Large eddy simulation of multiphase flows using the volume of fluid method: Part 1—Governing equations and a priori analysis

Markus Klein; S. Ketterl; J. Hasslberger

doi:10.1007/s42757-019-0019-9

Experimental and Computational Multiphase Flow 2019, 1(2): 130-144 https://doi.org/10.1007/s42757-019-0019-9

Research Article | Issue | Published: 02 May 2019

Large eddy simulation of multiphase flows using the volume of fluid method: Part 1—Governing equations and a priori analysis

Show Author's Information Hide Author's Information Markus Klein(

), S. Ketterl, J. Hasslberger

Department of Aerospace Engineering, Bundeswehr University Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany

Keywords:

two-phase flow LES, governing equations, filtering, Favre filtering, volume averaging, a priori analysis

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Klein M, Ketterl S, Hasslberger J. Large eddy simulation of multiphase flows using the volume of fluid method: Part 1—Governing equations and a priori analysis. Experimental and Computational Multiphase Flow, 2019, 1(2): 130-144. https://doi.org/10.1007/s42757-019-0019-9

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Abstract

Compared to Large Eddy Simulation (LES) of single-phase flows, which has become a mature and viable turbulence modelling technique, the LES of two-phase flows with moving immiscible interfaces is at a rather early development stage. There is no standard set of governing equations for two-phase flow LES, but rather a variety of different formulations, all with advantages and disadvantages. This paper discusses and analyses in detail the governing equations for two-phase flow LES in the context of the Volume of Fluid method, as well as suitable Subgrid Scale closures for the different unknown terms. A particular focus is on the Favre filtered one fluid formulation of the momentum equations, but a comparison with the filtered and the volume averaged version of the balance equations is made as well. Differences and commonalities between the different approaches are discussed and, based on a priori analysis of explicitly filtered Direct Numerical Simulation data, suitable closure models for a posteriori analysis are identified.

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About this article

Large eddy simulation of multiphase flows using the volume of fluid method: Part 1—Governing equations and a priori analysis

Show Author's information Hide Author's Information Markus Klein(

), S. Ketterl, J. Hasslberger

Department of Aerospace Engineering, Bundeswehr University Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany

Abstract

Keywords: two-phase flow LES, governing equations, filtering, Favre filtering, volume averaging, a priori analysis

References(45)

Alajbegovic, A. 2001. Large-eddy simulation formalism applied to multiphase flows. In: Proceedings of ASME 2001 Fluids Engineering Division Summer Meeting, 529-534.

Aniszewski, W., Bogusławski, A., Marek, M., Tyliszczak, A. 2012. A new approach to sub-grid surface tension for LES of two-phase flows. J Comput Phys, 231: 7368-7397.

DOI Google Scholar

Buonfiglioli, M., Mendonça, F. 2005. LES-VOF simulation of primary diesel spray break-up with synthetic inlet perturbations. In: Proceedings of the 18th International Conference on Liquid Atomization and Spray Systems, 93.

Chesnel, J., Menard, T., Reveillon, J., Demoulin, F. X. 2011a. Subgrid analysis of liquid jet atomization. Atomization Spray, 21: 41-67.

DOI Google Scholar

Chesnel, J., Reveillon, J., Menard, T., Demoulin, F. X. 2011b. Large eddy simulation of liquid jet atomization. Atomization Spray, 21: 711-736.

DOI Google Scholar

Clark, R. A., Ferziger, J. H., Reynolds, W. C. 1979. Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J Fluid Mech, 91: 1-16.

DOI Google Scholar

De Villiers, E., Gosman, A., Weller, H. 2004. Large eddy simulation of primary diesel spray atomization. SAE Technical Paper 2004-01-0100.

DOI Google Scholar

Fulgosi, M., Lakehal, D., Banerjee, S., de Angelis, V. 2003. Direct numerical simulation of turbulence in a sheared air-water flow with a deformable interface. J Fluid Mech, 482: 319-345.

DOI Google Scholar

Garnier, E., Adams, N., Sagaut, P. 2009. Large Eddy Simulation for Compressible Flows. Dordrecht: Springer Netherlands.

DOI

Hasslberger, J., Ketterl, S., Klein, M., Chakraborty, N. 2019. Flow topologies in primary atomization of liquid jets: A direct numerical simulation analysis. J Fluid Mech, 859: 819-838.

DOI Google Scholar

Hasslberger, J., Klein, M., Chakraborty, N. 2018. Flow topologies in bubble-induced turbulence: A direct numerical simulation analysis. J Fluid Mech, 857: 270-290.

DOI Google Scholar

Herrmann, M. 2013. A sub-grid surface dynamics model for sub-filter surface tension induced interface dynamics. Comput Fluids, 87: 92-101.

DOI Google Scholar

Herrmann, M. 2015. A dual-scale LES subgrid model for turbulent liquid/gas phase interface dynamics. In: Proceedings of the 15th International Symposium on Numerical Methods for Multiphase Flow, Paper No. AJKFluids2015-21052.

DOI

Ishii, M. 1975. Thermo-fluid dynamic theory of two-phase flow. NASA Sti/recon Technical Report A.

Google Scholar

Joshi, J. B. 2001. Computational flow modelling and design of bubble column reactors. Chem Eng Sci, 56: 5893-5933.

DOI Google Scholar

Kempf, A. M., Wysocki, S., Pettit, M. 2012. An efficient, parallel low-storage implementation of Klein’s turbulence generator for LES and DNS. Comput Fluids, 60: 58-60.

DOI Google Scholar

Ketterl, S., Klein, M. 2018. A-priori assessment of subgrid scale models for large-eddy simulation of multiphase primary breakup. Comput Fluids, 165: 64-77.

DOI Google Scholar

Klein, M., Chakraborty, N., Gao, Y. 2016. Scale similarity based models and their application to subgrid scale scalar flux modelling in the context of turbulent premixed flames. Int J Heat Fluid Flow, 57: 91-108.

DOI Google Scholar

Klein, M., Sadiki, A., Janicka, J. 2003. A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J Comput Phys, 186: 652-665.

DOI Google Scholar

Kobayashi, H. 2005. The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow. Phys Fluids, 17: 045104.

DOI Google Scholar

Kobayashi, H. 2018. Improvement of the SGS model by using a scale-similarity model based on the analysis of SGS force and SGS energy transfer. Int J Heat Fluid Flow, 72: 329-336.

DOI Google Scholar

Labourasse, E., Lacanette, D., Toutant, A., Lubin, P., Vincent, S., Lebaigue, O., Caltagirone, J. P., Sagaut, P. 2007. Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests. Int J Multiphase Flow, 33: 1-39.

DOI Google Scholar

Lakehal, D., Smith, B. L., Milelli, M. 2002. Large-eddy simulation of bubbly turbulent shear flows. J Turbul, 3, .

DOI Google Scholar

Larocque, J., Vincent, S., Lacanette, D., Lubin, P., Caltagirone, J. P. 2010. Parametric study of LES subgrid terms in a turbulent phase separation flow. Int J Heat Fluid Flow, 31: 536-544.

DOI Google Scholar

Lefebvre, A. H. 1989. Atomization and Sprays. Hemisphere Publishing Corporation.

DOI

Ling, Y., Zaleski, S., Scardovelli, R. 2015. Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model. Int J Multiphase Flow, 76: 122-143.

DOI Google Scholar

Liovic, P., Lakehal, D. 2007a. Interface-turbulence interactions in large-scale bubbling processes. Int J Heat Fluid Flow, 28: 127-144.

DOI Google Scholar

Liovic, P., Lakehal, D. 2007b. Multi-physics treatment in the vicinity of arbitrarily deformable gas-liquid interfaces. J Comput Phys, 222: 504-535.

DOI Google Scholar

Liovic, P., Lakehal, D. 2012. Subgrid-scale modelling of surface tension within interface tracking-based large eddy and interface simulation of 3D interfacial flows. Comput Fluids, 63: 27-46.

DOI Google Scholar

Liu, S. W., Meneveau, C., Katz, J. 1994. On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J Fluid Mech, 275: 83-119.

DOI Google Scholar

Lu, J. C., Tryggvason, G. 2008. Effect of bubble deformability in turbulent bubbly upflow in a vertical channel. Phys Fluids, 20: 040701.

DOI Google Scholar

Mitran, S. M. 2000. Closure Models for the Compuation of Dilute Bubbly Flows. Forschungszentrum Karlsruhe GmbH, Karlsruhe.

Nicoud, F., Toda, H. B., Cabrit, O., Bose, S., Lee, J. 2011. Using singular values to build a subgrid-scale model for large eddy simulations. Phys Fluids, 23: 085106.

DOI Google Scholar

Sabisch, W. 2000. Dreidimensionale numerische Simulation der Dynamik von aufsteigenden Einzelblasen und Blasenschwärmen mit einer Volume-of-Fluid Methode. Forschungszentrum Karlsruhe, Wissenschaftliche Berichte FZKA 6478.

DOI

Sabisch, W., Wörner, M., Grötzbach, G., Cacuci, D. G. 2001. 3D volume-of-fluid simulation of wobbling bubble in a gas-liquid system of low Morton number. In: Proceedings of the 4th International Conference on Multiphase Flow.

Sagaut, P. 2002. Large Eddy Simulation for Incompressible Flows. Springer Berlin Heidelberg.

DOI

Schumann, U. 1975. Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J Comput Phys, 18: 376-404.

DOI Google Scholar

Shinjo, J., Umemura, A. 2011. Detailed simulation of primary atomization mechanisms in diesel jet sprays (isolated identification of liquid jet tip effects). P Combust Inst, 33: 2089-2097.

DOI Google Scholar

Smagorinsky, J. 1963. General circulation experiments with the primitive equations. Mon Wea Rev, 91: 99-164.

DOI

Toutant, A., Chandesris, M., Jamet, D., Lebaigue, O. 2009. Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 1: Theoretical development. Int J Multiphase Flow, 35: 1100-1118.

DOI Google Scholar

Toutant, A., Labourasse, E., Lebaigue, O., Simonin, O. 2008. DNS of the interaction between a deformable buoyant bubble and a spatially decaying turbulence: A priori tests for LES two-phase flow modelling. Comput Fluids, 37: 877-886.

DOI Google Scholar

Tryggvason, G., Dabiri, S., Aboulhasanzadeh, B., Lu, J. C. 2013. Multiscale considerations in direct numerical simulations of multiphase flows. Phys Fluids, 25: 031302.

DOI Google Scholar

Tryggvason, G., Scardovelli, R., Zaleski, S. 2011. Direct Numerical Simulations of Gas-Liquid Multiphase Flows. Cambridge University Press.

Vincent, S., Larocque, J., Lacanette, D., Toutant, A., Lubin, P., Sagaut, P. 2008. Numerical simulation of phase separation and a priori two-phase LES filtering. Comput Fluids, 37: 898-906.

DOI Google Scholar

Vreman, A. W. 2004. An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications. Phys Fluids, 16: 3670.

DOI Google Scholar

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Publication history

Acknowledgements

Publication history

Received: 27 February 2019

Revised: 29 March 2019

Accepted: 30 March 2019

Published: 02 May 2019

Issue date: June 2019

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Acknowledgements

Support by the German Research Foundation (DFG, KL1456/1-1 and KL1456/4-1) is gratefully acknowledged. Computer resources for this project have been provided by the Gauss Centre for Supercomputing/Leibniz Supercomputing Centre under Grant No. pr48no. The authors also express their gratitude to the developers of PARIS for providing the source code.