Integral analysis applied to radial film flows

Abstract

Radial thin film flows are obtained by the impingement of circular free liquid jets on surfaces. The surfaces may be in the form of a circular plate, cone or that of a sphere. These flows are governed by the effects of inertia, viscosity, gravity and surface tension. Based on the film Reynolds number and Froude number, a circular hydraulic jump can be obtained in such flows. In this paper a new integral method is proposed for such axisymmetric laminar flows. The boundary layer approximation is used. The equations are solved using a cubic velocity profile, considering the radial hydrostatic pressure gradient in the film flow. In the new approach the coefficients of the cubic profile depend on the pressure gradient and body force terms and are allowed to vary with radial distance. Thus for example, separation can be predicted. The effect of the jet Reynolds number, Froude number and the surface dimension is considered. For flows with the circular hydraulic jump, the region upstream and downstream of the jump is solved separately using the boundary condition at the surface edge.