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

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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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References

  • 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., Boguslawski, 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.

    Article  MathSciNet  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.

    Article  Google Scholar 

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

    Article  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.

    Article  Google Scholar 

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

  • 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.

    Article  Google Scholar 

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

    Book  Google Scholar 

  • 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.

    Article  MathSciNet  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.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  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.

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

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

    Article  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.

    Article  MathSciNet  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.

    Article  MathSciNet  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  Google Scholar 

  • Lakehal, D., Smith, B. L., Milelli, M. 2002. Large-eddy simulation of bubbly turbulent shear flows. J Turbul, 3, DOI: https://doi.org/10.1088/1468-5248/3/1/025.

    Article  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.

    Article  Google Scholar 

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

    Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

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

    Article  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.

    Article  MathSciNet  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.

    Article  MathSciNet  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.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • 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.

    Article  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.

    Google Scholar 

  • 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.

    Book  Google Scholar 

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

    Article  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.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  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.

    Article  MathSciNet  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.

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Vreman, B., Geurts, B., Kuerten, H. 1995. A priori tests of large eddy simulation of the compressible plane mixing layer. J Eng Math, 29: 299–327.

    Article  MathSciNet  Google Scholar 

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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.

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

    Markus Klein, S. Ketterl & J. Hasslberger

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  1. Markus Klein
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  2. S. Ketterl
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  3. J. Hasslberger
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Correspondence to Markus Klein.

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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. Exp. Comput. Multiph. Flow 1, 130–144 (2019). https://doi.org/10.1007/s42757-019-0019-9

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  • DOI: https://doi.org/10.1007/s42757-019-0019-9

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