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4.3.2.2.Performance optimization for a Lifting Airfoil The second optimization problem is the design of optimal lifting airfoils. This problem is the same described in 4.3.1.2 for inviscid computations. The shape representation retained for the complete airfoil derives from that adopted in the study of a half profile, and it’s the same already introduced in 4.3.1.2. RANS equations are used. The flow conditions retained for the study are M∞=0.85, incidence angle 1°, Reynolds number (based on free-stream conditions and the airfoil chord) 9x106. The same optimization strategy already described in 4.3.1.2 is adopted: to simultaneously optimize the lift coefficient CL (Σ;OP#1) for an operating condition OP1 such that flow past the baseline NACA0012 configuration is subcritical and consequently characterized by no wave drag but relatively poor lift, and the lift-to-drag ratio CL /CD(Σ;OP#2), for an operating condition OP2 such that the flow past the baseline airfoil is supercritical, and offers quite high lift, but poor aerodynamic efficiency. Precisely, conditions OP1 and OP2 correspond exactly to those introduced in 4.3.1.2 for the inviscid case. The two objectives 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 39 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. Specifically, there are four individuals of the Pareto front that possess higher lift at condition OP1 and higher lift-to- drag ratio at condition OP2 than the NACA0012. Note that the Pareto front resulting from an inviscid optimization run, also represented in Figure 39, is well above the Pareto front for the viscous run. This of course due to the fact that, for the inviscid computation, there is no viscous drag exerted on the airfoils, and that wave drag is extremely small due to BZT effects, which results in extremely high lift-to- drag ratios. The point representative of perfect gas flow past the NACA0012, characterized by slightly negative lift, is also reported for completeness. 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 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 maximization of the lift-to-drag ratio. The optimal solution obtained is plotted in Figure 39 in the lift / lift- 96PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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