An analytical study of a confined viscous vortex

A composite solution for the flow field of a three dimensional, incompressible laminar, viscous vortex confined inside a conical converging nozzle is presented. This model is used to study the strong mainstream boundary layer interaction that occurs in confined vortex flows. The confined vortex flow field is divided into mainstream and boundary layer regions. A particular class of solutions of the general equations of motion is used to represent the vortex flow in the mainstream region. That is, the tangential velocity in the mainstream region is assumed to be of the form W = T(e)/R. Velocity and pressure profiles from the mainstream region are used as boundary conditions to generate an integral momentum solution in the boundary layer region. The mainstream boundary layer interaction is modeled by iteratively matching the transverse velocity at the common edge of the two regions, while conserving the mass flow and radial momentum of the total system at all points along the length of the nozzle. The results for the velocity profiles and the boundary layer growth obtained by separately considering each region of the flow field are presented and discussed. The velocity and pressure profiles obtained from the composite solution are compared with experimental data from previous investigations --Abstract, page ii