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A Detailed Analysis of Radial Turbines

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A Detailed Analysis of Radial Turbines ( a-detailed-analysis-radial-turbines )

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by the following relationship. Θ=1− 1− b 1− b 􏰘 􏰚 θw 􏰙 􏰘 􏰚 θb 􏰙 wb (3.33) (3.34) 􏰘 􏰚 δw 􏰙 􏰘 􏰚 δb 􏰙 ∆=1− 1− b 1− b wb The subscripts w and b indicates the boundary layers on the end walls and the blade surfaces respectively. The Volute A performance analysis can be performed with the volute divided into two sections which yield three stations where the geometry is specified, as in figure 3.6. The geometry needed is presented in table 3.3. Table 3.3.: The geometrical parameters which are needed to conduct the perfor- mance analysis. Inlet radius r1 Inlet area A1 Mid passage radius r2 Mid passage area A2 Exit radius r3 Exit width b3 Surface finish erms Since this is the first component of the turbine all the inlet conditions are available. From a mass balance at the inlet station together with the fact that the velocity is in general entirely tangential, the flow conditions can be calculated. Assuming that the velocity is still entirely tangential at the mid passage and that half of the mass flow has turned off toward the nozzle blades a similar analysis can be conducted at this station. The tangential velocity at the exit station is estimated assuming that the angular momentum is conserved between the mid passage and exit. c =cr2 (3.35) 3θ 2r3 The volute is exposed to two types of losses. The profile loss is determined using the relations in chapter 3.2. The second type Aungier terms ”circumferential distortion loss” [2]. This loss occurs due to the fact that the angular momentum is in fact not conserved and the flow is thereby mixed, hence mixing losses result. The loss coefficient for this 25

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