Journal Home > Volume 1 , Issue 3

Multiphase flows with two or more immiscible liquids, separated by a sharp interface with surface tension, occur in a large variety of environmental and industrial flow problems. The ability to accurately predict such flows has implications for safety, economy, and ecology. As a scale resolving technique, large eddy simulation (LES) is a turbulence model that has the potential to describe such flows with good accuracy. However, during the filtering process of the two-phase flow equations, several unclosed terms appear that are unknown from single-phase flow and their modelling is not yet standardized in the open literature. In this paper, the unknown terms are systematically analyzed based on a-posteriori LES and comparison with a direct numerical simulation (DNS) database. It is shown that the closures for each unknown term strongly interact with the other terms and as well with the numerical scheme. Therefore, only a modelling strategy consisting of a complete set of sub-models and numerical discretization can be identified, rather than individual optimal models. Several promising alternatives are identified and discussed, based on existing and newly developed turbulence and interfacial subgrid scale (SGS) closures.


menu
Abstract
Full text
Outline
About this article

Large eddy simulation of multiphase flows using the volume of fluid method: Part 2—A-posteriori analysis of liquid jet atomization

Show Author's information S. Ketterl1M. Reißmann2Markus Klein1( )
Department of Aerospace Engineering, Bundeswehr University Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
Department of Computer Science, Bundeswehr University Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany

Abstract

Multiphase flows with two or more immiscible liquids, separated by a sharp interface with surface tension, occur in a large variety of environmental and industrial flow problems. The ability to accurately predict such flows has implications for safety, economy, and ecology. As a scale resolving technique, large eddy simulation (LES) is a turbulence model that has the potential to describe such flows with good accuracy. However, during the filtering process of the two-phase flow equations, several unclosed terms appear that are unknown from single-phase flow and their modelling is not yet standardized in the open literature. In this paper, the unknown terms are systematically analyzed based on a-posteriori LES and comparison with a direct numerical simulation (DNS) database. It is shown that the closures for each unknown term strongly interact with the other terms and as well with the numerical scheme. Therefore, only a modelling strategy consisting of a complete set of sub-models and numerical discretization can be identified, rather than individual optimal models. Several promising alternatives are identified and discussed, based on existing and newly developed turbulence and interfacial subgrid scale (SGS) closures.

Keywords: two-phase flow LES, a-posteriori analysis, liquid jet atomization

References(53)

Abadi, M., Barham, P., Chen, J., Chen, Z., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., Isard, M. et al. 2016. TensorFlow: A system for large-scale machine learning. In: Proceedings of USENIX Symposium on Operating Systems Design and Implementation, 16: 265–283
Alajbegovic, A. 2001. Large eddy simulation formalism applied to multiphase flows. In: Proceedings of the ASME 2001 Fluids Engineering Division Summer Meeting, 1: 529–534.
Allauddin, U., Klein, M., Pfitzner, M., Chakraborty, N. 2017. A priori and a posteriori analyses of algebraic flame surface density modeling in the context of Large Eddy Simulation of turbulent premixed combustion. Numer Heat Tr A: Appl, 71: 153–171.
Anderson, B. W., Domaradzki, J. A. 2012. A subgrid-scale model for large-eddy simulation based on the physics of interscale energy transfer in turbulence. Phys Fluids, 24: 065104.
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.
Bianchi, G. M., Minelli, F., Scardovelli, R., Zaleski, S. 2007. 3D large scale simulation of the high-speed liquid jet atomization. SAE Transactions, 116: 333–346.
Chesnel, J., Menard, T., Reveillon, J., Demoulin, F.-X. 2011a. Subgrid analysis of liquid jet atomization. Atomization Spray, 21: 41–67.
Chesnel, J., Reveillon, J., Menard, T., Demoulin, F.-X. 2011b. Large eddy simulation of liquid jet atomization. Atomization Spray, 21: 711–736.
Chollet, F. et al. 2015. Keras: Deep learning library for theano and tensorflow. Available at https://keras.io/.
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.
De Villiers, E., Gosman, A. D., Weller, H. G. 2004. Large eddy simulation of primary diesel spray atomization. SAE Transactions, 113: 193–206.
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.
Garnier, E., Adams, N., Sagaut, P. 2009. Large Eddy Simulation for Compressible Flows. Dordrecht: Springer Netherlands.
DOI
Grosshans, H., Movaghar, A., Cao, L., Oevermann, M., Szász, R. Z., Fuchs, L. 2016. Sensitivity of VOF simulations of the liquid jet breakup to physical and numerical parameters. Comput Fluids, 136: 312–323.
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.
Hasslberger, J., Klein, M., Chakraborty, N. 2018. Flow topologies in bubble-induced turbulence: A direct numerical simulation analysis. J Fluid Mech, 857: 270–290.
Herrmann, M. 2013. A sub-grid surface dynamics model for sub-filter surface tension induced interface dynamics. Comput Fluids, 87: 92–101.
Herrmann, M., Gorokhovski, M. 2008. An outline of a LES subgrid model for liquid/gas phase interface dynamics. In: Proceedings of the 2008 CTR Summer Program, 171–181.
Jiang, G.-S., Shu, C.-W. 1996. Efficient implementation of weighted ENO schemes. J Comput Phys, 126: 202–228.
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.
Klein, M. 2002. Direkte Numerische Simulation des primären Strahlzerfalls in Einstoffzerstäuberdüsen. Ph.D. Thesis. Technical University Darmstadt.
Klein, M., Ketterl, S., Hasslberger, J. 2019. 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.
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.
Kobayashi, H. 2005. The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow. Phys Fluids, 17: 045104.
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 Fl, 72: 329–336.
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.
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 Fl, 31: 536–544.
Leonard, B. P. 1979. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput Method Appl M, 19: 59–98.
Li, X. G., Tankin, R. S. 1991. On the temporal instability of a two-dimensional viscous liquid sheet. J Fluid Mech, 226: 425–443.
Liao, Y. X., Ma, T., Liu, L., Ziegenhein, T., Krepper, E., Lucas, D. 2018. Eulerian modelling of turbulent bubbly flow based on a baseline closure concept. Nucl Eng Des, 337: 450–459.
Ling, Y., Fuster, D., Tryggvason, G., Zaleski, S. 2019. A two-phase mixing layer between parallel gas and liquid streams: Multiphase turbulence statistics and influence of interfacial instability. J Fluid Mech, 859: 268–307.
Ling, Y., Fuster, D., Zaleski, S., Tryggvason, G. 2017. Spray formation in a quasiplanar gas–liquid mixing layer at moderate density ratios: A numerical closeup. Phys Rev Fluids, 2: 014005.
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.
Liovic, P., Lakehal, D. 2007a. Multi-physics treatment in the vicinity of arbitrarily deformable gas–liquid interfaces. J Comput Phys, 222: 504–535.
Liovic, P., Lakehal, D. 2007b. Interface–turbulence interactions in large-scale bubbling processes. Int J Heat Fluid Fl, 28: 127–144.
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.
McCulloch, W. S., Pitts, W. 1943. A logical calculus of the ideas immanent in nervous activity. B Math Biophys, 5: 115–133.
Ménard, T., Tanguy, S., Berlemont, A. 2007. Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet. Int J Multiphase Flow, 33: 510–524.
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.
Pohlheim, H. 2013. Evolutionäre Algorithmen: Verfahren, Operatoren und Hinweise für die Praxis. Springer-Verlag.
Rider, W. J., Kothe, D. B. 1998. Reconstructing volume tracking. J Comput Phys, 141: 112–152.
Roe, P. L. 1986. Characteristic-based schemes for the Euler equations. Annu Rev Fluid Mech, 18: 337–365.
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. Berlin, Heidelberg: Springer Berlin Heidelberg.
DOI
Sagaut, P., Germano, M. 2005. On the filtering paradigm for LES of flows with discontinuities. J Turbul, 6: N23.
Shirani, E., Ghadiri, F., Ahmadi, A. 2011. Modeling and simulation of interfacial turbulent flows. J Appl Fluid Mech, 4: 43–49.
Shu, C.-W., Osher, S. 1988. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J Comput Phys, 77: 439–471.
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.
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.
Tryggvason, G., Scardovelli, R., Zaleski, S. 2011. Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge: 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.
Vreman, A. W. 2004. An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications. Phys Fluids, 16: 3670–3681.
Zhou, G. 1995. Numerical simulations of physical discontinuities in single and multi-fluid flows for arbitrary Mach numbers. Ph.D. Thesis. Goteborg, Sweden: Chalmers Univ. of Tech.
Publication history
Copyright
Acknowledgements

Publication history

Received: 28 February 2019
Revised: 17 April 2019
Accepted: 18 April 2019
Published: 05 September 2019
Issue date: September 2019

Copyright

© Tsinghua University Press 2019

Acknowledgements

Support by the German Research Foundation (DFG, KL1456/1-1) 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.

Return