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Mathematics 2020, 9, 50 25 of 30 net power for all operating temperatures. For 40,000 rpm, on the other hand, the rate of increase of heat input from 430 to 450 K is 8.60% compared 4.17% of net power. From 450 to 471.55 K, the rate of increase in heat input is 4.07% compared to 5.80% of net power. This clarifies the trend of cycle thermal efficiency operating with 40,000 rpm. 6.4. Results of Finite Element Analyses (FEA) For safe operation, the maximum von Mises stress and stress and total displacement should not exceed be the material tensile strength and the tip clearance gap between the rotor and casing. Figure 28 presents the results of the FEA at the design point using Fullcure 720. In addition, Table 7 summarizes the FEA at design and off-design points for the considered types of material. As can be seen in Figure 28, the maximum stress and deformation due to fluid pressure are 0.54 MPa and 0.001 mm which are well below the limits (60 MPa and 0.6 mm). However, it is apparent from Table 7 that maximum stress and deformation due to rotation increase significantly. Although the maximum stress (29.22 MPa) is still below the material tensile strength, the deformation at the blade tip is 0.48 mm which is very close to the assigned clearance gap (0.6 mm). Therefore, although Fullcure 720 is cost-effective, using such material in the current application is risky due to the possibility of metal fusion near the blade tip. It is evident from Figure 28 that the maximum stress occurs at the blade root in the hub for both fluid pressure and rotation. The maximum deformation, on the other hand, occurs at the at exit tip for both fluid pressure and rotation. Similar locations of maximum stress and deformation are also noticed for all considered types of materials and with different operating conditions (i.e., off-design operation). It is worth mentioning that the locations of maximum stress and deformation agree with locations mentioned in Moustapha et al. [68]. For other types of material, the maximum stress and deformation are well below limits for both fluid pressure and rotation. Table 7. Minimum and maximum stresses and total deformations of rotor blades at design and off-design conditions. Design Point, Due to Pressure (CFX Conditions: Inlet Pressure = 900 kPa, N = 40,000 rpm) Material Fullcure 720 Aluminium alloy Stainless steel Titanium alloy Max. von Mises Stress (Pa) 5.41 × 105 4.79 × 105 5.00 × 105 4.46 × 105 Msx. Deformation (m) 9.99 × 10−7 4.43 × 10−8 1.58 × 10−8 3.41 × 10−8 Design Point, Due to Rotation (CFX Conditions: Inlet Pressure = 900 kPa, N = 40,000 rpm) Material Fullcure 720 Aluminium alloy Stainless steel Titanium alloy Max. von Mises Stress (Pa) 2.92 × 107 7.20 × 107 1.98 × 108 1.24 × 108 Max. Deformation (m) 4.83 × 10−4 4.59 × 10−5 4.72 × 10−5 5.67 × 10−5 Off-Design, Due to Pressure (CFX Conditions: Inlet Pressure = 390 kPa, N = 30,000 rpm) Material Fullcure 720 Aluminium alloy Stainless steel Titanium alloy von Mises Stress (Pa) 6.03 × 105 5.34 × 105 5.57 × 105 4.98 × 105 Deformation (m) 1.13 × 10−6 4.99 × 10−8 1.79 × 10−8 3.85 × 10−8 Off-Design, Due to Rotation (CFX Conditions: Inlet Pressure = 390 kPa, N = 30,000 rpm) Material Fullcure 720 Aluminium alloy Stainless steel Titanium alloy von Mises Stress (Pa) 1.64 × 107 4.05 × 107 1.11 × 108 6.98 × 107 Deformation (m) 2.72 × 10−4 2.58 × 10−5 2.66 × 10−5 3.19 × 10−5PDF Image | Generation of 3D Turbine Blades for Automotive ORC
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