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Chapter 6: Case studies heat source is difficult to measure in a cost-effective way. On the other hand, the working fluid flow rate is easily accessible, either by direct measurement, or by relation to the pump speed. Since the superheating is fixed, M ̇ hf can be directly correlated to M ̇ f , provided that the evaporating temperature and the heat source temperature are known. The optimal evaporating temperature can therefore be correlated to the heat source temperature, to the condensing temperature and to the working fluid mass flow rate. To determine this optimum over a broad range of working conditions the dynamic model described above is implemented in steady-state in Engineering Equation Solver (Klein, 2011). The optimum evaporating temperature is determined using the Golden Section Search method for 38 working points and for working conditions varying in the following range: 20 ≤ Tcd (°C) ≤ 40 0.1 ≤ M ̇ f (kg/s) ≤ 0.3 150 ≤ Thtf ,su,ev(°C)≤ 250 (99) (100) (101) This range of working conditions is typical of a kW-scaled waste heat recovery ORC working with a heat source varying from 150 to 250°C. A linear regression is then performed to predict T ev , optim . A first order polynomial is preferred to higher order expressions in order to avoid the Runge phenomenon. Due to the quadratic character of the relationship between Tev,optim and Thtf ,su,ev , ln(Thtf ,su,ev) is used instead. The following relationship is obtained, predicting the optimal evaporating temperature with R2=93.7%: Tev ,optim=77.6+4.93⋅10−05⋅pcd+23.8⋅ln(M ̇ )+7.65⋅ln(Thtf ,su ,ev) (102) The principle of this regulation is presented in Figure 92. Figure 92: Second regulation strategy: optimal evaporating temperature 2.5 Simulation results Figure 93 and Figure 94 show the superheating and the evaporating temperatures with their set point for the second regulation strategy. As expected, the evaporating temperature matches its set point temperature 26PDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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