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Next, a dense gas flow optimization is considered. The working fluid is supposed to be a BZT politropic van der Waals with a specific heat ratio equal to 1.02. When dense gas flows are considered, the free-stream Mach number and the angle of attack are no longer sufficient to completely determine the flow field, but information about free-stream thermodynamic conditions has to be added: for all computations presented in the following, the operating pressure and density, normalized with their critical-point values, are taken equal to p∞ / pc = 1.0696, ρ∞ / ρc = 0.735 . With this choice, the free-stream value of the fundamental derivative is Γ∞ = 0 . Viscous effects are neglected. Previous studies on BZT flows past airfoils (see [40]) show that, on the one hand, the peculiar behavior of the sound speed in BZT flows considerably delays the transonic drag rise with respect to a perfect gas flow over an airfoil of the same thickness; for the BZT gas and operating conditions considered in this study, the critical Mach number is found to be around 0.94 for an airfoil of 12% thickness. On the other hand, even when the flow finally becomes supercritical, shock waves characterizing the flow-field for M∞>Mc are not only weak, as previously observed about PFG flows, but they also generate losses (entropy gradients) up to one order of magnitude weaker than those generated in a PFG for a shock wave of the same intensity if their jump conditions are located in the vicinity of Γ∞ = 0 . Firstly, BZT flow at M∞=0.95 is considered, i.e. slightly above critical conditions. In order to get a more detailed knowledge of the search space, a design of experiment (DOE) is performed over a sample of 600 individuals. The DOE analysis uses a Sobol sequence technique, which ensures a uniform covering of the search space. The results are summarized by means of a frequency histogram (see Figure 48). Individuals are collected into 20 classes according to their fitness (drag coefficient). A considerable number of individuals, corresponding to 3% of the whole population, belong to the lowest drag- coefficient class. These are quite different in shape, i.e. a large variety of shapes providing good values of the fitness function exists. The best 36 individuals detected by the DOE are used to initialize the GA, whose population is allowed to evolve during 30 generations. The GA population appears to have reached a stabilized optimal value of the drag coefficient after the prescribed number of generations. In order to investigate the sensitivity of the GA to the starting population, four optimizations runs are performed with different randomly generated starting populations. All optimization runs converge within 109PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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