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Centrifugal Turbines for ORC Applications st 1 rot nd 2 rot rd 3 rot th 4 rot th 5 rot MW3= 0.88 M =0.40 U3 0.97 0.99 0.61 0.97 0.81 M =0.53 C3 MC2= 0.95 M =0.37 U2 0.43 0.98 0.45 0.58 0.48 0.38 0.41 0.97 1.00 0.91 M =0.61 W2 0.61 0.52 0.39 0.45 0.99 0.71 0.53 0.96 0.93 th 5 rot th 4 rot rd 3 rot nd 2 rot st 1 rot 23 Rotational axis 0 20 40 60 80 100 ROT radius [mm] 40 20 0 -20 -40 (a) (b) Figure 3.10: Results for the design of the 5-stage transonic 10 kWM turbine designed following the novel methodology presented in this chapter, adopting the boundary conditions reported in Tab. 3.7, and the Traupel loss estimation method [21]. Fig. 3.10a shows the velocity triangles, in black those referring to the rotor inlet section, in grey to the rotor outlet. The Mach numbers corresponding to the different velocity components are also detailed. The meridional section is depicted in Fig. 3.10b. among the two models are found in the predictions of the secondary loss coefficient in the first stages, characterized by aspect ratios close to one. From this perspective, the Craig & Cox model resulted to be somehow more conservative. 3.7 Conclusions The first critical evaluation of the centrifugal or radial-outflow turbine (ROT) architecture as a can- didate technology for ORC turbo-generators is presented. All the special features involved in ROTs design are enlightened, the main findings being that, in order to design efficient centrifugal turbines it is needed that i) the blade discharge geometric angles, the radial chords, the stage expansion ra- tios, and the reaction degrees are allowed to vary among each cascade, and ii) the diameter and the speed of revolution are included among the optimization variables. It is discussed how simplifying assumptions usually adopted in the axial turbines practice are typically not applicable. A novel design methodology is derived and presented for the preliminary sizing of ROTs in the power size range from several MWE down to few kWE. The in-house mean- line optimization code zTurbo, which allows to determine the preliminary design of ORC turbines of various configurations and working with different fluids, is presented and adopted to verify the novel method by presenting several exemplary design exercises. First, the design of two 1 MWE centrifugal turbines is presented, a transonic six-stage and a supersonic three-stage machines. These expanders handle an expansion ratio of 60, and rotate at 3000 rpm. Simplifications derived from the axial-turbines practice are adopted in order to illustrate 79 H [mm]PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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