Organic Rankine Cycles for Waste Heat Recovery and Solar Uses

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Organic Rankine Cycles for Waste Heat Recovery and Solar Uses ( organic-rankine-cycles-waste-heat-recovery-and-solar-uses )

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Chapter 6: Case studies pressure ratio ( rp ,1=rp,2=√(rp)). However, the efficiency also depends on the flow rate flowing through the expander because a higher flow rate entails a higher output power and makes the constant losses (e.g. friction losses) relatively smaller. In the polynomial correlations, the influence of the flow rate is reflected by the dependence in terms of supply vapor density or pressure. To determine the optimal first-stage pressure ratio, the overall isentropic efficiency is maximized using the following equation: dε = d [h1−h3 ]=0 (87) drp,1 drp,1 h1−h3s This can be done numerically or analytically. For the latter solution, ε must be expressed in terms of rp,1, which can be achieved using the ideal gas hypothesis. The analytical solution of Eq. 87 is obviously more efficient than the numerical one in terms of computational effort. It is derived in Appendix G. Pumps. Two pump consumptions are taken into account: the heat transfer fluid pump and the working fluid pump. They are modeled by a constant isentropic efficiency. For the HTF pump, the pressure difference is given by the pressure drop in the evaporator and in the collector while for the ORC pump, it is given by the difference between evaporating and condensing pressures. A constant, realistic value of 70% is assumed for both pump efficiencies. Condenser model. Since air condensers are well-known components in HVAC applications, a simplified model based on manufacturer data (Witt, 2004) is used to compute the condenser performance and fan consumption. The two inputs are the pinch point, defined as the difference between the condensing temperature and the ambient temperature, and the condensing power. Special attention is paid to the fan consumption since it can amount for a non- negligible share of the generated power. The fan consumption is computed as a function of the heat transfer power and of the pinch point with the following relation (Witt, 2004) : W ̇ f a n , c d = 5 4 . 5 + 0 . 0 1 8 5 ⋅ Q ̇ c d ⋅ 8 . 3 3 pinchcd (88) Cycle model. The global model of the system is obtained by interconnecting each subcomponent model according to Figure 78. Several performance indicators can be defined. The overall collector efficiency: ηcol=M ̇ htf⋅c̄phtf⋅(Thtf ,ex, col−Thtf ,su ,col) (89) S beam⋅Lcol⋅W col The net electrical output power: W ̇ net=W ̇ exp−W ̇ pp−W ̇ fans−W ̇ pp ,htf (90) 9

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