Numerical simulations of shock waves in viscous carbon dioxide flows using finite volume method

Authors

  • Ilya V. Alekseev
  • Elena V. Kustova

DOI:

https://doi.org/10.21638/spbu01.2020.312

Abstract

An efficient numerical tool for studying shock waves in viscous carbon dioxide flows is proposed. The developed theoretical model is based on the kinetic theory formalism and is free of common limitations such as constant specific heat ratio, approximate analytical expressions for thermodynamic functions and transport coefficients. The thermal conductivity, viscosity and bulk viscosity coefficients are expressed in terms of temperature, collision integrals and internal energy relaxation times. Precomputed in the wide temperature range thermodynamic functions and transport coefficients are implemented to the numerical code which is used for the simulations of the shock wave structure. Including the bulk viscosity to the kinetic model results in the increasing shock width and improves the agreement with experimental data.

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References

Литература

1. Bird G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford, England, UK: Clarendon, 1994.

2. Kosuge S., Aoki K. Shock-wave structure for a polyatomic gas with large bulk viscosity // Phys. Rev. Fluids. 2018. Vol. 3. Art. no. 023401. https://doi.org/10.1103/PhysRevFluids.3.023401

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4. Kustova E., Mekhonoshina M., Kosareva A. Relaxation processes in carbon dioxide // Phys. Fluids. 2019. Vol. 31. Art. no. 046104. https://doi.org/10.1063/1.5093141

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9. Cramer M. S. Numerical estimates for the bulk viscosity of ideal gases // Physics of Fluids. 2012. Vol. 24. Art. no. 066102. https://doi.org/10.1063/1.4729611

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References

1. Bird G.A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford, England, UK: Clarendon, 1994).

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3. Timokhin M., Struchtrup H., Kokhanchik A., Bondar Ye., “Different variants of R13 moment equations applied to the shock-wave structure”, Phys. Fluids 29, 037105 (2017). https://doi.org/10.1063/1.4977978

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5. Elizarova T.G., Khokhlov A.A., Montero S., “Numerical simulation of shock wave structure in nitrogen”, Physics of Fluids 19, 068102 (2007). https://doi.org/10.1063/1.2738606

6. Chikitkin A.V., Rogov B.V., Tirsky G.A., Utyuzhnikov S.V., “Effect of bulk viscosity in supersonic flow past spacecraft”, Applied Numerical Mathematics 93, 47–60 (2015). https://doi.org/10.1016/j.apnum.2014.01.004

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Published

2020-09-04

How to Cite

Alekseev, I. V., & Kustova, E. V. (2020). Numerical simulations of shock waves in viscous carbon dioxide flows using finite volume method. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7(3), 500–510. https://doi.org/10.21638/spbu01.2020.312

Issue

Section

Mechanics