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One difference between a 2-D linear and a 3-D annular cascade flow with radial effects is that the 3-D relative flow angles are taken with respect to the meridional velocity as opposed to the axial. Assuming uniform properties and axisymmetric flow where Am is the cross sectional area of the streamtube normal to the meridional velocity, the derivation of A1/A2 is as follows: Continuity states that Continuity also states that P =(ρ1A1W1)=(ρ2A2W2) ∴ A1/A2 = (ρ2W2) / (ρ1W1) (C13) (C14) (C15) (C16) (C17) (C18) (C19) P =(ρ1Am1Wm1)=(ρ2Am2Wm2) Combining Equations (C13) and (C15) results in A1 = Am1 * Wm1/W1 and A2 = Am2 * Wm2/W2 The velocity triangles produce Cos(β1) = Wm1/W1 and Cos(β2) = Wm2/W2 Hence A1/A2 = A1m/A2m* Cos(β1) / Cos(β2) So that A1/A2 = MVDR* Cos(β1) / Cos(β2) Hence, there exists a relationship between AVDR and MVDR that can be derived from velocity triangles: MVDR = AVDR * Cos(φ1)/Cos(φ2) (C20) 78PDF Image | Gas Turbine Design Axial Flow Compressors
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