Aerodynamic drag in a windy environment

J.P. Howell    Tata Motors European Technical Centre, UK

ABSTRACT

The aerodynamic drag of a road vehicle is defined by the measurement obtained at zero yaw in the idealised simulation environment found in the wind tunnel, or when using CFD. This beneficial environment has allowed a continuous improvement in the aerodynamics of passenger cars over many years but it is recognised that it may be unrepresentative of the conditions in which the car usually operates. While the simulated ambient conditions are characterised by very low turbulence and are steady state, the car in the real world experiences an unsteady environment, caused by the effects of the natural wind and by traffic, which can include high levels of turbulence. The potentially inappropriate simulated aerodynamic drag value is then used to determine fuel economy. In the past a wind-averaged drag measurement has been proposed to account for varying yaw conditions experienced by a vehicle on the road, but this is still an essentially steady state solution. In this paper the additional unsteady drag component arising from the vehicle operating in a turbulent flow field is assessed using a quasi steady analysis. The increase in drag at a given yaw angle is shown to be a function of the drag and the gradient of drag with yaw. This modified data is then used to recalculate an unsteady wind-averaged drag coefficient.

1 NOTATION

A Frontal area

CD, CD0, CD? Drag coefficient (= 2D/(?U2A)), CD at 0° yaw, CD at yaw ?

CDW Wind averaged drag coefficient

CDWU Unsteady wind averaged drag coefficient

D Drag force

K constant (CD = CD0 + k?2)

K Roughness coefficient (ground)

L´ Vehicle Length

LU, LV Length scales

n, ñ Frequency, non-dimensional frequency

SDD Non-dimensional aerodynamic drag psd

SUU, SVV Non-dimensional wind velocity psd

|T(?)| Transfer functions

u, v Turbulence velocities in resultant velocity frame

UR, UV, UW Resultant, Vehicle, Wind velocity

UW 10 Wind velocity at 10 m

? Admittance function

f Wind angle with vehicle path

? Air density

sU, sV rms turbulence

? Yaw angle

2 INTRODUCTION

Environmental concerns, primarily relating to increasing CO2 levels in the atmosphere, produced in car exhaust gases, has led to renewed interest in improving vehicle efficiency by reducing the overall resistance to motion. Aerodynamic drag is a significant contributor to that resistance.

Major improvements in the aerodynamic characteristics of cars and other road vehicles have been achieved over many years, mainly through the detail fine tuning of vehicle shapes in automotive wind tunnels. To facilitate this development process required relatively low levels of wind tunnel turbulence. It was recognised that the wind tunnel simulation was flawed in that the boundary conditions were poorly represented, leading to major efforts to understand blockage corrections and to introduce moving belts to improve the ground representation. Less effort has been applied to the simulation of the flow field experienced by vehicles on the road, which is generally unsteady and includes turbulence and shear. In part this is because these flows are highly variable, cannot be simply characterised or easily simulated.

The environment simulated by the low turbulence automotive wind tunnel is that of a vehicle travelling along a road in complete isolation and in windless conditions. These situations do exist but they are rare. The natural wind is usually present and its effects are experienced directly by the car and indirectly by its action upon road features, such as embankments and cuttings, and upon roadside objects including buildings, trees and barriers. The vehicle is also usually in the presence of others, which introduces additional turbulence to the flow field. The effects of natural wind and traffic are cumulative. The unsteady environment experienced by road vehicles has been reviewed, by Cooper and Watkins [1] and earlier by Watkins and Saunders [2] and Howell [3].

Some attempts have been made to introduce turbulence into wind tunnel facilities. The pioneering work of Cogotti, (4), who installed the Turbulence Generating System (TGS) in the Pininfarina Wind Tunnel has been followed by similar model scale systems at FKFS and Durham University. Coastdown tests have been conducted to measure aerodynamic drag on the road in a windy environment by Buckley et al., (5), and Hamabe et al., (6), on trucks and cars respectively, but these experiments are rare. K. Cooper has derived theoretical estimates of unsteady drag of trucks with and without aerodynamic aids, (7), (8), and shown qualitative agreement with measurements on truck models in grid generated turbulence.

Fuel economy data produced by car manufacturers has been criticised for not being representative of the customer experience, although it was only intended as a comparative measure. Draft proposals to improve the test procedures used to provide fuel economy data; Worldwide Light vehicle Test Procedures, (WLTP), have mandated sophisticated wind tunnel ground simulations and low turbulence environments, but these will similarly fail to represent the natural environment in which the car normally operates by only considering drag at zero yaw.

At various times over the years the use of a wind averaged drag coefficient to account for the effects of the natural wind on drag have been advocated. While there are objections to this approach, see Sovran, (9), it has merit when applied to global emissions. Different levels of complexity, relating to the probability of wind speed and direction and vehicle speed, can be applied in the determination of wind averaged drag. For this paper details of the wind averaged drag calculation are given in section 3.3. Wind direction is assumed to be equi-probable and the probability of a certain windspeed is obtained from a weighting function.

To understand the implications of not representing the unsteady environment a theoretical estimate of the drag increment arising from an unsteady wind input is derived and applied in a wind averaged form. The unsteady loads acting on a vehicle under the influence of a natural wind input are determined using a psd, (power spectral density), approach. A simple quasi-steady analysis is adopted for the time dependent aerodynamic forces. A similar psd approach to understanding vehicle behaviour in windy conditions has previously been applied to high speed trains, R. Cooper, (11), and to SUVs, Howell, (12).

3 SIMULATION

The unsteady aerodynamic loads acting on a road vehicle are evaluated here in power spectral density (psd) terms. The turbulent wind energy psd at low level is known from the field of building aerodynamics, although the data must be extrapolated into the near-ground domain occupied by road vehicles. The spectra must then, in addition, be converted to give the longitudinal and lateral turbulence components in the resultant velocity frame for a moving vehicle. The aerodynamic load psd, SAA, is obtained from the wind input psd, SUU, using the basic relationship:

AA=|T?A|2×|X?|2×SUU

  (1)

where |T(?)A| is a transfer function relating aerodynamic load to an unsteady wind input, and |?(?)| is an aerodynamic admittance function, which accounts for the attenuation of aerodynamic loads under high frequency inputs. The transfer function, |T(?)A|, includes both resultant velocity and yaw angle terms and the wind energy psd consists of longitudinal, u, and lateral, v, turbulence components. The overall aerodynamic load psd, SAA, is then given by:

AA=|T?A|U2×SUU+|T?A|V2×SVV×|X?|2

  (2)

and is shown schematically in Figure 1.

3.1 Wind input

Consider the velocity diagram shown in Figure 2. UV is the vehicle velocity, UW represents the wind speed and the wind direction is at an angle ? to the vehicle path. The resultant velocity, UR, and the yaw angle for the vehicle, ?, are then given by:

R=UV2+UW2+2UVUWcos?1/2

  (3)

=tan-1UWsin?/UV+UWcos?

  (4)

The spectral functions for wind turbulence experienced by a moving vehicle have been comprehensively defined by K. Cooper [13], based on the model of atmospheric...