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Mathematics 2020, 9, 50 21 of 30 flow pattern improves better with 40,000 rpm than 30,000 rpm at high temperatures since Mathematics 2020, 8, x FOR PEER REVIEW the fluid density at the stator exit is 33% lower. 22 of 34 Mathematics 2020, 8, x FOR PEER REVIEW Figure 23. Turbine efficiency and power output at various pressure ratios. Figure 23. Turbine efficiency and power output at various pressure ratios. Different Turbine Inlet Temperatures 23 of 34 Temperatures of exhaust gases in an internal combustion engine vary considerably according to vehicle’s operation. As mentioned in the previous study [14], the turbine inlet temperature increases linearly with increasing heat source temperature. Therefore, turbine performance is also investigated at different inlet temperatures and rotational speeds in the current study. Like the design point, flow vortices are noticed downstream of the rotor blades at the suction side for all off-design points, as shown in Figure 24. This indicates that this part of the blade is not optimum. Figure 24 also indicates that flow pattern improves with increasing turbine inlet temperature for the same rotational speed. The closer inlet temperature gets to design point, the more uniform flow results as shown in Figure24a,b. At off-design rotational speed (30,000 rpm), the flow is more uniform than that in design point speed (40,000) for low temperatures due to low fluid densities at the stator exit. In contrast, flow pattern improves better with 40,000 rpm than 30,000 rpm at high temperatures since the fluid density at the stator exit is 33% lower. 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. Figure 24. Temperature distributions, Mach numbers, and velocity streamlines at 50% span for (a) T Figure 24. Temperature distributions, Mach numbers, and velocity streamlines at 50% span for (a) T = 430 K, N = 40,000 =430K,N=40,000rpm,(b)T=450K,N=40,000and(c)T=430K,N=30,000(d)T=450K,N=30,000 rpm, (b) T = 450 K, N = 40,000 and (c) T = 430 K, N = 30,000 (d) T = 450 K, N = 30,000 rpm. rpm. 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 powerPDF Image | Generation of 3D Turbine Blades for Automotive ORC
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