Abstract
Cavity flow past an obstacle in the presence of an inflow vorticity is considered. The proposed approach to the solution of the problem is based on replacing the continuous vorticity with its discrete form in which the vorticity is concentrated along vortex lines coinciding with the streamlines. The flow between the streamlines is vortex free. The problem is to determine the shape of the streamlines and cavity boundary. The pressure on the cavity boundary is constant and equal to the vapour pressure of the liquid. The pressure is continuous across the streamlines. The theory of complex variables is used to determine the flow in the following subregions coupled via their boundary conditions: a flow in channels with curved walls, a cavity flow in a jet and an infinite flow along a curved wall. The numerical approach is based on the method of successive approximations. The numerical procedure is verified considering a body with a sharp edge, for which the point of cavity detachment is fixed. For smooth bodies, the cavity detachment is determined based on Brillouin’s criterion. It is found that the inflow vorticity delays the cavity detachment and reduces the cavity length. The results obtained are compared with experimental data.
Highlights
The theoretical study of cavity flows is usually based on the model of ideal liquid with the assumption that the liquid is incompressible, inviscid and irrotational
The exception is flows with a constant vorticity, for which the velocity potential can be introduced in the form of a superposition of a potential vortex-free flow and a flow generated by a single vortex
A general approach to the solution of steady cavity flows in the presence of an inflow vorticity is presented
Summary
The theoretical study of cavity flows is usually based on the model of ideal liquid with the assumption that the liquid is incompressible, inviscid and irrotational. We investigate how the vorticity generated by the fluid viscosity in the boundary layer may affect the position of cavity detachment. For this purpose, we apply the methodology [7], which allows one to reduce the problem of a flow with a continuously distributed nonuniform vorticity to a set of problems of vortex-free potential flows related to one another via boundary conditions that account for the vorticity of the original flow.
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