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As high values of the sound speed are associated to low values of the compressibility parameter, flows with low Γ∞ conserve a behavior closer to the incompressible one. In summary, for ”sufficiently low” Γ∞ (< 1): (a) the flow past the airfoil is subsonic; (b) the drag coefficient vanishes; (c) lift is lower than in the perfect gas case, because of the reduced flow compressibility; (d) lift tends to increase with Γ∞. When Γ∞ is approximately in the range 1÷1.5 the flow patterns change dramatically. In this range, a significant growth in both lift and drag is observed with respect to the previous case (see Figure 4 a). Nevertheless, the lift-to-drag ratio is still about one order of magnitude greater than in the perfect gas case due, on the one hand, to high values obtained for the lift and, on the other, to very low wave drag. In this regime, the flow becomes supercritical. For operation points lying on S1 to S4, the flow-field displays significant BZT effects, which are responsible for the high aerodynamic performance. On the other hand, no BZT effects appear for operating conditions S5: however, since the fundamental derivatives takes very small albeit positive values, the overall flow behavior does not differ very much from the other two cases: the flow patterns are similar to those obtained at operating conditions S1-S4 at slightly higher pressures. A typical view of the pressure contours for this flow regime is presented in Figure 7, whereas Figure 8 shows the wall distributions of the Mach number, pressure coefficient, fundamental derivative, and sound speed. For this kind of flows, characterized by higher free-stream Γ, the reversed behavior of the sound speed associated to flow regions with Γ < 1 is delayed, and the flow expands to supersonic conditions downstream the leading edge. Along the upper surface, if the free-stream values of Γ and of the entropy are sufficiently low, Γ may become negative just downstream the stagnation point, where the pressure is still steeply falling, so that an expansion shock is generated. Downstream of this shock, the pressure coefficient drops to values much lower than in the perfect gas case. The expansion shock is followed firstly by a continuous expansion and then by a gradual compression, which terminates in a compression shock as soon as the flow exits the inversion zone. Increasing Γ∞ and/or the free-stream entropy, the change of sign of the fundamental derivative is delayed, or never happens (this is the case of conditions S5), and no expansion shock appears, the flow being 51PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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