Shock wave structures ahead of nonuniform fan cascades

Abstract

We study shock wave structures (SWS), consisting of shock waves and expansion waves between them, that occur in supersonic flow past nonuniform fan cascades when the velocity component normal to their front (“axial” component) is subsonic. The cascade nonuniformity is due to the scatter in the setting angles of identical blades, either sharp or blunt. A result of the uniformity is the generation of combined noise, whose frequencies are much smaller than the fundamental frequency of the uniform cascade, and slower nonlinear SWS attenuation. The accurate and fast “simple wave method” and “nonlinear acoustics approximation”, together with numerical algorithms for integrating Euler equations on overlapping grids (in calculating flow past blunt edges) and on SWS-adapted grids, are applied to determine the “guiding” action of nonuniform cascades and to describe the SWS evolution. The application of the Fourier analysis gives the sound field spectrum. The use of blades with rectilinear initial regions of the “backs” for reducing supersonic fan blade noise is efficient only at small (less than 0.25°) scatter in the setting angles. The shock wave structures attenuate more rapidly ahead of nonuniform cascades composed of blunt blades than ahead of those with sharp blades. For uniform cascades the blade bluntness effect is not large.