1 INTRODUCTION
This paper seeks to provide an overview of the current state of Computational Fluid Dynamics (CFD) as applied to the field of sports engineering. It is by no means exhaustive and since CFD is still developing as a technology no claim is made that the complete spectrum of possible sporting applications for CFD is covered. However, an attempt is made to map out the territory of CFD in sport by way of examples related to the commercial code FLUENTTM. The current limitations of CFD technology will be discussed together with suggestions for possible future areas of application for CFD in sport.
As the title of this paper suggests, the old Olympian ideal of going faster, jumping longer and leaping higher than the opposition is embedded within competitive sports. The difference between winning and losing in sport may be fractions of a second which in turn may be related to a number of factors including the physique (even posture) of the athlete, the skill of the athlete and the equipment being used. With global media interest in all types of sport and the multimillion pound industries leading sports support it was inevitable that science and engineering technologies would be applied systematically to a variety of sports to give the leading competitors that extra winning edge.
Computational Fluid Dynamics deals with the computer simulation of aerodynamics and hydrodynamics of bodies in the presence of moving fluids. Historically, wind tunnel and water modelling techniques have dominated the field of aircraft, ship and chemical industry equipment research and development. These techniques have had the drawbacks however of being expensive to run; there are difficulties with generating good experimental measurements; they involve time consuming tasks and they have usually been limited to the more sophisticated government, university and industrial laboratories around the world.
The basic mathematical equations that describe fluid flow, the transfer of heat and some turbulence phenomena in fluids have been known in the scientific community for a long time (Versteeg et al, 1995). It has only been with the rapid advances in digital computers over the last 30 years that a numerical solution of these fundamental non-linear differential equations has been attempted (Patankar, 1980). The general class of equations commonly referred to as the “Navier-Stokes equations” describe the behaviour of a Newtonian fluid. These equations can, however, be written in many different forms; differential, integral, 2D, 3D, axisymmetric, stationary-grid, moving grid, laminar, turbulent, etc. A representative selection of the formulations for these governing equations are presented below in integral form.
Navier-Stokes Equation
Conservation of Mass
Conservation of Momentum
Conservation of Energy
Conservation of Turbulent Kinetic Energy
Conservation of Turbulent Dissipation
where, ρ = fluid density, t = time, V = cell volume, A = cell interface area, p = local static pressure, υ = velocity, τ = fluid shear stress, g = gravitational constant, E = total energy of the fluid, δij = Kronecker Delta, q = heat flux source, k = turbulent kinetic energy, μe = fluid effective viscosity, P = production of turbulence, ε = dissipation of turbulent kinetic energy, σk, σε, C1, and C2 are empirical constants, R = source term for turbulent dissipation and i,j, are vector notations.
It is not the purpose of this paper to deal with the detailed mathematics associated with CFD. The reader is referred to Weiss et al, 1994, for more information on the techniques used in some of the applications reported here.
Modern computers have the ability to solve millions of mathematical expressions per second and this has been one of the keys to the emergence of CFD and commercial codes over the last ten years. Another driving force for CFD has been the rapid development of Computer Aided Design (CAD) software, structural stress analysis codes and even automotive crash dummy computer simulations. Both stress analysis and...