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geometry of this airfoil to Airfoil 4 and to the NACA0012. As for the previous non-lifting case, the airfoil optimized for viscous flow displays thinner leading and trailing edges with respect to the one optimized for inviscid flow, and a slightly thicker trailing edge when compared to the NACA0012. The iso-Mach lines and wall pressure distributions computed on the NACA0012 airfoil, Airfoil 4, and Airfoil* for subcritical (OP1) and supercritical (OP2) conditions are plotted in Figure 41 and Figure 42. The flow over Airfoil* and, to a smaller extent, over Airfoil 4, separates at the upper surface, downstream of the compression shock at conditions OP2. Such shock is stronger with respect to that forming at NACA0012’s upper surface, and closer to the trailing edge. This produces higher lift, but also higher drag, both related to shocks and to post-shock separation; nevertheless for Airfoil 4, which is specifically shaped for viscous flow, the lift-to-drag ratio remains slightly above that of the NACA0012 (about + 3%), whereas for Airfoil*, which displays a quite extended separated region at the upper surface, this ratio is 12% lower than for the baseline geometry. Then, it’s possible to say that the additional cost related to evaluations of the fitness function via a Navier-Stokes solver is completely justified by performance improvements offered by the optimized airfoils. OP1 ( p∞/pc=1.01, ρ∞/ρc=0.676) CL CD CL/CD CL TEST2 (p∞/pc=1.17, ρ∞/ρc=1.11) CL CD CL/CD 0.056 0.0897 0.63 0.128 0.0990 1.29 0.155 0.0981 1.58 0.165 0.0999 1.65 -0.016 0.1120 -0.14 0.138 0.0980 1.41 0.057 0.0952 0.60 0.022 0.1041 0.22 0.017 0.0899 0.18 0.076 0.0983 0.77 TEST1 OP2 (p∞/pc=1.05, ρ∞/ρc=0.794) CD CL/CD CL (p∞/pc=1.08, ρ∞/ρc=0.882) CD CL/CD Airfoil 1 0.675 Airfoil 2 0.618 Airfoil 3 0.722 Airfoil 4 0.658 Airfoil 5 0.538 Airfoil 7 0.725 Airfoil 8 0.663 Airfoil 9 0.585 Airfoil* 0.537 (inviscid run) NACA0012 0.0167 40.4 0.763 0.0160 38.6 0.699 0.0169 42.8 0.819 0.0159 41.3 0.750 0.0161 33.4 0.604 0.0167 43.3 0.819 0.0162 41.0 0.757 0.0156 37.5 0.668 0.0157 34.2 0.608 0.0174 44.0 0.346 0.0179 39.1 0.499 0.0195 42.1 0.326 0.0174 43.2 0.549 0.0183 33.1 0.496 0.0196 41.9 0.287 0.0179 42.4 0.475 0.0175 38.2 0.485 0.0171 35.5 0.442 0.0142 15.0 0.253 0.0621 5.58 0.0650 7.67 0.0615 5.29 0.0722 7.60 0.0626 7.92 0.0616 4.67 0.0681 6.98 0.0615 7.89 0.0688 6.43 0.0345 7.34 (DG flow) 0.183 0.0128 14.4 0.213 Table 2: Parametric study of the aerodynamic performance of several airfoil shapes. 98PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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