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small values of Γ∞ , in the subcritical regime, the lift-to-drag ratio tends to infinity (for inviscid flows) because the flow remains subsonic everywhere, thus avoiding the occurrence of wave drag. When Γ∞ is in the range 2÷3 a significant growth in both lift and drag is observed: the increase in lift is produced by the formation of an expansion shock close to the leading edge, that strongly enhances the suction peak at the airfoil upper surface; the increase in drag is due to the occurrence of shocks on the airfoil surface. In this regime, the lift-to-drag ratio remains one order of magnitude greater than in the perfect gas case. Finally, when Γ∞ reaches higher values, transonic BZT regime, the flow becomes qualitatively similar to that of a perfect gas with even poorer aerodynamic performances. In summary, results presented in Cinnella& Congedo [40] suggest that the choice of upstream conditions within or very close to the transition line is not only not mandatory in order to improve airfoil performance, as suggested in previous studies, but also not optimal. Specifically, optimal aerodynamic performance (i.e. the best trade-off between high lift and low drag) is obtained for, more precisely, Γ ≈ 3 . This is of great importance, in light of the design of BZT Organic Rankine Cycles, since it suggests the possibility of enlarging the operation range of the expansion stage without loosing the benefits of dense gas effects. Results presented in Cinnella & Congedo [40] have been obtained using the van der Waals equation of state, also used in many former studies, as the simplest gas model accounting for BZT effects: it is computationally inexpensive, and allows capturing qualitative features of BZT fluid flows. On the other hand, this model is not very accurate for thermodynamic conditions close to saturation, i.e. the region of interest in the present study, and largely over-predicts the extent of the inversion zone [6]. Another limitation of the study reported in Cinnella & Congedo [40] is related to the fact that thermo-viscous effects are completely neglected, as also done in almost all previous studies. A numerical investigation of two-dimensional inviscid and viscous dense gas flows past an isolated airfoil is presented by Cinnella & Congedo [41]. For the inviscid case similar qualitative conclusions have been drawn as in [40] where the parametric study has been repeated using the more realistic Martin-Hou (MAH) equation of state (EOS). Beneficial effects deriving from the use of a dense working fluid are also observed when the airfoil viscous performance is considered. Namely, the nonclassical variation of the Mach number with density in conjunction with reduced friction heating contribute to reduce friction drag and to avoid boundary layer separation due to large adverse pressure gradients. In addition, 25PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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