INTEGRAL ANALYSIS APPLIED TO RADIAL FILM FLOWS

Radial thin film flows are obtained by the impingement of circular fre e liquid jets on surfaces. The surfaces may be in the form of a circul ar plate, cone or that of a sphere. These flows are governed by the ef fects 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 pro posed for such axisymmetric laminar flows. The boundary layer approxim ation is used. The equations are solved using a cubic velocity profile , considering the radial hydrostatic pressure gradient in the film flo w. In the new approach the coefficients of the cubic profile depend on the pressure gradient and body force terms and are allowed to vary wi th radial distance. Thus for example, separation can be predicted. The effect of the jet Reynolds number, Froude number and the surface dime nsion is considered. For flows with the circular hydraulic jump, the r egion upstream and downstream of the jump is solved separately using t he boundary condition at the surface edge. (C) 1998 Elsevier Science L td. All rights reserved.