Inversion of the transverse force on a spinning sphere moving in a rarefied gas. (25th February 2022) - Taguchi, Satoshi; Tsuji, Tetsuro
Abstract: Abstract : 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 F_L = πρ a^3 ( × v) h_L, where ρ is the density of the surrounding gas, a is the radius of the sphere, is its angular velocity, v is its velocity and h_L is a numerical factor that depends on the Knudsen number. Then, 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 h_L varies with the Knudsen number monotonically from 1 (the continuum limit) to -23 (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.