Computational Sports Aerodynamics of a Moving Sphere: Simulating a Ping Pong Ball in Free Flight

Abstract

Fluid dynamics associated with many sports involving spheric shaped equipments such as tennis, golf and ping pong balls tends to be very unsteady and viscous, with occasionally transitional behaviors. Some of the intricate aerodynamic behaviors are the mechanisms that make these sports competitive and spectacular. In this paper we discuss using highorder method as an effective method for solving unsteady fluid dynamics pertaining to sports. In particular, we perform direct numerical simulation of unsteady viscous flow past a spinning sphere. Taking a different approach from the usual computational practice of performing simulations of fixed free-stream and fixed Reynolds number flows, we compute the flow field around the spheric body together with the dynamic motion of the body. By coupling the sphere dynamic to the aerodynamic flow, we are able to simulate the flight trajectory of the sphere in free flight and examine the effect of introducing different varieties of spin on game play. The flow solver is based on the high-order Spectral Difference method. Coupling of fluid and structure is enforce weakly by advancing the equation of motion and flow equations in time together using the explicit multi-stage Runge-Kutta scheme. We rely on the inherent numerical dissipation in the high order method to resolve transitional flow, which effectively acts as a kind of implicit Large Eddy Simulation (ILES).