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appears. The aerodynamic coefficients are CD = 5.28e−2 and CL = −0.012, the negative sign being due to significant upstream displacement of the upper shock due to flow separation (shock stall). Also note that the drag coefficient is very close (actually, slightly lower) than the value given in 4.1.2 for an inviscid computation. In practice, reduced strength of shock waves due to their interactions with the boundary layer leads to lower wave drag with respect to the inviscid case, and this counterbalances the effect of viscous drag. Wall distributions of the pressure coefficient for viscous and inviscid flow are displayed in Figure 11 (b). The computed values of the aerodynamic coefficients for PP10 at various operating conditions are reported in Figure 12. If the free-stream state is taken close enough to the inversion zone, the flow remains subsonic: no shock waves are formed and flow separation is suppressed. In this regime (subcritical BZT regime), the drag coefficient drops from its PFG value as wave drag disappears, whereas the lift coefficient is considerably higher. For operation points at higher free-stream Γ, in the regime previously christened as ”low-pressure transonic BZT”, a supersonic region forms. This enhances lift, whereas wave drag remains quite low with respect to the perfect gas case. Two mechanisms contribute to this effect: the first one is of inviscid nature, and is related to the fact that shock waves have jump conditions in the neighbourhood of the transition line, and are therefore less dissipative than normal; on the other hand, such weak shock waves do not cause flow separation, so that pressure drag is further reduced. Further increasing the free-stream pressure (high-pressure transonic BZT regime) leads to increase the strength of shock waves: thus, wave drag grows and the flow finally separates because of shock/boundary layer interactions. As a consequence, both the lift coefficient and the lift- to-drag ratio drop. Figure 11 (c,e,g) shows typical pressure coefficient contours and flow streamlines in the three regimes; wall distributions of the pressure coefficient for inviscid and viscous flow are shown in Figure 11 (d,f,h). Figure 13 compares skin friction distributions for a perfect gas and for PP10 at different operating conditions. Note that the extended separated regions characterizing the perfect gas flow at both airfoil surfaces are absent in dense gas flows insofar as the operating conditions are chosen sufficiently close to the inversion zone. In the subcritical case, for flows at high Reynolds number, the pressure distribution remains essentially similar to the inviscid one, with just only some smoothing of the suction peaks at both surfaces downstream the leading edge. The lift coefficient is slightly below the inviscid value, whereas the lift-to-drag ratio now takes of 60PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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