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3 2.5 2 1.5 1 0.5 2 4 6 8 10 12 N row Ψ w 10 8 6 8 6 4 2 ζp ζs 1 2 3 4 5 6 7 8 9 10 11 12 N row Centrifugal Turbines for ORC Applications (a) (b) Figure 3.6: Design results for the 6-stage transonic 1 MWM turbine of Fig. 3.5. 3.6a: evolution of the load distribution among the stages, in terms of the aerodynamic loading expressed by Ψ (solid line), and of the stage specific work w (dashed line). 3.6b: row-by-row evolution of the kinetic energy loss coefficients ζp (solid line), and ζs (dashed line) accounting for profile-, and secondary- losses. The presented results are obtained with the Craig & Cox model [15]. throughout the machine, as shown in Fig. 3.6b. This is a direct consequence of the turbine config- uration, featuring stages characterized by very different geometrical quantities (e.g. solidity, aspect ratio etc.). In particular, end-wall loss coefficients are found to be more influential in the first stages, characterized by lower blades aspect-ratios. The same trend characterizes also the profile losses, which assume larger values in the high deflection blades of the first stages. As a result, the stage efficiency increases along the machine, passing from about 75% in the first stage to about 95% in the last one. 3.5.4 Results: Slightly Supersonic Turbine The main features of the optimized 3-stage turbine are shown in Tab. 3.4. The increased aero- dynamic loading lead to an efficiency penalty with respect to the 6-stage machine. The optimal velocity triangles are shown in Fig. 3.7a and, as expected (§3.4), the optimized blades geometrical angles vary along the machine in this case. It can be noted that the application of the design procedure proposed in §3.4 allows to avoid any converging part in the meridional channel, as shown in Fig. 3.7b. At the same time, the con- straint on the maximum flaring angle is respected notwithstanding the fact that the same expansion is performed with three stages only. This is achieved by an increase of the chords in the last stages, accompanied by a reduction of the deflection and a consequent increase of the radial velocity com- ponent. 73 Ψ w [kJ/kg] ζ [%]PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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