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to-drag plane: it remains well below the optimal solutions associated with the DG flow: the optimized airfoil displays good aerodynamic efficiency, but its lift coefficient is considerably lower with respect to optimal individuals for dense gas flow. In order to select a single individual among the eight ones composing the Pareto front, the aerodynamic performance of the airfoil is also studied at two off-design conditions. The objective is to select an airfoil shape ensuring good aerodynamic performance over the largest range of operating conditions. Results are reported in Table 2 for the 8 airfoils, the baseline NACA0012 airfoil, and an airfoil shape belonging to the inviscid Pareto front, which has been retained because, among the set of non-dominated solutions, it displays the thickness distribution in the trailing edge region that is the most likely to preserve good aerodynamic performances in the viscous case. The thermodynamic conditions retained for the study are OP1, OP2 and two test points TEST1 ( p ∞ / p c = 1. 005 , ρ ∞ / ρ c = 0. 794 ) a n d TEST2 ( p∞ / pc = 1.17 , ρ∞ / ρc = 1.11), the first one corresponding to an intermediate state between OP1 and OP2, and the second one being characterized by operating pressure and density much higher than the design ones. Several considerations are in order: at the lowest pressures and densities, all airfoils of the Pareto front offer a much higher lift coefficient than the baseline airfoil, whereas their drag coefficient remains approximately the same (it is actually slightly higher): this results in values of the lift-to-drag ratio that are more than twice with respect to the NACA0012. At OP2 conditions, all airfoils display much higher lift than the NACA0012, whereas the lift-to-drag ratio is roughly similar. Finally, at TEST2 conditions just a few airfoils conserve a superior performance, whereas the others are similar or even worst than the NACA0012. Based on these considerations, the airfoil indicated as Airfoil 4 in Table 2, which is the one offering the best overall performance at all operating conditions, is retained for further investigations. The last line of Table 2 illustrates the viscous aerodynamic performance of an airfoil shape optimized for inviscid dense gas flow (referred-to as Airfoil*). At conditions OP2 and TEST2, where the flow is dominated by shock waves, its performance is in line with airfoils derived from the viscous optimization run. At conditions OP1 and TEST1 one, its performance is still much better than the NACA0012, but it is well below the other airfoils, mainly because of its lower lift coefficient. It would be possible to extract from the inviscid Pareto front airfoils ensuring a much higher lift, but their viscous performance at high-pressure conditions is quite poor because of their thick trailing edges. Figure 40 compares the 97PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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