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A Unified Algorithm for Interfacial Flows with Incompressible and Compressible Fluids

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Advances in Fluid Mechanics

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

Abstract

The majority of available numerical algorithms for interfacial two-phase flows either treat both fluid phases as incompressible (constant density) or treat both phases as compressible (variable density). This presents a limitation for the prediction of many two-phase flows, as treating both phases as compressible is computationally expensive due to the very stiff pressure–density–temperature coupling of liquids. A framework with the capability of treating one phase compressible and the other phase incompressible, therefore, has a significant potential to improve the computational performance and still capture all important physical mechanisms. We propose a numerical algorithm that can simulate interfacial flows in all Mach number regimes, from \(M=0\) to \(M > 1\), including interfacial flows in which compressible and incompressible fluids interact, within the same pressure-based framework and conservative finite-volume discretisation. For interfacial flows with only incompressible fluids or with only compressible fluids, the presented algorithm reduces to numerical frameworks that have already been presented in the literature. Representative test cases are used to validate the proposed algorithm, including mixed compressible–incompressible interfacial flows with acoustic waves, shock waves and rarefaction fans.

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Notes

  1. 1.

    The term “acoustically-conservative” refers to the acoustic properties of this discretisation method in the context of fully compressible flows and is not indicative of its application to incompressible fluids.

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Acknowledgements

This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant numbers 420239128 and 447633787.

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Authors and Affiliations

  1. Chair of Mechanical Process Engineering, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Fabian Denner & Berend van Wachem

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  1. Fabian Denner
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  2. Berend van Wachem
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Correspondence to Fabian Denner .

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Editors and Affiliations

  1. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan

    Dia Zeidan

  2. Department of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA

    Lucy T. Zhang

  3. ISAE-ENSMA, Institut Pprime, Chasseneuil-du-Poitou, France

    Eric Goncalves Da Silva

  4. MNZ, Leipzig University of Applied Sciences, Leipzig, Germany

    Jochen Merker

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Denner, F., van Wachem, B. (2022). A Unified Algorithm for Interfacial Flows with Incompressible and Compressible Fluids. In: Zeidan, D., Zhang, L.T., Da Silva, E.G., Merker, J. (eds) Advances in Fluid Mechanics. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-1438-6_5

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