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194 Laurent Dumas C Fig. 7.2 Wake flow behavior behind Ahmed’s bluff body 7.1.4 Drag Variation with the Slant Angle A B A dimensionless coefficient, called drag coefficient and related to the drag force acting on the bluff body, is defined as follows: Cd = Fd 1 2ρV 2 . (7.1) ∞S In this expression, ρ represents the air density, V∞ is the freestream velocity, S is the cross section area and Fd is the total drag force acting on the car projected on the longitudinal direction. Note that the drag force Fd can be decomposed into a sum of a viscous drag force and a pressure drag force. A first striking result observed by Morel is that the slant surface and the rear base are responsible for more than 90% of the pressure drag force. Moreover, the latter represents more than 70% of the total drag force. These observations have been confirmed by the Ahmed experiment where only 15% to 25% of the drag is due to the viscous drag. Such results can be explained by the analysis of the wake flow discussed in Sect. 7.1.3, that is, the large separation area will induce the major part of the total drag force.
7 CFD-based Optimization for Automotive Aerodynamics 195 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 Cd 0.00 0 10 20 30 40 50 60 70 80 90 α 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 Cd 0.00 0 5 10 15 20 25 30 35 40 Fig. 7.3 Drag measured for the Morel (left) and Ahmed (right) bluff-body for various slant angles The variations of the drag coefficient for the Morel and the Ahmed bluff body with respect to the slant angle α are displayed in Fig. 7.3. Both graphs exhibit the same variations, in particular with a peak value at a critical angle αc near 30 degrees, already introduced in the previous subsection. The shape of the curve can also be explained by referring to the wake flow behind the car: for small values of α for which the flow is twodimensional, the drag is directly linked to the dimensions of the separated area. Then, when the flow becomes three dimensional, the separation bulb that appears absorbs a growing amount of the flow energy, thus leading to a large increase of the drag coefficient until α reaches αc. Above this value, the airflow no longer feeds the vortex systems. Consequently, the static and total pressure experience a sudden rise at the base thus drastically reducing the drag coefficient almost to its value at a zero slant angle. 7.2 The Drag Reduction Problem After the description in the previous section of the main features of automotive aerodynamics, the car drag reduction problem is now stated for real cars in Sect. 7.2.1. The numerical modelization of this problem in view of an automatic drag minimization is then presented in Sect. 7.2.2. α
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Optimization and Computational Flui
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Editors: Prof. Dr.-Ing. Dominique T
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vi Preface Our first research proje
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viii Contents 2.4.1 GoverningEquati
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x Contents 6.2.3 Parameterization..
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xii Contents 9.4.1 Multi-objectiveO
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xiv List of Contributors Gábor JAN
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Part I Generalities and methods
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4 Dominique Thévenin 12 10 8 6 4 2
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6 Dominique Thévenin Objective 10
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8 Dominique Thévenin Objective 10
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10 Dominique Thévenin Parameter 2
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12 Dominique Thévenin three-dimens
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14 Dominique Thévenin Let us come
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16 Dominique Thévenin References 1
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18 Gábor Janiga 2.1 Introduction D
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20 Gábor Janiga y Tinlet = 293 K 0
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22 Gábor Janiga y [mm] 25 20 15 10
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24 Gábor Janiga Table 2.1 Number o
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26 Gábor Janiga A dominates the in
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28 Gábor Janiga be shown later, th
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30 Gábor Janiga INPUT FILE Gambit
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34 Gábor Janiga ∆T ∆P Position
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36 Gábor Janiga ∆P [mPa] 2.2 2.0
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38 Gábor Janiga Table 2.3 Speed-up
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40 Gábor Janiga For all computatio
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42 Gábor Janiga y [mm] 4 2 0 -1 0
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44 Gábor Janiga Air mass flow-rate
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46 Gábor Janiga Temperature variat
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50 Gábor Janiga The modified k-ω
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52 Gábor Janiga Error for Re∗ =
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54 Gábor Janiga Error for Re∗ 20
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56 Gábor Janiga References 1. Ali,
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58 Gábor Janiga 43. Janiga, G., Th
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Chapter 3 Mathematical Aspects of C
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3 Mathematical Aspects of CFD-based
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Chapter 4 Adjoint Methods for Shape
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4 Adjoint Methods for Shape Optimiz
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Part II Specific Applications of CF
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112 Nicolas R. Gauger Nomenclature
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114 Nicolas R. Gauger Fig. 5.1 Cost
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116 Nicolas R. Gauger and the four
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118 Nicolas R. Gauger CL := 1 � C
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120 Nicolas R. Gauger the cost func
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122 Nicolas R. Gauger Table 5.1 An
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124 Nicolas R. Gauger The main adva
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126 Nicolas R. Gauger Spalart-Allma
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128 Nicolas R. Gauger (a) (b) Fig.
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134 Nicolas R. Gauger Fig. 5.10 Plo
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136 Nicolas R. Gauger drag, lift, s
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138 Nicolas R. Gauger solution of t
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140 Nicolas R. Gauger the presence
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142 Nicolas R. Gauger Fig. 5.16 Con
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8 Multi-objective Optimization in C
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Chapter 9 CFD-based Optimization fo
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9 CFD-based optimization for paperm
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292 Index heat exchanger, 222, 224,
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