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Appl. Sci. 2020, 10, 5069 16 of 20 TIT The Tokyo institute of technology Um Rotor blade mean velocity [m/s] U Blade velocity [m/s] V Relative Velocity [m/s] s Blade pitch [mm] α Absolute flow angle [◦] β Relative flow angle [◦] ∆hos Enthalpy drop across the stage [kJ/kg] ∆ho Enthalpy drop across the entire turbine [kJ/kg] ζ Enthalpy loss coefficient [-] ηtt Total to total Efficiency [%] ηts Total to static Efficiency [%] λ Enthalpy loss coefficient [-] Λ Degree of reaction [-] ρb Density of blade material [kg/m3] ψ Blade loading coefficient [-] φ Flow coefficient [-] Appendix A. Design Steps From the thermodynamic specification of the turbine and an assumed turbine efficiency the enthalpy drop across the entire turbine ∆ho can be readily found. The blade speed U and axial velocity component Ca then follow from the loading coefficient ψ and flow coefficient φ: 2∆hos U= (A1) ψ Ca = Uφ (A2) The blade angles for the stator and rotor are determined as a function of the blade speed U, the loading coefficient ψ , flow coefficient φ and degree of reaction ∧: 1ψ tanβ2=2φ 2−2∧ (A3) tan α2 = tan β2 + 1 (A4) φ 1ψ tanβ3=2φ 2+2∧ (A5) tan α3 = tan β3 − 1 (A6) φ From the calculated angles, the absolute and relative velocities can be found and thus the thermodynamic properties at the inlet and outlet of each stage can be determined. C2= Ca (A7) cos α2 C3= Ca (A8) cos α3 V2= Ca (A9) cos β2 V3= Ca (A10) cos β3PDF Image | Mean-Line Design of a Supercritical CO2 Micro Axial Turbine
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