Inviscid Flow Through a Cascade of Thick, Cambered Airfoils: Part 1—Incompressible Flow

Abstract

Conformal mapping is one means of determining the inviscid, incompressible, two-dimensional flow through a cascade of airfoils. The complex potential flow about a unit circle is a convenient picture plane. The form of mapping function required to transform this circle to thick, cambered airfoils in cascade is derived and then compared with the analogous mapping function for the isolated airfoil. Two analytical mapping functions that conform to this form are derived. One, which is in differential form and so necessitates numerical integration to yield the profile shape, has seven free parameters giving the solidity and stagger of the cascade and the camber and leading and trailing edge radii of the blading: the two remaining parameters control the thickness and camber distributions. The second analytical mapping function is in an integral form but has only five degrees of freedom corresponding to solidity, stagger, camber, leading and trailing edge radii in its basic form. Due to its simplicity, the second of these mapping functions is useful in determining basic features of the flow through cascades. These features are illustrated by some results.