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Subscript c indicates critical point values. Both operation points lay on an isentrope crossing the inversion zone, respectively at lower and higher pressure than peak efficiency conditions. In the third run, both objectives (i.e. efficiencies at OPT1 and at OPT2) are simultaneously maximized. Here again, a DOE is preliminarily run in order to properly initialize the population of the GA. Figure 44 shows optimal individuals for operating conditions OPT1 and OPT2 and an individual selected on the Pareto front resulting from the two-point optimization. The baseline profile is also represented. For each configuration, a parametric study of cascade efficiency at off-design conditions has been performed. In addition to operation points OPT1 and OPT2, two test points corresponding to operating conditions pinl/pc = 1.02, ρinl/ρc = 0.813, Γinl = 0.886 (TEST1) and pinl/pc = 1.05, ρinl/ρc = 0.944, Γinl = 1.62 (TEST2) are considered. Results are summarized in Table 3. Note that optimal individuals provide an improvement of 1 ÷ 2% only over the baseline at optimization conditions. However, improvements up to 7% are obtained at conditions TEST1 and TEST2, which lay close to peak efficiency conditions for the baseline cascade. The best overall results are obtained for the individual derived from the two-point optimization (”Pareto 1”). Note that its shape is quite similar to that of the optimal individual for perfect gas flow. Figure 46 a and Figure 46 b show iso-Mach lines for the baseline configuration and for individual ”Pareto 1” at operating condition TEST2. Figure 46 c and Figure 46 d show the Mach number and Γ distributions at the wall for the best individuals from single-objective optimizations, the ”Pareto 1” individual and the baseline blade. Here again the mechanism leading to efficiency improvement is a reduction in the maximum Mach number of the flow and hence of shock strength: major gains come from a significant weakening of the trailing edge shock for the optimized configuration. This is related to lower values of Γ at the rear part of the suction side, causing slower growth of the Mach number when the flow re-expands downstream of the first shock. Table 3: Efficiencies (%) for optimal blade shapes at several operating conditions. 103PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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