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Mathematics 2020, 9, 50 22 of 30 Figure 24 shows also that the Mach number at stator exit increases with increasing the turbine inlet temperature for the same rotational speed. Mach number is a function of flow absolute velocity and speed of sound. As temperature increases, flow velocity increases resulting in higher Mach number. Compared to Figure 24d, Mach number in Figure 24c decreases by 19.74% since the absolute velocity decreases by 31.87%. Figure 24 shows also that Mach number decreases with increasing rotational speed for the same temperature and pressure ratio, according to the flow velocity. At 30,000 rpm (Figure 24c), the flow velocity at the stator exit is 20.80% higher than that at 40,000 rpm (Figure 24a). The relationship between flow velocity and rotational speed is explained in the velocity triangle in a previous study [31]. Lowering the rotor rotational speed results in higher tangential velocity in the interspace which results in higher absolute velocity, and consequently, higher Mach number. Turbine performance is explored at different turbine inlet temperatures and rotational speeds as shown in Figure 25. For the design point speed, turbine efficiency increases with increasing inlet temperature, reaching a maximum value at the design point inlet temperature (471.55 K). For the 30,000 rpm, turbine efficiency decreases linearly with increasing inlet temperature. At 430 K, enthalpy drop with 30,000 rpm is higher than that in 40,000 rpm clarifying the higher efficiency and power output at this point. As the temperature increase, the enthalpy drop with 40,000 rpm becomes higher which results in higher turbine efficiency and power output. Figure 25 shows also that turbine efficiency decreases with increasing turbine inlet temperature for 30,000 rpm. This is due to the flow deficiency downstream of the rotor blades at the suction side. Although flow vortices are created in both cases (Figure 24c,d), the latter results in lower flow velocity (compared to the upstream flow) which increases the strength of the vortices and consequently lower Mathematics 2020, 8, x FOR PEER REVIEW turbine efficiency. Figure 25. Turbine efficiency and power output at various turbine inlet temperatures. Figure 25. Turbine efficiency and power output at various turbine inlet temperatures. One of the main aims of the CFD simulation at the design point is to validate the mean-line 6.2. Comparison between the Mean-Line Model and CFD Results 6.2. Comparison between the Mean-Line Model and CFD Results One of the main aims of the CFD simulation at the design point is to validate the mean-line model as presented in Table 6. ANSYS provides a summary of the mass averaged model as presented in Table 6. ANSYS provides a summary of the mass averaged solution variables solution variables (total pressure, total temperature and static temperature), area-averaged (total pressure, total temperature and static temperature), area-averaged solution variables (static solution variables (static pressure and velocities), and derived quantities (as total to static pressure and velocities), and derived quantities (as total to static efficiency and power output). These efficiency and power output). These variables are computed at the inlet and exit of variables are computed at the inlet and exit of each component of the turbine, as shown in Table 6. Such variables are selected as the comparison variables between the 1D and 3D simulations. 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 24 of 34PDF Image | Generation of 3D Turbine Blades for Automotive ORC
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