An approximate blade-element design method is developed for compressible or incompressible nonviscous flow in high-solidity stators or rotors of axial-, radial-, or mixed-flow compressors, turbines, or two-dimensinal cascades. The method is based upon channel-type flow between blade elements on a specified surface of revolution that lies between the hub and shroud (casing) and is concentric with the axis of the compressor turbine. The blade elements is designed for prescribed velocities along the blade-element profile as a function of distance along meridonal lines on the surface of revolution. Two numerical examples are presented: (1) the design of a blade-element profile for a plane two-dimensional cascade in compressible flow with the prescribed velocities along the profiles; and (2) the design of a blade element for the impeller of a mixed-flow centrifugal compressor.

The external wave drag of bodies of revolution moving at supersonic speeds can be expressed either in terms of the geometry of the body, or in terms of the body-simulating axial source distribution. For purposes of deriving optimum bodies under various given condtions, it is found that the second of the methods mentioned is the more tractable. By use of a quasi-cylindrical theory, that is, the boundary conditions are applied on the surface of a cylinder rather than on the body itself, the variational problems of the optimum bodies having prescribed volume or caliber are solved. The streamwise variations of cross-section area and drags of the bodies are exhibited, and some numerical results are given. The solutions are found to depend upon a single parameter involving Mach number and radius-lenght ration of the given cylinder. Variation of this parameter from zero to infinity gives the spectrum of optimum bodies with the given condition from the slender-body result of the two-dimensional. The numerical results show that for increasing values of the parameter, the optimum shapes quickly approach the two-dimensional.

A technique is developed for the application of a channel design method to the design of high-solidity cascades with prescribed velocity distributions as a function of arc length along the blade-element profile. The technique applies to both incompressible and subsonic linearized compressible (ratio of specific heats equal to -1.0), nonviscous, irrotational, fluid motion. An impulse cascade with 90 degree turning was designed for incompressible flow and was tested at the design angle of attack over a range of downstream Mach number from 0.2 to choke flow. To achieve good efficiency, the cascade was designed for prescribed velocities with maximum allowable blade loading according to limitations imposed by considerations of boundary-layer separation.