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Centrifugal Turbines for ORC Applications 300 250 200 150 100 -0.4 -0.2 0 p =10bar T,in CR IN = 0.17 bar 0.6 0.8 0.2 0.4 p out -1o -1 s[kJkg C] Figure 3.4: Saturation curve of siloxane MDM in a T-s diagram, showing the thermodynamic boundary conditions for the turbine design, i.e. the inlet total conditions, point IN, and the discharge pressure. Point CR indicates the liquid-vapour critical point of the fluid. efficiency, in particular during off-design operations [6, 17]. However, the choice of dealing with highly supersonic flows is typically justified by the opportunity of minimizing the number of stages [9]. As mentioned in §3.3, however, the adoption of the centrifugal architecture allows to increase the number of stages with relative ease, thus relaxing this constraint. Therefore, all the machines whose design is proposed in the following belong to one of these general classes, i.e., they are either transonic or slightly supersonic ones. To this end, it is possible to tentatively vary the number of stages, or to include also this among the optimization variables. In the present case, the designs of a subsonic six-stage turbine, and of a three-stage transonic one featuring supersonic post-expanding flows are presented. The losses-estimation method proposed by Craig & Cox is adopted here [15], see §3.2.1, and the only losses modelled are the profile, and the secondary ones. 3.5.2 Design Methodology The variables and parameters involved in the design are collected in Tab. 3.2, see also §3.2.1. Primarily, the rotational speed ω is constrained to the value of 3000 rpm, in order to directly couple the turbine and the electrical generator. This, in fact, adds an important economic benefit to the resulting machine, in that electronic converters are not required. Both the tip clearance tcl and the trailing-edge thickness te are set to minimum values, related to mechanical resistance or manufac- turing limits, and common to all the rows [5, 23]. The radial clearance cl, i.e. the gap between the cascades, is also assigned a fixed value, since a proper optimization of this parameter is outside the capabilities of a generalized mean-line approach. However, considering its strong impact on the performance of axial turbines [34], an even larger influence may be expected in radial machines. In centrifugal turbines, in fact, the radial gap directly affects the variation of the radial coordinate and, 69 o T [ C]PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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