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3.1. Scaling Scaling is used when a turbine application which is going to operate at conditions similar to an existing turbine is desired. Instead of designing a new turbine, the existing turbine is scaled in accordance with non dimensional groups. This will reduce the cost and effort and thereby the time used in developing the turbine. The non dimensional groups are made up by parameters describing the turbine, the fluid used and the flow conditions. One group is a function of one or more of the other groups, e.g. Π1 = f(Π2,Π3,Π4,Π5) (3.1) The groups used when working with turbo machines handling compressible fluids can be found in basic textbooks about turbo machinery. Here those in [7] are recited. ∆h0s P m ̇ρ01a01DND a2,η,ρa3D2=fρaD2, μ,a,γ (3.2) 01 01 01 01 01 01 When the machine is run with a perfect gas some alterations to the groups stated above can be made. This simplifies the situation. The derivation can be found in Dixon, [7]. Here, just the results are presented. p01 ∆T0 m ̇ √γRT01 ND p ,η,T =f D2p ,√γRT,Re,γ 010 01 01 01 (3.3) The groups in equation (3.3) are readily used when running experiments on a turboma- chine because the inlet and outlet conditions are determined in a simple manner. If the machine under observation is running with only one gas, the ratio of specific heats, γ, can be excluded from equation (3.3) and if the machine works only at high Reynolds number, this group can also be omitted. The results is shown below. p ∆T m ̇cpT01 ND 01,η, 0 =f 2 ,√ (3.4) p010 T01 D p01 γRT01 In the industry working with turbomachines is has become praxis to delete R, γ, cp and D from equation (3.4). This further simplifies the situation. 15PDF Image | A Detailed Analysis of Radial Turbines
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