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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Skin friction cf The reynolds number for all components of the radial turbine will be based on the discharge density ρ3, velocity u3 and dynamic viscosity. Since it is on the annular end walls in all the radial turbine components, except the volute, that the boundary layers occur, it is natural to base the reynolds number on the width, b3 between these end walls as non-dimensional length instead of the usual, the diameter, d. In the volute the dimensional length will be taken as the equivalent diameter, Deq, of the section which is under observation. This gives. Red → ρ3u3b3 (3.19) μ Red → ρ3u3Deq (3.20) μ This assumes that the boundary layers are fully turbulent, which according to Aungier is not completely true. However, he says that this does not flaw the model because the skin friction coefficient is not strongly a function of the reynolds number. Aungier cites Nikuradse’s model [13] of pipe skin friction coefficient and says that this can be used in this case. The flow is considered to be laminar if the reynolds number does not exceed 2000. Red < 2000 (3.21) The skin friction coefficient is then given by the laminar skin friction coefficient. cf = cfl = 16 (3.22) Red When the flow is turbulent, care most be taken to examine if the peak-to-valley surface roughness, e, will yield a rough wall skin friction coefficient, cftr, or a smooth wall skin friction coefficient, cfts. 1 􏰪4c 􏰥 2.51 􏰦 Re 􏰪4c = −2log10 1 􏰨e􏰩 (3.23) (3.24) fts d fts 􏰪4c = −2log10 3.71d ftr The actual (peak-to-valley) surface roughness, e, is estimated by assuming a sin-wave form, [2]. e = erms (3.25) 0.3535 23

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