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26 2 Organic Rankine Cycles applications and values as high as 200-300 can be found in high-temperature ORC appli- cations. The two main difficulties related to turbines having high expansion ratios are the high relative Mach numbers at the turbine rotor inlet as well as large rotor blade height variations between the rotor inlet and outlet (Macchi, 1977). In ORC processes adopting high pressure ratio over a single turbine stage, zero reaction turbines are not feasible be- cause of the large pressure ratio over the turbine stator, highly supersonic flow, and large relative Mach number at the turbine rotor inlet (Macchi, 1977). If 50% reaction turbines are considered, significant changes in the turbine rotor blade height and flow area are needed because of the large change in the volumetric flow rate from the turbine rotor inlet to rotor outlet (Macchi, 1977). Thus, the degree of reaction r is recommended to be 0 < r < 0.5. The degree of reaction can be defined by dividing the isentropic enthalpy change in the turbine rotor by the total isentropic enthalpy change over the turbine stage. Verneau (1987) presented experimental results for two 50 kW ORC turbines, using FC 75 as the working fluid. The total pressure ratio of the turbine was about 150, and the first design was a supersonic two-stage axial turbine. The second design was a single stage turbine having a pressure ratio of 150. Their test results showed that relatively high total to static efficiencies in the range from 70 % to 80 % were achieved for both the two-stage and single-stage turbine. The turbine design presented by van Buijtenen et al. (2003) showed reasonably good performance in test runs, despite the large pressure ratio of about 120 over a single-stage radial turbine. In many ORC systems adopting turbines, despite the moderate flow velocities in tur- bine flow passages, the flow tends to be supersonic since most of the organic fluids are characterized by a low speed of sound. This leads to losses related to the occurrence of oblique shock waves and their reflections in the turbine flow passages (Hoffren et al., 2002; Colonna et al., 2006a; Harinck et al., 2010). Methods to improve the design of supersonic ORC stators have been developed in the recent years, for example by Harinck et al. (2013), presenting a turbine optimization method based on automated CFD design. Their results indicated that by bending and turning the stator flow channels the losses caused by the occurrence of oblique shock waves can be reduced significantly (Harinck et al., 2013). One important parameter when designing turbine flow channels using organic fluids with high molecular complexity can be identified as the fundamental derivative of gas dynam- ics. The fundamental derivative of gas dynamics relates to the molecular complexity of the fluid and can be used to classify the gas dynamic behavior during the expansion (Har- inck et al., 2009; Guardone et al., 2013). The fundamental derivative of gas dynamics is a quantitative measure of variation of the speed of sound to the specific volume in an isentropic expansion and can be defined as Γ = 1 − v(∂a)s. (2.1) a ∂v Fluids having Γ > 1 and hence (∂a/∂v)s < 0 in the vapor region can be classified as lowPDF Image | WORKING FLUID SELECTION AND DESIGN OF SMALL-SCALE WASTE HEAT RECOVERY SYSTEMS BASED ON ORGANIC RANKINE CYCLES
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