Thin film flows : integral methods and experiments on the circular hydraulic jump

Abstract

This work is an integral analysis of radial and planar thin liquid film flows and an experimental study on the circular hydraulic jump on a circular horizontal plate. These thin film flows are obtained either by the impingement of circular free liquid jets on surfaces for radial case and for example by liquid issuing out of a slot on a horizontal plate. We derive integral equations for the momentum and energy for general axisymmetric flows and planar two dimensional flows from the governing equations for thin film N laminar flows. The boundary layer approximation is used. The equations are solved using a velocity profile for the film flow, for the free surface velocity and the film height for regions both upstream and downstream of the circular hydraulic jump. The efFect of the jet Reynolds number, Froude number and the plate length on the film height upstream and downstream of the jump is considered. Further, a relation for the momentum� balance across the jump taking into account the wall shear stress and the finite length of the jump region for both uniform and nonuniform velocity profiles has been derived. It is possible to estimate the efFect of the wall shear stress and the velocity profile on the height ratio upstream and downstream of the hydraulic jump. Experiments aimed at the study of the radial film flow and the accompanying circular hydraulic jump on a horizontal plate, formed by the impingement of circular laminar and turbulent free liquid jets are carried out. The hydraulic jump radius, separation bubble length and the liquid film thickness are measured for various jet flow rates, plate material and plate edge boundary conditions. Flow visualisation studies using high speed still camera are carried out to study the wave structure both upstream and downstream of the hydraulic jump and the transition from laminar to turbulent flow of the thin liquid film before the hydraulic jump.