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where ∆ represents a change in a given fluid property through the shock. As a result, in order to satisfy the second law of thermodynamics, a negative change in the specific volume, i.e. a compression, is required if Γ > 0, whereas a positive change, i.e. an expansion, is the only physically admissible solution when Γ < 0. Then, for these fluids, known as the Bethe-Zel’dovich-Thompson fluids [4], that exhibit a value of Γ < 0 in a range of thermodynamic conditions above the liquid/vapor coexistence curve, the well- known compression shocks of the perfect gas theory violate the entropy inequality and are therefore inadmissible [4][8][15]. The thermodynamic region characterized by negative values of Γ is usually called the inversion zone, and the Γ = 0 contour is said the transition line. BZT properties are generally encountered in fluids possessing large heat capacities and formed by complex, heavy molecules, such as some commercially available heat transfer fluids. An important property of BZT fluids is that the shock strength is reduced up to one order of magnitude from that predicted by equation (Eq. 4) for thermodynamic conditions where Γ≈0. Cramer and Kluwick [8] 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. Then, summarizing the different thermodynamic behaviors related to the dense gas flows, the following considerations can be underlined: 1) for such conditions of pressure and density that Γ<1, and Γ=O(∆v), compression shocks are weaker than normal, and the sound speed and the density are related by the (Eq. 3), that is in contrast with the PFG equation. 2) for such conditions of pressure and density that Γ<0, the compression shocks are also completely forbidden (BZT fluids). The unusual properties of dense gases could find application in technology. One of the more obvious applications is the use of dense gases in turbomachinery and in the ORCs. Because of the use of a few, highly loaded, expansion stages, ORC turbines typically work in the transonic/low supersonic regime and their major loss mechanism is related to the generation of shock waves and their interactions with the blade boundary layers. Therefore, on the one hand a detailed study of turbomachinery flows of dense gases is necessary to 19PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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