Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-19T04:47:28.462Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust Conservative Level Set Method for 3D Mixed-Element Meshes — Application to LES of Primary Liquid-Sheet Breakup

Published online by Cambridge University Press:  03 June 2015

Thibault Pringuey  and
R. Stewart Cant
Thibault Pringuey*
Affiliation:
CFD Laboratory, Department of Engineering, University of Cambridge, UK
R. Stewart Cant
Affiliation:
CFD Laboratory, Department of Engineering, University of Cambridge, UK
*
*Corresponding author.Email:tp299@cam.ac.uk
Get access

Abstract

In this article we detail the methodology developed to construct an efficient interface description technique — the robust conservative level set (RCLS) — to simulate multiphase flows on mixed-element unstructured meshes while conserving mass to machine accuracy. The approach is tailored specifically for industry as the three-dimensional unstructured approach allows for the treatment of very complex geometries. In addition, special care has been taken to optimise the trade-off between accuracy and computational cost while maintaining the robustness of the numerical method. This was achieved by solving the transport equations for the liquid volume fraction using a WENO scheme for polyhedral meshes and by adding a flux-limiter algorithm. The performance of the resulting method has been compared against established multiphase numerical methods and its ability to capture the physics of multiphase flows is demonstrated on a range of relevant test cases. Finally, the RCLS method has been applied to the simulation of the primary breakup of a flat liquid sheet of kerosene in co-flowing high-pressure gas. This quasi-DNS/LES computation was performed at relevant aero-engine conditions on a three-dimensional mixed-element unstructured mesh. The numerical results have been validated qualitatively against theoretical predictions and experimental data. In particular, the expected breakup regime was observed in the simulation results. Finally, the computation reproduced faithfully the breakup length predicted by a correlation based on experimental data. This constitutes a first step towards a quantitative validation.

Keywords

65M0876-0476N99Multiphase flowlevel set methodflux limiterMULESWENO schemethree-dimensionalunstructured meshmixed elementconservative methodatomisationprimary breakupflat sheet breakup.
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 2 , August 2014 , pp. 403 - 439
Copyright
Copyright © Global Science Press Limited 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Barreras, F., Experimental study of the break-up and atomization of a planar liquid sheet, Ph.D. thesis, University of Zaragoza (1998).Google Scholar
[2]Bianchi, G., Pelloni, P., Toninel, S., Scardovelli, R., Leboissetier, A., Zaleski, S., Improving the knowledge of high-speed liquid jets atomization by using quasi-direct 3D simulation, Tech. Rep. 2005-24-089, Society of Automotive Engineers (2005).Google Scholar
[3]Book, D., Boris, J., Hain, K., Flux-Corrected Transport II: Generalization of themethod, Journal of Computational Physics 18 (1975) 248–283.CrossRefGoogle Scholar
[4]Boris, J., Book, D., Flux-Corrected Transport I: SHASTA, a fluid transport algorithm that works, Journal of Computational Physics 11 (1973) 38–69.Google Scholar
[5]Boris, J., Book, D., Flux-Corrected Transport III: Minimal-error FCT algorithms, Journal of Computational Physics 20 (1976) 397–431.CrossRefGoogle Scholar
[6]Bourlioux, A., A coupled Level Set and Volume of Fluid algorithmfor trackingmaterial interfaces, Proceedings of the 6th International Symposium On Computationnal Fluid Dynamics 6 (1995) 15–22.Google Scholar
[7]Brackbill, J., Kothe, D., Zemach, C., A continuum method for modeling surface tension, Journal of Computational Physics 100 (1992) 335–354.Google Scholar
[8]Chang, Y., Hou, T., Merriman, B., Osher, S., A Level-Set formulation of Eulerian capturing methods for incompressible fluid flows, Journal of Computational Physics 124 (1996) 449–464.Google Scholar
[9]Cousin, J., Dumouchel, C., Effect of viscosity on linear instability of a flat liquid sheet, Atomization and Sprays 6 (1996) 563–576.CrossRefGoogle Scholar
[10]de Villiers, E., Gosman, A., Weller, H., Large eddy simulation of primary Diesel spray atomization, Tech. Rep. 2004-01-0100, Society of Automotive Engineers (2004).Google Scholar
[11]DeBar, R., A method in 2D Eulerian hydrodynamics, Tech. Rep. UCID-19683, Lawrence Livermore National Laboratory (1974).Google Scholar
[12]Desjardins, O., Numerical methods for liquid atomization and application in detailed simulations of a diesel jet, Ph.D. thesis, Stanford University (2008).Google Scholar
[13]Desjardins, O., Moureau, V., Knudsen, E., Herrmann, M., Pitsch, H., Conservative Level Set/ghost fluid method for simulating primary atomization, Proceedings of the 20th Annual Conference of the Institute for Liquid Atomization and Spray Systems - Americas.Google Scholar
[14]Dubief, Y., Delcayre, F., On coherent-vortex identification in turbulence, Journal of Turbulence 1 (2000) 1–22.CrossRefGoogle Scholar
[15]Dumbser, M., Kaser, M., Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems, Journal of Computational Physics 221 (2007) 693–723.CrossRefGoogle Scholar
[16]Enright, D., Fedkiw, R., Ferziger, J., Mitchell, I., A hybrid Particle Level Set method for improved interface capturing, Journal of Computational Physics 183 (2002) 83–116.Google Scholar
[17]Fernandez, V., Berthoumie, P., L. G., , Liquid sheet disintegration at high pressure: An experimental approach, Comptes Rendus Mecanique 337 (2009) 481–491.Google Scholar
[18]Fureby, C., Tabor, G., Weller, H., Gosman, A., A comparative study of subgrid scale models in homogeneous isotropic turbulence, Physics of Fluids 9 (1997) 1416–1429.Google Scholar
[19]Fuster, D., Bague, A., Boeck, T., Le Moyne, L., Leboissetier, A., Popinet, S., Ray, P., Scardovelli, R., Zaleski, S., Simulation of primary atomization with an octree adaptive mesh refinement and VOF method, International Journal of Multiphase Flow 35 (2009) 550–565.Google Scholar
[20]Glimm, J., McBryan, O., Menikoff, R., Sharp, D., Front tracking applied to Rayleigh-Taylor instability, SIAM Journal on Scientific and Statistical Computing 7 (1987) 230–251.Google Scholar
[21]Gorokhovski, M., Herrmann, M., Modeling primary atomization, Annual Review of Fluid Mechanics 2008 40 (2008) 343–366.CrossRefGoogle Scholar
[22]Hirt, C., Amsden, A., Cook, J., An arbitrary Lagrangian-Eulerian computing method for all speeds, Journal of Computational Physics 14 (1974) 227–253.CrossRefGoogle Scholar
[23]Hirt, C., Nichols, B., Volume of Fluid method for the dynamics of free boundaries, Journal of Computational Physics 39 (1981) 323–345.CrossRefGoogle Scholar
[24]Hu, C., Shu, C.-W., Weighted essentially non-oscillatory schemes on triangular meshes, Journal of Computational Physics 150 (1999) 97–127.Google Scholar
[25]Hunt, J., Wray, A., Moin, P., Eddies, , streams and convergence zones in turbulent flows, Tech. Rep. CTR-S88, Center for Turbulence Research (1988).Google Scholar
[26]Issa, R., Solution of the implicitly discretised fluid flow equations by Operator-Splitting, Journal of Computational Physics 62 (1985) 40–65.Google Scholar
[27]Jacqmin, D., An energy approach to the continuum surface tension method, Tech. Rep. 960858, American Institute of Aeronautics and Astronautics (1996).Google Scholar
[28]Kim, D., Desjardins, O., Herrmann, M., Moin, P., The primary breakup of a round liquid jet by a coaxial flow of gas, Proceedings of the 20th Annual Conference of the Institute for Liquid Atomization and Spray Systems - Americas.Google Scholar
[29]Kraichnan, R., The structure of isotropic turbulence at very high Reynolds numbers, Journal of Fluid Mechanics 5 (1959) 497–543.CrossRefGoogle Scholar
[30]Kraichnan, R., Direct-interaction approximation for shear and thermally driven turbulence, Physics of Fluids 7 (1964) 1048–1062.Google Scholar
[31]Kraichnan, R., Eulerian and Lagrangian renormalization in turbulence theory, Journal of Fluid Mechanics 83 (1977) 349–374.CrossRefGoogle Scholar
[32]Lax, P., Wendroff, B., Systems of conservation laws, Communications on Pure and Applied Mathematics 13 (1960) 217–237.Google Scholar
[33]Lopez, J., Hernandez, J., Gomez, P., Faura, F., An improved PLIC-VOF method for tracking thin fluid structures in incompressible two-phase flows, Journal of Computational Physics 208 (2005) 51–74.Google Scholar
[34]Magnaudet, J., Rivero, M., Fabre, J., Accelerated flows past a rigid sphere or a spherical bubble. part I Steady straining flow, Journal of Fluid Mechanics 284 (1995) 97–135.Google Scholar
[35]Menard, T., Tanguy, S., Berlemont, A., Coupling Level Set/VOF /ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet, International Journal of Multiphase Flow 33 (2007) 510–524.Google Scholar
[36]Noh, W., Woodward, P., SLIC (simple line interface calculation), Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics Springer-Verlag New York 59 (1976) 330–340.Google Scholar
[37]Olsson, E., Kreiss, G., A conservative level set method for two phase flow, Journal of Computational Physics 210 (2005) 225–246.Google Scholar
[38]Olsson, E., Kreiss, G., Zahedi, S., A conservative level set method for two phase flow II, Journal of Computational Physics 225 (2007) 785–807.CrossRefGoogle Scholar
[39] OpenCFD Ltd, OpenFOAM, User Guide, version 1.5 (July 2008).Google Scholar
[40]Osher, S., Fedkiw, R., Level Set Methods and Dynamic Implicit Surfaces, Applied Mathematical Sciences, 153, New York: Springer, 2002.Google Scholar
[41]Osher, S., Sethian, J., Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics 79 (1988) 12–49.Google Scholar
[42]Pope, S., Turbulent Flows, Cambridge University Press, 2000.Google Scholar
[43]Popinet, S., Zaleski, S., A front tracking algorithm for the accurate representation of surface tension, International Journal for Numerical Methods in Fluids 30 (1999) 775–779.Google Scholar
[44]Pringuey, T., Large eddy simulation of primary liquid-sheet breakup, Ph.D. thesis, University of Cambridge (2012).Google Scholar
[45]Pringuey, T., Cant, R., High order schemes on 3D mixed-element unstructured meshes, Tech. Rep. CUED/A-AERO/TR29, University of Cambridge, Department of Engineering (2010).Google Scholar
[46]Pringuey, T., Cant, R., High order schemes on three-dimensional general polyhedral meshes — Application to the level set method, Communications in Computational Physics 12 (2012) 1–41.Google Scholar
[47]Puckett, E., Almgren, A., Bell, J., Marcus, D., Rider, W., A high order projection method for tracking fluid interfaces in variable density incompressible flows, Journal of Computational Physics 130 (1997) 269–282.Google Scholar
[48]Rusche, H., Dispersed two-phase flows at high phase fractions, Ph.D. thesis, Imperial College of Science, Technology & Medicine (2002).Google Scholar
[49]Ryskin, G., Leal, L., Numerical solution of free boundary problems in fluid mechanics. part I The finite-difference technique, Journal of Fluid Mechanics 148 (1984) 1–17.Google Scholar
[50]Scardovelli, R., Zaleski, S., Direct numerical simulation of free-surface and interfacial flow, Annual Review of Fluid Mechanics 31 (1999) 567–603.Google Scholar
[51]Sethian, J., A fast marching Level Set method for monotonically advancing fronts, Proceedings of the National Academy of Science USA 93 (1996) 1591–1595.Google Scholar
[52]Sethian, J., Fast marching methods, SIAM Review 41 (1999) 199–235.Google Scholar
[53]Shu, C., Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics 77 (1989) 439–471.Google Scholar
[54]Sussman, M., Almgren, A., Bell, J., Colella, P., Howell, L., Welcome, M., Adaptive Level Set approach for incompressible two-phase flows, Journal of Computational Physics 148 (1999) 81–124.CrossRefGoogle Scholar
[55]Sussman, M., Fatemi, E., Smereka, P., Osher, S., An improved Level Set method for incompressible two phase flows, Computers and Fluids 27 (1998) 663–680.Google Scholar
[56]Sussman, M., Puckett, E., A coupled Level Set and Volume-of-Fluid method for computing 3D and axisymetric incompressible two-phase flows, Journal of Computational Physics 162 (2000) 301–337.Google Scholar
[57]Sussman, M., Smereka, P., Osher, S., A Level Set approach for computing solutions to incompressible two phase flow, Journal of Computational Physics 114 (1994) 146–159.Google Scholar
[58]Titarev, V., Tsoutsanis, P., Drikakis, D., WENO schemes for mixed-element unstructured meshes, Communications in Computational Physics 8 (2010) 585–609.Google Scholar
[59]Tryggvason, G., Unverdi, S., Computations of three-dimensional Rayleigh-Taylor instability, Physics of Fluids A 2 (1990) 656.CrossRefGoogle Scholar
[60]Tsoutsanis, P., Titarev, V., Drikakis, D., WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions, Journal of Computational Physics 230 (2011) 1585–1601.CrossRefGoogle Scholar
[61]Unverdi, S., Tryggvason, G., A front tracking method for viscous incompressible multi-fluid flows, Journal of Computational Physics 100 (1992) 25–37.Google Scholar
[62]Van der Pijl, S., Segal, A., Vuik, A., Wesseling, P., A mass-conserving Level Set method for modelling multi-phase flows, International Journal for Numerical Methods in Fluids 7 (2005) 339–361.Google Scholar
[63]Wang, R., Spiteri, R., Linear instability of the fifth-order WENO method, SIAM Journal on Numerical Analysis 45 (2007) 1871–1901.Google Scholar
[64]Weller, H., http://www.opencfd.co.uk/openfoam/index.html#openfoam.Google Scholar
[65]Wu, P., Faeth, G., Aerodynamic effects on primary breakup of turbulent liquids, Atomization and Sprays 3 (1993) 265–289.CrossRefGoogle Scholar
[66]Yoshizawa, A., A statistically-derived subgrid model for the large-eddy simulation of turbulence, Physics of Fluids 25 (1982) 1532–1538.Google Scholar
[67]Yoshizawa, A., A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows, Journal of the Physical Society of Japan 54 (1985) 2834–2839.Google Scholar
[68]Yoshizawa, A., Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling, Physics of Fluids 29 (1986) 2152–2164.Google Scholar
[69]Zalesak, S., Fully multidimensional flux-corrected transport algorithms for fluids, Journal of Computational Physics 31 (1979) 335–362.Google Scholar
[70]Zhang, Y.-T., Shu, C.-W., Third order WENO scheme on three dimensional tetrahedral meshes, Communications in Computational Physics 5 (2009) 836–848.Google Scholar