Analytical and experimental studies on stratified flows

Abstract

Stratified flows are the fluid motions caused or influenced by the density differences. The density currents, the intrusion of salt wedge, the gravitational circulation, diffusion and dispersion of pollutants in estuaries and thermally elevated water layers in lakes, rivers and estuaries are the stratified flow problems that are of interest to hydraulic engineers. These problems of stratified flows are of concern to man as they affect his environment. The thesis presents theoretical and experimental studies on the following aspects of stratified flows: A. The length and shape of the arrested salt wedge, B. Circulation and salinity distribution in coastal inlets, C. Spread and temperature decay of buoyant jet flows. The governing equations of motion for the case of arrested salt wedge involve interfacial, bed and wall shear terms. No proper shear laws are available for evaluation of shear terms in these equations. So by assuming the flow in the upper layer to be smooth turbulent and in the salt wedge to be laminar and making other reasonable assumptions, the shear terms in the proposed model have been evaluated. By making use of these evaluated shear terms, the governing equations of motion along with the continuity equation have been reduced to a single ordinary differential equation. The lengths and shapes of arrested salt wedges have been obtained by numerical integration. A noteworthy contribution of the present work is that it eliminates the evaluation of interfacial friction by a separate procedure. The mathematical model developed by Hansen and Rattray based on Pritchard’s equations for a coastal plain estuary has been analysed to study the circulation and salinity distribution in coastal inlets with constant width and depth. Numerical solutions of the basic equations have been obtained without placing any restriction on Rayleigh numbers. The circulation and salinity are depicted graphically. The effect of higher Rayleigh numbers is to increase the vertical advection, making the salinities in the upper and lower layers more uniform with a sharp halocline near the mid?depths. A brief review of the existing literature on horizontal discharge of surface and submerged buoyant jets is presented. The review indicates that the effects of lateral confinement (B/D? effect, where B is the width of the ambient flume and D? is the diameter of the nozzle) and Reynolds number have not been studied so far. Hence an experimental study of the effect of B/D? and Reynolds number on the horizontal and vertical spread and the associated temperature decay of the warm water circular jet has been taken up. Based on this study, the following conclusions are drawn. The temperature profiles are similar in lateral and vertical directions until the jet reaches the side walls. After some distance from the point where the jet reaches the walls, the lateral temperature profiles become uniform. The distance at which the jet reaches the wall and the distance at which the lateral temperature profiles become uniform are functions of B/D? and the densimetric Froude number. The effect of lateral confinement is in general to reduce the temperature decay. The lateral spread is more for jets discharging into confined ambient basins than for jets discharging into infinitely wide basins. The effect of confinement seems to be less on the vertical spread of the jet. The thickness (in vertical direction) of jet attains a constant value after some distance and remains constant for some further distance from the nozzle; this distance depends again on B/D? and densimetric Froude number. A very important conclusion which is useful in modelling the buoyant jet flows is that the Reynolds number does not seem to have any effect in the range of 5390 to 21000. A comparative study has been made of surface and submerged buoyant jets by conducting experiments for two submergences of the nozzle and a single ratio. It is concluded that the lateral spread is less for the submerged jets and is independent of submergence until the jet reaches the surface. Once it reaches the surface, the spread is more for smaller submergence ratios. The vertical spread is more for submerged jets than for surface jets. Generalised equations considering the effect of B/D? and submergence are given wherever applicable. It is felt that these equations are of use to hydraulic engineers in the design of thermal power plant outfall structures.