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Chapter 5: Fluid selection and cycle optimization It is uneasy to define a firm limit for each turbine parameter since these parameters are sometimes set empirically by the turbine manufacturers, stating that exceeding a certain values reduces the efficiency. Moreover, these boundary values sometimes vary from one manufacturer to another. For the purpose of this work, the selected boundary values are extracted from the scientific literature and from discussions with turbine manufacturers. They should not, however, be considered as absolute constraints. In particular, the current experience and textbooks regarding turbine design do not cover the case of high-expansion ratios with organic working fluids. The ongoing scientific works aiming at addressing this gap (see for example Harinck, Turunen-Saaresti, Colonna, Rebay, & van Buijtenen, 2010) might displace the current boundaries. A first important limitation of turbines is the maximal allowable tip speed U2, given by: U2 =π⋅N⋅D2 (64) D2 being the wheel diameter and N the rotating speed. As a general rule, a high tip speed is always preferred since it increases the stage specific work. It is however limited by the strength of materials at the wheel periphery. A maximum value of 370 m/s is chosen. The maximum turbine efficiency is generally well described by its specific speed Ns, given by: N =2⋅π⋅N⋅√(V ̇ex) [rad] (65) S Δ h0.75 s Where V ̇ex is the exhaust volume flow rate and Δhs is the isentropic enthalpy drop. Figure 7 in Chapter 2.4.1 shows a typical wheel efficiency curve based on manufacturer data: the given efficiency is the maximum efficiency for a given specific speed, i.e. the efficiency obtained when the ratio U2/Cs is optimized for the given working conditions, where Cs is the isentropic speed, given by: C = (2⋅Δh ) (66) s√s For the present analysis a minimum wheel efficiency of 84% is assumed, which corresponds to a specific speed varying roughly between 0.3 and 0.9 (Figure 7). This value is in good agreement with Dixon's recommended optimal boundaries for radial turbines, comprised between 0.3 and 1 (Dixon, 2005). An important limitation of single stage radial inflow turbines is the maximum Mach numbers in both the turbine nozzle and rotor. The turbine speed triangles are calculated with the following assumptions: ➢ The degree of reaction is set to 50% ➢ The ratio between inner and outer wheel diameters is set to 0.3 13PDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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