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The flow path length is given by. The sub sonic flow angle is determined according to. rth = r9 − o2 sin φ9 m dm L= sinβ (3.67) (3.68) (3.69) (3.70) (3.71) (3.72) (3.73) 0 2s9 th s9b9 9 rth th The incidence loss can be determined using a relationship derived by Carmichael [6], it is recited in [2] and the results in [2] are presented here. c∗7θ = σ(U7 − c7m)cotβ7 cotα∗ = c7m 7 c∗7θ Yinc = sin2(α7 − α7∗)p′07 − p7 p′09 − p9 sinα′ = btho tanα′ = r9 tanα′ In the expressions above, c∗7θ and α7∗ are the ideal inlet tangential velocity and ideal inlet flow angle respectively. The slip factor can be modeled according to Aungier’s expression from [2]. It is a modification to Wiesner’s model. √ σ = |sinφ7| sinβ7 (3.74) N 0.7 Aungier argues that the expression yielding the slip factor above needs correction if the solidity becomes too low. The expression above can be used until the radius ratio r9/r7 exceeds a value of r9/r7 > (r9/r7)lim. (r9/r7)lim = σ − σ0 1 − σ0 σ0 = sin(19◦ + β7/5) When this value is exceeded, the slip factor is calculated according to. (3.75) (3.76) (3.77) (3.78) σcorrected =σ(1−ξ) r9/r7 − (r9/r7)lim √ β7/10 ξ = 1 − (r /r ) 9 7lim 34PDF Image | A Detailed Analysis of Radial Turbines
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