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With these input parameters, the impeller tip is sized using the following relations. All equations are taken from R.H. Aungier’s book - ”Turbine Aerodynamics - Axial-flow and radial-inflow turbine design and analysis” [2]. The static pressure at the impeller exit is calculated using the total to static expansion ratio and the total inlet pressure. p9 = p01 (A.1) p01 /p9 Assuming that the flow through the turbine is adiabatic it can be stated that the total temperature at the impeller tip is equal to the stage inlet total temperature and since it has been assumed that the gas is perfect the total enthalpy is easily determined. T07 = T01 h01 = h07 = cpT01 It can be shown that for a perfect gas the following relationship holds 1 R=cp 1−γ Where, R, is the gas constant and γ is the ratio of specific heats. R= Ru J/kg K M γ= cp cv (A.2) (A.3) (A.4) (A.5) (A.6) The spouting velocity is determined, using the definition which where stated in chapter 3. It is rewritten here. c0s = 2∆h0,ideal (A.7) The ideal total enthalpy drop, ∆h0,ideal can be calculated using an isentropic efficiency of unity. η = h01 −h09 = cpT01 −cpT09 (A.8) (A.9) (A.10) T h01 − h09,s p γ−1 cpT01 − cpT09,s p γ−1 09γ 0101 01 ⇔ 09 09γ T = p ⇒ T09 = T01 p ⇒ ∆h0 = cp(T01 −T09) = cpT01 73 p γ−1 1 − p 09 γ 01PDF Image | A Detailed Analysis of Radial Turbines
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