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Finally, a detailed analysis of GA convergence for shape optimization problems in perfect and real gas flows has been considered. Specifically, a set of drag minimization problems for a symmetric non-lifting airfoil are considered. A statistical tool, namely, the fitness distance correlation (FDC) parameter, has been introduced: FDC measures how difficult is for a GA to converge toward the global optimum for a given problem. Numerical results show that problems characterized by low values of the FDC tend to stagnate in the vicinity of the global optimum without never reaching it, and are therefore quite sensitive to the starting population used to initialize the GA, and to numerical parameters such as the computational grid and numerical scheme used to solve the flow governing equations. Analysis of the flow physics shows that the greatest convergence difficulties (and the lowest FDC parameter) are encountered for optimization problems such that airfoil shapes close to the optimum generate flow-fields characterized by extremely weak shocks. For this kind of flows, numerical viscosity acts as a low-pass filter that levels many different airfoil shapes to almost the same degree of fitness, slowing down or preventing at all GA convergence toward the optimum. This is particularly true for flows of BZT gases, whose peculiar property is to give rise to flow discontinuities much weaker than those characterizing perfect-gas flows. In order to improve GA convergence and to reduce its sensitivity to the starting population it is recommended to use high-accurate numerical schemes and fine meshes (as much as allowed by CPU time available to complete an optimization run), in order to minimize numerical errors on the fitness function. A very efficient objective-function evaluation procedure based on Richardson extrapolation is proposed, allowing to drastically reduce GA-hardness with a very moderate increase in computational cost of optimization runs. Suggestion for futures study The future study could concern the extension of this work to the 3D case. Then, first a detailed analysis of a 3D dense gas flow over an isolated airfoil and a turbine blade would be necessary. A 3D optimization of a turbine blade could produce the first 3D blade, conceived for an ORC, by taking into full account dense gas effects. 119PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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