The numerical solution to the governing equations predicts density profiles at successive time steps during mixing, given the initial density profile, the area-depth ratio for the impoundment, the heights of inlet and jet discharge tubes, and the jet outlet and diameter. 50m Measured and simulated temperature profiles for FWPCA field experiment at Lake Vesuvius Measured and simulated temperature profile for FWPCA field experiment at Lake Boltz Simulated density profiles for “Run No.
CHAPTER 1
Attempts have thus been made to improve the quality of the water while it is in the excavation. Water was pumped from the lower part of the collection point and sprayed into the upper area.
CHAPTER 2
In addition to the gross features of the pumping system described above, several other phenomena can affect the density structure of the enclosure. Since the only influence on the fill density structure to consider is the pumping system, the problem is an initial value problem.
REGION 2
There is no transport of fluid from the jet or withdrawal layer (Region 2) to the collection site (Region 1) between elevations D and E. Selective withdrawal creates the negative transport from the collection site between elevations E and F. The specific shape of the q distribution in this . zone is given in Sect. There is no additional transport between regions from the top of the retraction layer, F, to the surface, G. The integration of q over the retraction layer, E to F, gives -Q.,.
These changes do not affect the similarity solution for the velocity distribution across the sampling layer, but provide new estimates of layer thickness. A value for k2 of the order of 10 is assumed. • These two values for the thickness of the removal layer are assumed to limit the area of the growing layer.
CHAPTER 3
Such a tracer represents a dissolved chemical or biological substance that has little effect on the density of the solution relative to the effect of temperature. The vertical profile of the tracer concentration at the start of pumping can have any shape. The calculation technique requires few adjustments to handle tracer profiles, because all changes in the tracer concentration profiles are due to the same local displacements calculated for the density profile (with the exception of the calculated concentration).
The discontinuities in the slope of the tracer profiles during mixing are due to the fact that the tracer concentration in the fluid discharged from the fill stream at the level of neutral motion is not the same concentration as exists in the ambient fluid at that height. These discontinuities are attenuated in the lower closure regions as the neutral cruise level occurs at higher altitudes. The simulation technique was developed under the assumption that the fluid density is a linear function of salt concentration or temperature (see Sect.
That is, the temperature of the liquid delivered to the fill from the current of this height was not the temperature of the ambient liquid. A more useful approximation to the situation that exists when feedback is possible uses the simulation developed for a non-reacting tracer.
CHAPTER 4
The positions of the extraction tube and jet discharge tube in the tank were changed. In most of the experiments, the jet tube was placed near the bottom of the tank and the extraction tube was above it, near the surface. The inlet and outlet pipes are directed along the longitudinal center line of the tank near one end or at the center (Fig. 4. l.
The shape of the density-depth profile was dependent on the way in which the tank was filled. Stratification for many of the experiments in the 2-meter tank was accomplished by a technique that allows continuous filling (Fig. 4. 3. A mass balance for the well-mixed tank shows that, if the discharge of tap water into tank one is -half of the discharge from the tank, the resulting concentration c will vary linearly in time from c to c1 • This discharge.
A second method was found to be more effective. The tank was divided into two by a temporary dam. On one side was added the amount of salt required to produce a salt solution of the maximum density.
ELEVATION
Since each tank was equipped with an instrument carriage mounted on rails for longitudinal traverses, the mixing plate was attached to the carriage with a single vertical strut (Fig. 4. 5. The plates were about one centimeter shorter in length than the widths of tanks with which they were used i. The plate was moved at approximately 30 em/sec in the case of depths of the order of 40 centimeters and at approximately 10 em/sec in the case of depths of the order of 20 centimeters.
After the plate was dragged through the two-layer system, the tank was left undisturbed for two to five hours to allow for turbulent mixing. The salt solutions were made using tap water and Morton Culinox Food Grade Salt 1199911• The value of the density of the liquid in grams/milliliter was derived from the salt concentration and temper-. The concentration of the salt solution was determined by measuring the conductivity of the liquid with conductivity probes calibrated with a set of standards.
The electrodes were of the same size and spacing, but they were connected by short pure platinum wires, which were silver soldered to copper wires, which extended to the electrical connector at the top of the probe. Electrodes were first cleaned in chromic-sulfuric acid and platinized in standard fashion (44).
LONGITUDINAL SECTION
CROSS SECTION
Platinization was repeated during the course of the investigation whenever reduced sensitivity was detected. No difference in the quality of performance was observed between the two types of probes. The conductivity measurements were recorded by means of a two-channel Sanborn 150 recorder with 1100 AS Carrier Pre-Amplifier.
The probes were connected to the recorder through an external half-bridge circuit as shown in fig. As the time between successive measurements of the concentration profile in the tank was often hours, readjustment of the recorder's bridge was occasionally necessary. After each profile measurement, the baseline or lowest concentration to which the probe had been calibrated was checked.
The probe was held by a small clamp which was attached to a vertical walking scale with a nominal reading of ± 0. Vertical concentration profiles were measured by fixing the probe at uniform vertical intervals and recording the conductivity reading.
TO PROBE
SA NBORN INTERNAL
EXTERNAL HALF- BRIDGE
CIRCUIT
CHAPTER 5
Mixing was achieved by a barge-mounted pumping system that pumped water near the bottom of the lake and discharged it horizontally near the surface. The mixing experiment at Boltz Lake was accompanied by observations of natural changes in the stratification of a similar-sized lake nearby. Although field experiments do not provide all the boundary conditions and closed system assumptions that underlie the simulation technique, the simulation was used to mix Vesuvius and Boltz lakes.
Similar results were noted for some laboratory experiments discussed in Chapter 4. The validity of the simulation technique cannot be sufficiently verified from these two experiments, although the effects of the closed system boundary condition and one-dimensional aspects of the simulation model can be observed. Simulated density profiles from the height of the jet to the surface are shown in Fig. In the case of the field experiments shown, the effects of the environment outside the impoundment may be responsible for the lack of agreement.
Coupling the simulation technique with a simulation of the reservoir heat budget can provide closer agreement with the field measurements. Better agreement with the laboratory experiment used for comparison may require modification of the simulation technique to.
CHAPTER 6
An initial density-depth profile which is linear allows a generalization of the pumping system parameters and the closure response. This can be demonstrated more rigorously by examining the governing equations of the simulation model. The enclosure width and the distance from the intake to the enclosure boundary are related to S indirectly.
Each such time history of mixing is a function of the initial densimetric Froude number, F, and the plume parameter, P. An example of the results of a simulated mixing experiment in generalized form is shown in Fig. 6pgd. The backwater energy is calculated at regular intervals during the simulation of the mixing process.
The results of the simulated mixing experiments in a generalized form provide some guidelines for the design of efficient pumping. The simulation results do not consider the effect of the shape parameter S on the mixing process.
CHAPTER 7
The simulation technique developed in Chapter 2 predicts the time history of the density profiles in an impoundment which is mixed by a pumping system. The deposit's response to the pumping system is determined by the transport of liquid between these two areas. The simulation model requires as input a description of the starting conditions and of the pumping system.
Comparisons of the results of two field mixing studies with simulation predictions (Chapter 5) were inconclusive. The applicability of the simulation technique to cases of mixing lakes and reservoirs that are clearly not closed systems is discussed in It is possible to apply the simulation technique and generalized results obtained in this study to mixing lakes and reservoirs with pumping systems. with certain limitations.
Application of the generalized results (Fig. 6.12) requires that the densimetric Froude number of the jet is F ~ 3. Laboratory experiments have shown (Chapter 4) that at large values of the shape parameter S there are lateral density gradients into the holdup contrary to the one-dimensional assumption on which it is based simulation model.
