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Finally the total pressure and the tangential velocity at the tip are determined. To calculate the total pressure at the tip I am using the relationship found in [2]. Rotational speed ρ01 = p01 RT01 p =p −ρ ∆h 07 01 01 0,ideal (A.21) 1−ηts (A.22) 4 The tangential velocity at the impeller tip is approximated using the assumption that the flow at the outlet of the impeller is entirely meridional, giving: c9θ = 0. ∆h0 = U7c7θ − U9c9θ = U7c7θ (A.23) ⇒ c7θ = ∆h0 = ∆h0,ideal ηts (A.24) U7 U7 While the method of sizing the tip when the specific speed is used as input variable is a direct one, an iterative manner has to be conducted when the rotational speed is provided. Initially a guess of the specific speed is made. This guess will be updated until the iteration converge on the specific speed. The equations used are the following. ηts = 0.87 − 1.07(Ns − 0.55)2 − 0.5(Ns − 0.55)3 h09 = h01 − ∆h0,ideal ηts T09 = h09 cp ρ09 = p9 RT09 Q9 = ρm ̇ 09 √ (A.25) (A.26) (A.27) (A.28) (A.29) (A.30) Ns = N Q9 ∆h0.75 0,ideal When the specific speed is determined the total to static velocity ratio, the tip blade speed, the tip radius, the tip total pressure and the tip tangential velocity will be calcu- lated using equations (A.12), (A.14), (A.20), (A.21), (A.22) and (A.24). This completes the sizing of the impeller tip. The designer will now proceed with the geometrical design of the impeller. I have, just like in ”RIFTSIZE”, chosen to let the user decided whether to use the default values provided by Aungier or to specifies the variables. The benefit of using the default values 76PDF Image | A Detailed Analysis of Radial Turbines
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