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to PP10 flow past the optimal airfoils. As a consequence, the strength of the shock waves becomes lower and lower, and the flow field past the optimal airfoils is essentially shock- free. Nevertheless, while the airfoil obtained neglecting viscous effects, characterized by a thick nose, still displays a supersonic bubble in the leading edge region that terminates in a weak shock, the thin-nosed airfoil issued from the “viscous” optimization furthers a more gradual expansion, and the flow reaches just slightly supersonic conditions at about midchord. This is confirmed by inspection of Figure 37, showing wall distributions of the pressure coefficients for the four cases. It is interesting to inspect the streamline distributions for the four configurations (Figure 36). Both perfect and dense flows past the NACA0012 remain attached (Figure 36 A, B); the airfoil issued from the inviscid dense gas flow optimization, because of its thick trailing edge, allows reducing losses due to shock waves, but displays an extended separation bubble: this inconvenience is avoided by taking into account viscous effects during the optimization process, which leads to an airfoil ensuring at the same time low wave drag and attached flow in the trailing edge region. Actually, as shown in Figure 36 C, a very small separation bubble appears, but it has a negligible influence on the overall drag coefficient. Since, ideally, a consistent drag reduction is expected for the whole range of freestream Mach numbers, the wave drag produced by these modified shapes, which are optimized for a specific value of M ∞ , are next checked for different values of M ∞ , taken in the interval [0.85, 0.99]. The computed evolution of the drag coefficient with increasing values of the freestream Mach number is plotted in Figure 38: the present optimal shape at M ∞ = 0.96 is far superior to the original NACA0012 airfoil, since its drag coefficient is lower for the whole range of Mach numbers and the transonic drag rise is delayed. Conversely, the airfoil issued from inviscid optimization is decidedly better than the NACA0012 for the highest values of the Mach number, but its drag is somewhat higher at lower velocities. 92PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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