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S. Quoilin et al. / Renewable and Sustainable Energy Reviews 22 (2013) 168–186 179 Fig. 12. Operating principle of a scroll expander. Fig. 13. Under (left) and over (right) expansion losses. To optimize the performance of the expander and to minimize under-expansion and over-expansion losses, this built-in volume ratio should match the operating conditions. However, volume expansion ratios achieved in Rankine cycle systems are typically larger than those achieved in vapor compression refrigeration systems, which justifies the development of adapted designs of such expanders, rather than retrofitting existing compressors. Generally speaking, piston expanders are more appropriate for applications with large expansion ratios because their design allows for higher internal built-in volume ratios. A major difficulty associated with the use of a positive displacement machine is its lubrication. One solution consists in installing an oil separator at the expander exhaust. In this case, unlike with compressors, an oil pump is necessary to drive the separated oil back to the expander suction. Another solution consists in circulating the oil with the refrigerant through the cycle and to install an oil separator at the evaporator exhaust. Separated oil is injected into the bearings, while the lubrication of the two spirals (in the case of a scroll expander) relies on the slight inefficiency of the separator. Alternatively, oil-free machines can be used, but these generally exhibit lower volu- metric performance and high leakage due to larger tolerances between moving parts [67,69]. In some operating conditions (wet fluids with limited super- heating at the expander supply), liquid may appear at the end of the expansion. This could pose a damage threat for piston expanders, but not for scroll and screw expanders, since the latter can generally accept a large liquid mass fraction. 6.2.1. Performance indicators for positive-displacement expanders The literature review regarding the performance of volumetric expander prototypes reveals that different performance indica- tors are in use. Some authors [68,70–73] define the isentropic efficiency as the ratio between the measured enthalpy difference and the isentropic enthalpy difference, while some others [66,69,74] define it as the ratio of the measured output power divided by the isentropic expansion power: The difference between the two definitions depends on the ambient heat losses and can be obtained by performing an energy balance over the expander: W_ M_ ðhsuhexÞQ_ amb Q_ amb es,2 1⁄4 M_ ðhsuhex,sÞ 1⁄4 M_ ðhsuhex,sÞ 1⁄4 es,1 M_ ðhsuhex,sÞ ð4Þ where W_ is the output power, hsu is the supply enthalpy, hex is the exhaust enthalpy) and M_ (the mass flow rate) are measured values. Q_ amb is the ambient heat loss and hex,s is the isentropic exhaust enthalpy. The isentropic efficiency defined as the enthalpy ratio (es,1) should be used for adiabatic processes only (i.e. ambient heat losses are neglected). However, according to [74], volumetric expanders, even insulated, release a non-negligible amount of heat to their environment. This can lead to biased values of the measured isentropic efficiency: if an expander produces 0.7 kW of shaft power for an isentropic expansion power ðM_ :ðhsuhex,sÞÞ of 1kWe, the efficiency is es1⁄470%. However, if this expander also exchanges 0.5 kW of thermal power with its environment, the ‘‘enthalpy ratio’’ definition of the isentropic efficiency leads to es,11⁄4120%, which is obviously erroneous. Therefore, in order to provide a fair comparison between different reported efficiencies, the more general definition should be used. This is the one selected for the further developments of this paper: W_ es 1⁄4 M_ ðhsuhex,sÞ ð5Þ Another difference between reported efficiencies lies in the type of output power: electrical or mechanical. Mechanical isentropic efficiencies are usually used for open-drive expanders while electrical isentropic efficiencies are used for hermetic expanders (in which the shaft is not accessible). The difference between both definitions is the generator efficiency (usually between 80% and 95%). Therefore, the type of reported efficiency should always be provided. A second indicator must also be defined to account for the volumetric performance of the machine. In compressor mode, such indicator is called volumetric efficiency. In expander mode, this number can be higher than one because of internal leakage [74]. Therefore, a different variable name, the filling factor, is used. It is defined by j 1⁄4 M_ vsu ð6Þ V_ s 6.2.2. Reported performance Table 6 summarizes the reported performance in experimental studies on volumetric expanders. The selected performance indi- cators are the mechanical/electrical isentropic efficiency (Eq. (5)) and the filling factor. Note that because of divergences in the definitions of these indicators in the papers, some efficiencies have been recalculated or evaluated from plots. In these studies, the best performance was achieved with scroll expanders, with mechanical efficiencies higher than 70% and electrical efficiencies es,11⁄4 hsu hex hsuhex,s ; es,21⁄4 W_ M_ ðhsuhex,sÞ ð3ÞPDF Image | Techno-economic survey of Organic Rankine Cycle (ORC) systems
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