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

Peng Wang, Lei Wu, Minh-Tuan Ho, Jun Li, Zhui-Hui Li, Yonghao Zhang

Research output: Contribution to journalArticle

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 molecular diameter. The accuracy and efficiency of the present model enable simulations of non-equilibrium flow of dense gases for practical applications.
Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalJournal of Fluid Mechanics
Publication statusAccepted/In press - 17 Oct 2019

Fingerprint

nonequilibrium flow
Kinetics
kinetics
Gases
gases
collisions
Kinetic theory of gases
normal shock waves
Molecules
Boltzmann equation
spectral methods
Shock waves
mean free path
molecules
operators

Keywords

  • gas kinetic theory
  • Enskog equation
  • Boltzmann equation
  • rarefied gas dynamics

Cite this

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title = "The kinetic Shakhov-Enskog model for non-equilibrium flow of dense gases",
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 molecular diameter. The accuracy and efficiency of the present model enable simulations of non-equilibrium flow of dense gases for practical applications.",
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author = "Peng Wang and Lei Wu and Minh-Tuan Ho and Jun Li and Zhui-Hui Li and Yonghao Zhang",
year = "2019",
month = "10",
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language = "English",
pages = "1--22",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
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The kinetic Shakhov-Enskog model for non-equilibrium flow of dense gases. / Wang, Peng; Wu, Lei; Ho, Minh-Tuan; Li, Jun ; Li, Zhui-Hui; Zhang, Yonghao.

In: Journal of Fluid Mechanics, 17.10.2019, p. 1-22.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The kinetic Shakhov-Enskog model for non-equilibrium flow of dense gases

AU - Wang, Peng

AU - Wu, Lei

AU - Ho, Minh-Tuan

AU - Li, Jun

AU - Li, Zhui-Hui

AU - Zhang, Yonghao

PY - 2019/10/17

Y1 - 2019/10/17

N2 - 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 molecular diameter. The accuracy and efficiency of the present model enable simulations of non-equilibrium flow of dense gases for practical applications.

AB - 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 molecular diameter. The accuracy and efficiency of the present model enable simulations of non-equilibrium flow of dense gases for practical applications.

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KW - rarefied gas dynamics

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