Confined vortex flows with boundary-layer interaction

Axisymmetric flow of an incompressible fluid in a right-cylindrical vortex tube bounded by planar end walls is considered. The mutual interaction of the primary vortex flow field and the end- wall boundary layers is studied by relating the stream function and circulation in these regions. An interaction parameter is defined which determines the magnitude of the influence of the boundary layers on the circulation and mass-flow distributions in the primary flow. These distributions are obtained numerically, primarily as functions of the interaction parameter and the Reynolds number based on the radial flow. Experimental results are interpreted in the light of this theory, and it is concluded that substantial turbulence levels (though somewhat less than estimates made without consideration of boundary-laye r effects) must be assumed to explain the experimental results.