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Appl. Sci. 2018, 8, 2038 2 of 16 Flexible Tolerance Method to search for the optimal design at the preliminary design stage for radial inflow turbines. The results showed that better design could be found without violating the specified constraints. Ebaid et al. [10] developed a unified approach for designing a single stage nozzleless radial inflow turbine, in which an optimization method was also used to determine the turbine principal dimensions, and the rotor geometry and the nozzleless volute were designed simultaneously. Mistry et al. [11] investigated the influence of different parameters such as inlet absolute Mach number, relative exit Mach number, solidity, relative velocity ratio and hub to shroud radius ratio on efficiency and provided guidelines for the optimal design of radial inflow turbines. Feng et al. [12] proposed a radial inflow turbine design method that took the stress limitation into account using the positive axial displacing method and skewing technique. The results indicated that the method could produce a high-performance design without violating the stress constraint. Deng [13] presented an optimized matching method between reaction degree and stage velocity ratio for a radial inflow turbine design, and the method was validated by both numerical simulation and experiment. Suhrmann et al. [14] validated the applicability of commonly known and well-established loss models for small size radial inflow turbines. Besides some improvement, they developed new correlations to improve the accuracy of loss prediction for small size radial inflow turbine. Ghosh et al. [15] developed a theoretical model to predict the off-design performance of a cryogenic turboexpander. The model could predict the complete performance map in a fast way and help the designer to understand the influence of design and operating parameters on the performance. Fu [16,17] developed an integrated optimization design approach for radial inflow turbines. This approach considered the aerodynamic performance, stress constraint, and the rotor weight sequentially. An initial design is generated in the first iteration, and then the outlet radius and the axial length are reduced by a small step in the following iterations until the aerodynamic performance, the stress constraint and the weight constraints are all satisfied. Ventura et al. [18] developed an automated approach for radial inflow turbine preliminary design in the same year. This approach specifies a certain range for the loading coefficient, flow coefficient, and the rotational speed, and explores all the design space to find a promising design. Shao [19] presented a multidisciplinary integrated design and an optimization method for radial inflow turbines in which aerodynamic performance and structure realization were considered simultaneously. Al Jubori et al. [20,21] presented the mathematical approach combined mean line design and 3D Computational Flow Dynamics (CFD) analysis for organic Rankine cycle turbines. The results revealed that the radial outflow turbine configuration exhibited a considerably higher turbine performance, with the overall isentropic efficiency of 82.9% and power output of 14.331 kW. Lio et al. [22] developed a mean line model using Matlab (R2018b, Mathworks, Natick, MA, USA) that includes the design and performance analysis procedure, and the results indicated that how different design choices in terms of specific speed and velocity ratio, and different working conditions in terms of expansion and turbine size may affect the efficiency of single stage radial inflow turbines in Organic Rankine Cycle (ORC) systems. Mounier et al. [23] proposed a new non-dimensional performance map tailored for small-scale turbines, and the results showed that the geometrical dependencies on the map had a strong impact on the shroud to tip radius ratio. Lv et al. [24] proposed an optimization design approach to quickly acquire a preliminary optimal radial inflow turbine configuration, and the results indicate that the designed turbine using the proposed optimization design approach had a superior performance under design and off-design conditions. Zhou et al. [25] presented a design method for a supercritical carbon dioxide radial inflow turbine, and the results were consistent with each other. It can be seen from the above-mentioned references that a lot of research has been performed on radial inflow turbine design from different aspects. Some focus on aerodynamic performance simply, some aim to satisfy stress or weight limitation without deteriorating efficiency, and some devote to reduce dependency on designer’s technical expertise through optimization algorithms. However,PDF Image | Design and Optimization Approach for Radial Inflow Turbines
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