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Mathematics 2020, 9, 50 4 of 30 with extensive CFD analyses and presented a maximum deviation of 5.02% in turbine power. Recently, Schuster et al. [46] presented an optimization model for ORC radial inflow turbines supported by CFD analyses. Their results showed sufficient agreement between 1D and CFD results. The brief review shows that CFD analysis allows the calculation of the flow field considering the viscous effects which are usually neglected in 1D model. Moreover, CFD can be applied as a reference of validation of mean-line models. Al Jubori et al. [47] developed a 1D mean-line model for designing a single stage radial turbine accompanied with CFD and experimental investigations. The results showed a tight race between the mean-line model and CFD. Flores et al. proposed a unidimensional design approach for a 10 kW radial inflow turbine. Both theoretical and numerical, proved to be in a good approximation. In turbomachines, the rotor is the key component to produce work [48]. As small-scale radial inflow turbines are characterized with small mass flow rates, the turbine usually adopts radial blades at the inlet (zero-degree blade angle). Radial inlet blades are beneficial to avoid bending stresses. To increase the turbine work (enthalpy drop within the rotor), the tangential velocity at the rotor inlet should be increased according to the Euler equation as explained un the previous study [31]. Using backswept (non-radial) blades result in a positive relative angle which results in larger tangential velocity and hence, larger enthalpy drop. However, utilizing backswept blades results in higher bending stresses at the rotor leading edge. Failure is likely to occur when stresses are greater than the yield stress of the material of the rotor which may lead to catastrophic consequences both physically and economically [49]. The main challenge in the operation of turbine blades is the harsh operating environment (high temperature, high pressure and high rotational speed) in which thermal and structural stresses can result which further leads to creep and fatigue phenomenon and finally failure of the blades. Therefore, it is very essential to ensure that the turbine rotor can withstand the operating conditions of the flow and have adequate life in service. Therefore, structural evaluation of the turbine stage using FEA, which is widely applied in the analysis of engineering problems [50], is essential. Research on bending stresses in ORC turbines is an area in which little available literature exists. However, enough studies were conducted aiming at analyzing bending stresses on air and steam turbines. Chen and Xie [51] created a finite element model of a low-pressure turbine blade to investigate the elastic-plastic conditions considering centrifugal load and aerodynamic load. Similarly, Fu [52] created a three-dimensional finite element model of the turbine blade to analyze the stress distribution of the turbine blade based on the thermo-elastic-plastic finite element under the conditions of centrifugal load and temperature load. Odabaee et al. [53] presented an FE analysis of a high-pressure ratio single stage radial-inflow turbine using ANSYS. The results showed a good agreement between the numerical and experimental data. Gad-el-Hak [54] presented a coupled CFD- FEA study with air as the working fluid and compared the results with experimental data. Similarly, Xie et al. [55] investigated the flow environment and blade thermal stresses using ANSYS with air as the working fluid. The authors considered both the thermal load and the centrifugal load. Banaszkiewicz [56] presented a methodology for analyzing both axial and radial stresses in steam turbine rotors and compared the proposed model with different methods available in the literature. Wang et al. [57] studied the effects of active thermal management on failure risk of disks and explores possible means for risk control. They concluded that the probability of disk failure increases with increasing the load cycle. They also concluded that the disk hub is the riskiest part and strongly influences the disk safety. The brief literature review in the above paragraphs indicates the importance of devel- oping a fast and accurate mathematical modelling of blade generation. Moreover, CFD and FE analyses are crucial steps for checking the turbine feasibility before sending the turbine for manufacturing and hence saving money. Moreover, ORC radial inflow turbines usually operate with the high-pressure ratio which necessities a careful examination of the flow environment, especially at the stator exit (due to the high Mach numbers at this region). In addition, ORC systems operate with high dense real fluids (organic fluids). Therefore,PDF Image | Generation of 3D Turbine Blades for Automotive ORC
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