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P. Colonna, S. Rebay, J. Harinck and A. Guardone Recently, Span and Wagner13 have developed a numerically stable multi-parameter EoS for non-polar and weakly polar fluids. This state-of-the-art EoS in the Helmholtz- explicit functional form allows for accurate computations of all relevant thermodynamic properties over the entire thermodynamic range, i.e., even close to the critical point, with the accuracy required for design and analysis of advanced technical applications. The Span-Wagner (SW) EoS has by far superior accuracy and numerical stability compared with older multi-parameter EoS’s.13 In the EoS, the reduced Helmholtz energy, i.e., ψ = Ψ/(RT), is expressed as a function of the reduced density, δ = ρ/ρc, and the inverse of the reduced temperature τ = Tc/T. The functional form uses 12 substance specific parameters and reads: ψ(τ,δ) = ψ0 (τ,δ) = ψ0(τ,δ) + ψr (τ,δ) + n1δτ0.250 + n2δτ1.125 + n3δτ1.500 + n4δ2τ1.375 + n5δ3τ0.250 + n6δ7τ0.875 (5) + n7δ2τ0.625e−δ + n8δ5τ1.750e−δ + n9δτ3.625e−δ2 + n10δ4τ3.625e−δ2 + n11δ3τ14.5e−δ3 + n12δ4τ12.0e−δ3 Here, n1,...,n12 are the parameters, ψ0 represents the ideal gas contribution to the Helmholtz free energy and ψr accounts for the difference between real gas behavior and ideal gas behavior. Eq. (5) is valid for many classes of non-polar and weakly polar fluids and was developed by means of an optimization algorithm that considered data sets for different classes of fluids simultaneously. Important features of (5) are: 1. The functional form (5) allows for numerically stable and consistent predictions of thermodynamic data over the entire range of interest for technical applications, therefore one and the same EoS can be used to for example design an ORC plant and for gasdynamic simulations; moreover, it has the potential to be a true reference EoS: it has been proved14 that it can predict thermodynamic data within the uncertainty of the best available experimental data (provided that enough experimental data are available and that the optimization is done properly) and is therefore often used as a reference EoS. 2. Due to the relatively small number of substance dependent parameters, the func- tional form allows for fast computations of thermodynamic properties. This is an important requirement if the EoS is implemented in a thermodynamic-properties library which is used to provide data to a CFD solver, as it requires many evalua- tions. 3. The 12 parameters can be determined from a restricted set of experimental data; furthermore, due to its optimized functional form the equation of state can be 5PDF Image | REAL-GAS EFFECTS IN ORC TURBINE FLOW SIMULATIONS
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