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Chapter 3 10.6 ηTχ=0.5 0.79 Pm [kW] Mmax Din [mm] Hin [mm] δmax [◦] ( pT,in / pS,out )stg R Table 3.7: Main results for the 5-stage 10 kWM transonic turbine. geometrical angles vary along the machine, suggesting that customized geometry configurations are needed in order to achieve highly efficient mROTs. As already observed in §3.5.4, the proposed design procedure proves successful in obtaining a smooth increase of the blade heights along the machine, with the concurrent increase of the radial chords. The resulting meridional contour is depicted in Fig. 3.10b. The maximum flaring angles, of the order of 9◦ are, are located on the last stage. The relation between the stages aerodynamic loading, the imposed deflections, and the corre- sponding profile losses, is similar to what already observed and discussed in the previous sections. In particular, the specific work elaborated by the stages decreases along the machine, while the de- flections and consequently the losses tend to follow an opposite trend, as shown in Fig. 3.11. As a result, also in this case the stage efficiency increases along the machine, passing from about 72% in the first stage to about 88% in the last one. As expected, tip leakages heavily affect the performance, and the associated loss coefficient reaches maximum values in the first two rotors, characterized by larger tip clearance/blade-height ratios. Notably, tip-leakage losses are comparable in magnitude with profile and secondary ones. 3.6.4 Results: Slightly Supersonic Turbine The main features of the slightly supersonic 3-stage design are shown in Table 3.8. As anticipated, the design is performed adopting two different loss-estimation methods, i.e. the Craig & Cox [15], and the Traupel one [21]. The comparison among the predictions of such models is included in all the figures presenting the outcome of the design. It can be concluded that the obtained turbine design is scarcely dependent from the adopted loss prediction method. Coherently with the similarity theory [13], stating that the smaller the machine, the higher the speed of revolution needed to achieve better performance, the three-stage turbine rotates at 15400 rpm. The optimal velocity triangles are shown in Fig. 3.12a and, also in this case, the blades geometrical angles vary along the machine. The meridional channel of the optimal design is depicted in Fig. 3.12b, and its appearance is similar to that of the 5-stage machine. With respect to the transonic machine, the use of only three stages increases the blade aero- dynamic loading, as shown in Fig. 3.13a, thus lowering the overall turbine efficiency. The main sources of loss are reported in Fig. 3.13b, from where it can be noted that the major differences 0.98 53 2 9.0 ω [rpm] 12400 Dout [mm] 180 Hout [mm] 15 Stage 2nd 3rd 1st 2.2 4th 5th 2.4 2.3 2.5 2.6 0.31 0.36 0.39 0.40 0.40 78PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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