A method is presented for calculating the design point efficiency potential of a multistage compressor. Design parameters that affect the efficiency are vector diagram shape, aerodynamic loading level, aspect ratio, solidity, clearances, airfoil maximum and edge thicknesses, annulus area contraction, Mach number, Reynolds number, airfoil surface finish, and part-span shroud placement. Losses associated with off-design operation, blading unsuited to the aerodynamic environment, or poor hardware quality are not considered. The loss model is constructed using rational fluid-dynamic elements, such as boundary layer theory, whenever feasible in an attempt to minimize empirical influences, although some empiricism inevitably enters. The resulting formulation is found to be in satisfactory agreement with multistage compressor experience that covers a wide range of the design parameters.
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.
An approximate method for including the effects of sweep and dihedral when designing axial-flow turbomachinery blading is presented. Blades are said to have sweep when the flow direction is not perpendicular to the spanwise direction, and dihedral when the blade surface is not normal to the surface of an end wall. It is shown that blade cross sections should be cut by sectioning surfaces that are tangent to the axisymmetric stream surfaces of the meridional flow, but that these cross sections should be viewed by looking parallel to the axis (stacking line) of the blade. When this is done the observed blade shapes and flow angle distributions are most nearly comparable to those obtained from two-dimensional cascade experiments and analyses. This approach is found to be inadequate at the blade ends, however, and an analytical method is presented which yields a wall correction for blade rows of semi-infinite span. For all practical variations of the parameters involved in the design of axial-flow compressors and turbines, the wall correction can be conveniently calculated from a set of approximate formulas presented in this paper. The importance of an adequate axisymmetric solution (method not presented herein) as the first step in the analysis is pointed out; many of the effects of sweep and dihedral are traceable to the skewness of the force and thickness-blockage fields of the axisymmetric model. Finally, the paper summarizes the blading design procedure and applies the present work within the framework of the overall design. As an example, the method is used to design a swept cascade; previously reported test results for a similar cascade tend to substantiate the validity of the design procedure, but experimental results for a direct comparison with the theory are not available.
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