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Γ∞, the drag is almost equal to zero (order 10-4), then increases monotonically. The lift coefficient initially grows, reaches a maximum, and then drops dramatically. The lift-to- drag ratio is very poor for high Γ∞ flows, but tends to infinity as the free-stream value of the fundamental derivative approaches unity. The best aerodynamic performance, offering a satisfactory trade-off between high lift and low drag is obtained for Γ∞ approximately in the range 1÷1.3: in such conditions, the flow displays higher lift and significantly reduced wave drag compared to PFG results. Note that the curves exhibit quite sudden changes in slope, which are related to corresponding changes in the flow patterns. In order to explain the computed behavior of the aerodynamic performance, a detailed analysis of the flow fields obtained for each operating condition is undertaken, which allows identifying three typical flow regimes, described in the following. For flows characterized by relatively low free-stream pressures and small values of the free- stream fundamental derivative (Γ∞ less than about 1), the computed lift-to-drag ratio is extremely high, due to the very low values taken by the drag coefficient, although the lift coefficient is lower than in the perfect gas case. Inspection of the Mach number field shows that such flows remain entirely subsonic. Since the free-stream is uniform and steady and no viscous effects are taken into account, the flow should also be isentropic, with drag coefficient exactly equal to zero. In practice, small entropy gradients are generated close to the wall, because of numerical errors introduced by the numerical scheme and boundary conditions, which lead to small nonzero values, O(10−4), for the computed drag. As a consequence, the computed lift-to-drag ratio is not unbounded, but O(103). A typical pressure contour plot for this flow case is displayed in Figure 5 along with Γ = 0 contours. Typical distributions of the Mach number, pressure coefficient, fundamental derivative, and sound speed at the wall are presented in Figure 6. When a fluid particle from the free-stream approaches the airfoil along the wall streamline, it undergoes a compression and the local fundamental derivative grows, reaching a maximum at the stagnation point where Γmax ≈ 1.5÷2. Then, Γ suddenly drops when the flow begins to expand accelerating over the top of the airfoil. Both pressure coefficient and Γ variations in the neighborhood of the stagnation point are very large, O(1). If Γ∞ is sufficiently small, roughly Γ∞ < 1, the local fundamental derivative becomes smaller than 1, or even negative, less than 0.01 chords downstream the leading edge: consequently, the speed of sound grows sharply enough to counterbalance the increase of velocity and the flow remains subsonic. The smaller Γ, the steeper is sound speed growth. 50PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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