COURSE ON VEHICLE AERODYNAMICS
Prof. Tamás Lajos University of Rome “La Sapienza” 1999 1. Introduction Subject of the course: basics of vehicle aerodynamics ⇒ ground vehicle aerodynamics ⇒ examples in car, bus, truck aerodynamics. Main objectives of vehicle aerodynamics: - reduction of drag and fuel consumption, - improvement of operational characteristics (stability, safety, handling characteristics) - improvement of comfort characteristics (noise generation, mud deposition etc.) 3 flow fields: - flow past vehicle bodies, - flow in passenger compartment (ventilating, heating), - flow in and around components (cooler, brakes etc.) 2. History 4 periods: - 1900 -1920 Adaptation of the form of different vehicles (e.g. boats and airships) and devices like bodies (e.g. torpedoes), - 1920 -1970 Utilisation of the results of aeroplane aerodynamics. Gap between aerodynamic achievements and the mass production of cars. Pál Járay, Klemperer: optimum body shape near the ground, car bodies constructed by combining wing and airship sections. Kamm: cut of long tail of Járay's cars. - 1970 - Form optimisation: starting from a given car body configuration meeting the needs of consumers, technological, styling and safety requirements etc. and changes of body shape will be carried out to improve the aerodynamic characteristics. - 1980 - Development of aerodynamically optimal body shape and its use as the starting point for the development of a car body. 3. Forces and moments The forces and moments acting on a car body:
where: D drag L lift S side force MY yawing moment MP pitching moment MR rolling moment.
3.1. Regarding a given vehicle body shape, the following relation can be written between a force component (e.g. D) and the related physical quantities (undisturbed approaching velocity v, density ρ, dynamic viscosity µ, characteristic size (e.g. wheel base) L and angle of attack β: F (D, v∞, ρ, µ, L β) = 0 Using Buckingham's Π theorem, 3 dimensionless groups can be formed: Π1 = D ρ 2 2 v∞ L 2 ∞
Π2 = v ∞ Lρ = Re µ Π3 = β
Since L2 is proportional to the largest cross wind area A, D cD = ρ 2 v∞ A 2 ∞ Where cD is drag coefficient and Re is Reynolds number. Similar force coefficients can be defined: lift- and side force coefficient. 3.2. The moment coefficients are defined as follows: MY cY = ρ 2 v∞A L 2 yaw coefficient. 3.3. The possibilities of drag reduction Cars: cD - without any deeper aerodynamic considerations 0.5 - on the basis of literature 0.45 - with form optimisation and model experiments 0.4 - starting from an optimum body shape, long development 0.3 - future perspectives 0.2 Busses, trucks: from cD = 0.6 - 1 through aerodynamic developments cD = 0.35 - 0.4. 4. Wind characteristics Wind is generated by a pressure difference on the surface of the Earth. Because of the Coriolis forces caused by the rotation of the Earth and the relative velocity of the air, the streamlines of wind coincide approximately with the isobars. The thickness of the atmospheric boundary layer (gradient height) is z [m] where gradient velocity vG prevails. The wind profile can be approximated by expression: v z = vG zG
The turbulence of wind can be characterised v 10 by the gust factor: where subscript 10 means the height of observation in [m] and t is the time of observation in [s]. So the gust factor is the quotient from the mean velocity for a time span t [s] and the mean velocity for one hour. The main characteristics of atmospheric wind depend on the roughness of the Earth surface: smooth surface rough surface (e.g. lake) (e.g. downtown) z gradient height in m 1/n exponent F 310 gust factor 200 0.12 1.4 550 0.3 2 t F10 = t v 10
The roughness of the surface considerably increases the turbulence intensity. The wind influences the flow past vehicle bodies.
u vehicle velocity v absolute (wind) velocity w relative velocity
The consequences of the wind: - the average drag and so the fuel consumption...
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