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148 π3π βππ‘ππ = 4 π πΎππππΆπ +πΎππππΆπ +πΎπ,π πππππΆππΆπ (β5-88) 8π πΆπ and πΆπ are the axial and radial coefficients for the tip clearance model calculated using equations(β5-89) and (β5-90), respectively [233], [257]: 1 β π5,π π πΆπ= π4 πΆπ4π4 πΆπ = π5,π π ππ βπ4 ππΆππ 4 π555 (β5-89) (β5-90) ο· Windage Loss Another leakage occurs between the back-face and the housing of the rotor due to the existinggap, which results in another frictional loss. This gap also generates high centrifugal stresses at the gaps in the tip clearance [264]. The behaviour of fluid flow in the region was investigated by Daily and Nece[265],who considered a rotating disc in an enclosed casing, as shown in equation (β5-91). βππ€ππππππ = ππ ππ3π2 44 2π (β5-91) ππ denotes the empirical correlation for frictional torque bySuhrmann[265]with two equations based on the nature of the flow as follows: 3.7 π 0.1 (β5-92) π = π4 for laminar flow (π π < 105) π π π0.5 0.102 π 0.1 (β5-93) π = π4 for Turbulent flow (π π > 105) π π π0.2 π is the mean fluid density evaluated by the static condition of rotor inlet and outlet. Ξ΅ denotes the clearance gap between the back face and the housing of the rotor wheel.PDF Image | Automotive Radial Turbine Expander Design WHR
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