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always recompressed through a classical shock at the rear part of the upper surface. Along the lower surface, only a weak compression shock forms. Both expansion and compression shocks have jump conditions in the vicinity of the transition line: the entropy jump across such shocks (normalized with the free-stream entropy) is O(10−5), whereas it is O(10−2) for perfect gas flow. Accordingly, the wave drag is approximately one order of magnitude lower with respect to the PFG value. In summary, flows in the second regime (called hereafter the low pressure transonic BZT regime) are supercritical and characterized by high lift and very low wave drag, due to the fact that shock waves occurring in the vicinity of the transition line are much weaker than usual. For operation points characterized by sufficiently low values of Γ∞ and s∞, the aerodynamic performance is even further improved by the formation of an expansion shock close to the leading edge, which strongly enhances the suction peak, and consequently the lift, at the airfoil upper surface. This mechanism is similar to that observed in [40] for BZT flows of a van der Waals gas. When Γ∞ and/or s∞ are even higher, the flow becomes qualitatively similar to that of a perfect gas. The flow accelerates from the stagnation point to supersonic velocities and then recompresses at the rear part of the airfoil by means of compression shocks. As the free-stream fundamental derivative is increased, the region of flow characterized by Γ < 0 becomes smaller and finally disappears. At the same time, the lift coefficient decreases, and the drag increases, due to the stronger entropy gradients generated across the shocks. This progressively reduces the airfoil aerodynamic performance, which finally becomes very poor. Figure 9 shows typical pressure contours for this kind of flow. Figure 10 illustrate the wall Mach number, pressure coefficient, fundamental derivative and sound speed at operating conditions p∞/pc = 1.17, ρ∞/ρc = 1.11 on isentrope S4 (Γ∞ = 1.91). At these extreme conditions, the fundamental derivative remains positive everywhere, and no BZT effects appear. 52PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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