K. H. M Ali and K. Whyte

Department of Civil Engineering, University of Liverpool

Brownlow Street, Liverpool L69 2DQ

Tel: 0151 794 5234

Fax: 0151 794 5218

E-mail: k.h.m.ali@liv.ac.uk

Abstract: The paper presents an experimental investigation of the circulation and mixing produced by buoyant and heavy radical jets discharging into a circular reservoir. Time variations of surface velocities and water densities, at different levels, were obtained.

??An approximate analysis is also given for calculating the entrained discharge and the time variation of the level of the interface.

In the United Kingdom, water supply reservoirs are usually isothermal in the winter and the spring (Tolland, 1977). The circulation is usually generated and maintained by wind action, excluding the effects of inlets and outlets. Warmer weather results in the surface layers becoming warmer and less dense and therefore floating on the cooler water underneath. Stratification is usually stable by May or June provided wind action is not very strong (Tolled, 1977). The water column is divided into three layers: the epilminion which is the upper layer of warm water which is usually kept in circulation by the wind, the thermocline which is a layer in which the temperature decreases rapidly with depth. The third layer, the hypolimnion is usually cool and relatively static. Decomposition of organic matter reduces the store of oxygen available in the hypolimnion resulting in deoxygenation and deterioration of water quality. These problems may be overcome by using inlet jets to artificially overturn reservoirs so that they become isothermal with their bottom water oxygenated.

The paper gives a summary of some of the experimental results obtained at Liverpool. These represent a small part of a longstanding research program (Ali et al, 1978, 1981, 1983, 1997). Also given is an approximate method for predicting the circulating discharge and the time variation of the interface's level.

Figures 1 and 2 show dye mixing and velocity distributions in a homogenous reservoir produced by a radial jet. This circulation is related to that produced by a tangential jet in Figure 3. The small element of entrained water in the reservoir is (Figure 3c). The corresponding entrained discharge is

                                            (1)

where = entrained velocity given by

                                            (2)

where h = thickness of moving layer, V = local peripheral velocity, = density of heavy layer, = density of freshwater, g = acceleration due to gravity and c = constant to be obtained experimentally. Substituting for W_e from Eq. (2) into Eq. (1) gives

                                            (3)

We need to integrate Eq. (3) in the r and directions.

Ali and Pateman (1981) obtained the following relationships for the circulation in a homogenous reservoir:

                                            (4)

                                            (5)

                                            (6)

where y = normal distance from the wall, y_m = value of y where V = 0.5 V_m, V_m = maximum peripheral velocity at a given section, V_j = jet velocity and R = radius of the reservoir. The parameter are functions L/h and are given in Ali and Pateman (1981), L = diameter reservoir.

Substituting from Eqs. (4), (5) and (6) into Eq (3) and conducting a double integration, we obtain

                                            (7)

Equation (7) can, also, be written in the following form:

                                            (8)

where Q_j = inlet jet discharge Q_e = entrained discharge, d_o = diameter of inlet jet and F = densimetric Froude number given by

                                            (9)

Using Eq(7) together with the continuity equation, Ali (2000) obtained:

                                            (10)

where t = time from start of jet action. Equation (10) can be used to calculate the change in level of the interface with time.

A circular model reservoir 2.0m in diameter was used (Figure 4). The reservoir's wall was 0.5m high. The outlet was in the form of an open channel 0.3m wide with an end weir 0.4m high. A circular jet 15mm in diameter was positioned at 0.05m and 0.37m above the bed to act either as a wall jet or a surface jet. The model is shown in Figure 4. Also shown are the locations of the measuring stations. Velocity of the jet was measured volumetrically. Fluorescence dye was introduced through the radial jet in order to enhance flow visualisation. Water densities were measured using a PAAR meter.

Two types of experiments were carried out:

(1) Freshwater was introduced through the radial surface jet into a reservoir filled with saline water of a different density, and

(2) Saline water, of different density, was introduced through a radial wall jet discharging into a reservoir filled with freshwater.

For each experiment, water densities were measured at the various stations at various times. A video camera was used to track the movement of surface floats. The video film was later analysed to obtain the surface velocity distribution at different times.

Figures (5a) and (5b) show variation of surface velocity with distance from the jet (measured along the line ABCDKJI).

Decay in velocity with distance is very marked between C and D. There is a general reduction in velocity with time. Figures 6a - 6d show changes in density profiles with time at section G for a surface jet and for a heavy wall jet.

Using the results of the experimental, changes in the position of the level of the interface were obtained and are plotted in Figure 6. Figure 7 verifies Eq. (10) and gives an average value of C = 6.9x10^-4 for a surface jet and C = 3.8x10^-3 for a heavy wall jet. Figure 7 shows that a wall jet is much more effective in entraining reservoir water than a surface jet.

(1) A heavy three-dimensional wall jet is more efficient in mixing a stratified reservoir than a surface jet having the same densimetric Froude number.

(2) Mixing of a stratified reservoir, by a jet, is dependent on the reservoir's aspect ratio, the jet's dimensionless time ratio and densimetric Froude number (Eq. 10).

It is with great pleasure for the authors to acknowledge the help of Stuart Taylor in conducting the experiments described in this paper.

Ali, K H M, Hedges, T S and Whittington, R B, “Scale model investigation of the circulation in reservoirs”, Proc. ICE, Part 2, 1978, March, pp 29 - 161.

Ali, K H M and Pateman, D, “Prediction of the circulation in reservoirs”, Proc. ICE, Part 2, June, 1981, pp 427 - 461.

Ali, K H M, and Jaefar-Zadeh, M R, “Circulation and mixing in a stratified reservoir”, Jour. of Hyd. Res., Vol. 27, No 5, 1989, pp 683 - 697.

Ali, K H M and Karim, O A, “Investigation of jet-forced water circulation in reservoirs”, Proc. ICE Wat., Marit. And Energy, 1997, 124, March, pp 44 - 62.

Tolland, H G, “Destratification/aeration in reservoirs”, WRC Technical Report, TR50, August, 1977, 37 pages.