Withdrawal Layer Thickness Research Articles

Bottom Withdrawal of Viscous Stratified Fluid

A theoretical investigation was conducted to predict the fundamental behavior of nondiffusive, viscous flow to a sink located at the bottom of a density-stratified reservoir. The governing partial differential equation was transformed into an ordinary differential equation by utilizing a similarity technique. Numerical and series solutions were obtained and predict a flow field characterized by a withdrawal layer near the reservoir bottom moving toward the sink bounded above by a narrower reverse flow with a much smaller volumetric discharge. The theoretical development further indicates that normalized profiles of horizontal velocity, vertical velocity, and horizontal shear are similar, i.e., have shapes that are independent of the fluid and flow parameters. Mathematical expressions were developed for various aspects of the fluid motion such as horizontal and vertical velocity, horizontal shear, withdrawal layer thickness, and the distribution of flow within the withdrawal layer.

Two-dimensional sink flow of a stratified fluid contained in a duct

A reservoir is assumed to be filled with water which has a linear variation of density with depth. The geometry of the boundaries is simplified to a parallel walled duct with the line sink at the centre of the fluid. The primary focus is on partitioning the flow into distinct flow regimes and predicting the withdrawal-layer thickness as a function of the distance from the sink; the predictions are verified experimentally.For fluids with a Schmidt number of order unity, the withdrawal layer is shown to be composed of distinct regions in each of which a definite force balance prevails. The outer flow, where inertia forces are neglected, changes from a parallel uniform flow upstream to a symmetric self-similar withdrawal layer near the sink. For distances from the sink smaller than a critical distance, dependent on the flow parameters, inertia forces become of equal importance to buoyancy and viscous forces. The equations valid in this inner region are derived. Using the inner limit of the outer flow as the upstream boundary condition, these inner equations are solved approximately for the withdrawal-layer thickness by an integral method. The inner and outer variations of δ, the withdrawal-layer thickness, are combined to yield a composite solution and it is seen that the inclusion of inertia forces yields layers thicker than those obtained from a strict buoyancy-viscous force balance. In terms of the inner variables the only parameter remaining is the Schmidt number.Laboratory experiments were carried out to verify the theoretical conclusions. The observed withdrawal-layer thicknesses were shown to be closely predicted by the integral solution. Furthermore, the data could be represented in terms of the inner variables by a single curve dependent only on the Schmidt number.

MANAGEMENT OF WATER QUALITY IN RELEASES FROM SOUTHWESTERN IMPOUNDMENTS1

ABSTRACT. The objective of this investigation was to determine the selectivity of withdrawal which is possible in southwestern reservoirs. Two stratified flow solutions were examined to test their applicability under field conditions. Although both appeared capable of accurate prediction of the outflow velocity profile, the Bohan‐Grace solution, which required less input data, was utilized to predict the chemical constituents of single and simultaneous releases from several southwestern impoundments. Prediction of outflow water quality was within fifteen percent for southwestern reservoirs as shallow as fifty‐five feet. The withdrawal layer thickness for the subject Texas impoundments included the entire hypolimnion or epilmnion depending on outlet location. The sensitivity of the velocity profile to seasonal changes, reservoir discharge rate and withdrawal port dimensions also is illustrated.