A Prandtl–Batchelor model of flow in the wake of a cascade of normal flat plates

Abstract

The steady large-Re flow through a cascade of normal flat plates is considered in the limit of small blockage ratio. Evidence is presented suggesting the existence of a branch of Prandtl–Batchelor solutions comprising two symmetric inviscid regions, each with constant vorticity, surrounded by thin shear layers which enable smooth matching with the external flow. The wake length is proportional to the cascade half-width. The solutions are of particular note in that they constitute non-unique solutions of the system, i.e. a bifurcated branch. The calculation requires however the postulation of an infinite sequence of small secondary vortices near the plate's rear stagnation point; elucidation of the implied structure is seen not to be possible without full Navier–Stokes computation.