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NACA0012 airfoil the dense gas flow for OP#1 remains subcritical with a computed lift coefficient CL = 0.2265 for the SGS and a drag coefficient very close to zero. For OP#2, the dense gas flow becomes supercritical with CL = 0.4467 , CD = 0.0510 . Note the perfect gas flow is such that C L = 0.373 , C D = 0.0574 ; thus, though the dense gas allows to achieve extremely high lift-to-drag ratio in the subcritical OP#1 conditions, the corresponding lift level remains below that of the perfect gas flow whereas the dense gas aerodynamic performance in the supercritical OP#2 conditions tends to come close to that of the perfect gas. The possibility to simultaneously achieve higher lift values for operating conditions where BZT effects are important and to improve the lift-to-drag ratio when these effects become less significant is considered. Then, the lift coefficient in the OP#1 conditions, CL(Σ;OP#1), and the lift-to-drag ratio in the OP#2 conditions, CL /CD (Σ;OP#2), are simultaneously maximized by applying the MOGA with a population of 36 individuals during 24 generations. A partial view of the computed individuals is shown in Figure 27 along with the set of non-dominated solutions eventually obtained: it clearly illustrates that the initial NACA0012 airfoil aerodynamic performances in dense gas flow have been substantially improved through the optimization process. In particular, almost all of the Pareto-optimal individuals have now a lift coefficient at OP#1 and a lift-to-drag ratio at OP#2 greater than the lift coefficient and the lift-to-drag ratio generated by the NACA0012 airfoil for a perfect gas flow. In order to draw a fair comparison with perfect gas flow, a shape optimization is also performed for the perfect gas (γ=1.4) flow at M ∞ = 0.85 and α = 1° of incidence over an airfoil of 12% thickness- to-chord ratio with a geometry based on the Bezier curves previously described; with unique thermodynamic conditions for this PFG flow, the problem is expressed as the simultaneous maximization of the lift and minimization of the drag. The optimal solutions obtained are plotted in Figure 27 in the lift / lift-to-drag plane: they remain well below the optimal solutions associated with the DG flow. Figure 28 displays one of the optimal solution selected along the final Pareto front: this particular shape, hereafter denoted OAB to recall it results from a bi-objective optimization process, has been retained because, among the set of non-dominated solutions, it displays the thickness distribution in the trailing edge region that is the most likely to preserve good aerodynamic performances in the viscous case. The wall pressure and Mach number distributions computed on the 81PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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