Spanwise Mixing in Axial-Flow Turbomachines

Flow measurements taken in multistage axial-flow turbomachines suggest that substantial spanwise mixing of flow properties often occurs. In addition, measured blade row turnings often show considerable deviation from two-dimensional cascade theory, particularly in the end-wall regions. An approximate method is presented with which both of these effects can be included in design through-flow calculations. The method is based on inviscid, small-perturbation secondary flow theory. Frictional effects are not directly included but secondary flows caused by annulus wall and blade boundary layers are included in an approximate way. The secondary flow model includes effects of 1) main-stream nonfree-vortex flow, 2) end-wall boundary layers, 3) blade end clearances, 4) blade end shrouding, and 5) blade boundary layer and wake centrifugation. The spanwise mixing phenomenon is modeled as a diffusion process, where the mixing coefficient is related to the calculated spanwise secondary velocities. Empirical adjustments are employed to account for the dissipation of the secondary velocities and interactions with downstream blade rows. The induced blade row overturnings are related to the calculated cross-passage secondary velocities. The nature of the assumptions employed restricts the method to design-point-type applications for which losses are relatively small and significant regions of separated flow are not present.