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130 c d ab Figure 5-7: Effect of loading coefficient 𝛹 on the investigated parameters. Figure 5-8 presents the effects of turbine rotational speed 𝑁 on the four investigated parameters. Figure 5-8a shows that the static efficiency 𝜂𝑡𝑠 increases gradually with the turbine speed 𝑁 with an increase of 11.7% from 20,000 rpm to 70,000 rpm. In agreement with the Euler equation in equation (5-23), the turbine power output 𝑊𝑜𝑢𝑡 presents the same trend as the static efficiency 𝜂𝑡𝑠 with an increase of 12.5% from 20,000 rpm to 70,000 rpm. Figure 5-8bpresents the effect of 𝑁 on the two remaining parameters. The increase in turbine speed 𝑁 is significantly beneficial to the turbine size 𝑟1 . As 𝑁 increases, 𝑟1 substantially decreases with a decrease of 27.14% from 20,000 rpm to 70,000 rpm. This observation can be justified by the definition of loading coefficient 𝛹 in equation (4-7). For constant 𝛹, the rotor radius 𝑟4 is inversely proportional to the turbine speed 𝑁. This result also explains the increase in turbine efficiency 𝜂𝑡𝑠 , where the friction and exit loss decrease with turbine size. The losses model is presented in detail in Section 5.7.1. The effect of turbine speed on thePDF Image | Automotive Radial Turbine Expander Design WHR
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