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The kinetic Shakhov–Enskog model for non-equilibrium flow of dense gases

Published online by Cambridge University Press:  28 November 2019

Peng Wang Open the ORCID record for Peng Wang [Opens in a new window] ,
Lei Wu Open the ORCID record for Lei Wu [Opens in a new window] ,
Minh Tuan Ho ,
Jun Li Open the ORCID record for Jun Li [Opens in a new window] ,
Zhi-Hui Li  and
Yonghao Zhang Open the ORCID record for Yonghao Zhang [Opens in a new window]
Peng Wang
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering,University of Strathclyde, GlasgowG1 1XJ, UK
Lei Wu
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering,University of Strathclyde, GlasgowG1 1XJ, UK
Minh Tuan Ho
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering,University of Strathclyde, GlasgowG1 1XJ, UK
Jun Li
Affiliation:
Center for Integrative Petroleum Research, College of Petroleum Engineering and Geosciences,King Fahd University of Petroleum and Minerals, Saudi Arabia
Zhi-Hui Li
Affiliation:
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang621000, PR China
Yonghao Zhang*
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering,University of Strathclyde, GlasgowG1 1XJ, UK
*
†Email address for correspondence: yonghao.zhang@strath.ac.uk
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Abstract

When the average intermolecular distance is comparable to the size of gas molecules, the Boltzmann equation, based on the dilute gas assumption, becomes invalid. The Enskog equation was developed to account for this finite size effect that makes the collision non-local and increases the collision frequency. However, it is time-consuming to solve the Enskog equation due to its complicated structure of collision operator and high dimensionality. In this work, on the basis of the Shakhov model, a gas kinetic model is proposed to simplify the Enskog equation for non-ideal monatomic dense gases. The accuracy of the proposed Shakhov–Enskog model is assessed by comparing its solutions of the normal shock wave structures with the results of the Enskog equation obtained by the fast spectral method. It is shown that the Shakhov–Enskog model is able to describe non-equilibrium flow of dense gases, when the maximum local mean free path of gas molecules is still greater than the size of a molecular diameter. The accuracy and efficiency of the present model enable simulations of non-equilibrium flow of dense gases for practical applications.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A48
Copyright
© 2019 Cambridge University Press

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