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Non-equilibrium Model for Weakly Compressible Multi-component Flows: The Hyperbolic Operator

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Non-Ideal Compressible Fluid Dynamics for Propulsion and Power (NICFD 2018)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

We present a novel pressure-based method for weakly compressible multiphase flows, based on a non-equilibrium Baer and Nunziato-type model. Each component is described by its own thermodynamic model, thus the definition of a mixture speed of sound is not required. In this work, we describe the hyperbolic operator, without considering relaxation terms. The acoustic part of the governing equations is treated implicitly to avoid the severe restriction on the time step imposed by the CFL condition at low-Mach. Particular care is taken to discretize the non-conservative terms to avoid spurious oscillations across multi-material interfaces. The absence of oscillations and the agreement with analytical or published solutions is demonstrated in simplified test cases, which confirm the validity of the proposed approach as a building block on which developing more accurate and comprehensive methods.

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Notes

  1. 1.

    The discretization of \(\mathsf {H}_P\) is obtained by assuming uniform \((u_i)^n\) and \((P_i)^n\) in (11) and substituting into its left-hand side \((\alpha _i m_i)_{j+\frac{1}{2}}^*=(\alpha _i \rho _i)_{j+\frac{1}{2}}^{n+1}\) the discretization of \((\alpha _i \rho _i)_{j+\frac{1}{2}}^{n+1}\) from (9).

References

  1. Munkejord, S.T., Hammer, M.: Int. J. Greenhouse Gas Control 37, 398 (2015). https://doi.org/10.1016/j.ijggc.2015.03.029

    Article  Google Scholar 

  2. Coquel, F., Hérard, J.M., Saleh, K.: J. Comput. Phys. 330, 401 (2017). https://doi.org/10.1016/j.jcp.2016.11.017

    Article  MathSciNet  Google Scholar 

  3. Wenneker, I., Segal, A., Wesseling, P.: Int. J. Numer. Methods Fluids 40(9), 1209 (2002). https://doi.org/10.1002/fld.417

    Article  Google Scholar 

  4. Guillard, H., Viozat, C.: Comput. Fluids 28(1), 63 (1999). https://doi.org/10.1016/S0045-7930(98)00017-6

    Article  MathSciNet  Google Scholar 

  5. Guillard, H., Murrone, A.: Comput. Fluids 33(4), 655 (2004). https://doi.org/10.1016/j.compfluid.2003.07.001

    Article  Google Scholar 

  6. Xiao, F.: J. Comput. Phys. 195(2), 629 (2004). https://doi.org/10.1016/j.jcp.2003.10.014

    Article  MathSciNet  Google Scholar 

  7. Harlow, F.H., Amsden, A.A.: J. Comput. Phys. 3(1), 80 (1968). https://doi.org/10.1016/0021-9991(68)90007-7

    Article  Google Scholar 

  8. Bijl, H., Wesseling, P.: J. Comput. Phys. 141(2), 153 (1998). https://doi.org/10.1006/JCPH.1998.5914

    Article  MathSciNet  Google Scholar 

  9. Munz, C.D., Roller, S., Klein, R., Geratz, K.J.: Comput. Fluids 32(2), 173 (2003). https://doi.org/10.1016/S0045-7930(02)00010-5

    Article  MathSciNet  Google Scholar 

  10. Kwatra, N., Su, J., Grétarsson, J.T., Fedkiw, R.: J. Comput. Phys. 228(11), 4146 (2009). https://doi.org/10.1016/J.JCP.2009.02.027

    Article  MathSciNet  Google Scholar 

  11. Ventosa-Molina, J., Chiva, J., Lehmkuhl, O., Muela, J., Pérez-Segarra, C.D., Oliva, A.: Int. J. Numer. Methods Fluids 84(6), 309 (2017). https://doi.org/10.1002/fld.4350

    Article  Google Scholar 

  12. Saurel, R., Pantano, C.: Ann. Rev. Fluid Mech. 50, 105 (2018). https://doi.org/10.1146/annurev-fluid-122316-050109

    Article  Google Scholar 

  13. Baer, M.R., Nunziato, J.W.: Int. J. Multiphase Flow 6, 861 (1986)

    Article  Google Scholar 

  14. Pandare, A.K., Luo, H.: J. Comput. Phys. 371, 67 (2018). https://doi.org/10.1016/j.jcp.2018.05.018

    Article  MathSciNet  Google Scholar 

  15. Bernard, M., Dellacherie, S., Faccanoni, G., Grec, B., Penel, Y.: ESAIM Math. Model. Numer. Anal. 48(6), 1639 (2014). https://doi.org/10.1051/m2an/2014015

    Article  MathSciNet  Google Scholar 

  16. Saurel, R., Abgrall, R.: J. Comput. Phys. 150(2), 425 (1999). https://doi.org/10.1006/JCPH.1999.6187

    Article  MathSciNet  Google Scholar 

  17. Abgrall, R., Bacigaluppi, P., Tokareva, S.: Comput. Fluids (2017). https://doi.org/10.1016/J.COMPFLUID.2017.08.019

    Article  Google Scholar 

  18. Abgrall, R., Karni, S.: J. Comput. Phys. 229(8), 2759 (2010). https://doi.org/10.1016/j.jcp.2009.12.015

    Article  MathSciNet  Google Scholar 

  19. Abgrall, R.: J. Comput. Phys. 125(1), 150 (1996). https://doi.org/10.1006/JCPH.1996.0085

    Article  MathSciNet  Google Scholar 

  20. Saurel, R., Chinnayya, A., Carmouze, Q.: Phys. Fluids 29(6), 1 (2017). https://doi.org/10.1063/1.4985289

    Article  Google Scholar 

  21. Paill‘ere, H., Corre, C., García Cascales, J.: Comput. Fluids 32, 891 (2003). https://doi.org/10.1016/S0045-7930(02)00021-X

  22. Haller, K.K., Ventikos, Y., Poulikakos, D.: J. Appl. Phys. 93(5), 3090 (2003). https://doi.org/10.1063/1.1543649

    Article  Google Scholar 

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Acknowledgments

This publication has been produced with support from the NCCS Centre, performed under the Norwegian research program Centres for Environment-friendly Energy Research (FME). The authors acknowledge the following partners for their contributions: Aker Solutions, Ansaldo Energia, CoorsTek Membrane Sciences, Emgs, Equinor, Gassco, Krohne, Larvik Shipping, Norcem, Norwegian Oil and Gas, Quad Geometrics, Shell, Total, Vår Energi, and the Research Council of Norway (257579/E20).

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Authors and Affiliations

  1. Institute of Mathematics, Universität Zürich, 8057, Zürich, Switzerland

    Barbara Re & Rémi Abgrall

Authors
  1. Barbara Re
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  2. Rémi Abgrall
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Correspondence to Barbara Re .

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Editors and Affiliations

  1. Ruhr University Bochum, Bochum, Germany

    Francesca di Mare

  2. Politecnico di Milano, Milan, Milano, Italy

    Andrea Spinelli

  3. Delft University of Technology, TU Delft, The Netherlands

    Matteo Pini

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Re, B., Abgrall, R. (2020). Non-equilibrium Model for Weakly Compressible Multi-component Flows: The Hyperbolic Operator. In: di Mare, F., Spinelli, A., Pini, M. (eds) Non-Ideal Compressible Fluid Dynamics for Propulsion and Power. NICFD 2018. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-49626-5_3

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  • DOI: https://doi.org/10.1007/978-3-030-49626-5_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-49625-8

  • Online ISBN: 978-3-030-49626-5

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