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The final model parameters are summarized in Table 11. Chapter 4: Modeling Parameter Value 6.38 W/K 21.22 W/K 34.2 W/K 0.00591 m Parameter Tm Aleak rv Vs,cp Value 0.4067 N.m 4.858 mm2 4.05 148 cm3 AUamb AUsu AUex dsu Table 11: Parameters of open-drive scroll expander model Polynomial model A semi-empirical thermodynamic model such as the one proposed in the previous section is well suited for the simulation of one particular machine. However, it cannot be used for bigger or smaller machines since the model parameters would need to be scaled according to a law that cannot be known without testing a large range of expanders with different swept volumes. To obtain a generic non-dimensional efficiency curve, a polynomial fit of the effectiveness can be defined using carefully selected input variables. If ambient heat losses are neglected, scroll expanders can indeed be modeled by their isentropic effectiveness and filling factor as defined in Eq. (4) and (9). To simulate realistic performance close to the actual experimental data, εs ,exp and φexp are expressed as a polynomial laws of the main working conditions. The three selected working conditions are the fluid inlet density ρsu , the rotational speed Nrot and the pressure ratio over the expander rp since they turned out to be the main representative variables of the working conditions. The polynomial fits are expressed in the following form: [i , j ,k]∈Ω The filling factor shows a very limited dependency with the pressure ratio. It can therefore be expressed as a function of the rotating speed and the supply density: 1 Ω is defined by: where σ=(i, j,k) is a 3rd order circular permutation defined by: ε= ∑ a ⋅ln(r )i⋅ρj ⋅Nk =f(r ,ρ ,N ) ijk p su rot p su rot (20) Where Ω is a set defined as a two-by-two combination of the working conditions1. 7PDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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