Inverse Magnus Effect in a Rarefied Gas

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.