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(c) (d) Figure 46: DG flow, isoMach lines: a) baseline; b) optimized. c,d) Wall distributions. 4.5. GA-Hardness of Drag minimization problem A reference single-objective optimization problem, namely, wave drag minimization for a non-lifting inviscid transonic flow past a symmetric airfoil, is considered. This study show a difficulty to converge toward a global optimum. Several optimization runs are performed for a perfect diatomic gas (specific heat ratio γ =1.4) and for a polytropic BZT van der Waals gas with γ=1.02 flowing past an airfoil at different free-stream conditions. If not specified otherwise, numerical results are obtained using the Jameson’s scheme [66] on a half-C grid composed by 100×30 cells; the outer boundary is located about 10 chords away from the airfoil, and the mean height of the closest cell to the wall is about 5×10-3. Sensitivity of GA convergence to different choices of the starting population, computational grid, and discretization scheme is carefully analyzed. 4.5.1. Drag Minimization for a Symmetric Airfoil An inviscid perfect gas (PFG) flow at M∞=0.83, α=0°, with M∞ the free-stream Mach number and α the angle of attack, is considered first. The chosen value of the Mach number is slightly above the transonic drag rise condition for an airfoil of 12% thickness (about 0.8). As it is well-known, transonic drag rise is related to the occurrence of supersonic flow regions around the airfoil, with subsequent appearance of shock waves and associated losses, i.e. wave drag. As a consequence, for flow Mach numbers above a 106PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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