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Chapter 4: Modeling be noted that the selection between input and output can be dependent on the target application. For example in Figure 32, the mass flow rate M ̇f and the rotational speed Nexp are imposed to the expander, which imposes the supply pressure psu in return. If the supply pressure and the rotational speed were imposed, the mass flow rate would be recalculated by the expander model. Model validation As detailed above, the proposed model is a semi-empirical model, i.e. its parameters must be tuned to fit the measurements. To this end, the measurements on the ORC test bench regarding the open-drive scroll expander working with refrigerant HCFC-123 are used. The model parameters are tuned to best fit the three model outputs (supply pressure, exhaust temperature, shaft power) to experimental data. The input variables of this calculation are: the expander rotational speed, the refrigerant mass flow rate, the supply temperature and the exhaust pressure. Model parameters can be of two types: ➢ Some parameters are given by the constructor or can be directly measured in the device. This is the case for Vs,cp or rv,in . The ambient heat transfer conductance and the friction torque could also be directly measured, but this was not the case with the present test rig. ➢ Other parameters are not given and cannot be calculated, such as the internal heat transfer conductances or the leakage areas. Those parameters have to be identified from the measurements. This second type of parameters is identified by minimizing an error-objective function F (using a genetic algorithm) defined as a weighted sum of the errors for each output: 39 F = ∑ [ F 1 ⋅ ( T f , e x , e x p , m e a s − T f , e x , e x p p r e d ) 2i 1 p −p 2 +F2⋅( f , su,exp,meas f , su,exp, pred ) (19) pf ,su ,exp,meas W ̇ −W ̇ 2 i +F ⋅ sh, meas 3 ( ̇ sh ,pred ) ] Wsh,meas i The weighting factors F1, F2, and F3 are selected to give each term the same approximate weight: F1=1/√(60) ; F2=1 ; F3=1/√(2) . Comparisons between the model predictions and the measurements for the exhaust temperature and the output power are given in Figure 33, Figure 34 and Figure 35. The maximum deviations between the measurements and the predictions of the model are 3 K for the temperature, 6% for the shaft power and 2% for the supply pressure. 5PDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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