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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Depending on whether the designer is choosing to specify a rotational speed or a spe- cific speed, different ways of calculating the conditions at the impeller tip have to be conducted. If he is choosing to specify a rotational speed an iterative approach has to be undertaken, however, if the choice fall on the specific speed, a direct approach is possible. Specific speed If the specific speed is chosen as speed variable it is possible to apply a direct calculation scheme. The total to static velocity ratio, νt−s was defined in chapter 3 as the ratio of blade speed to spouting velocity. νts = cU (A.11) 0s In Aungier’s book , [2], he provides two equations which correlates the total to static velocity ratio and the total to static efficiency as functions of specific speed. ν = 0.737N0.2 (A.12) ts s ηts = 0.87 − 1.07(Ns − 0.55)2 − 0.5(Ns − 0.55)3 (A.13) The equations are plotted in figure A.2. When the total to static velocity ratio and the spouting velocity are calculated the blade tip speed is given by. U7 = νts c0,s (A.14) The total enthalpy and temperature at the impeller outlet can be calculated using the stage inlet total enthalpy, the ideal heat drop, the total to static efficiency, given by equation (A.13) and the specific heat. h09 = h01 − ∆h0,idealηts (A.15) T09 = cpT09 (A.16) Since I have chosen to use a perfect gas the ideal gas law can be applied. From it the density at the impeller outlet is calculated. ρ9 = p9 (A.17) RT9 Since it is not possible to determine the static temperature, T9, without applying some loss model the density will have to approximated using the total temperature, T09 instead of the static temperature. This can be said not to influence the results greatly because the absolute velocity at the impeller outlet should be kept low to yield a proper design. 74

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