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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Previous authors have considered the unsteady lift of a flat-plate (zero-cambered) airfoil travelling through sinusoidal gusts. The present paper extends the analysis to cambered airfoils with angle of attack moving through both longitudinal and transverse gusts. Closed-form analytical solutions are obtained. The results are used to calculate the unsteady lift on a blade moving through periodic wakes in an axial-flow turbomachine. Knowledge gained by this analysis clearly indicates design trends to obtain minimum lift fluctuations. Since the interference effects of neighboring blades are ignored in this analysis, the conclusions on turbomachinery are strictly valid only for cascades with low solidity.