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the prescribed limit of 30 generation; nevertheless, quite different optimal shapes are generated (differences up to 22.6%). The resulting profiles are shown in Figure 49. The corresponding values of the fitness function are 0.00117, 0.00109, 0.00121, 0.00112, respectively. Evaluation of the FDC for this case returns a value of 0.534, much lower than that obtained for the previous perfect-gas problem. The high sensitivity of the GA to the starting population can be related to the fact that, due to the peculiar BZT fluid properties, shock waves are extremely weak for a large range of airfoil shapes in the neighborhood of the optimum: for all of these shapes, numerical drag represents a large part of the total one and tends to “hide” differences of the fitness function for airfoil shapes close to the optimum. The effect of numerical errors on the computed solution and, subsequently, on GA convergence properties, are investigated through a systematic analysis of the influence of different computational grids and discretization schemes on the results. On the finer grid of 150×50 cells, optimal shapes much closer to each other (3.1% difference) are obtained for different choices of the starting population. The computed fitness of the global optimum is now CD=4.94×10-4, which is about 40% lower than the value computed on the coarser grid! That is, a considerable amount of the computed drag is due to numerical viscosity. Reduction of numerical errors results in an improvement of the FDC, which grows to 0.654. To further check how the flow physics (shock strength) affects GA convergence, the free-stream Mach number is increased to 0.98: very similar optimal shapes are obtained for any choice of the starting population (about 1.5% maximum difference), even when the second-order scheme and the coarsest mesh are used to evaluate the fitness. In this case however, the flow field is characterized by a strong shock close to the trailing edge and numerical dissipation is negligible (for at least second-order accurate numerical schemes) with respect to wave drag. Accordingly, the computed FDC for this case is much closer to one, FDC=0.926 110PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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