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Chapter 3 3.2 Preliminary Design Method The preliminary design of a turbine is the phase in which the fundamental machine features, such as the number of stages, the velocity triangles, the speed of revolution, and the blading geometry, are selected. As detailed in the seminal work of Macchi [5], this step is fundamental particularly if no previous experience is available regarding the specific machine to be designed. In other words, although advanced design methods based on computational fluid-dynamics constitute a precious help for the designer, they can yield high turbine performance only if the boundary conditions es- tablished in the preliminary design phase allow for it [5]. This is often obtained for conventional turbines by making use of simple rules based on statistical information on existing similar machines [13]. As anticipated, since this is generally not available when designing an expander for an ORC power system, a more general approach must be followed. In particular, a simultaneous optimiza- tion process accounting for all the main variables affecting the turbine efficiency is desirable: this is typically achieved by resorting to so-called 0-D mean-line methods [14]. Several studies reported a good agreement between the results of such calculations and measurements, if reliable loss and flow angle correlations are applied [15–17]. The mean-line design code zTurbo, specifically conceived for ORC turbines and developed within the present research, is described in §3.2.1. zTurbo has been thus introduced in an optimization pro- cedure, in order to automatically determine the optimal design features of the machines, depending on the designer’s objective, as detailed in §3.2.2. 3.2.1 Mean-line Design Tool for ORC Turbines The main aim of this code, whose development has been directly contributed by the author, is to provide a preliminary machine design without any limitation on the adopted working fluid, flow regime, and architecture: axial, radial-inflow, and radial-outflow turbine arrangements can be de- signed with zTurbo. The code is coupled with the FluidProp software library, allowing for an accurate evaluation of the working fluid thermophysical properties [18]. The balance equations for mass, energy, and momentum, alongside a loss model to evaluate entropy generation, are written in a generalized formulation, and both subsonic and supersonic flows are properly treated in the stationary and rotating frames of reference. The calculation scheme of a single turbine stage, as performed by zTurbo, is briefly summarized in the following: 1. At the beginning, the total upstream thermodynamic conditions, the stage expansion ratio, and the mass flow rate are provided as external inputs (e.g. as outputs of the thermodynamic cycle optimization). This is the case also for several geometric quantities related to manu- facturing limits (e.g. trailing-edge thickness, hub/tip clearance, and stator/rotor gap). The values of several design variables are thus initially assumed, among others: the rotational speed, the reaction degree, the blades chords and outlet geometric angles, and the channel minimum width (throat dimension). 2. By assigning the stage reaction degree, the stator outlet velocity and the corresponding isoentropic Mach number can be calculated. If the flow is supersonic, for instance, isen- tropic expansion is assumed from the inlet section where total conditions are given (e.g. pressure PT,in and temperature TT,in), up to the choked throat where sonic conditions are 60PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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