Inverse Magnus effect in a rarefied gas

TL;DR

This study investigates the inverse Magnus effect in a rarefied gas, analyzing how the transverse force on a rotating sphere changes sign with the Knudsen number and surface properties, extending previous work.

Contribution

It clarifies the transition of the Magnus force sign in rarefied gases, showing the threshold depends weakly on surface accommodation, extending prior diffuse reflection results.

Findings

Threshold Knudsen number for force sign change is weakly dependent on accommodation.

The inverse Magnus effect occurs at specific Knudsen numbers in rarefied gases.

Robustness of the force transition threshold across different surface conditions.

Abstract

The transverse force exerted on a rotating sphere immersed in an otherwise uniform flow of a rarefied gas is investigated based on the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation assuming the Maxwell boundary condition on the sphere. In several existing studies, it has been shown that the transverse force acting on the sphere, also known as the Magnus force, has opposite signs in the free molecular and continuum flows. The present study intends to clarify the force's transition in terms of the Knudsen number (i.e., the reciprocal ratio of the sphere radius to the molecular mean free path) with a particular interest in the impact of the sphere's surface accommodation. It is found that the threshold of the Knudsen number, at which the transverse force changes the sign, depends only weakly on the accommodation coefficient, suggesting certain robustness in the threshold. The present study is an extension of the previous work [S. Taguchi and T. Tsuji, J. Fluid. Mech. 933, A37 (2022)], in which the case of complete accommodation (diffuse reflection) is exclusively considered.