A Simple Approach to an Approximate Two-Dimensional Cascade Theory

The following simple approach to an approximate theory of incompressible two-dimensional flow past cascades, Fig. 1, is based on the so-called singularity method, in which the blade sections are replaced by sheets of vortexes, sources and sinks, and the flow induced by these singularities is calculated. The condition that the flow must be tangential to the blade surface, sometimes termed as the tangency condition, leads to a relation between the geometrical shape of the blade sections (camber and thickness), the cascade parameters (solidity and stagger angle), and the singularity distributions along the mean camber lines. As soon as these distributions are known, the pressure distribution and the lift may be determined. The calculation of the velocities at the blades is the most laborious portion of the whole problem. It has been carried out by various authors [1–4], with different mathematical methods. In this paper, a short, simple method of calculating the velocities induced by the singularities will be described. This approach has already been applied by others [5, 6], in less elaborate form.