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NACA0012 airfoil and OAB for subcritical (OP#1) and supercritical (OP#2) conditions are plotted in Figure 29 and in Figure 30. For subcritical conditions, both airfoils display zero drag but OAB yields a much higher lift coefficient ( C L = 0.794 ) than the NACA0012 airfoil (CL =0.226) thanks to a much stronger expansion of the flow around the upper leading edge. For supercritical conditions, the OAB yields more than twice the drag of the NACA0012 airfoil ( C D = 0.116 versus C D = 0.051 ) but also generates almost three times the lift of the NACA0012 airfoil ( C L = 1.3 versus C L = 0.45 ) so that its lift-to-drag ratio of 11.2 is indeed better than the value of 8.8 obtained with the NACA0012 airfoil, as expected from the optimization process. An overview of the optimized airfoil performance is provided in Figure 31 where the lift coefficient and the lift-to-drag ratio are plotted for dense gas flow around both the baseline NACA002 airfoil and the optimized airfoil for different free-stream thermodynamic conditions covering the subcritical as well as the low- and high-pressure transonic BZT flow regimes: as expected from the two-point optimization the modified airfoil systematically ensures a level of lift for dense gas flow in subcritical regime at least equivalent to the highest level achievable with a PFG flow while preserving a high lift-to-drag ratio in the subcritical and low-pressure supercritical regime. The airfoil viscous performance has also been checked for this lifting case, as already seen in the previous subsection. The viscous computations have been performed on an O-grid of 200x64 cells, with a mean first cell height in the direction normal to the wall equal to about 6x10-5 c, and on a finer grid of 200x128 cells, with a mean first cell height equal 5x10-6 c. The outer boundary is located about 12 chords away from the airfoil. The freestream conditions are successively taken equal to OP#1 and OP#2. The corresponding fine-grid values of the lift and drag coefficients, and of the lift-to-drag ratio are reported in Table 1. For comparison, viscous solutions for dense gas flows past the NACA0012 airfoils at the same thermodynamic conditions are also presented. The optimized airfoil conserves a superior aerodynamic performance over the NACA0012 even when viscous effects are relevant. It should be noticed however that the viscous performance of both dense and perfect gas flows significantly differs from inviscid results. At flow conditions OP#1, the flow-field is entirely subsonic, and boundary layer is attached, both for the NACA0012 and for the OAB airfoil. However, because of the high total pressure of the incoming stream, the flow strongly accelerates downstream of the stagnation point, and a deep suction peak appears at the upper surface downstream of the leading edge. In fact, the 82PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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