The use of two-phase screw expanders in power generation cycles can achieve an increase in the utilisation of available energy from a low-temperature heat source when compared with more conventional single-phase turbines. The efficiency of screw expander machines is sensitive to expansion volume ratio, which, for given inlet and discharge pressures, increases as the expander inlet vapour dryness fraction decreases. For single-stage screw machines with low inlet dryness, this can lead to underexpansion of the working fluid and low isentropic efficiency. The cycle efficiency can potentially be improved by using a two-stage expander, consisting of a machine for low-pressure expansion and a smaller high-pressure machine connected in series. By expanding the working fluid over two stages, the built-in volume ratios of the two machines can be selected to provide a better match with the overall expansion process, thereby increasing the efficiency. The mass flow rate though both stages must be matched, and the compromise between increasing efficiency and maximising power output must also be considered. This study is based on the use of a rigorous thermodynamic screw machine model to compare the performance of single- and two-stage expanders. The model allows optimisation of the required intermediate pressure in the two-stage expander, along with the built-in volume ratio of both screw machine stages. The results allow specification of a two-stage machine, using either two screw machines or a combination of high-pressure screw and low-pressure turbine, in order to achieve maximum efficiency for a particular power output. For the low-temperature heat recovery application considered in this paper, the trilateral flash cycle using a two-stage expander and the Smith cycle using a high-pressure screw and low-pressure turbine are both predicted to achieve a similar overall conversion efficiency to that of a conventional saturated vapour organic Rankine cycle.
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