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Master Thesis Report Verification of 2D Fitting Results The absolute axial velocity can then calculated as follows: Cax = MassFlow = MassFlow (5.2) Area 2πRmeanH Using the local speed of sound, the inlet tip relative velocity can be calculated. Vrel,tip = Mrel,tip ∗ alocal (5.3) The relative stagnation pressure and temperature can then be computed using the isentropic relation as follows: γair − 1 2 γair P01,rel = P1 ∗ [1 + 2 M1 ]γair−1 (5.4) T01,rel = T01,rel ∗ [1 + γair − 1M12] (5.5) 2 Using the inlet relative velocity and the constant axial velocity Wax = Cax, the relative tangential velocity can be computed: Wθ = W 2 − Wa2x (5.6) Using the peripheral speed U = Rm,1Ωdesign, the absolute tangential speed can be calculated as follows: Cθ,1 = Wθ − U (5.7) From the computed absolute tangential velocity and tip radius, the free vortex constant and the absolute tangential velocity at other radial position can be found. λfreevortex = RtipCθ,1 (5.8) Cθ = λfreevortex (5.9) Rother Using the value of Cθ, axial velocity Cax as well as the peripheral speed U, the value of the absolute and relative velocity at other radial position can be computed. C = Ca2x + Cθ2 (5.10) W=W2 +W2=C2 +(C +U)2 (5.11) ax θ ax θ With the given new value of W, the value of P01,rel, T01,rel and βin at a new radial position can be computed using equation 5.4, 5.5 and 5.12. βin = arccos Wax (5.12) W A summary of the calculated boundary values at the tip radius are provided in table 5.3. 39PDF Image | Aerodynamic Design of the NASA Rotor 67 for Non Uniform Inflow
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