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3.5 3 2.5 2 1.5 1 12 246 N row Ψ w 24 22 20 18 16 14 10 8 6 4 2 123456 N row ζp ζs Centrifugal Turbines for ORC Applications (a) (b) Figure 3.8: Design results for the 3-stage supersonic 1 MWM turbine of Fig. 3.7. 3.8a: evolution of the load distribution among the stages, in terms of the aerodynamic loading expressed by the work coefficient Ψ (solid line), and of the stage specific work w. 3.8b: row-by-row evolution of the kinetic energy loss coefficients ζp (solid line), and ζs (dashed line) accounting for profile-, and secondary-losses. The presented results are obtained with the Craig & Cox loss model [15]. follows the work documented in Ref. [12], which constitutes also the first assessment of the down- scaling potential of the ROT architecture, considering its implementation in the field of low power- output mini-ORC turbo-generators. The modelling framework resembles closely the one presented in §3.5.1, and is discussed in §3.6.1. 3.6.1 Design Assumptions The results of the thermodynamic cycle analysis provide the needed inputs to the turbine prelimi- nary design procedure. The solution presented by Lang [35] for an ORC turbo-generator recovering thermal power from the exhaust of an heavy-duty truck engine is adopted here. The main charac- teristics of this cycle, resumed in Tab. 3.5, are common to all the machines designed in the present section. The working fluid is siloxane D4, whose T–s diagram is represented in Fig. 3.9. The outlet pressure corresponds to a condensation temperature of about 100 oC. The mass flow rate value is imposed in order to obtain a power-output close to the target one of about 10 kWM. Also in this case the first part of the expansion takes place in the so-called dense gas region, where the compressibility factor is lower than unity, see also Tab. 3.5. Relevant real gas effects are therefore expected, and accurate thermodynamic models are needed [6, 18]. For the reasons detailed in §3.5.1, two machine configurations are presented: a five-stage tran- sonic turbine, and a three-stage one, which is slightly supersonic. The loss estimation method adopted is the one proposed by Traupel [21]. However, as already mentioned, the predictive capability of these models is expected to decrease as the flow Mach numbers increase, and as the size of the machine is reduced. Thus, a comparison among different models is presented for the three-stage expander, by re-designing the same machine using the Craig 75 Ψ w [kJ/kg] ζ [%]PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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