The Engineering of Sport

Steve Haake, Steve Haake

• Éditeur: CRC Press
• Année: 2020
• ISBN:
  9781000150759
• Édition: 1
• Sujet: Derecho
• Sous-sujet: Derecho de los medios y el entretenimiento

Science and technology has been usedmore and more in the last few decades to gain advantage over competitors. Quite often, however, the actual science involved is not published because a suitable journal cannot be found. The Engineering of Sport brings together work from a very diverse range of subjects including Engineering, Physics, Materials and Biomechanics.

The Engineering of Sport represent work which was represented at the 1st International Conference on the Engineering of Sport held in Sheffield, UK in July 1996. Many sports were represented and the material covered split into nine topics coveringaerodynamics, biomechanics, design, dynamics, instrumentation, materials, mechanics, modelling, motion analysis, and vibrations. It should be of interest to specialists in all areas of sports research.

1 Aerodynamics

Going faster, higher and longer in sport with CFD

R. K. Hanna
Fluent Europe Ltd, Sheffield, UK

ABSTRACT

Digital computers have increased dramatically in both speed and capacity over the last 5-10 years. More and more powerful machines are being used routinely on the desks of design engineers. In parallel with this growth of computer platform power and usage, more sophisticated software is being developed and commercially marketed to exploit these advances. One such area is Computational Fluid Dynamics (CFD) where the fundamental non-linear differential equations that describe fluid flow, heat transfer and turbulence phenomena are now routinely solved numerically for a range of industrial applications from hypersonic flows around rockets to low speed cooling of electronic components in computers.

Some sports and sporting teams have been keeping abreast of the rapid rise of CFD technology over recent years. In the vanguard has been motor racing teams such as the Benetton Formula 1 team who started to use CFD as a design tool to improve the aerodynamics of their championship-winning cars four years ago. Very soon other teams followed suit and a new era in F1 design was ushered in. Now, a number of teams use CFD to model their cars computationally prior to wind tunnel testing to both optimise their proposed designs and understand the flow fields around new chassis configurations. CFD is proving to be more cost effective than conventional approaches. It also provides a wealth of data for aerodynamicists to analyse and produces rapid project turnaround times in this highly competitive field of sport. Now ten configurations can be studied in the same time as two would have been looked at before.

Areas of sport that are showing the benefits of computational methods for improving equipment design and techniques are yachts (both the hull and sail designs), ski jumpers, golf and even the humble frisbee. With reference to the above examples, this paper aims to highlight the approach to these problems designers have adopted using software supplied by Fluent Europe Ltd, the market leader in commercial CFD software. Nowadays, many designers and aerodynamicists can ask the “what if …?” question and get answers before a ball is struck, a yacht built or a racing car model constructed.

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, δ_ij = Kronecker Delta, q = heat flux source, k = turbulent kinetic energy, μ_e = fluid effective viscosity, P = production of turbulence, ε = dissipation of turbulent kinetic energy, σ_k, σ_ε, 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...