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corresponding, for a perfect diatomic gas, to sonic isentropic exit conditions. For dense gas flows, inlet thermodynamic conditions, i.e. the thermodynamic operation point, should be also specified. All the computations presented in the following are performed on C-grids composed by 192 × 16 cells, with average non-dimensional height of the closest cells to the wall approximately equal to 5 × 10−3. This mesh refinement provides a reasonable tradeoff between accuracy and computational cost. Since the objective function chosen for optimization runs is cascade efficiency (defined as real-to-ideal static enthalpy drop), preliminary computations have been performed, for the baseline configuration, to investigate the sensitivity of this parameter to mesh refinement. Results computed on finer grids composed by 382 × 32 (first cell height 10−3) at several flow conditions show that the magnitude of cascade efficiency tend to increase of about 2 ÷ 3% when refining the grid, but trends of behavior (e.g. efficiency dependency on inlet conditions) are well conserved. Firstly, a single-objective shape optimization for a diatomic perfect gas (PFG) has been performed in order to maximize turbine efficiency. The initial population of the genetic algorithm is selected after a preliminary DOE over 100 individuals. After about 20 generations the mean and maximum value of the objective function in the population reach approximately the same value, indicating that the GA has converged to a population of almost identical (optimal) individuals. The solution for the baseline blade is characterized by an oblique shock at about 70% the chord and a second shock attached to the trailing edge (Figure 45 a); computed efficiency is 93.2%. Figure 45 b shows the solution after shape optimization: the oblique shock is almost suppressed, the trailing edge shock is weaker with respect to the reference case and efficiency grows to 96.2%. Figure 45 c and Figure 45 d display Mach number and pressure (normalized by inlet stagnation conditions) distributions at the wall. For the optimal configuration the maximum Mach number at the wall and, consequently, shock strength, is noticeably reduced compared to the baseline configuration; consequently, wave drag lowers and cascade efficiency improves. The optimal individual (Figure 43) has a thicker leading edge, thinner trailing edge, and greater camber than the baseline configuration. Then, computations are performed with the BZT fluorocarbon PP10 as the working fluid. Three optimization runs are undertaken. In the first and second run, a single objective function is maximized, i.e. cascade efficiency at fixed operating conditions pinl/pc = 1.00, ρinl/ρc = 0.752, Γinl = 0.416 (optimization point OPT1) and pinl/pc = 1.10, ρinl/ρc = 1.09, Γinl = 1.91 (optimization point OPT2), respectively. 102PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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