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145 As previously stated, the conservation of angular momentum can be applied in the interspace [244]. Therefore, the tangential component of the velocity at the rotor leading edge πΆπ4 is calculated using equation (β5-37). The rest of the velocity parameters and static thermodynamic properties are calculated iteratively with a first assumption of πΆπ4 = πΆπ3 until convergence is achieved, as shown in equations (β5-73) to (β5-77). πΆ= πΆπ2+πΆπ2 444 π= πΆπ2+(πβπΆπ)^2 4444 π =πβ1πΆ2 04 4 24 π ,π =πΈππ π ,π,π ,π,πππ’ππ 44 4444 πΆπ4 = π. π4π΄4 (β5-73) (β5-74) (β5-75) (β5-76) (β5-77) Predicting the velocity triangle and the thermodynamic properties at the rotor exit is a relatively long process. The isentropic and actual enthalpies are calculated using equations (β5-6) and (β5-7), respectively, after an initial value of the total to static efficiency ππ‘π is specified. The tangential velocity of the rotor exit πΆπ5 is calculated at the off-design process using the Euler equation, as shown in equation (β5-23). The relative flow angle of the rotor exit π½5 is calculated using the equation presented in [263].Benson[263] stated that π½5 should be calculated based on the cosine rule at the mean radius, and some deviation due to rotor speed may be present. Therefore, cosine rule is applied in the current study and flow deviation πΏπ is considered, as shown in equation(β5-78). The velocity triangle is now complete at the rotor exit, and the thermodynamic properties are subsequently obtained using the EoS. π½5=βcosππ,πππ +πΏπ π π,πππ (β5-78)PDF Image | Automotive Radial Turbine Expander Design WHR
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