Full Paper Proc. of Int. Conf. on Recent Trends in Transportation, Environmental and Civil Engineering 2011
Numerical Model of Slug Development on Horizontal Two-phase Flow S.Y.Razavi1, M M.Namin2 1
Consultant Engineer of Shahrab Khazar Consultant, Rasht, Iran Email: email@example.com 2 Associate Professor, Faculty of Civil Engineering, Tehran, Iran Email: firstname.lastname@example.org and Hanratty). By development of numerical simulation, some researchers tend to study such a phenomenon by CFD simulation in different aspects. Surveying slug length and fluctuations beside, also pressure downfall (Marruaz et al) using experimental and numerical study. Moreover, understanding of the general fluid dynamic mechanism leading to slug flow (Vallee and Hohne) have done by means of air-water horizontal channel that was validated by CFD calculations on the same experimental case. Prediction of slug formation in multi -slope channels beside the study of parameters uncertainty (Bohlouly (was the one of remarkable attempts using experimental case and numerical code. Finally, study of slug initiation, growth and its development considering turbulence K-å model was one of the most recent numerical research( Razavi and Namin). In the previous work of Razavi and Namin (2010), it was demonstrated that the numerical presented model is capable of capturing slug initiation and development in horizontal channel. Numerical simulations were made starting from small waves and superficial instabilities that could grow to block the channel and form slugs. The simulation results showed satisfactory adaption with generalized flow regime map for horizontal two-phase flow presented by Taitel and Duklerý. Also, mechanism of slug generation compared favorably with experimental data. This recent paper traces the effect of slug regime on significant parameters of flow such as velocity and pressure using the previous research founding done by authors.
Abstract— In an earlier paper it was show a numerical model to simulate two-phase (liquid/gas) slug flows that can predict the slug initiation and development in horizontal channels. In this work, we consider to the effect of slug generation on significant variables such as velocity and pressure by this numerical model. Quasi-three dimensional simulation results for slug characteristics are validated by the existing multiphase flow model available in the commercial code ANSYS CFX and experimental optical observations captured at the horizontal Channel, referred to in the literature. The commercial CFD package, FLUENT, is used for this numerical study. In order to reduce the time of solution, parallel version of solver is considered. Comparison between FLUENT code, experimental data and validated ANSYS code shows some noticeable points. Keywords- Slug flow, Numerical simulation, Horizontal channel, parallel processing
I. INTRODUCTION The most important characteristic of two-phase flow is interface between liquid and gas phases that consist of various forms. Using classification of various interface distribution of two phases that so-called fluid flow patterns, this type of flow can be expounded. Generally, seven types of flow patterns in horizontal gravity pipe can be described as follow: Bubble flow, Plug flow, Stratified smooth flow, Stratified wavy flow, Slug flow, Annular flow and Spray flow. Slug flow regimes have been found in horizontal conduit for high liquid flow rates, and it is one of the most possible flows in horizontal and near horizontal closed channels. When the airflow rate is increased, surface wave amplitudes become larger to seal the conduit, and wave forms frothy slug where it touches the roof of the conduit. Slugs that travel with a higher velocity than average liquid velocity can cause severe vibration and extremely hazard in equipment that located in the direction and assemblage centers. The significant factors of slug flow are regular fluctuations in pressure and amount of fluid accumulation that can be maintained as appropriate criteria for recognition of this type of flow regime. Review on previous studies shows some researchers such as Taitel and dukler, Mandhane, Omen and Gover  provided flow pattern maps for estimation of onset of noted flow regimes. In the other hand, some experimental investigation have been carried out in order to understanding slug flow properties. That most important investigated characteristics are velocity of slug bubble (Wallis) , the effect of pipe diameter on the flow regime (Hanratty and Lin), hydromechanics of slug motion (Buzkus and Wiggert), pressure fluctuations due to slug flow (Soleimani © 2011 ACEE DOI: 02.TECE.2011.01.36
II. GOVERNING EQUATIONS The basis of the two-fluid model is the formulation of conservation equations for the balance of mass, momentum for each of the phases. Furthermore, transport equation of volume fraction is solved for an isothermal flow. In addition, the realizable model of K-ε is a two-equation model in which two separate transport equations are solved for turbulence kinetic energy and rate of dissipation independently For one-dimensional stratified and slug flow they are . Equations (1), (2) are conservation equations of mass and momentum those are named Navier–Stokes equations. Where ρ is density, μ shows viscosity P represents pressure and g is gravity vector. Term of Fs is the identity interaction between phases across the interfaces. Equation (3) is transport equation of volume fraction that is pointed by C. this formula demonstrates the transport of interfaces by means of velocity vectors ui and uj. (1) u 0 .
Full Paper Proc. of Int. Conf. on Recent Trends in Transportation, Environmental and Civil Engineering 2011 C (u C ) 0 t
the variables and properties in any given cell are either purely representative of one of the phases, or representative of a mixture of the phases, depending upon the volume fraction values. In other words, if the qth fluid’s volume fraction in the cell is denoted as αq, then the following three conditions are possible. αq = 0: The cell is empty (of the qth fluid). αq = 1: The cell is full (of the qth fluid). 0 < αq < 1: The cell contains the interface between the qth fluid and one or more other fluids.
In case of two-phase flow, since density and viscosity variations are just affected by phase changes in domain, these variables are determined based on percent of volume that each phase occupies in any given cell as follows. In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoyancy, YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. C2 and C1 are constants. σk and σε are the turbulent Prandtl numbers for k and ε, respectively. Sk and Sε are user-defined source terms. C 1 (1 C ) 2
Volume Fraction Equation The tracking of the interfaces between the phases is accomplished by the solution of a continuity equation for the volume fraction of one (or more) of the phases. For the qth phase, this equation has the following form. where mqp is the mass transfer from phase q to phase p and mpq is the mass transfer from phase p to phase q.
C 1 (1 C ) 2
The modelled transport equations for turbulence kinetic energy, k and its rate of dissipation, ε in the realizable k-ε model are.
The Geometric Reconstruction Scheme Control-volume formulation requires that convection and diffusion fluxes through the control volume faces be computed and balanced with source terms within the control volume itself. Geometric reconstruction applies a special interpolation treatment to the cells that lie near the interface between two phases. It assumes that the interface between two fluids has a linear slope within each cell, and uses this linear shape for calculation of the advection of fluid through the cell faces. The first step in this reconstruction scheme is calculating the position of the linear interface relative to the center of each partially-filled cell, based on information about the volume fraction and its derivatives in the cell. The second step is calculating the advecting amount of fluid through each face using the computed linear interface representation and information about the normal and tangential velocity distribution on the face. The third step is calculating the volume fraction in each cell using the balance of fluxes calculated during the previous step. Fig 1-a and 1-b show an actual interface shape along with the interfaces assumed during computation by this method.
III. NUMERICAL METHOD A. Finite volume technique This study employ finite volume method as a numerical technique in which, values are calculated at discrete places on a meshed geometry. Generally, “Finite volume” refers to the small volume surrounding each node point on a mesh. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. The method is used in many computational fluid dynamics packages. B. Volume Of Fluid Model Theory The VOF (Volume Of Fluid) model is not only simple model but also efficient method that used in order to track the liquidgas interface. Generally, the VOF model can model two or more immiscible fluids by solving a single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain. In case of water flow in a channel with a region of air on top and a separate air inlet, VOF method is appropriate technique for prediction of .Interface between phases .The employed formulation relies on the fact that two or more fluids (or phases) are not interpenetrating. For each additional phase that is added to the model, a variable is introduced: the volume fraction of the phase in the computational cell. In each control volume, the volume fractions of all phases sum to unity. The fields for all variables and properties are shared by the phases and represent volume-averaged values, as long as the volume fraction of each of the phases is known at each location. Thus © 2011 ACEE DOI: 02.TECE.2011.01. 36
C. Parallel Processing Parallel processing involves an interaction between software, a host process, and a set of compute-node processes. Software interacts with the host process and the collection of compute nodes using a utility called cortex that manages user interface and basic graphical functions. Fig.2 shows the parallel architectures. Parallel solver splits up the grid and data into multiple partitions, then assigns each grid partition to a different compute process. The number of partitions is an integral multiple of the number of compute nodes available. The compute-node processes can be executed on a massively parallel computer, a multiple-CPU workstation, or a network cluster of computers.
Full Paper Proc. of Int. Conf. on Recent Trends in Transportation, Environmental and Civil Engineering 2011 As it was the goal of the CFD calculation to induce surface instabilities, which are r generating waves and slugs sequentially, the interfacial momentum exchange and also the turbulence parameters had to be modeled correctly. To this end, turbulent model of Realizable K-ε model was selected as a viscosity model that is able to model instabilities and turbulence of slug flow. Solution time for calculating 5.0 s of simulation time on the 6 processor lasted about 20 hours using parallel processing method. Selected discretization schemes were presto for pressure, Geo Reconstruction for volume fraction, and first order upwind for other cases. Variable time step between 10-6and 10-3 was appropriate step for simulation of this instable phenomena. Using amounts of 10-3 for residuals, the acceptable convergence has been achieved based on courant number 0.1 for VOF method. Fig 2. Parallel solver Architecture 
V. RESULTS AND DISCUSSION
IV. SETUP AND SOLUTION
Fig. 4 shows calculated sequence of void fraction of quasi3D model and fig 5-a and 5-b show the optical measurements and numerical study of HAWAC channel were performed by Vallee and Hohne, accordingly . Qualitative comparison between quasi-3D model and others shows that the behavior of the slug creation and its propagation is similar in all cases. presented model confirms that stratified flow is generated after exit of slugs. However,there might be a little differences about moment slugs generation in experimental and other CFD models. As can be seen,experimental sequences do not include time lables, and there is not evident that displayed sequences belong to first slug generation or further slugs. Numerical models are, also, different in the moment of slug generation. Because two mentioned models are not quite similar in various features of simulation. Although some efforts done for resemblance of slug conditions, Some features such as initial conditions, The physical setting, turbulance model and interface tracing method lead to differences in superficial instabilities. In the other word, prereqiursit for compelet similarity slug onset moment is certainty in all aspects of initial superficial instabilities.
Based on the experimental study that has been undertaken by Vallee and Hohne, the channel with rectangular crosssection was modeled using a commercial CFD (Computational Fluid Dynamics) package, FLUENT . Dimensions of the model are 4000 x 100 x 30 mm³ (length x height x width). Simulation was performed by a grid consists of 4 x 104 hexahedral elements and 82086 nodes using specific technique of quasi-3D model that can consider the wall effect of channel in a 2Dmodel. Since twodimensional geometry only able to show upper and lower Walls as boundary, the lateral walls and their effect, which play important role in generation of slugs, are neglected in 2D models. In order to avoid this issue, width of any elements is fitted into the width of channel. Using this technique, it can be possible to decline number of elements in comparison of a 3D model, also take advantage of reduction of computation in a 2D model. Fig. 3 shows the maintained quasi-three dimensional geometry. Interface shape represented by geometric reconstruction scheme Two-phase flow with a superficial water velocity of 1.0 m/s and a superficial air velocity of 5.0 m/s was chosen for the CFD calculations. The model inlet was divided into two parts: in the lower 50% of the inlet cross-section, water was injected and in the upper 50% air. An initial water level of 50 mm was assumed for the entire model length. In addition, initial velocity 1.0 m/s was considered for liquid and air phases, and the velocity of air phase was increased gradually until it archived its final amount that was 5.0 m/s. During the simulation, reference pressure was 1 bar, Surface tension was supposed to be 0.0073 n/m. A hydrostatic pressure was assumed for the liquid phase.
Fig 4.Sequence of void fraction calculated by numerical model
Fig 3:quasi-three dimensional geometry
© 2011 ACEE DOI: 02.TECE.2011.01.36
Full Paper Proc. of Int. Conf. on Recent Trends in Transportation, Environmental and Civil Engineering 2011 of velocity in this noted area. Fig. 6-b shows contour of velocity at the moment of slug generation. These contours confirm existence of high gradients in velocity at the position of slug. Because when the slug is forming, it will block the airflow also keep large amount of air close to the ceiling of channel. As a result, it will create high velocity gradient in this area. Fig 5-a. result of experimental study done by Vallee 
Fig 6-b. velocity contour at the moment of slug formation
Figure 7, also, shows the fluctuation of pressure and during the time. It can be found that these irregular series inform us the slug initiation by onset of large-scale fluctuations.
Fig 5-b. result of numerical study done by Vallee and Hohne 
In addition to simulation of slug generation mechanism done on same experimental case of Vallee et al, quasi-3D model presented new founding about behavior of significant parameters of flow such as velocity and pressure due to slug formation. Furthermore, by simulation of slug generation and propagation it is possible to display the pressure fluctuations and outgoing mass flow rate changes that was absent in studies done by vallee. Fig 6-a shows longitudinal velocity profiles during slug generation in different depths at t=3.17s. As can be seen, in the depth of 0.06m located close to the interface, profile reduction in intermediate regions of channel indicates that superficial instabilities and fluctuations are generated in this area, also cause rapid changes in velocity of airflow and finally lead to generation of slug in this zone. The dramatic changes that is shown by pick points are, also, formed in the profile of 0.03m where cells are filled with liquidphase completely, and noted the effect of slug generation close to the bottom of conduct.
Fig 7:series of pressure fluctuations during slug flow
Finally table 1 shows the result of The parallel transient calculation of 6.0s of simulation time. As can be seen, Parallel processing increases the speed of calculations distinctly. By using different number of CPU, it appears that parallel processing on 4 processors can present best result in parallel simulation. It is noteworthy that in noted research done by vallee, the parallel transient calculation of 5.0 s of simulation time on 4 processors lasts 4 days, while in presented model calculation time on same number of processors lasted for just 13:30. TABLE 1. DIFFERENT PARALLEL PROCESSORS TEST
Fig 6-a. velocity profiles at the moment of slug formation
When it comes to the profile of 0.09m, it can be seen that the values of velocity in this depth decrease to the values of water phase velocity. On the other word, the water liquid reaches to the cells located near the roof of conduct. This phenomenon results in compression volume of air volume after the point of slug generation ,and it causes high gradient ÂŠ 2011 ACEE DOI: 02.TECE.2011.01.36
Full Paper Proc. of Int. Conf. on Recent Trends in Transportation, Environmental and Civil Engineering 2011  Vatani,A. and Mokhatab,S., (1999),” Hydraulic design of two phase flow pipelines”,University of Tehran publication.  Soleimani,A.and Hanratty,T.J. (2003), “Critical Liquid Flows for the Transition From the Pseudo-Slug and Stratified Patterns to Slug Flow,” International Journal of Multiphase Flow 29, pp. 5167.  Marruaz,K.S. and Goncalvez,A.L.(2001), “Horizontal Slug Flow in a Large-size Pipeline: Experimental and Modeling” Journal of Brazilian Society of Mechanical Sciences, Vol. 22 No.4.  Vallee, C. and Hahne,T., (2007), “CFD Validation of stratified two-phase flows in a horizontal channel”, Forschungzentrum Dresden-Rossendorf, Germany.  Bohluly,A. And Borghei.S.M, (2010), “ Numerical simulation of two-phase air-water flow in multi slope closed channel”, PHD Thesis, Sharif University of Technology.  Razavi,Y. and Namin,M.M. (2010), “CFD Validation of Slug Two-Phase Flows in a Horizontal Channel” Ovidius University Annals Series: Civil Engineering, Vol. 1 Issue 12,199-206  FLUENT.Inc., (2006),Version 6.3.2, User Manual.  Hirt, C. W. and Nichols, B. D., (1981), “Volume Of Fluid (VOF) Method for the dynamic of free boundaries”, Journal of Computational Physics 39, 201-225.  R.I. Issa and M.H.W. Kempf (2003), “Simulation of slug flow in horizontal and nearly horizontal pipes with the two-fluid model,” International Journal of Multiphase Flow, 29, 69–9
CONCLUSIONS To draw forth a conclusion, The ability of modeling slug flow by quasis-3D model, which was simulated using a threedimensional model by vallee, can be taken into account as one of the most important achievements of this study. moreover the considerable reduction of computing time using a parallel processing system and quasi-three dimensional elements is the other leading result of this paper.Finally,investigation the behavior of major parameters of flow such as velocity and pressure due to slug generation would lead to discover new founding about this uncertain and unknown phenomenon, and it can help to recognize location and the moment of slug formation. REFERENCES  Lauchlan,C.S. and Scaramela,M., (2005), “Air in pipeline”, A literature review, Report SR 349.  Taitel,Y. and Dukler,A.E., (1976), “A model for predicting flow transition in horizontal and near horizontal liquid flow”, AICHE, Journal, Vol.22, No.1, pp47-55.
© 2011 ACEE DOI: 02.TECE.2011.01.36