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G Compounding two scroll expanders in series. Summary. This appendix derives an analytical expression of the optimal intermediate pressure between two expanders assembled in series. This expression is useful while designing and optimizing ORC cycles with two-stage expansion in an effective way. If the expander efficiency was only dependent on the pressure ratio, the optimal first-stage pressure ratio would be defined as the square root of the overall pressure ratio (rp,1=rp,2=rp ). However, the efficiency also depends on the flow rate through the expander since a higher flow rate entails a higher output power and makes the constant losses (e.g. friction losses) relatively smaller. Figure 106: Two-stage expander In the polynomial correlations proposed in section 4.2.1, the influence of the flow rate is reflected by the dependence in terms of supply vapor density or pressure. The present analysis corresponds to the case where pressure ratio and density are the two input variables. However, the same method could easily be extended to the case in which the two inputs of the polynomial laws are the pressure ratio and the supply pressure. The following developments aim at determining the optimal pressure ratio r p ,1 that maximizes the overall expansion efficiency for the two expansion stages. If the vapor is treated as an ideal gas, the isentropic overall effectiveness for the two expanders can be written: h [1−] 3s=r hp where the enthalpy reference is taken at 0K. The different expansion efficiencies are defined as follows: (117) 1 XXVPDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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