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Energies 2020, 13, 2118 3 of 19 ratios. Al Jubori et al. [20] studied an axial turbine and a radial outflow turbine for the organic Rankine cycle. The performance of each turbine was compared through CFD, but the difference was insignificant. Maksiuta et al. [21] presented a unique preliminary design technique for multi-stage radial outflow turbines with different enthalpy drops of each stage. The radial outflow turbine designed with this technique has an 11% mechanical output power improvement over the original radial inflow turbine. There are only a few studies of radial outflow turbines, and information on the design procedure is insufficient in the abovementioned studies. Specifically, variables such as the basis of the selected rpm and blade number, the variables for which the iterative calculation was performed, the loss model used, and the accuracy of the developed design algorithm were not clearly presented. In addition, too many variables are optimized to meet the target performance, and the procedure is very complicated. This study clearly presents a preliminary design algorithm for a radial outflow turbine to meet the target performance of turbines. The preliminary design algorithm for the radial outflow turbine proposed in this study corresponds to a new approach based on the enthalpy loss models and the deviation angle models. The developed preliminary design algorithm shows satisfactory accuracy, which greatly simplifies the optimization process to fully meet the design goals. In addition, off- design analysis is performed in this study for the designed turbine, and the flow variables that dominate the turbine efficiency are considered. 2. Preliminary Design for a Radial Outflow Turbine 2.1. Basic Theory The basic concepts required for the preliminary design algorithm and performance analysis of a radial outflow turbine are as follows. The turbine stage velocity triangle and enthalpyβentropy diagram of a radial outflow turbine are shown in Figures 2 and 3, respectively. Figure 2. Schematic of a turbine stage velocity triangle for a radial outflow turbine (Adapted from [2]). The total power of the turbine can be expressed as Equation (1) with the Euler equation and total enthalpy drop [22]. A radial outflow turbine does not have the same peripheral velocity at the inlet velocityoftherotorexit(πΆπΆΜ )inordertomaximizethespecificpoweroftheturbine.Themassflow 3ππ rate of Equation (1) is equal to Equation (2). ππ = ππΜ ( h 0 1 β h 0 3 ) = ππΜ ( ππ 2 πΆπΆ 2 ππ β ππ 3 πΆπΆ 3 ππ ) ( 1 ) and exit of the rotor. In the radial outflow turbine, it is necessary to minimize the tangential absolutePDF Image | Analysis of a Radial Outflow Turbine for Organic Rankine Cycles
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