Optimization and Computational Fluid Dynamics - Department of ...

More documents

Recommendations

Info

40 Gábor Janiga For all computations presented in this paper, the complete set of chemical species and elementary reactions, with their Arrhenius coefficients Ai (preexponential factor), β (temperature exponent) and Ei (activation energy), is taken for methane/air flames from [50]. This detailed reaction scheme involves 29 species and 141 elementary reactions. It thus involves 28 supplementary transport equations in the form of Eq. (2.8) plus Eq. (2.12), leading to a tremendous increase of the requested computing time compared to Case A. 2.4.2 Numerical Solution The numerical simulation is performed using UGC + . This code has been optimized for the computation of steady laminar low-Mach number flows with chemical reactions [7, 68]. It is designed as an application of the multipurpose UG library [8]. UG is a modular numerical toolbox originally aimed at investigations of multigrid methods on various model problems described by sets of partial differential equations. UGC + is based on two main modules: a low-Mach Navier-Stokes solver and a thermo-reactive solver. A joint module has been developed to achieve the full coupling of the two sub-modules into one single Partial Differential Equations (PDE) system. The two solvers are in charge of their own diagonal block of the Jacobian matrix and there is an information interchange between them (mass fluxes, density and viscosity). The optimization procedure varies the mass flows of the fuel and air at the two inlets. The corresponding velocity values are used at the inlets for the Navier-Stokes equations. On both sides of the numerical domain, symmetry conditions are applied. The temperature of the fresh gas and walls at the inlets is 298 K. The total quantity of methane and air injected in the system (primary + secondary inlet) is kept constant, so that in principle the same energy is always available. At the outlet atmospheric pressure is imposed. The UGC + code attempts to find steady solutions through time-marching. Time discretization is of first-order implicit type. The value of the time-step can be adapted at each iteration, according to convergence or any user-defined condition. The unsteady equations are solved by fixed-point or approximate- Newton iterations and the user can freely specify how often the Jacobian matrix has to be assembled. The linearized equations are then solved by a Bi-CGSTAB [77] algorithm, preconditioned by multigrid V- or W-cycles with an ILU smoother [69]. A dynamic adaptive grid is used to increase resolution for such multi-scale problems (thin reaction zones, large geometries). The numerical simulation of a physical problem can be performed using various geometries and/or boundary conditions. For the present burner, the computational geometry is fixed for all computations, but the boundary conditions (composition of the mixture for the primary and the secondary inlets) are varied during the optimization procedure.
2 A Few Illustrative Examples of CFD-based Optimization 41 In previous works [43, 44, 74], the optimization problem was simple (single objective) and the Simplex method [28, 63] has been used to speed-up the computational procedure. Here a multi-objective problem is considered and an EA is employed to investigate the optimization domain for the retained input parameters. For the present problem, one evaluation is extremely costly in CPU time. One possibility to speed-up the evaluation is to perform every numerical simulation on parallel computers [42] or to use simplified methods to describe the chemical processes (e.g., the flamelet or tabulated chemistry approach [11, 25, 26, 27, 41, 52, 65]). In the presented application, the Navier-Stokes equations are solved for a two-dimensional flow. In the case of detailed chemistry, 29 species conservation equations are solved additionally. Tabulated chemistry involves only three supplementary transport equations. In UGC + , both the detailed reaction mechanism and the tabulated chemistry (FPI, for Flame-Prolongation of ILDM) are implemented and available for the computations [41]. In the first case, all chemical parameters are computed using the standard software CHEMKIN [45] while FPI computations rely on tabulated values. The computation using detailed chemistry can be performed either with simple molecular transport using the unity Lewis number assumption or using detailed transport modeling [39]. The presented investigation is based on both detailed chemistry and detailed transport computation. This high level of physical accuracy is important to reduce the modeling uncertainty associated with the CFD solutions, especially for cases with minor differences in the objective functions. However, the stability and the speed of the evaluations are greatly enhanced by starting the simulation using the simplified method (FPI, see [41]) during 30 time-steps. The corresponding results are converted into an initial, detailed chemistry solution based on the tabulated values. The detailed chemistry computation is then continued for another 40 time-steps, leading to the “final” result of the evaluation, used to evaluate the objective functions after the necessary post-processing. Unfortunately, the detailed chemistry computations are extreme stiff. Therefore, in many cases, the residual values will still be very high after this fixed number of iterations, indicating convergence problems. Such simulations are marked as non-feasible results and dismissed from the optimization. “Non-feasible” means also that either no converged solution can be found or that the CPU time required until convergence would be unacceptably long. All CFD evaluations rely on adaptive time-steps in order to stabilize the solution procedure. A starting value of 0.1 s has been always used here for the restart of the detailed computation from the tabulated chemistry results. Further investigations are needed to check if other time-step values would improve the number of valid evaluations. Although the detailed computations considerably decrease the number of feasible solutions, they deliver also more realistic and accurate results. The smallest grid spacing employed in the present computations is 62.5 μm. This resolution is needed for very stiff intermediate radicals like HCO and
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 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 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 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 93 and 94: Chapter 4 Adjoint Methods for Shape
Page 95 and 96: 4 Adjoint Methods for Shape Optimiz
Page 105 and 106:
4 Adjoint Methods for Shape Optimiz
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 235 and 236:
Page 237 and 238:
8 Multi-objective Optimizatio Fig.
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Chapter 9 CFD-based Optimization fo
Page 283 and 284:
9 CFD-based optimization for paperm
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
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 ...

Create successful ePaper yourself

Delete template?

Save as template?