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dynamics of dense gas flow and the shape optimization for dense gas flow. In the following, the state of art concerning the study of GA-Hardness is presented. 1.1.1. Fluid-Dynamic of Dense Gas Flow The possibility of having expansion shock for particular equation of state was first discussed by Bethe [1] and Zel’dovich [2] in two pioneer papers in 1942 and in 1946. But, it was Thompson [4], who first link the monotonic behavior of the Fundamental Derivative of Gasdynamics to the possibility to have expansion shocks. In this paper he discussed about the potential property of a fluid which could exhibit Γ<0, even if there was no evidence that such a fluid could exist. In [5] it was seen that particular complex fluids can present BZT properties based on published thermodynamic data. In [6] Thompson analyzed the formation and evolution of a rarefaction shock wave. Such shock satisfy stability conditions and have a positive small entropy jump. Cramer and Kluwick in [8] studied the one dimensional small amplitude waves in which the local value of the fundamental derivative changes sign. They showed in fact that Γ=O(∆v) for small volume changes in the vicinity of the transition line. Thus, shock waves having jump conditions in the thermodynamic region near the Γ=0 contour are expected to be much weaker than normal. Indeed, they introduced the second nonlinearity ⎝ ⎠s Van der Waals equation, in which the specific heat is taken to be large enough to generate an embedded region of negative non linearity close to the thermodynamic critical point. In [10] they showed how the shock formation process may differ from that predicted by the perfect gas theory for an isolate pulse and periodic wave trains. In [11] they presented the exact closed-form solution for finite amplitude sonic shocks. The solutions are provided for both single and double sonic shocks. Cramer [14] used the Martin-Hou equation (introduced by Martin and Hou in 1955 in [3]) to compute the fundamental derivative of Gasdynamics for seven commercially available fluorocarbons. Each fluid was found to have a region of negative nonlinearity large enough to include the critical isotherm. The inversion region foreseen by the Martin-Hou equation is reduced with respect to that one computed with the Van der Waals equation. Cramer in [15] showed that inadmissible discontinuities give rise to shock splitting over a finite range of pressure and temperatures 21 ⎛∂Γ⎞ parameter Λ = ρ⎜ ∂ρ ⎟ . In [10] and [11], Cramer & Sen considered a gas described by thePDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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