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Chapter 5: Fluid selection and cycle optimization Choked flow should be avoided in the whole rotor, the critical part being the rotor exhaust (point 3). The Mach number is calculated by: M3= W3 (67) Csound,3 W3 being the relative speed at the rotor exhaust and Csound,3 the sound speed at the same place. A maximum Mach number of 0.85 is generally recommended in order to avoid any local choking of the flow in the rotor. The maximum Mach number in the turbine nozzle constraints the maximum allowable pressure/volume ratio over the turbine. Most turbine manufacturers allow the nozzle flow to be supersonic, but a too high Mach number might decrease the efficiency and should be avoided. For the present analysis, a maximum value of 1.8 is selected. M2= C2 (68) Csound,2 The order of magnitude of the tip speed U2 is usually quite independent from the size of the turbine (Persson, 1990). Micro-scale turbines therefore show a very high rotational speed since D2 is low in Eq 64. Decreasing the nominal turbine power therefore increases the bearing losses, which can become prohibitive compared to the output power. A maximum rotational speed can therefore be defined: (De Vlaminck, 1988) recommends a maximum speed of 50,000 rpm, while (Sauret & Rowlands, 2011) selected a number of 24,000 rpm. For the present work a value of 50,000 rpm is selected. Turbines can usually absorb a much higher flow rate than volumetric expanders for a given machine size (i.e. wheel diameter). A limitation on the volume factor, as set for the scroll and screw technologies, is therefore not taken into account for this technology. A summary of the turbine boundaries is provided in Table 16. U2 Ns M2 M3 N Minimum Value 0.30 Maximum value 370 m/s 0.89 1.8 0.85 50000 rpm Table 16: Boundary conditions for the radial inflow turbine 14PDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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