Transitional flow of a rarefied gas over a spinning sphere

Abstract

AbstractThree-dimensional transitional flow of a rarefied monatomic gas over a spinning sphere is studied numerically by the direct simulation Monte Carlo method. Gas molecules interact with each other as hard spheres. The Maxwell model of specular–diffuse scattering is used to describe the interaction between gas molecules and the sphere surface. The effect of all dimensionless governing parameters of the problem on the flow structure, distributions of stresses and heat flux density on the sphere surface, aerodynamic force and torque exerted on the sphere, and heat flux on the sphere surface is analysed. Simulations are conducted at Mach numbers raging from $0. 03$ to $2$ and Knudsen numbers raging from $0. 01$ to $20$. Two qualitatively different streamline patterns are observed around the sphere depending on its dimensionless rotational velocity. The direction and magnitude of the transverse Magnus force in transitional flow depend on the Knudsen and Mach numbers. The torque and heat flux coefficients are found to be functions of the Mach number and dimensionless rotational velocity. The effect of rotation on the sphere aerodynamics weakens with an increase in the sphere temperature with respect to the gas temperature in the free stream. A complete set of equations is developed to fit the computed values of the aerodynamic and heat flux coefficients in a case when the sphere temperature is equal to the temperature of the free stream.