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where, Nonclassical Gasdynamics of Vapour Mixtures Acknowledgments The authors acknowledge the contribution of their colleague and friend T.P. van der Stelt for devel- opment of the mixture thermodynamic models. A.1 iPRSV-WS Thermodynamic Model The thermodynamic model adopted for the multi-component fluids is briefly described here. The volumetric equation of state (EoS) is provided by the so-called improved Stryjek-Vera Peng-Robinson (iPRSV) model complemented by a usual polynomial expression for the isobaric ideal-gas specific heat,seeRef. [69],andbythemixingrulesproposedbyWongandSandler[70]. [84], see also [85], proposed to use the Peng Robinson [86] cubic EoS, with the Soave [87] α-function, but with a different temperature and acentric factor dependence in order to improve the correlation of vapor pressures for a wide variety of fluids. Notably, the proposed functional form for α results in the Stryjek-Vera Peng-Robinson (PRSV) EoS featuring a discontinuity in all the properties at the absolute critical temperature, Tc, for water and alcohols, and at temperature T = 0.7 · Tc for all the other fluids. Recently, [69] proposed a modification of the PRSV EoS aimed at eliminating the discontinuity in the prediction of thermodynamic properties. The iPRSV EoS is similar to the cubic form characteristic of the PRSV EoS, v−b v2 +2bv−b2 a = 0 . 4 5 7 2 3 5 R 2 T c2 / P c α , b = 0 . 0 7 7 7 9 6 R T c / P c , α = 1 + κ 1 − T r 2 . Here, R = R/μ is the gas constant, with R the universal gas constant, a is the attractive term, b is the co-volume parameter, P and v are the pressure and the specific volume, respectively. The subscript c indicates properties at the vapour-liquid critical point. The parameter κ depends on the temperature as follows RT a P=−, (5) with κ = κ0 + κ1 1 + Tr (0.7 − Tr) , (6) κ0 = 0.378893 + 1.4897153ω − 0.17131848ω2 + 0.0196554ω3 , (7) where ω is the acentric factor. The empirical parameter κ1 in eq. (6) is a pure-component parameter chosen in order to obtain accurate predictions of saturated properties. From low temperatures up to reduced temperatures of Tr = 0.7, Stryjek and Vera recommend using values for κ1 tabulated in their papers [84, 85]. Alternatively, κ1 can also be obtained by regressing experimental data. According to Stryjek and Vera, for water and alcohols the tabulated values can be applied up to the critical point. For other compounds, slightly better results are obtained with κ1 = 0 for 0.7 < Tr < 1. For super critical temperatures (Tr 1) they recommend κ1 = 0, because there would be no advantage in using eq. (6) in this region. The κ-function therefore introduces a discontinuity in α(T ) either at Tr = 0.7 or at Tr = 1, and in thermodynamic properties dependent upon and derivatives thereof. The iPRSV EoS is obtained by modifying the equation for the calculation of the κ-value, such that it is continuous with the temperature, but by keeping the same parameters κ0 and κ1 in the functional form, and in such a way that the same values can be used. This is a notable advantage, because 219PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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