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4.3.2. Viscous Case In the cases widely described in 4.3.1.1 and 4.3.1.2 the optimizer was linked to an Euler solver and after the optimized airfoils were analyzed to check their viscous performances. It seems really interesting to couple the optimizer to a NS code, because it’s important to understand if it is necessary a viscous optimization to generate a profile with good viscous performances, or it suffers just to make a faster optimization neglecting viscous effects, followed by an evaluation of viscous effects on the optimized airfoil. Obviously there is a huge difference in the computational cost (order of seven times more expensive for the viscous case). In order to reduce computational costs for viscous dense-gas flow optimization problems, the flow solver (actually viscous computations have been just done with SGS) and GA are coupled with an artificial neural network (ANN). The procedure used to couple the ANN with the flow-solver and the optimizer is the following: • The fitness function is computed “exactly” by means of the Navier-Stokes solver for all individuals of the first two generations. • These individuals form an initial training set for the ANN. • Starting from the third generation, just only 30% of the individuals are computed “exactly”. • At each generation, new exactly computed individuals are added to the training set, and the ANN is re-trained, in order to improve ANN accuracy while approaching the solution optimum. Because of the growing size of the linear system associated to the training problem, the ANN is not trained using all individuals in the data set. Instead, the ANN is trained “locally” by extracting from the global data set, a small number of individuals close to the one to be evaluated. This means that, for each new individual, a new local ANN is constructed. Based on numerical tests, a subset of 6 individuals was found to provide reasonable accuracy. In any case, the best individuals retained for elitism are always computed exactly. 4.3.2.1.Drag Minimization for a Symmetric Airfoil The problem is to find the minimal value of the drag coefficient CD (Σ) where Σ denotes an airfoil symmetric shape. It’s the same problem considered in 4.3.1.1. But in this case, NS equations are used also for the evaluation of each profile. The same parameterization 90PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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