Optimization and Computational Fluid Dynamics - Department of ...

More documents

Recommendations

Info

232 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto L/2 �in (a) (b) L �out h y � � � i j 4 x 1 2 3 7 8 9 (c) (d) � Lwave L Fig. 8.5 Periodic channels and geometrical parametrization. (a) Linear piecewise channel; (b) NURBS channel; (c) Linear piecewise parametrization; (d) NURBS parametrization and control points the linear-piecewise and the NURBS, are depicted in Figs. 8.5(a) and 8.5(b), respectively. 8.5.1.1 2D Linear Piecewise Parametrization The linear piecewise wall profile of the channel is characterized by a small number of design variables or Degrees Of Freedom (DOFs). Their exact meaning will be described in Sect. 8.6. Here it is sufficient to say that they represent the independent variables that may be adjusted, during the optimization process to achieve the desired goal(s). The variables introduced in this wall parametrization are presented in Fig. 8.5(c) and summarized in Table 8.1. There are four DOFs requested for describing the wall profile. Realized by defining a set of points and connecting them with straight lines, the profile is constructed only for convenience in order to have the edge of the corrugation centeredonthewall. 5 6
8 Multi-objective Optimization in Convective Heat Transfer 233 Table 8.1 Variables defining the linear piecewise channel Variable Symbols Range module length L [0.8;2.0] corrugation height h [0.0;0.5] forward edge angle ϕin [10 ◦ ;60 ◦ ] backward edge angle ϕout [10 ◦ ;60 ◦ ] translation of upper wall transl [−0.5L;0.5L] Table 8.2 Control points for the NURBS-profile and parameters required Point x y DOFs 1 0 0 0 2 (L − Lwave)/2 0 0 3 x2 + ∆x 23 0 1 4 x5 + ρ 54 cos ϑ54 y5 + ρ 54 sinϑ54 2 5 x1 + ∆x5 y1 + ∆y5 2 6 x5 + ρ 56 cos ϑ56 y5 + ρ 56 sinϑ56 2 7 x8 − ∆x 87 0 1 8 x2 + Lwave 0 1 9 L 0 1 8.5.1.2 2D NURBS Parametrization In order to generate the NURBS channel during the optimization process, let’s start by defining first the wall profile. As a good compromise between the number of DOFs and the geometrical complexity, a 9 control-point periodic cubic NURBS has been chosen, to ensure the periodicity of the channel itself. A large number of DOFs allows to describe minutely the profile, but if this number is excessive, it would make the optimization process quite difficult and expensive. For this reason, it has been also decided to fix to a unitary value the curve’s weights. This, together with the uniform knots distribution we adopted, makes our NURBS curve practically equivalent to a B-Spline curve [18, 38]. As depicted in Fig. 8.5(d), both the first and the last three aligned control points are needed to maintain the entrance and the exit of the profile parallel to the x direction. The remaining ones give freedom to the wavy section. The parameters required for the definition of the lower profile are explained in Table 8.2 and numbered as in Fig. 8.5(d). The symbol ∆ means the difference between the coordinates of two points while ρ ij is the module and ϑij the phase of a polar-coordinate system centered on the point i. The phase is positive counterclockwise with respect to the positive direction of the x axis. The profile is again constructed, for convenience, in order to have the wavy
Page 1 and 2:
Optimization and Computational Flui
Page 3 and 4:
Editors: Prof. Dr.-Ing. Dominique T
Page 5 and 6:
vi Preface Our first research proje
Page 7 and 8:
viii Contents 2.4.1 GoverningEquati
Page 9 and 10:
x Contents 6.2.3 Parameterization..
Page 11 and 12:
xii Contents 9.4.1 Multi-objectiveO
Page 13 and 14:
xiv List of Contributors Gábor JAN
Page 15:
Part I Generalities and methods
Page 18 and 19:
4 Dominique Thévenin 12 10 8 6 4 2
Page 20 and 21:
6 Dominique Thévenin Objective 10
Page 22 and 23:
8 Dominique Thévenin Objective 10
Page 24 and 25:
10 Dominique Thévenin Parameter 2
Page 26 and 27:
12 Dominique Thévenin three-dimens
Page 28 and 29:
14 Dominique Thévenin Let us come
Page 30 and 31:
16 Dominique Thévenin References 1
Page 32 and 33:
18 Gábor Janiga 2.1 Introduction D
Page 34 and 35:
20 Gábor Janiga y Tinlet = 293 K 0
Page 36 and 37:
22 Gábor Janiga y [mm] 25 20 15 10
Page 38 and 39:
24 Gábor Janiga Table 2.1 Number o
Page 40 and 41:
26 Gábor Janiga A dominates the in
Page 42 and 43:
28 Gábor Janiga be shown later, th
Page 44 and 45:
30 Gábor Janiga INPUT FILE Gambit
Page 46 and 47:
Page 48 and 49:
34 Gábor Janiga ∆T ∆P Position
Page 50 and 51:
36 Gábor Janiga ∆P [mPa] 2.2 2.0
Page 52 and 53:
38 Gábor Janiga Table 2.3 Speed-up
Page 54 and 55:
40 Gábor Janiga For all computatio
Page 56 and 57:
42 Gábor Janiga y [mm] 4 2 0 -1 0
Page 58 and 59:
44 Gábor Janiga Air mass flow-rate
Page 60 and 61:
46 Gábor Janiga Temperature variat
Page 62 and 63:
Page 64 and 65:
50 Gábor Janiga The modified k-ω
Page 66 and 67:
52 Gábor Janiga Error for Re∗ =
Page 68 and 69:
54 Gábor Janiga Error for Re∗ 20
Page 70 and 71:
56 Gábor Janiga References 1. Ali,
Page 72 and 73:
58 Gábor Janiga 43. Janiga, G., Th
Page 75 and 76:
Chapter 3 Mathematical Aspects of C
Page 77 and 78:
3 Mathematical Aspects of CFD-based
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Chapter 4 Adjoint Methods for Shape
Page 95 and 96:
4 Adjoint Methods for Shape Optimiz
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123:
Part II Specific Applications of CF
Page 126 and 127:
112 Nicolas R. Gauger Nomenclature
Page 128 and 129:
114 Nicolas R. Gauger Fig. 5.1 Cost
Page 130 and 131:
116 Nicolas R. Gauger and the four
Page 132 and 133:
118 Nicolas R. Gauger CL := 1 � C
Page 134 and 135:
120 Nicolas R. Gauger the cost func
Page 136 and 137:
122 Nicolas R. Gauger Table 5.1 An
Page 138 and 139:
124 Nicolas R. Gauger The main adva
Page 140 and 141:
126 Nicolas R. Gauger Spalart-Allma
Page 142 and 143:
128 Nicolas R. Gauger (a) (b) Fig.
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
134 Nicolas R. Gauger Fig. 5.10 Plo
Page 150 and 151:
136 Nicolas R. Gauger drag, lift, s
Page 152 and 153:
138 Nicolas R. Gauger solution of t
Page 154 and 155:
140 Nicolas R. Gauger the presence
Page 156 and 157:
142 Nicolas R. Gauger Fig. 5.16 Con
Page 158 and 159:
144 Nicolas R. Gauger optimization
Page 161 and 162:
Chapter 6 Numerical Optimization fo
Page 163 and 164:
6 Numerical Optimization for Advanc
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196: 6 Numerical Optimization for Advanc
Page 203: 6 Numerical Optimization for Advanc
Page 206 and 207: 192 Laurent Dumas 7.1 Introducing A
Page 208 and 209: 194 Laurent Dumas C Fig. 7.2 Wake f
Page 210 and 211: 196 Laurent Dumas Table 7.1 Example
Page 212 and 213: 198 Laurent Dumas Fig. 7.5 Numerica
Page 214 and 215: 200 Laurent Dumas 7.3.1.1 Genetic A
Page 216 and 217: 202 Laurent Dumas START Random init
Page 218 and 219: 204 Laurent Dumas • if ˜ J(x ng
Page 220 and 221: 206 Laurent Dumas Table 7.3 Compari
Page 222 and 223: 208 Laurent Dumas Fig. 7.9 General
Page 224 and 225: 210 Laurent Dumas Table 7.4 Four ex
Page 226 and 227: 212 Laurent Dumas Fig. 7.13 Blades
Page 228 and 229: 214 Laurent Dumas Table 7.5 Converg
Page 231 and 232: Chapter 8 Multi-objective Optimizat
Page 233 and 234: 8 Multi-objective Optimization in C
Page 237 and 238: 8 Multi-objective Optimizatio Fig.
Page 245: 8 Multi-objective Optimization in C
Page 281 and 282: Chapter 9 CFD-based Optimization fo
Page 283 and 284: 9 CFD-based optimization for paperm
Page 297 and 298:
9 CFD-based optimization for paperm
Page 299 and 300:
Page 301 and 302:
Page 303:
Page 306 and 307:
292 Index heat exchanger, 222, 224,
show all

Optimization and Computational Fluid Dynamics - Department of ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?