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109 given pressure ratio. Therefore, the isentropic enthalpy π5π can be found using EoS, as shown in equation (β5-5). 5.3.2 π,π =πΈπππ,π,π,πππ’ππ 01 01 01 01 01 π=π,π =π =πΈπππ,πππ’ππ 5π 55π 01 5π (β5-4) (β5-5) Subsequently, the isentropic βπππ and actual βππππ‘ enthalpies drops, and the turbine power output πππ’π‘ can be obtained using the following equations: βπππ = ππ1 β π5π βππππ‘ = Ι³π‘π βπππ = π01 β π05 π =πβπ ππ’π‘ πππ‘ Rotor Modelling (β5-6) (β5-7) (β5-8) Rotor is the most significant component in the turbine stage because work transfer occurs in this region. Therefore, this component will be analysed first. In the DPC, the designer has the option to select either specific speed approach, or loading Ρ°and flow π coefficients approach. 5.3.2.1 Mean-line Based on Specific Speed, π΅π In this approach, ππ is defined by the user, the rotational speed π is calculated using equation(β2-3)and π is specified by the user in the second approach, which will be shown in the next section. Once π£π is calculated, rotor tip speed π4 , tangential speed πΆπ4 and absolute flow angle πΌ4 are calculated using equations (β5-9), (β5-10)and(β5-11), respectively [234]. It is worth mentioning that equation (β5-11) is used in ideal gases. Therefore, the velocity triangle at the rotor inlet (Figure β5-2) is completed using trigonometry rules. Figure β5-3 presents the flowchart of the design point using ππ correlation. π4=π£π 2βπππ (β5-9)PDF Image | Automotive Radial Turbine Expander Design WHR
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