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112 According to the Euler equation, equation (β5-23), the power output of the turbine increases with negative values of the exit swirlπΆπ5. However, some reduction in efficiency will occur[233]. Therefore, πΆπ5 is assumed to be zero to minimise the leaving loss of the rotor. The wheel speed at the rotor exit π5 can be easily obtained because the radius ratios are given as inputs. One of the triangle parameters has to be obtainedto complete the velocity triangle at the rotor exit (Figure β5-2). Aungier [234]proposed an effective procedure to estimate meridional speed πΆπ 5 , equation (β5-24). When this equation is applied, the velocity triangle at the rotor exit can be obtained using trigonometry rules. π =π.(ππΆ βππΆ ) ππ’π‘ππ’π‘ 4 π4 5 π5 πΆπ5=πΆπ4 1+5π42 Subsequently, the static enthalpy π5 is calculated using the First Law of Thermodynamics, as shown in equation (β5-25), and the other thermodynamic properties are calculated using EoS, as shown in equation (β5-26). Given that π 05 = π 5 , Figure β4-3, the stagnation thermodynamic properties can be found using equation (β5-27). π =π +1πΆ2 5 π5 25 π,π =πΈπππ,π,π,π ,πππ’ππ 55 5555 π,π =πΈπππ,π,π,π,πππ’ππ 05 05 05 05 05 05 (β5-25) (β5-26) (β5-27) To fully define the rotor geometry, the axial length and blade thickness of the rotor at its trailing edge are defined using equations(β5-28) and (β5-29), respectively [234]. The rotor mean throat π5, which is the smallest distance between two adjacent blades, is calculated based on the value of the relative Mach number π5πππ , as shown in equation (β5-30)[234]. βπ§=1.5(π βπ ) 5π‘ 5π π‘ =0.02π π5 4 (β5-28) (β5-29) π 4 (β5-23) (β5-24)PDF Image | Automotive Radial Turbine Expander Design WHR
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