Numerical Modelling of the Magnus Force and the Aerodynamic Torque on a Spinning Sphere in Transitional Flow

Abstract

Three dimensional transitional flow over a spinning sphere is studied numerically by the direct simulation Monte Carlo method. The flow is assumed to be steady-state, gas molecules interact with each other as hard spheres and the speculardiffuse scattering model describes the interaction between molecules and the sphere surface. The translational and rotational velocities of the sphere is assumed to be perpendicular to each other. The drag coefficient, the Magnus force coefficient and the torque coefficient are found as functions of the Mach and Reynolds numbers and the dimensionless rotation parameter for subsonic and supersonic flows. Computational results are compared with the analytical solution for a spinning sphere in free molecular flow and with available semi-empirical data. The "critical" Knudsen number when the Magnus force is equal to zero is found as a function of the Mach number.