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Common parameters tcl [mm] cl [mm] δmax [◦ ] Design Variables Din [mm] (x 1) ω [krpm] (x 1) ( pT,in / pS,out )stg (x Nstgs ) R (x Nstgs ) BDA [◦] (x Nrows) b [mm] (x Nrows) 0.1 te [mm] 0.1 1 Hmin [mm] 2 ±12 LB UB 20 100 520 25 0.1 0.6 55 75 212 Centrifugal Turbines for ORC Applications and the associated tip leakage losses estimated. Shrouded rows are generally preferred in small turbines in order to reduce tip-leakages [37] but, in the present chapter, greater importance has been attributed to easy the machine realization, see e.g. §3.3. 3.6.2 Design Methodology The design of the machines considered here, given their comparatively low power-output, is per- formed following the novel design procedure purposely introduced at the end of §3.4. In particular, the pressure drops, the degrees of reaction, the radial chords, and the blades outlet geometric angles are allowed to assume different values among the stages. The variables and the geometric param- eters needed to perform the turbine design, see e.g. §3.2.1, are collected in Tab. 3.6. The design framework is similar to the one described in §3.5.4, and all the quantities are described therein. As anticipated, both the inlet diameter Din and the speed of revolution ω appear in this case among the variables to be optimized, see e.g. §3.4. For the blade height H, which is a critical quantity given the low power-output, the minimal value compatible with mechanical resistance and manu- facturing limits is assigned as the lower bound [5, 23]. Further analysis conducted on the machines presented in §3.5 by means of CFD tools highlighted that, for centrifugal turbines, is beneficial for the machine performance to adopt maximum flaring angles lower than those suggested from the axial turbines practice [11]. Following this results, the range of variation of the flaring angle δ is now reduced to ±12◦. Table 3.6: Design variables, with relative lower (LB) and upper (UB) bounds, and parameters involved in the proposed design methodology as applied to a N-stages centrifugal turbine. 3.6.3 Results: Transonic Turbine The main features of the optimized 5-stage mROT are shown in Table 3.7. Is to be noted that the optimal angular velocity, i.e. 12400 rpm, is considerably lower than the values encountered for traditional axial or centripetal machines designed for a comparable application and power output, see e.g. [35]. The optimal velocity triangles are shown in Fig. 3.10a and, as expected, the blades 77PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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