Density Currents in Circular Clarifiers
Scott A. Wells
David M. LaLiberte
Abstract
To understand the effect of density currents
on circular clarifiers, a field study was performed on three uncovered
circular tanks in Oregon during periods of low flow and high surface
cooling. Temperatures were measured as a function of radial position
and tank depth. Meteorological parameters were also measured in
order to compute the surface heat flux from the water surface.
The water temperatures in the tank were often 20 to 30oC
warmer than the equilibrium temperature.
These studies showed that density currents
and temperature inversions were common. Surface temperatures were
often about 1oC cooler than bottom temperatures. The
momentum and suspended solids of the inflow caused a density current
that moved along the clarifier bottom and then rose near the middle
of the tank. In the winter, this density current rose as a result
of the decrease of initial momentum of the inflow, the buoyancy
of the inflow after suspended solids had settled, and the geometry
of the tank. Also, vertical velocities induced by surface cooling
were two orders of magnitude greater than the overflow rate. This
suggests that particles may be kept in suspension by convective
currents.
Key Words
sedimentation, clarifier, temperature, suspended
solids, overflow rate, density currents, convective cooling, heat
loss
Introduction
Design of sedimentation tanks for water and
wastewater treatment processes are often based on the surface
overflow rate (Q/A, where Q is the flow rate and A is the clarifier
surface area) of the tank. This design variable is predicated
on the assumption of uniform unidirectional flow through the tank.
Dick (1982), for example, showed that many full-scale sedimentation
tanks do not follow ideal flow behavior because suspended solids
removal in a clarifier was often not a function of the overflow
rate. Because of uncertainties in the hydrodynamics of clarifiers,
designers typically use safety factors to account for this non-ideal
flow behavior (Abdel-Gawad and McCorquodale, 1984).
Non-ideal flow behavior can be the result of
the following (DeVantier and Larock, 1987; Tay and Heinke, 1983;
Wells, 1990):
Non-ideal flow behavior as a result of temperature
and suspended solids differentials in uncovered, circular tanks
was studied at three locations in Oregon. The magnitude of vertical
velocities induced by surface heat losses was computed and compared
with tank overflow rates and particle sedimentation velocities.
Experimental Methods
Experiments were conducted during the winter
at wastewater treatment plants in Lake Oswego and Bend, Oregon.
Primary and secondary sedimentation tanks were evaluated in Bend,
Oregon. The circular tank in Lake Oswego was functioning as a
chlorine contact chamber rather than its intended design as a
secondary clarifier.
In order to examine the effects of surface
cooling, study periods were chosen coinciding with winter weather
conditions when surface heat losses would be significant. These
conditions were most significant during the early morning hours
when plant flow rates were low and winter cooling was greatest.
All the tanks had a centerwell feed, an inlet
baffle and a perimeter effluent weir. Figure 1 shows a schematic
of the circular tanks, and Table 1 shows physical characteristics
of those tanks. Table 2 shows the five study periods and the average
flow rates, overflow rates, and detention times for each period.
In order to measure the temperature distributions
in these tanks, thermistors at five varying depths were attached
to poles 3.3 m in length at three radial positions in the tank.
Each thermistor was attached to a computer data logger that recorded
temperature continuously during the study periods. The study period
for the Bend primary and secondary sedimentation tanks was between
2 and 3 hours. At the Bend treatment plant for both the primary
and secondary clarifiers, the thermistors had to be removed and
reinstalled into the tank every half hour because of the skimmer
and rake arm rotation. Because the Lake Oswego plant had no skimmer
or rake arms, the study period was continuous over a period of
4 days. The thermistors were calibrated in the laboratory with
a typical error of 0.2oC. Figure 2 shows approximate
locations of the thermistor array in the circular tank.
Table 1 Clarifier tank data (variables named below are referenced in Figure 1).
| Tank parameter | Chlorine contact | Primary clarifier | Secondary clarifier |
| Treatment plant | Lake Oswego | Bend | Bend |
| Tank radius (R), m (ft) | 11.4 (37.5) | 9.9 (32.5) | 12.2 (40.0) |
| Tank inlet baffle radius (rb), m (ft) | 1.2 (4.0) | 2.1 (7.0) | 2.1 (7.0) |
| Depth of inlet baffle, m (ft) | 1.8 (6.0) | 2.4 (8.0) | 2.4 (8.0) |
| Maximum depth at center-well (Hmax), m (ft) | 3.0 (9.9) | 3.5 (11.5) | 4.6 (15.0) |
| Minimum depth at tank edge (Hmin), m (ft) | 2.7 (8.9) | 3.2 (10.5) | 3.5 (11.5) |
| Area, surface, m2 (ft2) | 410 (4420) | 308 (3320) | 467 (5027) |
| Volume, m3 (MG) | 1175 (0.31) | 1035 (0.27) | 1900 (0.5) |
Table 2. Physical and hydraulic data during study periods.
| Parameter | Oswego chlorine contact, 2/3/89-2/7/89 | Bend primary clarifier, 1/21/89 | Bend secondary clarifier, 1/22/89 | Bend primary clarifier, 3/4/89 | Bend secondary clarifier, 3/5/89 |
| Average flow rate, m3/s (MGD) | 0.1 (2.4) | 0.03 (0.6) | 0.04 (0.9) | 0.06 (1.3) | 0.03 (0.7) |
| Overflow rate, m3/m2/day (gal/ft2/day) | 21.7 (533) | 7.4 (182) | 6.9 (169) | 15.3 (375) | 5.5 (135) |
| Inflow temperature, oC | 11.0 | 14.3 | 13.7 | 13.0 | 12.5 |
| Detention time (for entire tank volume), hr | 3.0 | 11.0 | 14.1 | 5.3 | 17.0 |
| Sludge layer thickness, m (ft) | 0 (0) | 0.54 (1.8) | 1.0 (3.3) | 0.54 (1.8) | 1.0 (3.3) |
| Effective Detention time*, hr | 3.0 | 9.3 | 10.6 | 4.6 | 13.4 |
* This is the approximate detention time of the liquid computed by subtracting the volume of the measured sludge layer from the total tank volume.
On-site meteorological data (air temperature,
relative humidity, barometric pressure, solar radiation, wind
direction and speed) were measured to calculate the surface heat
flux in the tanks . Suspended solids measurements were also made
of the inflow and at locations throughout the tank. Details of
this procedure were discussed in LaLiberte (1990).
Experimental Results
Temperature measurements
The inflow to the clarifier could be distinguished
from the colder ambient water by using temperature as a tracer.
The inlet baffle for each tank caused the inflows to enter initially
as an underflow.
Experimental data indicated that surface heat
loss between the tank inlet and outlet caused temperature losses
ranging from 0.5oC to 1.2oC. The inlet tank
water temperature varied from 11oC to 14.3oC,
while the equilibrium temperature (see Appendix A) varied from
-9oC to -30oC during the study periods.
Evidence of thermal inversions was found during each study period.
The first study was performed on the primary
clarifier in Bend on 1/21/89. Well-mixed vertical conditions were
typical for much of the study period since most water temperatures
ranged between 14.6oC and 14.2oC. For about
1.5 hours of the 2 hour study period, temperatures at a depth
of 2.3 m and at a radial distance of 7.6 m were consistently about
0.5oC greater than in other areas of the tank.
For the secondary clarifier on 1/22/89, water
temperatures varied from 13.6oC to 12.9oC.
Again the probe at a depth of 2.3 m and a radial distance of 7.6
m indicated warmer temperatures than all the other probes by approximately
1oC. In order to obtain more information about temperature
inversions, the bottom temperature probes were set at a depth
of 2.7 m during the next studies at Bend.
At Bend on 3/4/89 and 3/5/89 in both the primary
and secondary clarifiers, a characteristic warmer inflow moving
along the tank bottom and rising in the middle of the tank was
observed. Figure 3 shows temperature as a function of depth and
radial position at 5:20 am on 3/4/89 for the primary clarifier.
These data illustrate that the warm inflow rose after the initial
momentum decayed and the suspended solids of about 200 mg/l settled.
This phenomenon was more clearly observed during
the 3/5/89 study on the Bend secondary clarifier, where overflow
rates were less and suspended solids were higher (inflow suspended
solids were about 2000 mg/l) than in the primary clarifier. Figure
4 shows the temperature regime in the tank at 2:46 am on 3/5.
These data show that the inflow temperature
was often warmer than that of the water on the tank surface. The
inlet baffle caused the inflow to enter as a density underflow.
The buoyancy of the inflow became more dominant as solids settled
and momentum diminished. Figures 5 and 6 demonstrate clearly the
warmer bottom temperatures and cooler surface temperatures by
comparing temperature as a function of time and radial position
at depths of 0.1 m and 0.9 m, respectively. The temperatures were
always warmest at the radial position of 7.6 m, and coolest near
the outer walls of the tank. Apparently the inflow rises near
the 7.6 m radial position and then cools along the surface as
it moves outward toward the perimeter. The cool surface water
seemed to plunge near the outer wall since vertical temperatures
near that boundary were of the same magnitude as the surface temperatures.
The study at Lake Oswego was performed between
2/3/89 and 2/7/89. The flow rate and the air temperature during
this period are shown in Figure 7. The coolest air temperatures
coupled with the lowest flow rates resulted in the greatest cooling
potential. Figures 8, 9 and 10 show temperature data from
the Lake Oswego treatment plant's radial chlorine contact chamber
at radial distances of 1.5 m, 2.4 m, and 10 m from the center
of the tank, respectively. This tank had the highest overflow
rates and hence the greatest inflow turbulence. Hence, the inflows
often produced vertically well-mixed conditions. At the position
nearest the outflow located at a radial distance of 10 m, a similar
pattern of warm water at the bottom and cooler water at the surface
was seen. Though temperatures in the bottom layer were generally
1oC warmer than those in the surface layer, this did
not occur at all times.
Heat flux calculations
Using measured meteorological data, the net
surface heat flux was computed during each study. Details of the
calculation technique are shown in Appendix A.
A hydraulic parameter that characterizes the hydrodynamic regime during winter cooling is the Richardson Flux number, f (Turner, 1974). This number is a ratio of the turbulent energy absorbed by buoyancy to that generated by shear. This term is defined as
where : von Karman constant 0.4
: buoyancy flux=
n: net surface heat flux (see Appendix A for calculation procedure)
h: surface layer depth (assumed to be the tank depth)
u*: shear velocity=
U: average fluid velocity=Q/Ac (for this study with radial flow, Ac was the radial cross-sectional area approximated at the midpoint of the tank between the inlet baffle and the outer wall)
fo: Darcy-Weisbach bottom friction factor 0.01
cv: specific heat of water at constant volume 4.186 J/g/oC
: coefficient of thermal expansion of water 10-4 oC-1
g: acceleration due to gravity 981 cm/s2
: density of water 0.9997 g/cm3
at 10oC
For f <0, buoyancy or surface cooling augmented the turbulence in the tank. Whenever f <<-1, turbulence from surface cooling dominated turbulent production. The approximate turbulent velocity scale, ut, associated with this convective mixing, assuming that the production rate of turbulence by buoyancy is B and this is balanced by the dissipation of turbulence, u3t/h (Turner, 1974), could be estimated as
In a radial tank, the magnitude of the inflow
velocity decreases rapidly from the inlet baffle to the tank perimeter.
Hence, the turbulence induced by the inflow and boundary shear
has less and less importance away from the inlet baffle. If the
order of magnitude of thermally induced vertical mixing is greater
than the overflow rate, particle sedimentation could be significantly
affected.
Table 3 provides a summary of the recorded
meteorological data and calculated hydraulic parameters for the
5 study periods. The large negative value of the net surface heat
fluxes indicated that considerable heat loss occurred during the
study periods. These data demonstrated that turbulence induced
by surface cooling was the predominant source of turbulence in
the tank. Because f was <<-1, the turbulent velocity
scale, ut, was appropriate for estimating the magnitude
of the convective vertical mixing induced by surface cooling.
Since ut was about two orders of magnitude greater
than Q/A, particle sedimentation may be significantly inhibited
for those particles with settling velocities of magnitude ut
or less. The magnitude of the vertical velocity scales was
of order 0.6 cm/s. This vertical velocity corresponds to the settling
velocity of a 150 m diameter particle or floc with a density of
1.5 g/cm3.
Table 3. Summary of meteorological data and computed parameters.
| Parameter | Oswego chlorine contact,
2/3-7/89 | Bend primary clarifier, 1/21/89 | Bend secondary clarifier, 1/22/89 | Bend primary clarifier, 3/4/89 | Bend secondary clarifier, 3/5/89 |
| Air temperature, oC | -9.7 | 2.8 | -2.2 | -7.2 | 2.8 |
| W2, wind speed, m/s | 0.2 | 0 | 1.3 | 0 | 1.1 |
| Relative humidity, % | 60 | 100 | 50 | 90 | 90 |
| Atmospheric pressure, mb | 1034 | 958 | 958 | 958 | 958 |
| Equilibrium temperature, oC | -30.5 | -16.7 | -13.8 | -30.6 | -8.9 |
| u*, cm/s | 9.0 X10-3 | 1.5 X10-3 | 1.9 X10-3 | 3.0 X10-3 | 1.5 X10-3 |
| n, net heat flux, W/m2 | -376 | -235 | -413 | -358 | -256 |
| B, buoyancy flux, cm2/s3 | 8.8 X10-4 | 5.5 X10-4 | 9.7 X10-4 | 8.4 X10-4 | 6.0 X10-4 |
| f, Richardson flux number | -1.4X105 | -2.2X107 | -2.3X107 | -4.1X106 | -2.8X107 |
| ut, cm/s | 0.63 | 0.57 | 0.73 | 0.65 | 0.62 |
Summary and Conclusions
Temperature data from this study indicated
that ideal, uniform flow often does not occur in sedimentation
tanks when subject to winter cooling. The degree of non-uniformity
is a complex function of inflow conditions (temperature, suspended
solids, flow rate, tank geometry, and inlet baffle design) and
meteorological conditions. Hence, design approaches for sedimentation
tanks should consider how inflow conditions and meteorological
conditions impact tank hydraulics. This impact can be evaluated
by the use of flow models which account for these processes. For
example, DeVantier and Larock (1987) had to neglect the effect
of buoyancy production on turbulence in the tank because of computational
limitations and because the effect of buoyancy on tank hydrodynamics
was considered of secondary importance. McCorquodale (1997) showed
that currently available models of these processes account for
the impact of the inlet baffle on tank hydrodynamics, but do not
account for the impact of atmospheric heating or cooling.
In uncovered clarifiers subject to significant
winter cooling, vertical convective currents induced by surface
cooling have the potential to hinder the settling of suspended
solids.
Specific conclusions of this study were:
Acknowledgments
Credits. The
authors acknowledge the support of the personnel at the Tyron
Creek Wastewater Treatment Plant and at the City of Bend Wastewater
Control Plants. Brad Baird and John Harris of Portland State University
were responsible for much of the data gathering and computer support.
Appreciation is also expressed to a Faculty Development grant
from Portland State University which provided resources to conduct
this study.
Authors. Scott
Wells is a Professor of Civil Engineering, Portland State University,
P. O. Box 751, Portland, OR 97207-0751, (503)725-4276 FAX (503)725-4298
e-mail: scott@eas.pdx.edu . David LaLiberte was a Graduate Research
Assistant at Portland State University and is now an Environmental
Engineer at Montgomery-Watson, Inc., 1800 S.W. First Ave, Suite
350, Portland, OR 97201.
References
Abdel-Gawad, S. M. and McCorquodale, J. A. (1984) "Hydrodynamics of Circular Primary Clarifiers," Canadian J. Civil Engr. ,11, 299-307.
DeVantier, B. A. and Larock, B. E. (1987) "Modeling Sediment-Induced Density Currents in Sedimentation Basins," J. Hydr. Engr., ASCE, 113(1), 80-94.
Dick, R. I. (1982) "Sedimentation Since Camp," J Society of Civil Engrs, 68, 199-235.
LaLiberte, D. M. (1990) "Density Currents in Circular Wastewater Treatment Tanks," M. S. Thesis, Department of Civil Engineering, Portland State University, Portland, Oregon.
McCorquodale, J. A. (1997) "Mathematical Modeling of Settling Tanks," Proceedings American Filtration and Separations Society, 6th Education Conference, Houston, TX, S21-S216.
Ryan, P. J. ; Harleman, D.R.F.; and Stolzenbach, K. D. (1974) "Surface Heat Loss from Cooling Ponds," Water Resources Research, 10(5), 930-938.
Tay, A. J. and Heinke, G. W. (1983) "Velocity and Suspended Solids Distribution in Settling Tanks," J. Water Pollution Control Fed., 55, 261-269.
Turner, J. S. (1973) Buoyancy Effects in Fluids, Cambridge Univ. Press, New York, N.Y.
Wells, S. A. (1990) "Effect of Winter
Heat Loss on Treatment Plant Efficiency," J. Water Pollution
Control Fed., 26(1),34-39.
Appendix A. Surface Heat Flux Calculations
The following equation from Ryan et al.
(1974) was used to compute the net surface heat flux, n:
where sc is the clear sky solar radiation in W/m2
Ta is the air temperature in oC
Ts is the surface temperature in oC
es is the saturated vapor pressure at water surface temperature, mb
ea is the vapor pressure of the air, mb
Tsv and Tav are the virtual surface and air temperatures, respectively, in
deg K
p: atmospheric pressure, mb
C is cloud cover fraction from 0 to 1
W2: wind speed, m/s, measured at
a height of 2 m above water surface
The equilibrium temperature, the theoretical temperature that the water body would reach at steady-state, was computed by solving for Ts in the above equation when n was set equal to zero.
Figure captions
Figure 1. Schematic of circular tank.
Figure 2. Location of temperature probes and computer data acquisition system for a circular tank.
Figure 3. Temperature profile across the primary sedimentation tank at the Bend treatment plant on 3/4/89 at 5:20 am.
Figure 4. Temperature profile across the secondary sedimentation tank at the Bend treatment plant on 3/5/89 at 2:46 am.
Figure 5. Temperatures for the Bend secondary clarifier on 3/5/89 near the surface at radial distances of 4 m (13 ft), 7.6 m (25 ft), and 11.2 m (37 ft) from the center of the tank.
Figure 6. Temperatures for the Bend secondary clarifier on 3/5/89 0.9 m (3 ft) below the surface at radial distances of 4 m (13 ft), 7.6 m (25 ft), and 11.2 m (37 ft) from the center of the tank.
Figure 7. Flow rate and air temperature during study period for Oswego study between 2/3/89 and 2/7/89.
Figure 8. Vertical temperatures measured at Lake Oswego at a radial distance of 1.5 m.
Figure 9. Vertical temperatures measured at Lake Oswego at a radial distance of 5.5 m.
Figure 10. Vertical temperatures measured at
Lake Oswego at a radial distance of 10 m.
