Optimization and Computational Fluid Dynamics - Department of ...

More documents

Recommendations

Info

268 J. Hämäläinen, T. Hämäläinen, E. Madetoja, H. Ruotsalainen shape of a domain is not known a-priori. Instead, a shape is sought such that the cost function is minimized (or maximized), and the state equation and possible constraints are fulfilled. The cost function, also known as the objective function, measures the quality of the shape. Typically, it is formulated such that its minimum (or maximum) value corresponds to the best possible shape (optimal shape). The state equation is a model describing the physical phenomenon to be studied, as in the case of the Navier-Stokes equations, for example. The constraints ensure that the optimal shape is reasonable, for instance, by setting limits to total material usage in solid mechanical problems, minimum and maximum material thicknesses. Optimal control is a special case of shape optimization. Instead of the shape of the domain, the boundary data, for example, are now a-priori unknown. A typical optimal control problem related to CFD is the search for an optimal velocity profile at an inlet or optimal heat flux through a wall. Optimal shape design is said to have originated with Hadamard in 1910 [9], who first supplied a formula for a partial differential equation in order to evaluate the change due to a boundary modification of the domain. The first engineering applications were in solid mechanics. CFD emerged through potential flows, Euler equations, and finally viscous Navier-Stokes equations including turbulence models. For further information, see [18, 29, 32] and the bibliographical studies cited there. In traditional optimal shape design or optimal control problems, there is only one objective (also known as cost function) to be optimized. However, everyday engineering problems typically involve several conflicting objectives that should be achieved simultaneously. A single objective function can be derived from multiple functions, as a weighted sum, for example, but then the practical relevance of the cost function values may be lost. Instead, it is more reasonable to handle multiple objectives as they arise naturally from engineering problems, by using methods of multi-objective optimization [26, 34]. The importance of multi-objective optimization becomes even more significant when dealing with large industrial processes and taking into account consecutive unit-processes, raw material, energy consumption, and end-product quality and price, each of which have their own objectives. Applications of multi-objective optimization are not only necessary to handle engineering problems, but will play an important role also in decision support systems in the future. Computing capacity is always limited which leads to compromises between accuracy, scope and computing time as illustrated in Fig. 9.1. Naturally, there is a need for detailed small-scale modeling such as Direct Numerical Simulation (DNS) which requires high performance computing even without any optimization. But the detailed models cannot be coupled with optimization if total computational (CPU) time is to be kept reasonable. When a new product is being designed, a relatively long CPU time, days or even weeks, is considered acceptable. Therefore, the optimal shape design can be used based on a complex CFD model. But when a fast response, in seconds or
9 CFD-based optimization for papermaking 269 Accuracy Phenomenon Design Cpu - time Control Decision support Extent Fig. 9.1 Compromise between accuracy and extent of CFD when coupled with optimization minutes, is required, the cost function evaluation has to be carried out extremely quickly. This is possible only with the use of reduced CFD models. Moreover, when the scope extends to a large system consisting of numerous unit-process models coupled with multi-objective optimization, models need to be reduced even further. Such is the case when modeling the entire papermaking process. Evidently, CFD and different CFD based optimization applications involve varying demands for accuracy, complexity and CPU time. CFD-based optimization tools developed for the paper industry are discussed in this paper. Applications vary from headbox optimal shape design (Sect. 9.2) and optimal control (Sect. 9.3) to multi-objective optimization (Sect. 9.4) and decision support systems (Sect. 9.5) designed for the whole paper machine, all having basis in reduced CFD models. In this paper, one such model, the depth-averaged Navier-Stokes equations, has been validated in a contracting channel. 9.2 Optimal Shape Design of the Tapered Header A traditional design problem in the paper machine headbox is the tapering of the header that allows even outlet flow rate distribution across the full width of the paper machine [1, 24, 35]. The headbox is the first part of the paper machine from where the fiber-water mixture starts the papermaking process by going through the header as the first flow passage (Fig. 9.2). The fiber-
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:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Page 203:
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 281: Chapter 9 CFD-based Optimization fo
Page 285 and 286: 9 CFD-based optimization for paperm
Page 303: 9 CFD-based optimization for paperm
Page 306 and 307: 292 Index heat exchanger, 222, 224,
show all

Optimization and Computational Fluid Dynamics - Department of ...

Create successful ePaper yourself

Delete template?

Save as template?