per mole of 1,3,5-trichlorobenzene. The ammonolysis step can be conducted without removing the by-products. The nitration of 3,5-dichloroanisole has the activating effect of the methoxyl group on electrophilic aromatic substitution. Then, the process shows excellent yield at lower temperature (100oC), without the need of nitric acid excess or the use of oleum and the complete conversion of the starting material were obtained when the excess of nitric acid was merely 5% over the stoichiometric amount in 125oC of temperature for two hours. The displacement of the chlorine and methoxy groups of 3,5-dichloro-2,4,6-trinitoanisole by ammonia occurred to give TATB. Ammonolysis of the reactions using limited amounts of ammonia give a mixture of TATB and starting materials 1,3,5-trichloro-4,6trinitrobenzene or 3,5-dichloro-2,4,6-trinitroanisole, with only very small quantities of mono- and diamino compounds. However, from reactions in which mixtures of 1,3,5-trichloro-4,6-trinitrobenzene and 3,5-dichloro2,4,6-trinitroanisole were treated with limited quantities of ammonia, it was found that 3,5-dichloro-2,4,6trinitroanisole reacted several times faster then 1,3,5trichloro-4,6-trinitrobenzene. Ammonolysis at low temperature results in TATB precipitating as extremely small crystals. Nevertheless, this reaction does not occur at low temperatures, since ammonium chloride is insoluble in toluene, and when better solvents for the chloride, such as dimethylformamide or dimethyl

sulfoxide, are employed, or added to the toluene, the yield of TATB is substantially reduced, even at low temperatures. Figure 1 shows the reactions sequence. Lee and Kennedy (2002) described a method for producing fine-grained TATB powders with improved detonation-spreading performance and, hence, increased shock sensitivity when compared with that for ultrafine TATB. The method consists on a single-step amination of trichloro-trinitrobenzene using ammonium hydroxide solution in a sealed vassel, where a solution of trichlorotrinitrobenzene in a solvent is ultrasonically mixing and a solution of ammonium hydroxide in a cooled, sealed vessel such that an emulsion of triaminotrinitrobenzene is formed; and separating the triamino-trinitrobenzene from the emulsion. During the step of ultrasonically mixing the solutions, the temperature is maintained between 1 and 15oC. A solution of TCTNB in toluene is added to an ammonium hydroxide solution in an air-scaled sonication reactor, having a sonicator horn powered by a 20 kHz (275330W), with the horn disposed below the liquid level, between 10 and 40 minutes. The TATB was collected by filtration, washed sequentially with water, toluene and acetone, and dried in an oven. The material produced has approximately 6 Âľm median particle diameter, and increased shock sensitivity. A method to convert surplus nitroarene explosives (picric acid, ammonium picrate) into TATB is proposed by Mitchell et al. (2005). This method consists on three steps where the picric acid or ammonium picrate is converted into picramide; the latter is converted into TATB; and the last step is the purification of TATB. Picramide is formed by suspending picric acid or ammonium picrate with an ammonium salt in a dipolar aprotic solvent, and then heating the suspension under low pressure. The mole equivalents of ammonium salt to picric acid ranges from 2 to 30 and the mole equivalents of ammonium salt to ammonium picrate ranges from 1 to 30. The suspension is typically heated between 2 to 22 hours to temperatures in the range of 175 to 185oC, under 138 to 552 kPa of pressure. The reaction of picric acid or ammonium picrate with an ammonium salt in dipolar aprotic solvents, such as sulfolane or N-methylpyrrolidinone (NMP), for several hours at 175-185oC, followed by a water wash, produces picramide, which is free of cyanuric acid and ammonium salts. Ammonium hydroxide (28% NH3 in H2O) is unsatisfactory for use like a NH3 reagent, as picric acid/ammonium picrate is decomposed to black solids when exposed to the ammonium hydroxide. A

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good conversion of ammonium picrate or picric acid to picramide (87-94%) can be obtained when the ammonium salt is diammonium hydrogen phosphate [(NH4)2HPO4] or ammonium carbamate (NH4CO2NH2), and the substrate concentrations are between 1.1 to 2.5 M. The picramide obtained in these syntheses can be used, without purification, to produce TATB.

Hydroxylamine in combination with a strong base, an aprotic dipolar solvent (DMSO) and an elevated temperature (65-95oC), reacts with picramide to yield TATB in 50 to 74% yield with about 97% purity. The concentration of picramide is typically 0.1 to 0.25 M, which gives rise to highly viscous reaction suspensions.

The conversion of picramide to TATB using vicarious nucleophilic substitution (VNS) chemistry depends on the particular reagent employed, where the partial or full replacement of DMSO (dimethyl-sulfoxide) with less expensive solvents can be done. The VNS synthesis involves heating a VNS reagent with picramide in the selected solvent/solvent mixture and heating to reflux temperatures, while concomitantly distilling off the solvent.

DMSO is an effective solvent in the vicarious nucleophilic substitution synthesis of TATB. The substitution of DMSO by methanol or toluene as methanol-toluene mixtures predictably provides TATB in lower yield and contaminated with DATB from the incomplete amination of picramide. Reaction of picramide with 4-amino-1,2,4-triazole (ATA) in methanol (60oC) in the presence of sodium methoxide provides primarily DATB and little or no TATB.

Figure 1: Reactions sequence of Ott and Benziger process.

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Synthesis of 2,4,6-triamino-1,3,5-trinitrobenzene

The low solubility of TATB in most solvents is the problem of purification process. Impure TATB contains from 1 to 15% of impurities that can be eliminated by converting impure TATB preparations to relatively soluble derivatives, which, after purification, are converted to purified TATB by ammonolysis (from 90 to 130oC for 0.5 to 4 hours). Figure 2 shows the reactions sequence of the method proposed by Mitchell et al. (2005).

with 1,1,1-trimethylhydrazinium chloride, a more active vicarious nucleophilic substitution reagent, affords DAP in 91% yield. DAP is heated in aqueous base (e.g., alkyl hydroxide) and acidified to yield trinitrophloroglucinol (TNP) in 84% yield. TNP can be used to produce TATB by means of Wolff-Limbach or Bellamy syntheses. Although, DAP can be directly converted to TATB by its reaction with diammonium hydrogen phophate.

In another publication, Mitchell at al. (2006) taught a method to convert surplus nitroarene explosives, such as picric acid and ammonium picrate in trinitrophloroglucinol and TATB. The process is conducted directly by amination of picric acid by vicarious nucleophilic substitution of hydrogen yield diaminopicric acid. Treatment of diaminopicric acid with sodium hydroxide in water or water DMSO mixtures produces, upon neutralization with acid, trinitrophloroglucinol and its subsequent conversion into TATB.

Picric acid (1.20 mmol) and 1,1,1-trimethylhydrazinium halide (6.00 mmol) are dissolved in a mixture of DMSO (3.6 mL) and toluene (4.8 mL) and a 25% by weight of sodium methoxide solution in methanol (3.00 mL, 13.1 mmol) is added. The suspension formed is stirred and heated from room temperature to 95oC over one hour, after that, being cooled to 4oC, treated with glacial acetic acid (14 mL) and warmed to room temperature with stirring. The precipitated material is collected and washed with acetic acid and water giving, after vacuum drying (80oC), 0.176 g of diaminopicric acid.

The picric acid, ATA and sodium methoxide react in a mixture of methanol, toluene and DMSO to produce diaminopicric acid (DAP) in 68% yield. But, the replacement of ATA

Diaminopicric acid (0.748 mmol) and diammonium hydrogen phosphate (7.50 mmol) are suspended in dry sulfolane (3 mL), and they are stirred. The suspension

Figure 2: The three-step conversion of picric acid or ammonium picrate to TATB.

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is heated with stirring from room temperature at 177oC over two hours and kept in this condition for six hours. The reaction system is cooled to 4oC and the resulting suspension is mixed with water (40 mL). The precipitated product is collected, washed with water and dried to yield TATB in the form of a brown solid (80%). The process is represented in Fig. 3.

Characterization The molecular structure of TATB crystal is triclinic. Strong hydrogen bonding is indicated by the lack of a distinct melting point and the almost total insolubility of TATB in common solvents. The only suitable solvent seems to be concentrated sulfuric acid (H2SO4). The inorganic impurity NH4CI is trapped within the TATB crystal as discrete crystals (Dobratz, 1995). This structure is similar to that of graphite, which indicates anisotropy for all directionally dependent properties. This effect is particularly obvious in thermal expansion and thermal cycling (Dobratz, 1995). In agreement with Schmidt, Mitchell and Pagoria (1998) study, chemicals analysis such as nuclear

magnetic resonance (NMR) or chromatography are not practicable to TATB, due its low solubility in most solvents. Then, Fourier Transform Infrared Spectroscopy (FT-IR) can be applied to the quantification of this HE. The amine N-H stretching modes in TATB produce two characteristic absorptions at approximately 3225 and 3325 cm-1, while those for DATB occur at 3360 and 3390 cm-1, using Nujol mull preparations for the samples. Schmidt, Mitchell and Pagoria reported yet the detection of DATB in TATB at concentrations of 1% or greater by means of FT-IR. The Differential Scanning Calorimetry (DSC) thermogram of the TATB presents an exothermic peak between 360 and 390oC with the maximum peak in 385oC, related by Boddu et al. (2010) as the thermal decomposition of the material, showing its excellent thermal stability in respect to the others HE (for example: 285oC to HMX , 241oC to RDX and 318oC to HNS). An efficient characterization routine can be the application of the elementary analysis, FT-IR and thermal analysis (DSC and TG), by means of the results comparison with a standard material, as shown by Silva

Figure 3: The production process of TATB by conversion of surplus nitroarene (Mitchel et al., 2006)

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Synthesis of 2,4,6-triamino-1,3,5-trinitrobenzene

(2006) and Mattos (2004) used for characterization of HNS and HMX, respectively. Performance Benziger (1976) taught a highly insensitive and heatresistant PBX containing 90% by weigh of TATB and 10% by weigh of a fully saturated copolymer of chlorotrifluoroethylene and vinylidene fluoride, using a slurry process. In agreement with his study, the Kel-F 800® or Kel-F827® are the preferred binder, because they are chemical resistant, they have thermal stability, high density, elastomeric properties, and solubility characteristics enabling the use of the slurry process in preparing molding powder. A slurry of TATB in water is prepared by mixing powdered TATB in water. A Kel-F 800 lacquer is prepared by dissolving of Kel-F 800 in butyl acetate. The TATB/water slurry is heated to 75oC, with agitation, and the Kel-F 800 lacquer heated to 40oC is added. The resultant dispersion is heated with a steam sparger to distill the solvent as the butyl acetate/water azeotrope. The sparger is used to reduce the supposed heating surface, because during the formation of the molding powder granules, the mixture adheres strongly to heated surfaces. The degree of the dispersion agitations also effects particle size. Then, the agitation is preferentially reduced during the solvent removal step. The dispersion is then cooled to 40oC and filtered. Finally, the resultant powder is dried at 100oC in a forced draft oven. This produces a material with 90% by weight of TATB and 10% by weight of Kel-F 800, having a bulk density of approximately 0.9 g/cm3. A density of 1.920 g/cm3, 98.7% of the theoretical maximum density, can be obtained by pressing larger pieces at 120oC and 137.9 MPa psi. A high performance explosive composition was taught by Hildebert and Pierre (1992), this composition can be prepared by mixing 40 to 60% by weight of TATB, 35 to 58% by weight of a second explosive (chosen among HMX, RDX, PETN and HNS) and 2 to 5% by weight of a thermoplastic binder chosen in the poly-ether phenolic group, whose vitreous transition temperature is between 70 and 120oC and the dilatation coefficient is equal or higher than 6.105/oC. In agreement with them, the composition shows sensibility in the same level than the second explosive, but the security is almost the same of the TATB. The binder improves the tensile strength and mechanical properties of the composition. The binder should be soluble in an organic solvent immiscible in water. A lacquer is produced by the polymer

addition in the organic solvent. The two explosives are dispersed in water and, after that, the lacquer is introduced in the explosive suspension. The organic solvent is eliminated by means of the increment in the system temperature (evaporation). A filter should be used to separate solid particles of the explosive to the liquid portion. These solid particles are dried and the warhead is produced by means of the melting and compression of them in a cast (120 to 140oC and 180 to 220 MPa).

FINAL CONSIDERATIONS The analysis of the synthesis processes studied shows several possibilities for the starting material in the TATB’s synthesis. Obviously, the choice of the reagents must be made considering not only the cost, but also the activating effect of each radical in the aromatic ring, which reduces the complexity of the synthesis mechanism and increases, typically, the reaction rate. Particularly, the synthesis of TATB in an emulsified system may be advantageous, since, due its low solubility, the recrystallization process (commonly performed in HE) can be complex and inefficient, hence the advantage of obtaining the reduced size of TATB particle. As noted, the energy performance of TATB is suitable for its use in warheads, even when its use is done in association with other HE. The literature also provides information for the appropriate characterization of the material.

REFERENCES Akhavan, J., 2004, “The Chemistry of Explosives”, 2nd Edition, The Royal Society of Chemistry, Cambridge, pp. 43-44. Boddu, V.M., Viswanath, D.S., Ghosh, T.K. and Damavarapu, R., 2010, “2,4,6,Triamino-1,3,5trinitrobenzene (TATB) and TATB-based formulations – A review”, Journal of Hazardous Materials, Vol. 181, 1-8. Benziger, T.M., 1976, “Insensitive explosive composition of halogenated copolymer and triaminotrinitrobenzene”, U.S. Patents 3,985,595. Dobratz, B M., 1995, “The Insensitive High Explosive Triaminotrinitrobenzene (TATB): Development and Characterization – 1888 to 1994”, Los Alamos National laboratory L.A- 3014-H. Hildebert, K., Pierre, C., 1992 “Composition explosive at procédés de préparation d’une poudre et d’une pièce de cette composition”, Institut National de la Propriété Industrielle, FR2671549.

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Lee, K.Y., 1996, “Sonochemical Synthesis of 1,3,5triamino-2,4,6-trinitrobenzene TATB”, Los Alamos National laboratory L.A- UR 96-971.

Mitchell, A.R. et al., 2006, “Synthesis of trinitrophloroglucinol and triaminotrinitrobenzene (TATB)”, U.S. Patents 7,057,073.

Lee, J.S., Hsu, C.K. and Chang, C.L., 2002, “A Study on the Thermal Decomposition Behaviors of PETN, RDX, HNS and HMX”, Thermochimica Acta, Vol. 392-393, pp. 173-176.

Mitchell, A.R. et al., 2005, “Synthesis and purification of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)”, U.S. Patent Application Publication US2005/0038297.

Lee, K.Y., Kennedy, J.E., 2002, “Synthesis of finegrained TATB”, U.S. Patent Application Publication US2002/0129880. Mattos, E.C. et al., 2004, “Determination of the HMX and RDX content in synthesized energetic material by HPLC, FT-MIR, and FT-NIR spectroscopies”, Química Nova, Vol. 27, No. 4, pp. 540-544. Meyer, R., Köhler, J. and Homburg, A., 2007, “Explosives”, 6th Edition, Wiley-VCH Verlag GmbH, Weinheim, 341p.

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Ott, D.G., Benziger, T.M., 1991, “Preparation of 1,3,5-triamino-2,4,6-trinitrobenzene from 3,5dichloroanisole”, U.S. Patents 4,997,897. Schmidt, R.D., Mitchell, A.R. and Pagoria, P.F., 1998, “New synthesis of TATB process development studies”, Proceedings of the 29th International Annual Conference of ICT, Karlsruhe, Federal Republic of Germany. Silva, G., et al., 2006, “Caracterização de 2,2’,4,4’,6,6’hexanitroestilbeno via análises instrumentais”, Química Nova, Vol. 29, No. 4, pp. 681-684.

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doi: 10.5028/jatm.2011.03019310

Guilherme G. Peixoto* Instituto Tecnológico de Aeronáutica São José dos Campos − Brazil guilhermeggp@iae.cta.br

Mauro Angelo Alves Instituto de Aeronáutica e Espaço São José dos Campos − Brazil pacmauro@yahoo.com

Alberto José de Faro Orlando Instituto Tecnológico de Aeronáutica São José dos Campos − Brazil faro@ita.br

Mirabel Cerqueira Rezende Instituto de Aeronáutica e Espaço São José dos Campos − Brazil mirabelmcr@iae.cta.br *author for correspondence

Measurements in an Outdoor Facility and Numerical Simulation of the Radar Cross Section of Targets at 10 GHz Abstract: This paper presents preliminary data from an ongoing study on the radar cross section (RCS) of targets with simple and complex surface geometries (a flat square plate, a 90° dihedral corner reflector and a retired air-to-air missile). Measurements and computer simulations of these metallic targets were carried out at 10 GHz and also when the surfaces of the targets were completely coated with a radar absorbing material (RAM), consisting of flexible sheets of carbonyl iron dispersed in a silicone rubber matrix. Experimental measurements were obtained in an outdoor facility, and computer simulations were performed using a commercial software package. The main objective of this study was to compare results in order to highlight some of the issues related to the determination of the RCS of an actual target. Additionally, a Brazilian research institute has demonstrated the capability to produce and characterize materials related to the main aspects of RCS research, namely, measurement, simulation, and production of RAM. This paper introduces the reader to the research being carried out in this area at the Materials Division in the Instituto de Aeronáutica e Espaço. Keywords: Radar cross section, Computer simulations, Outdoor measurements, Radar absorbing materials.

INTRODUCTION The community of researchers interested in problems related to the electromagnetic scattering and measurement of radar cross section (RCS) of real-sized targets is now faced with an interesting predicament: should one measure the RCS of a target in an outdoor facility or in an anechoic chamber? Is it acceptable to simulate the RCS of a target using one of the many software packages available in the market? Both approaches have advantages and disadvantages. It can be argued that measurements will always produce more realistic RCS values (provided that equipment and experiment are well designed and of good quality), but these measurements can be quite expensive and logistically difficult to carry out. On the other hand, simulations using computers have become more reliable and the costs are significantly smaller, but the results from simulations depend on the quality of models used and on the simulation software itself; besides, results from computer simulations need to be validated by experimental data. Usually, the researcher may be pressured for choosing one method over another because it is not always possible to count on both methods (experimental and simulation) to determine the RCS of a target.

Received: 26/10/10 Accepted: 15/02/11

In order to better understand the differences between measurements and simulations, the RCS of two targets − a metallic 90° dihedral corner reflector and a retired air-toair missile − was determined experimentally in an outdoor RCS facility and simulated with a commercial software. Also, the RCS of these two targets was measured and simulated after their surfaces were coated with a radar absorbing material (RAM). This paper gives a brief description of the RCS facility, the RAM used, the method of characterization of the RAM, and the software simulation tool. This work is part of an ongoing research project carried out at the Materials Division of the Instituto de Aeronáutica e Espaço on studies of the RCS of complex targets and the production of RAM (Folgueras, Alves and Rezende, 2010; Gama and Rezende, 2010; Peixoto et al., 2009; Silva et al., 2009; Alves, Peixoto and Rezende, 2007a).

EXPERIMENTAL SETUP Experimental data were collected in an outdoor RCS facility (Peixoto et al., 2009; Alves, Peixoto and Rezende, 2007b). Targets are mounted on a rotating table (rotation in azimuth) placed atop an 8-m high pylon. Figure 1 shows an illustration of the pylon together with a study target; the structure is made of steel-reinforced concrete.

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Target

Turntable !

8m

1.4m

Figure 1: Support pylon for radar cross section measurements. Note the presence of a turntable to rotate targets in azimuth.

In order to minimize spurious reflections during measurements, the pylon is completely covered with commercial pyramidal radar absorbers. Figure 2 shows a square aluminum plate (1 m x 1m), used for calibration purposes, mounted on the rotating table and the support pylon covered with radar absorbers. Two radar antennas are mounted on a metal structure and their position is fully adjustable so that they are at the same height as the target. The diameter of the antennas is 1.5 m. The antennas are in a quasi-monostatic configuration, i.e., there is a transmitting and receiving antenna. The distance between the radar antennas and the target is 230 m. The beam width of the transmitting antenna is about 3°. At a distance of 230 m, the radar antenna illuminates the whole pylon, justifying the use of the radar absorber. The electronic circuit used for the RCS measurements consists of emitting and receiving modules. The emitting module is composed of a synthesized microwave generator (Agilent, model E8257D), operating from 250 kHz to 40 GHz and power of 15.85 mW (12 dBm), coupled to a 74

Figure 2: Outdoor radar cross section (RCS) facility. Support pylon used for RCS measurements (background; height, 8 m). The pylon is covered with pyramidal radar absorbers. The radar absorbers are used to cover part of the ground surface (foreground). Atop the pylon, there is a 1 m² metal plate used for calibration of the system.

20 W power amplifier operating from 0.8 GHz to 20 GHz (Amplifier Research, model 20ST1G18). The microwave generator is protected against return signals by an isolator circuit. The radar pulse width can be modulated from 10 ns to 42 s. The amplified signal produced by the generator is coupled to the transmitting antenna. The radar signal scattered by the target is collected by the receiving antenna. The signal is amplified by a low-noise amplifier and sent to a spectrum analyzer (Anritsu, model MS6226C). A DC blocker protects the spectrum analyzer from spurious signals. This system can be used for measurements in the S, C and X bands (2-12 GHz). In this study, measurements and simulations were performed in the X-band (10 GHz). This frequency band is commonly used in radars for the identification and discrimination of targets.

SIMULATION SOFTWARE The RCS of a target can be defined as the area intercepting an amount of electromagnetic power which − when scattered isotropically − produces at the receiver an energy density equal to that scattered by the actual target (IEEE, 1989). The RCS usually depends on many factors, such as the shape and size of the target, polarization,

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Measurements in an Outdoor Facility and Numerical Simulation of the Radar Cross Section of Targets at 10 GHz

frequency and angle of incidence of the radar wave, and the electromagnetic properties of the surface of the target. It can be expressed by Eq. 1 (Knott, Schaeffer and Tuley, 1993): ı = lim 4›r2 ES r' EI

2

2



(1)

where ES is the scattered field; EI is the incident field at the target; and r is the distance between the target and the antenna. The RCS defined by Eq. 1 is often referred to as either monostatic or backscattered RCS. Equation 1 is valid when the target is illuminated by a plane wave (farfield approximation) (Knott, Schaeffer and Tuley, 1993). However, it is important to note that Eq. 1 is deceivingly simple; the calculation of scattered fields using this equation requires the solution of Maxwell’s equations using complicated boundary conditions. Analytical solutions only exist for a small number of objects with simple surface geometry. Therefore, computer simulations are the only means to calculate the RCS of complex targets. There are several software packages in the market to simulate RCS. In this study, CADRCS was used (CADRCS, 2009). This software combines ray-tracing and ray-shadowing techniques with physical optics to calculate the RCS of the target. According to its developers, CADCRS can calculate the RCS of a target larger than the radar wavelength with great accuracy, reproducing results from an actual radar (Essen et al., 2002). Simulations using CADRCS can be carried out under different sets of conditions, such as wave polarization, target reflectivity and surface roughness. A PC running Windows Vista™, with a 2.2 GHz clock and 2 GB RAM, was used for the simulations.

Figure 3: Front and rear views of the CAD model of the airto-air missile. Note the glass dome (light blue) protecting the heat-seeking device, and the rocket nozzle cavity (red).

Figure 4: Side view of the actual air-to-air missile.

The surfaces of the models of the flat plate, corner reflector and missile used in the simulations were meshed with 2,024, 4,096 and 377,000 triangular elements, respectively. The largest dimension of the triangular elements for the missile model was set at 4 mm.

RADAR ABSORBING MATERIAL TARGETS The targets used in this study were a flat square plate, a 90° dihedral corner reflector and a retired air-to-air missile. The flat plate measures 1 m² and is made of aluminum. The corner reflector is made of two 0.5 m x 0.5 m aluminum plates welded together at a 90° angle. Figure 3 shows the CAD model of the missile used in the simulations. Figure 4 shows a photograph of the actual missile. The total length of the missile is 2.84 m, the diameter of the cylindrical body is 0.15 m, and the span of tail wings is 0.66 m. The body, the wings and the fins are made of aeronautical aluminum. In the nose of the missile, there is a heat-seeking device protected by a glass dome. The rocket nozzle is made of a non-metallic heatresistant material.

For this study, the RAM was produced as flexible sheets by the dispersion of industrial-grade high purity carbonyl iron in a matrix of silicon rubber (60/40% in mass, respectively). This formulation resulted in good attenuation of electromagnetic energy in the X band, and the production of the RAM using these components was relatively simple (Gama, 2009; Gama and Rezende, 2010). The microwave attenuation properties of the RAM in the X-band were characterized using the waveguide technique, in which measurements of the energy reflected and absorbed by the material and S-parameters were performed. The measurement system comprises a HewlettPackard X752C waveguide with rectangular cross section coupled to a system consisting of a Agilent 8510C vector network analyzer, a Hewlett-Packard 8340B frequency

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generator (10 MHz-26.56 GHz), and a Hewlett-Packard 8510AS-parameter test (45 MHz-26.56 GHz) (Laverghetta, 1976). The complex values of the electric permittivity (ε) and magnetic permeability (μ) of the material as a function of frequency were calculated from the S-parameters using the Agilent 85017E software. The relative values of ε and μ at 10 GHz are εr = 5.5 – 0.3i and μr = 1.5 – 0.5i. Figure 5 shows the attenuation of electromagnetic energy of this material as a function of frequency. Note that the value of the attenuation at 10 GHz is marked in red (-10.5 dB, which corresponds to a reflectivity coefficient r = 0.32 or an attenuation value higher than 90%). Figure 6 shows the missile coated with RAM sheets with a thickness of 2.5 mm. For the simulations, the dimensions of the CAD model were adjusted accordingly. The RAM was applied to cylindrical body, wings and fins of the missile and over the whole surface of the corner reflector.

For the simulation, the models were rotated in azimuth 360°, and RCS values were calculated at 1° intervals. Simulation time for the missile model was about 48 hours for a total of 360 RCS values, and for the corner reflector and flat plate models, it was less than hour for the same number of RCS values. At 10 GHz, the far-field condition (r > 2D2/λ), where D is a constant related to the dimention of the target, λ is the radar frequency, and r is the distance between target and antenna (Knott, Schaeffer and Tuley, 1993) is valid for objects smaller than 2 m. Since the missile is 2.9 m long, simulations were carried out taking into account the actual distance between radar and target. Measurements with the square flat plate were made to determine that the system was working properly. Figures 7 and 8 show measurements and simulations of the RCS of the flat square plate. In the case of simulations, the RCS for a RAM coated plated was also calculated. Note that the vertical scale is not the same in these figures; for

-6 -30

-8 -10 8

9

10 11 Frequency (GHz)

12

Figure 5: Experimental measurements of the attenuation as a function of the frequency for the radar absorbing material (RAM) consisting of carbonyl iron dispersed in a silicon rubber matrix. Thickness of the RAM is 2.5 mm. The attenuation at 10 GHz is marked in red.

Reflectivity (dBm)

Attenuation (dB)

-4

RESULTS

Flat Plate Measurements Metal

-40 -50 -60 -70

-30

-20

-10

0

10

20

30

Aspect Angle (degrees) Figure 7: Measured radar cross section (RCS) of a flat square aluminum plate. Radar frequency of 10 GHz.

Figure 6: Air-to-air missile coated with radar absorbing material (RAM) sheets (gray color). The thickness of the RAM sheets can be observed in the photograph on the right (red arrows). 76

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40 30 20 10 0 -10 -20 -30 -40 -50 -30

-35 Flat Plate Simulation — Metal — RAM

-20

-10

0

10

20

-40 RCS (dBsm)

RCS (dBsm)

Measurements in an Outdoor Facility and Numerical Simulation of the Radar Cross Section of Targets at 10 GHz

-45 -50 -55

-30

-15

0

15

35

45

Aspect Angle (degrees)

Aspect Angle (degrees) Figure 8: Simulated radar cross section (RCS) of a flat square aluminum plate. Metallic surface and surface coated with a radar absorbing material (RAM). Radar frequency of 10 GHz.

— Metal — RAM

-60 -65 -45

30

Dihedral corner Measurements

Figure 9: Measured radar cross section (RCS) of an aluminum dihedral corner. Metallic surface and surface coated with a radar absorbing material (RAM). Radar frequency of 10 GHz.

measurements and simulations, RCS values are expressed as dBm and dBsm, respectively.

30

In the case of simulations of flat plates, the RCS is proportional to inverse of the square of the reflectivity coefficient (r-2) of the hypothetical RAM used to coat the plate. This fact can be easily observed by performing simulations with plates consisting of materials with different reflectivities.

RCS (dBsm)

20

-20 -30

Measurements and simulations of the RCS of the missile are shown in Figs. 11 and 12, respectively. Some interesting features are easily recognizable in both measured and simulated RCS patterns, such as the side view RCS (-90° and 90°), the reflection of radar waves by the mirror of the heat seeking device (0°), and the RCS signature of the rocket nozzle cavity (-180° and +180°). Nevertheless, differences between simulated and measured results are as important as similarities.

-30

-15

0

15

35

45

Aspect Angle (degrees) Figure 10: Simulated radar cross section (RCS) of an aluminum dihedral corner. Metallic surface and surface coated with a radar absorbing material (RAM). Radar frequency of 10 GHz.

20 Missile Measurements

10 RCS (dBsm)

The overall patterns for both metal and RAM-coated dihedral corner are similar when simulations and measurements are compared (Figs. 9 and 10). These graphs indicate that the data acquisition system and the simulation software performed satisfactorily for both targets configurations. However, there are some minor differences between measured and simulated RCS patterns, and these differences can be explained by several factors, such as misalignment between target and radar antennas, surface irregularities on the target, instrumental errors and spurious reflections, among others.

— Metal — RAM

-10

-45

The measured and simulated RCS diagrams of the dihedral corner are shown in Figs. 9 and 10, respectively. The RCS of this object was measured with and without RAM using the experimental setup. The simulations were performed under the same conditions. Similar to the flat plate, the vertical scale is not the same in these graphs.

Dihedral corner Simulations

10 0

0

— Metal — RAM

-10 -20 -30 -180 -135 -90

-45

0

45

90

135 180

Aspect Angle (degrees) Figure 11: Measured radar cross section (RCS) of an air-to-air missile. Metallic surface and surface coated with a radar absorbing material (RAM). Radar frequency of 10 GHz.

The simulation uses models whose surfaces need to be discretized, resulting in deviations from the actual surface of the target and simulation errors. On the other hand, whenever measurements are made, there are always errors associated with the measurements

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RCS (dBsm)

20 0

Alves, M.A., Peixoto, G.G. and Rezende, M.C., 2007b, “Orientation of a support pylon used in radar cross section measurements”, Proceedings of the Microwave and Optoelectronics Conference, IMOC 2007. SBMO/IEEE MTT-S Internacional, pp. 406-408, Salvador, BA, Brazil.

Missile Measurements — Metal — RAM

-20 -40 -180 -135 -90

-45

0

45

90

135 180

Aspect Angle (degrees) Figure 12: Simulated radar cross section (RCS) of an air-to-air missile. Metallic surface and surface coated with a radar absorbing material (RAM). Radar frequency of 10 GHz.

themselves, as mentioned previously. Therefore, the comparison of simulations and measurements may be used simultaneously to better understand and predict the RCS of actual targets.

CONCLUSION These preliminary results provide some insight into the intricacy to determine the RCS of targets with complex geometry. The results obtained so far indicate that differences will occur and they need to be explained satisfactorily. Other experiments and simulations will be carried out to better characterize the RCS of the targets. The outdoor facility for RCS measurements is operational and it will be used to measure the RCS of many types of targets and objects and to characterize the electromagnetic behavior of materials for civilian and military use.

ACKNOWLEDGEMENT The authors thank the Departamento de Ciência e Tecnologia Aeroespacial (DCTA) and Instituto de Aeronáutica e Espaço (IAE) for the financial support. Mauro Angelo Alves and Mirabel Cerqueira Rezende also thank CNPq for the financial support (Proc. 1500048/2010-6, 305478/2009-5).

Essen H. et al., 2002, “On the scattering mechanism of power lines at millimeter-waves”, IEEE Transactions on Geosciences and Remote Sensing, Vol. 40, No. 9, pp. 1895-1903. doi: 10.1109/TGRS.2002.805144  Folgueras, L.C., Alves, M.A. and Rezende, M.C., 2010, “Microwave absorbing paints and sheets based on carbonyl iron and polyaniline: measurement and simulation of their properties”, Journal of Aerospace Technology and Management, Vol. 2, No. 1, pp. 63-70. doi: 10.5028/ jatm.2010.02016370 Gama, A.M., 2009, “Comportamento da permissividade e permeabilidade complexas, de 2 a 18 GHz, de absorvedores de micro-ondas à base de ferro carbonila e ferrita de MnZn”, Ph.D. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil. Gama, A.M. and Rezende, M.C., 2010, “Complex permeability and permittivity variation of carbonyl iron rubber in the frequency range of 2 to 18 GHz” Journal of Aerospace Technology and Management, Vol. 2, No. 1, pp. 59-62. doi: 10.5028/jatm.2010.02015962 IEEE, 1989, “IEEE Standard Definitions for Terms for Antennas,” IEEE Trans. On Antennas and Propagation, Vol. AP-37, pp. 956-966. Knott, E.F., Schaeffer, J.F., and Tuley, M.T., 1993, “Radar cross section”, Artech House, Boston, USA. Laverghetta, T.S., 1976, “Microwave measurements and techniques”, Artech House, Dedham, Massachusetts, USA. 560 p. Peixoto, G. G. et al., 2009, “A medium open range radar cross section facility in Brazil,” PIERS Online, Vol. 5, No. 4, pp. 381-384.

REFERENCES Alves, M.A., Peixoto, G.G., and Rezende, M.C., 2007a, “Simulations of the radar cross section of a generic air-to-air missile covered with radar absorbent materials”,  Proceedings of the Microwave and Optoelectronics Conference, IMOC 2007. SBMO/IEEE MTT-S Internacional, pp. 409-412, Salvador, BA, Brazil.

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CADRCS, 2007, “CADRCS – Revolutionary PC based software for radar cross section simulation”. Available from: http://www.cadrcs.com

Silva, V.A. et al., 2009, “Comportamento eletromagnético de materiais absorvedores de micro-ondas baseados em hexaferrita de Ca modificada com íons CoTi e dopada com La”, Journal of Aerospace Technology and Management, Vol. 1, No. 2, pp. 255-263.

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doi: 10.5028/jatm.2011.03010611

Paula C. P. M. Pardal National Institute for Space Research São José dos Campos – Brazil paulacristiane@gmail.com

Rodolpho Vilhena de Moraes* Federal University of São Paulo São José dos Campos – Brazil rodolpho.vilhena@gmail.com

Helio K. Kuga National Institute for Space Research São José dos Campos – Brazil hkk@dem.inpe.br *author for correspondence

Orbit determination modeling analysis by GPS including perturbations due to geopotential coefficients of high degree and order, solar radiation pressure and luni-solar attraction Abstract: The purpose of this paper was to analyze the modeling of an artificial satellite orbit, using signals of the GPS constellation and least squares algorithms as the method of estimation, with the aim of analyzing the performance of the orbit estimation process. One pursues to verify how differences of modeling can affect the final accuracy of orbit determination. To accomplish that, the following effects were considered: high degree and order for the geopotential coefficients; direct solar radiation pressure; and Sun-Moon attraction. The measurements were used to feed the batch least squares orbit determination process, in order to yield conclusive results about the orbit modeling issue. An application has been done, using GPS data of the TOPEX/Poseidon satellite, whose accurate ephemeris are available on the Internet. It is shown that from a poor but acceptable modeling up to all effects included, the accuracy can vary from 28 to 9 m in the long-period analysis. Keywords: Orbit determination, GPS, Orbit perturbations, Geopotential, Solar radiation pressure, Luni-solar gravitational attraction

INTRODUCTION The problem of orbit determination consists essentially of estimating parameter values that completely specify the trajectory of a body in space, processing a set of information (measurements) from this body. Such observations can be collected through a tracking network on Earth or through sensors, like the GPS receiver onboard TOPEX/Poseidon (T/P). The Global Positioning System (GPS) is a powerful and low cost means to allow computation of orbits for artificial Earth’s satellites. The T/P satellite is an example of using this system for space positioning.

based on the data equations that describe the linear relation between the residual measurements and the estimation parameters. In this work, the algorithm was implemented through orthogonalization using Givens rotations.

LEAST SQUARES METHODS Parameters estimation aims at estimating things that are constant along the estimation process. It is necessary a set of measurements to mathematically shape the relationship between these measurements and the parameters or state to be estimated.

The orbit determination of artificial satellites is a nonlinear problem in which the disturbing forces are not easily modeled, like geopotential and direct solar radiation pressure. Through an onboard GPS receiver, it is possible to obtain measurements (pseudo-ranges) that can be used to estimate the state of the orbit.

One of the most used parameter estimator is the least squares algorithm. Basically, the algorithm minimizes the cost function of the residuals squared (Kuga, 2005). The recursive least squares algorithm, when applied to parameters or state estimation, presents two advantages: avoids matrix inversion in the presence of uncorrelated measurement errors and requires smaller matrices, which means less need of memory storage.

Usually, the iterative improvement of the orbit parameters of a satellite is carried out using the least squares methods. On a simple way, the least squares estimation algorithms are

Recursive Least Squares using sequential Givens rotations

Received: 24/02/11 Accepted: 21/03/11

The Givens rotations are used when it is fundamental to cancel specific elements of a matrix. Alternative formulations were developed, based on the QR factorization methods, to

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solve this deficiency. Using orthogonal transformations, the equation matrix of data can be transformed on an upper triangular form, to which the least squares solution is obtained by a simple back substitution. The aim of applying orthogonal transformations in matrices and vectors on the least squares problem is to substitute the matrix inversion for a stronger method, with less numerical errors. The Givens rotations (Givens, 1958) are a method to solve recursive least squares through orthogonal transformations (Silva, 2001). In this procedure, a given matrix H becomes triangular by the multiplication of a series of orthogonal matrices. The full transformation generically can be given by: Š R š ª º"  0  Š d š ª º"  r 

U

U

m

m

U m 1 ... U 3

U m 1 ... U 3

U2

U2

H " Q H







(2)

where Âľ is Earthâ&#x20AC;&#x2122;s gravitational constant; RT is Earthâ&#x20AC;&#x2122;s radius; r is the spacecraft radial distance; Ď&#x2020; is the geocentric latitude; Îť is the longitude on Earth fixed coordinates system; Cnm and Snm are the normalized harmonic spherical coefficients, of degree n and order m; Pnm are the associated normalized Legendre functions. The constants Âľ, RT, Cnm, and Snm determine a particular gravitational potential.

Perturbations due to Direct Solar Radiation Pressure

T

(1)

y " Q y T

where R is an upper triangular matrix, U i " U i,max (i 1, n) $ U i,2 U i,1  denotes the sequence of rotations made in order to eliminate the elements of the sub-diagonal on the i-th row of H, and Q is an orthogonal matrix. At each step, the orthogonalization of the H matrix is performed (producing a transformed measurement vector d and r), and the results are stored to the next set of measurements. At the end, the final solution is computed. See details in Silva (2001), and Montenbruck and Suarez (1984).

MODEL OF FORCES â&#x20AC;&#x201C; DISTURBING EFFECTS CONSIDERED The main disturbing forces that affect the orbit of an Earthâ&#x20AC;&#x2122;s artificial satellite are: the non-uniform distribution of Earthâ&#x20AC;&#x2122;s mass; ocean and terrestrial tides and the gravitational attraction of Sun and Moon. There are also the non-gravitational effects, such as: Earthâ&#x20AC;&#x2122;s atmospheric drag; direct and reflected solar radiation pressure; electric drag; emissivity effects; relativistic effects and impacts of meteorites. The disturbing effects are in general included according to the physical situation presented and to the accuracy that is intended for the orbit determination.

Perturbations due to Earth Gravitational Field The Earth is not a perfect sphere with homogeneous mass distribution, and cannot be considered as a material point. Such irregularities disturb the orbit of an artificial satellite and the keplerian elements that describe the orbit do not stay constant. The potential function can be given by (Kaula, 1966):

80

n

R h n ŠR š U ( r , K , Q ) " ¨ ¨ ª T º Pnm sin K Cnm cos mQ  S nm sin mQ r n" 0 m" 0  r 

The solar radiation pressure is a force of non-gravitational origin that disturbs the motion of an artificial satellite. The way as the perturbations due to solar radiation pressure will affect the keplerian elements depends on the pressure model adopted (if it includes or not shadow, for example). Meanwhile, in the general case, it causes secular and periodic perturbations on the variables (â&#x201E;Ś, Ď&#x2030;, and M) and periodic perturbations on the metric variables (a, e, and i). The components of solar radiation pressure force can be expressed in several systems. Throughout these systems, the orbital elements of the satellite can be connected with Sunâ&#x20AC;&#x2122;s position. This procedure was used here, for the direct solar radiation pressure model adopted for the TOPEX/Poseidon satellite (Marshall, Antreasian, Rosborough and Putney, 1991). Since the force due to the emerging radiation flux on the surface of the satellite depends on the angle of incidence, the attitude of the satellite must be also taken into account (Antreasian and Rosborough, 1992). According to Marshall and Luthckeâ&#x20AC;&#x2122;s model (Marshall and Luthcke, 1994), the total force acting on T/P is: Fk "

Ÿ š GAk cos V k  Š I k ­ 2 ª  W cos V k º nk  1  Wk s ½ c  ­Ž  3 ½ž



8

¥ F " ¨ Fk 

(3)

k "1

where G is solar radiant flux (W/m2); A is the surface area of each plate (m2); δ is difusive reflectivity, percentage of the total incoming radiation; Ď is specular reflectivity, percentage of the total incoming radiation; n is surface normal vector; s is source incidence vector; θ is the angle between surface normal and solar incidence; and c is the speed of light (m/s). Subscript I k varies from 1 to 8, representing each plate, and F is the total direct solar radiation force acting on the satellite.

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Orbit determination modeling analysis by GPS including perturbations due to geopotential coefficients of high degree and order, solar radiation pressure and luni-solar attraction



Perturbations due to Luni-Solar Gravitational Attraction

I I I yk " hk xk ,t  vk

These perturbations are due to Sun and Moon attraction force and they can be meaningful if the satellite is far from the Earth. As the orbital variations are of the same type, whatever is the Sun or the Moon the attractive body, they should be studied without distinguishing the third body. The luni-solar gravitational attraction mainly acts on â&#x201E;Ś and Ď&#x2030;, what causes precession of the orbit and the orbital plane.

I I where yk is the m-observations vector; hk xk is the M I state xk nonlinear function of dimension m; and vk is the measurement error vector of dimension m.

The general three-body problem model is here simplified by the circular restricted three-body problem, where the orbital motion of a third body, which mass can be neglected, around two other massive bodies is studied. The motion equation that provides the third body acceleration can be expressed as (Prado and Kuga, 2001):

r3 " Gm1

r13 3 13

r

 Gm2

r23 r233





The pseudorange observations are a measurement between the GPS satellites and the receiver antenna. These measurements will be used in the orbit determination problem via GPS and they can be written as (Eq. 7):



Pi " Wi  c dt  dTi  D ION  D TROP  v

(7)

which corresponds to the real pseudorange Ď i plus the



relativistic corrections c dt  dTi , the ionospheric and tropospheric deviations DION and DTROP, and the noise v. RESULTS

DYNAMICAL MODEL The problem of orbit determination is essentially nonlinear due to the fact that the orbital motion description is based in ordinary differential equations in the form (Kuga, 1989) (Eq. 5): r "v r a w r3 

(6)

(4)

I I I I I I I where r13 " r 3  r1 , r23 " r 3  r2 , and ri , i "1, 2, 3 , is the i-th body distance to the center of mass of the system

v " -R



(5)

b"0 I and written in the inertial reference frame. In Eq. 5, r I corresponds to the position vector; v is the velocity vector; I w is the white noise vector with zero mean and covariance I I Q; a represents the modeled perturbations vector; and b is the vector of the user clock deviation polynomial model coefficients.

MEASUREMENT MODEL The nonlinear equation that represents the measurements is given by (Eq. 6):

Here, the tests and the analysis from the algorithm developed to compute direct solar radiation pressure are presented. On the analysis of direct solar radiation pressure is already included TOPEX GPS antenna location that, lately, consists of the influence of the satellite attitude motion in the orbit determination process (Binning, 1996). The algorithm was implemented through FORTRAN 77 language (Pardal, 2007). To validate and to analyze the proposed method, real data from the T/P satellite were used. Position and velocity to be estimated were compared with T/P precise orbit ephemeris (POE), from the Jet Propulsion Laboratory (JPL) of NASA. The test conditions considered pseudorange real data, collected by GPS receiver onboard TOPEX, on November 19, 1993. The tests covered the same day, for a short (2 hours) and a long (24 hours) period of orbit determination. The force model included perturbations due to high order geopotential (50x50), with harmonic coefficients from JGM-2 model, due to direct solar radiation pressure (Vilhena de Moraes, Raimundo and Kuga, 2008), and due to luni-solar attraction. These model improvements were also investigated for other estimation techniques, aiming at the same orbit determination problem (Pardal, Kuga and Vilhena de Moraes, 2010). The measurement model considered ionospheric correction, although the accuracy on position and velocity is not meaningful (Chiaradia, Kuga and Prado, 2000). The obtained data were evaluated through one parameter: error in position, which represents the difference between the POE/JPL reference and the estimated position components. Such parameter is given by:

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¬ x  ˆx ¼ ½ I ­ r } ­ y  ˆy ½ ­ z  ˆz ½ ® ¾

(8)

which is after translated to radial, normal, and transverse components of orbit fixed system. First, only geopotential was considered for the mentioned periods of orbit determination. After, the direct solar radiation pressure force acting on TOPEX center of mass and the way how such force acts on satellite orbit determination were analyzed. And, finally, perturbations due to Sun-Moon gravitational attraction were added to the model of forces. The direct solar radiation pressure analysis already includes TOPEX GPS antenna location, which is one of the steps to determine the direct solar radiation pressure effects. The obtained data were after translated to RTN (radial, transverse, and normal) system. In this system, “R” points

to the nadir direction, “N” is perpendicular to orbital plane, and “T” is orthogonal to “R” and “N”, and is also the velocity component. Thus, it is possible to analyze what happens with the orbital system components, and with the orbit evolution too. This is better than carry out an analysis from an Earth referential, where is more difficult to interpret the physical situation. Figure 1 shows the behavior of the error in position, given in meters, along time, given in seconds, considering only geopotential. In Fig. 2, the geopotential and direct solar radiation pressure effects were considered, shown in two different curves. In Fig. 3, the Sun-Moon gravitational attraction in the model of forces was also taken into account. In the legends of Figs. 1 to 3, “R” means radial component; “N”, normal component; and “T”, transverse component of orbit fixed system. The subscript “geo” means perturbations due to geopotential only, “srp”, perturbations due to geopotential and direct solar radiation pressure, and “sm”, the effects due to Sun-Moon attraction.

! Errors in position, given in RNT coordinates, for 2 hours (on the left) and 24 hours (on the right), considering perturbations Figure 1: due to geopotential (geo). R: radial component; N: normal component; T: transverse component. 82

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Orbit determination modeling analysis by GPS including perturbations due to geopotential coefficients of high degree and order, solar radiation pressure and luni-solar attraction

Figure 2: Errors in!position, given in RNT coordinates, for 2 hours (on the left) and 24 hours (on the right), considering perturbations due to geopotential only (geo) and due to geopotential and direct solar radiation pressure (srp). R: radial component; N: normal component; T: transverse component.

Figure 3: Errors in position, given in RNT coordinates, for 2 hours (on the left) and 24 hours (on the right), considering perturbations due to geopotential and direct solar radiation pressure (srp), and Sun-Moon attraction (sm). R: radial component; N: normal component; T: transverse component. J. Aerosp.Technol. Manag., SĂŁo JosĂŠ dos Campos, Vol.3, No.1, pp. 79-86, Jan. - Apr., 2011

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Table 1 shows the maximum and minimum amplitudes of the curves from Figs. 1 to 3, for short period (2 hours) and long period (24 hours) of orbit determination. Table 1:

Maximum and minimum values of the errors in position, for the two cases of test, on November 19, 1993

Error (m)   Value Maximum geo Minimum Maximum srp Minimum Maximum sm Minimum

R 1.48 -0.75 0.84 -0.71 0.86 -0.61

2 hours N T 4.44 2.19 -2.28 -2.09 4.49 1.89 -2.21 -0.16 0.39 1.34 -0.20 -1.05

R 5.70 -4.67 4.90 -2.69 2.68 -2.78

24 hours N T 26.26 9.27 -28.63 -12.43 25.60 7.70 -27.92 -8.70 1.99 6.37 -1.81 -4.40

R: radial component; N: normal component; T: transverse component; geo: perturbations due to geopotential only; spr: perturbations due to geopotential and direct solar radiation pressure; sm: effects due to Sun-Moon attraction.

Figure 1, especially for long period graphics, shows a sinusoidal behavior of the errors in RTN coordinates, with a period near once per revolution of the satellite orbit (around 2 hours). Following verification of all know dynamic models, there may exist a residual signature in the orbit as a result of unmodeled accelerations, which come in many forms (CNES, 2007; Soyka and Davis, 2001). In the case of geopotential, the acceleration is due to truncation of geopotential field. The used model is JGM-2 50×50, while the full model is 70×70, which is computationally intensive and may cause numerical problems, due to the order of some terms (10-127), which was not suitable in this work. The same sinusoidal behavior appears in long period graphics of Fig. 2, in the curves corresponding to geopotential and direct solar radiation pressure. It is also result of unmodeled accelerations, but solar radiation pressure is responsible for another acceleration, caused by limitations in the modeling of solar pressure as a function of the satellite attitude, surface properties and space environment. So, in Fig. 2, there are two unmodeled accelerations in the curves associated within the two disturbing effects.

long periods of orbit determination, when Sun-Moon effects are not considered. Table 1 also confirms the information of the graphics: solar radiation pressure has more meaningful effects in transverse component, and less effects in normal one. It was expected, because solar radiation pressure acts especially on along track component, which is here represented by transverse component, the one associated with velocity of the satellite. As Table 1 shows, for the short period, the solar radiation pressure decreases up to 43% the radial component value and up to 16% the transverse one. For the long period, solar radiation pressure reduces up to 42% the radial component value and up to 30% the transverse one. In both cases, such perturbation does not act favorably on the normal component. However, the SunMoon attraction has more meaningful effects on normal component. For the short period, it decreases up to 91% the normal component value, and for the long period, it reduces up to 94%. Figure 4 shows residuals of pseudorange evolution along time for the short 2-hour period (at left), and for the long 24-hour period (at right) of orbit determination on November 19, 1993. These results were obtained considering the complete model of forces, including perturbations from geopotential up to Sun-Moon gravitational attraction. The behavior showed next is the same for all the analyzed cases, as it is possible to verify in Table 2, which presents the residuals of pseudorange statistics, mean and standard deviation, for the three models of forces considered in this analysis, and for the short and the long periods of orbit determination. As can be seen, the statistics of the residuals are similar in all cases.

The previously detected sinusoidal behavior also appears in long period graphics of Fig. 3, in the curves corresponding to the model of forces up to direct solar radiation pressure and to the completed model including Sun-Moon gravitational attraction. It is also result of unmodeled accelerations explained before. According to Table 1, it is possible to see that the minor amplitude variation occurs in radial component, and the higher, in normal component, such for short and 84

Figure 4: Residuals of pseudorange for 2 hours (on the left) and 24 hours (on the right), considering perturbations due to geopotential and direct solar radiation pressure and Sun-Moon gravitational attraction.

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Orbit determination modeling analysis by GPS including perturbations due to geopotential coefficients of high degree and order, solar radiation pressure and luni-solar attraction

Table 2:

Residuals of pseudorange statistics for the three studied cases

Residuals of pseudorange (m) – 11/19/1993 Model of Forces Statistics 2 hours 24 hours mean -0.499 -0.181 geo standard deviation 4.014 12.774 mean -0.014 -0.018 srp standard deviation 3.623 12.792 mean -0.005 0.011 sm standard deviation 3.675 11.058 geo: perturbations due to geopotential only; spr: perturbations due to geopotential and direct solar radiation pressure; sm: effects due to Sun-Moon attraction.

CONCLUSIONS The principal aim of this paper was to determine the orbit of an artificial satellite, using signals of the GPS constellation and least squares algorithms using sequential Givens rotations as a method of estimation. The analysis period covered a short period (near once T/P period) and a long period orbit determination. Pseudorange measurements were corrected from ionospheric effects, although the accuracy on orbit determination was not expressive. Real time requirements were not present; nevertheless, it was appropriate to keep low computational cost, with accuracy enough to satellite positioning at 10 m level for one day. The results were compared with real data from TOPEX POE/JPL (Precision Orbit Ephemeris/Jet Propulsion Laboratory), available on the Internet. For short period orbit determination, the magnitude of error in position varied from 5.1 to 3.7 m, and for long period, the magnitude varied from 27.7 to 9.3 m, according to the complexness increase of the model. As the numbers show, the model that includes direct solar radiation pressure decreases at most around 5% the precision in position. Geopotential, direct solar radiation pressure, and Sun-Moon gravitational attraction were taken into consideration and the analysis occurred without selective availability on the measurements of the signals. Throughout the results, it was found that least squares method through sequential Givens rotations and positioning using GPS showed reliability and accuracy enough for artificial satellites orbit determination.

ACKNOWLEDGEMENTS The authors wish to express their appreciation for the support provided by CNPq (National Council of Research), under contract 07840/2008-2. The authors also wish to thank INPE (National Institute for Space Research) and UNESP (São Paulo State University).

REFERENCES Antreasian, P.G., Rosborough, G.W., 1992, “Prediction of Radiant Energy Forces on the Topex/Poseidon Spacecraft”, Journal of Spacecraft and Rockets, Vol. 29, No. 1, p. 81-90. doi: 10.2514/3.26317. Binning, P.W., 1996, “GPS, Dual Frequency, SA Free Satellite Navigation. Navigation Technology for the 3rd Millennium”, Proceedings of the 52nd Annual Meeting of the Institute of Navigation, June 19-21, Cambridge, MA, USA, pp. 803-812. Chiaradia, A.P.M., Kuga, H.K. and Prado, A.F.B.A., 2000, “Investigation on Ionospheric Correction Models for GPS Signals”, Proceedings of the 9th Colóquio Brasileiro de Dinâmica Orbital, Advances in Space Dynamics, Prado, A.F.B.A., Editor, Águas de Lindoia, Brazil, pp. 214-219. CNES, 2007, Topex/Poseidon. The beginnings of satellite oceanography, Available at: http://www.cnes.fr/web/1461topexposeidon.php. Access on May 10, 2007. Givens, J.W., 1958, “Computation of Plain Unitary Rotations Transforming a General Matrix to Triangular Form”, SIAM Journal on Applied Mathematics, Vol. 6, pp. 26-50. Kaula, W.M., 1966, “Theory of Satellite Geodesy: Applications of Satellites to Geodesy”, Blaisdell Publ. Co., Waltham, MA, USA. Kuga, H.K., 2005, “Noções Práticas de Técnicas de Estimação”, Class Notes of Optimization on Dynamical Systems II”, INPE, São José dos Campos, Brazil. Kuga, H.K., 1989, “Determinação de órbitas de satélites artificiais terrestres através de técnicas de estimação combinadas a técnicas de suavização de estado”. (INPE-4959-TDL/079). Ph.D. Thesis, National Institute for Space Research, São José dos Campos, Brazil, 249 p. Marshall, J.A., Antreasian, P.G., Rosborough, G.W. and Putney, B.H., 1991, “Modeling radiation forces acting on satellites for precision orbit determination”, Advances in Astronautical Sciences, Astrodymanics Conference, AAS 91-357, Vol. 76, Part I, p. 72-96. Marshall, J.A., Luthcke, S.B., 1994, “Modelling radiation forces acting on TOPEX/Poseidon for precision orbit determination”, Journal of Spacecraft and Rockets, Vol. 31, No. 1, p. 89-105. Montenbruck, O., Suarez, M., 1984, “A Modular Fortran Library for Sequential Least-Squares Estimation Using QR-

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Pardal P.C.P.M., Moraes R.V., Kuga H.K.

Factorization”, DLR, German Space Operations Center, Oberpfaffenhofen, Germany (DLR-GSOC IB 94-05). Pardal, P.C.P.M., 2007, “Determinação de Órbita via GPS Considerando Modelo de Pressão de Radiação Solar para o Satélite Topex/Poseidon”, Masters Dissertation, National Institute for Space Research, São José dos Campos, Brazil. Prado, A.F.B.A., Kuga, H.K. (Eds), 2001, “Fundamentos de Tecnologia Espacial”, National Institute for Space Research, São José dos Campos, Brazil, 220 p. ISBN: 8517-00004-8. Silva, A.A., 2001, “Determinação de Órbitas com o GPS através de Mínimos Quadrados Recursivo com Rotações de Givens”, Masters Dissertation, São Paulo State University, Guaratinguetá, Brazil. Soyka, M.T., Davis, M.A., 2001, “Estimation of Periodic Accelerations to Improve Orbit Ephemeris Accuracy”,

86

Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, Advances in the Astonautical Sciences, Vol. 108, Part II, California, USA, pp. 1123-1140. Vilhena de Moraes, R., Raimundo, P.C.P. and Kuga, H.K., 2008, ���Orbit Determination Using GPS Including Perturbations due to Geopotential Coefficients of Higher Degree and Order and Solar Radiation Pressure”, Advances in the Astronautic Sciences, Galveston, Proceedings of the 18th AAS/AIAA Space Flight Meeting, Vol. 130, San Diego: American Astronautical Society, p. 923-933. Pardal, P.C.P.M., Kuga, H.K. and Vilhena de Moraes, R., 2010, “Comparing the Extended and the Sigma Point Kalman Filters for Orbit Determination Modeling Using GPS Measurements”. In: 23rd International Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR. Proceedings of the 23rd International Meeting of the Satellite Division of the Institute of Navigation (under publication).

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doi: 10.5028/jatm.2011.03016810

João Alves de Oliveira Neto Instituto Tecnológico de Aeronáutica São José dos Campos – Brazil alves@ita.br

Edson Basso Instituto de Aeronáutica e Espaço São José dos Campos – Brazil edsonbassoeb@iae.cta.br

João Luiz F. Azevedo* Instituto de Aeronáutica e Espaço São José dos Campos – Brazil joaoluiz.azevedo@gmail.com *author for correspondence

Aerodynamic study of sounding rocket flows using Chimera and patched multiblock meshes Abstract: Aerodynamic flow simulations over a typical sounding rocket are presented in this paper. The work is inserted in the effort of developing computational tools necessary to simulate aerodynamic flows over configurations of interest for Instituto de Aeronáutica e Espaço of Departamento de Ciência e Tecnologia Aeroespacial. Sounding rocket configurations usually require fairly large fins and, quite frequently, have more than one set of fins. In order to be able to handle such configurations, the present paper presents a novel methodology which combines both Chimera and patched multiblock grids in the discretization of the computational domain. The flows of interest are modeled using the 3-D Euler equations and the work describes the details of discretization procedure, which uses a finite difference approach for structure, body-conforming, multiblock grids. The method is used to calculate the aerodynamics of a sounding rocket vehicle. The results indicate that the present approach can be a powerful aerodynamic analysis and design tool. Keywords: Chimera grids, Patched multiblock grids, Sounding rockets.

INTRODUCTION In the present work, the results obtained for the simulation of aerodynamic flows concerning a typical sounding rocket, SONDA-III, are presented. This work is inserted into the effort of development of computational tools necessary to simulate aerodynamic flows over aerospace geometries, especially those related to the Brazilian Satellite Launcher (VLS, acronym in Portuguese). Details of the work developed so far, as well as results that illustrate the advancements that have been accomplished up to now in this long term research effort, can be seen, among other references, in Azevedo, Menezes and Fico Jr. (1996), Azevedo, Strauss and Ferrari (1997), Strauss and Azevedo (1999), Bigarella (2007) and Bigarella and Azevedo (2007). The SONDA-III presents a quite complex geometric configuration with four front fins and four back fins around a central core. The fins are arranged symmetrically around the central body. An illustrative outline of this configuration is presented in Fig. 1, including a closer view of the frontal fin region. The research group has a fair amount of experience with Chimera and patched multiblock flows simulations for Received: 11/05/10 Accepted: 22/10/10

launch vehicle aerodynamics. The present application represents, however, the first time that the group used the two techniques in the same code. This is also the first time that the group simulates a vehicle with fins. The fundamental objective of the present effort is, therefore, to demonstrate that the use of the two techniques combined will enable the generation of better quality grids for the problems at hand. Hence, the major contribution of the present work rests upon the creation of the capability of simulating the flow over launch vehicles with fins, using a combined patchedChimera grid approach. The governing equations are assumed written in conservative form and they are discretized in a finite diference context. Spatial discretization uses secondorder accurate, central diference operators. The time march method is based on a five-stage, Runge-Kutta algorithm described in Jameson, Schmidt and Turkel (1981), which also has second-order accuracy in time. The artificial dissipation terms added are based on the nonisotropic artificial dissipation model described in Turkel and Vatsa (1994). In the present case, Chimera and patched grid techniques are used to simulate ows over the complete SONDA-III sounding rocket. These techniques together provide the capability to use structured meshes for the discretization of the calculation domain over truly complex configurations. The paper

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Z X

Y

Z X

Y

Figure 1: Perspective view of the SONDA-III (left) and detail of the front fin region (right).

will briefly describe the theoretical formulation used with a discussion of the numerical implementation aspects. Details of the current implementation of Chimera and patched grid techniques are also presented, with the boundary conditions adopted. Results with applications to SONDA-III are described and some concluding remarks are presented.

THEORETICAL FORMULATION In the present work, it is assumed that the flows of interest can be represented by the Euler equations in three spatial dimensions. These equations can be written in conservative law form, in a curvilinear coordinate system: y Q y E y F yG    " 0 yY y] yM y_

(1)

where Ē, and are the inviscid flux vectors, which can be seen in more detail in Vieira et al. (1998), and Q is the vector of conserved variables, defined as: Q=J -1[l lp lp lt e]Z

(2)

A suitable nondimensionalization of the governing equations has been assumed in order to write Eq. 1. In particular, the values of flow properties are made dimensionless with respect to freestream quantities, as described in Pulliam and Steger (1980). The governing equations were discretized in a finite diference context in structured hexahedral meshes which would conform to the bodies in the computational domain. Since a central difference spatial discretization method is used, artificial dissipation terms must be added to the formulation in order to control nonlinear instabilities. The artificial dissipation terms used here are based in the work of Turkel and Vatsa (1994). This model is nonlinear and nonisotropic, with the scaling of the artificial dissipation operator in each coordinate direction weighted by its own spectral radius of the corresponding flux Jacobian matrix. In the present implementation, the residue operator is defined as: RHS n " ) t (I ] E n  I M F n  I_ G n )



where δξ the δζ and δη terms represent mid-point central diference operators in the ξ, ζ and η directions, respectively. The numerical flux vectors and artificial dissipation operators are defined as:

where ρ is the density, u, v and w are the Cartesian velocity components, e is the total energy per unit volume and J is the Jacobian of the transformation, represented as (Eq. 3):

Ei t 1 , j , k "

1 ( E  Ei1, j ,k )  di t 1 , j ,k , 2 i , j ,k 2

Fi , j t 1 ,k "

1 ( Fi, jk,  Fi , j  1,k )  di , j t 1 ,k , 2 2

J " ( x] yM z_  xM y_ z]  x_ y] zM  x] y_ zM  xM y] zM  x_ yM z] )1  (3)

Gi , j ,k t 1 "

1 (G  Ei , j ,k  1)  di , j ,k t 1 . 2 i , j ,k 2

The pressure can be obtained from the equation of state for a perfect gas:

[

p " (L  1)[e 

88

]

1 W ( u 2  v 2  w2 )  2

(4)

(5)

2

2

2



(6)

The artificial dissipation operators are defined precisely as described in Turkel and Vatsa (1994). Since steady state solutions are the major interest in the present study, a variable time step convergence acceleration procedure has been implemented. The time march is performed based on

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Aerodynamic study of sounding rocket flows using Chimera and patched multiblock meshes

a five-stage, second-order accurate, hybrid Runge-Kutta time-stepping scheme, which can be written as:

order to save computational resources, 1/8 of the complete configuration in the azimutal direction was simulated. This simplification is valid in the present work because only simulations with zero attack-ofangle are considered. In this way, taking advantage of the symmetry of the problem, the configuration is reduced to 1/8 of the central body in the azimutal direction, 1/2 of the frontal fin and 1/2 of the back fin. In total, 13 meshes with relatively simple geometry are used to model the rocket and the fins. These meshes are distributed in the following way:

Qi( 0 ) = Qin , Qi(1)  Qi( 0 ) < _1 RHS ( 0 ) , Qi( 2 )  Qi( 0 ) < _ 2 RHS (1) , Qi( 3)  Qi( 0 ) < _ 3 RHS ( 2 ) , Qi( 4 )  Qi( 0 ) < _ 4 RHS ( 3) , Qi(5)  Qi( 0 ) < _ 5 RHS ( 4 ) , Qin+1 = Qi(5) ,



(7)

- seven meshes for the front fin, denominated m1, m2, m3, m4, m6 and m7;

where Îą1 =1/4, Îą2 = 1/6, Îą3 = 3/8, Îą4 =1/2 and Îą5 = 1. The time step is defined as (Eq. 8): ) ti , j ,k "

CFL ci , j ,k



- three meshes for the back fin, denominated m9, m10 and m11; - one mesh for central body, denominated m13, as seen in Fig. 2;

(8)

The CFL acronym stands for the Courant-Friedrichs-Lewy number, and the characteristic speed ci,j,k is defined as:

- one (background) mesh for front fin, denominated m8, as seen in Fig. 2;

(

)

ci , j ,k " max( U  a ]x2  ] y2  ]z2 , V  a nx2  n2y  nz2 ,|W|a +_ x2  _ y2  _ z2 ) - one (background) mesh for back fin, denominated m12, as seen in Fig. 2. V  a nx2  n2y  nz2  a _ x2  _ y2  _ z2 )  (9) The computational meshes used in the present work are all generated by algebraic methods within each block. where a is the speed of sound and U, V and W are the In particular, the multisurface algebraic grid generation contravariant velocity components. It should be emphasized technique described by Fletcher (1991) has been that only the convective operator inside RHS term indicated implemented in a fairly general code for the present in Eq. 8 is actually evaluated at every time step. The configurations. The code allows grid clustering at various artificial dissipation term is only evaluated in the first and regions and a fair amount of control on the grid point second stages of the time march procedure. It can be shown distribution along the normal direction. Both hyperbolic that this provides enough damping to maintain nonlinear tangent and exponential grid stretching functions are stability, as defined in Jameson, Schmidt and Turkel (1981), used to obtain the desired clustering and coarsening of whereas it yields a more efficient numerical scheme. the grid over the body. The meshes generated by that method are 2-D. The mesh that discretizes the central body is rotated around the longitudinal axis, obtaining a COMPUTATIONAL GRID TOPOLOGY 3-D mesh. Initially, for the fins, 2-D meshes are generated SONDA-III rocket possesses a central body where for the root and top sections. These meshes can be seen four frontal fins and four back fins are mounted. In in detail in Fig. 3. The root surface is deformed through

)

z z

x

x m12 m12

m8

m8

Figure 2: Central body mesh (left) and the m8 and m12 background meshes (right). J. Aerosp.Technol. Manag., SĂŁo JosĂŠ dos Campos, Vol.3, No.1, pp. 87-98, Jan. - Apr., 2011

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Oliveira Neto J.A., Basso E., Azevedo J.L.F.

Y

Y x

x

Figure 3: Two-dimensional surface on the root (left) and on the top (right) of the front fin generated by an algebraic method.

a coordinate transformation to conform to cylindrical and conical sections of the central body. Finally, intermediate surfaces are obtained through an interpolation from the top and bottom surfaces previously calculated, as shown in Fig. 4.

Y x

Y z

x

xz

Figure 4: Intermediate surfaces obtained by interpolation of the tip and root surfaces of the front fin.

Previous work on tridimensional configuration of launch vehicles, using the VLS configuration, as can be seen in Basso, Antunes and Azevedo (2003), used only Chimera grids to discretize the computational domain. However, during the initial phase of planning of the meshes for SONDA-III, the research group noticed that, due to the geometric characteristics of the new problem, using only Chimera meshes would not be viable. The adopted solution was to use Chimera in conjunction with patched grids, since this procedure allowed the generation of meshes in a much simpler way, in comparison with other proposals that just used one technique or another. The Chimera subroutines of the original solver for the VLS were adapted, and additional subroutines were implemented for the use of patched grids. Routines for the control of the flow of information among the meshes were also implemented, and all the particularities of the original code (Antunes, 2000; Basso, Antunes and Azevedo 2003) for the configuration of the VLS were eliminated. With that, the research group developed a somewhat general code that can work with Chimera and patched grids, in complex configurations. The number of meshes that the code can manage is just limited by the amount of memory of the machine. 90

Basically, the m1 to m7 meshes, that involve the front fin, exchange information amongst themselves using the patched mesh technique. These seven meshes exchange information, through of the Chimera interfaces with the m8 mesh (background mesh), and finally, the m8 mesh exchanges information with the central body mesh, m13. For the back fins, the process is similar. The background meshes, m8 and m12, have the function of serving as transition between the fin meshes, that possess a large number of points, and the central body mesh, that possesses few points. Besides, the background meshes hide the complexity of the configuration, since the central body mesh does not see the fin meshes. If the background meshes were not used, the central body mesh would have many more points in order to communicate in an efficient way with the fin meshes. The flow of information among the meshes can be seen in Fig. 5.

m3

m4

m2

m1

m5

m6

m8

m1

m2

m3

m4

m5

m6

m7

Y m13

x

xz

m7

m9

m12

m10 m9

m10

m11

m11

Figure 5: Information flow of the Chimera meshes (left) and the patched meshes (right).

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Aerodynamic study of sounding rocket flows using Chimera and patched multiblock meshes

BOUNDARY CONDITIONS For the configurations of interest here, the types of boundary conditions that should be considered include upstream (entrance), solid-wall, far-field, symmetry, upstream centerline and downstream (exit) conditions. The upstream centerline of the rocket grid is a singularity of the coordinate transformation and, hence, an adequate treatment for this boundary must be provided. The approach consists in extrapolating the property values from the adjacent longitudinal plane and averaging the extrapolated values in the azimuthal direction in order to define the updated properties at the upstream centerline. The vast majority of the previous experience of the research group in the use of Chimera or patched multiblock grids considered the VLS configuration (Basso, Antunes and Azevedo, 2003; Bigarella, 2007), without including afterbody or plume effects. For such a configuration, the number of grid blocks required is rather small. Therefore, it is possible to have the boundary conditions hard-coded for each specific case. However, in the present case, the procedure of writing 13 separate subroutines to work with the 13 meshes would be extremely difficult and prone to mistakes. Furthermore, the objective should always be to try to come up with a code as general as possible and, certainly, it should not depend on the particularities of the configuration under consideration. Again, the approach is to eliminate the particularities of the original code and to create a more powerful subroutine that could work with the diversity of boundary conditions that the meshes of SONDA-III present.

The blocks of the mesh are considered as hexahedra in computational space and each one of the six faces is numered as indicated in Fig. 6. The code, that represents a certain boundary condition, is associated to each face. With this method, the solver implements 78 boundary conditions in a simple format for the user. The boundary conditions and the number of points of each block of the mesh can be observed in Table 1. In case one wants to change some boundary conditions, it is sufficient to alter the values of a table, without the need to modify any code line.

6 k

1

j i

4

3

face: i=1 face 2: i lMAX face 3: j=1 face 4: j=JMAX face 5: k=1 face 6: k-KMAX 2 5

Figure 6: Definition of the meshes faces for the boundary conditions.

Table 1: Boundary conditions imposed in the mesh faces.

Mesh

Face 1

Face 2

Face 3

Face 4

Face 5

Face 6

Points

m1

patched

symmetry

wall

Chimera

patched

wall

65,340

m2

patched

symmetry

patched

Chimera

patched

Chimera

53,460

m3

patched

symmetry

patched

symmetry

wall

Chimera

53,460

m4

patched

Chimera

patched

Chimera

patched

wall

26,136

m5

patched

Chimera

patched

Chimera

patched

Chimera

21,384

m6

patched

Chimera

patched

symmetry

patched

Chimera

21,384

m7

wall

Chimera

patched

symmetry

patched

wall

26,136

m8

Chimera

Chimera

symmetry

symmetry

wall

Chimera

137,940

m9

exit

symmetry

wall

Chimera

patched

wall

65,340

m10

exit

symmetry

patched

Chimera

patched

Chimera

53,460

m11

exit

symmetry

patched

symmetry

wall

Chimera

53,460

m12

exit

Chimera

symmetry

Chimera

symmetry

Chimera

117,612

m13

exit

centerline

wall

freestream

symmetry

symmetry

192,375

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TREATMENT OF PATCHED GRID INTERFACES In the present work, a patched grid block always shares a common face of points with other patched grid block, as indicated in Fig. 7. In order to illustrate this procedure, it is assumed that there are two meshes, denominated A and B, as presented in Fig. 7. Those meshes should be expanded, in order to allow the implementation of a code with the capability of transferring information through the common faces. It is desirable to maintain the order of the artificial dissipation operators at all points. Therefore, taking into account that the artificial dissipation operators use five points, a possible solution is to expand the meshes such that there is an area of five rows of points in common, as indicated in the right side of Fig. 7. It can be observed that two rows of points were added to each mesh, which caused the displacement of the first columm of points. The following steps are executed: 1. Initially, the properties of all interior points located in the expanded A mesh are calculated, advancing one step in time; 2. The points located in the first column of the B mesh receive the values of the properties of the points from the fifth column of the A mesh; 3. The points located in the second column of the B mesh receive the values of the properties of the points from the fourth column of the A mesh; 4. All the interior points of the B mesh are calculated, advancing one step in time for this mesh; 5. The values of the points located in the fifth column of the B mesh are transferred for the first column of the A mesh, and values of the fourth column of

the B mesh are transferred for the second column of the A mesh; 6. The interior points of the A mesh are calculated again and the process repeats. The third column of the two meshes is left “free” and its value is determined by the calculation of the interior points, without any imposition of values for the properties, as it happened with the first and the second columns. Attempts of imposing any value for the properties in the third column − as, for example, an average between the two meshes − resulted in a significant decrease of the convergence rate. In 3-D, instead of lines or columns, the meshes have planes in common. In the present paper, the meshes are built with a single face in common, and an additional code takes care of reading a connection matrix to decide which faces of each mesh should be expanded. More details on this procedure can be found in Papa and Azevedo (2003).

THE CHIMERA HOLECUTTING PROCESS The Chimera grid possesses a superposition area but, unlike the patched grid, there is no need for the points to coincide. Again, this area is responsible for the exchange of information among the meshes. However, as not all of the points are necessary for the communication among the meshes, one can logically eliminate some points. Actually, all of the points continue to exist in the computer memory. The user creates an auxiliary matrix that associates to each point of the mesh an on-value or an off-value. The points are eliminated by two reasons. The first one concerns the fact that points of a certain mesh may be located inside an area without physical meaning of another mesh as, for example, inside a body of some other component of the configuration. An example of such situation could be found in the points of the m8 mesh that are located inside the front fin. The left side of Fig. 8 exhibits the m8 mesh

A

A

B

B

Figure 7: A and B meshes before (left) and after (right) the expansion process. 92

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Aerodynamic study of sounding rocket flows using Chimera and patched multiblock meshes

z z

X

X

Figure 8: Detail of the m8 background mesh (left) and m13 central body mesh (right) after the holecutting process.

with the points eliminated and the outline of the fin. In practice, a virtual volume larger than the solid volume is created, and all points of the mesh that are inside the virtual volume are eliminated. The creation of the virtual volume allows for the control of the number of points to be eliminated. The second reason to eliminate points is to reduce the sobreposition area. An example can be found in the central body mesh, m13, that contains the two background meshes, m8 and m12. A virtual volume completely contained in a background mesh is created and all points of the mesh, that are inside this volume, are eliminated. The right hand side in Fig. 8 displays the result of this process. After the holecutting process, described in Antunes, Basso and Azevedo (2000), the next step consists in identifying the Chimera boundary points. These points are those which were not eliminated by the previous process, but they have at least one neighbor that was eliminated. The Chimera boundary points are not calculated in the same way as the other interior points. They have the values of their properties interpolated. Each Chimera boundary point is located inside of an hexahedron whose vertices are formed by points of the other Chimera grid. As described in Antunes (2000), the distances between a Chimera boundary point of the first mesh and each of the eight vertices of the second mesh are calculated, respectively. It should be emphasized that there is no attempt to satisfy conservation in the present interpolation process. Since shocks may be crossing the interface, it would be interesting to have the enforcement of some conservation statement at grid interfaces. However, this was not implemented in the present case due to the high computational costs associated with such implementation, especially in the 3-D case, and because the present effort should be seen as an evolutionary step towards a more complete simulation capability.

Furthermore, the use of a conservative interpolation process would certainly increase the requirements of code memory, which the authors would like to avoid at this time. An interpolation method at the interfaces among Chimera meshes that satisfies conservation was developed by Wang, Buning and Benek (1995). A detailed discussion of the procedure can be found in Wang and Yang (1994). Current work in this issue is also going on in the laboratory where the present work was developed (Pio et al., 2010), but, as stated, this is beyond the scope of the present paper.

RESULTS AND DISCUSSION The results presented refer to simulations of the flow over SONDA-III rocket during its first stage flight. Preliminary results for this configuration have been presented in Papa and Azevedo (2003). In the cited reference, however, the total number of grid points was of the order of 275,000, which did not allow for a more detailed visualization of some critical regions of the flow about the fins. The present work has performed similar simulations, however considering a much finer mesh, with approximately 900,000 grid points. Such a level of grid refinement allows for a considerably better visualization of flow details about the configuration. The specific results included here consider only the case with freestream Mach number Mâ&#x2C6;&#x17E; = 2.0 and zero angle-of-attack, which is representative of the simulations performed so far for the configuration. Moreover, as the flight time in the lower atmosphere for these rockets is very short and the vehicle is at supersonic speeds during most of this flight, it seems appropriate to select a supersonic flight condition for the present discussion. As previously mentioned, the major interest in this work concerns the evaluation of the joint use of Chimera and patched grid techniques as

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Oliveira Neto J.A., Basso E., Azevedo J.L.F.

a tool for flow analysis over geometries of interest for Instituto de Aeronáutica e Espaço. Within the supersonic speed regime, several interesting aspects of Chimera and patched grid techniques can be analyzed, such as the communication of information across internal boundaries among blocks with discontinuities in the flow properties. Figure 9 exhibits the residue history for all the meshes. The CFL number used is 0.9 and approximately 9,000 iterations are necessary in order to reach convergence. In Fig. 9, one can observe that the mesh with the slowest convergence rate is the one that contains the recirculation zone, i.e., the m 6 mesh. Mach number contours over the vehicle body, in regions around the front and back fins, can be observed in Figs. 10

and 11. These figures show in detail the region of interaction between the front and back fins and the conical region of the central body. One can observe that the thickness of the shock in the leading edge of the front fin increases when it approaches the plane of symmetry. Pressure contours for the sounding rocket and its front and back fins can be observed in Figs. 12 and 13. In these figures, one can observe the formation of shock waves in the leading edges of the fins, as well as the expansion regions in the trailing edges. In the conical region, there is an increase in pressure due to a shock wave that cannot be observed in these visualizations. It can also be observed that, after the conical region, the pressure decreases due to the expansion region in the intersection between the conical and cylindrical body regions.

0

X

-2

m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12 m13

-4 -6 -8 -10 -12

Y

M 2,42 2,12 1,82 1,52 1,22 0,92 0,62 0,32 0,02

-14 -16 0

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 iterations

Figure 9: Residue history for all the meshes used in the simulation (M∞ = 2.0 and CFL = 0.9).

Figure 11: Mach number contours for the front fin region.

Z ZY X Y

Y M 2,42 2,12 1,82 1,52 1,22 0,92 0,62 0,32 0,02

Figure 10: Mach number contours for the back fin region. 94

X

P 3,9 3,15 2,4 1,65 0,9 0,15

Figure 12: Dimensionless pressure contours on the surface of the sounding rocket.

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Aerodynamic study of sounding rocket flows using Chimera and patched multiblock meshes

It is important to emphasize that the Missile Datcom (Blake, 1998) approach is typically used for stability and control purposes. Furthermore, it is also important to emphasize that the calculations with the Missile Datcom approach were performed by the present authors themselves. From a physical perspective, one can observe that, essentially, at supersonic freestream conditions, there is an oblique shock impinging on the fins downstream of the cylinder intersection. A sudden increase in the pressure coefficient distribution is observed at x/c = 9, for the computational solution. The increase in pressure coefficient (Cp) is due to the oblique shock wave created by the compression corner along the central body. Finally, the reader should observe that the authors did not have access to experimental aerodynamic results for the present configuration. Therefore, the validation here discussed is performed using Missile Datcom data.

Z3,15 2,4 1,65 0,9 X Y 0,15

Figure 13: Dimensionless pressure contours on the front fin region.

Figure 14 shows a quantitative comparison of the results obtained in the present computations. The numerical pressure coefficient distribution over a longitudinal line along the vehicle, which is located half way between two fins, is shown to be in very good agreement with results obtained with the Missile Datcom approach (Blake, 1998). Such program is a widely used semi-empirical data sheet component build-up method for estimating the aerodynamic characteristics of missiles and other rocket-like bodies.

CONCLUDING REMARKS The paper has presented results for 3-D Euler simulations of the flow over the SONDA-III vehicle, a typical sounding rocket. A structured multiblock code has been implemented, using Chimera and patched multiblock grid approaches for handling the geometric complexity of the configuration. All codes used were developed by the research group and represent a powerful aerodynamic analysis and design

8

CFD (Euler) Missile datcom

6

Cp

4 2

0

-2

-4 4

6

8 x/c

10

12

14

Figure 14: Cp distributions over the SONDA-III at Mâ&#x2C6;&#x17E; = 2.0 and zero angle-of-attack. J. Aerosp.Technol. Manag., SĂŁo JosĂŠ dos Campos, Vol.3, No.1, pp. 87-98, Jan. - Apr., 2011

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tool. The present methodology, using a combination of Chimera and patched grid approaches, seems to be quite powerful to work on similar problems, even with the presence of several fins. The main advantages observed in the present approach are: 1. Flexibility: the joint use of Chimera and patched grids, in the same simulation, allows the generation of meshes in a much easier and quicker fashion than other competing approaches; 2. Modularity: the use of background meshes, hiding the complexity of the meshes that involve the fins, also seems to be a very interesting approach for these rocket-like configurations. With such an approach, small grid modifications, or even small configuration modification, are quite simple to be accommodated in the sense that one does not need to regenerate all the meshes or, even, to reschedule the flow of information; 3. Point concentration: the use of multiblock meshes allows the refinement of localized regions in a way very similar to unstructured meshes, hence providing the needed flexibility to discretize complex configurations. Finally, the power of this combined Chimera and patched grid simulation capability becomes evident when one considers that it was possible to simulate the flow over a complete sounding rocket and, at the same time, to capture details of phenomena occurring along the trailing edge of the frontal fins. This indicates that the methodology presented allowed grid refinement characteristics similar to those found in unstructured meshes, without the inconvenience of indirect addressing, as described in Long, Khan and Sharp (1991).

ACKNOWLEDGEMENTS The authors gratefully acknowledge the partial support provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under the Integrated Project Research Grant No. 312064/2006-3.

REFERENCES Antunes, A.P., 2000, “Simulation of aerodynamic flows using overset multiblock grids,” M.S. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil (in Portuguese, original title is “Simulação de Escoamentos Aerodinâmicos Utilizando Malhas de Blocos Múltiplos Sobrepostos”).

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Antunes, A.P., Basso, E., and Azevedo, J.L.F., 2000, “Holecut: a program for the generation of Chimera grids,” Instituto de Aeronáutica e Espaço, CTA/IAE/ASE-N, São José dos Campos, SP, Brazil (in Portuguese, original title is “Holecut: Um Programa de Geração de Malhas Chimera”). Azevedo, J.L.F., Menezes, J.C.L., and Fico Jr., N.G.C.R., 1996, “Accurate turbulent calculations of transonic launch vehicles flows,” Proceedings of the 14th AIAA Applied Aerodynamics Conference, AIAA Paper No. 96-2484-CP, Vol. 3, New Orleans, LA, USA, pp. 841-851. Azevedo, J.L.F., Strauss, D., and Ferrari, M.A.S., 1997, “Viscous multiblock simulations of axisymmetric launch vehicle flows,” Proceedings of the 15th AIAA Applied Aerodynamics Conference, AIAA Paper No. 97-2300-CP, Vol. 2, Atlanta, GA, USA, pp. 664-674. Basso, E., Antunes, A.P., and Azevedo, J.L.F., 2003, “Chimera simulations of supersonic flows over a complex satellite launcher configuration,” Journal of Spacecraft and Rockets, Vol. 40, No. 3, pp. 345-355. Bigarella, E.D.V., 2007, “Advanced turbulence modelling for complex aerospace applications,” Ph.D. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil. Bigarella, E.D.V., Azevedo, J.L.F., 2007, “Advanced eddy-viscosity and Reynolds-stress turbulence model simulations of aerospace applications,” AIAA Journal, Vol. 45, No. 10, pp. 2369-2390. Blake, W.B., 1998, “Missile Datcom – User’s Manual,” Wright-Patterson AFB, Ohio, USA. Fletcher, C.A.J., 1991, “Computational techniques for fluid dynamics,” Vol. 2, Spring-Verlag, NewYork, USA. Jameson, A., Schmidt, W., and Turkel, E., 1981, “Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes,” Proceedings of the 14th Fluid and Plasma Dynamic Conference, AIAA Paper No. 81-1259, Palo Alto, CA, USA. Long, L.N., Khan, M.M.S., and Sharp, H.T., 1991, “Massively parallel three-dimensional Euler/NavierStokes method,” AIAA Journal, Vol. 29, No. 5, pp. 657666. doi: 10.2514/3.10635 Papa, J.C., Azevedo, J.L.F., 2003, “Three dimensional flow simulations over a typical sounding rocket”, Proceedings of the 21st AIAA Applied Aerodynamics Conference, AIAA Paper No. 2003-3421, Orlando, FL, USA.

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Pio, D.M., Basso, E., Souza, C.E., Azevedo, J.L.F., and Silva, R.G.A., 2010, “Numerical simulations of the aerodynamic load distributions over the VS-30 sounding rocket,” Proceedings of the 13th Brazilian Congress of Thermal Sciences and Engineering - ENCIT 2010, Uberlândia, MG, Brazil.

Vieira, R., Azevedo, J.L.F., Fico Jr., N.G.C.R., and Basso, E., 1998, “Three dimensional flow simulation in the test section of a slotted transonic wind tunnel,” Proceedings of the 21st Congress of the International Council of the Aeronautical Sciences, ICAS, Paper No. 98-R.3.11, Melbourne, Australia.

Pulliam, T.H., Steger, J.L., 1980, “Implicit finitedifference simulations of three-dimensional compressible flow,” AIAA Journal, Vol. 18, No. 2, pp. 159-167. doi: 10.2514/3.50745

Wang, Z.J., Buning, P., and Benek, J., 1995, “Critical evaluation of conservative and non-conservative interface treatment for Chimera grids,” Proceedings of the 33rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper No. 95-0077, Reno, NV, USA.

Strauss, D., Azevedo, J.L.F., 1999, “A numerical study of turbulent afterbody flows including a propulsive jet,” Proceedings of the 17th AIAA Applied Aerodynamics Conference, AIAA Paper No. 99-3190-CP, Norfolk, VA, USA, pp. 654-664. Turkel, E., Vatsa, V.N., 1994, “Effect of artificial viscosity on three-dimensional flow solutions,” AIAA Journal, Vol. 32, No. 1, pp. 39-45.

Wang, Z.F., Yang, H.Q., 1994, “A unified conservative zonal interface treatment for arbitrarily patched and overlapped grids,” Proceedings of the 32nd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper No. 94-0320, Reno, NV, USA.

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Thesis abstracts This section presents the abstract of most recent Master or PhD thesis related to aerospace technology and management

Widely linear processing in antenna array: purpose, evaluation and hardware implementation Adilson Walter Chinatto Junior State University of Campinas chinatto@espectro-eng.com.br Thesis submitted for Masters in Electrical Engineering at State University of Campinas, UNICAMP, Campinas, São Paulo State, Brazil, 2011. Advisors: Dr. João Marcos Travassos Romano and Dr. Cynthia Cristina Martins Junqueira Keywords: Smart antenna array, Widely linear processing, Adaptive algorithm, Beamforming, FPGA. Abstract: Widely Linear Processing, developed during the 1990s, has led to an improved performance of adaptive algorithms under certain situations that involve improper signals. When applied to antenna arrays, this type of processing shows to be potentially more robust and efficient than the classical filtering techniques. The objective of this work was to extend several classic adaptive beamforming algorithms to the widely linear form, verifying by means of simulations the potential gains in performance when applied to the task of mitigating interference in antenna arrays. Trained, restricted and blind algorithms are considered, covering a relatively broad range of feasible scenarios. Addressing the use of antenna arrays in scenarios in which the incident signals involved have real modulation, optimizations for the widely linear algorithms are proposed, thereby promoting reductions in the computational complexity, while maintaining the original algorithm performance. These optimizations are applied to trained, restricted and blind algorithms, and their performance is compared through simulations with the performances obtained using the original algorithms in their largely linear and strictly linear versions. Finally, an antenna array test platform is implemented in the hardware, allowing practical tests to be carried out. A set of measures taken with the antenna array test platform is exhibited, which includes characterization of antennas, non-adaptive beamforming and interference mitigation using adaptive algorithms.

Study of the influence of different types of environmental conditionings on the mechanical properties of carbon/epoxy composites José Antonio Peixoto Cunha Technological Institute of Aeronautics comitequalidade301@sp.senai.br Thesis submitted for PhD degree in Aeronautical and Mechanical Engineering at Technological Institute of Aeronautics, ITA, São José dos Campos, São Paulo State, Brazil, 2010. Advisors: Dr. Mirabel Cerqueira Rezende Keywords: Epoxy/carbon composites, Environmental conditioning, Mechanical behavior. Abstract: The wide range of structural composite material applications, mainly in aeronautical and naval fields, can result in an almost inevitable contact with liquids and vapors, which can affect the mechanical performance of processed components. In this context, the present work aimed to contribute in the understanding of different environmental conditioning effects on the mechanical behavior of carbon fiber/ epoxy 8552 composites. Five different conditionings were performed: room temperature, hygrothermal (80°C and 90% relative humidity), salt spray, ozone and water immersion. Compression, interlaminar shear, longitudinal and transversal tension strength tests were carried out in two different temperatures: room (22°C) and high (82°C) temperatures. The obtained results show that the mechanical behavior of the studied composites is mainly affected by humidity exposition, as found in hygrothermal chamber and water immersion. Conditionings in both salt spray and ozone chambers show also deleterious effects on the mechanical behavior of material, but in minor intensity. This behavior is attributed to the slow water diffusion in the composites in salt environment and also to the ozone attack to occur preferentially on the external surface of the specimen. Fractografic analyses of the fracture surfaces show that the mechanical properties decreasing are associated with the polymer matrix degradation, delamination presence and interface weakness.

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Thesis Abstract

Analysis of the wind profile in the surface boundary layer and meteorological systems at the Alcântara Launching Center Carlos Alberto Ferreira Gisler National Institute for Space Research gisler@icea.gov.br

High-order unstructured spectral finite volume method for aerodynamic applications Carlos Breviglieri Junior Technological Institute of Aeronautics carbrevi@yahoo.com.br

Thesis submitted for Masters in Meteorology at National Institute for Space Research, INPE, São José dos Campos, São Paulo State, Brazil, 2009.

Thesis submitted for Masters in Electronic and Computation Engineering at Technological Institute of Aeronautics, ITA, São José dos Campos, São Paulo State, Brazil, 2010.

Advisor: Dr. Gilberto Fisch

Advisor: Dr. João Luiz F. Azevedo

Keywords: Anemometric Tower, Weibull distribution, Beta distribution, Principal Components Analysis (PCA).

Keywords: High-order methods, CFD, Aerodynamics, Spectral finite volume methods, Unstructured grids.

Abstract: This study aimed to conduct a thorough analysis of the profiles of wind speed and direction and the atmospheric systems characteristics associated with the data collected by the Tower of Wind or Anemometric Tower (TA) at the Alcântara Launching Center, including the verification of the data quality collected in this center. The wind data was collected at the TA from the period from 1995 to 1999 and it was obtained in six different levels (6.0; 10.0; 16.3; 28.5; 43.0 and 70.0 m). The statistical distributions Beta, Normal and Weibull distribution were adjusted for analysis, identifying the best approximation of the complex to the distributions. The Weibull distribution for the period of study presented a good adjustment for values between 3.0 and 9 ms-1 as well as the Normal distribution a good adjustment for values between 4.0 and 9.0 ms-1. The correlation between the values of wind speed and direction for the levels of TA was performed and the results showed that the profiles are higher than 0.70 (strong correlation). The study made use of the technique of Principal Components Analysis (PCA) in vertical profiles of wind, which allowed the identification of existing structures in the profiles and the identification of the influence of atmospheric systems in wind vertical profiles. The components of the wind direction for the rainy season (March) present percentage of 60% in 1ACP, 20% for 2ACP and 10% for 3ACP. This information is associated with the frequencies of the systems operating in the CLA. Regarding the analysis of wind speed of ACP, it was presented in 1ACP percentage above 93%, in both periods (rainy or dry) associated with a predominant physical process in the CLA. It was also carried out a case study on a rainy season in March 2005 in order to analyze the wind profiles and the atmospheric systems.

100

Abstract: An implicit finite volume algorithm is developed for higher-order unstructured, cell-centered, steady-state computation of inviscid compressible flows, i.e., governed by the Euler equations. The Spectral Finite Volume method is used to achieve high-order spatial discretization of the domain, coupled with a matrix-free LU-SGS algorithm to solve the linear system arising from implicit discretization of the governing equations, avoiding the explicit storage of the flux Jacobian matrices. A proper limiter implementation for higherorder discretization is discussed and a new formula for limiting the higher-order terms of the reconstruction polynomial is introduced. The issue of mesh refinement in accuracy measurements for unstructured meshes is investigated. A straightforward methodology is applied for accuracy assessment of the higher-order unstructured approach based on entropy levels and direct solution error calculation. The accuracy, fast convergence and robustness of the proposed higher-order unstructured solver for different speed regimes are demonstrated via several test cases for the 2nd-, 3rd- and 4th-order discretizations. Solutions of different orders of accuracy are compared in detail through the analysis of several test cases. The possibility of reducing the computational cost required for a given level of accuracy using highorder discretization is demonstrated. The main features of the present methodology include the reconstruction algorithm that yields 2nd-, 3rd- and 4th-order spatially accurate schemes, an implicit time march algorithm, high-order domain boundaries representation and a hierarchical moment limiter to treat flow solution discontinuities.

J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 99-102, Jan. - Apr., 2011


Thesis Abstract

Nonlinear turbulent transonic flow phenomena influence on aeroelastic stability analysis

states obtained by rational interpolating polynomials. The complete system of equations is written in state space format in the Laplace domain. The aeroelastic stability condition can, then, be determined by standard eigenvalue analyses of the system dynamic matrix.

Hugo Stefanio de Almeida Technological Institute of Aeronautics almeida_hsa@yahoo.com.br Thesis submitted for Masters in Aeronautical and Mechanical Engineering at Technological Institute of Aeronautics, ITA, São José dos Campos, São Paulo State, Brazil, 2010. Advisor: Dr. João Luiz F. Azevedo Keywords: Aeroelastic analysis, Stability, Transonic flow, Turbulent flow, CFD. Abstract: The work is aimed at studying the influence of viscous effects in transonic aeroelastic analyses. To achieve this goal, a two-dimensional and viscous aeroelastic computational solver, for CAE analysis, is developed, which uses unstructured computational meshes and which is able to capture the main aeroelastic phenomena relevant in the transonic regime of flight. The aeroelastic system considered to test the present methodology is the classical typical section model. The system has two structural degrees of freedom. These are pitching and plunging, or heaving. The structural degrees of freedom can be treated within the solver in a coupled manner or separately, in a loosely coupled fashion. The typical section model is an approximation to the treatment of a full wing, in which the airfoil at 75% of the semi-span is analyzed. The structural response is obtained by solving a set of second order ordinary differential equations in time, with aerodynamic forcing. The coupling of the structural degrees of freedom occurs primarily through the aerodynamic forcing terms. The unsteady aerodynamic problem is treated through the numerical solution of the Reynolds-averaged NavierStokes equations. These equations are solved using a finite volume method for unstructured computational grids, which uses a centered second-order spatial discretization and a second-order time marching scheme. Turbulence closure is achieved through the Spalart-Allmaras oneequation eddy viscosity turbulence model. A reduction of the computational time for the unsteady aerodynamic simulations is obtained through the implementation of a few convergence acceleration methods, which includes the use of a constant CFL number, implicit residual smoothing and unsteady multigrid methods. The aeroelastic problem is solved through the coupling of the aerodynamic and structural formulations. In the present case, the structural equations are cast in a modal formulation and the unsteady aerodynamic responses are represented by aerodynamic

Automation of H-infinity controller design and its observer-based realization Fausto de Oliveira Ramos National Institute for Space Research fausto_ramos@yahoo.com Thesis submitted for double-diploma PhD degree in Space Engineering and Technologies at National Institute for Space Research, INPE, São José dos Campos, Brazil, and in Control Systems and Flight Dynamics at Institut Supérieur de l’Aéronautique et de l’Espace, ISAE, Toulouse, France, 2011. Advisors: Dr. Waldemar de Castro Leite Filho and Prof. Dr. Daniel Alazard Keywords: Control, Design, Automation, Observer-Based Realization, Computational intelligence, Robustness. Abstract: This work discusses the advantages of combining established techniques in the field of control engineering with elements of artificial intelligence, providing a certain level of automation and the ability to explore innovative proposals for better compliance with design specifications. The rationale for adopting this philosophy is justified by the complexity of certain systems, where multiple conflicting requirements must be met for each operating point. It is almost inevitable that the original problem must be adapted (either through simplifications or linearizations) in order to become feasible. If on one hand the designer must define and propose structures and techniques related to solving the problem, sometimes he will realize that certain choices should be made at the expense of other alternatives that could also be explored. In this context, a mechanism based on computational intelligence can accelerate the development of the project and expand the horizons of research revealing new possibilities, which is shown here in two case studies, both based on a time-variant model of a launch vehicle, where gain-scheduling is applied with the linear quadratic and H-infinity techniques. Since interpolation is an important factor for stability because of the varying parameters of the model, one includes the smoothing of certain elements of the control system into the design specifications which include other factors such as stability,

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Thesis Abstract

performance and robustness. From these two scenarios, a mechanism based on computational intelligence ─ consisting of a genetic algorithm (responsible for an evolutionary process mirrored from the Darwinian natural selection) and fuzzy systems (where the design specifications are stored) ─ searches for controllers and selects those ones that best comply with the  specifications. In the linear-quadratic case, besides the smoothing of the controller gains, one obtains the optimization of the control system for the entire trajectory of the vehicle, a fact which is not only demonstrated but also validated through hardware-in-the-loop simulations. In the H-infinity case, the focus is more complex: firstly, taking into account the robust aspect specifically for time-varying systems, it is proposed in this paper a metric for assessing the impact of exponential variations in the plant model regarding the robust stability of the control system. The metric is simple and based on existing functions within MATLAB(R). Moreover, one adds to the aforementioned objectives the functional duplication of the controller, allowing to use it

also as an observer, with obvious utility for detecting and isolating faults; as the greatest interest lies in the quality of the estimation of the interpolated controllers in observer form during non-linear digital simulations, the smoothing is applied to the gains used to obtain these estimates from the state vector controller, and to the values of the closed-loop poles as well to ensure system stability at each operating point. Finally, one of the tasks required by this technique is the choice of the closed-loop poles combinatoric in order to provide the best characteristics in relation to noise and signal error for each estimate: again, the computational intelligence can be used to select these combinations in situations where the number of poles and thus combinations is considerably high. Therefore, the main objective of this work was to allow the contemplation of the possibilities arising from the synergy between computational intelligence and control engineering, motivating these professionals to experiment modern tools as a way to obtain better results in meeting the design specifications.

Errata In the work “Synthesis of a boron modified phenolic resin”, Vol.2, Nº.2, May. – Aug., 2010, pp.173, in “Results and Discussion”, the Scheme 3: Synthesis of BPFR monomer, described as:

should be replaced by:

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Instructions to the Authors

Scope and editorial policy The Journal of Aerospace Technology and Management is the official publication of Institute of Aeronautics and Space (IAE) of the Department of Aerospace Science and Technology (DCTA), São José dos Campos, São Paulo State, Brazil. The journal is published three times a year (April, August 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 the author should classify it according to the area selected from the topics: • Acoustics • Aerodynamics • Aerospace Systems • Applied Computation • Automation • Chemistry • Defense • Electronics

• Management Systems • Materials • Mechanical Engineering • Meteorology • Propulsion • Structures • Vibration

The journal uses the “double blind peer review process” for evaluation of the manuscript. The submissions, except thesis and book reviews, will be evaluated by three Editorial board members or ad hoc referees, and may be selected for publication according to the editorial policy of the journal.

Mandatory requirements All papers must include: type of contribution (review article, original paper, short communication, case report, book reviews or theses), title, authors’ names, abstract and key words (three to six items that should be based on NASA Thesaurus volume 2 – Access Vocabulary). All authors should be identified with full name, e-mail, institution to which they are related, city and country. One of them should be indicated as the author for correspondence.

Contents • Editorial Any researcher may write the editorial on the invitation of the Editor-in-Chief. • Review articles They should cover subjects falling within the scope of the journal. These contributions should be presented in the same format as a full paper, except that they should not be divided into sections such as introduction, methods, results and discussion. However, they must include a 150 to 200-word abstract, key words, concluding remarks, acknowledgment and references. The article should not exceed 20 pages. • Technical papers These articles should report the results of original research and must include: a 150 to 200-word abstract, key words, introduction, methods, results and discussion, acknowledgment, references, tables and/or figures. The article should not exceed 16 pages. •Communications These articles should report previous results of ongoing research. They should include a 150 to 200-word abstract, key words, tables and/or figures, acknowledgment and references. The communication should not exceed eight pages. • Thesis abstracts The journal welcomes Masters and PhD thesis abstracts for publication.

Paper submission Manuscript should be written in English or Portuguese and submitted electronically. The manuscripts written in Portuguese must present the title and the abstract translated into English, with the exact same content. If there is any conflict of interest with regard to the evaluation of the manuscript, the author must send a declaration indicating the reasons, for the review process occur fairly. See the instructions on www.jatm.com.br/papersubmission.

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After submitting the manuscript, the corresponding author will receive an e-mail with the Term of Copyright Transfer, in which the author agrees to transfer copyright to the Institute of Aeronautics and Space (IAE), in case of acceptance for publication, thus being forbidden any means of reproduction (printed or electronic) without previous authorization of the Editor-in-Chief. If the reproduction is allowed, it is mandatory to mention the Journal of Aerospace Technology and Management. The author also declares that the manuscript is an original paper and that its content is not being considered for publication in other periodicals and that all co-authors participated satisfactorily in the paper elaboration as to make public the responsibility for its content. The declaration must be printed, signed by the main author and sent back by mailing to the following address: Instituto de Aeronáutica e Espaço (IAE)/ATTN: Helena Prado/ Praça Mal. Eduardo Gomes, 50 – Vila das Acácias/ CEP 12228-901/São José dos Campos/ São Paulo/Brazil. References References should be cited in the text by giving the last name of the author(s) and the year of publication. Either use “Recent work (Smith and Farias, 1997)” or “Recently Smith and Farias (1997)”. With four or more names, use the form “Smith et al. (1997)”. If two or more references would have the same identification, distinguish them by appending “a”, “b” etc., to the year of publication. Acceptable references include journal articles, numbered papers, books and submitted articles, if the journal is identified. References from private communications, dissertations, thesis, published conference proceedings and preprints from conferences should be avoided. Self citation should be limited to a minimum. It is recommended that each reference contains the digital object identifier number (DOI). References retrieved from the internet should be cited by the last name of the author(s) and the year of publication, or n.d. if not available, followed by the date of access. Standards should be cited in text by the acronym of entity followed by their number, and doesn’t need to appear in the reference list. References should be listed in alphabetical order, according to the last name of the first author, at the end of the article. Some sample references follow: Alves, M. B., Morais, A. M. F., 2009, “The management of Knowledge and Technologies in a Space Program”, Journal of Aerospace Technology and Management, Vol. 1, No 2, pp. 265-272. doi:10.5028/jatm.2009.0102265272 Bordalo, S. N., Ferziger, J. H. and Kline, S. J., 1989, “The Development of Zonal Models for Turbulence”, Proceedings of the 10th Brazilian Congress of Mechanical Engineering, Vol. 1, Rio de Janeiro, Brazil, pp.41-44. Coimbra, A. L., 1978, “Lessons of Continuum Mechanics”, Ed. Edgard Blücher, São Paulo, Brazil, 428p. Clark, J. A., 1986, Private Communication, University of Michigan, Ann Harbor. 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. EMBRAPA, 1999, “Polítics of R&D”, Retrieved in May 8, 2010, from http://www.embrapa.br/publicacoes / institucionais/polPD.pdf,. 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. Illustrations All illustrations, line drawings, photographs and graphs should be referred as “Figure” and submitted with good definition (1 to 2 mega pixels). References should be made in the text to each illustration using the abbreviated form “Fig.”, except in the beginning of the phrase. Explanations should be given in the figure legends, so that illustrations are kept clean Tables Authors should take notice of the limitations set by the size and layout of the journal. Therefore, large tables should be avoided. All tables must be numbered and mentioned in the text as “Table”. Equations Equations should be typed on individual lines, identified by numbers enclosed in parenthesis. References should be made in the text to each equation using the abbreviated form “Eq.”, except in the beginning of the phrase, where the form “Equation” should be used. Acknowledgments The financial support received for the elaboration of the manuscript must be declared in this item.

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J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 103-104, Jan. - Apr., 2011



Vol.3 N.1 - Journal of Aerospace Technology and Management