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described in 4.3.1.1 is used, then the family of airfoil shapes is entirely described by 11 parameters. The minimization of CD (Σ) is performed for the following flow conditions: M ∞ = 0.96 , reduced freestream pressure and density equal to 0.985 and 0.622, respectively ( Γ∞ ≈ 0.02 ). At the considered free-stream conditions, the flow Reynolds number is about 107. The calculation is performed using a half C-grid of 100x50 cells, selected after a proper mesh study (not reported for brevity) as the best compromise between accuracy and computational cost; the population contains 36 individuals, which are let to evolve during 24 generations. This is enough to reach a stabilized optimum, as shown by Figure 34: when iterating on the generation number, the minimal and the mean value of the fitness function in the population converge to the same asymptotic value, which indicates that the population tends to converge to a set of almost identical (optimal) individuals. The optimal geometry stemming from the optimization run is represented in Figure 35, along with the original NACA0012 profile. The computed drag coefficient for the optimal individual equals 1.010×10-2. The value obtained for the flow past the NACA0012 airfoil at the same free-stream conditions is 1.544×10-2. Perfect gas flow past the NACA0012 and the optimal airfoil obtained yields a drag coefficient equal to 6.320×10-2. Provided that the main reduction in drag is related to the working fluid properties (the drag for PP10 flow past the baseline airfoil is about 5 times lower than for perfect gas flow past the same shape), the subsequent optimization run allows further reducing the drag of about 53%. In order to evaluate how important is taking into account viscous effects during the optimization process, an optimization run at the above operating conditions was also performed by neglecting fluid viscosity. The resulting optimal airfoil shape is also reported in Figure 35. Note that this airfoil is thicker than the optimal shape provided by the viscous optimization run. The performance of this individual is then a posteriori checked for a viscous turbulent flow at the previously specified conditions: the resulting drag coefficient is found equal to 1.388×10-2, i.e. about 37% higher than the drag exerted on the “viscous” optimal individual. Figure 36 displays the iso-lines of the Mach number and a close-up of the flow streamlines close to the trailing edge for perfect gas flow past the NACA0012, dense-gas flows past the same airfoil, and dense-gas flow past optimal airfoil shapes obtained by either including or neglecting viscous effects. The maximum Mach number in the flow lowers progressively when passing from perfect gas flow to PP10 flow and from the latter 91PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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