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where the fundamental derivative is negative. In [16] Cramer & Best showed that the Mach number may increase, rather than decrease, with density or pressure if the specific heats of the fluid are sufficiently large. Conditions are also reported under which isentropic expansions through converging–diverging nozzles are not possible, regardless of the imposed exit pressure. In such cases, the nozzle must be replaced with one having multiple throats. Applications to external transonic flows are also briefly considered for the first time. Investigations of the viscous structure of one-dimensional non classical shocks have been presented for the first time in [17]. New results included the first computation of the structure of finite-amplitude expansion shocks and examples of shock waves in which the thickness increases, rather then decreases, with strength. Morren in his thesis [18] presented the transonic flow of dense gases for two dimensional, steady-state flow over a NACA0012 airfoil using the Euler equations and the van der Waals equation of state. The results indicated that dense gases with undisturbed thermodynamic states in the negative Γ region show a significant reduction in the extent of the transonic regime as compared to that predicted by the perfect gas theory. Cramer & Tarkenton in [19] examined the steady transonic flow of BZT fluids over two-dimensional thin wings and turbine blades by solving an extended transonic small disturbance equation derived for flows with Γ ≈ 0 , M ≈1 (with M the Mach number) and also characterized by small values of the second ⎛∂Γ⎞ nonlinearity parameter Λ = ρ ⎜ ∂ρ ⎟ ([8]). The free-stream state is taken to be in the ⎝ ⎠s neighborhood of one of the zeros of Γ. They found a significant increase of the critical Mach number in flows of BZT fluids over profiles. Numerical solutions of the small disturbance equation completed by the Martin-Hou (MAH) gas model revealed substantial reductions in the strength of compression shocks. Emanuel [20] showed that the Martin- Hou equation of state can be considered the reference thermodynamic model for dense gases. Cramer [21] presented a numerical investigation of laminar flows of dense gases over a flat plate. The results indicate a failure of classical scaling laws for compressible boundary layers (Chapman-Rubesin scaling), and a reduction of the boundary layer friction heating in complex gases with large heat capacities. Numerical solutions of the Euler equations for isenthalpic flows through turbine cascades by using the Martin-Hou gas model had been provided by Monaco [22] for incoming flow conditions characterized by small values of Γ. It was found that the natural dynamics of BZT fluids can result in 22PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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