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ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES

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ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES ( analysis-and-optimization-dense-gas-flows-application-to-org )

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4. Results This Chapter is constituted by five sections. The first two are devoted to a better understanding of dense gas flows fluid-dynamics. Dense gas flows past an isolated airfoil and transonic dense gas flows through a turbine cascade are considered. The section third and fourth concern the results obtained by means of shape optimization related to an isolated airfoil and a turbine blade. In the last section the analysis of the GA-Hardness for dense gas flow optimization problems is presented. 4.1. Dense gas flow past an airfoil A flow over a NACA0012 is considered. The working fluid in the following computations is PP10. The objective is to explore the influence of dense-gas effects on the airfoil aerodynamic performance, also in comparison with reference results for a perfect gas (PFG) flowing at the same free-stream conditions. Always a flow at M∞ = 0.85, α = 1° is considered. The accurate MAH equation of state is used as state law. 4.1.1. Choice of the operating conditions For a dense gas, the parameters governing the flow are, in addition to the free-stream Mach number and angle of attack, the free stream thermodynamic conditions, i.e. the thermodynamic operation point. Just high subsonic freestream conditions are considered here. (A detailed study also about sonic, and low-supersonic freestream conditions over a NACA0012 airfoil are presented in [41]). For BZT inviscid steady flows, the flow adiabatic in the p−v plane is roughly superposed to the isentrope corresponding to free- stream conditions. In the p−v diagram, the locus of possible thermodynamic states of a flow field is then approximately superposed with the arch of the isentrope included between the minimum and maximum pressures in the flow. If the locus crosses the inversion zone, the flow field exhibits a region of BZT effects. The operation points chosen for the present study are picked on five different isentropes of the p−v plane. Figure 2 shows the five isentropes, the operation points, the inversion zone, and the dense gas region (Γ < 1) for PP10. Moving right to left along an isentrope the free-stream fundamental derivative Γ∞, initially positive, decreases, changes its sign where the isentrope crosses the inversion zone, reaches a minimum, then increases again (see Figure 47

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