Transient behaviour of a rarefied gas around a sphere caused by impulsive rotation

Taguchi, Satoshi; Tsuji, Tetsuro; Kotera, Masashi

doi:10.1017/jfm.2020.907

Cited by 4 publications

(1 citation statement)

References 26 publications

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“…Concerning h M , Taguchi et al (2019) investigated the steady flow around a rotating sphere (problem S) based on the ellipsoidal statistical model (and the BGK model), in which the numerical values of h M (k) were obtained for both the BGK and the ellipsoidal statistical model. We also mention that the time-dependent behaviour of a gas caused by the impulsive rotation of a sphere has been recently studied (Taguchi, Tsuji & Kotera 2021). For readers' convenience, we summarize the values of h D (k) and h M (k) obtained in those studies in tables 3 and 4, respectively, together with new data obtained in the present study.…”

Section: Summary Of the Force And Torque Acting On The Spherementioning

confidence: 73%

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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Section: Summary Of the Force And Torque Acting On The Spherementioning

confidence: 73%

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 impulsive swirl of a gas

Sader

2021

J. Fluid Mech.

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Oscillatory Couette flow of rarefied binary gas mixtures

Guo

Wang

2021

Physics of Fluids

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The oscillatory Couette flow of binary gas mixtures is numerically investigated on the basis of the McCormack model. The dependence of the velocity and shear stress amplitudes and the penetration depth on the gas rarefaction and the oscillation parameters is studied numerically. Two typical mixtures of noble gases, i.e., a neon–argon (Ne–Ar) mixture with a molecular mass ratio less than 2 and a helium–xeon (He–Xe) mixture with a molecular mass ratio of about 32, are considered to explore the influences of the molecular mass ratio and molar concentration. It is found that the Ne–Ar mixture exhibits similar behavior with a single gas, while significant deviations can be observed between a single gas and the He–Xe mixture. Particularly when the gases are in the transitional and near-continuum regimes and the oscillation frequency is high, the amplitudes of velocity and shear stress for the He–Xe mixture vary non-monotonically between the plates as the molar concentration of the light species He exceeds 50% due to the oscillation superposition of the two species. These findings are helpful to design the structure of micro-electromechanical devices.

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Transient behaviour of a rarefied gas around a sphere caused by impulsive rotation

Abstract: Abstract

Cited by 4 publications

References 26 publications

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

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

The impulsive swirl of a gas

Oscillatory Couette flow of rarefied binary gas mixtures

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