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As shown in the above, the optimization procedure leads to minimal drag airfoils with increasingly better performance when their shape tends to become closer to the sonic arc, the better is the airfoil performance. Unfortunately, the sonic arc shape is not optimal if the flow of a viscous fluid is considered, because of its blunt trailing edge that can lead to flow separation. For this reason, Rusak’s low-drag airfoil [25] is essentially obtained by modifying the trailing edge of the optimal sonic arc shape, replaced by a sharp tail similar to that of the NACA0012 airfoil. In order to check the viscous performance of the optimal shapes derived from the present MOGA optimization procedure, a numerical investigation of viscous turbulent flows past such optimal airfoils is undertaken. In particular viscous flows past the OA095 and OAB airfoils, which have been found to provide the best inviscid performance in the previous study of Rusak’s optimization problem, are computed and compared with results obtained for the reference NACA0012 and Rusak-Wang airfoils in the same conditions. The computations are performed using half-O grids of 100x64 cells, with a mean first cell height of about 6x105, representing a reasonable tradeoff between accuracy and computational cost. The gas thermodynamic response is modeled using MAH equation of state. The thermodynamic freestream conditions are taken equal to p ∞ / p c = 0.985 , ρ ∞ / ρ c = 0. 622 , t h e M a c h n u mbe r i s v a r i e d i n t he i n t e r va l [ 0 . 8 5 , 0 . 9 9 ] and the flow Reynolds number based on free-stream conditions and the airfoil chord is 107. The flow past the NACA0012 and Rusak-Wang airfoils is attached for freestream values of the Mach number less than about 0.97. In both cases, at M ∞ = 0.98 the flow becomes separated close to the trailing edge; the flow at M∞ =0.99 is massively separated. Conversely, the flow field around the OAB airfoil already exhibits a recirculation region close to the trailing edge for the lowest values of M ∞ . In fact, this airfoil shape is the closest to the sonic arc, which greatly enhances its inviscid performance, but represents a serious drawback for viscous flows. An intermediate behavior is found for OA095 since the flow becomes separated at about M ∞ = 0.95 for that shape. Figure 25 shows the flow fields (Mach number contours and streamlines) for the four airfoils, at M ∞ = 0.96 : flow past OAB is characterized by significant separation at the trailing edge, whereas flow past OA095 is just slightly separated and flows past the NACA0012 and Rusak-Wang airfoils are completely attached. Figure 26 shows the drag coefficient versus the Mach number for the four airfoils analyzed. For the lowest values of M ∞ , the thicker trailing edges of 72PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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