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21 AN OVERVIEW ON MOTOR VEHICLE AERODYNAMICS The forces and moments the vehicle receives from the surrounding air depend more on the shape of the body than on the characteristics of the chassis. A detailed study of motor vehicle aerodynamics is thus beyond the scope of a book dealing with the automotive chassis. However, aerodynamic forces and moments have a large influence on the longitudinal performance of the vehicle, its handling and even its comfort, so it is not possible to neglect them altogether. Even if the goal of motor vehicle aerodynamics is often considered to be essentially the reduction of aerodynamic drag, the scope and the applications of aerodynamics in motor vehicle technology are much wider. The following aspects are worth mentioning • reduction of aerodynamic drag, • reduction of the side force and the yaw moment, which have an important influence on stability and handling, • reduction of aerodynamic noise, an important issue for acoustic comfort, and • reduction of dirt deposited on the vehicle and above all on the windows and lights when driving on wet road, and in particular in mud or snow conditions. This aspect, important for safety, can be extended to the creation of spray wakes that can reduce visibility for other vehicles following or passing the vehicle under study. G. Genta, L. Morello, The Automotive Chassis, Volume 2: System Design, Mechanical Engineering Series, c Springer Science+Business Media B.V. 2009  115 116 21. AN OVERVIEW ON MOTOR VEHICLE AERODYNAMICS The provisions taken to obtain these goals are often different and sometimes contradictory. A typical example is the trend toward more streamlined shapes that allow us to reduce aerodynamic drag, but at the same time have a negative effect on stability. Another example is the mistaken assumption that a shape that reduces aerodynamic drag also has the effect of reducing aerodynamic noise. The former is mainly influenced by the shape of the rear part of the vehicle, while the latter is much influenced by the shape of the front and central part, primarily of the windshield strut (A-pillar). It is then possible that a change in shape aimed at reducing one of these effects may have no influence, or sometimes even a negative influence, on the other one. At any rate, all aerodynamic effects increase sharply with speed, usually with the square of the speed, and are almost negligible in slow vehicles. Moreover, they are irrelevant in city driving. Aerodynamic effects, on the contrary, become important at speeds higher than 60÷70 km/h and dominate the scene above 120÷140 km/h. Actually these figures must be considered only as indications, since the relative importance of aerodynamic effects and those linked with the mass of the vehicle depends on the ratio between the cross section area and the mass of the vehicle. At about 90 ÷ 100 km/h, for instance, the aerodynamic forces acting on a large industrial vehicle are negligible when it travels at full load, while they become important if it is empty. Modern motor vehicle aerodynamics is quite different from aeronautic aerodynamics, from which it derives, not only for its application fields but above all for its numerical and experimental instruments and methods. The shapes of the objects dealt with in aeronautics are dictated mostly by aerodynamics, and the aerodynamic fields contains few or no zones in which the flow separates from the body. On the contrary, the shape of motor vehicles is determined mostly by considerations like the possibility of locating the passengers and the luggage (or the payload in industrial vehicles), aesthetic considerations imposed by style, or the need of cooling the engine and other devices like brakes. The blunt shapes that result from these considerations cause large zones where the flow separates and a large wake and vortices result. The presence of the ground and of rotating wheels has a large influence on the aerodynamic field and makes its study much more difficult than in the case of aeronautics, where the only interaction is that between the body and the surrounding air. One of the few problems that are similar in aeronautical and motor vehicle aerodynamics is the study of devices like the wings of racing cars, but this is in any case a specialized field that has little to do with vehicle chassis design, and it will not be dealt with here in detail. Traditionally, the study of aerodynamic actions on motor vehicles is primarily performed experimentally, and the wind tunnel is its main tool. The typical wind tunnel scenario is a sort of paradigm for interpreting aerodynamic phenomena, to the point that usually the body is thought to be stationary and 21.1 Aerodynamic forces and moments 117 the air moving around it, instead of assuming that the body moves through stationary air. However, while in aeronautics the two wiewpoints are coincident, in motor vehicle aerodynamics they would be so only if, in the wind tunnel, the ground moved together with the air instead of being stationary with respect to the vehicle. Strong practical complications are encountered when attempting to allow the ground to move with respect to the vehicle, and allowing the wheels to rotate. Usually, in wind tunnel testing, the ground does not move, but its motion is simulated in an approximate way. Along with wind tunnel tests, it is possible to perform tests in actual conditions, with vehicles suitably instrumented to take measurements of aerodynamic forces while travelling on the road. Measurements of the pressure and the velocity of the air at different points are usually taken. Recently powerful computers able to simulate the aerodynamic field numerically have became available. Numerical aerodynamic simulation is extremely demanding in terms of computational power and time, but it allows us to predict, with increasing accuracy, the aerodynamic characteristics of a vehicle before building a prototype or a full scale model (note that reduced scale models, often used in aeronautics, are seldom used in vehicular technology). There is, however, a large difference between aeronautical and vehicular aerodynamics from this viewpoint as well. Nowadays, numerical aerodynamics is able to predict very accurately the aerodynamic properties of streamlined bodies, even if wind tunnel tests are needed to obtain an experimental confirmation. The possibility of performing extensive virtual experimentation on mathematical models greatly reduces the number of experimental tests to be performed. Around blunt bodies, on the other hand, it is very difficult to simulate the aerodynamic field accurately, given their large detached zones and wake. Above all, it is difficult to compute where the streamlines separate from the body. The impact of numerical aerodynamics is much smaller in motor vehicle design than has been in aeronautics. As said, the aim of this chapter is not to delve into details on vehicular aerodynamics, but only to introduce those aspects that influence the design of the chassis. While the study of the mechanisms that generate aerodynamic forces and moments influencing the longitudinal and handling performance of the vehicle will be dealt with in detail, those causing aerodynamic noise or the deposition of dirt on windows and lights will be overlooked. In particular, those unstationary phenomena, like the generation of vortices that are very important in aerodynamic noise, will not be studied. 21.1 AERODYNAMIC FORCES AND MOMENTS In aeronautics, the aerodynamic force acting on the aircraft is usually decomposed in the direction of the axes of a reference frame Gx y  z  , usually referred to as the wind axes system, centered in the mass center G, with the x -axis 118 21. AN OVERVIEW ON MOTOR VEHICLE AERODYNAMICS directed as the velocity of the vehicle with respect to air −Vr and the z  -axis contained in the symmetry plane. The components of the aerodynamic forces in the Gx y  z  frame are referred to as drag D, side force S and lift L. The aerodynamic moment is usually decomposed along the vehicle-fixed axes Gxyz. In the case of motor vehicles, both the aerodynamic force and moment are usually decomposed with reference to the frame xyz: The components of the aerodynamic force are referred to as longitudinal Fxa , lateral Fya and normal Fza forces while those of the moment are the rolling Mxa , pitching Mya and yawing Mza moments. In the present text, aerodynamic forces will always be referred to frame xyz, which is centred in the centre of mass of the vehicle. However, in wind tunnel testing the exact position of the centre of mass is usually unknown and the forces are referred to a frame which is immediately identified. Moreover, the position of the centre of mass of the vehicle depends also on the loading, while aerodynamic forces are often assumed to be independent of it, although a change of the load of the vehicle can affect its attitude on the road and hence the value of aerodynamic forces and moments. The frame often used to express forces and moments for wind tunnel tests is a frame centred in a point on the symmetry plane and on the ground, located at mid-wheelbase, with the x -axis lying on the ground in the plane of symmetry of the vehicle and the y  -axis lying also on the ground (Fig. 21.1). Since the resultant air velocity Vr lies in a horizontal plane, angle α is the aerodynamic angle of attack. From the definition of the x axis, it is a small angle and is often assumed to be equal to zero. Remark 21.1 From the definitions here used for the reference frames it follows that α is positive when the x-axis points downwards. The forces and moments expressed in the xyz frame can be computed from those expressed in the x y  z  frame (indicated with the symbols Fx , Fy , Fz , Mx , My and Mz ) through the relationships ⎧ ⎨ Fx = Fx cos(α) − Fz sin(α) Fy = Fy ⎩ Fz = Fx sin(α) + Fz cos(α) (21.1) ⎧ ⎨ Mx = Mx + Fy hG My = My − Fx hG + Fz xG ⎩ Mz = Mz − Fy xG . (21.2) Distance xG is the coordinate of the centre of mass with reference to the x y z frame and is positive if the centre of mass is forward of mid-wheelbase (a < b).    21.1 Aerodynamic forces and moments 119 l = = b a x’G z’ z’ z Fz Fz F’z G My O y F’y Fy M’z Mz O Fy x hG x’ M’y y’ F’z α Fx Mx G y F’y y’ O M’x Fx G F’x x x’ FIGURE 21.1. Reference frame often used to express aerodynamic forces in wind tunnel tests. The air surrounding a road vehicle exerts on any point P of its surface a force per unit area  t = lim ΔF , (21.3) ΔS→0 ΔS where ΔS and ΔF are respectively the area of a small surface surrounding point P and the force acting on it. The force per unit area t can be decomposed into a pressure force acting in a direction perpendicular to the surface tn = pn , (21.4) where n is a unit vector perpendicular to the surface and p is a scalar expressing the value of the pressure, and a tangential force tt lying on the plane tangent to the surface. The latter is due to fluid viscosity. These force distributions, once integrated on the entire surface, result in an aerodynamic force, which is usually applied to the centre of mass of the vehicle, and an aerodynamic moment. By decomposing the force and the moment in Gxyz frame, it follows: 120 21. AN OVERVIEW ON MOTOR VEHICLE AERODYNAMICS ⎧ ⎪ ⎪ Fxa = ⎪ ⎪ ⎪ ⎪ ⎨ Fy a = ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ Fza = ⎧ ⎪ ⎪ Mxa = − ⎪ ⎪ ⎪ ⎪ ⎨ My a = − ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ Mza = − tt × idS + S tt × jdS + S tn × jdS tt × kdS + tn × kdS S ytt × kdS − ztt × jdS + S xtt × kdS + S S xtn × kdS + ztt × idS − ytt × idS + ytn × kdS ztn × jdS + S S S (21.5) S S S tn × idS S ztn × idS S xtt × jdS − S S ytn × idS + S xtn × jdS . S (21.6) At standstill, the only force exerted by air is the aerostatic force, acting in the vertical direction. It is equal to the weight of the displaced fluid. It reaches non-negligible values only for very light and large bodies and it is completely neglected in aerodynamics. If air were an inviscid fluid, i.e. if its viscosity were nil, no tangential forces could act on the surface of the body; it can be demonstrated that in this case no force could be exchanged between the body and the fluid, apart from aerostatic forces, at any relative speed since the resultant of the pressure distribution always vanishes. This result, the work of D’Alembert, was formulated in 17441 and again in 17682 . It is since known as the D’Alembert Paradox. In the case of a fluid with no viscosity, the pressure p and the velocity V can be linked to each other by the Bernoulli equation 1 1 p + ρV 2 = constant = p0 + ρV02 , 2 2 (21.7) where p0 and V0 are the values of the ambient pressure and of the velocity far enough upstream from the body3 . The term pd = 1 2 ρV 2 0 (21.8) is the so-called dynamic pressure. The sum ptot = p0 + pd (21.9) is the total pressure. 1 D’Alembert, Traité de l’équilibre et du moment des fluides pour servir de suite un traité de dynamique, 1774. 2 D’Alembert, Paradoxe proposé aux geometres sur la résistance des fluides, 1768. 3 Considering the actual case of the vehicle moving in still air, instead of the wind tunnel situation with air moving around a stationary object, V0 is the velocity of the body relative to air −Vr . 21.1 Aerodynamic forces and moments 121 TABLE 21.1. Pressure, temperature, density and kinematic viscosity of air at various altitudes, from the ICAO standard atmosphere. Only the part of the table related to altitudes of interest for road vehicles is reported. z [m] p [kPa] -500 107.486 0 101.325 500 95.458 1000 89.875 1500 84.546 2000 79.489 2500 74.656 3000 70.097 T [K] ρ [kg/m3 ] 291.25 1.2857 288.16 1.2257 284.75 1.1680 281.50 1.1123 278.25 1.0586 275.00 1.0070 271.75 0.9573 268.50 0.9095 ν [m2 /s] 13.97 × 10−6 14.53 × 10−6 15.10 × 10−6 15.71 × 10−6 16.36 × 10−6 17.05 × 10−6 17.77 × 10−6 18.53 × 10−6 The values of the ambient pressure, together with those of the density, temperature, and kinematic viscosity at altitudes of interest in road vehicle technology, are reported in Table 21.1 from the ICAO standard atmosphere. The density at temperatures and pressures different from pa and Ta in standard conditions can be computed as ρ = ρa p Ta , pa T (21.10) where temperatures are absolute. The dynamic pressure is extremely low, when compared to the ambient pressure: consider, for instance, a vehicle moving air at the temperature and pressure equal to those indicated in Table 21.1 at sea level, at a speed of 30 m/s (108 km/h). The pressure is about 101 kPa, while the dynamic pressure is 0,55 kPa, corresponding to 0,5% of pressure. The variations of pressure due to velocity variations are thus quite small with respect to atmospheric pressure; however, such small pressure changes, acting on surfaces of some square meters, yield non-negligible, and sometimes large, aerodynamic forces. Note that the Bernoulli equation, which holds along any streamline, was written without the gravitational term, the one linked with aerostatic forces. It states simply that the total energy is conserved along any streamline. An example of the D’Alembert Paradox is shown in Fig. 21.2, where the cross section of a cylinder of infinite length, whose axis is perpendicular to the direction of the velocity Vr of the fluid, is represented. The streamlines open around the body and the local velocity of the fluid increases on its sides, leading to a decrease of pressure as described by the Bernoulli Equation. On the front of the body there is a point (actually in the case of the cylinder it is a line) which divides the part of the flow which goes “above” the body from that going “below” it. At this point, known as the stagnation point, the velocity of the fluid reduces to zero and the pressure reaches its maximum, equal to the total pressure. 122 21. AN OVERVIEW ON MOTOR VEHICLE AERODYNAMICS FIGURE 21.2. Streamlines and pressure distribution on a circular cylinder whose axis is perpendicular to the flow. This is a case of a fluid with no viscosity. Since there is no viscosity, no energy is dissipated, and when the fluid slows down again, after reaching the maximum velocity at the point where the width of the body is maximum, the pressure is fully recovered: The pressure distribution is symmetrical and no net force is exchanged between the fluid and the body. This holds for any possible shape, provided that the viscosity is exactly nil. No fluid actually has zero viscosity and the Paradox is not applicable to any real fluid. Viscosity has a twofold effect: It causes tangential forces creating so-called friction drag, and it modifies the pressure distribution, whose resultant is no longer equal to zero. The latter effect, which for fluids with low viscosity is generally more important than the former, generates the lift, the side force and the pressure drag. The direct effects of viscosity (i.e. the tangential forces) can usually be neglected, while the modifications of the aerodynamic field must be accounted for. Owing to viscosity, the layer of fluid in immediate contact with the surface tends to adhere to it, i.e. its relative velocity vanishes, and the body is surrounded by a zone where there are strong velocity gradients. This zone is usually referred to as the “boundary layer” (Fig. 21.3) and all viscous effects are concentrated in it. The viscosity of the fluid outside the boundary layer is usually neglected and the Bernoulli equation can be used in this region. Remark 21.2 The thickness of the boundary layer increases as the fluid in it loses energy owing to viscosity and slows down. If the fluid outside the boundary layer increases its velocity, a negative pressure gradient along the separation line between the external flow and the boundary layer is created, and this decrease of pressure in a way boosts the flow within the boundary layer fighting its tendency 21.1 Aerodynamic forces and moments 123 FIGURE 21.3. Boundary layer: Velocity distribution in direction perpendicular to the surface. The separation point is also represented. to slow down. On the contrary, if the outer flow slows down, the pressure gradient is positive and the airflow in the boundary layer is hampered. At any rate, at a certain point the flow in the boundary layer can stop and a zone of stagnant air can form in the vicinity of the body: The flow then separates from the surface, possibly starting the formation of a wake. If the velocity distribution outside the boundary layer were known, the pressure distribution at the interface between the boundary layer and the external fluid could be computed. Provided that the boundary layer is very thin, and this is the case except where the flow is detached from the surface, the pressure on the surface of the body can be assumed to be equal to that occurring at the outer surface of the boundary layer, and then the aerodynamic forces and moments can be computed by integrating the pressure distribution. While this can be applied to computing the lift of streamlined objects, for blunt bodies, like the ones studied by road vehicle aerodynamics, and for drag, few results can be obtained along these lines. To generalize the results obtained by experimental testing, performed mainly in wind tunnels, the aerodynamic force F and moment M are expressed as 1 1 ρVr 2 SCf , M = ρVr 2 SlCm , (21.11) 2 2 where forces and moments are assumed to be proportional to the dynamic pressure of the free current 1 ρVr 2 , 2 to a reference surface S (in the expression of the moment a reference length l is also present) and to nondimensional coefficients Cf and Cm to be experimentally determined. Such coefficients depend on the geometry and position of the body, and on two non-dimensional parameters, the Reynolds number F = Re = Vl , ν 124 21. AN OVERVIEW ON MOTOR VEHICLE AERODYNAMICS and the Mach number Ma = V , Vs where ν is the kinematic viscosity of the fluid (see Table 21.1) and Vs is the velocity of sound in the fluid. The former is a parameter indicating the relative importance of the inertial and viscous effects in determining aerodynamic forces. If its value is low, the latter are of great importance, while if it is high aerodynamic forces are primarily due to the inertia of the fluid. In this case (for vehicles, if Re > 3,000,000), the dependence of the aerodynamic coefficients on the Reynolds number is very low and can be neglected. This is usually the case for road vehicles, at least for speeds in excess of 30 ÷ 40 km/h. If, on the contrary, the Reynolds number is low, aerodynamic forces and moments are essentially due to viscosity. In this case, their dependence on the velocity V should be linear rather than quadratic or, to use equations (21.11), the aerodynamic coefficients should be considered as dependent on the speed, increasing with decreasing speed. The Mach number is the ratio between the airspeed and the speed of sound4 . When its value is low, the fluid can be considered as incompressible; aerodynamic coefficients are then independent of speed. Approaching the speed of sound (Ma ∼ 1), the compressibility of the fluid can no longer be neglected and aerodynamic drag increases sharply. It is commonly thought that the Mach number is irrelevant in automotive aerodynamics, since the speeds road vehicles may reach, with the exception of some vehicles built to set speed records, lead to Mach numbers low enough to have practically no influence on aerodynamic coefficients. Actually this is true for streamlined bodies, for which the influence of Mach number is negligible for values up to 0, 5 ÷ 0, 6 (speeds up to 600 ÷ 700 km/h), while for blunt bodies fluid compressibility starts to play a role at a lower speed, even for Mach numbers slightly larger than 0,2 (V = 70 m/s = 250 km/h). As a consequence, the effects of the Mach number start to be felt at speeds that can be reached by racing cars. It is important to note that, owing to this effect of the Mach number, it is not possible to perform tests on reduced scale models by increasing the speed to increase the Reynolds number. The reference surface S and length l are arbitrary, to the point that in some cases a surface not existing physically, like a power 2/3 of the displacement for airships, is used. These references simply express the dependence of aerodynamic forces on the square of the dimensions of the body and that of the moments on their cube. It is, however, clear that the numerical values of the coefficients depend on the choice of S and l, which must be clearly defined. In the case of road vehicles, the surface is that of the cross section, with some uncertainty about whether the frontal projected area or that of the maximum cross section has been used (Fig. 21.4). 4 For air at sea level in standard conditions Vs = 330 m/s = 1.225 km/h.