Skip to main content
SpringerLink
Log in

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

  • Research Article
  • Published:
Experimental and Computational Multiphase Flow Aims and scope Submit manuscript

A Correction to this article was published on 05 February 2022

This article has been updated

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Change history

References

  • 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

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • 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.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Chollet, F. et al. 2015. Keras: Deep learning library for theano and tensorflow. Available at https://keras.io/.

    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.

    MATH  Google Scholar 

  • De Villiers, E., Gosman, A. D., Weller, H. G. 2004. Large eddy simulation of primary diesel spray atomization. SAE Transactions, 113: 193–206.

    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.

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  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.

    MathSciNet  MATH  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.

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • 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.

    Google Scholar 

  • Jiang, G.-S., Shu, C.-W. 1996. Efficient implementation of weighted ENO schemes. J Comput Phys, 126: 202–228.

    MathSciNet  MATH  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.

    MathSciNet  MATH  Google Scholar 

  • Klein, M. 2002. Direkte Numerische Simulation des primären Strahlzerfalls in Einstoffzerstäuberdüsen. Ph.D. Thesis. Technical University Darmstadt.

    Google Scholar 

  • 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.

    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.

    MATH  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.

    MATH  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 Fl, 72: 329–336.

    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.

    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 Fl, 31: 536–544.

    Google Scholar 

  • Leonard, B. P. 1979. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput Method Appl M, 19: 59–98.

    MATH  Google Scholar 

  • Li, X. G., Tankin, R. S. 1991. On the temporal instability of a two-dimensional viscous liquid sheet. J Fluid Mech, 226: 425–443.

    MATH  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • 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.

    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.

    MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    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.

    MathSciNet  MATH  Google Scholar 

  • McCulloch, W. S., Pitts, W. 1943. A logical calculus of the ideas immanent in nervous activity. B Math Biophys, 5: 115–133.

    MathSciNet  MATH  Google Scholar 

  • 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.

    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.

    Google Scholar 

  • Pohlheim, H. 2013. Evolutionäre Algorithmen: Verfahren, Operatoren und Hinweise für die Praxis. Springer-Verlag.

    Google Scholar 

  • Rider, W. J., Kothe, D. B. 1998. Reconstructing volume tracking. J Comput Phys, 141: 112–152.

    MathSciNet  MATH  Google Scholar 

  • Roe, P. L. 1986. Characteristic-based schemes for the Euler equations. Annu Rev Fluid Mech, 18: 337–365.

    MathSciNet  MATH  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.

    Google Scholar 

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

    MATH  Google Scholar 

  • Sagaut, P., Germano, M. 2005. On the filtering paradigm for LES of flows with discontinuities. J Turbul, 6: N23.

    MathSciNet  Google Scholar 

  • Shirani, E., Ghadiri, F., Ahmadi, A. 2011. Modeling and simulation of interfacial turbulent flows. J Appl Fluid Mech, 4: 43–49.

    Google Scholar 

  • Shu, C.-W., Osher, S. 1988. Efficient implementation of essentially nonoscillatory shock-capturing schemes. J Comput Phys, 77: 439–471.

    MathSciNet  MATH  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.

    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.

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Vreman, A. W. 2004. An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications. Phys Fluids, 16: 3670–3681.

    MATH  Google Scholar 

  • 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.

    Google Scholar 

Download references

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.

Author information

Authors and Affiliations

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

    S. Ketterl & Markus Klein

  2. Department of Computer Science, Bundeswehr University Munich, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany

    M. Reißmann

Authors
  1. S. Ketterl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Reißmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Markus Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Markus Klein.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ketterl, S., Reißmann, M. & Klein, M. Large eddy simulation of multiphase flows using the volume of fluid method: Part 2—A-posteriori analysis of liquid jet atomization. Exp. Comput. Multiph. Flow 1, 201–211 (2019). https://doi.org/10.1007/s42757-019-0026-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42757-019-0026-x

Keywords

Search

Navigation