Cascades with arbitrary end wall contraction

Abstract

A linearised theory for the steady flow of an incompressible, inviscid fluid through a linear cascade of aerofoils set in a channel with contracting or expanding walls is developed first for uniform, potential, flow at inlet and then for a shear flow to represent thick boundary layers near the endwalls. The results are compared with earlier work in which the effects of endwall contraction or expansion are expressed in terms of the Axial Velocity Ratio, i.e. the ratio of downstream and upstream axial velocities at mid-span, and it is shown that these earlier theories are in substantial error because they neglect the effect of the variation of circulation along the aerofoils and the velocities induced by the trailing vortices. Experimental studies of a cascade of NACA 0012 symmetrical uncambered aerofoils at a small deflection and pitch-chord ratio in a porous endwall tunnel, in a tunnel with contracting endwalls, and also with a substantially thickened endwall boundary layer are described and compared with the theory.