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Combining Equations (C7) and (C9) results in A1/A2 = AVDR* Cos(β1) / Cos(β2) (C10) Note that Ax1 and Ax2 do not include the blockage due to boundary layers. Therefore, the AVDR cannot be measured strictly from the geometry of the casing although that usually provides a good approximation. Annular Cascade Theory Unlike linear cascades in which the relative flow velocity vectors can be described as 2-D, the relative flow in annular cascades is 3-D. Therefore, the areas perpendicular to the relative flow differ from those in Equation (C10). However, if we define a new variable called the Meridional Velocity Density Ratio, MVDR, an analogy to the AVDR is obtained. The meridional velocity is the vector sum of the axial and radial velocity vectors. The following is the definition of the MVDR: MVDR = (ρ2Vm2) / (ρ1Vm1) (C11) where Vm is the absolute meridional velocity. Because the blade velocity is perpendicular to the meridional velocity, the absolute meridional velocity (Vm) and the relative meridional velocity (Wm) are equivalent. Vm1 = Wm1 and Vm2 = Wm2 (C12) Figure C2 shows the front and side views of an annulus. Streamtubes Vx θ V φ Vr mr x r Figure C2 Figure C2 Front and Side Views of a 3-D Annulus 77PDF Image | Gas Turbine Design Axial Flow Compressors
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