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Mathematics 2020, 9, 50 23 of 30 each component of the turbine, as shown in Table 6. Such variables are selected as the comparison variables between the 1D and 3D simulations. Table 6. Comparison between 1D mean-line and CFD results. Thermodynamic data through turbine stage Velocity triangles Performance Parameter T02 (K) T03 (K) (K) T05 (K) P02 (bar) P03 (bar) P04 (bar) P05 (bar) T2 (K) T3 (K) T4 (K) T5 (K) P2 (bar) P3 (bar) P4 (bar) P5 (bar) M3 (-) M5t (-) α4 (deg) C2 (m/s) C3 (m/s) C4 (m/s) C5 (m/s) U4 (m/s) W4 (m/s) W5 (m/s) R (-) m. (kg/s) ηts (%) Wout N (RPM) Mean-Line CFD 471.5 471.5 470.60 470.84 470.60 470.35 449.64 451 9.00 9.00 7.87 7.53 7.87 7.40 1.56 1.65 469.79 471.06 460.44 457.71 459.24 457.28 449.06 447.98 8.50 8.73 4.0 3.08 3.67 3.04 1.30 1.30 1.35 1.38 0.58 0.54 66.44 68.28 24.93 26.10 89.84 96.70 96.07 107.81 24.57 35.04 102.98 113.86 26.56 31.02 57.81 58.50 0.517 0.49 0.8 0.788 74.4 72.10 13.6 12.94 40,000 40,000 Deviation (%) 0.00 0.05 0.05 0.30 0.00 4.52 6.35 5.45 0.27 0.60 0.43 0.24 2.63 8.70 1.38 0.00 2.17 7.40 2.69 4.48 7.09 10.89 15.39 9.56 14.38 1.18 5.51 1.52 2.28 5.10 0.00 As seen in Table 6, the majority of the 1D parameters are in excellent agreement with 3D simulations. Maximum deviations of 15.39% can be noticed in rotor exit absolute velocity. This is justified by the assumption of the isentropic flow through the stator as shown in [31]. As a result, at a fixed mass flow rate, the meridional velocity, Cm4 , increases to conserve the mass flow rate. This increase in the meridional velocity results in higher absolute velocity, and consequently, higher deviation in rotor relative velocity, W4. This is not the case in the CFD analysis where the stagnation pressure drop in the stator is considered; therefore, the flow is not isentropic as shown in Figure 18. The deviation in the turbine efficiency and work output are 2.28% and 5.10%, respectively. Overall, the CFD results indicate that the proposed 1D design methodology can accurately predict the turbine performance and flow features for high-pressure ratio ORC radial inflow turbines. 6.3. Results of the ORC System Results of ORC System at Design and Off-Design Conditions The effects of turbine operating conditions on cycle thermal efficiency and net power are also investigated as shown in Figures 26 and 27. Increasing the pressure ratio results in higher cycle network due to the increased turbine power as discussed in Figure 23 Similarly, cycle efficiency increases as turbine pressure ratio increases. It is worth mentioning that cycle optimum point differs from the turbine one. The former is obtained at a pressurePDF Image | Generation of 3D Turbine Blades for Automotive ORC
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