I. R. Wood

Vertical and lateral turbulent dispersion: some experimental results

The results of an experimental programme designed to investigate turbulent dispersion of a continuous contaminant source in a wide channel are presented. Both two-dimensional vertical dispersion and the determination of the lateral diffusion coefficient are described. The eigenfunction solution to the turbulent diffusion equation, presented in Nokes et al. (1984) and discussed in greater detail in Nokes (1985), is strongly supported by the results of vertical mixing described here. A variety of source locations are examined in this study and the location of the ideal source, predicted by theory, is verified by the experimental results. For the two smooth-bed flows investigated the depth-averaged values of e z , deduced from the rates of lateral spreading of the plume, lie at the lower end of the range of values obtained by other researchers. Considering only the results obtained in wide channels, the authors demonstrate that previously published values of the lateral diffusion coefficient, non-dimensionalized by the shear velocity u * and the flow depth d are independent of all flow parameters except the friction factor f = 8 u * /ū where ū is the mean velocity in the flow. Indeed, above a value of f = 0.055 e z / u * d is also found to be independent of f , and takes a value of 0.134. A brief mathematical analysis of the three-dimensional mixing processes in the near-source region is presented, and utilized to investigate the coupling between the lateral and vertical diffusion processes in this region. Based on these mathematical arguments the experimental results imply that the vertical and lateral diffusion processes are essentially uncoupled in the near-source zone, and thus the lateral diffusivity and longitudinal velocity have similar vertical dependence.

Extensions to the theory of selective withdrawal

Most reservoirs contain stratified fluid and selective withdrawal is used to obtain water with the desired properties. We initially deal with a layered density distribution. The theory for the critical discharge for a single layer and a point sink is reviewed and extended to cover the case where there is gate discharge (a line sink). The theory for the case when the upper layer depth is large and the flow is coming from both layers is reviewed and it is shown that the valve controls the discharge and a virtual control determines the ratio of the discharge in each layer. This virtual control moves further from the valve as the total discharge increases. We determine the position of the virtual control and the criteria for the maximum for two layers when the upper layer is finite and below a stationary layer

On the head-discharge relation of a "duckbill" elastomer check valve

Duckbill-shaped elastomer check valves are often installed on wastewater effluent diffusion systems and stormwater outfalls to prevent baekflow or sea water intrusion. Unlike fixed diameter ports, the jet velocity varies nonlinearly with port discharge flow. A new theory to predict the hydraulic characteristics of a duckbill elastomer check valve (DBV) is presented, and it provides a theoretical basis for the correlation of all DBV hydraulic data. It is shown that a DBV can be considered as a smooth converging nozzle. By modelling the duckbill valve as a two-dimensional rubber membrane, a theory is developed to relate the DBV material properties and flow conditions to the valve deformation. The valve opening area is predicted as a function of the driving pressure head: a linear head-discharge relation is predicted. The predictions are in excellent agreement with ex peri mental data. The derived head-discharge relation can be readily incorporated into a diffuser internal hydraulics code to determine the variation of discharge flow and jet velocity along a multiport diffuser fitted with duckbill check valves.

The behaviour of a single, horizontally discharged, buoyant flow in a non-turbulent coflowing ambient fluid

An integral model of the behaviour of a single horizontally discharged buoyant flow in a coflowing ambient fluid is presented. The usual integral equations for the conservation of mass, momentum and buoyancy flux are used. However, the model differs from those presented previously by using the spread assumption rather than the more usual entrainment assumption and by explicitly forcing the initially gaussian velocity distribution to become a thermal distribution. The position and the form of this transition is determined from laboratory data (Brown [1984], Knudsen [1988]) and field data (Lee and Neville-Jones [1987]). The performance of the model is compared with both laboratory and field data and it reproduces the data for a wide range of cases. A model of this type is essential in gaining an understanding of the range of behaviour of merging plumes (Cheng, Davidson and Wood) and is a preliminary to the understanding of the more general case where the buoyant discharge is ejected at an angle to the flow.

A study of a buoyant axisymmetric jet in a small co-flow

This paper deals with measurements of and an integral model for a buoyant axisymmetric jet in a very small co-flow. The integral model is based on the insights gained from the measurements presented here and other recent experiments, which suggest that the turbulent flow is simply advected and the entrainment is that normal for a jet or plume in a still ambient fluid. General equations for the turbulent flow trajectories are also developed. The predictions of the theory are verilied for the no cross-flow case and the cases where the jet or plume is ejected vertically or horizontally into a very small cross-flow. The results of experiments in which a buoyant jet is released in the same direction as the horizontal ambient flow, show that outside the turbulent region the entrainment velocities can be represented with uniform flow and the appropriate sink. Direct measurement of the strength of the sink allows the transition from weakly- to strongly-advected behaviour to be determined. The departure of the trajectory measurements from the theory also provides information about the transition. The transition location is then compared with recent measurements in which the jets and plumes are ejected vertically into a very small cross-flow.

The axisymmetric and the plane jet in a coflow

The approximate variation of the mean properties in an axisymmetric jet and a two dimensional jet with an ambient coflow in an infinite duct have been determined using the excess momentum equation and an entrainment function. The turbulent velocity flux, consisting of a portion due to the excess jet velocity and a portion due to the turbulent coflow velocity, is carried by a velocity approximately equal to the top hat velocity. The entrainment into this flow is driven by the excess jet velocity and the entrainment function varies to allow for the change in entrainment from the strong jet to the weak jet. The entrainment constant is determined from the data of Nickels and Perry [14] for the axisymmetric case and the data of Bradbury and Riley [6] for the two dimensional case. All coflow experiments are in ducts and the effect of the duct is explored for the axisymmetric case. This paper is a prelude to the study of a buoyant jet in a coflow and a buoyant jet in a crossflow.

A New Approach To Predicting The Dispersion Of A Continuous Pollutant Source

A new approach to diffusion of a continuous source has enabled non-uniform conditions to be modelled. The method used is described and some results given.

The Behaviour of Merging Buoyant Jets

Most outfalls consist of a long length pipe with a diffuser at the seaward end. The diffuser is a continuation of the outfall pipe, but it has ports on either side through which the effluent is discharged. The flow region close to the pipe is extremely complicated particularly at either end of the diffuser. However, an approximate solution to the dilution may be obtained by considering an infinite array of equally spaced merging buoyant jets. This solution is verified for the single buoyant jet and buoyant slot jet and gives reasonable results for the dilutions and the trajectories from experiments for merging buoyant jets. This is the first stage of understanding the behaviour of merging jets in a crossflow and some results are presented in the crossflow case.

The effect of an intermittant flapping motion on the properties of merging plumes

Experiments with merging buoyant jets revealed the existence of an intermittent flapping motion in the flow trajectory. The flapping commences beyond the point where the initially axi-symmetric buoyant jets merge to form a plane plume. The size and relative positions of large-scale vortices on either boundary of the plane plume determine whether the flapping flow state occurs. The effect of the flapping on the short term timeaveraged flow properties was measured and the flapping was found to increase the spreading rate and also change the shape of the concentration fluctuation distribution in the plane plumes. The intermittent presence of flapping in plane plumes is shown to be the cause of widely accepted differences between plane and axisymmetric plumes. The new findings on the flapping behaviour were used to improve an integral model which describes merging buoyant jets.

Merging buoyant discharges in an ambient current

The results of a preliminary experimental investigation into the merging of buoyant discharges in an ambient current are presented. Trajectory and dilution data from the merging buoyant flows are reported. The investigation shows that the conditions at the point of merging have an important effect on the behaviour of such flows. It is also shown that if there is an ambient current there may be some advantage in designing an outfall such that the buoyant flows merge.