School of Engineering, University of Warwick
Coventry, West Midlands, U.K
Abstract: It is possible to improve the aerodynamic efficiency of road vehicles and reap many benefits. Fuel consumption being one of them, this report identifies how basic theoretical and experimental fluid mechanics can work in harmony to allow one to understand the key mechanisms that affect the aerodynamic properties of road vehicles and suggest ways in which to analyse them. From this it is possible to learn and improve upon current design practices to ensure cleaner more fuel efficient, environmentally friendly road vehicles of the future. 1. Introduction
In the 70’s with the emergence of the worldwide oil crisis nations were being urged to adopt energy conservation methods. The United Nations estimate the world’s population is set to reach 8 billion by 2025 based on current rate of growth. The demand on producing energy is placing great stress on our environment. Considering almost every household owns at least 1 car by 2025 there could be 1 billion cars alone on the road requiring fuel of some sort. Therefore it is necessary to produce road vehicles that are fuel efficient. Aerodynamic drag and fuel consumption are linked, simply the poorer the aerodynamic efficiency of your road vehicle the more fuel it needs to consume in order to power it. It is estimated that the aerodynamic drag effects fuel consumption of the average car by some 30% at urban cycles and 75% at highway speeds . Therefore it is of paramount concern for manufacturers to reduce the drag force that affects road vehicles. 2. What is Drag?
Drag is a mechanical force generated by a solid object moving through a fluid. An indication of how good or bad a solid object travels through a fluid is termed the coefficient of drag value, Cd. Cd=Fd12ρV2A 2.1 where Fdis the force in Newton’s, ρ is the density of air in kg/m3, V is velocity in m/s and A is the frontal area of the body in m2. It is possible to derive the relationship between the drag force acting on a solid object like a sphere and key parameters that influence the force using Buckingham Pi method . Knowing that drag acting on a sphere for example depends on the velocity, V, diameter ,D, fluid density, ρ and fluid viscosity, μ following the steps set out by the method one can obtain a set of dimensionless groups useful for comparison with experimental data. Where: F=fρ,V,D,μ
F V D ρ μ n=5 dimensional parameters MLt2 Lt L ML3 MLt r=3 primary dimesnions
Selecting repeating parameters ρ, V, D. m=r=3 repeating parameters
To determine the number of dimensionless groups that exist we subtract n from m. Hence 2 dimensional groups will result. π1= ρaVbDcF and ML3aLtb(L)c MLt2= M0L0t0
Equating exponents of M, L and t:
M: a+1=0 a=-1
L: -3a+b+c+1=0 c=-2
t: -b-2=0 b=-2
Pi group 1:
Using same method to obtain the second pi group using μ instead of F we obtain Pi group 2:
Finally it is possible to create a functional relationship by checking dimensions of F, L and t.
π1= FρV2D2 and FL4Ft2tL21L2=1
π2=μρVD and FtL2L4Ft2tL1L=1
Therefore the functional relationship of drag is:
3. Drag Mechanisms
A basic analytical understanding of what drag is has been gained from previous sections but how does this force act on a body. The complex nature of flow that exists around a body can be difficult to theoretically analyse therefore much experimental work has been carried out. Two important studies have been carried out on examining bluff...