WATER POLLUTION CONTROL RESEARCH SERIES  •  16080 DWP 11/70
        Induced Air Mixing of
         Large Bodies of Polluted  Water
ENVIRONMENTAL PROTECTION AGENCY • WATER QUALITY OFFICE

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Report Number                          Title/Author

l6o80DRX10/69         Stratified Reservoir Currents; by Oregon State Univ.,
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16080	06/69         Hydraulic and Mixing Characteristics of Suction Mani-
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                        the Hydroponic Culture of Cool Season Grasses; by
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16080	11/69         Nutrient Removal from Cannery Wastes by Spray Irriga-
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             Induced Air Mixing of Large Bodies
                     of Polluted  Water
                             by
                    Stefan A. Zieminskl
                           and
                   Raymond C. Whittemore
             Chemical Engineering Department
                                    /*
                    University of Maine
                     Orono, Maine  OM73
                            for the
                  ENVIRONMENTAL PROTECTION AGENCY
                       WATER QUALITY OFFICE
                          Program #16080 DWP
                           November  1970
For sate by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price 60 cents

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                    WQO Review Notice
This report has been reviewed by the Water Quality Office
and approved for publication.  Approval does not signify
that the contents necessarily reflect the views and
policies of the Water Quality Office, nor does mention
of trade nanes or comnercial products constitute endorsement
or recomnendation for use.

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                                Abstract
    The work discussed in this report constitutes the Phase I of the
investigation of induced air mixing of large bodies of water.  The
objective of this work was to conduct a pilot scale study to estimate
the effects of variables such as the air flow rate, geometry of the
body of water, energy input, size of air bubbles, and the pumping
capacity of the air plume on the time of mixing.  The latter was de-
fined as the time required to reach 90% of the equilibrium concentra-
tion of the KC1 tracer.  In the study emphasis was put on the
direction and relative magnitudes of the variables in order to obtain
guidelines for large-scale investigation.  Considerable time was spent
on the development of the various experimental techniques.  The tests
were conducted in a plexiglas tank of 180 gallons capacity.  It is
stressed that the induced air system was investigated only from the
viewpoint of its mixing performance.  Its effect on aquatic life was
not considered in this work.

    This report was submitted in fulfillment of project #16080 DWP
under the sponsorship of the Federal Water Pollution Control Adminis-
tration.

Key Words:  Air Plume, Diffusion, Dispersion, Bubble Size, Energy
            Input, Mixing, Mixing Time,  Tracer.

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                                Contents

                                                                    Page
Section
                                                                      vi
            Conclusions 	

                                                                    viii
            Recommendations 	

                                                                      1
    I       Introduction  	


   II       Equipment and Operational Procedures  	

                                                                     23
   III       Discussion  of Results 	

                                                                     45
   IV       References  	
                                    ii

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                            List of  Figures
                                                                    Page
                                                                      3
Figure  1   Test Equipment	

Figure  2   Photograph of Test Equipment	     5

Figure  3   Photograph of Restricted System 	     6

Figure  4   Photograph of Air Bubbles 	     8

Figure  5   Photograph of Air Plume  	     8

Figure  6   Photograph of the Rising Disturbance of  the Plume  .  .     10

Figure  7   Photograph of Anemometer in Calibrator	     12

                                                                      13
Figure  8   Pumping Action of Plume  	

Figure   9   Photograph of Water  Velocity  Determination by
                  Stroboscopic photography 	

Figure  10  Photograph of Liquid Tracer  Introduction	     15

 Figure 11   Conductivity Cell Locations  	     l6

 Figure 12   Conductivity vs. Time Chart (Solution Tracer
                  Introduction)	

 Figure 13   Photograph of Solid Tracer Introduction 	     18

 Figure 14   Conductivity vs. Time (Solid Tracer Introduction.  . .    20

 Figure 15   Conductivity vs. Time (Continuous Tracer
                   Introduction)	

 Figure  16   Mixing Time  vs. Air Rate  (Solution Tracer)	     24

 Figure  17   Mixing Time  vs. Air Flow Rate  (Solid  Tracer)	     25

 Figure  18   Photograph  of  Circulation Pattern (Solution Tracer,
                   10  seconds)	

 Figure  19   Photograph  of  Circulation  Pattern (Solution Tracer,
                   30  seconds)	

 Figure  20   Photograph  of  Circulation Pattern (Solution Tracer,      ^
                   1 minute)  	


                                     iii

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                       List of Figures (continued)
                                                                    Page
Figure 21   Photograph of Circulation Pattern (Solution Tracer,
                 2 minutes)	    29

Figure 22   Photograph of Circulation Pattern (Solution Tracer,
                 3 minutes)	    30

Figure 23   Stack Flow vs. Air Flow Rate	    31

Figure 24   Photograph of Circulation Pattern (Solid Tracer,
                 10 seconds)	    32

Figure 25   Photograph of Circulation Pattern (Solid Tracer,
                 30 seconds)	•	    32

Figure 26   Photograph of Circulation Pattern.(Solid Tracer,
                 1 minute)	    33

Figure 27   Photograph of Circulation Pattern (Solid Tracer,
                 2 minutes)	    33

Figure 28   Photograph of Circulation Pattern  (Solid Tracer,
                 3 minutes)	    34

Figure 29   Mixing Time  vs. Power/Unit  Volume  (Liquid  Tracer)  .  .    37

Figure 30   Flow in  Stack vs.  Bubble Size	    40

Figure 31   Mixing Time  vs. Bubble Size	    41

Figure 32   eg)1/2  vs.  (M-0'™	    «*
                                     iv

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                                 Tables





                                                                    Page





  I   Water  Flow in Restricted System.	    26




 II   Percentage of Water Pumped During  Mixing Operation 	    27




III   Efficiency of the Restricted System	    35




 IV   Diffused Air Mixing of Large Bodies of Water	    38
  V   Effect of Disperser Submergence on Mixing Time
39

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                              Conclusions


    The conclusions given in this section refer only to the equipment and
operating conditions used in this work.

    (1) The mixing time, as experimentally determined, depends to some
extent on the tracer technique used.  Great care must be taken to ensure
uniformity of the introduction of the tracer.  Because of the randomness
of the bubble motion, the circulation pattern undergoes random changes
except for the well defined horizontal and surface jets.  This random-
ness is responsible for the comparatively poor reproducibility of mixing
time determinations.

    (2) With air flow rates between 300 and 2000 cc/min, and volumes of
water ranging from 100 to 180 gallons, the mixing time decreased slowly
with increased air flow rate.  However, below 300 cc/min a sharp increase
in mixing time could be observed.  It appears that decreasing the rate
of flow a critical value is reached beyond which the currents generated
are not sufficiently strong to establish a circulation of an appreciable
magnitude in the whole body of water.

    (3) The spread of experimental data increased with decrease of the
air flow rate.  The probable error of the mixing time determination in-
creased from 8.6% at 2000 cc/min to 18% at 150 cc/min.  Preliminary
anemometric measurements of surface velocities in the vicinity of the
plume indicated values ranging from 1 ft/sec at 2000 cc of air/min to
0.3 ft/sec at 150 cc/min.  The velocity fluctuated between 25 to 50%
with a tendency to  increase at lower air flow rates.

    (4) A good correlation was obtained between the mixing time and
power input per unit volume of water.  This correlation is of interest
in scaling up model studies to large scale installations.

    (5) Except for very low air rates  (<150 cc/min) there was no appar-
ent effect of water height on the mixing time.  However, at  the low air
flow rate the mixing time was shorter at lower water heights.  For two
water depths the introduction of air at the side of the tank resulted
in longer mixing times as compared with the central location of the dis-
perser.  The tests  indicate that the central location of the plume gives
a better mixing performance.

    (6) Limited data was taken for  two different depths of submergence
of the disperser at  the same air flow  rate and water depth.  The results
showed that  the smaller the energy  input  (smaller submergence) the
longer was the mixing.  It is emphasized  that  the greater  is the distance
between  the  disperser  and the bottom of  the  tank the  thicker is the  com-
paratively stagnant bottom layer which hinders efficient mixing.


                                    vi

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    (7) Tests conducted with bubbles of different sizes showed that for
bubble radii above the range of 0.06 to 0.12 cm the mixing time did not
depend much on bubble sizes.  However, below this range the velocity of
rise of the bubbles, and therefore the density of the plume, dropped
rapidly resulting in a shorter mixing time.

    (8) The mixing time, the depth of water, and the principal dimen-
sion of the tank were successfully correlated by dimensional analysis
with the densimetric Froude number.  It is expected that still better
correlation could be obtained with the use of a larger tank where the wall
effect would be of smaller magnitude.
                                    vii

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                            Recommendations
    It is strongly recommended that the present research be continued
in a tank of an approximate capacity of 5,000 gallons and at air flow
rates of about 5 to 50 liters/min.  The larger dimensions of the tank
would allow a more accurate correlation of the variables.  The experi-
mental techniques as developed in the present work could be success-
fully applied without major modifications.  The use of a larger tank
would also allow a study of multiple air introductions which was im-
possible in the present work because of the small dimensions of the
tank.  The recommended investigation would thus constitute an inter-
mediate step between the pilot scale studies as discussed in this
report and the actual large scale investigation defined as Phase II
in the original research proposal (WP-01376-01, Nov. 28, 1967, page 8).
                                  viii

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                               SECTION I

                              Introduction
     The storage of water in large lakes or reservoirs gives rise to pro-
blems of physical, chemical, and biological nature.  Organic matter of
industrial and natural origins tends to settle on the bottom where it
decays, depleting the water of dissolved oxygen necessary to insure nor-
mal aquatic life.  Although the upper surface of water which is in
direct contact with the atmosphere may be saturated with oxygen, the
mixing resulting from the density differences or the action of wind is
usually too small to replenish the oxygen deficiency in the lower layers.

     In order to alleviate these adverse conditions and improve the qual-
ity of water, attempts were made to destratify large bodies of water by
artificial means of which the use of induced air seems to be one of the
more promising.

     A considerable amount of work has been conducted in the general
field of circulation and destratification of large bodies of water by
means of induced air (21).  Little, however, has been published of a
nature basic enough so that the results obtained in one case could be
used to predict  the results in another.

     The objective of this work was to conduct a pilot scale study to
estimate the effects of variables such as the air  flow rate, geometry of
the body of water, energy input, size of air bubbles, and the pumping
capacity of  the air plume on  the time of mixing.   The latter was defined
as the time  required to reach 90% of the equilibrium concentration of
the KC1 tracer.   In studying  the effects of  the various variables, empha-
sis was put  on their direction and  relative  magnitude in order  to obtain
better guidelines for  large-scale investigation.   It is expected that
the rather successful  correlation derived by dimensional analysis could
be used as a starting  point in correlating  the  results of large-scale
tests.

      The tests were  conducted in  a  comparatively  small  tank (180 gallons)
and  therefore  the obtained  results  should  not be  directly extrapolated
 to large bodies of water.

      One of  the main  difficulties  in conducting this  kind of  research is
the pronounced randomness of  the  system caused  by the random motion  of
bubbles.   A  great number  of tests had  to be conducted in order  to obtain
reliable averages.

     Another difficulty was the unavailability  of some  of  the measuring
techniques.   E.g.  the  determination of the velocity of  rise of  the  air
plume,  required for  the estimation  of  the  density of  the plume  and
therefore  for  estimation  of the densimetric Froude number.   Some of  the
techniques which have  proved  successful in one  set of  experimental

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conditions gave erratic results when the conditions were changed.

     A considerable part of this report will therefore be devoted to the
description of the various experimental techniques and measurements
even though some of them were later discarded as less reliable under
conditions used in this work.  They may, however, prove valuable under
a different set of experimental conditions and therefore of interest to
a future investigator.

     It must be stressed that the induced air system was investigated
only from the viewpoint of its mixing performance.  Its effect on aquat-
ic life was not considered in this work.

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 ROTAMETERS
                                     ION EXCHANGER

                                                 WATER IN
               MANOMETER
                              FLUORESCENT LIGHT
                                 —*-
                        tV«»•^""*'!"!!"	 ".-	 !
                                                               BDLEX CAMERA
                                            CONDUCTIVITY
                                                CELL
                                             SOLU-
                                             METER
  ANEMOME
  MODULE
                       TANK; isoo**  H2o
                                              DISPERSER
                                                              RECORDER
                             QUICK OPENING VALUE
AIR CYLINDER
    FIGURE
TEST EQUIPMENT

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                               SECTION II

                  Equipment and Operational Procedures
General
     The tests were conducted in a plexiglas tank  (Figures 1 & 2)
having a maximum capacity of 1500 Ib. of water  (180 gallons).  The tank
was rectangular in shape and was 48" long, 32" wide, and 36  high.
was mounted on a steel support with  facilities  for mounting auxi
equipment and instruments.  The plexiglas construction enabled phot
graphic and motion picture  investigation of the interior of the
In addition to the drain, the bottom of the tank had two openxngs
insertion of the air  disperser.  One of them was located in the cente:
and the other 12" from the  side and  15" from the front wall.

     The water used  in the  tests was first passed  through  a porous
filter to remove suspended  matter and  then purified  in an  ion  exchange
demineralizer.  The  specific  resistance of this water was  about
cm.  The high resistivity water was  necessary  in the determination of
the mixing  time which involved  the measurement of  the changer:  of  conduc-
tivity after  introduction  of  the  KC1 tracer.   The  air to  the disperser
                       Photograph, of Test Equipment
                                  Figure 2

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was supplied from a breathing air cylinder and metered by two rota-
meters.  The air disperser consisted of an Aloxite plate, one inch in
diameter, cemented in a brass holder.  The height of the holder could
be adjusted to vary the depth of submergence of the disperser.

The Restricted System (Figure 3)

     The air plume issuing from the disperser undergoes a random
swaying motion during its rise to the surface.  This lack of stability
affects the dimensions of the plume, the water flow pattern, and makes
difficult the anemometric measurement of the water flow produced by
the plume.
                     Photograph of Restricted System
                                 Figure 3

      In order to decrease this difficulty, and to improve the repro-
 ducibility of the water flow measurements, some tests were conducted in
 a system in which a plexiglas cylinder was mounted around the plume.  In
 a later part of the report this cylinder is referred to as stack.  The
 cylinder was 4 inches in diameter, 18 inches long, and its lower end
 was at a distance of 4 inches from the bottom of the tank.  The upper
 end was 2 inches below the level of water.  Although the presence of
 this cylinder increased somewhat the flow resistance of the system,
 enabled at the same time to obtain valuable data on the pumping perfor-
 mance of the plume.  It is of interest to note that under identical
 operating conditions the mixing timesobtained with and without the
 cylinder were practically the same.  The above indicates that the
                                   6

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presence of  the  cylinder did not exert any major  effect on the
operating efficiency  of the system despite the fact  that  the flow pat-
tern  in the  vicinity  of the plume was changed.  In the freely rising
plume the surrounding water entered  the plume through its sides up to
the level just below  the surfact jet.  In the restricted  system this
side  inflow  was  eliminated by the presence of the cylinder and the
water was forced to flow at a uniform rate from the  bottom to the top
of the cylinder.

                    Determination of the Bubble Size

      Since the pumping action of the plume depends on its buoyancy and
therefore on the density of the air-water dispersion, it was decided to
investigate  the  effect of the size .of the bubbles.   It was expected that
the decrease in  the size of the bubbles and the resulting drop in the
velocity of  rise would increase the air-holdup, decrease  the density of
the plume and thus improve the pumping effect.  It appears from our
literature survey that very little information is available in this
field.

      The bubble  size  was determined  in this work  by  photographing the
bubbles rising in the air plume.  A Bolex 16 mm movie camera with a
telephoto lens and Kodak 4X negative film were used  in this determina-
tion.  The lighting was accomplished by a 1531-A  Strobotac and 1539-A
Stroboslave  (G.R.C.).  The lamp of the Stroboslave was placed in the
back  of the  tank and  the flash was directed through  the tank into the
lens  of the  camera.   A white paper backing was used  at the back of the
tank  to reduce intensity of the flash.  A metal rod  of known diameter
was used as  a standard of reference.  It was mounted at an angle to the
camera so that a  part of it was always in focus.  Pictures obtained by
this  back lighting technique were of excellent contrast (See Figure 4).
After developing, the film was projected and the  major and minor axes of
at least 40  bubbles were measured and the equivalent spherical radius
was calculated for each bubble.  The average equivalent spherical radius
was then used in  evaluation of results.  The accuracy of  this method was
checked by means  of glass spheres of known diameters and was found to be
+ 1.5%.

      Since the photographs taken at  the bottom of the plume and at its
top showed practically the same bubble sizes and  distribution, the
bubbles were photographed only at the top of the  plume.

      The uniformity of bubble sizes was very satisfactory at air flows
of 500 cc/min S.T.P.  and higher.  At lower flows, however, the unifor-
mity  of sizes decreased resulting in a greater error of measurement.  To
obtain a conservative estimate of the reproducibility of  the measurement,
the probable error was estimated at the low flow  rate of  300 cc/min
S.T.P. and was found  to be 6.2%.

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Photograph" of Air Bubbles
         Figure 4
  Photograph of Air Plume
         Figure 5

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              Determination of the Shape of the Air Plume

     The shape of the air plume is necessary for the determination of |he
plume density required in the densimetric Froude number.  The measure-
ments of the plume were taken by photographing the plume and a refer-
ence scale by means of a Polaroid MP-3 camera.  The black and white
photographs were projected and the diameters were measured at various
heights of the plume  (See Figure 5).  The impression that the bubbles
did not reach the surface of the water was caused by the tilt of the
camera when taking this particular photograph.  At first the pictures
were taken from both  sides of the tank to estimate the possible effect
of the different plume to wall distances.  Since no difference was ob-
served, only one side of the plume was photographed and in the calcu-
lations the plume was assumed to be a perfect cone.

     For rates of air flow below 2000 cc/min  S.T.P. the plume was very
stable.  However, at  higher flow rates the plume became unstable due to
horizontal swaying.   On  two occasions the bubbles in the plume formed a
vortex.  The volume of the plume was calculated by the equation:


                         V=(ff)(rl2 + rir2  +r22)

              where      V = volume, cc.

                         H = depth  of  immersion of disperser, cm.

                       ri = radius at plume  top,  cm.

                       ro = radius at plume  bottom, cm.

From the known volume of the  plume and  the instantaneous  volume of  air
 (air holdup), the plume  density can be  easily calculated  from the rela-
tionship:
                        pw =  v - v Pw + vpa
                                    V

               where:    v = instantaneous volume of air, cc.

                        pw = density of water, g/cc.

                        pa =    "    of air, g/cc.

                    The Velocity of Rise of the Plume

      The velocity of rise of the plume is an important quantity for the
 determination of the instantaneous volume of air (air holdup) necessary
 for estimation of the density of the plume.  The principle of this
 measurement is based on creating a disturbance in the plume and follow-
 ing this disturbance by means of motion picture photography.

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     The disturbance was produced by an abrupt discontinuation of the
air flow by means of a quick release valve which vented the air into the
atmosphere (See Figure 6).

     The vertical displacement was determined with the help of a refer-
ence scale mounted parallel to the plume.  The corresponding time was
obtained from the number of frames and the known framing rate of the
Bolex movie camera.
           Photograph of  the Rising Disturbance  of  the  Plume
                                Figure  6

     For each  run  5 or  6.  determinations were made and the  results  aver-
 aged.  The framing rate of  the  camera was  checked by photographing the
 dial of a milli-second  timer and  counting  the  number of frames  for a  set
 time.  This method of velocity  determination was subject to two errors.
 At  low air velocities  (below 600  cc/min) the line of disturbance started
 to  become irregular because of  increasing  irregularity  in  the size of
 the bubbles and, therefore  in their velocity of  rise.   This problem did
 not occur at higher air flow rates.  The other difficulty  was caused  by
 the effect of  the  disturbance on  the velocity  of circulation in the
 tank.  In order  to decrease this  effect, the velocity of rise was
 measured up to a distance of 8  to 10 inches above the disperser.  In
 this way, the  air  flow  was  interrupted  for only  about one  second.
 check this technique a  hot  film anemometer was mounted  within the  plume
 and the water  velocity  was  measured after  the  interruption of the  air
 flow.  The measurement  showed that the  water velocity remained  constant
 for approximately  1 second  within the region used in our measurements.
                                   10

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     The instantaneous air volume "v" (air holdup) in the tank was cal-
culated from the equation:

                           v = (H/vr)Q

            where:       H = depth of immersion of disperser

                         Q = air flow rate

                        v  = velocity of rise of plume

Measurement of the Water Flow in the Tank

     The rate of water flow produced by the air plume was measured by
means of hot film anemometry.  A cylindrical hot film sensor (TSI Model
1210 60W) and the anemometer module  (TSI Model 1053-B) were used in
this work.  The constant  temperature anemometer measured the fluid
velocity by sensing  the rate of heat transfer from the heated sensor to
the surrounding water which was kept at constant temperature.  As the
water velocity increased,  the sensor tended to cool, changing the resis-
tance.  The amplifier then adjusted  the current to the sensor to main-
tain constant temperature.  These  changes  in the output of the amplifier
were then related to changes  in water velocity by means of calibration.

     The use of anemometer in this work was not without errors.  Lint or
other suspended impurities could have collected on the sensor, producing
change  of heat transfer unrelated  to the  change in water velocity.  For-
mation  of minute air bubbles  on  the  wire  of the anemometer was another
potential source of  error.   In order to detect bubble formation,  the
sensor  was illuminated by a beam of  light and observed with  a magnifying
glass.  Usually a light knock on the sensor holder would displace the
bubble.  Decrease of the  sensor  temperature by lowering  the  current was
of help in decreasing bubble  formation  but at  the same time  adversely
affected the sensitivity  of  the  instrument.

     The sensors were calibrated in  a TSI Model  1125 Calibrator.   A
cross-section through the calibrator nozzle  and  the  sensor  is  shown  in
Figure  7.  The sensor wire (invisible on  the  photograph)  is  in the
center  of the nozzle supported by  the V-shaped arms  of the  probe. In
order  to avoid breaking of the  delicate and  expensive sensor,  a spe-
cial protecting device was constructed  (see  upper part of  the Figure)
which  prevented damage  to the sensor while inserting and removing it
from the calibrator. The flow of  water through the  instrument was
measured by  a calibrated  rotameter.   Addition of dye showed a flat
velocity profile  at the  plane of the sensor.   To insure  against changes
 in calibration  each probe was calibrated before and  after each test.

      Initially  it was proposed to determine the pumping  effect of the
 air plume  from the velocity profile of  the surface jet (Figure 8).  Un-
 fortunately,  the randomness and turbulence of flow in the surface jet
                                   11

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                  Photograph  of  Anemometer  in Calibrator
                                 Figure  7

gave erratic results.  Consequently, no attempt was made to measure the
velocity profiles in this region.  The measurement of the water velocity
was therefore limited to the restricted system where the velocity was
measured in the cylinder at a level below the disperser.

     A photographic technique for measuring the flow of water was also
briefly investigated.  Selected polystyrene beads (Comak Chemicals Ltd.,
London, K.E. England) of density close to that of water were allowed to
circulate in the tank.   The beads were photographed by means of the
Polaroid MP-3 camera and stroboscopic illumination.  Every time the
stroboscope flashed an image of the bead appeared on the film (Figure 9).
From the distance between the images and the known rate of flashing, the
velocity component in the vertical direction was calculated.  Usually a
few pictures were taken and the average velocity was calculated.  The
difference between the anemometer and photographic measurements was in
the range of 10 to 15%.

     The anemometric technique was selected in this work because of its
simplicity and the fact that it can be used for measurement of point
velocities.

                    Determination of the Mixing Time

     The mixing time is one of the most important quantities studied in
                                  12

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i,,
                SURFACE JET
                     WATER
                             WATER INFLOW
                                                      VERTICAL JET
WATER INFLOW
                                                                    WATER
                                                 AIR SOURCE
                                           FIGURE  Q




                                 PUMPING  ACTION OF PLUME

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 Photograph  of  Water Velocity  Determination by Stroboscopic  Photography
                                Figure 9

this work.  Considerable time was spent on developing of various tech-
niques and on estimation of their relative merits.  The principal
difficulty of this measurement lies in the randomness and poor repro-
ducibility of the system itself.  The randomness of bubble motion is
mostly responsible for it.  It is therefore practically impossible to
find out to what extent this poor reproducibility is due to the method
of determination.

     Gay and Hagedorn (5) in their study of mixing of stratified bodies
of water measured changes in salinity.  Similarly Harrell (7) used
changes in conductivity in'his flow of fluid system.  Zlokarnik (24)
estimated the mixing time by adding acid to a  solution of a base in the
presence of phenolphthalein and following the  change of color.  Nicker-
son (14) introduced a fluorescent dye, Rhodamine, into a water reservoir
and monitored the changes with a fluorometer.   In other investigations
(16) changes in temperature and oxygen concentration profiles were used
to advantage.
                                  14

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     In the methods applied, in this work the mixing time was estimated
by introducing a KC1 tracer and following the changes in conductivity.
A Beckman Solu-Meter (Model RA-5) with temperature compensation and
Leeds & Northrup Speedomax recorder were used in the investigation.  The
cells were Epoxy Dip Type fabricated from 5/16" diameter epoxy rod 2 ft.
long and having unshielded platinized nickel electrodes of 0.2/cm cell
constant.

     Three different tracer techniques were investigated.  In the first
method 200 cc of KC1 solution was introduced at the surface through a
1/8 inch opening.  The concentration of the solution was so selected as
to give a conductivity change of 20 micromhos.  At this conductivity
change one full tank of water could have been used for 8 tests.
                 Photograph of Liquid Tracer Introduction
                                Figure  10

Figure 10 shows a black dye being  introduced by  this  technique.  The
tube was located 2 inches  from  the right  side wall.   The conductivity
cells were placed on the opposite  side of  the tank  in several locations
(See Figure 11).

     Before each test the  air flow was adjusted  to  the required value
and allowed to flow through the tank for  at least 30  minutes before
introduction of the tracer.  This  was  necessary  to  establish a uniform
flow pattern and avoid temperature gradients in  the tank which would
affect the conductivity measurements.   At  the end of  the test when the
conductivity approached equilibrium value, the contents of the tank
                                  15

-------
INJECTION

TUBE
               CELLS
                   w
                             H
                                                     h
                                              2 From Wall
i.
  FRONT VIEW
                                             TOP VIEW
                               INJECTION    \
                               TUBE 2"FROM WALL
                         FIGURE ]|

                CONDUCTIVITY CELL  LOCATIONS

-------
      60
   8  50
   c
   o
   q  40


    i

   2

   O
   O
   2
   I
   O
      30
      20
      10
                                   90% —J
                                 EQUILIBRIUM
                                   I
I
        EQUILIBRIUM

        VALUE
                       \
       012345678

                                TIME - MINUTES

                                   FIGURE 12

CONDUCTIVITY VS TIME CHART ( SOLUTION TRACER  INTRODUCTION )

-------
were vigorously mixed with a paddle and the terminal (equilibrium) con-
ductivity determined.  In the analysis of the charts, the time corres-
ponding to 90% of the terminal conductivity was arbitrarily selected as
the mixing time.  A representative sample of a recorder chart is shown
in Figure 12 where the horizontal axis was reduced by a factor of two
and the vertical axis was expanded by the same factor.

     For each set of experimental conditions a total of eight tests
were conducted  (2 tests for each cell location) and the results aver-
aged.  A series of photographs showing the progress of tracer distri-
bution will be shown in the section dealing with the interpretation of
results.

     A number of tests conducted under analogous experimental conditions
showed a probable error of a single determination to be 8.6% and 18% at
the air flow of 2000 and 150 cc of air/min respectively.  As was men-
tioned before, this value reflects also on the effect of the randomness
of the system.

     In the second tracer technique, ground KC1 crystals were spread
over the top of the air plume.  The crystals were ground to a fine
powder to ensure their dissolution before reaching  the bottom of the
tank.  They were spread uniformly by means of a perforated dish over a
circular surface, 5  inches in diameter.  A metal ring of this diameter
was placed above the top of  the plume  to insure a uniform and more re-
producible addition  of the tracer.  Figure  13 shows a dye being intro-
duced by this  technique.  The conductivity  cells were placed in
                Photograph of  Solid Tracer Introduction
                                Figure 13
                                  18

-------
geometric centers of each half of the tank.  The conductivity versus
time data were obtained by switching from one cell to the other every
10 seconds.  In the analysis of the chart the two conductivity readings
were averaged and plotted against time  (See Sigure 14).  The mixing
time was defined as that point at which the average conductivity was
_+ 5% of the terminal  (equilibrium) value.  The average value of the
2 cells was used because there was always some tendency of the crystals
to be carried more to one side than to  the other.  The probable error
of this measurement was found to be 9.2%.  As in the first method the
effect of the randomness of the system  is included in this figure.

     The third method investigated in this work consisted of adding a
dilute KC1 solution at a constant rate  over a period of 30 minutes.  It
was expected that in  this way the effect of the randomness of the flow
pattern on the mixing time would be decreased.  Again as in previous
methods enough salt was added to produce in the mass of water a change
in conductivity of 20 micromhos.  If the mixing time were zero (instan-
taneous mixing), the  conductivity vs. time curve (line A Figure 15)
would form a straight line starting from the origin.  However, since
the mixing is never instantaneous, the  actual curve is displaced by the
amount corresponding  to the time required for mixing.  This method has
an unquestionable advantage over the previous techniques in the fact
that the time of tracer introduction was much longer and therefore the
effect of the randomness of the system  considerably decreased.  This
method was not used in our work because of the lengthy analysis of the
charts.

     On the whole it may be said that the estimation of mixing times
from conductivity measurements was experimentally simple.  It had,
however, the disadvantage of the use of large quantities of low conduc-
tivity water and therefore the necessity of frequent  (each 6 to 8 tests)
exchange of the contents of the tank.
                                   19

-------
  20
o
o
z 18
o
c
o
  '6
o
X
o
w
   14
   12
  10
                          I       I       I

                                    o   o

                          00°
                        \
                         95% VALUE
            o   o
   o


o    o
                    o o
     >  o
                                                     EQUILIBRIUM

                                                     VALUE  	
           36      9      12      15      18      21      24


                            TIME - MINUTES

                             FIGURE 14


        CONDUCTIVITY  VS  TIME  ( SOLID TRACER  INTRODUCTION )

-------
   20
o
O  18

o
c
o
H  l6

i

2
O
:o
o
I
O
   14
   12
   10
                         INSTANTANEOUS  MIXING

                         LINE A
                  ACTUAL MIXING
                          O  O
        o   ?
                                             AVERAGE LAG = 3.1 MINUTES
                                                              I
                   8
                                               24      28      32      36
                       12     16      20

                          TIME -  MINUTES

                             FIGURE 15


CONDUCTIVITY VS TIME (CONTINUOUS  TRACER INTRODUCTION)

-------
                             Section III

                        Discussion of Results

The Effect of Air Flow Rate on the Mixing Time.

     The results of this group of tests are summarized in Figures 16 and
17.  In Figure 16 the height of the water in the tank was used as a
parameter while Figure 17 also shows the effect of the location of the
air disperser.  It must be noted that in Figure 16 the branch of the
curve between air flows of 300 to 2000 cc/min is an average of the three
water heights (15, 24, 30 inches) investigated in this work.  This was
done because in this region the water heights studied did not show a
definite effect on the mixing time.  In the region of air flows below
300 cc/min. curve A represents the average of the data taken at 24 and
30 inches of water while curve B represents the average for 15 inches.
In Figure 16 the liquid tracer was used while in the tests presented in
Figure 17 solid tracer was introduced over the plume for estimation of
mixing times.  The curves, therefore, are not directly comparable.

     In both figures the bubble sizes  (equivalent spherical radius)
varied from 0.07 cm at 150 cc/min to 0.18 cm at 2000 cc/min of air.  It
will be shown later that the effect of this difference in bubble sizes
on the mixing time is negligible.  The effect of geometry (water height
and disperser location) will be discussed in a separate section of the
report.

     It can be seen from both figures  that the mixing time becomes
shorter with increase of the air flow  rate.  This dependence, however,
becomes less pronounced at higher rates of flow.  As was mentioned before,
the mixing time, as measured in this work, is  influenced by the ran-
domness of the system, as well as by the details of the tracer technique.
It seems therefore advisable to discuss first  the circulation currents
established in the tank as a result of the pumping action of the air
plume.

     The water entering the plume is pumped  upwards because the potential
energy of the rising bubbles is transformed  into  the kinetic energy of
the water  (1, 11, 13).  In the forthcoming discussion this water current
will be referred to as the vertical jet  (Figure 8).  Upon reaching  the
surface the bubbles escape into the atmosphere but the momentum of  the
vertical jet is converted into a  thin  horizontal  surface jet  (1, 10,  18).
According to Baines  (1) the thickness  of this  current is less than  5%
of the depth of the submergence of  the disperser.  It can be seen from
Figure 13 that this surface jet is very  thin.
                                    23

-------
  26
  ,'4
  . V.

X
z  16
d
ni  '*


|  12
c

w  10
         e
                                          JL
                                                                      o   WATER  HEIGHT • 30 '
                                                                          WATER HEIGHT • 24'
                                                                      .   WATER HEIGHT -15
                                                                      A   AVERAGE OF 30* AND 24"
                                                                      8   AVERAGE OF IS'
                                                              J.
                                                                                           i
              300
                       600
                                900       1200       1500      1800

                                      AIR  FLOW RATE - CC/ MINUTE
                                                                       2100
                                                                                24OO
                                                                                          2700
                                             FIGURE 16

                       MIXING TIME  VS  AIR  RATE  ( LIQUID TRACER INTRODUCTION )
                                                                                                   3000

-------
I
>-
6)
 -i
i
m
            12
            to
            8
             6
          H
         fr,
                DISPERSER IN CENTER
                                     1
                                                     o  24" Water
                                                     •  15 "Water
                                                     a  24 " Water
                                                     •  15 "Water
                                                 DISPERSER ON  SIDE
                                          J
1
                                                                           1
              0
            100     200     300    400     500     600     700
                         AIR FLOW RATE  - CC / MINUTE
                                  FIGURE I?

       MIXING TIME  VS AIR FLOW RATE  (SOLID TRACER INTRODUCTION)

-------
     This surface current produced by the vertical jet has been studied
by a number of investigators (1, 4, 10, 18, 19).  Most of them (4, 10,
18, 19) were interested in its damping action on ocean waves (pneumatic
breakwaters).  They found that the water velocity of the surface jet
was inversely proportional to the distance from the plume.  Hence, the
momentum of the surface jet was used to generate currents in the layers
below.

     Gay and Hagedorn (5) studying induced air mixing of a stratified
body of water found in addition to the surface jet a strong bottom
current toward the disperser and a stagnant zone in the vicinity of the
disperser.  The presence of this stagnant layer was also noticed by
Straub et al. (18) in their work on pneumatic breakwaters.  It is also
of interest to note that the presence of this zone may constitute a
potential source of error in mixing time determination.  Figures 24 to
28 give a good idea of the water circulation pattern encountered in the
present work.

     The effect of the air flow rate on the water flow  (and therefore
on the mixing time) can best be seen in Figure  23 where the restricted
system was used and the water velocity was measured directly by hot
film anemometry.  The results shown in this figure were taken at a con-
stant water height.  The form of this curve is  in agreement with the
data of Kurihara  (10) obtained  in  an unrestricted system.  He found that
the flow of water is proportional  to the air-flow rate  to  the 1/3 power.
     Table  I gives  the values of Q1'3  calculated  from  Figure  23.  It can
be seen that except for  the lowest rate of  air  the  above relationship
between the flow of water  (F) and that of air  (Q) applies well to the
system investigated in this work.

                               Table I
                    Water Flow in Restricted System
Flow of Water
(F) liters/min





10
20
30
40
50
Air Flow
(Q) cc/min
50
110
225
500
1050
F
J73
2.7
4.2
4.9
4.9
4.9
                                   26

-------
This interdependence was also confirmed by Cyr (3) for higher air flow
rates.  Taylor (19), in fact, showed theoretically that the maximum ver-
tical current of water produced by a flow of gas is proportional to the
1/3 power of the gas flow rate.  Table II shows the dependence of the
mixing time on the water pumped in the restricted system.  The mixing
times were determined by the solid tracer technique.

                               Table II
          Percentage of Water Pumped During Mixing Operation
      Air Flow         Mixing Time     Total Water       % Tank
       cc/min            Minutes        Pumped in       Capacity
                                       Mixing Time,      Pumped
	Liters	

        150               8.34             200             33

        300               4.92             170             28

        600               4.11             175             29

                           Water volume = 610 liters

The table shows a close dependence  of  the mixing time on the amount of
the water pumped.   It  is of  interest to note that only about 30% of the
tank capacity had to be pumped  in order to approach closely the equilib-
rium concentration.

     Bryan  (25) states that  in  the  diffused air mixing of the Blellam
Tarn reservoir only 26% of its  volume  was pumped during the time required
for mixing.  Although  the reservoir may not have been as well mixed as
the tank used in this  research, this information does serve to illustrate
the importance of the  currents  generated by air dispersion.

     It was  already stressed before that Figures 16 and 17 differ  in
the method  of tracer introduction.   In the former,  liquid tracer was
introduced  close to the smaller wall of the tank,  while in the latter
the solid tracer was added over the top of the plume.  On the whole it
may be said  that the liquid  tracer  introduction  (Figure 16) showed great-
er mixing time than the corresponding  curve for solid tracer  (Figure 17,
disperaer in center).  This  difference in results  was probably due to
the fact that in the case of liquid tracer, the whole volume of  the
solution was introduced in a pulse  which  spread into  the region  of
comparatively stagnant liquid at  a  considerable distance from  the  plume.
On the other hand,  the solid tracer was added  in  the  center of the surface
jet where the chance of its  rapid distribution was much better.
                                     27

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Photograph of Circulation Pattern; 10 seconds. Solution Tracer
                       Figure 18
Photograph of Circulation Pattern; 30 seconds. Solution Tracer
                       Figure 19
                            28

-------
Photograph of Circulation Pattern; 1 minute Photograph of Solution Tracer
                               Figure 20
        Photograph of Circulation Pattern.  2 minutes Solution Tracer
                                Figure 21
                                     :

-------
Figures 18 to 22 show addition of dye introduced by the liquid tracer
method.  The time after introduction of the dye is noted in each Figure.

     It can be seen from the figures that the tracer introduced in the
form of a pulse forms a highly concentrated zone in the right-hand side
of the tank which has to be "pulled" by the slowly circulating liquid to
the left-hand side (cell location) before any changes in the conductivity
can be detected.  It may therefore be expected that because of this initial
lag the liquid tracer method should give longer mixing times as shown in
Figure 16 and 17 (lower curve).

     However, in the case of solid tracer introcuced above the plume,
that is in the center of the surface jet, the situation was different.
In order to illustrate the distribution of the tracer, a small quantity
of a black dye was mixed with the KC1 crystals and photographs were taken
at time intervals between 10 sec. and 3 minutes.  The results are shown
in Figures 24 to 28.  The tiny crystals dissolved rapidly and the
resulting solution was spread uniformly over the whole surface of the
tank.  This, already dilute solution, was then distributed throughout
the mass of water by the circulation currents produced by the plume.
      Photograph  of  Circulation Pattern.  3 minutes  Solution Tracer
                              Figure 22
                                   30

-------
              60
u>
                       200
400
600
80O
1000
1200
                                                                  1400
                                            1600    1800
                                      AIR FLOW RATE - CC/ MINUTE
                                             FIGURE 23
                                   STACK FLOW VS AIR  FLOW  RATE

-------
Photograph of Circulation Pattern.Solid Tracer: 10 sec,
                     Figure 24
Photograph of Circulation Pattern.Solid Tracer: 30 sec,
                     Figure 25
                            32

-------
Photograph of Circulation Pattern. Solid Tracer: 1 minute
                       Figure  26
Photograph of Circulation Pattern. Solid Tracer: 2 minutes
                       Figure 27


-------
     The greater degree of the initial dispersion of the tracer seems
to be the main reason for the shorter mixing times obtained by this
tracer method.  It must therefore be emphasized that the mixing time is
not an absolute value but depends on the method of determination and
only the results obtained by the same method can be subject to general
correlation.
       Photograph of Circulation Pattern.
                               Figure 28
Solid Tracer: 3 minutes
     It is of interest to note the sharp increase in the mixing time
which can be seen in Figure 16 at an air flow rate between 150 and 300
cc/min.  This sudden break in Figure 16 can be attributed to the
magnitude of the currents generated in the mass of water.  It can
be expected that decreasing the rate of air flow some critical value
would be reached at which the currents generated would not be suffi-
ciently strong to establish a circulation of an appreciable magnitude
in the whole body of water.  Apparently at 150 cc/min. the system was
handicapped in that the surface jet was unable to completely overcome
the inertia of the stagnant body of water.  Figure 17  (lower curve)
which was obtained with the solid tracer technique, shows a similar
break but of much smaller magnitude.  This apparent discrepancy can be
readily explained by the differences in the two tracer techniques which
were discussed before.  It may be expected a sharp transition of this
                                     34

-------
kind would occur independently of the tracer method used, although at
different air flow rates.

     Another important observation which can be made from Figures 16
and 17 is the spread of data which decreases with increased air flow
rate.  This is especially noticeable in Figure 16.  In the case of
the liquid tracer the probable error of a single determination was
8.6% at 2000 cc/min while at 150 cc/min it increased to 18%.  This
relatively poor reproducibility at low air flow rates is attributed to
the smaller intensity and greater randomness of the generated water
currents.

     Preliminary studies of surface velocities conducted by hot film
anemometers indicated values ranging from 1 ft/sec at 2000 cc/min of air
to 0.3 ft/sec at 150 cc/min.  It was further noted that  the fluctuations
in these velocities ranged from 25 to 50% with a  tendency to increase
at lower flow rates of air.  In order to obtain some idea of the circula-
tion pattern in the body of water, polystyrene beads were dropped in the
tank and allowed to circulate freely.  Except for  the surface and the
vertical jets, it was rather difficult to discern any definite flow pattern.
Very little circulation was observed near the bottom of  the tank, especial-
ly at the corners.  Gay and Hagedorn  (5) found in their  work that a
bottom layer approximately 1" thick was relatively unaffected by the
mixing.

          Efficiency of the Pumping Action  of the Air Plume

     The efficiency E of the air plume as a  pump  is defined, in this
work, as the fraction of the net energy of  the entering  air En which is
transformed into the kinetic energy Ek of water.   The net energy of  the
air  is expressed as the  difference between  the work of isothermal
compression and the sum  of the  entrance,  exit and frictional losses  in
the  cylinder of the restricted  system.   Calculations  showed that  the energy
losses caused by the presence of the  cylinder were practically negligible
 (10% or  less) .  The results are summarized  in Table  III.
                                  En
                               Table III
                  Efficiency of the Restricted System
                 Air Flow Rate          Efficiency
                    cc/min.	Ex 100

                     150                   5.42

                     300                   8.25

                     600                   7.05
                                      35

-------
     Although a direct comparison of the restricted system with that of
a free rising plume is not fully justified,  some interesting observations
can be made from these figures.   Kurihara (1,  10) in his studies
(open plume) found a marked decrease in efficiency with decrease of the
depth of submergence.  The comparatively small efficiency in the present
system might have been due to the very small height of the plume
(1 1/4 - 2 1/2 ft as compared with 5 1/2 - 25 ft).  Another point of
interest is that under the same operating conditions (depth of water and
air flow) the mixing times for both the restricted and unrestricted
systems were practically identical.  This was rather surprising because
in the restricted system the water inflow from the side of the plume
was absent whereas in the open plume it formed an essential part of the
circulation pattern.  There was therefore a considerable difference in the
flow characteristics of the systems.

             Average Mixing Time vs. Power Per Unit Volume

     Figure 29 presents the mixing time as a function of the power in-
put per unit volume.  The power input was calculated by the equation:

                        H - Q,P, In It
     where:         H = Power

                    Q = Air  flow rate

                    P - Absolute pressure

             Subscripts 1  & 2 refer  to  initial  and
             final conditions respectively.

 Because for  a given depth the  power input  IS proportional  to  the air flow
 rate,  the curve resembles closely Figure 16 where  the mixing  time ^ was plot-
 ted against  the air flow.  The power per unit  volume vs. mixing time
 correlation  is of interest in  scaling  up model studies  to  large scale
 installations (see also Parker Ref . 15).

      It is of interest to compare the  magnitudes of the power per unit
 volume values obtained in this work with those of  large-scale studies
 (Table IV).   The comparison  is only approximate because the degree  of mixing
 was in this  work considerably  greater  than in  the  large-scale tests where
 the only goal was to  break thermal  stratification. The data  obtained in
 this research ranged  from 1CT6 to 1.3  x 1(T7.   The difference in  the order
 of magnitude can be due  to the fact that in this research  the contents  of
 the tank were mixed close to the  equilibrium concentration whereas  in the
 large-scale  tests this was not required.   It  is of interest to note that
 despite the  wide differences in size and geometry  of  the model as compared
 with the reservoirs the  difference  in power input  was  not  that great.
                                     36

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ni
o
m
2


c
H

CO
17


16





14





\2
S
X
Z   10
G>
    8
                                    LIQUID TRACER
                                     INTRODUCTION
o WATER HEIGHT = 30"


• WATER HEIGHT = 24"


• WATER HEIGHT =15"
             2       4       6       8       10

                POWER/UN fT VOLUME - ( HP/ft3 ) X 10s

                          FIGURE 29

          MIXING TIME VS POWER/UNIT   VOLUME
                12   13
                        37

-------
                                Table IV
            Diffused Air Mixing of Large Bodies of Water (21)
Reservoir
Indian Brook
Wohlford
Blelham Tarn
Volume
13.8 x 106
10.9 x 106
26.0 x 106
Power Input
hp/ft3
5.8
4.4
3.5
x 10"7
x 10"7
x 10~8
                 Effect of Geometry on the Mixing Time

      Figures 16 and 17, in addition to the effects of air flow rate,
indicate also the effect of the geometry of the system on the mixing time.
In this work the geometry is expressed in terms of the height of water
level and location of the disperser.

      It can be seen from Figure 16 that except for very low air flows
(< 150 cc/min.) there was no apparent effect of water height on the
mixing time.  However, at 150 cc/min. and at a water height of 15 inches
(curve B), the mixing time was about 20% lower than those for the other
two heights (curve A).  The lower curve of Figure 17 (solid tracer) shows
a similar behavior indicating practically no effect of depth  (15 and 24
inches) on the time of mixing.  The effect of introducing the air at the
side of the tank is shown by the two upper curves of Figure 17.  For
both the water depths used in this work, the side location of the air
disperser resulted in longer mixing times.  A similar behavior was also
observed by Gay and Hagedorn (5).  It can also be seen from Figure 17 that
the effect of the side location of the disperser was more pronounced for
the greater depth, resulting in longer mixing times for 24 inches as
compared with 15 inches of water.

      The adverse effect of the side location can probably be explained
by the proximity of the wall and therefore its greater damping effect on
the generated water currents as compared with the central location.

      Limited data was also taken for two different disperser submergences
at the same air flow rate and water depth.  The results are shown in
Table V.

      It can be seen that the smaller the energy input (smaller submergence)
the longer was the mixing time. In addition to the smaller energy input,  the
system with a disperser raised 13 cm off the tank bottom, was further
handicapped in that the water level below the disperser was relatively
stagnant and thus more resistant to the currents produced by the plume.
                                      38

-------
                                Table V
             Effect of Disperser Submergence on Mixing Time
Air Flow
cc/min
150
300
600
150
300
600
Depth of
Disperser, cm
43
43
43
56
56
56
Water Height
cm
61
61
61
61
61
61
Mixing Time
min.
7.34
5.00
3.78
5.13
3.67
2.50
The above is in agreement with the observation of Gay and Hagedorn
(5) who found that for a fixed flow rate of air, mixing was achieved
more rapidly when the disperser was placed at the bottom of the tank
rather than at an elevated position.

   Effect of Bubble Size on the Pumping Capacity and the Mixing Time

      Since the density of the plume depends on the air holdup and there-
fore on the velocity of rise of bubbles, it was expected that the small
slowly rising bubbles should give a better pumping effect and therefore
a shorter time of mixing.

      Figures 30 and 31 show the effect of the bubble size  (equivalent
radius) on the pumping capacity and mixing time respectively.

      The tests were conducted in the restricted system.  The size of
the bubbles was adjusted by introduction of a small amount  of n-heptanol
to reduce bubble coalescence (22).  The largest bubble size was obtained
by mounting over the disperser a small cap with a hole 1/32" in diameter.
The mixing times were determined by means of the solid tracer.

      It can be seen from Figures 30 and 31 that a 6-fold decrease in the
bubble radius resulted in a 23% increase in the water flow  and a 19%
decrease in the mixing time.

      Baines and Hamilton  (1), studying the effect of orifice size on the
surface jet velocity, found that a change in the orifice size from 0.10
to 0.30 cm had no effect.  Similarly, Evans  (4) in a study  of pneumatic
breakwaters noticed only a small change in the velocity of  the surface jet
when the bubble diameter was changed from 0.45 to 0.65 cm.  Cyr (3),
                                      39

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Tl

o
O)

>
o
z
c
H
   50
   40
   30
   20
    10
                                   AIR  FLOW RATE

                                   = 600 CC/MINUTE
    0.00
0.050   0.100
0.150
0.200   0.250   0.300    0.350   0.400   0.450
                    AVERAGE  BUBBLE SPHERICAL  RADIUS - CM

                                  FIGURE 30

                    FLOW  IN STACK  VS BUBBLE  SIZE

-------
m
m
   4.75  -
   4.50
x
o  4.25
m
 1   4.00
2
z
c
m
    375
3.50
  0.00
                                                AIR  FLOW RATE
                                                = 600  CC/MINUTE
                               -L
                                            _L
                                                                _L
                                                  J.
              0.050
0.100    0.150    0.200   0.250   0.300   0.350
AVERAGE BUBBLE  SPHERICAL  RADIUS - CM
               FIGURE 3|

  MIXING TIME  VS  BUBBLE  SIZE
                                                                      0.400   0.450

-------
investigating the effect of process variables on the performance of a gas
lift circulator found that a 25% increase in the water flow was obtained
by decreasing the bubble radius from 0.33 to 0.04 cm.

      Inspection of charts relating bubble velocities to their sizes
(17, 6) shows that for bubble radii above the range of 0.06 to 0.08 cm
the velocity of rise (and therefore the holdup) does not depend much on
the bubble size.  However, below this range the bubble velocity drops
rapidly with the size of the bubbles resulting in a greater air holdup.

      It is noted that for both the work of Baines and Hamilton (1) and
Evans (4) the bubble sizes were in the region where the velocity of rise
was relatively independent of size.  Hence, no significant change in the
pumping effect would be expected.

      In the present research the bubble size was decreased to a radius
less than 0.05 cm.  Bubbles of this size have velocity of rise about
10 cm/sec while those having a radius of 0.3 cm; rise with a velocity almost
three times as great (28 cm/sec).  The smaller velocity of the bubbles used
in this work, and the resulting increase in the residence time must have
been the main factor responsible for the increased pumping effect.

      Although the effect of bubble size on both the pumping performance
and mixing time was not very great, it was, however, sufficiently pronounced
to be considered as a design variable.

      This point may be of special importance in the case where bubble coal-
escence occurs at the surface of the air disperser.  Minute quantities of
surfactants or other coalescence preventing agents would then have a
marked effect on the size of the bubbles.  A similar effect could be
expected in solutions of inorganic salts (e.g. sea water) but at a higher
concentration (23).

                          Correlation of Data
      The experimental variables were correlated by means of Dimensional
Analysis assuming isothermal operating condition.  This last assumption
was in agreement with the conditions of the work and at the same time
gave the advantage of reducing the number of variables to those of
essential importance in the system.  The analysis resulted in the
following relationship:


                                "(fR

      where:       0 * Mixing time, min.
                                                      2
                   g = Acceleration of gravity, cm/sec

                   D = Principal dimension of tank, cm
                                      42

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                   H = Height of water in tank, cm

                   Fr = Froude number, dimensionless.

The appearance of Froude number in the above equation is understandable
since both inertia and gravitational forces are of primary importance in
this system.  The above correlation is shown graphically in Figure 32 in
which the Froude number was defined as the densimetric Froude number
expressed as (26):
                   Fr .
      where:     Q = Air flow rate, cc STP/min

                 A = Cross  section of  tank,  cm

                 Ap = Density difference between water and plume,Sr/cc

                 pw » Density of  water Sr/cc

 Although  there is a considerable spread  of  data,  this correlation  shows
 a satisfactory relationship,  especially when the small size  of  the  tank
 is taken into consideration.
                                        43

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  5000

  4000

  3OOO



  2000 -
  1000
^  900
•se  eoo
°  700
   5OO

   4OO


   300



   2OO
    100
SOLUTION  TRACER
  INTRODUCTION
o  30 WATER
•  24* WATER
«  15" WATER
                                  I   '	I—LJ_L
                       5   6 7 8 9 10
                                                       30
                         0,5    -050   3
                     (FR)   IH/D)   x 10
                             FIGURE 32
               e
              vs
                                         -0.20

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                               SECTION IV

                               References
 1.   Baines,  W.  D.  and Hamilton,  G.  F., "On the Flow of Water Induced
     by a Rising Column of Air Bubbles," 8th Congress.  Int.  Assoc.  of
     Hydraulic Res.,  Aug.  1959.

 2.   Cook, M. W. and  Water, E. D., "Operational Characteristics of  Sub-
     merged Gas Lift  Circulators," U.S. Atomic Energy Commission, Dec.
     1955.

 3.   Cyr, Steven, "Induced Air Circulation of Water,"  Unpublished
     M.S. Thesis, U.  Maine, Orono, 1970.

 4.   Evans, J. T.,  "Pneumatic and Similar Breakwaters," Proc. Royal
     Soc., A231, 1955, p.  456.

 5.   Gay, F.  and Hagedorn, Z., "Forced Convection in a Stratified Fluid
     by Air Injection," M.I.T. Thesis, Jan. 1962.

 6.   Haberman, W. and Morton, R.  K., "An Experimental Investigation of
     the Drag and Shape of Air Bubbles Rising in Various Liquids,"  David
     Taylor Model Basin, U.S. Navy,  Sept., 1953.

 7.   Harrel,  J.  E., "Mixing of Fluids in Small Diameter Tanks by Circu-
     lation," AEC Y-1531,  April,  1966.

 8.   Hinze, J. 0.,  "Turbulence,"  McGraw-Hill Book Co.,  New Ydrk, 1959,
     pp. 119-122.

 9.   Johnstone,  R.  E. and Thring, M. W., "Pilot Plant Models and Scale-
     up," McGraw Hill Book Co., New York, 1957, pp. 33-35.

10.   Kurihara, M.,  "Pneumatic Breakwaters," Parts I, II, and III,  Proc.
     of 1st Conferences on Coastal Eng. in Japan, Nov., 1954.

11.   Lament,  A.  G.  W., "Air Agitation and Pachuca Tanks," Can. J.  of
     ChE., Aug.  1958, pp.  153-160.

12.   Morton,  B.  R., et al, "Turbulent Gravitational Convection from
     Maintained and Instantaneous Sources," Proc. Royal Soc., 234A,
     Jan. 1956, pp. 1-23.

13.   Nevers,  Noel De, "Bubble Driven Fluid Circulations," AIChE J.,
     March, 1968, pp. 222-226.

14.   Nickerson, H., "Gloucester-Forced Circulations of Babson Reser-
     voir," Div. of San. Eng., Mass. Dept. of Health, Boston, 1960.

15.   Parker,  N. H., "Mixing," ChE, June 8, 1964, pp. 165-220.
                                   45

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16.  Riddick, T. M.,  "Forced Circulation of Reservoir Waters," Water
     and Sewage Works, Vol. 104, No. 6, June, 1957, pp. 231-237.

17.  Rosenberg, B., "The Shape and Drag of Air Bubbles Moving in
     Liquids," Report 727 Navy Dept., Sept., 1950.

18.  Straub, L. G., and others, "Experimental Studies of Pneumatic and
     Hydraulic Breakwaters," U. Minn., St. Anthony Falls Hydraulic Lab.,
     Tech. Paper No.  25, Series B, Aug., 1959.

19.  Taylor, G., "The Action of a Surface Current Used as a Breakwater,"
     Proc. Royal Soc., A231, 1955, pp. 467-478.

20.  Thermal Systems, Inc. Bulletin TBS, St. Paul, Minn.

21.  U. S. Dept. of H.E.W., Public Health Service, "Water Qualities
     Behavior in Reservoirs," compiled by J. Symons.  (1969)

22.  Zieminski, S. A., et al, "Behavior of Air Bubbles in Dilute Aqueous
     Solutions," Ind. Eng. Chem., May, 1967, pp.  233-242.

23.  Zieminaki, S. A. and Whittemore, R.C., "Behavior of Gas Bubbles in
     Aqueous Electrolyte Solutions," ChE. Sci., Publication  Pending.

24.  Zlokarink, M., "Homogenisieren von Flussigkeiten durch Aufsteigende
     Gasblasen," Chem. Ing.-Techn., 4_0, 1968, pp.  765-769.

25.  Bryan,  J.  G., "Improvement in  the Quality of Reservoir Discharges
     Through Reservoir Mixing and Aeration," R. A. Taft San. Eng. Center,
     Cinn.,  Ohio,  April 3-5, 1963, PHS Publ. No.  999-WP-30, June 1965,
     pp.  317-34.

26.  King,  D.L.,  "Hydraulics of Stratified Flow," Report No. Hyd-563,
     Hydraulics Branch, Division of Research, U.  S.  Dept. of Interior,
     June 3, 1966.
                                    46

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1

5
Accession Number
n Subject Fii-ld & Group
05G
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization

          University of Maine, Orono, Maine 04473
          INDUCED AIR MIXING OF LARGE BODIES OF POLLUTED WATER
10

Auttt9t
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          WATER POLLUTION CONTROL RESEARCH SERIES

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