Drag and thermophoresis on a sphere in a rarefied gas based on the Cercignani–Lampis model of gas–surface interaction

Kalempa, Denize; Sharipov, Felix

doi:10.1017/jfm.2020.523

Cited by 22 publications

(14 citation statements)

References 77 publications

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“…Thermophoresis on a sphere is a classic problem in rarefied gas flows, which has been studied by many researchers; see, e.g. Yamamoto & Ishihara (1988), Takata, Aoki & Sone (1994), Takata & Sone (1995), Beresnev & Chernyak (1995), Takata (2009), Padrino, Sprittles & Lockerby (2019) and Kalempa & Sharipov (2020). The model developed in the present work can also be used to investigate thermophoresis on an evaporating droplet in the future.…”

Section: Discussionmentioning

confidence: 99%

-theorem and boundary conditions for the linear R26 equations: application to flow past an evaporating droplet

et al. 2021

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Section: Discussionmentioning

confidence: 99%

-theorem and boundary conditions for the linear R26 equations: application to flow past an evaporating droplet

et al. 2021

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“…Then, the well-known gas–solid interaction Cercignani–Lampis–Lord (CLL) model is formed and used widely today (Bird 1994). For example, Kalempa & Sharipov (2020) adopted the model to investigate the rarefied gas flow around a spherical particle and revealed the strong dependence of the thermophoretic and drag forces on the ACs.…”

Section: Introductionmentioning

confidence: 99%

Establishing a data-based scattering kernel model for gas–solid interaction by molecular dynamics simulation

et al. 2021

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Scattering kernel models for gas–solid interaction are crucial for rarefied gas flows and microscale flows. However, most existing models depend on certain accommodation coefficients (ACs). We propose here to construct a data-based model using molecular dynamics (MD) simulation and machine learning. The gas–solid interaction is first modelled by 100 000 MD simulations of a single gas molecule reflecting on the wall surface, which is fulfilled by GPU parallel technology. The results showed a correlation of the reflection velocity with the incidence velocity in the same direction, and also revealed correlations that may exist in different directions, which are neglected by the traditional gas–solid interaction model. Inspired by the sophisticated Cercignani–Lampis–Lord (CLL) model, two improved scattering kernels were constructed to better reproduce the probability density of velocity determined from MD simulation. The first one adopts variable ACs which depend on the incidence velocity and the second one combines three CLL-like kernels. All the parameters in the improved kernels are automatically chosen by the machine learning method. Compared with the numerical experiments of a molecular beam, the reconstructed scattering kernels are basically consistent with the MD results.

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“…The drag (e.g. Knudsen & Weber 1911;Epstein 1924;Willis 1966;Cercignani, Pagani & Bassanini 1968;Sone & Aoki 1977a,b;Law & Loyalka 1986;Aoki & Sone 1987;Beresnev, Chernyak & Fomyagin 1990;Loyalka 1992;Takata, Sone & Aoki 1993;Kalempa & Sharipov 2020) and torque (e.g. Loyalka 1992;Andreev & Popov 2010;Taguchi, Saito & Takata 2019) acting on the sphere in this situation have been investigated extensively in the past.…”

Section: Introductionmentioning

confidence: 99%

“…The problem for Φ (1) U (hereafter referred to as problem U) is equivalent to the boundary-value problem describing a uniform flow of rarefied gas past a sphere in the absence of sphere rotation, which has been extensively studied in the literature (e.g. Cercignani et al 1968;Sone & Aoki 1977a;Takata et al 1993;Kalempa & Sharipov 2020; see also Sone 2007).…”

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confidence: 99%

Inversion of the transverse force on a spinning sphere moving in a rarefied gas

Taguchi

Tsuji

2021

J. Fluid Mech.

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The flow around a spinning sphere moving in a rarefied gas is considered in the following situation: (i) the translational velocity of the sphere is small (i.e. the Mach number is small); (ii) the Knudsen number, the ratio of the molecular mean free path to the sphere radius, is of the order of unity (the case with small Knudsen numbers is also discussed); and (iii) the ratio between the equatorial surface velocity and the translational velocity of the sphere is of the order of unity. The behaviour of the gas, particularly the transverse force acting on the sphere, is investigated through an asymptotic analysis of the Boltzmann equation for small Mach numbers. It is shown that the transverse force is expressed as $\boldsymbol{F}_L = {\rm \pi}\rho a^3 (\boldsymbol{\varOmega} \times \boldsymbol{v}) \bar{h}_L$ , where $\rho$ is the density of the surrounding gas, a is the radius of the sphere, $\boldsymbol {\varOmega }$ is its angular velocity, $\boldsymbol {v}$ is its velocity and $\bar {h}_L$ is a numerical factor that depends on the Knudsen number. Then, $\bar {h}_L$ is obtained numerically based on the Bhatnagar–Gross–Krook model of the Boltzmann equation for a wide range of Knudsen number. It is shown that $\bar {h}_L$ varies with the Knudsen number monotonically from 1 (the continuum limit) to $-\tfrac {2}{3}$ (the free molecular limit), vanishing at an intermediate Knudsen number. The present analysis is intended to clarify the transition of the transverse force, which is previously known to have different signs in the continuum and the free molecular limits.

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Drag and thermophoresis on a sphere in a rarefied gas based on the Cercignani–Lampis model of gas–surface interaction

Abstract: Abstract

Cited by 22 publications

References 77 publications

-theorem and boundary conditions for the linear R26 equations: application to flow past an evaporating droplet

-theorem and boundary conditions for the linear R26 equations: application to flow past an evaporating droplet

Establishing a data-based scattering kernel model for gas–solid interaction by molecular dynamics simulation

Inversion of the transverse force on a spinning sphere moving in a rarefied gas

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