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zero wave-drag over a larger range of incoming flow velocities. Specifically, the analytical study presented in [29] derives the geometry of an airfoil with a 12% thickness-to-chord ratio that shows lower wave drag than the NACA0012 airfoil at zero incidence for specific freestream thermodynamic conditions ( Γ∞ =0). [29] has the merit of facing for the first time optimization problems for dense gas flows past airfoils, even though an optimization procedure in the proper sense is not undertaken. In practice, such an approach is incomplete, as it does not take into account the effect of the optimization on the airfoil lift. Moreover, the small disturbance approximation does not model accurately the important flow variations at the airfoil leading and trailing edges, which have a crucial influence on the airfoil performance, especially for high-Γ incoming flow conditions. In [42], Congedo& Corre& Cinnella present first results on optimal airfoil geometries for transonic dense gas flows by making use of evolutionary optimization strategies, by taking in account just Euler effects. Two optimization problems are considered: the first one, as in Rusak and Wang’s work [29], aims at finding a minimal drag airfoil shape for a non-lifting flow in the BZT regime. This symmetric problem is relatively simple to treat since the flow symmetry reduces the computational expense, while a single objective function to minimize, namely the drag, implies lower optimization complexity. It is shown that, if the optimal airfoil shape derived in [29] does exhibit lower drag than a reference airfoil with the same thickness-to-chord ratio, viz. the NACA0012 airfoil, the approach presented allows to obtain even higher performances by combining an efficient Euler solver to a genetic algorithm. The second application deals with the optimization of a lifting airfoil. The following optimization strategy is adopted: find an airfoil shape that allows on the one hand allows to obtain high lift at BZT subcritical conditions, where the wave drag is in any way expected to be zero and, on the other hand, to minimize wave drag while maximizing lift for supercritical BZT flow conditions. These results will be widely presented in Chapter 4. Cinnella& Congedo presents in [46] dense-gas flow optimization problems considered in [42] by taking fully into account viscous effects. Optimal airfoil shapes for viscous transonic flows of dense gases have been generated by using a multi-objective genetic algorithm coupled with a dense gas flow solver. Computational costs related to the great number of evaluations of the objective function by means of the Navier-Stokes solver have been substantially reduced by using a properly calibrated artificial neural network to interpolate the response surface. When solved both for inviscid and viscous flow, the drag 28PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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