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Many modern compressor simulations assume 3-D loss terms to be equivalent to those obtained in the 2-D case and neglect centrifugal effects introduced when converting from 2-D linear to 3-D annular cascades. The derivation in Appendix E illustrates a method of converting the 2-D loss to a 3-D loss. This derivation results in a relationship between ω 2D and ω 3D such as that shown in Equation 2.11. ω 3D ≅ (Ptr2ideal / Ptr1) ∗ ω 2D (2.11) An additional adjustment in converting from a 2-D to a 3-D flowfield is manipulating the 2-D Axial Velocity Density Ratio (AVDR) into an analogous 3-D Meridional Velocity Density Ratio (MVDR). The AVDR, as shown in Figure 2.12, is widely used to measure the degree to which the flow streamtubes in a 2-D cascade are contracted due to increasing density and decreasing area (Shreiber, 1984). AVDR = (ρ2Vx2) / (ρ1Vx1) = Ax1/Ax2 (2.12) In Equation 2.12, ρ is the density, Vx the absolute axial velocity, Ax is the cross sectional area perpendicular to the axial, and the subscripts (1) and (2) imply the inlet and exit of the blade rows, respectively. The value of the AVDR is normally quoted when listing results from 2-D linear cascades. When applying these results to the prediction of the performance of 3-D annular cascades, the AVDR must be altered so as to apply to the corresponding 3-D annular flow. In this investigation, a new parameter, the MVDR, was developed to account for boundary layer effects in 3-D annular cascades. The development relating the definition of the MVDR to the AVDR is found in Appendix C. Losses such as those due to mid-span dampers, casing and hub boundary layers, vortices between the casing and the rotor tip, and additional secondary losses not present in 2-D linear cascades must be obtained using experimental data from 3-D annular cascades. One approach to obtain these losses is to subtract the analytically calculated profile and shock losses in 2-D linear cascades from the experimentally obtained total loss in 3-D annular cascades. 11PDF Image | Gas Turbine Design Axial Flow Compressors
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