EPA-R2-72-053
NOVEMBER 1972 Environmental Protection Technology Series
Initial Mixing in
Coagulation Processes
Office of Research and Monitoring
U.S. Environmental Protection Agency
Washington, D.C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and
Monitoring, Environmental Protection Agency, have
been grouped into five series. These five broad
categories were"established to facilitate further
development and application of environmental
technology. Elimination of traditional grouping
was consciously planned to foster technology
transfer and a maximum interface in related
fields. The five series are;
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
H. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL
PROTECTION TECHNOLOGY series. This series
describes research performed to develop and
demonstrate instrumentation, equipment and
methodology to repair or prevent environmental
degradation from point and non-point sources of
pollution. This work provides the new or improved
technology required for the control and treatment
of pollution sources to meet environmental quality
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EPA-R2-72-053
November 1972
INITIAL MIXING IN COAGULATION PROCESSES
by
Richard J. Stenquist
Warren J. Kaufman
Project 17030 DLX
Project Officer
Dr. Sidney A. Hannah
National Environmental Research Center
Environmental Protection Agency
Cincinnati, Ohio 45268
Prepared for
OFFICE OF RESEARCH AND MONITORING
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D. C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office
Washington, D.C., 20402 - Price $2.25
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EPA Review Notice
This report has been reviewed by the Environ-
mental Protection Agency and approved for
publication. Approval does not signify that the
contents necessarily reflect the views and policies
of the Environmental Protection Agency, nor does
mention of trade names or commercial products
constitute endorsement or recommendation for
use.
u
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ABSTRACT
This investigation was undertaken with the objective of determining the
importance of the initial mixing step in water and wastewater treatment
processes and determining whether increasing the rapidity of the initial
mixing could improve process performance. The principal process con-
sidered was alum coagulation-flocculation of a kaolin suspension in water.
The initial mixing device under consideration was a biplane, square-mesh
grid of bars placed in a turbulent flow, tubular reactor; a 2-in. pipe
was used in the present studies. Studies were made using a single electrode
"point" conductivity probe and NaCl solution tracer to determine what para-
meters affect the mixing which occurs in the turbulent flow field down-
stream from a grid, and from these results a general mixing model was
developed. The relation between initial mixing and process performance
was studied by using two of the grids from the mixing studies as initial
mixing devices in coagulation of a kaolin suspension.
This report was submitted by University of California Sanitary Engineering
Research Laboratory, College of Engineering and School of Public Health,
Berkeley, California, in fulfillment of Project 17030 DLX under the
sponsorship of the Environmental Protection Agency.
iii
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CONTENTS
Section Page
I Summary and Conclusions 1
II Recommendations 5
III Introduction 7
IV Review of Fundamental Theory: Turbulence,
Mixing and Coagulation 11
V Mixing Studies: Apparatus and Methods 47
VI Mixing Studies: Results and Analysis 71
VII Initial Mixing and Alum Coagulation
Flocculation 91
VIII Acknowledgments 115
IX Appendices 117
X Glossary 151
XI References 157
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FIGURES
PAGE
1 MEAN AND FLUCTUATING COMPONENTS
OF VELOCITIES i3
2 LONGITUDINAL AND LATERAL CORRELATION
FUNCTIONS AND LATERAL MICROSCALE, \ ,
FOR ISOTROPIC TURBULENCE g 15
3 DECAY OF TURBULENCE AS MEASURED BY VARIOUS
INVESTIGATORS 22
4 INTEGRAL SCALE OF TURBULENCE AS
MEASURED BY VARIOUS INVESTIGATORS 23
5 UNIVERSAL FORMS OF SCALAR AND VELOCITY
SPECTRA 29
6 CONCENTRATION OF VARIOUS ALUMINUM
SPECIES IN EQUILIBRIUM WITH FRESHLY
PRECIPITATED Al(OH)3 36
7 EFFECT OF COLLOID CONCENTRATION ON
COAGULANT REQUIRED FOR DESTABILIZATION
(AT CONSTANT pH) 40
8 FRACTIONAL CONVERSION AS A FUNCTION OF
ACCOMPLISHED MIXING 45
9 ILLUSTRATION OF CONDUCTIVITY PROBE 51
10 SINGLE ELECTRODE CONDUCTIVITY PROBE 52
11 PROBE IN PLACE IN TUBULAR REACTOR 52
12 BLOCK DIAGRAM FOR TEKTRONIX TYPE 3C66
CARRIER AMPLIFIER 54
13 AC BRIDGE CIRCUIT 55
14 PROBE CONNECTED IN PARALLEL WITH
120-OHM RESISTOR 57
15 TYPICAL CALIBRATION CURVE FOR SINGLE
ELECTRODE CONDUCTIVITY PROBE 59
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FIGURES (Continued)
PAGE
16 ELECTRONIC EQUIPMENT FOR MIXING
EXPERIMENTS 60
17 SCHEMATIC ILLUSTRATION OF EXPERIMENTAL
SETUP FOR MIXING EXPERIMENTS 61
18 CUTAWAY VIEW OF INJECTION MANIFOLD
AND GRID SECTION 63
19 CUTAWAY VIEW OF PROBE SECTION 64
20 MULTIPLE-ORIFICE GRID 66
21 INJECTION MANIFOLD AND GRID SECTION 66
22 HEAD LOSS COEFFICIENTS FOR SQUARE-
MESH GRIDS 69
23 DECAY OF CONCENTRATION FLUCTUATIONS
DOWNSTREAM FROM A GRID 72
24 a1 vs. QT FOR GRID WITH M/d = 4 75
25 EFFECT OF SCALE OF TURBULENCE ON
SCALAR DECAY RATE 77
26 EFFECT OF THE NUMBER OF ORIFICES ON
SCALAR DECAY RATE 79
27 INVERSE RELATIONSHIP BETWEEN NUMBER
OF SOURCES AND a FOR GRIDS WITH M/d =4 80
28 EFFECT OF CHANGING ORIENTATION OF
TRACER INJECTION SYSTEM ON SCALAR
DECAY RATE 82
29 RESULTS OBTAINED FROM GEOMETRICALLY
SIMILAR GRIDS 84
30 EFFECT OF VARYING M 85
31 GENERAL MIXING MODEL: RESULTS FOR
SEVEN GRIDS 90
vi i
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FIGURES (Continued)
32 EFFECT OF SEGREGATION ON COAGULATION-
FLOCCULATION JAR TESTS
33 RELATION OF pH AND ALKALINITY AT
"OPTIMUM" ALUM DOSAGES
34 INITIAL MIXING APPARATUS FOR CONTINUOUS
FLOW COAGULATION-FLOCCULATION STUDIES
35 EFFECT OF INITIAL MIXING DEVICE ON
FLOCCULATION PERFORMANCE: SINGLE
COMPARTMENT, T = 5 MIN 106
36 EFFECT OF INITIAL MIXING DEVICE ON
FLOCCULATION PERFORMANCE: TWO
COMPARTMENTS, T = 10 MIN 107
37 EFFECT OF INITIAL MIXING DEVICE ON
FLOCCULATION PERFORMANCE: THREE
COMPARTMENTS, T = 15 MIN 108
38 EFFECT OF SEGREGATION ON COAGULATION-
FLOCCULATION: CONTINUOUS FLOW TESTS 109
39 EFFECT OF INITIAL MIXING ON FLOCCULATION
PERFORMANCE: COMPARISON BETWEEN FLASH
MIXER AND NO INITIAL MIXING UNIT, ALKALINITY
= 70 mg/l 110
40 SEGREGATION JAR TESTS FOR VARIOUS
SEGREGATION TIMES -ALUM COAGULATION
OF RAW SEWAGE 113
vui
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TABLES
No. Page
1 Types of Reactions Involved in Hydrolysis
ofAl(III) 38
2 Grid Characteristics 65
3 Head Loss Through Grids at Various Velocities 70
4 Aggregation Rate Coefficients for Continuous
Flow Experiments 109
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SECTION 1
SUMMARY AND CONCLUSIONS
The purpose of this investigation has been to determine criteria for
the design of turbulent flow, tubular reactors for the initial mixing of
chemicals in water treatment processes using a biplane grid to inject
the chemical and produce the turbulence. Initial mixing is important
because certain physical-chemical reactions, if they occur before the
mixing of the chemical with the main stream, are detrimental to pro-
cess performance. Use of a grid initial mixer can provide a more
rapid mixing of the chemical with the waste stream. The principal
process under consideration was alum coagulation-flocculation of
turbid suspensions in the clarification of surface waters. Other pro-
cesses considered were wastewater chlorination and chemical
coagulation of wastewater with alum or ferric chloride.
A salt solution tracer and a single electrode conductivity probe used
in conjunction with an AC bridge amplifier and an rms voltmeter were
utilized to determine the parameters governing the mixing which occurs
when a tracer is injected into a tubular reactor through multiple
orifices. An attempt was made to correlate the results to allow pre-
diction of the mixing characteristics for other grids.
Two of the grids used in the mixing studies v/ere then utilized as
initial mixing units in a pilot-scale coagulation-flocculation of a kaolin
suspension, and the results were compared with those obtained using
a flash mixer. It was possible to attain some understanding of the
time of mixing necessary to obtain better process performance. It
should be emphasized that while the prediction of mixing produced by
larger grids may be possible, the larger grids will necessarily pro-
duce greater times of mixing and poorer process performance. Part
of the prototype design problem will be the construction of a fairly
fine grid rnesh in relatively large conduits.
Attempts were also made to determine whether the initial mixing
step is important in coagulation or chlorination of wastewater.
Specific conclusions follow.
MIXING EXPERIMENTS
Sections V and VI describe experiments intended to ascertain the
parameters which determine the degree of mixing downstream from
a grid in a turbulent flow, tubular reactor- A summary of the results
is as follows;
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1. Mixing in a grid type tubular reactor takes place in two stages.
The first, termed wake-mixing, takes place in a region very
close to the grid bars as the tracer spreads out across^the^cross-
section of the reactor. The rms concentration fluctuation just
downstream from the wake-mixing region may be less than 1%
°f the calculated initial rms concentration fluctuation, a^ =
AT-y/QT/QM>. However, beyond the region of wake-mixing, the
"point" concentration may still vary considerably from the
spatial mean concertratioru The second stage occurs in a region
which begins at a point several grid bar diameters downstream
from the grid. In this region isotropic turbulence and scalar
fields exist, and the decay of rms concentration fluctuations with
time or distance from the grid can be plotted as a straight line
on log-log paper.
2. The scale of turbulence has a definite effect on the scalar decay
rate in the region where isotropic turbulence is present beyond
the region of wake-mixing. For example, small grid bars result
in a lower rate of decay than large bars, and the scale of turbulence
is proportional to the grid bar diameter.
3. The number of tracer injection orifices per unit area of reactor
cross-section does not appear to have a marked effect on the
rate of scalar decay. It does, however, greatly influence the
extent of wake-mixing and will be important when large conduits
are considered for tubular reactors in prototype treatment plants.
4. The direction of tracer injection (upstream or downstream)
has a marked influence on the rate of scalar decay (and also on
the wake-mixing), it being greatest when the injection orifices
face upstream. As the turbulent flow field is essentially inde-
pendent of the manner in which the tracer is introduced, it
must be concluded that the scalar decay rate must be dependent
on characteristics of the scalar field possibly the scale of
segregation.
5, Scalar decay downstream from a grid follows the relation
a1 n _
S. = <*" (x/d)"a
A
where a' is the rms concentration fluctuation, A is the mean
concentration of the tracer mixed with the main flow, ns is the
number of orifices per unit area of reactor cross-section, a"
is a coefficient which depends on the method of scalar injection,
x is the distance downstream from the grid, d is the grid bar
diameter, and a is the scalar decay rate which is dependent on
the method of scalar injection and the grid bar diameter.
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It appears that head losses incurred by grid mixing devices can
be kept to less than 6 in. providing the M/d ratio, the ratio of
the center-to-center bar spacing to bar diameter, is greater
than about 3. 0 (solidity less than approximately 50%). Allowable
head loss, of course, will depend on the specific details of each
situation.
TREATMENT PROCESSES
The effect of initial mixing in three treatment processes, alum coagula-
tion of a kaolin suspension, chlorination of wastewater, and chemical
coagulation of wastewater, was studied. The conclusions for each
process are given below:
Alum Coagulation of a Kaolin Suspension
7. The crucial "reactions" which occur are very rapid. This was
demonstrated by the fact that in a continuous flow experiment,
a high-speed flash mixer produced turbidity removals which were
no better than those obtained when the alum feed solution was
added directly to the first compartment of the pilot-scale
flocculator, a very poor initial mixing situation.
8. Performance was improved by using grid initial mixers (d = 1/8 in. ,
M/d =4) in a 2-in. diameter tubular reactor. One grid had 24
tracer injection orifices; the other had 4. The value of ns,
the injection orifice density, for each was 7. 60 in. "2 and 1. 27 in."?
respectively. Improvement in performance over, that of a flash
mixer was obtained with both grids, and the 24-orifice grid per-
formed better than the 4-orifice grid. From the results obtained,
it can be estimated that an orifice density of at least 1. 0 in. ~z is
needed to effect a significant improvement in performance. From
both a structual aspect and from consideration of head loss inside
the grid bars, this fine a grid for a prototype plant may be some-
what difficult to construct. Such techniques as placing smaller
grids within larger grids would probably be necessary.
9. It was found that the alkalinity of the raw water had a strong
influence on the importance of the initial mixing step, the effect
of rapid mixing increasing with increasing alkalinity. This may
be due to the buffering effect of the alkalinity (the reaction rates
and products appear to be pH dependent), or it may be due to more
direct action of the bicarbonate ion. Jar tests which simulate slow
and rapid initial mixing were utilized to demonstrate the effect of
the alkalinity. The effect was also seen in the continuous flow
experiments.
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Chemical Coagulation of Wastewater
10. To determine whether the initial mixing step may be important
in chemical coagulation of sewage, segregation jar tests
similar to those used with kaolin were done with sewage using
alum as the coagulant. It was found that, as with alum coagula-
tion of a kaolin suspension, the rapid initial mixing did provide
better results. More importantly, the crucial reactions in
sewage are apparently much slower than is the case with kaolin
suspensions. This means that it is not necessary to have the
high scalar injection orifice density required in the other pro-
cess, and the resultant design difficulties may not occur.
11. While these results may be extrapolated to include ferric
chloride coagulation of sewage, it has been found in other work
that in lime coagulation of sewage, the initial mixing step does
not appear to be critical.
Chlorination of Wastewater
12. Several experiments (described in Appendices A and B) were
done in order to determine if the initial mixing might be a
crucial step in that treatment process. The results indicated
that while at short contact times an improvement in performance
(as measured by coliform survival ratio) can be found, at
contact times similar to those found in practice no difference in
performance could be discerned. It does appear from the work
of others that a. tubular (plug flow) reactor, as opposed to a
back-mixed reactor, may improve performance.
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SECTION II
RECOMMENDATIONS
The recommendations resulting from this study can be divided into
two general areas: 1) designing a grid for full-scale plant experi-
ments and 2) continuing studies of the wake-mixing phenomenon.
The present investigation has shown that in pilot-scale operations,
initial mixing is an important step in alum coagulation-flocculation
of a clay suspension. It remains to be shown that sufficiently rapid
mixing can be effected in a full-scale treatment plant to provide a
significant improvement in performance. Future studies in initial
mixing should be directed toward this objective.
From the present studies it appears that wake-mixing may be critical.
From the results obtained it can be estimated that an injection orifice
density of at least 1. 0 in. ~2 is needed to obtain a significant improve-
ment in performance. The grid, however, must be fine enough to
allow the orifices to be spread evenly across the reactor cross-section.
With M/d = 3, 1/2-in. O. D. bars spaced 1-1/2 in. center-to-center
would be required for a biplane grid. An orifice would be located
halfway between each grid bar intersection. A grid consisting of one
row of bars would necessitate 1/2-in. bars spaced i in. center-to-
center (solidity = 50%).
It would be desirable to have grids with orifice densities greater than
1 in. ~2. To accomplish this, finer grids will have to be constructed.
Placing small grids (e.g., 1/4-in. bars spaced 1/2-in. center-to-
center) within larger grids (e. g. , 1-1/2-in. bars spaced 6-in. center-
to-center) used to feed the coagulant into the smaller bars is one way
of attacking the problem.
In such a demonstration it would be desirable to keep the head loss to
less than about 6 in. Solidities between approximately 25% and 50%
will usually accomplish this.
Since the effect of initial mixing depends upon the alkalinity of the
water, any plant-scale projects should be done with a water of high
alkalinity, preferably greater than 100 mg/i.
One area of possible exploration is the use of grids at more than one
point along a tubular reactor. It should be noted, however, that this
simulates backmixing, and if backmixing is detrimental to process
performance, the expected improvement may not be realized.
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Use of grid Initial mixers for other treatment processes should also
be considered. It seems that rapid initial mixing can result in a
significant Improvement In chemical coagulation of wastewater, a
process which is often found in advanced waste treatment schemes.
It is believed that the injection orifice density need not be as great as
that required for coagulation of kaolin suspensions. While it appears
from the present investigation that the Initial mixing step in waste -
water disinfection Is not as critical as first believed, the conclusions
reached are only tentative, and further research in this area merits
consideration.
Improvements in wake-mixing should be developed. For example,
it was found that when the tracer injection orifices faced upstream
wake-mixing provided less reduction In the concentration fluctuations.
Perhaps mixing could be improved by placing the orifices so that the
chemical would enter at right angles to the flow. Using square grid
bars instead of round bars might Improve performance. It appears
that wake-mixing is the critical step, and any improvement in this
area will probably improve process performance.
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SECTION III
INTRODUCTION
In any water or wastewater treatment process which requires the
addition of chemicals, the initial mixing step is often a poorly designed
aspect of the treatment scheme. This has been largely due to ignorance
concerning the importance of initial mixing and the lack of any basic
rational design criteria. In some respects it has been "essentially an
art" [ 1] , and most designs have been made on the basis of personal
experience, intuition, and trial and error.
Much of the contemporary mixing literature in the field of sanitary
engineering has been confined to the study of rotating impellor type
mixers and development of model laws applicable to them. Most
initial mixing units have been flash mixers; short residence time
CSTR's utilizing high-speed impellers to produce homogeneous mixtures
through convective dispersion and turbulent mixing.
It is believed that a different type of mixer which reduces quickly the
segregation between the added chemical and the water stream can be of
great importance in improving the performance of water and waste-
water treatment facilities. When the chemical is added to the water
stream, certain crucial physical-chemical reactions, if completed be-
fore segregation is eliminated, can result in less than optimal per-
formance or the use of greater quantities of chemical than actually
needed. In many processes a flash mixer cannot provide the required
very rapid rate of mixing.
Another feature of the flash mixer is backmlxing mixing between
fluid elements which have been present in the reactor for different
lengths of time. A result is that reactants entering the mixer may
"react" with previously formed "reaction" products rather than with the
constituents of the water stream which are of concern. A specific
example is aluminum sulfate coagulation-flocculation of a turbid
water in which the alum entering the backmixed reactor can react with
previously formed floes instead of with turbidity-producing particles.
A tubular reactor with characteristics close to plug flow would eliminate
the backmixing. A type of tubular reactor which is fairly amenable to
analysis has a square mesh grid of bars placed normal to the axis.
As the flow passes through the grid, turbulence is produced which can
be utilized to mix the two fluid streams. Orifices drilled in hollow
grid bars can be used to inject chemicals into the water stream. This
allows the chemical to be released at many points across the cross-
section of the pipe which may be an important consideration in quickly
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reducing segregation. Grids have been used extensively in studies
involving turbulence, and there have been a few studies involving
mixing with such devices.
OBJECTIVES
The principal objective of this investigation was to develop criteria
for the design of turbulent flow, tubular reactors, utilizing a biplane
grid to inject a reactant and to produce turbulence. This objective
gives rise to three related questions:
i. What parameters of the turbulent flow field, the scalar (tracer
or treatment chemical) field, and the scalar material determine
the "goodness of mixing" downstream from a grid initial mixer
(e. g. , molecular diffusivity and intensity of turbulence may be
important factors)? Implicit in this question is the necessity
of defining "goodness of mixing, "
2. What physical parameters should be used for design and scale -
up of such initial mixers (e. g. , mean flow velocity, grid bar
diameter and grid solidity)?
3. What level of "goodness of mixing" is necessary, and how
rapidly must this be achieved in order to attain a given level
of performance? It will be necessary to relate the level and
rapidity of mixing directly to process performance. This
is a question which the present investigation answers only
partially. Most of the effort of this study was directed toward
objectives 1 and 2. However, certain conclusions will be drawn
from experiments performed with three treatment processes:
alum coagulation-flocculation of a kaolin suspension in water,
chemical coagulation of wastewater (with alum or ferric chloride),
and chlorination of wastewater.
ORGANIZATION OF REPORT
Section IV is a review of turbulence.- mixing, and coagulation and
flocculation theory and experiments pertaining to this investigation.
A short review of research involving the initial mixing step in sanitary
engineering is also given.
Sections V and VI cover the experiments done to determine the parameters
which affect the degree of mixing downstream from a grid in a turbulent
flow, tubular reactor (objectives 1 and 2). A single electrode conductivity
probe was used to determine the root-mean-square concentration
fluctuations produced by various grids. An attempt was made to
correlate these results in a manner which allows prediction of the
"goodness of mixing" produced by any square mesh grid. Also covered
are experiments to determine head or energy loss which results from
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grids being placed in a tubular reactor. In some instances, the
allowable head loss will be restricted to not more than a few inches,
while in others several feet may be available.
In Section VII experiments are described which reveal the importance
of the initial mixing step in alum coagulation-flocculation of a kaolin
suspension in water. Two of the grids studied in experiments described
in Sections V and VI were used as initial mixing devices in a pilot-
scale study. Results produced by them were compared with results
obtained with a flash mixer and "with no initial mixing unit. The effect
of alkalinity of the raw water on the importance of the initial mixing
step was also studied. Jar tests which can be used to determine the
significance of initial mixing for a given process and raw water are
described. Also covered is alum coagulation-flocculation of waste-
water.
Appendices A and B cover the experiments concerned with initial
mixing and chlorination of wastewater. This aspect is presented
in appendices because the experiments were limited in nature and
the conclusions drawn are tentative.
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SECTION IV
REVIEW OF FUNDAMENTAL THEORY: TURBULENCE,
MIXING AND COAGULATION
ISOTROPIC TURBULENCE
Turbulence is a phenomenon associated with a fluid flowing at a high
Reynolds number. This fluid may be the atmosphere or water flowing
in a river. The conditions under which turbulence occurs are very
diverse. Its defining characteristic is random fluctuations of the fluid
velocity. Hmze [ 2] has defined turbulence in the following way: "Tur-
bulent motion is an irre'gular condition of flow in which the various
quantities show a random variation with time and space coordinates,
so that statistically distinct average values can be discerned. " This
report will be primarily concerned with a particular type of turbulence -
that produced by water flowing through a biplane grid of bars placed
in the cross -section of the pipe. As will be seen, this type, (isotropic,
decaying turbulence) is fairly amenable to theoretical analysis, can be
simply produced in the laboratory, and has been extensively studied.
The concept of turbulence in a particular system is very closely
associated with the energy being dissipated in that system. In ordinary
pipe flow, for example, an energy loss will occur due to wall friction,
and this energy is lost from the system through the dissipation of heat.
Approximately half of the energy lost from the flow produces heat
directly through internal viscous friction associated with gradients Ln
the flow. The other half of the energy goes first to turbulence pro-
duction and then to heat. In grid-produced turbulence probably most
of the energy goes into turbulence production.
Turbulence is a random phenomenon; a Fourier analysis of the instan-
taneous velocity fluctuations at a point in a turbulent flow field will
show that the fluctuations can be associated with a range of frequencies.
The lowest frequencies will be determined by the geometry of the
physical system, while the highest frequencies will be dominated by
viscosity effects. These velocity fluctuations are related closely to
the kinetic energy of turbulence. The turbulent kinetic energy is
distributed over the range of frequencies with a distribution termed
the energy spectrum. It has been found that energy introduced into a
system at lower frequencies is dissipated by viscosity at higher fre-
quencies. This results in a transfer of energy from lower to higher
frequencies. The form of the energy spectrum and the laws governing
the transfer of energy have been studied extensively in order to under-
stand better the phenomenon of turbulence.
A qualitative picture of turbulence has only limited value, and a more
detailed quantitative description is necessary. For a more complete
11
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coverage of the topics discussed herein, reference is made to Hinze
[ 2], Lee [ 3], Brodkey [ 4], and Batchelor [ 5].
If a grid is placed in a pipe through which water (or any fluid) is
flowing, turbulence will be produced downstream. Because energy is
added only at one point, the turbulence will decay with time (and
distance downstream) because of the action of viscosity. Homogeneous
turbulence is that which does not change itr character with translation
with a set of coordinate axes. Isotropy, a stronger condition which
includes homogeneity, occurs if the character of the turbulence is
such that its statistical features do not change with rotation or reflection
of a set of coordinate axes. While turbulence produced by a grid decays
in the downstream direction, isotropic turbulence is closely approximated
in these experimentSj and comparison between them and isotropic theory
shows good agreement.
Root-Mean-Square Velocity and Correlations
If the velocity in the direction of flow downstream from the grid is
measured with a hot-wire anemometer, it will be found to consist of a
mean and a fluctuating component: U1 = U1 + ut (Figure 1).
An important parameter of turbulence is the root-mean-square velocity
fluctuation:
u{ =Vuf
(i)
where the overbar indicates averaging. This is called the "intensity
of turbulence. "
Isotropy requires that all three components of the rms velocity
fluctuations be equal, i. e.
u< =U{ =u<2 =ui . (2)
The nature of isotropic turbulence also requires that there be no cross
velocity term, that is
u2 = ut u3 = u2u3 = 0 . (3)
These terms are the Reynold's stresses and are the contribution of
the turbulent motion to the total shear stress. In isotropic turbulence
there is no shear stress and no gradients of mean velocity.
Taylor [ 6] first pointed out that in turbulent flow there will be a
statistical correlation between the fluctuating velocities at two points
12
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0
o
o
U,
u,
FIGURE 1. MEAN AND FLUCTUATING COMPONENTS OF VELOCITY
a small distance apart, with correlation decreasing as the separation
distance increases. A statistical analysis can be made by studing
the mean product of the fluctuating velocity components at the two
points.
Correlation tensors and correlation functions can be defined by con-
sidering the fluctuating velocities at two points separated by a dis-
tance r.
13
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Two correlation functions are widely used in the study of turbulence;
The longitudinal correlation function, f(r), and the lateral correlation
function, g(r),
u (x) u (x+r)
, > n n
g(r) =
u'2
The subscript r denotes that the velocity fluctuation is measured in
the same direction as the vector r" The subscript^ indicates the
velocity fluctuation is measured normal to vector r, Batchelor [ 5]
has shown that only one scalar function is necessary to specify the
velocity correlation at two points in isotropic turbulence- Therefore
g(r) and f(r) cannot be independent. They are related by
(\
l^rM (6)
If the separation distance is reduced to zero, the values of f(r) and
g(r) become unity. As the separation distance is increased, the
correlation functions decrease (see Figure 2).
In defining the above correlation tensors and functions, a Eulerian
viewpoint has been taken with the correlation between velocities at
two fixed points in the flow field separated by a distance r considered.
It is also possible to define Lagrangian correlation functions which
would correlate the velocity fluctuations of a fluid particle at two
different times along its path of travel, For a more complete dis-
cussion of Lagrangian correlations see Hinze [ 2] or Brodkey [4]
Scales
The correlation functions given by Equations (4) and (5) can be used
to define certain scales of turbulence, The longitudinal and lateral
integral scales are defined respectively as
CD
f(r) dr
i
o-
CO
L = f g(r) dr
5 n J
(8)
14
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1. 0
FIGURE 2. LOGITUDINAL AND LATERAL CORRELATION
FUNCTIONS AND LATERAL MICROSCALE, \ , FOR
ISOTROPIC TURBULENCE
g
These scales can be considered measures of the longest distance which
results in a finite correlation between the velocity fluctuations at the
two points. In turbulent flow, attempts are often made to relate L£
and Lg to the geometry of the system. For example, in pipe flow L£
may be taken as a certain fraction of the pipe diameter. In grid-
produced turbulence attempts have been made to relate L.. to the bar
spacing or bar diameter.
Since f(r) a.nd g(r) are related by Equation (6), L. and L must also
be related. The equation is °
L = 1/2
g
(9)
-------
Two other important scales 'can be defined from the functions f(r) and
g(r). These scales are related to the shape of the correlation functions
near r = 0, It is possible to expand f(r) in a Taylor series:
f(r) -
21
r =o
4!
(10)
r =o
For very small values of r, f(r) approaches a parabolic function of r.
It is possible to introduce a length X,. such that
f(r)= 1 - f
(ID
Where X is called the microscale of turbulence Ignoring the higher
order terms in Equation (10) and equating Equations (10) and (11), it
follows that i
l/Xf2 = 1/2
12!
'=O
A similar scale, X ., is defined by
O
131
r =o
From Figure 2, it can be seen that X. is the intercept along the r
axis of a parabola "whose curvature af r = 0 is the same as g(r).
X.. can be interpreted similarly.
It is known that X is closely related to the velocity fluctuation fre-
quencies at which the most dissipation of turbulent energy into heat
takes place. For this reason, it is often called the dissipation scale.
The relation between \. and X is
f e
Xr = X
(14)
Energy Spectrum Functions in Isotropic Turbulence
It was previously qualitatively stated that it was possible to view the
kinetic energy of turbulence as being distributed over a range of
frequencies In 1938 Taylor [ 7] showed that there is a relation
16
-------
between the one-dimensional energy spectrum function that is, one which
considers the velocity fluctuations in one direction only and the correla-
tion function f(r).
Ej (kj ) is the one-dimensional energy spectrum function associated with
the wave number kj . t
k, = ££?-
Ui
where Uj is the mean flow velocity and n is the frequency. The sum of
Ej (kj ) over all wave numbers (or frequencies) must equal the total
turbulent kinetic energy in the Xj direction, or the mean square fluctua
ting velocity:
dkj =uf = u'2 (16)
Taylor showed that the longitudinal correlation function f(r) and one-
dimensional energy spectrum functions are Fourier cosine transforms
of each other, i. e. ,
00 '
f(r) = -V J Ei (ki ) cos (ki r) dki (1?)
u o
00
7 f
E'
O'
00
(kj ) =|u'2 ff(r) cos (kj r) dr . (18)
There is also a three-dimensional energy spectrum function E(k, t),
defined such that:
r* 3
J E(k,t) dk =| u'2
(19)
The one-dimensional energy spectrum function is related to E(k, t) in
the following manner.
r"0 / k 2 \
E! (k! , t) = J EIjp-) ( 1 - ^J- ) dk . (20)
ki \ /
Universal Equilibrium
It is known that the geometry of the physical system in which the flow
is taking place strongly affects the character of the low wave number
range of the turbulence spectrum. As has been noted, the integral
scale has often been related to a physical length involved, e. g. , the
pipe diameter in pipe flow. An equation can be derived [ 2] relating
Ej (o, t) and L,. However, it is found that at the higher wave numbers
17
-------
under certain conditions, i. e. , high Reynolds number, the form of the
spectrum is independent of the conditions in a particular turbulent
flow and. are universal in character. This theory was first proposed
by A. N. Kolmogoroff in 1941 [ 8-10] and is usually known as the
theory of universal equilibrium. It states that athigh wave numbers,
the turbulence is isotropic (no matter what the character of the over-
all turbulence may be) and that the spectrum in this universal equilib-
rium range will depend only on the rate of energy dissipation or
input, £, and on the kinematic viscosity, v.
Dimensional analysis reveals that a characteristic length and velocity
can be defined in terms of & and v. They are respectively,
un
v=(ve) . (22)
The length scale, T|, is often called the Kolmogoroff microscale of
turbulence. It should not be confused with \f and \g which were
discussed earlier and which are associated with G.I. Taylor. i / T)
= k^ can be taken as the wave number at which the maximum of the
diss ipation spectrum, k2 E(k, t), occurs.
A Reynolds number based on Equations (21) and (22) can be defined
and its value is equal to unity.
= i
V
This means that at the Kolmogoroff microscale, the inertial and
viscous forces are balanced. A higher wave numbers viscous
forces become predominant.
In order for the equilibrium range to exist, the energy input by
transfer must equal the energy dissipated by viscosity, or
3 Id u'2'
2ldt .
= 2 v J k2 E(k,t) dk . (23]
This will occur only if the wave numbers associated with the scale
Lf do not overlap with the wave numbers associated with the maximum
dissipation, or r\ <« Lf.
In terms of Reynolds number, this condition [ 2] is:
L (24)
In the universal equilibrium range, a dimens ionless function can be
found to relate E(k, t) to v and r\. Dimensional analysis shows that
-------
E(k.t) = v2 TI E (kri) (25)
e
or, substituting in Equations (21) and (22),
E(k,t) = v5/4 e1/4 E (kr|) . (26)
Thus, spectra, E(k, t), can be plotted in universal form by dividing by
v5'4 e1 '4 and plotting against kt|. The same holds for the one -dimensional
energy spectrum [11],
E! (kt t) =v5/4 e1/4 E! ^ r$ . (27)
An important corollary to the theory of universal equilibrium is that
for Reynolds numbers much higher than that given by Equation (24),
there is a subrange of wave numbers for which the form of the spec-
trum no longer depends on viscosity, but only on &. In other words,
energy is transferred in at the lower end of the wave number range
and is transferred out at the higher end of the range. No production
or dissipation of energy takes place. This is called the inertia!
subrange.
Hinze [ 2] concludes that the requirement for an inertial subrange to
occur is
' (28)
Gibson [11] derived the following criterion for the existence of an
inertial subrange:
u'Lf
- - > 3. 3 x 10s . (29)
It has been found that these criteria are essentially impossible to meet
with laboratory produced turbulence. Experiments have been done in
the ocean [ 12], however, with a Reynolds number, based on the channel
depth, of 10 8- It was found that an inertial subrange did exist and
extended over a wave number range of two orders of magnitude.
This conclusion was made by comparing measured spectra with the
form of spectra derived through dimensional analysis for the inertial
subrange.
E! (kj , t) = A! e2/3 kj " 5/3 . (3Q)
19
-------
A similar equation exists for the three -dimension spectrum,
E(k,t) =A e2/3 k'5/3 . (31)
It is widely accepted that this is the form of spectrum in the inertial
subrange.
For values of k > kT, in the universal equilibrium range, the dependency
r± _
on k is much greater, A relation [ 13] which agrees fairly well with
experiment is:
k-7 . (32)
Hinze [ 2] has noted certain errors in the derivation of Equation (32).
A summary of the above spectra "forms and the wave number ranges
is given in Figure 5 in the section on Review of Mixing Theory.
Decay of Isotropic Turbulence
The mixing which occurs downstream from a grid is in part governed
by the decay of the intensity of turbulence and the variation in the
scales of turbulence with increasing distance from grid. For this
reason it is important to review the theoretical and experimental
work in this field. As noted, isotropic turbulence is easily produced
by passing a fluid through a grid of bars. Development of the hot-
wire and hot-film anemometer have led to a great deal of experimenta-
tion, most of which has been done in air.
As the fluid passes through a grid with a center-to-center bar spacing,
M, and a bar diameter, d, turbulent wakes are produced behind the
grid bars a,s a result of vortex shedding.
This initial turbulence is highly anisotropic. However, these wakes
gradually coalesce and the resulting turbulence is reasonably close to
isotropic. The distance downstream at which this occurs is approximately
20 M.
Between 20M and 100 M to 150 M downstream, the initial period of
decay occurs. In this period, inertial forces are predominant in
determining the decay. At distances greater than approximately
500 M downstream, the Reynolds number of turbulence is very low,
and viscous forces predominate. As has been noted, the Ka.rma.n-
Haworth equation is soluble in this case, and the decay of the intensity
of turbulence has been found to follow the solution,
u12 = const x t" 5'2 (33)
20
-------
where t is the time.
In the initial period of decay, which is of greater interest, the most
well-known decay law is that proposed by Batchelor and Townsend [ 14]:
C
D
u,2
x-x
o
M
(34)
where c is a constant depending on grid geometry, Crj> is the drag per
unit area of the grid, x is the distance downstream from the grid, and
x is the distance from the grid of the apparent origin of the intensity
of turbulence. For round-bar, square-mesh grids, C-p can be obtained
from [ 2].
_ (d/M) (2 - d/M)
^D ~ (1 - d/M)4 '
Van der Hegge Zijnen [15] has reviewed the experimental work of
several experimental investigators, including Batchelor and Townsend.
He found that no general law such as Equation (34) holds for all ex-
periments. The rate of decay of u' (i. e. , the exponent in an equation
of the form u' = Kx~r) with distance varied from 1/2 as proposed by
Batchelor and Townsend to - 5/7, a value derived by Frenkiel [ 16].
Van der Hegge Zijnen found that it was possible to obtain a reasonable
correlation between the data of five different investigations by plotting,
MI '/Uj against (x-x )/d. There is considerable scatter which, makes
it difficult to rely on the graph to predict actual values of u1 for applica-
tion under a particular set of circumstances. The data are shov/n in
Figure 3.
It should be noted that, strictly speaking, it is inconsistent to plot
results as shown in Figure 3. It implies that there should be no
dependence of u1 on M/d. This ratio strongly influences the head loss
through the grid which determines the turbulent kinetic energy produced.
Inspection of Figure 35 however, shows no consistent dependence of
u1 on M/d. The conclusion which must be drawn is that other factors
such as experimental error must have produced differences in the
results which hide the dependence on M/d.
Van der Hegge Zijnen also compared results of six separate investiga-
tions of the variation of the integral scale, L., downstream from a
grid. L./d is plotted against (x-x )/d. M is the other parameter
often reiated to the scale of turbulence. Examination of Figure 4
shows no apparent dependence an M/d.
-------
po
10. 0.
8. 0
60
4. 0
2. 0
1. 0
0. 8
0. 6
0. 4
10
111
,v.
A a
A *
V
*
I
I
*
i
A M/d = 2. 0
V M/d =2.7
M/d =4
M/d = 5
O M/d = 8. 0
1 1 1 1
1 1
' BaB,
«
*
I
10
20
40 60 80 100
(x - x )/d
o
200
400 600 800 1000
FIGURE 3. DECAY OF TURBULENCE AS MEASURED BY VARIOUS INVESTIGATORS
(FROM VAN DER HEGGE ZIJNEN [ 15])
-------
10
8.0
6. 0
4. 0
2. 0
T3
M-l
J
1.0
0. 8
0.6
0.4
1 I 1 1 1 1 1 1 1
- « -
. £*ft»*"** -
.? *r*
'mf. s**r
-"."V"^4₯*|'V *
** ^° s^* *
A . v D M/d = 1.5
A M/d = 2. 0
£ v V M/d = 2. 7
D _
M/d = 4
9 M/d = 5
0 M/d = 8. 0
1 1 1 1 1 1 1 1 1
20 40 60 80 100 200 400 600 800 1000 200
(x - xo)7d
FIGURE 4. INTEGRAL SCALE OF TURBULENCE AS MEASURED
BY VARIOUS INVESTIGATORS
(FROM VAN DER HEGGE ZLJNEN [15])
-------
REVIEW OF MIXING THEORY
Criteria for Mixing
In a study of mixing it is first necessary to define the terms involved.
Brodkey [ 4] defines mixing to mean a blending into one mass "a
complex of two or more ingredients . . which, however thoroughly
commingled, are conceived as retaining a separate existence. " This
definition, however, does not allow visualization of the mixing process.
Consider, for example, the addition of a small amount of salt water to
a beaker of fresh water. If the water is stirred, the salt will become
spread throughout the beaker. Soon the salt concentration at all
"points" throughout the beaker will be the same. The mixing can then
be said to be complete. By a "point" is meant the smallest volume
which is still very much larger than the dimensions of the molecules.
How small this volume must be is not easily defined, Brodkey [4]
states that it must be submicroscopic, i. e. , smaller than that which
can be seen with the best microscope. Gibson [ 11] states that it
must be smaller than that volume associated with microscale of scalar
fluctuations, a term which will be defined later. The term scalar
is used to denote any tracer, contaminant, or chemical which is added
to and mixed with the fluid. All correlations defined with a scalar
are also scalars whereas correlations defined with velocities (a vector
or a first-order tensor) become higher-order tensors. A scalar is
a zero order tensor.
Before proceeding further, it is necessary to differentiate between
the terms mixing, diffusion, and dispersion or bulk diffusion. Dif-
fusion should be more precisely termed molecular diffusion. It is
due to the Brownian motion of individual molecules. Molecular
diffusion is very important in the mixing process with which this pro-
ject is concerned. The turbulence can act to create very small blobs
of scalar material, but even the smallest scales of turbulence cannot
act to eliminate all variations in "point" concentration. Molecular
diffusion must function in conjunction with the turbulence to accomplish
complete mixing. If turbulence were not present, the mixing would
eventually be completed by diffusion. However, the time required
would be quite long. The random motions of turbulence break large
blobs of scalar material down into the smallest blobs upon which
molecular diffusion can act with greater effectiveness. A slightly
different interpretation by Corrsin [ 17] is that the turbulence causes
an increase in the local, instantaneous concentration gradients which
allows molecular diffusion to act more effectively.
The term dispersion is used to describe the spreading of a scalar in
a flow field due to steady state spatial variations in the flow velocity.
The terms diffusion, bulk diffusion, or Taylor diffusion are often
used, but these are misleading because they tend to be confused with
molecular diffusion. Consider for example, turbulent flow in a pipe.
If a tracer is released from a point source in the center of the pipe
24
-------
the turbulence will tend to spread the tracer across the cross-section.
Near the walls, the velocity will be lower which will cause the tracer
to disperse longitudinally to a greater extent than would be produced
by the turbulence alone in a uniform velocity field. This type of
phenomenon also occurs in laminar flow. Molecular diffusion, rather
than turbulence, causes the lateral spreading in this case.
This project is concerned with the mixing which takes place down-
stream from a turbulence-producing grid. Only in the region very
close to the grid bars will gradients of temporal mean velocity exist.
The scalar field will be inhomogeneous in this region as there will
exist-gradients of mean concentration. The processes which occur
here are very complex and difficult to treat mathematically. Con-
siderable experimental work has been done on the turbulent wake
produced by a. circular cylinder [ 18, 19]. Mixing and chemical
reactions in the wake of a cylinder have been studied for the case of
two-dimensional spreading [ 20, 21], Such results might be expected
to apply to a grid in the limit as the spacing of the bars increases.
They clearly do not apply to the situation encountered in this study
where the maximum M/d ratio was 4, 0 and where the spreading Is
three -dimensional., Therefore, as has been done by previous investi-
gators [ 1 1, 22] , the problem of turbulence and transport in the vicinity
of the grid bars will be treated empirically and, consequently, some-
what superficially. That it is done in this manner does not mean that
the mixing which takes place in this region is unimportant. In fact,
it will be found that most of the decay of concentration fluctuations
occurs in this region.
Further downstream, the tempcral mean value of the tracer concentra-
tion will become constant across the cross-section, even though the
rms concentration fluctuations at a given point will not be zero. The
scalar field will become isotropic and will become amenable to theoret-
ical analysis.
Basic Definitions in Mixing
It will be seen that the basic equations used in mixing will bear a close
resemblance to equations used to describe turbulence, An isotropic
scalar field is very similar to an isotropic turbulent field, with the
exception that scalars rather than vectors are involved. It is possible
to view the mixing process as being analogous to the dissipation of
turbulent energy. When large blobs of scalar material are added to a
fluid, in terms of the scalar spectrum, these large blobs represent the
low wave number range. The turbulence then acts to create smaller
blobs which correspond to higher frequency, or higher wave number,
fluctuatrons. Finally, at the highest wave numbers, molecular dif-
fusion acts to spread out the smallest blobs in a manner analogous to
the way viscosity damps out the highest frequency velocity fluctuations.
25
-------
Consider an isctropic scalar field downstream from a grid. No spatial
variations in temporal mean concentration exist. At a particular point,
the instantaneous concentration can be taken equal to the sum of the
mean value plus a fluctuating value.
A = A + a . (36)
This is similar to the expression for instantaneous velocity with the
exception that vector notation is no longer required.
As with velocity, the rms value of the concentration fluctuations can
be defined:
a' =VlP. (37)
Dankwerts [ Z3] defined the mean square concentration fluctuation
divided by the initial mean square concentration fluctuation to be the
intensity of segregation, i. e. ,
s a '2 . (38)
o
This parameter, or its square root; will be used to indicate the
"goodness of mixing" obtained in a given system. When the scalar
is completely unmixed with the fluid to which it has been added, I = 1.
When the mixing is complete, and there are no deviations from the
mean concentration, I =0. 1 -~y I is sometimes defined as the
"degree of mixing'1 [ 24].
Dankwerts has defined another important parameter of mixing the
scale of segregation.
CO
L = f C(r) dr (39)
oj
where
r*t \ a(x) a(x-fr)
C(r) = ^72 (40)
C(r) is the Eulerian concentration correlation. It is analogous to the
Eulerian correlation function for velocity fluctuations. Lg may be
considered to be indicative of the size of the largest scalar blobs.
A scalar microscale, X , can also be defined from the C(r) vs. r
curve.
26
-------
1 _ _ _!_
X 2 2
s
8r2
r =o
Again, this is analogous to the Taylor microscales, \ and \ .
O
As with velocity spectra, considerable effort has gone into determining
the shape of the spectral curve in different wave number ranges. This
investigation will be concerned with the case where the scalar material
is added to a liquid- Under these conditions, the Schmidt number, NC^ ,
= v/D the ratio of kinematic viscosity to molecular diffusivity is
much greater than unity. Under conditions of mixing in a gas,
v/D « 1 and the spectral "curve has a different shape. The reason for
the difference in shape is related to the fact that under conditions of
high and low Schmidt numbers, the wave number at which molecular
diffusivity becomes important is either much higher or much lower
than the Kolmogoroff wave number. Thus, for v/D« 1, molecular
diffusivity becomes effective in a wave number range k < kj^ where vis-
cosity is not important. For v/D» 1, scalar transport due to con-
vection is important at the higher wave numbers where viscosity has a
strong effect on the velocity spectra.
Considering turbulence in a liquid with a fully developed inertial sub-
range, for -wave numbers k « k « kt^ the form of the scalar
6 Oj, S ^
spectra has been found to be
Es(k) = B e/1/3 k"5/3 (42)
where B is a constant coefficient, and £s is the time rate of "dissipation"
of the mean square concentration fluctuation.
This is called the inertial-convective subrange because inertial forces
dominate the velocity spectra and convective transport dominates the
scalar spectra for corresponding wave numbers. Batchelor [ 25] showed
that scalar transport due to convection and transport due to diffusion
become of the same order of magnitude at a wave number,
kB
1/4
T~I . (43)
m
This is analogous to the Kolmogoroff wave number k^. If D « v, it
follows from Equations (21) and (43) that kg » kj,.
For wave numbers k^ « k « kg, Batchelor determined that the
spectrum should take the form:
Eg(k) = A (£) l \ k"1 . (44)
-------
This is called the viscous-convective subrange, because while con-
vective transport is still dominant, viscous diss ipation becomes
important in the corresponding velocity spectrum.
Figure 5 shows the form of the scalar spectra discussed above as well
as that of the universal equilibrium range for turbulence. It should be
noted that the shape of the scalar spectrum depends on that of the
velocity spectra and if the Reynolds number is not high enough to pro-
duce the complete universal spectrum shown in Figure 5, then the
scalar spectrum will also be altered. As was noted previously, a
fully developed inertial subrange cannot be expected to be found in
laboratory-produced turbulence. Therefore, the resulting universal
scalar spectrum of Figure 5 cannot be expected to be found either.
However, this should not prevent these concepts from being used. The
Reynolds number necessary for universal equilibrium to occur can be
easily obtained. Several investigators [ 2, 11,26] have examined
velocity spectra and found a universal form. Usually, a line with a.
-5/3 slope, corresponding to the inertial subrange, can be drawn
tangent to the experimentally-determined spectrum curve. Therefore,
as a first approximation, the characteristic spectra of Figure 5 can
be used in the study of laboratory-produced turbulence and the mixing
resulting therefrom.
Decay of an Isotropic Scalar Field
When an isotropic scalar field is superimposed on a decaying isotropic
turbulent velocity field, it will decay in a manner at least partially
dependent upon the velocity field. Only recently has this rate of
decay been studied experimentally or theoretically.
Usually the rate of decay of the intensity of segregation in isotropic
decaying turbulence has been represented by an equation of the form:
(45)
(45a)
where a, a\ are coefficients, a is the decay rate. Only two investiga-
tions [ 11,22,26,27] have been made concerning the decay of an
isotropic scalar field in water (high NSC case). The resulting data
were shown to fit such a curve although the relationship of the
coefficients a and a to the physical parameters involved remained
uncertain.
Hinze [ 2] derived a relation for scalar decay based upon the Karm-an-
Howarth correlation equation for a scalar field, the assumption that
the form of the scalar correlation function maintains its shape during decay,
28
-------
w
o
o
o
5
w
o
o
_____ E(k)
.,__.- E (k), v/D
s
INERTIAL-CONVECTIVE
SUBRANGE (-5/3)
rn
INERTIAL
SUBRANGE
(-5/3)
\
\
VISCOUS -
CONVECTIVE SUB-
RANGE (-1)
\
\
\
\
HIGHER WAVE
NUMBER RANGE
(-7)
K
LOG (£/v3
LOG (e/vD 2 )* /4
rn
LOG k
FIGURE 5. UNIVERSAL FORMS OF SCALAR AND
VELOCITY SPECTRA. (FROM BRODKEY [ 4])
and Batchelor and Townsend's linear decay law for isotropic turbu-
lence (Equation 34). His equation is
/ x-3/2
/X-X \
T _ r{ _, o )
I - O\ -~: /
S -x lVl /
(46)
Note that a value for C is not given in this derivation.
Gibson [ 11] derived Equation (45) by dimensional analysis, assuming
that the rate of decay of a'2 was dependent only on U, M, t, and aQ'2.
-------
Recently, Corrsin [ 17, 28] has attempted to derive relations for the
rate of decay of scalar fluctuations in decaying and nondecaying
isotropic turbulence for different values of Schmidt numbers. The
case of interest here is high Schmidt number and decaying turbulence
[ 17]-
The mass transfer equation for the case_ of a homogeneous scalar
field with a conservative tracer (i. e. , A = constant) is
-fj +u. |^ =D V2 a . (47)
3t i 8x. m
l
One can convert this equation to a more useful form [ 2] by multiplying
by a, averaging, and putting u. inside the derivative.
dt
(48)
The scalar microscale is related to the derivative products in such a
way that
D
_
dt m \ 2 '
s
A corresponding equation can be derived for the mean square velocity
fluctuations from the Navier-Stokes equation:
ui '2 Uj l2
---2Qv- (50)
Dividing (49) by (50), one obtains the relative decay equation:
u, ' da1 _ 1 i f n/2
a' duj ' 5 N \X
s \ s
Equations for Xf and Xs in terms of the three-dimensional velocity and
scalar spectra can be developed
CO
k2 E(k) dk
30
-------
Es(k) dk
E (k) dk
s
Corrsin's method was to use the characteristic spectral form shown
in Figure 5 to obtain values for X£ and X-s. These in turn were sub-
stituted into Equation (6i). Corrsln did make one deviation from the
spectra shown in Figure 5 in that he ignored the higher wave number
range of the velocity spectrum and used a purely inertial spectrum.
His assumption was that the higher wave number range would not
contribute significantly to either integral in Equation (52).
Corrsin's final equation, bypassing the intermediate steps, Is
da
i
N
c
OC
/3 c 3/ 2 log
(54)
All the terms in the equation have been defined previously.
It is instructive to examine the influence of the various parameters on
Equation (54). The Schmidt number appears in two places. In the
numerator, if NSC > 10, its effect becomes insignificant. This is the
s ituation with which this project shall be concerned. In the denominator,
log NO appears. The rate of decay is weakly dependent on Ngc, but
note that if Ngc = v/Dm -* co, log NSC ~~*«> also, and the rate of decay
of a'goes to zero. This means that if the molecular diffusivity is
zero, mixing will not occur. This effect of no molecular diffusivity
was noted earlier.
It is important for this project that the dependence on Ngc should be
weak. The tracer used in the mixing experiments necessarily has a
molecular diffusivity different from the chemicals to be used in the
treatment processes. In fact, since the chemicals will be undergoing
reactions during the mixing process, their diffusivity will probably
be undergoing changes as mixing occurs. Very weak dependence of
the mixing rate on the molecular diffusivity means that results ob-
tained from the mixing experiments can be reasonably applied to the
treatment process experiments.
Since Equation (54) was developed on the assumption of an inertial
subrange, it applies only to cases where Nj^e^ is large. Under those
circumstances and if log NSC is not to° large, the second term in the
31
-------
denominator of Equation (54) will be small and dependence on
will be weak. At lower values of NRe. where, strictly speaking,
Equation (54) does not apply, it is possible that a dependence on N^e
may be discerned.
The other parameter in Equation (54) is (L /L ), the ratio of the scalar
and velocity integral scales. There is a physical interpretation of the
manner in which this parameter affects the rate of decay [ 22]. L£
itpresents the largest scale of turbulent motion. L represents
the largest scale of tracer blobs. If L. is small with respect to Lg,
then the turbulent motion cannot be as effective in breaking up the
blobs of tracer. If, however, L£ is large with respect to Ls, the tur-
bulence can be much more effective in mixing and a more rapid decay
of tiie concentration fluctuations results.
It L^ possible that by changing the physical characteristics of the grid
or the tracer injection system, (Lg/Lf) can be made smaller and the
decay rate greater. It was noted previously that Lf seems to be a
function of the grid bar diameter, d. This means that an increase in
d, with other factors held constant, should result in an increase in the
decay
It has been assumed by some [ 22, 29] that the scale of segregation is
a function of the number of tracer sources, LS decreasing when the
number of sources is increased. According to Equation (54), this would
cause an increase in the rate of scalar decay. There seems to be no
rational reason for assuming that Lg is a function of the number of
sources. The assumption seems to be based mostly on analogy -with
the dependence of Lf on d or, as some investigators claim, M.
It is possible, assuming that the right-hand side of Equation (54) remains
constant during the period of decay, to integrate Equation (54) and
obtain Equation (45). The right-hand side becomes essentially the decay
rate, a, of Equation (45). The coefficient, a, is dependent on the
initial conditions at a time, to. It should be noted that the derivation de-
pends on the assumption that u1 = f(x/M). If u1 = f(x/d), then d will
appear in Equation (45).
Since Equation (54) was derived for high Np^e, , there is the implication
that it cannot be applied to laboratory experiments. Strictly speaking,
this is true. However, it may be possible to qualitatively relate Equation
(54) to experimental results obtained under the conditions of low Reynolds
number. In particular; it may be possible to relate certain physical
characteristics of the experimental apparatus to Lg/Lf and, consequently,
the scalar decay rate.
Previous Experimental Investigations
There have been two previous investigations into the rate of decay of
concentration fluctuations of an isotropic scalar field in isotropic
32
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decaying turbulence produced by a grid: one by Gibson [ il, 26, 30]
and the othe r by Keeler [ 22, 27} , Both used single electrode con-
ductivity probes to attempt to determine "point" values of tracer
concentrations.
Gibson worked with a 6 in. x 6 in. water tunnel in which the flow was
recycled. For grids, he used 3/16 in. and 1/8 in. O. D. lucite tubes
in a square mesh grid with the bar spacing chosen such that M/d was
16/3. The tubes were perforated by drilling 12 mil holes on the up-
stream side halfway between the corners of the mesh. The tracer was
injected into the water stream through these holes. For tracers,, he
used NaCl solutions (v /D = 700) and heated water (v/D = 7).
Gibson, in his measurement of the rate of scalar decay attempted to
substantiate Hinze's equation, Equation (46), His curve had a slope
which was very close to - 3/2 but later work by Keeler and the present
study tend to indicate that this was merely a coincidence. Gibson also
made measurements of scalar spectra. They followed a universal form
and fit the curves given in Figure 5 fairly well.
Keeler's work was done after Corrsin's relation, Equation (54), had been
derived. He used three grids with the same M/d ratios but different
values of M. This was done in order to determine whether changing
the scale of turbulence would affect the scalar decay rate as predicted.
Keeler indicated that such a result was found although inspection of his
raw data seems to show that the difference is fairly small if not
negligible.
In order to insure homogeneity of the scalar field downstream from the
grid, Keeler used a "hairbrush" injection system which fed the tracer
into the water stream through many hypodermic needles connected to
a manifold. For a 4-Ln. pipe, 156 needles were used; for a Z-in. pipe,
37. The "hairbrush" injection device was placed upstream from the
grid and produced a scalar field which was homogeneous at the grid.
A drawback to this method was that the injection system introduced
turbulence which may have affected the turbulence field downstream
from the grid.
Keeler used two tracers, NaNO3 (v/D = 500) and ZnSO4 (v/D = 1000)
in an attempt to show the effect of Ngc on scalar decay rate as predicted
by Equation (54). His results do indicate a slight difference in decay rate
for the two tracers. This appears to be a consequence of the low
Reynolds number. Corrsin [ 17] showed that for N^ = 100, this dif-
ference in NSC should have essentially no "feet on decay rate. The fact
that a difference does occur may be significant in regard to the present
work for the reason previously noted.
Further reference will be made to the results of Keeler and Gibson as
they relate to the present work in Section VI.
33
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REVIEW OF COAGULATION-FLOCCULATION THEORY
Although alum coagulation-flocculation has long been one of the most
widely used water treatment processes, the actual mechanism of
destabilization of clay particles is still somewhat uncertain. The pro-
cess is simple in execution. Alurainum or ferric salts are added more
or less rapidly to the turbid water and after slow stirring, small
"floes" are formed which are removed by sedimentation and filtration.
The result is a clear water free of the colloidal clay particles which
are principally responsible for the turbidity.
Despite this apparent simplicity, uncertainty has arisen over the years
concerning the mechanisms involved in coagulation-flocculation. In
part, this concern is due to the fact that the mechanisms seem to vary
with pH, type and concentration of the material producing the turbidity,
and the coagulating agent used, Before proceeding with a review of
these theories, it is necessary to make a distinction between coagula-
tion and flocculation,. For the purposes of this investigation, the term
coagulation will refer to the destabilization of the colloidal particles
through the addition of coagulant to the water. Flocculation will refer
to the collision and aggregation of the destabilized particles into rel
atively large alggregat.es known as floes [ 31]. These definitions a.re
different from those given by LaMer [ 32] who defined coagulation as
processes which bring about the reduction of the repulsive potential of
the electrical double layer of the colloidal particles and flocculation
as being the bridging action of high molecular weight polyelectrolytes
which brings about a loose three-dimensional floe structure. LaMer's
definitions consider coagulation and fiocculation as two different
mechanisms of colloid destabilization and aggregation. The definitions
used in this paper consider coagulation as the process of destabiliza-
tion of colloidal particles without reference to the particular causative
mechanism. The term flocculation is applied to the hydrodynamics of
aggregation and floe formation.
The phenomena, which cause colloidal clay particles to remain suspended
in water are quite well known, from colloid chemistry and have long
been described in sanitary engineering texts and papers [ 3135] and
need not be reiterated in detail in this report. It is sufficient to note
that much of the theory concerning the mechanism of coagulation centers
on the reduction of the zeta potential to a level where the repulsive
forces are sufficiently low so that collision can occur and the Van der Waal
and other forces can be operative. The colloidal particles can then
collide,, aggregate,, and form large settleable or filterable floes.
Coagulation Theories
In 1949 Langelier and Ludwig [ 34] made a systematic study of various
clays suspended in water. Their main finding was a correlation between
the cation exchange capacity (CEC) of the colloidal material and the
34
-------
coagulant dose necessary to achieve a particular level of removal of
turbidity. Although this study has been criticized [ 36,37] because of
lack of pH control, it is important for two reasons. It demonstrated
that alkalinity is important in determining the coagulant dose necessary
to achieve satisfactory clarification. Also, it was noted that in many
instances efficient clarification requires a binder material of hydrolysis
products of aluminum or iron. They concluded that the addition of
highly charged cations Al+++ or Fe++ reduced the zeta potential
of the colloidal particle to a level where aggregation could take place.
Then the hydrous oxide would act to bind the destabilized particles and
form large floes which could then be removed.
In 1965 Kim» Ludwig, and Bishop [ 36] extended the work of Langelier
and Ludwig. Coagulation jar tests were made with the final pH a
controlled parameter. They found that at low kaolinite concentrations
(< 100 mg/.£) there was an inverse relationship between the clay con-
centrations and the amount of alum necessary to produce clarification.
At high concentrations of kaolin, and with bentonite, they found a
direct relationship between clay concentrations and the coagulant dose.
This implies that at different kaolin concentrations, different coagula-
tion mechanisms may be dominant. At low kaolin concentrations, they
found that the optimum pH for best coagulation was the same as the
isoelectric pH of the aluminum-hydroxo complex formed by the alum
and the alkalinity in the water. That is, turbidity removal was greatest
for a given kaolin concentration and alum dosage at the pH of least
solubility of aluminum hydroxide. At high concentrations of kaolin
and with bentonite they found tha't a slight positive charge on the
aluminum-hydroxo compounds which were formed resulted in best
turbidity removal. They concluded that for suspensions with high
particle concentrations, a reduction in zeta potential to the point where
aggregation of destabilized particles may take place provided the most
efficient clarification.
Packham [ 38] reported similar findings. Conditions for the most
rapid coagulation of dilute concentrations of kaolin were those leading
to the most rapid precipitation of aluminum hydrolysis products. He
noted that the turbidity in samples of river water from Britain behaved
similarly to dilute kaolin suspension. He also used bentonite and more
concentrated suspensions of kaolin and, as did Kim, Ludwig, and
Bishop, obtained results different from those obtained using dilute
kaolin suspensions.
Many authors [ 3741] have pointed out that when alum is added to
water,- the Al"^++ ion undergoes hydrolysis, the extent and character of
which depends on the pH and aluminum concentration. Figure 6 shows
the concentrations of various aluminum species at different pH values
in equilibrium with freshly precipitated Al(OH)3 , However, it should
be recognized that equilibrium may not be reached quickly and that the
transition from A1+^+to A1(OH)3 occurs through successive substitu-
tive reactions. Stumm and Morgan [41] noted that the net charge on
35
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ARANGE OF
ALUMINUM DOSES
NORMALLY
ENCOUNTERED IN
IWATER TREAT-
MENT
A113(OH)34
A17(OH)I7
pH
FIGURE 6. CONCENTRATION OF VARIOUS ALUMINUM SPECIES
IN EQUILIBRIUM WITH FRESHLY PRECIPITATED A1(OH)3
(FROM BLACK AND CHEN [ 39])
any aluminum-hydroxo compound is probably an average value, with
different charges being associated with different aluminum atoms or
groups of atoms. Moreover, the forms present are probably not
restricted to those shown in Figure 6[ 38,41], Polymers can be
formed by hydroxyl groups acting as a bridge between two or more
metal atoms. These are termed "olation" reactions.
36
-------
Table 1 [ 38] shows the various types of reactions which are involved
in aluminum hydroxide precipitation. Listed first are the ligand ex-
change reactions. These reactions occur in sequence when Al(III) is
added to water. Also listed are examples of olation reactions which
result in polynuclear polyhydroxo species. The important point is
that at a particular pH and concentration of aluminum in waters not
just one, but many aluminum-hydroxo compounds will be formed.
However, one species insoluble aluminum hydroxide for example
may predominates especially if sufficient time is allowed.
Black and Chen [39] made studies of coagulation of clay by alum using
microelectrophoretic techniques to help determine the mechanism of
coagulation. They noted that in most instances in water treatment, the
aluminum ion concentration falls between 10~6 and id"4 M (see Figure
6). For this range in aluminum ion concentration, the predominant
aluminum species in each of three pH ranges are as follows: Below
pH 4 the hydrated trivalent aluminum ion is the most active species.
In the region between pH 4 and pH 6, one or more of the hydrolyzed
aluminum polynuclear cations, such as Al6(OH)j+^+ or A18(OH)^,4,
may predominate. From pH 6 to pH 8, insoluble aluminum hydroxide
may be considered most important.
They concluded that different mechanisms were responsible for
coagulation in each of the three pH ranges. Below pH 4 the trivalent
aluminum ion acts to reduce the zeta potential of the colloidal particles
and produce destabilization and agglomeration of particles. In the
range where the multivalent polymeric aluminum-hydroxo species
exist; specific adsorption of these ions onto the surface of the clay
particle was concluded to be effective in producing destabilization by
reduction of zeta potential. Between pH 6 and 8, physical enmesh-
ment (or sweep flocculation or sweep coagulation) by aluminum hydroxide
or mutual coagulation between positively charged aluminum hydroxide
colloids and negatively charged clay particles were concluded to be
the mechanisms involved.
The concept of specific adsorption of multivalent aluminum-hydroxo
compounds onto the clay particles leads to consideration of a dif-
ferent concept of coagulation as discussed by LaMer [ 42], Stumm
and Morgan [41], Stumm and O'Melia [ 37], and Hahn and Stumm [ 40].
This may be termed the "chemical approach" as opposed to concern
with reduction of zeta potential by electro-kinetic attraction of counter-
ions. Although this division is convenient, it can be as with all
simplifications misleading. For example, while chemical forces
may act to cause adsorption of positively charged aluminum species,
the effect of this adsorption is the reduction of zeta potential, allowing
coagulation to occur [ 39«40]. Thus, both chemical and electrokinetic
phenomena are involved. Perhaps one of the best examples of the
chemical approach to colloid destabilization is the coagulation of a
negatively charged clay colloid by a negatively charged long chain
polymer. Since the two constituents are both negatively charged,
chemical forces must be acting in the process [ 42].
37
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TABLE 1
TYPES OF REACTIONS INVOLVED IN HYDROLYSIS OF Al(III)
(FROM PACKHAM [ 38])
00
Llgand Exchange Reactions
1 a. [ A1(H20)6]
-H-+
+ H2O
A1(H20)5 OH]
++
b. [ A1(H2O)5 OH] + H2O
c. [ A1(H20)4(OH)2]++H20
2 [ A1(H20)3(OH)3 ] +X=
3 [ A1(H2O)4(OH)2] + + X =
A1(H20)3 (OH)3 ] +H3 O"
A1(H2O)4 X] + + 2H2C
A1(H20)4 X] + +20H"
(X Represents a Divalent Ion)
Olation Reactions
4 a. 2[ A1(H2O)5OH]
b. [ (H20)4A1(OH)2A1(H20)4]
OH
OH
+ 4
> +2H2O
+ 4
c.
A1(H20)3OH]
A1(H20)5
[ (H2O)4A1(OH)2A1(H20)3 OH]
OH HJ° OH
(H2O)4A1/^ Al A1(H2O)4
\ S \ \ s"
OH ' ^ OH
+ 5
^ +2H2 O
-------
There has been considerable disagreement among investigators over
whether a "chemical" or "physical" approach should be taken in
attempting to understand the coagulation process. It has now become
apparent.- however, that both chemical and physical phenomena need
to be considered.
In 1967 Stumm and O'Melia [ 37] published a paper in which they
attempted to describe the mechanism of coagulation at various pH's
and colloid concentrations. They drew upon the work of others as
well as their own. They concluded that at high surface concentrations
(square meters of colloidal surface per liter), coagulation takes place
by adsorption of multinuclear hydrolysis products of Al(III). At low
concentrations of colloidal material particularly kaolin concentrations
less than 100 m.g/1 sweep flocculation, or enmeshment by insoluble
aluminum hydroxide, is responsible for removal of colloidal material
from suspension. For sweep flocculation to occur, the pH must be
such that there is a tendency to precipitate insoluble aluminum hydroxide.
Figure 7 summarizes Stumm and O'Melia's conclusions. At low sur-
face concentrations, coagulation takes place through nonstoichiometric
sweep flocculation (zone 4). At higher surface concentrations, adsorp-
tion of soluble Al(III) hydrolysis products is responsible for destabiliza-
tion of the clay particles (zone 2). Stumm and O'Melia also term this
stoichiometric coagulation.
It should be pointed out that mere physical enmeshment is not an
adequate description of Stumm and O'Melia's sweep flocculation (zone
4). This would imply that the presence of the clay particles does not
affect the hydrolysis reactions of the Al(III), i. e. , that the clay is
merely a passive component. This is probably not entirely correct.
The studies of Kim, Ludwig, and Bishop [ 36] and Packham [ 38] show
that for low concentrations of kaolin at constant pH, the concentration
of alum necessary to produce coagulation is inversely related to the
kaolin concentration. (Furthermore, in the present study, it has been
found that addition of alum to clear water resulted in floe of poorer
quality being formed much more slowly than when alum was added to
the same water containing 25 mg/^ of kaolin. )
Stumm and O'Melia point out two possible reasons for the inverse
relationship between colloid concentration and coagulant dose. With
colloidal particles providing interfaces for localized over-saturation,
the critical supersaturation necessary for rapid precipitation could
decrease with increasing clay concentration. The alternative explana-
tion considers mutual coagulation of the negatively charged colloids
with small particles of aluminum hydroxide precipitates or aluminum
hydroxo compounds. It can be postulated that at low colloid concentra-
tions, an insufficient number of particles is present to provide the
necessary contact opportunities in a reasonable time and the presence
of Al(OH)3 particles can produce efficient aggregation. Thus, in-
"creasing the clay particle concentration can reduce the necessary
coagulant dosage.
39
-------
O
i i
H
W
U
£
O
U
H
O
<
O
O
O
O
REGION OF
OAGULATION
NON-
STOICHIOMETRI
OR "SWEEP"
COAGULATION
STOICHIOMETRIC
COAGULATION
ZONE i
100 mg/l
KAOLIN
LOG COLLOID CONCENTRATION
FIGURE 7. EFFECT OF COLLOID CONCENTRATION ON COAGULANT
REQUIRED FOR DESTABILIZATION (AT CONSTANT pH)
(FROM STUMM AND O'MELIA [ 37] )
In summary, -while there is still confusion and disagreement over the
exact mechanism of coagulation which may be effective under particular
circumstances, some general statements may be made. Neither the
chemical or double layer models can adequately describe the phenomena
observed in the coagulation of various colloidal materials at all con-
centrations or pH values.
40
-------
At low concentrations of kaolin less than 100 mg/i and at pH values
near 7, it appears that rapid precipitation of uncharged insoluble
aluminum hydroxide is associated with efficient coagulation. This
implies a "sweep flocculation" model. At higher concentrations of
kaolin, and with other colloidal suspensions such as silica and bentonite
at moderate concentrations, some other mechanism is operative
most likely the adsorption of multivalent polynuclear aluminum-hydroxo
compounds onto the surface of the colloid leading to reduction of the
negative charge and destabilization.
Review of Flocculation Kinetics
Smoluchowski [ 43,44] first developed expressions for the frequency
of collisions of particles suspended in a fluid. Where the fluid is at
rest, collisions can take place due to Brownian motion. This is called
perikinetic flocculation. The frequency of such collisions is given by
Equation (55) :
I. . = 4 TT D. . R.. n. n. ,-.->
ij ij ij i j (55)
v/here I., is the number of contacts made per unit time and unit
n r
volume; l>Lj is the combined diffusion coefficient, D^ + D: ; R^j is the
collision radius which equals the sum of the particle radii, R^ + RiJ
and n^ and ni are the number concentrations of particles of radius
R. and R..
i J
In addition to perikinetic flocculation, particles can collide as a
result of their motion with the fluid. This is termed orthokinetic
flocculation and is perhaps of greater importance in water treatment.
Smoluchow ski showed that for laminar flow, the collision frequency is
given by
J.. - n. n. R.? (56)
ij 3 i j tj dZ
where Jjj is the collision frequency due to laminar motion; dU/dZ is
the laminar velocity gradient; and ni, nj, and RJJ have the same
definition as in Equation (55). This equation is not useful because it
is restricted to laminar motion. In all instances of orthokinetic
flocculation used in water treatment, turbulent motion is present.
In 1943 Camp and Stein [ 45] used Smoluchowski' s basic model to
develop a relationship giving the frequency of collision in turbulent
motion. Using a theory of Stokes, they related the energy input to the
system and the resulting root-mean-square velocity gradient.
G =-\ (S7,
41
-------
where G is the root-mean-square velocity gradient, P is the power
input, V is the volume, and fi is the viscosity.
The resulting collision frequency equation is
H.. =| n. n. R3. G (58)
ij 3 i J 1J
Several other equations [31, 4650] have been developed giving the
particle collision frequency in turbulent flow. Most bear a very close
resemblance to Equation (58), although various assumptions were made
in order to provide a more sophisticated treatment of the problem.
The above equation can be modified to give, instead of the frequency of
collisions, the rate of removal of the smallest, or primary, particles
from the system. A simplified form is
<59)
where K . is an aggregation rate coefficient. Argaman and Kaufman
[ 31,46] and Parker, Kaufman, and Jenkins [ 51] have added another
term which represents the formation of primary particles due to
surface erosion of larger particles. In simplified form this is
(60)
where KR is a breakup rate coefficient. This equation is usually of
interest when applied to a CSTR. For one compartment, a materials
balance at steady state gives
Qn? - Qn1 - K^1 GV r +KfiG2Vr =0 (61)
where Q is the flow rate, V is the reactor volume, n^ is the influent
concentration of primary particles, and n^ is the effluent concentration
of primary particles. Rearrangement of the above equation and re-
placing V /Q by T, the mean residence time, yields
n° 1 +K
+KG2T
42
-------
nj 'Hj is termed the "performance parameter" and is often used in
plotting results of flocculation studies. For convenience, the ratio
of the initial to final turbidity as measured by a light-scattering tur-
bidimeter is often taken to be equal to n° /n1 .
n 11
PREVIOUS WORK CONCERNING INITIAL MIXING
AND TREATMENT PROCESSES
There has been very little work published to indicate that rapid initial
mixing may be significant in water and wastewater treatment processes.
The reactions which occur when chemicals are added to the water
stream are often quite complex, as described earlier, as well as
quite rapid. Physical-chemical reactions can occur between the added
chemical, the component of the water stream which is the object of
treatment (e. g. , clay turbidity), and other constituents of the water
stream (e. g. , alkalinity). Reactions between the chemical and these
other constituents may act in such a way as to reduce the effectiveness
of the treatment process. For example, in alkaline waters poor
mixing may result in complete hydrolysis of the aluminum in only a
fraction of the stream being treated.
The relation between mixing and extent of reaction has been of interest
in chemical engineering studies* Toor [ 24] has studied the relation
between mixing and extent of reaction for a simple case, a very fast
reaction in-which two reactants, dissolved in separate streams of water,
of equal molecular diffusivity combine to form a product.
A + B -*C . (63)
By the term very fast reaction, it is meant that the rate of reaction
is much faster than the rate of mixing. Therefore the extent of the
reaction is controlled by the extent of the mixing process. For the
case where the reactants are present in stoichiometric amounts, it
is found that the fractional completion of reaction, F, is equal to the
fractional completion of mixing, r\, i. e. ,
F = r, = 1 -^- . (64)
For the case where one reactant is present in excess, for example,
3 times the stoichiometric amount, the expression is more com-
plicated.
F = 1 +(3-1 H+g
-i fi+g a; (1 r,) j
(65)
where
g(x) =ierc j . (66)
43
-------
Equations (64) and (65) are shown in Figure 8 for various values of (3.
This graph indicates that when one of the reactants is introduced in
excess, the reaction will be completed, L e. , the limiting reactant
will be completely utilized, before mixing is completed.
Keeler [ 22] and Vassilatos and Toor [ 52] have experimentally verified
Equations (64) and (65), and the concept behind Equation (64) had been
known and used previously [ 53].
In alum coagulation-flocculation of a turbid water, the alkalinity of
the water may be considered to be a reactant present in excess of that
needed to react completely with the coagulant added to the stream.
Reaction of the alkalinity with the alum before the alum has become
completely mixed with the turbid water may act to detrimentally affect
process performance. Of course, this process is much more com-
plicated than the simple case studied by Toor. First, the reactions
are very complex, their rate and extent depending upon alkalinity
and pH. Secondly, the rate of reaction does not appear to be so fast
that it cannot be overcome by providing much faster mixing. This
second point is fundamental to the present study: by providing more
rapid mixing, crucial reactions which can occur before the alum has
been dispersed evenly throughout the clay particles can be made to
occur after this mixing has taken place. Alternatively, these reactions
may be prevented in favor of desirable physical-chemical reactions
between the alum and the turbidity particles.
In a manner somewhat analogous to the way in which increasing one
of the reactants at a given degree of mixing will increase the fractional
completion of reaction in Figure 8, increasing the alkalinity may allow
completion of certain hydrolysis reactions at a lesser degree of
mixing, i. e. , at a time when greater segregation between the alum
and the turbidity exists. Thus, at high alkalinities, it may be even
more important to attempt to insure that the rate of mixing is faster
than the rate of the crucial reactions.
In a study concerned with water and wastewater treatment, Rudolfs and
Gehm [ 54] published a paper in 1936 describing treatment of waste-
water with FeCl3 . They found that slow mixing allowed undesirable
hydrolysis reactions to occur which decreased the efficiency of the
process.
More recently, Selleck and coworkers [ 5557] reached a preliminary
conclusion that rapid initial mixing can be very important in waste-
water chlorination efficiency. They concluded that the combined
chlorine residuals formed in wastewater undergo rapid reactions in
the first milliseconds of contact with the waste stream. These changes
result in a decrease in the bactericidal effectiveness of the chlorine.
If the mixing of the chlorine with the waste stream is rapid enough,
the more bactericidal compounds will come in contact with the bacteria,
and process performance will be improved. (Studies of chlorination
and initial mixing are presented in Appendices A and B. )
44
-------
0. 2
0.4 0. 6
= 1 - a'/a1
o
0. 8
1. 0
FIGURE 8. FRACTIONAL CONVERSION AS A FUNCTION OF
ACCOMPLISHED MIXING (FROM TOOR [ 24] )
The increasing study and use of polyelectrolytes as coagulants and
coagulant aids may provide another area in which rapid initial mixing
may be important. Riddick [ 58] notes that a long chain polymer may,
if mixing is not accomplished sufficiently rapidly, react with other
similar polymers or itself and would be unavailable for reaction with
the colloidal material.
45
-------
Recently, Vrale and Jorden [ 59] made studies of the relation between
rapid mixing and alum coagulation-flocculation, the same process with
which this study is concerned. A high-speed backmixed reactor (flash
mixer) and several i-in. I. D. tubular, plug flow reactors were used.
After the alum was mixed with the turbid water (tap water with SiO2
colloid, NaHCO3, and CaCl2 added) in the initial mixing device, jar
tests were made to determine if the various initial mixers caused
differences in performance. They concluded that more rapid initial
mixing resulted in better turbidity removal and that the high-speed
backmixed reactor, which is normally regarded as an adequate initial
mixing device and which is often used in plant design, actually is much
poorer than a plug flow system.
Similar results have been found by Wilson [ 60] in work done pre-
viously at the Sanitary Engineering Research Laboratory at the
University of California. In these experiments, kaolin was used to
provide the colloidal turbidity. With both jar tests and continuous
flow pilot plant flocculation experiments it was found that the tubular
reactor initial mixers produced better results than did the backmixed
reactor, presumably because segregation between the alum and water
streams was eliminated more rapidly when the tubular reactors were
used.
In one sense, rather than being a duplication, the two investigations,
one by Vrale and Jorden and the other by Wilson, complement each
other. Vrale and Jorden used colloidal SiO2 to provide turbidity.
They found a stoichiometric relationship between the colloid con-
centration and the coagulant dose necessary to produce coagulation
(at a constant pH). In Stumm and O'Melia's terminology [ 37], this
corresponds to an adsorption-destabilization mechanism of coagula-
tion. Wilson used a dilute kaolin suspension. As noted previously,
this seems to correspond to a sweep flocculation mechanism of
coagulation. It has been shown, therefore, that initial mixing seems
to be important regardless of the coagulation mechanism. This is
important with respect to application of such studies to full-scale
water treatment facilities where both types of colloidal material may
be present. It is also important in that it may mean that the sweep
flocculation mechanism and the adsorption-destabilization mechanism.
are not so different as they might first appear. As pointed out pre-
viously, the term sweep flocculation is somewhat inappropriate in that
the clay particles do not act as a passive component. That initial
mixing is important with both mechanisms seems to indicate other
more basic similarities between them.
46
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SECTION V
MIXING STUDIES: APPARATUS AND METHODS
INTRODUCTION
The experiments described in this and the following section were done
in order to determine what characteristics of the grid, the turbulent
flow field, and the scalar material affect the intensity of segregation at
points downstream from a biplane grid when a tracer is introduced into
the flow through numerous orifices in the grid bars. Closely related to
this is the question of what design parameters should be used in the
construction of such grids for use in water and wastewater treatment
facilities.
This second question can be divided into two parts. First, what
parameters related to the grid affect the time of mixing the time re-
quired to reach some arbitrarily-defined low value of the intensity of
segregation (for example, it could be defined as the time required for
Is to be such that a1 /A = 10%)? Second, what is the relation between
the time of mixing and process performance, i. e., how rapid must the
mixing be in order to produce a significant improvement in performance?
The latter question will be dealt with later when experiments involving
alum coagulation-flocculation of turbid water will be discussed.
The work of Gibson and Keeler [ 22, 27] was used as a starting point
for the present studies [ 11.26,30], In some instances, their con-
clusions have been substantiated by these experiments; in other instances,
new conclusions have been drawn which conflict with previously held
theories.
The present studies tested the theory of Corrsin [17, 28] in that an
effort was made to determine what design parameters may determine
the scales of turbulence and segregation which in turn should affect
the rate of scalar decay in the system being studied.
EXPERIMENTAL APPARATUS
S_ingle_E_Iec_trode Conductivity Probe
The total resistance of a uniform piece of conducting material is
related to its resistivity by the following equation,
R = PA (67)
47
-------
where R is the total resistance, p is the specific resistivity in ohm-ft,
L is the length of the material, and A is the cross-sectional area.,
In a standard conductivity cell, two electrodes of equal size are used.
They are separated by a distance L,, and the conducting solution between
the probes has a constant cross-section, A, Equation (67) can be
written in terms of a cell constant,
R = PK =-£ (68)
c cr
where KC = L/A is the cell constant and cr = p is the specific con-
ductivity of the fluid. Conductivity probes are usually calibrated in
terms of the cell constant. Knowing the resistance measured by the
cell in a given fluid; the conductivity can be calculated.
Consider a conductivity cell with two electrodes, A and B which vary
greatly in size. Assume that the conducting solution occupies only the
space between the electrodes. Equation (67) can be written in integral
form,
B
(69)
The greatest contribution to the total resistance will come from the
parts of the system where A(Jt) is very small, i. e. , near the small
electrode. Suppose now that p varies from point to point "within the
system. If this variation is not so great that it dominates the effect of
the changing area, then R will tend to be a function of the resistivity
near the small electrode.
With a probe of this type, a conducting tracer such as NaCl solution is
used. At low concentrations, the conductivity of the solution is pro-
portional to concentration. A change in conductivity will be detected by
the probe and, through the associated electronic apparatus, a voltage
can be measured which is proportional to the concentration at a "point"
defined by the effective volume of the probe.
This is the principle'upon which the single electrode conductivity probe
operates. The end of a small diameter wire protruding from the tip of
a probe acts as the small electrode. The ground of the system acts as
the other electrode* The single electrode probe was developed simul-
taneously by Gibson [ 11, 30] and Keeler [ 22, 27] and was an improve-
ment over the probe developed by Lamb, Manning, and Wilhelm [ 61 ].
Their probe consisted of a large and small electrode which allowed
current to leak to grounds in the system. Using the system ground as
the large electrode eliminated this problem.
It is possible to develop some estimate of the volume over which this
type of probe effectively measures resistivity by considering a spherical
48
-------
electrode of radius r_ immersed in an infinite body of electrolyte [11]
For this geometry, Equation (69) may be written
(71)
From Equation (68) the cell constant is
1
(72)
If the effective cell volume is taken to be that volume closest to the
sphere which contributes 90% of R , this volume can be easily found
from °°
°-9R« = ^ dr (73)
which leads to
0. 9 B = 10 r . (74)
o
Therefore, the effective probe radius can be considered to be approx-
imately 10 times the radius of the sphere. This gives some indication
of how close to a "point" the probe is measuring.
Keeler concluded that the shape of the probe tip was very important
in determining the spatial resolution of the probe because a blunt tip
disturbed the flow field in the vicinity of the tip. He noted that when
Gibson replaced a 50-micron blunt probe by one 20 microns in diameter,
there was no apparent increase in the ability to resolve high frequency
components of the scalar spectrum. Gibson also concluded that the
blunt shape of the tip may have been the limiting factor in spatial
resolution.
The major contribution to the rms concentration fluctuation is from the
lower wave number portion of the scalar spectrum. Therefore, when
rms values are measured, spatial resolution is not so important, and
larger, more blunt probes can be tolerated, which simplifies con-
struction problems.
49
-------
The probe used in this study had a tip 3 mils (75 microns) in diameter.
This is larger than those used by Gibson (10-51 (J.) and Keeler (125 p.)
and is the same size as the small electrode of the probe developed by
Lamb, Manning,, and Wilhelm. Attempts were made to build smaller
probes in order to compare the results obtained from using different
sized probes. However, difficulties were encountered and no reliable
results were obtained. While no photographs of the probes actually
used by Gibson are available, it is believed from his description of
their construction that the probes used in the present study may have
been of superior shape. He used a cast epoxy tip and attempted to
make the tip as sharp as possible using needle files and a microscope.
Keeler's probes were designed specifically to avoid the problems which
a blunt tip might incur. The method of construction was very tedious
and difficult [ 22}. All of his probes were small enough so that the
rms fluctuations measured with them were only weakly dependent on
the probe diameter beyond a distance of 10 mesh lengths from the
grid.
Noting that the purpose of the present study was to determine the
parameters which affect the rate of mixing downstream from a grid,
"true" values of rms concentration fluctuations were not essential in
the sense that what was sought was a comparison of the mixing obtained
from various grids. Nevertheless, the present work may be criticized
on the grounds that smaller probes, with better tip shapes, might
have resulted in higher observed rms values. All experiments of the
present study were made with probes of the same size so that the
results would be consistent. Furthermore, based on the results and
conclusions of Gibson and Keeler, the rms values obtained should be
reasonably close to the "true" rms concentration fluctuations. More-
over, comparison of results with those of Gibson (see Appendix C)
showed good agreement.
Probe Construction
A drawing of the single electrode conductivity probe used in the mixing
experiments is shown in Figure 9. Photographs are shown in Figures
10 and 11. It was constructed from 5/16-in. O. D. thin-walled glass
tubing. The tube was heated and drawn out to form a tapered tip,
having a hole only slightly larger than the 3-mil platinum wire used
for the electrode. It was found that tubing with reasonably thin walls
produced the best tips. A short section of 3-mil platinum wire was then
put through the tip and held in place at both ends, and a casting resin
was poured into the large end of the tip. The viscosity of this resin
was such that, before setting, a small ball of resin was formed out-
side the small end of the tip. The platinum wire protruding from this
ball of resin was cut off, and the ball of resin was carefully filed
down to a sharp point with the platinum electrode protruding from the
end. A binocular microscope was used to aid this process.
50
-------
Connector
Epoxy Seal
Glass Tubing
Filed - down Point
Wire Lead
Platinum Wire
Glass Tip
Casting Resin
Casting Resin
Epoxy Seal
Glass Tip
3 mil Platinum Wire
FIGURE 9. ILLUSTRATION OF CONDUCTIVITY PROBE
51
-------
FIGURE 10. SINGLE ELECTRODE
CONDUCTIVITY PROBE
FIGURE 11. PROBE IN PLACE IN
TUBULAR REACTOR
-------
No doubt some errors due to probe interference with the flow field
did occur, but the difficulty of making probes in a manner similar
to Keeler and the insensitivity of rms values to probe shape and size
made more sophisticated probes unnecessary.
After the probe tip was constructed, a wire lead was soldered to the
platinum wire and a glass tube with a 90° bend was cemented to the
probe tip with epoxy resin.
After the probe was constructed, the platinum electrode was coated
with platinum black (finely divided platinum). When current flows
across the surface of the electrode* hydrogen and oxygen gases are
formed. These gases add resistance to the system in addition to that
caused by the solution resistivity. A capacitive reactance is also
produced. An alternating current will allow some of the hydrogen and
oxygen to recombine and reduce the additional impedance. For this
reason, high frequency AC current is used in conductivity measure-
ments. It has also been found that adding a coat of platinum black by
electrolysis reduces the surface impedance.
For these experiments, the probes were platinized in a solution of
chloroplatinic acid and lead acetate according to the method proposed
by Standard Methods [ 62] with the exception that a Hewlitt-Packard
6215A DC power supply was used to supply the voltage. This allowed
control of the voltage to obtain best results. Approximately 2 volts
with a platinizing time of 30 to 40 seconds was used,
Electronic Equipment
A Tektronix 3C66 carrier amplifier was used to transform the resistivity
(and hence concentration) near the tip of the probe into a voltage which
could then be analyzed for rms and mean values. The 3C66 amplifier
is a plug-in unit for the Tektronix 560 series oscilloscopes. A model
564B storage oscilloscope was used.
The oscilloscope permitted the trace (representing concentration vs.
time for the present work) to be "stored" on the oscilloscope screen
as the trace was normally on the screen for only a few milliseconds.
Storing a trace allows better visualization of the concentration-time
signal. Although the storing apparatus was not used directly in this
work, it proved to be useful for demonstrating the use of the single
electrode conductivity probe.
A block diagram of the 3C66 carrier amplifier is shown in Figure 12.
[ 63]. It has the advantage of being a completely prepackaged unit.
Although it was designed for use with strain gauges, it was used for the
present work without any modifications. The 3C66 unit operates on
the principle of the AC bridge. A sketch of such a bridge is shown in
Figure 13. When the bridge is balanced, * = 0. The condition for
this is,
53
-------
TRANSDUCER
INPUT
dZ, ex dA
AC
BRIDGE
AMPLI-
FIER
PHASE -
SENSITIVE
DEMOD-
ULATOR
25-kc
OSCIL-
LATOR
FILTER
dE
SIGNAL
OUT
OUTPUT
AMPLI-
FIER
OSCILLOSCOPE
TRACE
FIGURE 12.
BLOCK DIAGRAM FOR TEKTRONIX TYPE 3C66
CARRIER AMPLIFIER
-------
25 kc
FIGURE 13. AC BRIDGE CIRCUIT
(75)
where
Z2, Z3 , Z4 are the impedance in each of the arms. It is
found that the maximum sensitivity occurs when Zt = Z2 and Z3 = Z4,
Under these circumstances a change in Z: will be reflected by a
change in £ as follows:
55
-------
d| _ 1 dZ,
E 'I Z, (76)
where E is the voltage drop accross the branches from A to B. This
relation holds as long as £ « E; otherwise the response becomes
nonlinear.
The probe was connected to the AC bridge in a manner which required
the use of only one external arm. A 120-ohm resistor was placed
parallel to the probe across arm No. 1 of the bridge as is shown in
Figure 14. Under such circumstances, the conditions for balance
are Zl = Z2 = Z3 = Z4, and the resistance in each arm is approximately
1ZO ohms. Ignoring the reactive portion of the impedances across
arm No. i, it is possible to determine the change in £ produced by a
change in R .
P R R'
, R1 « R (77)
(R +R')R' - R R1 R|Z
P. _ P - K (7S)
_ - _ . _ -
dR (R +R1)2 (R +R1)2
P P P
R +R1
dR - TT;,,-, ,4T-, dR
^
T
Since R1 « R ,
P
(R +R')2 R R1 p (R +R')R p . (79)
(80)
Ignoring the reactive impedance, Equation (80) can be substituted into
Equation (76)
^-i ^-P
P V
The change in probe impedance is represented by dZ in Equation
(76) and by dRp in Equation (81). In Equation (76), dZt represents
the change in probe impedance while in Equation (81), it is represented
by dRp. Using an arrangement which required only one external arm
made it necessary to sacrifice sensitivity, since R1 « R For
measuring rms values with the probes used in this study there was no
problem in obtaining a sufficiently strong signal. However, if attempts
56
-------
25 KC
.1-
B
R' = 120
R » R1
P
FIGURE 14. PROBE CONNECTED IN PARALLEL
WITH 120-ohm RESISTOR
had been made to measure high frequency, low amplitude portions of the
spectra, it might have been necessary to use an arrangement utilizing
two external arms of the bridge. The probe would be one arm, and a
variable capacitor and resistor, representing Z2 in Figure 14 would
be the other arm. A smaller probe might also require a similar
arrangement. As
an increase in R .
result.
R - R = p/4irr0, a decrease in ro would cause in
From Equation (81) a decrease in d£/E would
57
-------
A calibration curve for such a probe is shown in Figure 15. Above
2000 ing/* NaCl the response of the system began to show a non-
linearity due to excessive unbalancing of the bridge. The average
concentration in the experiments was about 50 mg/i so this was not
a problem.
To obtain the rms value of the concentration fluctuations, a TSI model
1060 rms voltmeter v/as used. This instrument represents an improve-
ment over the rms voltmeters used Ln previous studies in that it can
average the fluctuations over a longer period of time; the time con-
stant could be varied up to 100 seconds.
The rms voltmeter used by both Gibson and Keeler had a time con-
stant of only 2 seconds. They reported that the output reading of the
rms voltmeter fluctuated so greatly that an analog averager had to
be built to obtain steady readings. An important drawback to this
method of obtaining rms values is that because of the small time con-
stant, the contribution of low frequencies may be underestimated.
These may constitute a considerable fraction of the total rms value.
Thus, using an rms voltmeter with a greater time constant means
more accurate results. For most of the rms made in the present
study, a time constant of 10 or 30 seconds was used. These time
constants correspond to low frequency cutoffs of approximately 0. 3
and 1 cycle per second, respectively.
In order to be certain that the scalar field was homogeneous at the
points of rms measurements, it was necessary to know the mean
scalar concentration. This information was also useful in checking
probe calibration and the tracer flow rate. To make measurements
of mean concentration, a DC voltmeter with a low-pass DC filter was
used. The time constant for this meter was 47 seconds.
A disadvantage of using an averaging meter was the low input impedance.
When the rms voltmeter and the DC voltmeter were connected to the
output of the 3C66 unit simultaneously, the averaging meter tended to
affect the reading of the rms voltmeter. For this reason, it was
necessary to switch off the averaging meter while rms measurements
were being made.
A schematic drawing of the electronic apparatus and probe is shown
in Figure 1 6.
Flow Apparatus
Figure 17 shows a schematic illustration of the flow apparatus for the
mixing experiments. It consisted of a multiple-or ifice grid and
tracer injection system at the head of a 2-in. I. D. tubular reactor.
A nonrec irculating system was used to avoid the problem of tracer
buildup.
58
-------
12
Ui
O
W
PH
O
O
w
O
10
O
JL
_L
I
500 1000 1500 2000
CONCENTRATION OF NaCl, mg/f.
JL
2500
FIGURE 15. TYPICAL CALIBRATION CURVE FOR SINGLE
ELECTRODE CONDUCTIVITY PROBE
I
3000
-------
Q
TEKTRONIX
564B STORAGE
OSCILLOSCOPE
3C66
UNIT
A = A +a
1
E = E +
£<=< A
TSI MODEL 1060
rms VOLTMETER
E <* A
DC AVERAGING
VOLTMETER
FIGURE 16. ELECTRONIC EQUIPMENT FOR MIXING EXPERIMENTS
-------
Constant Head Tank
To
Waste
Water Supply
from 3" City Line
Nozzle Meter
Honeycomb to reduce
pre-grid turbulence
Conductivity Probe
Injection Manifold
and Grid Section
(Variable Length, Oto4 ft.)
Constructed from 2"I.D. Plastic Pipe
FIGURE 17. SCHEMATIC ILLUSTRATION OF EXPERIMENTAL SETUP FOR
MIXING EXPERIMENTS
-------
The raw water was taken directly from a 3-in. East Bay Municipal
Utilities District (EBMUD) line and fed to a constant head tank. This
tank was important for two reasons. It eliminated fluctuations in the
flow rate, and it helped to eliminate air bubbles from, the water by
allowing them to escape to the atmosphere. Air bubbles can cause
difficulties in that they represent a region of very high resistivity.
Any of these passing close to the probe would be detected by the probe
and would produce an error in the amplifier output.
From the constant head tank, the water flowed through an I. S. A.
nozzle flow meter and into the tubular reactor. A 4-in. section of
aluminum "honey-comb" was placed upstream from the grid to help
reduce the level of turbulence to avoid affecting the intensity of
segregation downstream from the grid.
A drawing of the injection manifold and grid section is shown in
Figure 18. It was constructed of clear plastic. The tracer flowed
from a constant head tank through a rotameter into the manifold,
entered the grid bars through the wall of the 2-in. pipe, and was
injected into the flow through the injection orifices drilled in the grid
bars.
Downstream from the grid was a variable length tubular reactor
(0, 4, 8, 12, 1 6, 24, or 48 in. ) which was also constructed of transparent
plastic. Flanges with rubber gasket seals were used to connect the
various sections together.
Beyond the tubular reactor section was the probe section as shown
in Figure 19- This section was also used to divert part of the flow
through the flocculator during the coagulation experiments. Two
valves, one upstream and one downstream of the reactor section,
were used to control the flow through and the pressure in the tubular
reactor.
Multiple-Source Grids
The grids used for this study were constructed from brass tubing,
1/4-in. or 1/8-in. O. D, Metal was chosen in preference to plastic
because it was easier to drill holes in metal having the same orifice
coefficient. With plastic there is a tendency for the edges of the
holes to become chipped. Gibson used plastic grid bars and found
that because it was impossible to drill perfect holes,, the tracer flow
from adjacent sources varied greatly and artificially augmented the
concentration fluctuations downstream. The orifices were 0, 021-in.
or 0, 0135-in. In diameter, depending on the number of sources. It
was desired that the tracer injection velocity be slightly greater than
the main stream velocity. Brass tubi.ng was chosen because it is
fairly resistant to corrosion. The bars were held in place with
silicone rubber cement.
62
-------
SCALE: 6" = I1
MANIFOLD
O-RING
TRACER
INJECTION
7////////f/TTTT/////
I I
BOLT HOLES FOR
MANIFOLD
BOLT HOLES FOR
CONNECTION TO
UPSTREAM SECTION
BOLTS FOR CONNECTION
TO OTHER SECTIONS
FIGURE 18. CUTAWAY VIEW OF INJECTION MANIFOLD AND GRID SECTION
-------
SCALE: 6" = I1
O-RING
GASKET
//////////////////
V \
BOLT HOLES FOR
CONNECTION TO
OTHER SECTIONS
FIGURE 19. CUTAWAY VIEW OF PROBE SECTION
-------
A photograph of one of the grids is shown in Figure 20. For this grid,
d = 1/8 in. , M/d = 4, and the number of sources is 12. Seven grids
were employed and their characteristics are listed in Table 2. Figure
21 shows the injection manifold section.
TABLE 2
GRID CHARACTERISTICS
Grid
No.
1
2
3
4
5
6
8
M( in. )
0. 5
0, 5
0. 5
0. 5
0. 5
0,25
0. 5
d(in. )
0. 25
0. 25
0. 125
0. 125
0. 125
0. 125
0. 125
M/d
2
2
4
4
4
2
4
No. of
Sources
4
9
9
24
12
21
4
Source
Diam
(in.)
0. 021
0. 021
0. 021
0. 0135
0. 0135
0. 0135
0. 021
EXPERIMENTAL PROCEDURE
During each run, measurements of mean concentration and rms con-
centration fluctuation were made with one grid, at a particular distance
downstream from that grid. Measurements were generally made at
the centerline, although the variation of mean and rms values across
the cross-section was investigated. The parameters which were
varied during a run were the ratio of mainstream flow to tracer in-
jection flow, QM/QT. and the mainstream velocity, VM- This latter
parameter determines the grid Reynolds number, Vj^d/v or
Several runs were made in order to determine the decay of rms
fluctuations with distance from the grid. Decay curves for different
grids could in turn be compared in an attempt to determine what
parameters might be appropriate for design. Also, it was desirable
to develop a rational model for predicting the scalar decay which
can be expected from any given grid.
Usually 20 liters of a 250-g/-? salt solution were prepared in advance
for several runs. On the day of the run, a portion of this was diluted
to a SQ-g/Jt concentration in the tracer solution tank (see Figure 17).
This tracer concentration was used for all runs. The tracer pump
65
-------
mmmm
mmmm
FIGURE 20. MULTIPLE-ORIFICE GRID
FIGURE 21. INJECTION MANIFOLD AND GRID SECTION
66
-------
was started and the manifold was filled with tracer solution. Then the
mainstream flow was started by passing water through the large con-
stant head tank. When there was flow through the tubular reactor, it
was necessary to have a small tracer flow rate into the system in
order to prevent backflow of fresh water into the manifold.
Because the water taken from the city line was much colder than the
ambient temperature, it was necessary to let the water run for
approximately 30 minutes in order to obtain an equilibrium temperature.
This was important as changes in conductivity are related to temperature
as well as concentration variations. The pressure in the tubular
reactor was adjusted to be great enough to prevent air bubble forma-
tion due to too low a pressure and low enough to allow the tracer to
flow into the reactor. Then the flow was stopped and the conductivity
probe put in place. The flow was started and adjusted to the desired
value. The tracer flow was shut off and the AC bridge of the 3C66
unit was balanced.
The conductivity measured under these conditions was due essentially
to dissolved minerals normally present in the water. However, there
was also a slight leakage of tracer from the grid bars which could
not be prevented. This meant an error in the mean scalar concentra-
tion reading because the balance condition of the bridge did not cor-
respond to conditions of zero tracer injection. In order to eliminate
this error from the results, the tracer flow was shut off and a relief
valve on the manifold was opened at the end of each run. This caused
fresh water to flow from the reactor into the grid bars and out of the
manifold through the relief valve. No leakage of tracer into the
tubular reactor occurreds and the amount of error previously incurred
due to such leakage could be determined. The rms value was not
affected by this error.
After the bridge was balanced, the tracer injection flow rate was set
to a desired value. The output of the 3C66 unit was connected to the
rms voltmeter and the rms voltage was read. The output of the 3C66
unit was then connected to the averaging DC voltmeter, and the mean
value of the signal was read. When this was completed, the tracer
injection flow rate or the mainstream flow rate was changed and the
measurements repeated.
Drift of the bridge balance condition was at times a problem, and it
was often necessary to shut off the tracer flow during a run to insure
that the bridge was still balanced and, if necessary, to rebalance it.
At the end of the run, the probe was calibrated in a beaker by adding
incremental amounts of tracer solution to tap water. During the
first few runs, a calibration was made both before and after the run.
However, it soon became apparent that the probe calibration was
fairly stable and that such checking was not necessary. The fresh
water used for the probe calibration was taken from the tubular
reactor waste stream at the end of the run to insure that the tempera-
ture was the same as that of the water used during the run. After a
67
-------
run the tracer supply apparatus was drained of tracer solution and
fresh water was pumped through it in order to inhibit corrosion.
HEAD LOSS THROUGH GRIDS
If grid initial mixers are used in water and wastewater treatment
plants, the head loss through the grid may be an important considera-
tion in design. In many cases, allowable head loss may be limited
to a few inches. Therefore, loss of head measurements were made
for two grids having different M/d ratios, and these were compared
with predicted values.
Baines and Peterson [ 64] have studied the head loss caused by flow
through grids. They assumed that all the loss takes place downstream
from the grid, in the region where flow expansion takes place. They
further assumed that the coefficient of contraction is 1. 0; i. e, , that
the maximum fluid velocity as it passes through a grid is defined by
that part of the cross -sectional area which the grid bars do not cover.
Using principles of momentum and energy, they found that
hL S2
KL = = (8Z)
where S = A, / AL . ,.
bars total
It can be shown that the drag coefficient,
KT
Therefore,
CD=~(fw ' (84)
It can also be shown that, when square-mesh grids are used, this
relation is equivalent to Equation (35) used in the linear decay law for
turbulence given by Batchelor and Townsend [ 14].
In a note on the article by Baines and Peterson [ 64], T. T. Siao noted
that as S -»O, C;p should become asymptotic to 1. 2, the value for
circular cylinders, instead of zero as Equation (84) predicts. Thus,
Equation (82) is in error for low solidity grids (i. e, , high M/d).
The modification suggested by Siao is shown in Figure 22. KL =
hL/(VM;/2g) is plotted against M/d. S is related to M/d for square-
mesh grids by
68
-------
40
30
20
10
5. 0
2. 0
1. 0
EXPERIMENTAL
RESULTS
0. 5
FROM BAINES
AND PETERSON [ 64]
0. 2
M/d
FIGURE 22. HEAD LOSS COEFFICIENTS FOR
SQUARE-MESH GRIDS
69
-------
S = 1 -
(f)2
(85)
The head loss coefficients for two grids of the present studies
(M/d = 4 and M/d = 2) are also shown in Figure 22. These coefficients
were determined by measuring the head a few inches upstream from
the grid and 4 ft downstream from the grid. An estimate was made of
the head loss due to wall friction by using a friction factor correspond-
ing to a smooth pipe. This estimated loss was subtracted from the
total measured head loss to obtain a value for the head loss due to the
grid alone. Measurements were made at five velocities in equal in-
crements from 1 to 5 fps, and at 0. 8 fps. There was a tendency to
have higher values of KL for some of the measurements at 0, 8 and
1. 0 fps - 10% to 20% higher. As will be suggested in Section VI, this
could be a sign that a change in the character of the turbulent wake
occurs at such velocities. This change, if it does occur, also affects
the mixing provided by the grid,
For higher velocities, the values of KL were quite consistent. It is
the average of these values which is plotted as experimental results
in Figure 22. For the low solidity grid (M/d = 4), the experimental
point falls close to the line. For the high solidity grid (M/d = 2), the
experimental point falls substantially below the curve. This may be
due to the fact that there was a slight space (d/2) between the horizontal
and vertical grid bars. Thus, the contraction of the flow was probably
not as great as assumed by Equation (82), and the head loss coefficient
was lower than predicted. The head loss which would be expected
from each grid at different velocities is given in Table 3.
TABLE 3
HEAD LOSS THROUGH GRIDS AT VARIOUS VELOCITIES
VM< f?S
1. 0
2. 0
3, 0
4. 0
5. 0
hr (inches)
M/d=4
S^O, 45
0. 2
0. 8
1. 7
3, 0
4. 7
M/d-2
S=0. 75
0. 6
2, 5
5. 7
10. 0
15. 7
70
-------
SECTION VI
MIXING STUDIES: RESULTS AND ANALYSIS
RESULTS
In this section the mixing experiments which were performed are
described. These experiments were intended to meet objectives
1) and 2), i. e. , to determine the parameters governing the degree of
mixing downstream from a grid initial mixer. The experiments were
designed in such a manner that as much information as possible was
obtained from them. After the various experiments are discussed,
a general model incorporating the results of these studies will be
developed.
Figure 23 shows a typical curve giving the rms concentration fluctua-
tions, at the pipe centerline, downstream from a particular grid (Grid
No. 1: M = 1/2 in. , d = 1/4 in. , 4 tracer orifices in the cross -section
of the 2-in. pipe). a'/aQ is plotted against x/d. From a study of
previous experiments concerning turbulence, in spite of the point
made in Section IV and M/d should affect the turbulence level, and
the present mixing studies, it appears that d is a more appropriate
parameter to use in normalizing the distance from the grid. The
decay curve of Figure 23 follows an equation of the form,
(86)
which is essentially the same as Equation (45a). Two important points
can be made regarding this graph.
The first point concerns the effect of mainstream velocity on the
mixing at downstream point. The figure shows data for three main-
stream velocities, Vjyj = 1, 2, and 3 fps (some measurements were
made at higher velocities during the first few runs). These velocities
correspond to grid bar Reynolds numbers ranging from Vj^d/v = 1. 7 x
103 to 5. 1 x 103 . At a particular value of QM/^T' tne ra-tio of main-
stream flow to tracer injection flow, there is no consistent difference
between the values of a'/aoat different mainstream velocities. That
a'/ai. is not a function of mainstream velocity is consistent with the
work of others [ 11, 22}.
In some of the runs, there was a tendency to obtain abnormally high
values of a'/a1 at the lowest mainstream velocity of 1 fps. This
71
-------
1. 00
0. 80
0. 60
0. 40
0. 30
o
o
- o
0. 20
0. 1!
0. 10
0. 08
0. 06
D
D QM/QT = 840
o QM/QT = 1,050
QM/QT = 1.250
V = 1,2, and 3 fps
M = 0. 50 In.
\
2 in.
-H
na \
\
\
\
GRID NO. 1
I 1 I
TRACER ORIFICES
DLa. = 0. 021 in.
d = 0. 25 in.
D
20
30 40 50 60 80 100
x/d
200
FIGURE 23. DECAY OF CONCENTRATION FLUCTUATIONS
DOWNSTREAM FROM A GRID
72
-------
may be due to some change in character of the turbulent wake behind
the grid bars at this velocity. Inspection of curves giving drag
coefficient and vortex shedding frequency vs. Reynolds number [ 18, 65]
for circular cylinders showed no change in character at any Reynolds
number near those at which the present experiments were done. A
grid with a low M/d ratio is not, however, a good approximation of
an infinitely long circular cylinder. Also, the measurements of head
loss through the grids showed that the head loss coefficient KL = hL/
(V^,/2g) was substantially greater at a velocity of 1 fps than at higher
velocities. This is another indication that some change in the turbulent
wake did indeed sometimes occur at the lowest mainstream velocity.
One of Gibson's graphs [11] showed a similar jump at a low velocity
although he did not comment on it.
The second point regarding Figure 23 involves the value of a1 used to
normalize a'. It can be shown [ 22] that if a tracer of concentration
A-p and flow rate QX enters a tubular reactor where the mainstream
flow rate is QM> the spatial root-mean-square concentration fluctua-
tion across the cross-section is,
~AT~VQT/QM . (87)
To use a1 as the initial rms concentration fluctuation for an isotropic
scalar field, the assumption must be made that the tracer is spread
out across the cross-section so that the mean concentration at all
points of the cross-section is the same while little decay of the con-
centration fluctuations has taken place. It might then be expected
that measurements of time-averaged rms concentration fluctuations
near the grid would give results of the same order of magnitude as
the calculated value given by Equation (87). However, this is not
what occurs. Measurements approximately i in. downstream from the
grid showed that the rms values were from 1% to 4% of the calculated
value (there was considerable variation because of substantial dif-
ferences in mean concentration across the cross-section).
It appears that two different mixing phenomena are occurring. The
first involves mixing in the turbulent wake of the grid bars. This
process is effective for only a few grid bar diameters downstream,
but it is very important. The vortices shed by the bars act to spread
the tracer as it leaves the orifice. This also acts to greatly decrease
the concentration fluctuations at a "point. " A short distance from the
grid, the turbulent wakes from the individual grid bars will coalesce,
and isotropic decaying turbulence will develop. The time-averaged
tracer concentration is fairly constant across the cross-section, and
the decay of the rms concentration fluctuations follows Equation (86).
It should be noted that there may still be considerable segregation
beyond the "wake-mixing" zone. For example, if A, the average
73
-------
concentration of the tracer following complete mixing with the main-
stream, is 50 mg/S., a1 can be computed as approximately 1500 mg/f.
for_the present work. If a1 = 15 mg/l at some point downstream,
a1 /A = 0. 30, which indicates an appreciable variation from the mean.
However, a1 /a1 = 0. 01, a small number which gives the impression
of very little segregation.
Both Gibson and Keeler observed similar phenomena, but their inter-
pretations were somewhat different. Keeler used a "hairbrush"
injection system upstream from the grid in order to obtain a homoge-
neous scalar field at the grid. In measurements very close to the
grid, he found that the rms values were approximately 10% of the
values given by Equation (87). He noted this and assumed that most
of the mixing took place between the injection system and the grid.
He did not, however, relate this reduction in scalar fluctuations to the
spreading which occurred as the tracer left the injection needles.
Gibson did not make any direct comment on the fact that his measured
rms values were much lower than the. calculated values. He was
concerned with the fact that at a given point downstream a1 was pro-
portional to QT/QM instead ofy/Qr/QM as would be the case if Equa-
tion (87) held. He developed a model to explain this phenomenon.
This model also almost inadvertently gives an explanation of why
the measured rms values were so low. Gibson's model will be ex-
amined more closely later.
Some of the scatter in Figure 23 is due to the increase of a1 /a1 with
increases of Q^ at a fixed value of QM- ^n most of the experiments,
QM/QT did not vary by more than a factor of 6 (for Figure 23, this
factor is 1. 5) and was set so that the mainstream velocity was of the
same order of magnitude as the tracer injection velocity. Furthermore,
for the grids with an M/d ratio of 4, the scatter due to variations of
was even greater.
Figure 24 shows a1 at a given x/d and QM plotted against QX for such
a grid. There is almost a direct proportionality between a1 and Q>j-
This is the same phenomenon Gibson observed. He concluded that
it was probably caused by the tracer injection orifices for his ex-
periment facing upstream. In most of the present experiments, the
tracer injection orifices faced downstream. It seems, therefore,
that the phenomenon is due to the fact that Equation (87) is inappro-
priate for describing the initial rms concentration fluctuation of the
isotropic scalar field. It is, however, appropriate for describing
the initial rms concentration fluctuation for the two unmixed streams
before the wake -mixing zone and should be used for this. The effect
of QM/QT in determining the value of a1 downstream from a grid will
be considered more closely later. Nowy other experiments designed
to ascertain how other parameters may affect the mixing will be
discussed.
74
-------
T
GRID NO. 5
M/d = 4, M = 0.5 in. , d = 0. 25 in.
12 ORIFICES
VM - 3 fps
AT = 50 g/l
x/d = 196
g
"ttf
0. 5
i.O
1.5
2. 0
FIGURE 24. a1 vs. QT FOR GRID WITH
M/d = 4
2. 5
75
-------
Effect of Scale of Turbulence on Decay Rate
In Section IV, it was noted that the scalar decay rate, a, in Equations
(45) and (86) was closely related to the right-hand side of Corrsin's
equation,
2 +N -1
Sc
3 2/
3 {L,B*/*7IS*/Z log NSc
6(2> XL ' ' "V3' N "
da'
du1
i
and is in fact equal to it if the right-hand side of Equation (54) is a
constant as decay proceeds.
L and L,. are the two most important parameters in this equation as,
in any mixing system, they are the parameters which can presumably
be varied by changing the physical configuration of the system. It was
noted in Section IV that L,. is apparently a function of the grid bar
diameter, d.Vj-
In order to show the effect of the scale of turbulence on the decay rate'';
experiments were carried out with two grids. The number of tracer
orifices for both grids was nine, and the center-to-center spacing of
the bars, M, was 1/2 in. The bar diameters for the two grids, ,.'
however, were 1/4 and 1/8 in. , respectively. The results are shown
in Figure 25. For the grid with the smaller value of d, L /L- should
be greater, and the decay rate (slope of the scalar decay curve) should
be less. This is what was observed.
Keeler also attempted to show qualitatively the effect of L /L- in
Equation (54). He used two grids with the same M/d ratios, but with
one grid, the values of M and d were twice that for the other. The
same hairbrush injector was used for both grids. Through a rather
ingenious method of plotting his results, he showed a pronounced dif-
ference in scalar decay for the two grids. More conventional plotting
of the data (as in Figure 25) shows that there was actually very little
difference in the two values of a. The reason for the different results
of his experiments and those of the present study is not clear. Perhaps
in his study the value of L /L. was low enough so that a. change in the
value did not affect the complete expression on the right-hand side of
Corrsin's equation.
In discussions of this sort, it should always be kept in mind that
Corrsin's equation strictly applies only to those conditions of high
unattainable in laboratory experiments. The values of Nj^e>, for the
present study varied from 30 to 60. Such values were termed "moderate
by Corrsin [17].
11
76
-------
bO
s
60
40
20
.10
9-ORIFICE GRIDS
M = 0. 50 in.
A = 47. 5 mg/f.
a' = i, 540 m.g/1
V, =1,2, and 3 fps
M
GRID NO. 3
M/d =4, d = 0. 125 in.
X
X
X
8
X
LX
GRID NO. 2
M/d =2, d = 0. 25 in.
X
X
\
X
X
\ D
X
X
\
x
I i I I L
14 20
40 60 80 100
x/d
200
400
FIGURE 25. EFFECT OF SCALE OF TURBULENCE
ON SCALAR DECAY RATE
77
-------
Gibson estimated that u'Lf/v should be greater than 3. 3 x 10s for an
inertial subrange to occur. For the present work, this parameter is
estimated to be approximately 10s .
Effect of the Number of Tracer Orifices
As was noted in Section IV, it has been assumed by some investigators
[ 22, 29] that the scale of segregation, Ls, is a function of the number
of tracer orifices with an increase in the number of orifices pre-
sumably decreasing Ls. Further, a decrease in Ls should cause an
increase in the scalar decay rate according to Equation (54). To test
this,, experiments were conducted with two grids, identical except for
the number of orifices; one had 4 and the other had 9. The scalar
decay curves for the two grids are shown in Figure 26. For the 9-
orifice grid, the rate of decay was actually slightly less, instead of
greater, as might be expected if the above assumption were true.
The conclusion which is drawn from this is that an increase in the
number of orifices does not increase the scalar decay rate. As noted
previously, there seems to be no rational basis for such an assumption,
and these results seem to refute it.
Figure 26 does seem to indicate that the "wake-mixing" is affected
by the number of tracer orifices. At low values of x/d, a1 is lower
for the 9-orifice grid,
Such a conclusion is further substantiated by studies involving grids
with M/d ratios of 4. Four such grids were used with 4, 9, 12, and
24 tracer orifices. It was assumed that the scalar decay rate of the
9- and 24-orifice grids applies to the other two grids even though
measurements involving the latter were only made at one x/d value
for each one. Starting with Equation (86),
TT = ff(f) (86)
ao
one can solve for a'.
a -
(x/d)
(88)
Figure 27 shows a plot of a vs. n, the inverse of the number of
tracer orifices. Except for the value at n = 4, there is a fairly strong
correlation between a and n 1 Extrapolation of the curves of
Figure 26 to x/d - 1 also shows a direct proportionality between n
and a. Therefore it will be concluded for the purposes of this study
that in fact a is proportional to n"1. Of course, it will be evident from
a study pf the plotted data that a slight shift of the line drawn through
the data points will change the value of a tremendously, perhaps by as
78
-------
bo
a
"rt
60
40
20
10
8
M = 0. 5 in. , d = 0. 25 in.
M/d = 2
A = 47. 5 mg/l
a1 = 1,540 mg/i
V= 1,2, and 3 fps
"xx
L Bx
x
x
x
X
X
O GRID NO. 2
9 ORIFICES
GRID NO. 1
4 ORIFICES
I I I I ! I
12
20
40
60
80 100
200
:/d
FIGURE 26. EFFECT OF THE NUMBER OF ORIFICES
ON SCALAR DECAY RATE, M/d = 2
79
-------
o
v-t
X
tf --,
m
O
n = 24, x/d = 384
n = 12, x/d = 384
Qn = 9, x/d = 384
n - 4, x/d - 192
M/d
d
A = 47. 5 mg/i
= 1, 540 mg/i
= 4, M = 0. 5 in.
= 0. 125 in
= 1, 2, and 3 fps
10 -
, 05
. 10
. 15
. 20
(NUMBER OF SOURCES)
-l
n
-l
25
FIGURE 27. INVERSE RELATIONSHIP BETWEEN NUMBER OF
SOURCES AND a FOR GRIDS WITH M/d = 4
80
-------
much as 50%. This sensitivity must be kept in mind when workirg
with log-log plots of this sort. Any value of a. obtained from such
extrapolation should be recognized to be of low accuracy.
Effect of Injection Sources JF/xcing Upstream
An effort was made to find ways of modifying the injection system in
order to increase the scalar decay rate through a change in the scale
of segregation. An experiment was carried out in which a grid was
turned around such that the tracer injection orifices faced upstream.
The scalar decay curve for this condition was compared with one for
a grid with normal orientation (tracer injection downstream). The
results are shown in Figure 28.
The values of a1 close to the grid are higher for the case in which the
orifices face upstream, apparently because the "wake-mixing" is not
so effective in reducing the scalar fluctuations. The rate of decay,
however, is much greater. Whether or not there is a difference in
the scale of segregation is not known. However, it has been shown
that a difference in the scalar field will affect the scalar decay rate
even though the turbulent flow field is essentially the same.
It was originally planned that measurements of Ls would be made by
using one probe, making measurements of a Eulerian time correlations
relating this to the Eulerian space correlation discussed in Section
IV, and calculating the scale of segregation, Ls. This was to have
been done by recording the data digitally on magnetic tape and utilizing
a CDC 6400 computer to make the calculations. However, because of
time limitations and a desire to proceed with experiments relating
process performance (in alum coagulation, wastewater coagulation,
and wastewater chlorination) to goodness of mixing, the studies
involving measurement of Ls were not carried out. Such an experiment
would prove very interesting, particularly in relation to Figure 28,
as the scale of segregation has apparently not been measured for any
system.
It is interesting to note that when the grid used for the experiment
described above was in the upstream injection orientation, the system
was very similar to one used by Gibson: upstream injection, d = 1/8
in. , and orifices placed halfway between grid bar intersections. M
was slightly different for the two studies 5/8 in. for Gibson's and
i/2 in. for the present work. A comparison of his results and those
of this study is presented in Appendix C.
Comparison of Geometrically Similar Grids
As it may be difficult to design grids with bars 1/4 or 1/8 in. in
diameter for full-scale treatment plants, it is important to attempt
to determine how scaling these grids in size affects the resulting
81
-------
30
20
1 T
10
24 - ORIFICE GRID
M = 0. 5 in. d = 0. 125 in.
M/d = 4
A =47.5 mg/i
= 1, 540 m.g/1
O
O
TRACER INJECTED
DOWNSTREAM
TRACER INJECTED
UPSTREAM
=1,2, and 3 fps
I
20
40 60 80 100
x/d
200
300 400
FIGURE 28. EFFECT OF CHANGING ORIENTATION
OF TRACER INJECTION SYSTEM
ON SCALAR DECAY RATE
82
-------
scalar decay. In order to make a study of the scaling effect, a grid
with M and d values one-half those of grid No., 1 was constructed with
21 orifices and designated as grid No. 6. For perfect similarity it
should have had 42 - 16 orifices. However, because of problems
with the geometry of the configuration, exact similarity could not be
obtained in this respect,
A comparison of results obtained with the two grids is shown in Figure
29. The results for grid No. 6 were very poor, giving a curve which
only with great imagination could be considered a straight line on
log-log paper. It would be very difficult to define a slope through
these points and impossible to estimate a value of a. with any accuracy.
It is apparent, however, that the smaller grid gives poorer results
than does the larger grid. Furthermore, attempting to compare
results from these two geometrically similar grids ignores two pre-
vious conclusions; the slope of the scalar decay curve (for downstream
injection from the grid bars) is a function of the grid bar size, and
the displacement of the scalar decay curve, or a, is a function of the
number of sources. For that reason, perhaps it is appropriate to
compare the results obtained using grid No. 6 with those obtained
using grid No. 4 (d = 1/8 in. , M = 1 /2 in. , 24 orifices). These two
grids are very similar with the exception that M/d = 4, 0 for grid
No. 4 and 20 for grid No. 6. The comparison of results is shown in
Figure 30. The agreement is quite good, and while it cannot be said
to confirm the previous conclusions, it is at least compatible with
them.
It should be noted that Keeler concluded, through comparison of his
results with Gibson's, that the M/d ratio affects the displacement of
the scalar decay curve. Such a conclusion seems intuitively reasonable.
However, because of differences in the tracer injection systems for
the two studies and differences in their methods of calculating a' , it
seems that comparison of results obtained in the two studies cannot
be made. Keeler measured a' very close to the grid and empirically
determined that the initial_rms concentration fluctuation in the isotropic
scalar field was equal to A,
Gibson, in developing a model to explain why a' was proportional to
QM/QT for his work, found that the initial rms concentration fluctu-
ation of the isotropic _scalar field was proportional to A, and he there-
fore apparently used A to normalize a'. Therefore, the two curves
which Keeler compares are graphs of (a1/A)2 vs. x/M, As the tracer
injection systems are different and the values of QM/^T are different
(approximately 100 for Keeler and 2000 for Gibson), the fact that there
is a difference in displacement between the two curves cannot be used
to prove that M/d affects the value of a in Equations (86) or (45).
SUMMARY OF MIXING STUDIES RESULTS
It would be desirable to relate the results produced by the various
grids and obtain an overall description of the mixing process which
83
-------
oo
10
so
a
00
M = 0. 5 in.,
d = 0. 25 in.
4 ORIFICES
M/d - 2
A = 47. 5 mg/t
a' = 1, 540 m.g/1
V =1,2, and 3 fps
\
) GRID NO. 6
M = 0. 25 in. ,
d = 0. 125 in.
21 ORIFICES
\
\
20..
50
100
200
500
x/d
FIGURE 29- RESULTS OBTAINED FROM GEOMETRICALLY
SIMILAR GRIDS
1000
-------
15
10
00
Ul
GRID NO. 6
M/d = 2, M = 0. 25 in
*21 ORIFICES
GRID NO. 4
oM/d = 4, M = 0. 50 in
24 ORIFICES
20
50
d
A
a1
o
VM
= 0. 125 in.
= 47. 5 mg/i
~ 1, 540 mg/t
- 1, Z, and 3 fps
100
200
500
x
/d
FIGURE 30. EFFECT OF VARYING M
-------
occurs under the conditions found in this study. To that end, the con-
clusions reached in the previous sections are summarized below,
1. The degree of mixing at a point downstream dees not depend on
the mainstream velocity. The time necessary to reach a given
degree of mixing is inversely proportional to the mainstream
velocity.
Z_ a' as calculated by Equation (87) is not a good indication of the
initial rms concentration fluctuations in the isotropic scalar
field, A great deal of mixing occurs as the tracer spreads upon
leaving the orifice in the turbulent wake of the grid bar,
3. At a point downstream^ a' can be said to be proportional to
QM/QT rather thanV/Qj^/Q^ as suggested by Equation (87),
This is the same as the phenomenon observed by Gibson and
is closely related to the "wake-mixing" described above,
4. Because it determines the integral scale of turbulence, the
grid bar size affects the rate of scalar decay as predicted by
Corrsin, the rate increasing as the grid bar diameter increases,
5. Within the limits of the present work, the number of tracer
orifices does not seem to greatly affect the scalar decay rate.
It is therefore concluded that the number of sources does not
affect the scale of segregation. Such parameters as method of
tracer injection (upstream or downstream, for example) do
seem to have a strong effect on the scalar decay rate when the
turbulent flow field is essentially unchanged. The conclusion
drawn is that Corrsin's prediction concerning the effect of the
scalar field, as described by L , on the scalar decay rate, has
been qualitatively shown.
6. The number of sources as well as the method of injection seems
to affect the "wake-mixing. " To a reasonable degrees the value
of a' measured at a given distance downstream is inversely pro-
portional to the number of tracer orifices in a given cross-
sectional area.
7. Within the limits of these studies, the M/d ratio seems to be
important only in that more closely spaced bars can provide
a greater number of tracer orifices per square inch,
Not all of the data substantiates each of these conclusions. In some
cases it has been necessary to allow considerable latitude in i.ncorpora
ting specific results into the general model. However^ such inter-
pretation is necessary if any general conclusions are to be drawn.
These conclusions have been drawn with the objective of determining
the design parameters for use with prototype grids. In particular, it
appears that "wake-mixing" may be the most important consideration
86
-------
in designing prototype grids. From results of the process studies
described in Section VII, the time necessary for adverse chemical-
physical reactions to occur seems to be sufficiently short such that
the degree of mixing taking place in the first fraction of a. second
determines whether process performance will be satisfactory. It
may be that the portion of the scalar decay in the isotropic scalar
and turbulence fields will be unimportant in this regard.
INTERPRETATION OF RESULTS:
MODEL DEVELOPMENT
A model which combines the above summary of results in a quantita-
tive and concise manner can be developed. It is a semi-empirical
model in that while the straight-line, log -log form of the decay curve
and the dependence on the scales of turbulence and segregation have
been derived theoretically, the actual values of the coefficients must
be determined from experiment. The general decay equation is
written,
le ==« (86)
o
where a = fi (n , Q-M/^T' injection system), a =f2(d, injection
system), and n = the number of tracer orifices per square inch of
2
reactor cross -section, in.
Let a' be the initial rms concentration fluctuation in the isotropic
scalar field
P- =<*'~a <89>
i
where a{ = fa (injection system).
To derive an expression for a1 , assume that the tracer becomes
partially mixed with a portion, of the mainstream flow rate which
passes close to the injection orifice. This portion will be Q and is
defined by,
Qp=KpnsQM ' QT<
where K,, = f4(injection system). Kp is essentially the cross -sectional
area with which the tracer is mixed. This approach is similar to
Gibson's but is different in that he arbitrarily set a value for Kp. He
also assumed that the tracer was completely mixed with the flow rate
Q . He called this premixing.
P
87
-------
In this wake-mixing region, the average concentration of the tracer
mixed with this portion of the flow is,
A - T T - T T (91)
p Q ~K n Q..
c p p s M
It will be assumed somewhat arbitrarily that the rms concentration
fluctuation over the cross-section is,
a' =K A (92)
i w p
where K = fs (injection system). Substituting in Equation (91).
w
K A Q
a' - T.w * L ,. (93)
i K n Q, ,
p s M
Eliminating aj from Equations (89) and (93),
' a1 K n Q^, -a
K A_ QT
w I T
Combining coefficients,
a'n Q -a
ATQT -« M'
This equation describes the rms concentration fluctuation, a', which
can be expected at a normalized distance downstream, x/d, in terms of
the known parameters n , QT^I QT, and A , and the experimentally
determined scalar decay rate, a, and wake-mixing coefficient, a".
a is determined by the grid bar diameter and the type of tracer in-
jection system (for example, upstream injection or downstream
injection from the grid bars), a/11 is determined by the type of tracer
injection system used, a11 has the units L~2 because it includes K ,
the cross-sectional area near each source which defines the flow "
rate involved in the wake-mixing, or premixing as Gibson terms it.
Since,
ATQT
A =-^r-i , (96)
88
-------
then Equation (95) can be modified to
a'n -a
-=T- = «" (j) . (97)
A d
This can be transformed to a relation involving a1 , the initial rms
concentration fluctuation of the two unmixed streams, by use of
Equations (87) and (96).
-a
d'
= «" (f) (98)
In order to illustrate that the results of this study can be described
reasonably well by this model, the data from seven different grids are
shown in Figure 31 a'ns/A a" is plotted against x/d. All the data
points represent injection from the downstream side of the grid bars.
ns varies from 1. 3 to 7. 6 orifices per square inch. A varies from 19
to 57 mg/L To reduce the total number of points plotted, only the
data for Vj^ = 2 fps are shown.
There is, as might be expected, considerable scatter, but it does
not seem excessive. For the grids with d = 1/4 in. , taking the tracer
source density into account actually increases the difference in results
between the 4-orifice and 9-orifice grids (see Figure 26 for comparison).
The wake -mixing, as manifested by the value of a11 which fits the data
best, does, however, seem to be described quite well by this model.
As mentioned previously, it could well be that the wake-mixing is the
crucial step in the mixing process.
The value of a" which seems to fit these data is 5 in. ~2. The decay
rate, -a, is approximately -0.4 for the 1/8-in. grid bars and -0. 8
for the 1/4-in. bars. The use of this model to compare results of
the present study with those of Gibson in the case of the tracer being
injected upstream is given in Appendix C. The agreement seems to
be quite good.
The question which naturally arises concerns the extrapolation of
these results to grids with larger bars. The results of the alum
coagulation tests suggest that the grid bars in prototype mixers will
probably be held to 1/2 in. or less. The decay rate for such a grid
will probably be somewhat greater than the -0. 8 for the 1/4-in. bars
used in the present work. How much greater cannot be determined.
Presumably, though, the value of a" which is controlled by the wake-
mixing would be the same. In Appendix D are estimates of the scalar
decay curves for grids with larger bar diameters.
89
-------
vO
o
1.0
0. 5
0. 1
0.05
. 01
0. 005
d = 1/8 in.
(a = 0.4)
GRID
NO.
1
2
3
4
5
6
8
d - 1/4 in.
(a - 0. 8)
\
10
50 100
500 1000
x/d
FIGURE 31. GENERAL MIXING MODEL: RESULTS FOR SEVEN GRIDS
-------
SECTION VII
INITIAL MIXING AND ALUM COAGULATION -
FLOCCULATION
The purpose of the experiments described in this section was to
demonstrate that rapid initial mixing is important in certain water
and wastewater treatment processes, specifically alum coagulati.on-
flocculation of a turbid water. Another purpose was to show that
grid-type initial mixers, the mixing characteristics of which were
described in Section VI, can be used to effect the rapid mixing. A.s
stated previously, very rapid mixing of the chemical with the water
stream before certain reactions can occur or be completed might
result in improved process performance.
Alum added to a turbid water with sufficient alkalinity undergoes very
complex, rapid, and irreversible reactions. This study and pre-
vious work have shown that if the Al(III) can come in contact with all
the turbidity particles before these reactions have proceeded too far,
then the alum can be more effective in performing its task of aiding
clarification. It will be shown that the effect of initial mixing is
dependent upon the alkalinity of the water. If the alkalinity is suf-
ficiently low, slow initial mixing will not detrimentally affect the
process performance. However, increasing the alkalinity results
in an increasing sensitivity to the adequacy of the initial mixing.
Because of the prohibitive cost and difficulty of performing field
experiments, the work described herein involves pilot-plant studies.
This allowed close control of all parameters involved, but from the
point of view of demonstrating the applicability of this concept to
full-scale water and wastewater treatment plants, there is one dif-
ficulty. While it is not difficult to develop a device producing very
rapid mixing in a 2-in. diameter pipe, it is a more difficult task to
design and construct a device producing mixing of equal rapidity in a
large pipe.
It is possible, through the use of mixing theory and experiments to
predict the intensity of segregation (or degree of mixing) at a partic-
ular distance downstream from a given grid. However, it is not
possible to predict precisely at the present time how rapid the mixing
of the chemical stream with the water stream must be in order to
avoid poor performance. The rates of the crucial reactions or
phenomena are not known. Evidence will be presented which shows
that for alum coagulation-flocculation of a turbid water, the time of
mixing, the time required to reach some low, arbitrarily defined
value of the intensity of segregation, must be very short if performance
is to be improved.
91
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This point is important because increasing the rapidity of initial
mixing only slightly, such as by improving the flash mixer, may not
lead to improved performance. It is believed that a grid-type initial
mixing device will help overcome this problem. The mixing pro-
vided by a grid in a pipe depends not on the diameter of the pipe but
on the physical configuration of the grid: the bar diameter, the bar
spacing, and the number of tracer injection orifices per square inch
of cross-sectional area. Thus, if grids which are fairly fine with a
high injection orifice density can be constructed and placed in large
pipes, it may be possible to utilize rapid initial mixing to provide
an improvement in water treatment processes or to decrease the
amount of chemicals needed for the processes.
SEGREGATION JAR TESTS
In order to show the effect of prolonged segregation in the mixing of
alum with a turbid water, a jar test which simulated the difference
between slow and rapid initial mixing was devised. Two 500-m^
samples of turbid water were used. In most instances the turbidity
consisted of a 25-mg/^ suspension of kaolin, although a 50-mg/J!
suspension of bentonite was used in a few experiments because of
the differences in coagulation characteristics between the two types
of clays [ 36, 38], An "optimum" alum dose was determined for the
turbidity and alkalinity of the sample by using jar tests. Various
concentrations of alum were added to samples of turbid water, and
the samples stirred in a jar test apparatus. The lowest alum dose
which resulted in the most rapid formation of visible floe was chosen
as optimum [ 33].
The experiment representing rapid initial mixing was essentially an
ordinary jar test. The previously selected alum dose was added
directly to one of the 500-m-f samples. This was vigorously stirred
with a glass stirring rod for a few seconds in order to effect complete
mixing, Then the sample was put in a jar test apparatus and stirred
usually for 6 minutes at 70 rpm. The floe formed -was allowed to
settle for 15 minutes, A pipette was used to remove a sample of
supernatant from approximately one-half inch below the surface of
the sample in order to avoid entrapping floating floe particles in the
supernatant. This supernatant was then analyzed for residual tur-
bidity using a light-scattering turbidimeter (the turbidimeter and
chemicals are described in the section on continuous flow coagulation-
flocculation experiments).
The experiment was repeated with a second 500-rrJ sample of turbid
water with the following modification. This sample was divided into
two portions, 100 ml and 400 m^ for example. The alum was then
added to the 100-m-f portion and was vigorously stirred for 3 to 5
seconds. Then this 100 -mf. portion was added to the remaining 400
ml The two portions were thoroughly mixed with a stirring rod,
92
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and the jar test was repeated. This experiment represented poor
initial mixing, i. e. , prolonged segregation between the alum and a
portion of the turbid water.
Generally, the jar test representing poor initial mixing resulted in a
higher residual turbidity than the jar test with rapid initial mixing,
This difference in results can be presented as the ratio of two aggre-
gation rate coefficients, KAm, the coefficient for the case of rapid
initial mixing, and KAS, the coefficient for the case of prolonged.
segregation. The values of rms velocity gradient, G, and time of
flocculation, T, were low enough to allow deletion of the breakup
term in the equation describing the rate of change of the concentration
of primary particles,
(70)
This equation can be easily solved for a batch system.,
In (n, /nf ) = K
In the segregation jar tests, the values of G and T were the same for
the experiments involving rapid and slow initial mixing and can be
eliminated from the equation giving the ratio of the two aggregation
rate coefficients.
ln(ni /n?) KA
=^7-^- <99)
/ / o \ -tv .
In n, /n ) A
1 s i s
where n: m and nj are the concentration of primary particles re-
maining for the case of good mixing and poor mixing, respectively.
As noted in Section IV, nx /nl can be taken as the fraction of
turbidity remaining after treatment as measured by a light scattering
turbidimeter.
Effect of Bicarbonate Alkalinity on Jar Test R.esults
The water which is normally delivered to the University of California
by the East Bay Municipal Utility District is taken from the Mokelumne
River in the Sierra Nevada Mountains. The concentration of dissolved
matter in this water is unusually low, the TDS concentration being
approximately 32 mg/1 The alkalinity, as CaCO3, is 20 mg/1 It
was found that with a. 25-mg/l suspension of kaolin in this water, no
effect of initial mixing, as measured by the segregation jar test, was
93
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apparent. Even with segregation times of up to 30 sec, the results of
the jar test representing poor initial mixing produced results which
were as good as those produced by the test representing rapid initial
mixing.
In order to determine whether increasing the alkalinity might have an
effect on the jar test results, sodium bicarbonate was added to the
tap water before the kaolin. The jar test described above was re-
peated at various alkalinities and alum doses. The results are shown
in Figure 32 where KAm/Kj\ is plotted against alkalinity. The
figure shows the results of initially adding the alum to 100 no? and
250 mf. of the 500-rrJ sample. It can be seen that increasing the
alkalinity causes the effect of segregation to be increased. Also,
initially adding the alum to a smaller portion of the total sample
causes the effect to be greater. The range of alum doses in Figure
32 is 23 to 40 mg/^, depending on the alkalinity. Not shown are the
results of segregation jar tests performed with a 50-nag/^ bentonite
suspension. The data involving bentonite are rather limited, but the
increase in the effect of segregation with an increase in alkalinity
is also found there. Vrale and Jorden [ 59] discuss the importance
of rapid initial mixing in conjunction with silica suspensions which,
as noted in Section IV, have coagulation characteristics similar to
bentonite suspensions.
It appears that the alkalinity of the water affects the process by
controlling the rate and extent of the hydrolysis and polymerization
(or olation) reactions of Al(III).which occur in the presence of the clay
particles in the segregated portion of the sample. This may be due,
in part at least, to the buffer effect that alkalinity has on the pH as
alurn is added. Stumm and O'Melia [37] have shown that the reaction
rates of Fe(III) and presumably Al(III) are, strongly affected by pH.
They found that the rate of removal of Fe from the system increases
100 times for every unit increase in pH. It is also known that the
polymerization reactions are considerably slower than the initial
hydrolysis reactions [ 66], but how they vary with pH is unclear. As
alum is added to a portion of the turbid water sample, the pH will be
depressed to an extent depending upon the buffer capacity of the
water the lower the alkalinity, the greater the reduction in pH.
And as the pH is lowered, the rate of removal of A1^^ from the
system decreases. Thus, at low alkalinities, the reactions which
can be detrimental to process performance might occur more slowly.
Figure 33 shows the final pH vs. the alkalinity for the optimum alum
dose in the segregation jar tests. The alum doses in mg/i are shown
next to the data points. The final pH increases with increasing
alkalinity. This adds to the effect of buffer capacity discussed above
since, at higher alkalinities, not only will the extent of depression
below the final pH in the segregated portion be less, but the final pH
94
-------
vO
U1
3. 75
3. 50
3. 25
3.00
2.
2,
2.
2.
i.
i.
i.
i.
0.
75
50
25
00
75
50
25
00
75
ALUM INITIALLY
ADDED TO 100 ml
OF 500-rrL? SAMPLE
ALUM INITIALLY
ADDED TO 250 mi
OF 500-m£ SAMPLE
20 40 60 80 100 120
ALKALINITY, mg/1
140
160
180 200
FIGURE 32. EFFECT OF SEGREGATION ON COAGULATION-FLOCCULATION:
JAR TESTS
-------
ffi
3
8. 0
7. 8
7. 6
7.4
7, 2
1. 0
6.8
6. 6
6.4
6. 2
6. 0
25 mg/4 KAOLIN
SUSPENSION
40
35
30
23
23
NUMBERS REPRESENT
ALUM DOSES IN mg/4
0 20 40 60 80 100 120 140 160 180 200
ALKALINITY, mg/1 as CaCO3
FIGURE 33. RELATION OF PH AND ALKALINITY AT
"OPTIMUM" ALUM DOSAGES
itself will be higher. Thus, it is to be expected that at higher
alkalinities, the pH in the portion to which the alum is first added
will be higher, and the rate of the hydrolysis and polymerizations
reactions will be faster.
Buffer capacity may affect the process in another way. At low
alkalinities the pH in the portion to which the alum is initially added
may be driven low enough to prevent the formation of the insoluble
96
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hydroxide (see Figure 1). Not until the mixing is almost complete
will the Al(OH)3 s tend to be formed, and this may be the crucial
reaction which it is necessary to avoid. At higher alkalinities the
pH in the portion to which the alum is added will not be driven so low,
and Al(OH)3 g can form before mixing is completed. More rapid
mixing may overcome this.
It is possible that alkalinity has an even more direct effect upon the
hydrolysis reactions. Kim, Ludwig, and. Bishop [ 36] found that the
isoelectric pH of the aluminum-hydroxo compounds was dependent
upon the alkalinity of the water and postulated that the bicarbonate
anion may have a stronger coordination tendency with the aluminum
ion than does a hydroxide ion, causing a decrease in isoelectric pH
with an increase in anion concentration. It can be concluded from
this that the character of the reactions which occur are directly re-
lated to the alkalinity.
It should be noted that Kim, Ludwig, and Bishop found that the iso-
electric pH decreased with increasing alkalinity. In the present study,
the final pH at optimum alum dose increased with increasing alkalinity.
Although the optimum pH decreases with increasing alkalinity, the pH
range for "good" coagulation becomes wider. Thus, "optimum per-
formance" in the present sense does not necessarily correspond to
isoelectric pH.
It is also possible that the hydrolysis and polymerization reactions
which occur when Al(III) is added to water are so rapid that their
degree of completion depends only on the degree of mixing (see Figure
8). It might then be postulated that the diffusion of the aluminum-
hydroxo compounds to the clay particles and the resulting destabiliza-
tion may take a relatively long time (still less than one second). Very
rapid mixing could allow the destabilization to occur in the presence
of more clay particles, and better performance would result. It is
unclear how varying the alkalinity (or pH) would affect this. It might
be that at lower alkalinities, a greater degree of mixing would be
necessary to reach a given degree of completion of the hydrolysis and
polymerization reactions. Thus, more clay particles would be mixed
with the destabilizing compounds, and initial mixing would not be as
crucial as at high alkalinities.
Adding the alum to a smaller portion of the turbid water sample results
in an increased effect of segregation because the alum is segregated
from a greater amount of the kaolin during the period that the crucial
reactions are taking place. If less kaolin ; < present during the
occurrence of these reactions, then the re^ dual turbidity after com-
pletion of the jar test will be greater.
It should be noted that there is a slight, although reconcilable, conflict
between this result and the conclusion regarding the effect of buffer
capacity on the phenomena. When the alum was initially added to
250 m.SL rather than 100 red of the turbid water sample, the alum
97
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concentration -was twice instead of five times the final dose in the total
500 rnl Therefore, the pH was not driven as low, and the reactions
could occur at a much faster rate, or, alternatively, Al(OH)3 could be
formed. It might be expected, therefore, that adding alum to a larger
portion of the 500 m.1 would result in an increased effect of segrega-
tion. That such a result does not occur means either that buffer
capacity is of little importance in the alkalinity-segregation effect
relation or that the number of clay particles present during the crucial
hydrolysis and polymerization reactions is more important. The
latter conclusion seems more likely.
CONTINUOUS FLOW COAGULATION-
FLOCCULATION EXPERIMENTS
In order to determine the effect of rapid initial mixing in a continuous
flow coagulation-flocculation system, two of the multiple-orifice grids
used in the mixing studies described in Section V -were utilized as
initial mixing devices in conjunction with a tubular reactor. Results
obtained using these devices were compared with results obtained
using a flash mixer a backmixed reactor utilizing a high-speed pro-
peller to mix the fluid streams. The flash mixer provided mixing
which would be considered sufficiently rapid by contemporary standards,
The purpose of these experiments was to determine the advantage, if
any, in using a multiple-source grid mixer at the head of a tubular
reactor.
EXPERIMENTAL APPARATUS
A diagram of the experimental arrangement utilizing the grid initial
mixers and, alternatively, the flash rnixer is shown in Figure 34.
It is a modification of the apparatus used for the mixing studies. At
a point 2 ft downstream from the grid a tube was used to divert part
of the flow into the multi-compartment flocculation chamber. The
diversion tube was necessary because the flocculator could accom-
modate only a portion of the flow which the tubular reactor and grid
mixer were designed to handle. A flow of ZO gpm was used in the
tubular reactor, but only 0. 73 gpm was passed through the flocculator.
In order to minimize additional mixing caused by the diversion tube,
the tube was centered in the tubular reactor. The diameter of the
tube was such that the flow velocity in the tubular reactor was equal
to that in the diversion tube. There were no valves in the tube to
create turbulence. Despite tK;se steps, the tube connecting the
tubular reactor to the floccu; cion chamber did, of course, provide
additional mixing of the alum with the turbid water. It was believed,
however, that the crucial period would occur upstream from this
point in the region very close to the grid, and the experimental
results seem to substantiate this.
98
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The flow from the tubular reactor to the flocculation chamber was
controlled by varying the pressure in the tubular reactor section.
This was accomplished by adjusting two valves, one downstream and
one upstream from the reactor section (Points A and B, Figure 34).
The flow was measured directly at the effluent end of the flocculator.
To add the kaolin suspension and the bicarbonate alkalinity to the raw
water, a Sigmamotor model T65 positive displacement pump, powered
by a Bodine NSH 54 RL motor and a Minarlk SH-53 speed controller,
was used. This type of pump can provide several streams of fluid
simultaneously. The kaolin was added to the 2-in. line at a point
approximately 10 ft upstream from the grid. A nozzle meter, a
valve, and a 90° elbow between the two points insured that the kaolin
was completely mixed with the raw water at the alum injection grid.
Sodium bicarbonate was added at a point several feet upstream from
the kaolin addition point. Alum was supplied from the same constant
head tank employed in the mixing experiments for the salt tracer.
When the alternative setup for using a flash mixer as the initial
mixing device was used, the raw water was put through the small
constant head tank previously used for the salt tracer and alum
solutions. A rotameter was used to measure and control the flow.
The Sigmamotor pump described above was used to add the alum to
the flash mixer in addition to being used to add the kaolin and sodium
bicarbonate to the raw water line. It should not matter, from a
hydrodynamic standpoint, that with the tubular reactor there was a
much greater flow in the initial mixing unit. At the point of diversion
in the tubular reactor, the intensity of segregation and the mean con-
centration of alum at all points of the cross-section were the same.
What was done was merely to divert a portion of this flow to the
flocculator. The actual flow through the tubular reactor is not
relevant in the sense that a comparison of the efficiency of the two
types of initial mixing systems can be made.
The pilot-plant flocculation chamber consisted of eight compartments,
each 8-3/4 in. x 8-3/4 in. with a water depth of approximately 11 in.
For these experiments, only three compartments were used. All
paddles were driven at the same speed by a Bodine NSH 54 RL electric
motor and a Minarik SH-53 speed controller.
As noted in Section IV the energy per unit fluid mass and per unit
time dissipated in the system by the paddles is an important parameter
in flocculation kinetics. It, together with fluid viscosity, determines
the rms velocity gradient, G. Others have discussed in some detail
the relation between G and the speed of rotation of the paddles [ 31,51],
For the paddles used in this experiment, this relation has been deter-
mined to be (67)
G = 0. 15 N1'55 (100)
where N is the paddle speed in rpm and G is in sec " * ,
100
-------
Initial Mixing Units
Two grid mixing devices in tubular reactors and one flash mixer
were used in these experiments. The grids were two of those used
in the mixing studies described in Section V (Grids 4 and 8, Table 2).
The M/d ratio for both grids was 4, and the bar diameters were
1/8 in. The only difference between them was that one had 4 alum
injection orifices, and the other had 24. This corresponds to orifice
densities of 1. 27 and 7. 60 in. ~l , respectively. From the mixing
studies, it seemed that the latter grid would provide better mixing
than the former because of the relation between wake-mixing phenom-
enon and the tracer injection orifice density.
The velocity through the tubular reactor was 2 fps. This value was
used in order to eliminate some of the problems which seemed to
occur at the lower velocities as described in Section VI. For a 2-ft
tubular reactor, the residence time was 1 sec. The tube connecting
the tubular reactor to the flocculator was about 1 ft long and resulted
in a total residence time before the flow entered the flocculation
chamber of approximately 1. 5 sec. The flash mixer was a 3-in.
diameter plastic tube sealed at one end. The turbid water entered
on one side at the bottom, and the alum solution entered on the other
side. The propeller mixer rotated at 1600 rpm, and the water left
the flash mixer near the top. The mean residence time was 23 sec.
Turbidimeter and Chemicals
A Hach laboratory turbidimeter, model I860, was used to determine
the relative number concentration of suspended particles in the
coagulation experiments by measuring the turbidity of samples. It
operated on the principle that light, passing through a substance,
before and after treatment, is reflected by particulate matter su's-
pended in the substance. The turbidimeter was standardized with a
polyacrylic plastic rod into which a special turbidity material had
been cast. Before each reading was taken, the turbidimeter was
checked with the standardized rod as the meter reading tended to
drift slightly. It was found in the course of doing the experiments
that there was a nonlinear relation between the concentration of kaolin
suspended in the water and the reading of the turbidimeter. Since
the parameter of interest was particle concentration (specifically,
relative particle concentration) rather than turbidity per se, it was
necessary to relate the two parameters by means of a calibration
curve.
The turbidity producing material used in these experiments was
kaolin N. F. colloidal, produced by Matheson, Coleman, and Bell.
Bentonite and silica are two other types of colloids which could have
been used. As noted in Section IV, the coagulation mechanism
associated with these types of suspensions appears to be somewhat
101
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different from the mechanism associated with dilute kaolin suspensioi
Packham [ 38] took samples from several streams in England and
found the suspension behaved similar to kaolimte. Both bentonitic an
kaolinitic type clays are found in natural waters, but the proportion
is seldom reported. While the differences between the two types
should be remembered, indications are, from the segregation jar tes;
and the work of Vrale and Jorden [ 59], that the effect of rapid initial
mixing seems to be independent of the type of colloidal material used.
The alurn used was of technical grade. A problem associated with
this was the fact that there was a considerable amount of insoluble
impurities present. In order to deal with this problem, the alum was
dissolved in deionized water in a 20-liter bottle at a concentration of
about 25 g/S. 24 hr prior to a run. This allowed most of the insoluble
material to settle out overnight. Then before the run was made, the
supernatant was transferred to another 20-1 bottle from which the alui
solution was fed to the system during the run. Reagent grade powden
NaHCO3 , manufactured by Mallinckrodt Chemical Works, was used
to provide the additional alkalinity during those runs where it was
needed.
The kaolin suspension to be fed to the system was usually prepared
the day of the run. The feed suspension concentration was usually
20 to 30 g/2 and was prepared with deionized water. The suspension
was stirred for several hours prior to the run in order to insure that
the clay was broken up into the smallest particles possible.
Because the kaolin would not remain in suspension without stirring,
the propeller mixer was kept operating during the run. Tests showed
that at all times during the run, the kaolin feed concentration re-
mained the same, demonstrating that the propeller mixer was effec-
tive in maintaining uniform concentration throughout the bottle. When
sodium bicarbonate was required to increase the alkalinity of the
water, it also was prepared with distilled water at a concentration of
approximately 6 gli. These concentrations apply to the use of the
grid-type initial mixers for which 20 gpm of water were passed
through the initial mixing unit. When the flash mixer was used, only
0. 73 gpm of water was passed through the initial mixing unit and the
feed concentrations were approximately 1/20 the concentrations for
the tubular reactor.
It was realized-that, while using the same feed concentrations for
both the grid and flash mixers, especially for the alum, might be
desirable from the standpoint of consistency, there is no apparent
reason why such a discrepancy might invalidate the experiment. The
concentration of alum was quite high in both cases, and the pH was
low enough to insure that the predominant species in both cases was
probably the same. It should be noted that changing the alurn feed
concentration will change the value of a' as discussed in Section
VI. It will be decreased in value with a decrease in the feed con-
centration. By lowering the value of a' , a1 at a given time will also
102
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be decreased, and the rate of mixing can be considered to be improved
by decreasing the alum feed concentration. In this way, any error
caused by using the lower feed concentration for the flash mixer can
be considered to be conservative because the rms concentration
fluctuations are lower than they would have been if the higher feed
concentrations had been used. Even with this advantage, the flash
mixer provided the poorest results.
EXPERIMENTAL PROCEDURE
The raw water from the city line was fed to the appropriate constant
head tank. The flow was adjusted to the desired value, and if the
tubular reactor was being employed, the flow diverted from the
tubular reactor was adjusted to the desired value using the valves
upstream and downstream from the reactor section. As mentioned
previously, this adjustment was very sensitive. When the flow was
adjusted to the desired value, the chemicals were fed into the system,
and the paddle speed was set to obtain the desired value of G. After
the flow from the final compartment had reached steady state, 45
min three times the mean residence time of 1 5 min was allowed
for the flocculation process to reach steady state. Then 100 rat.
samples were taken from each of the three flocculation compartments.
During the first runs, three replicate samples were taken from each
compartment. It was soon found that the results were fairly con-
sistent, and subsequently, only one sample was taken from each
compartment. The floe in the samples was allowed to settle for 30
min- and a pipette was used to remove a sample of supernatant for
analysis in the turbidimeter. The supernatant was shaken vigorously
to disperse any floe remaining and the turbidity measured using the
Hach turbidimeter.
The initial turbidity was measured by taking a sample from the out-
let of the final compartment to avoid floating material. It was found
that at low values of G this method resulted in measured values of
turbidity which were too low, due to settling of large floes in the last
compartment. Normally, the average value from several runs, dis-
regarding the low values, was used to determine the initial turbidity.
After the run at the first value of G was completed, the paddle speed
was changed in order to obtain another value of G. Then 30 min was
allowed two times the mean res idence time for the process to
reach steady state. The sampling procedure was repeated, and
another value of G was then selected. It was usually possible to
complete runs with four different values of G in one day.
RESULTS
Continuous flow coagulation-flocculation experiments were carried
out at two alkalinities, that present in the tap water at the time,
103
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25-28 mg/f., and tap water with sodium bicarbonate added to bring
the alkalinity up to 70 mg/1 For the lower alkalinity the alum dose
was 23 rcig/i for the 25 mg/S. kaolin suspension. , For the -higher
alkalinity, the alum dose was 30 mg/1 As noted in the discussion of
the segregation jar tests, it is not possible to change the alkalinity of
the water and keep all other parameters constant.
Results of continuous flow experiments made at the two alkalinities
are shown in Figures 35, 36, and 37. nt /n^, where m is the number
of compartments, is plotted against G, the rms velocity gradient in
the flocculation chamber. Figure 35 shows the results for one com-
partment with a mean residence time of 5 min; Figure 36, two com-
partments and 10 min; and Figure 37, three compartments and 15
min. Also shown are results obtained with three different initial
mixing devices the 24-orifice grid, the 4-orifice grid, and the flash
mixer. There was a pronounced tendency for the 24-orifice grid to
provide the best results and for the flash mixer to provide the poorest
results. The dependency on initial mixing increases with compart -
mentalization and with alkalinity.
It would be instructive to consider the values of both the aggregation
and breakup rate coefficients for the data presented in Figures 3537.
However, because in the range of high G values where breakup would
be important, the data are somewhat inconsistent, only the values of
KA, the aggregation rate coefficient, are presented here. For an
m-compartment flocculator, the resulting relation is
=d +K GT ) (101)
n Am
where Tm is the residence time per compartment. From these
equations, the value of K^ can be found from the low G part of the
performance curves in Figures 3537. These values are listed in
Table 4 for one, two, and three compartments at low and high alkalinity
using the flash mixer, 4-orifice grid, and the 24-orifice grid. Also
shown are the average values of K^ for each initial mixer at each
alkalinity.
Figure 38 shows the average values of K^ normalized with respect
to KA for the flash mixer. The effect of alkalinity can be easily
discerned.
The dependence on alkalinity has been discussed in relation to the
results of the segregation jar tests. Segregation of the alum with
a portion of the clay particles under conditions promoting rapid
hydrolysis and polymer ization results in a higher residual turbidity
after completion of the flocculation process. The alkalinity, through
its buffering capacity, or by more direct action of the HCO3 ion,
influences the rate and extent of these reactions. Thus, with higher
alkalinity, it becomes more important to quickly reduce the intensity
of segregation in the mixing process.
104
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Perhaps the formation of Insoluble aluminum, hydroxide is the crucial
reaction which results in poor coagulation. It has been noted that the
best coagulation of low concentrations of kaolin occurs under con-
ditions of least solubility of Al(III). It may be that the species res-
ponsible for the destabilization of the clay particles are some of the
positively charged hydrolysis and polymerization products of Al(III)
which are adsorbed on the colloidal surface. The insoluble hydroxide
would then form at the clay particle surfaces and act as a binder
material in the sense first proposed by Langelier and Ludwig [ 34].
Alternatively, it may be that some of the charged hydrolysis and poly-
merization products formed early may be better coagulating agents
than those formed later. Rapid mixing can bring these initial com-
pounds in contact with more of the clay particles and thus increase
their effectiveness.
Whatever the particular species responsible for the critical "reaction"
of the alum and the clay, very rapid mixing can result in avoiding the
premature formation of those species with poorer coagulating ability
in cases of high alkalinity. At lower alkalinities the problem of pre-
mature formation of critical species does not occur.
Figure 39 shows a comparison of results obtained when the flash
mixer was used and when the alum was added directly to the first
compartment of the flocculation chamber. The latter is a very poor
initial mixing device, especially at lower values of G. The measure-
ments were made at the higher alkalinity, 70 mg/-?. There was no
apparent difference in performance between the two systems. The
conclusion drawn from this experiment is that a difference in the time
of mixing will not necessarily result in a difference in process per-
formance. The time of mixing must be short enough to prevent the
critical physical-chemical reactions from occurring to any great degree
before the mixing is completed. For example, from Figure 1_9 it can be
found that for the 24-orifice grid it only took 0. 36 sec for a'/A = 10%
to be reached. A similar situation occurred in the segregation jar
tests where the results seemed to be more or less independent of the
time of segregation. This will be especially important in field applica-
tions where the required short times of mixing will be more difficult
to obtain.
TeKippe and Ham [ 68] recently reported on experiments similar to the
one described above in which a flash mixer at the head of a flocculator
was used to mix the alum with the turbid water in a pilot-scale study.
A silica suspension was used to produce the turbidity. The value of
G in the initial mixing unit was varied from 50 to 200 sec"1 , and the
value of Gt for the initial mixer was maintained at 48, 000. Subsequent
to the initial mixing step, the mean residence time and the rms velocity
gradient in the flocculator were 15 min and 50 sec"1 , respectively.
Samples of water were taken from the effluent end of the flocculator
and allowed to settle for 5 and 30 min. The residual turbidity in the
supernatant for a given settling time was taken as the measure of
105
-------
4. 0
3. 0
o ~
Z. 0
1. 0
Z4-ORIFICE
GRID
1 I
.4-ORIFICE GRID
0 ZO 40
I I
60 80 100 1ZO 140
G, SEC"1
a) ALKALINITY = Z8
160 180 ZOO ZZO
4. 0
3. 0
o -,
rt
\. 0
1. 0
I I
Z4-ORIFICE GRID
FLASH MIXER
I i
4-ORIFICE GRID
I l l I
I 1 i l
180 ZOO ZZO
0 ZO 40 60 80 100 1ZO 140 160
G, SEC"1
b) ALKALINITY = 70 mg/l
FIGURE 35. EFFECT OF INITIAL MIXING DEVICE ON
FLOCCULATION PERFORMANCE: SINGLE
COMPARTMENT, T = 5 MIN.
106
-------
rj (
a
7
6
5
4
3
2
1
o -,
fl
11
10
9
8
7
6
5
4
20
40
1 1 1 T~
4-ORIFICE GRID
24-ORIFICE GRID
I
I
0 20 40 60 80 100 120 140 160 180
G, sec-1
a) ALKALINITY = 28 mg/i
200 220
24-ORIFICE GRID
_L
_L
_L
_L
60
80
100 120 140 160 180 200 220
G, sec 1
b) ALKALINITY = 70 mg/f.
FIGURE 36. EFFECT OF INITIAL MIXING DEVICE ON
FLOCCULATION PERFORMANCE: TWO
COMPARTMENTS, T = 10 MIN.
107
-------
o
00
33
31
29
27
25
23
21
19
"a" 17
13
11
9
7
5
3
1
4-ORIFICE
GRID
o «
a
20 40 60 80 100 120 140 160 180 200 220
G, sec-1
a) ALKALINITY = 28 mg/4
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
i
24-ORIFICE
GRID
0 20 40 60 80 100 120 140 160 180 200 220
G, sec
-i
b) ALKALINITY = 70 mg/l
FIGURE 37. EFFECT OF INITIAL MIXING DEVICE ON FLOCCULATION
PERFORMANCE: THREE COMPARTMENTS, T = 15 MN.
-------
TABLE 4
AGGREGATION RATE COEFFICIENTS FOR
CONTINUOUS FLOW EXPERIMENTS
Alkalinity
mg /-fas
CaCO3
28 mg/t
70 mg/jf
No. of
Compart-
ments
1
2
3
Avg
1
2
3
Avg
Flash
Mixer
0. 0040
0. 0041
0. 0037
0. 0039
0. 0040
0. 0045
0. 0039
0. 0041
4-Orif ice
Grid
0. 0043
0. 0050
0. 0047
0. 0047
0. 0050
0. 0059
0. 0047
0. 0052
24-(3rif ice
Grid
0. 0054
0. 0059
0. 0057
0. 0057
0. 0061
0. 0073
0. 0071
0. 0068
1. 8
1. 6
1. 2
1. 0
0.
24-ORIFICE GRID
4-ORIFICE GRID
FLASH MIXER
-Q.
_L
_L
20 40
ALKALINITY, mg/t
60
-o- -
80
FIGURE 38. EFFECT OF SEGREGATION ON COAGULATION-
FLOCCULATION: CONTINUOUS FLOW TESTS
109
-------
0 -
q
11
10
THREE
COMPARTMENTS
T - 15 min
1 1 1 1 1 I
NO INITIAL MIXING UNIT
A O D
A FLASH MIXER
TWO
COMPART-
MENTS
T = 10 min
ONE COMPARTMENT
T = 5 min
I
40
60
80
100
G, sec
120
-l
140
160
180 ZOO 220
FIGURE 39. EFFECT OF INITIAL MIXING ON FLOCCULATION
PERFORMANCE: COMPARISON BETWEEN FLASH MIXER
AND NO INITIAL MIXING UNIT, ALKALINITY = 70 mg/S.
performance. They reported that the various values of G produced
no significant differences in results. This is consistent with the
conclusions drawn from the present study.
In considering Figures 3537, it is necessary to consider that with the
flash mixer being used as the initial mixing device (and with the alum
being added to the first compartment) backmixing is occurring. In
Section IV it was noted that backmixing may be inherently detrimental
110
-------
to coagulation because of reaction of incoming Al(III) species with
products of the completed reactions. For example, Vrale and
Jorden [ 25] point out that Al(OH)3 g particles may act as nuclei to
enhance the precipitation of Al . The present study produced no
conclusive evidence as to whether backmixing is inherently inferior
to plug -flow mixing for alum coagulation-flocculation. While the
mixing provided by the flash mixer was quite rapid, It is believed
that the time of mixing was probably lower than that provided by the
grid mixers. No attempt was made to measure the concentration
fluctuations at the outlet of the flash mixer. It was assumed that with
a mean residence time of 23 sec, t'he concentration fluctuations at the
outlet were probably quite low. That the flash mixer gave the poorest
results cannot be taken to mean that backmixing necessarily results
in poorer performance. It may only mean that it is difficult to obtain
very rapid mixing with such a device.
In terms of a full-scale treatment plant, the argument becomes
Irrelevant. While It Is conceivable that fairly fine grids might be
constructed, it would be impossible to construct a flash mixer which
would provide mixing times of a fraction of a second, and it seems
that mixing times this low are necessary to effect an improvement in
performance.
COAGULATION OF WASTEWATER
In order to ascertain whether the initial mixing step is critical in alum
coagulation of wastewater, a series of segregation jar tests were
conducted at the Sanitary Engineering Research Laboratory of the
University of California. As with the kaolin suspensions, a 500-mi
sample of raw domestic wastewater was divided into two portions,
100 rrJ and 400 rrJ. The optimum alum dose (found from ordinary
jar tests) was added to the 100-m^ portion and stirred vigorously for
a specified period of time (5 to 50 sec). Then this portion was added
to the remaining 400 -m^ portion. The 500 -mi. sample was then
stirred In a jar test apparatus for 6 mln, and the resulting floe was
allowed to settle for 15 mln. A sample of supernatant was taken and
analyzed for residual turbidity using a Rossum Model 600 turbldlmeter.
For comparison, an ordinary jar test was made with the alum dose
being added to the total 500 -rrJ sample. The relation giving the ratio
of the aggregation rate coefficients for the two experiments Is
KA In
m
K. In (nl /n )
s s i
0- . (99)
ill
-------
The results of these tests at various segregation times are shown in
Figure 40. It is significant that K^ /K^ continues to increase at
the higher segregation times (10 50 sec). This is in contrast to the
results from the kaolin suspension studies in which there seemed to
be little change in performance when the segregation time was increased
beyond 3 to 5 sec, the shortest segregation time practicable by the
test procedure. The same conclusion was reached by comparing
performance obtained from the flash mixer with that obtained by
adding the alum to the first compartment of the flocculator. The
results with wastewater indicated that it is possible to obtain a very
significant improvement in performance (over that of a poor initial
mixing device) without the extremely rapid initial mixing required
for improvement in a kaolin-water system. Consequently, such fine
grid meshes would not be needed and the grid construction problem
would be simplified.
It is instructive to make a calculation concerning the grid parameters
required to produc_e a given level of performance. It will be assumed
that a value of a '/A = 10% is the level of mixing required. This
assumption is strictly arbitrary. From Figure 40 it will be assumed
that this level is to be attained in 10 sec. From Appendix D the scalar
decay equation for 1/2-in. grid bars is estimated to be
a1 n
~1>13
=^ = 5.0(x/d)~1>1 . (102)
If the flow velocity is 2 fps,
x = vt = 20 ft = 240 in.
equation 102 can now be solved for n
s
n = 50 (480)"1'13 = 0. 0465 in. "2 = 6. 7 ft"2 .
s
This means that 6. 7 orifices per^ square foot of reactor cross-
section are required to give a1 /A = 10% at x = 20 ft when the main-
stream velocity is 2 fps. A grid with the necessary parameters
would be relatively easy to construct.
A calculation similar to the one above was not made for the kaolin
system because of the difficulty of estimating the segregation time
required to produce an improvement in performance. This is in
addition to the problem of estimating what the level of mixing should
be at that time.
The results of these tests can probably be assumed to hold if ferric
chloride is the coagulant. Lee [ 69] has found that in lime coagulation
of wastewater the rapidity of the initial mixing has only a slight
effect on performance.
112
-------
5. 0
4.0
3.0
2. 0
1. 0
I
a T. = 196 JTU
i
ALUM DOSE = 160 mg/l
O T. = 180 JTU
ALUM DOSE = 100 mg/t
I I
10
20 30 40
SEGREGATION TIME, sec
50
60
FIGURE 40. SEGREGATION JAR TESTS FOR VARIOUS SEGREGATION
TIMES -ALUM COAGULATION OF RAW SEWAGE
-------
SECTION VIII
ACKNOW LEDGMENTS
The research reported herein was supported in part by Research
Grant No. 17030 DLX from the Environmental Protection Agency.
Ray Campbell provided invaluable assistance in designing and con-
structing the experimental apparatus. Harvey Collins and the
California Department of Public Health aided in conducting the
chlorination experiments, and Fang Maw Lee assisted in performing
the wastewater coagulation experiments. Useful discussions con-
cerning water chemistry were held with R. Rhodes Trussell. The
support of this project by the EPA Project Officer, Dr. Sidney A.
Hannah, is also acknowledged.
115
-------
SECTION IX
APPENDICES
Page No.
A, Initial Mixing and Wastewater Chlorination . ...... 119
Table 1: Effect of Method of Applying Chlorine
on Reduction of Coliform Organisms . . . 121
Figure 1: Schematic Drawing of Experimental
Apparatus for Pilot-Scale Chlorination
Study 123
Table 2: Physical and Chemical Analyses of
Unchlorinated Effluent .......... 125
Table 3: Effect of Initial Mixing on Disinfection
of a Primary Effluent in a Tubular
Reactor 125
Figure 2: Performance of Various Non-Backmixed
Chlorination Units 127
B. Plant-Scale Study of the Effect of Initial Mixing in
Wastewater Chlorination. . . . 129
Figure 1: PVC Chlorination Grid 133
Figure 2: Multiple-Or if ice Grid used as
Initial Mixing Device ........... 134
Figure 3: Schematic Drawing of Rancho
Cordova Chlorination System ....... 136
Table 1: Analyses of Unchlorinated Secondary
Effluent . . . 137
Table 2: Operating Parameters and Bacterial
Survival Ratios .............. 133
Figure 4: Coliform Survival Ratio in an Activated
Sludge Effluent ~ Effect of Initial Mixing . 139
117
-------
Page No.
Figure 5: Fecal Coliform Survival Ratio in a
Chlorinated Activated Sludge Effluent
Effect of Initial Mixing .' . . 140
C. Comparison of Results With Those of Gibson 143
Table 1: Parameters for Mixing Experiments . . . 145
Figure 1: Scalar Decay Downstream from a Grid:
Comparison of Results From Present
Study with those from Gibson's Study . . 146
D. Prediction of Mixing for Larger Grids 147
Figure 1: Prediction of Scalar Decay Curves from
Experimental Data for d = 1/4 in 149
118
-------
APPENDIX A
INITIAL MIXING AND WASTEWATER CHLORINATION
119
-------
APPENDIX A
INITIAL MIXING AND WASTEWATER CHLORINATION
Recent studies at the Sanitary Engineering Research Laboratory of
the University of California showed that rapid initial mixing may be
important in the wastewater chlorination process as well as in alum
coagulation-flocculation. Selleck and Collins [ 55] and Selleck,
Collins, and White [ 56] have discussed the reason which they believe
causes prolonged segregation of the chlorine from the bacteria to
result in poorer performance. The bactericidal compounds are
formed by the reaction of chlorine with nitrogenous and carbonaceous
matter to form chlorine complexes. The speed of these reactions
varies; some are quite fast while others are relatively slow. Selleck
and Collins have concluded that the residuals initially formed are
apparently much more bactericidal than the compounds formed later.
They concluded that rapid initial mixing allows these "hot" residuals
to come in contact with the bacteria and act as killing agents.
Selleck and Collins also concluded that backmixing may contribute
to poorer disinfection. They noted that reactions may take place
between the more bactericidal residuals initially formed upon entering
the reactor and the more complex residuals which form over a longer
time. Thus, these simple and more bactericidal compounds may be
"destroyed" before they can act.
In one experiment described by Selleck, Collins and White [ 56],
chlorination was effected in two alternative _ways. In one arrangement,
the chlorine was added directly to a CSTR (t = 37. 5 min) near the
paddle which rotated at 50 rpm. Under the alternative arrangement,
the chlorine was added to a short (t = 0. 12 min) tubular reactor placed
upstream from the CSTR. The tubular reactor consisted of a 1/4-in.
PVC tee acting as a constriction in a 3/4-in. line. The chlorine was
added through the stem of the tee. Settled wastewater was the effluent
to be treated and an aqueous solution of chlorine gas was the disinfec-
ting agent.
Table 1 summarizes the data they obtained with these two systems.
Although the total mean residence time was essentially the same, the
kill obtained when the chlorine was added at the head of the tubular
reactor was much greater. The coliform survival ratio the parameter
used to indicate bactericidal effectiveness was about one order of
magnitude lower in this case. However, -the coliform survival ratio
for the CSTR alone was approximately the same regardless of whether
the chlorine was added directly to the CSTR or to the tubular reactor.
The increase in kill was due solely to the more rapid mixing which
occurred in the tubular reactor.
120
-------
TABLE 1
EFFECT OF METHOD OF APPLYING CHLORINEjON
REDUCTION OF COLIFORM ORGANISMS
(From Sclleck, Collins, and White [ 56])
Run
No.
Chlorine Residual
mg/t
Coliform Survival
Ratio
A, _CHLORINE APPLIED IN TUBULAR REACTOR
(t = 0. 12 min) Ahead of CSTR (t = 37. 5 min)
1
2
3
3. 2
5. 1
8. 1
0. 00286
0. 00419
0. 00049
B. CHLORINE APPLIED DIRECTLY TO CSTR
1
2
3
4. 2
6. 1
8. 8
0. 0378
0. 052
0. 012
Another result is that for each run, the chlorine residual in the CSTR
was, slightly lower when the chlorine was applied to the tubular reactor.
It was concluded that the various reactions involved were driven to a
greater degree of completion because of the more rapid mixing.
PILOT-PLANT STUDY
Based on the evidence presented above that the rapidity of the initial
mixing is an important parameter in wastewater chlorination, a pilot-
scale study was undertaken in cooperation with the California State
Department of Public Health. The purpose of the study was to determine
if any difference in performance could be effected by using two different
initial mixing devices in a tubular reactor, one which produced very
rapid mixing, and one which produced relatively slow mixing. If more
rapid mixing resulted in better performance, then it would indicate
the desirability of carrying out studies at a full-scale treatment plant.
121
-------
Equipment
A schematic diagram of the apparatus is shown in Figure 1. The waste -
water was pumped from a large storage tank through the tubular reactor,
a 2-in. I. D. PVC pipe. The distance from the point of chlorine injection
to the last of three sampling points was 38 ft. There was a section of
straight pipe approximately 8 ft long upstream from the point of chlorine
injection to help insure that the flow and turbulence characteristics at
the initial mixing device were not affected by the bend.
Sketches of the two initial mixing devices are also shown in Figure 1.
The first device was a 3/8-in. I. D. tube which introduced the chlorine
feed solution at a point in the center of the tubular reactor. The diameter
of the tube was such that the velocity of the chlorine solution entering the
reactor was approximately the same as the wastewater velocity, reducing
the shear between the two streams. Only the turbulence generated by
wall friction and the variation in temporal mean velocity across the pipe
cross-section, also produced by the wall friction, acted to mix the
chlorine with the waste stream. Studies by Gibson [ 1 l] , Keeler [ 22],
and Lee [ 3 ] and the present mixing experiments have shown that this
produces relatively slow mixing in comparison with the other device.
The second initial mixing device was a biplane grid of 1/4-in. bars
spaced 1/2 in. center-to-center, similar to those studied in Section VI.
In order to obtain maximum benefit from the wake-mixing phenomenon,
thirteen 1/16-in. orifices were used as chlorine injection sources.
This was a much more efficient mixing device which, it was believed,
would produce greater bacterial kills.
Procedures
The experiments were run in the following manner, Effluent from the
primary waste treatment plant was collected over a period of several
hours in two large storage tanks. Since the two tanks were being filled
simultaneously, the composition of the sewage in each was the same.
The wastewater in the tanks was stirred slowly to prevent settling of
particulate matter in order to further assure constant wastewater com-
position during the course of the experiment- The chlorine feed line
(an aqueous solution of chlorine gas was used) was connected to one of
the initial mixing devices. When the single source mixer was used, the
section containing the grid and manifold was removed. Wastewater was
pumped through the tubular reactor at a velocity of 2 fps (a flow rate of
20 gpm). The chlorine solution was then fed into the reactor.
At each of three points 10, 24, and 38 ft downstream a sample was
taken and the total chlorine residual determined amperometrically
according to the method suggested by Standard Methods [ 62], Then
three replicate samples for determination of coliform concentrations
were taken at each point They were dechlorinated as quickly as possible
with a sodium thiosulfate solution. Samples were also taken at a point
122
-------
N)
OJ
FROM PRIMARY TREATMENT
Q = ZO gpm
V =2. fps
PUMP
STORAGE TANK
I. S. A. ORIFICE FLOW METER
/
INITIAL MIXING
UNIT
Z-in. I. D.
P-VC PIPE
1/Z"
1/41
SAMPLING POINTS
TO WASTE
!
I A I
L -c> +
p " t> >
-1 J
b
4
U( ^
^ <
1
b
1/16" Dia.
/ 7 / / / / /// / / /i / /
3/8M
/ /./ //////////////I
MULTIPLE-ORIFICE
GRID
SINGLE SOURCE
FIGURE 1. SCHEMATIC DRAWING OF EXPERIMENTAL APPARATUS FOR
PILOT-SCALE CHLORINATION STUDY
-------
upstream from, the initial mixing unit to determine the initial coliform
concentration. The task of determining the coliform concentrations
was performed by the California State Department of Public Health Ln
accordance with Standard Methods.
A sample of wastewater was analyzed at the Sanitary Engineering
Research Laboratory at the University of California to determine
ammonia nitrogen, organic nitrogen, total suspended solids, volatile
suspended solids, and COD concentrations. The techniques were those
recommended by Standard Methods. The results of these analyses are
shown in Table 2.
Results
The results are shown in Table 3. Two runs were made several
weeks apart. During the first run difficulties were encountered which
make the results somewhat unreliable, but they have been included for
completeness. The main problem centered on uncertainty regarding
the wastewater flow rates. This is manifested by the fact that the
chlorine residuals were somewhat lower when the grid was used as
the initial mixing device. Still, a compar ison between the multiple-
Orifice grid and the s ingle-source chlorine injector can be made. Using
the grid resulted in coliform survival ratios about one order of magni-
tude lower.
During the second run the wastewater flow rate was controlled more
closely. Use of the grid resulted in a coliform survival ratio approxi-
mately two orders of magnitude lower than did the single source. In
fact, the survival ratios for the grid were probably lower than those
shown because in the laboratory analysis the MPN's were biased
toward higher-than-likely values.
With the single source of chlorine, Table 3 shows that for the first
sampling point (contact time = 0. 08 min) the chlorine solution was not
spread evenly over the cross-section of the tubular reactor at that
point. It should be noted that the chlorine contact time will not be
the same for all the fluid particles. It might be suspected that this
is the reason for the difference in results obtained with the two initial
mixing units. However, inspection of the results shows that this is
probably not true. It can be assumed that the chlorine was completely
mixed with the wastewater by the second sampling point when the
single source was being used. Thus, at the third sampling point the
chlorine contact time for all the fluid particles was at least 7 sec.
The coliform survival ratio at this point was higher than for the grid
initial mixer at the first sampling point (contact time = 5 sec).
Therefore, the difference in contact times for individual fluid particles
cannot be cited as the reason for the difference in results.
The conclusion drawn from this experiment is that prolonged segrega-
tion of the chlorine from the coliform organisms allows the formation
124
-------
TABLE 2
PHYSICAL AND CHEMICAL ANALYSES OF
UNCHLORINATED EFFLUENT
Run
No.
1
2
Volatile
Suspended
Solids
mg/£
46
33
Total
Suspended
Solids
mg/^
77
35
Ammonia
Nitrogen
mg/i
24. 6
15, 7
Organic
Nitrogen
mg/i
7. 6
3- 9
COD
mg/i
170
104
PH ,
7. 8
TABLE 3
EFFECT OF INITIAL MIXING ON DISINFECTION OF A
PRIMARY EFFLUENT IN A TUBULAR REACTOR
Run
No,
(1)
Single Source
Multiple -Source
Grid
U)
Single Source
Multiple -Source
Grid
___
Contact
T ime
min
0. 08
0. 20
0. 32
0- 08
0. 20
0. 32
0. 08
0- 20
0- 32
0. 08
0, 20
Chlorine
Res idual
mg/i
5. 10
6. 30
6. 30
4. 85
4. 70
4. 80
5- 70
6. 25
6. 20
6. 20
6. 10
0. 32 6. 20
L
Coliforrn
Survival
Ratio
0. 88
0. 41
0. 45
0. 159
0. 056
0. 026
0. 45
0. 37
0. 50
<0. 006
< 0. 008
£ 0, 006
125
-------
of less bactericidal chlorine residuals from the more bactericidal
residuals initially formed. Thus, more rapid initial mixing results
in better kills. It is important to note that very short contact times
were involved in this experiment, from 5 to 19 sec. This means that
if the above conclusion is true, the most bactericidal compounds must
exist for only a very short time certainly less than 5 sec and pro-
bably much less.
RAPID INITIAL MIXING AND LONG CONTACT TIMES
Because the experiments described above involved short contact times
(<0. 3 min) and because an attempt to improve performance in a pro-
totype treatment plant by effecting improved initial mixing failed (see
Appendix B), an experiment utilizing the venturi type initial mixing
device used in the work of Selleck and Collins and longer contact times
(up to 5. 2 min) was devised. The initial mixing device was the 1/4-in.
PVC tee described earlier.
The tubular reactor consisted of approximately 20 ft of 3/4-in. PVC
pipe and approximately 250 ft of 1/2-in. rubber hose. This provided
a contact time of 2. 0 min. Samples to determine coliform kill were
taken at four points along the tubular reactor. A small beaker was
filled with chlorinated wastewater from the end of the tubular reactor
in order to obtain a sample with a longer contact time, 5. 2 min. The
residence time of the tubu]?»T reactor, 2. 0 min, was much greater
than the time necessary to fill the beaker, 0. 09 min. This minimized
backmixing during the filling of the beaker. During the interval that the
chlorinated wastewater was in the beaker, it was stirred continuously
with a magnetic stirrer.
The data were analyzed by the methods discussed earlier, and the
results are shown in Figure 2. The coliform survival ratio, y/y , is
jplotted against Rt where R is the total chlorine residual in rag/f. and
t is the contact time in minutes. Also shown are results cited above
for the 2-in. tubular reactor and those from the work of Selleck [ 57].
For convenience, two of the initial mixing situations, the 75-gal batch
reactor with the paddle mixer rotated at 50 rpm and the 2-in. tubular
reactor with the single chlorine injection tube, have been designated
as "poor. " The other two initial mixing situations, the i/4-in. tee
in the 3/4-in. pipe and the 2-in. tubular reactor with the 13-orifice
grid, have been designated as "good. " This classification is strictly
subjective. While the times of mixing for both "poor" or both "good"
mixing situations is probably not the same, it is believed that they
are probably sufficiently similar to allow the above classification to
be made.
Figure 2 reveals that while rapid initial mixing provided improved
performance, i. e. , lower coliform survival ratios, at low values of
Rt, the "poor" and "good" initial mixing produced the same results
126
-------
1. 0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
D
D
"POOR" INITIAL
MIXING
"GOOD" INITIAL
MIXING
POOR" INITIAL MIXING:
O 75-gal BATCH REACTOR
FROM [ 57]
D 2-in. TUBULAR REACTOR
WITH SINGLE-SOURCE
CHLORINE INJECTION TUBE
"GOOD" INITIAL MIXING:
v 13-ORIFICE GRID IN
Z-in. PIPE
1/4-in. CONTRACTION IN
3/4-in. PIPE FROM [ 57]
i/4-in. CONTRACTION IN
3/4-Ln PIPE
I
00
I O
0. 1
FIGURE 2.
1.0 10 100 1000
Rt, mg/t AND MINUTES
PERFORMANCE OF VARIOUS NON-BACKMIXED
CHLORINATION UNITS
127
-------
when t was increased with R maintained constant. Thus, in situations
where a long pipeline is used to provide contact time for disinfection
in wastewater treatment, any reasonably good initial mixing device
will probably produce the best obtainable results, those of the batch
reactor (see Appendix B).
The reason for the merging of the two curves at the higher values of
Rt is unclear. It may be related to varying resistance of the organisms
to disinfection. The more resistant organisms, if not killed by the
highly bactericidal residuals which are initially formed and which can
be utilized under cond_itions of rapid initial mixing, must be subjected
to the same value of Rt as would have been the case if the initial mixing
had been relatively slow. Whatever the actual reason, the answer
seems to lie in the mechanism of chlorine disinfection and the reactions
which chlorine undergoes in wastewater.
It may still be possible to utilize the high initial kill which rapid initial
mixing provides. For example, existing plants which have backmixed
reactors for chlorination could be improved by installing a chlorine
injection device in the pipe, if one exists, leading to the chlorine con-
tact unit. As noted, backmixing seems to be inherently detrimental
to chlorination efficiency.
Use of tubular reactors also provides a much better residence time
distribution than a CSTR. This is particularly important in chlorina-
tion because the coliform kill is so strongly time dependent. Use of
a backmixed reactor allows "short-circuiting" of fluid particles with
short chlorine contact times and thus a very high concentration of
coliform organisms.
128
-------
APPENDIX B
PLANT-SCALE STUDY OF THE EFFECT OF INITIAL MIXING
IN WASTEWATER CHLORINATION
129
-------
APPENDIX B
PLANT-SCALE STUDY OF THE EFFECT OF INITIAL MIXING
IN WASTEWATER CHLORINATION
INTRODUCTION
Because of the success of the initial experiments involving rapid
initial mixing and wastewater chlorination (see Table 3 of Appendix
A) and also because of the recognized limitations of such small-scale
studies, it was decided that a full-scale investigation at a wastewater
treatment plant was called for. Although it should be possible to
extrapolate the results of model mixing studies and estimate the degree
of mixing produced by larger grids, it is difficult to assess the com-
bined effects of mixing, chlorine reactions with impurities present in
the waste, and probable coliform kills. With grids much larger than
those used in the pilot-scale investigations (in terms of bar diameter
and spacing), a much longer time of mixing time required for the
concentration fluctuations to decay to some arbritrarily defined low
value would result. Thus, the mixing might not occur fast enough
to allow the most bactericidal chlorine residuals, which may be very
short-lived, to act as killing agents. The short contact times involved
in the pilot-scale studies also limited their usefulness and prevented
their application to prototype systems.
Another reason for full-scale plant tests was that if improved initial
mixing were to result in improved performance, the evidence indica-
ting that initial mixing is an important parameter would be much more
compelling than if only pilot-scale studies had been made. This would
be the case even if the pilot-plant studies had no obvious limitations
such as those discussed above.
CHARACTERISTICS OF THE RANCHO CORDOVA
WASTEWATER TREATMENT PLANT
The Rancho Cordova Wastewater Treatment Plant is located approxi-
mately 15 miles east of Sacramento. It is a secondary plant featuring
the Spirovortex activated sludge system. The average flow through
the plant is approximately t, 7 mgd (at the time of day that the tests
described herein were run, the flow was approximately 2. 4 mgd).
The Rancho Cordova facility was chosen for the project for several
reasons. It was desired that the initial mixing system of the plant
be of good design by contemporary standards. It is well known that
gross segregation of the chlorine from the waste stream over a period
130
-------
of a minute or longer will give poor results. An example of such gross
segregation would be where the chlorine was added to the waste stream
by placing the chlorine hose into a large contact basin where the level
of turbulence was quite low. Gross segregation can occur and poor
performance will result. Backmixing in the initial mixing step is also
to be avoided. Selleck and Collins [ 55] and Selleck, Collins, and
White [ 56] have noted that backmixing, such as may occur in a typical
rapid or flash mixer, seems to have an inherently detrimental effect
upon the wastewater chlorination process. The alternative to backmixing
is a tubular reactor with characteristics as close to plug flow as pos-
sible. Thus, to test the grid mixer it was necessary to find a plant
where the chlorine was added to the waste stream in a pipe leading from
the treatment plant, the pipe comprising the tubular reactor. Such an
arrangement was desired for another reason. Samples of chlorinated
wastewater must be taken to determine coliform kill and the correspond-
ing contact times should be determined fairly accurately. This is
possible in a pipe, but not in most chlorine contact basins where short -
cLrcuiting occurs and dead space exists.
The Rancho Cordova plant met these criteria quite well. From the
final clarifier, the effluent entered a large box structure by passing
over a weir. From there it passed through an 800-ft, 27-in. diameter
pipe to a pond. The chlorine injection device was a 6-ft long, 3-in.
PVC pipe placed in the bottom of the 27-in. pipe at the point where
the flow left the box. The chlorine was injected through 3/8-in. holes,
spaced 1-1/4-in. apart along the top of the PVC pipe. It was possible
to sample at the point wher'e the 27-in. line entered the pond as it was
not submerged. It was also possible to sample at a point 184 ft down-
stream from the chlorinator.
There were three other criteria for the plant to be used. These con-
cerned installation of the grid. First, it was necessary to be able
to tap into the existing chlorine piping system in order to deliver the
chlorine solution to the grid. This was fairly easily done at Rancho
Cordova. Second, it was necessary to be able to gain access to the
point where the grid was to be installed by diverting the flow around
this point or stopping the flow. At Rancho Cordova the flow could be
stopped for about one hour which allowed rapid installation and re-
moval of the grid. Finally, it was necessary to have a physical con-
figuration such that placing the grid in the pipe could be easily
accomplished. This was possible at Rancho Cordova.
After permission was obtained from the County of Sacramento to use
the Rancho Cordova plant, the grid was designed and built, and the
tests were run.
DESIGN OF THE GRID
The grid used as the initial mixing device in this experiment was
designed on the basis of several criteria. First, and most important,
131
-------
it had to provide more rapid mixing of the chlorine solution with the
waste stream than did the system which was being used at the treat-
ment plant. This required that the grid bars be as small in outside
diameter as possible, that the spacing of the grid bars be small, and
that the number of points at which the chlorine was injected into the
waste stream be as many as possible.
Other criteria, however, led to design features different from those
above. Since at many plants, excessive headloss through the grid
could not be tolerated although at this plant, a headloss of up to 2 ft
could have been allowed the grid bars could not be spaced too closely.
Excessive headloss of the chlorine solution flowing inside the grid
bars could not be allowed as this would lead to an unequal distribution
of chlorine flowing from each of the sources. This made larger
diameter grid bars necessary. In order to avoid the possibility of
clogging very small orifices, larger orifices were preferable although
this meant fewer holes if a reasonably high injection velocity was to
be maintained, A high injection velocity was necessary to decrease
the effect of chlorine solution headloss inside the grid bars and thus
insure uniform chlorine distribution. Finally, the grid had to be
reasonably strong to withstand the force of the wastewater flow. This,
too, called for larger grid bars. In order to have a grid meeting these
criteria it was necessary to sacrifice mixing performance.
A drawing of the grid mixer is shown in Figure 1. Photographs are
shown in Figure 2. The grid was constructed from 3/4-in. PVC
pipe and fittings. The ratio of the center-to-center bar spacing to
the bar diameter, a parameter used in mixing studies, was approxi-
mately 3. 5, and the solidity, the fraction of the cross-sectional area
occupied by the grid, was about 0. 48, The main line in the center of
the grid was a 2-in. PVC pipe. This allowed the chlorine solution
to be distributed evenly to all parts of the grid without excessive
headloss. The chlorine injection orifices, were 220 1/8-in. diameter
holes on the downstream side of the grid. These did not point directly
downstream, but alternated up or down at an angle of approximately
45° from the horizontal. It was believed that this arrangement would
improve mixing. The value of n was 0. 39 in. ?
s
Based upon a chlorine solution flow rate of 20 gpm, the velocity at
which the chlorine was injected into the wastewater stream was 2. 4
fps. The existing chlorine diffuser injected the chlorine into the
waste stream at approximately 1 fps.
The maximum velocity of the effluent flowing through the grid was
approximately 2 fps From previous studies, the headloss through
such a grid at this velocity was approximately 0. 8 in. and the total
force on the grid was 16 Ib. At a velocity of 1 fps, the velocity when
the tests were being made, the headloss and force were 0. 2 in. and
4 Ib, respectively.
132
-------
2-in. sch. 80
PVC PIPE
3/4-in. sch. 40 SOCKET TYPE
TEES AND CAPS, JOINED BY
3/4-Ln. sch. 40 PVC PIPE (IN
SOME INSTANCES THE SOCKETS
OF THE TEES AND CAPS WERE
PARTIALLY CUT OFF).
EXISTING 3-in.
PVC DIFFUSER
r27-in. DIAMETER
R. S. PIPE
FIGURE 1. PVC CHLORINATION GRID
133
-------
i
A. FRONT VIEW OF GRID
.» '
B. GRID IN PLACE IN 27-in. TUBULAR REACTOR
FIGURE 2. MULTIPLE-ORIFICE GRID USED AS
INITIAL MIXING DEVICE
134
-------
The grid was connected to a frame constructed from i/2-in. iron
pipe and fittings. The frame was used to fix the grid in place inside
the 27-in. pipe. Jacks mounted on the frame could be extended until
the grid and frame were firmly held in place. The adva'ntage in using
friction to keep the grid in place was that no permanent brackets had
to be installed in the plant, and installation and removal of the grid
was quickly and s imply accomplished.
EXPERIMENTAL PROCEDURE
A schematic drawing of the chlorination system at the Rancho Cordova
Wastewater Treatment Plant is shown in Figure 3. Two runs, one
with the grid mixer and one with the pipe diffuser, were made each
day for four consecutive days. When the pipe diffuser was being
tested the grid was removed to insure that the grid would not interfere
or contribute in any way to the turbulence characteristics of the existing
arrangement.
The runs were made in the following manner. Each day the first run
was made with whichever device had been used last the day before.
This meant that it was necessary to stop the flow, de-water the box,
and remove or install the grid only once each day. When the flow from
the secondary clarifier reached a nearly constant rate, at approximately
1000 hours each day, the chlorine gas flow rate was set to obtain the
desired total chlorine residual at the second sampling point. Residuals
were measured amperometrically according to the method given by
Standard Methods [ 62], The residual was varied during the study
from approximately 1 to 6 mg/f.. When the desired residual was
obtained, samples were taken to determine the fraction of coliforms
killed. For each determination of coliform concentration, four re-
plicate samples were collected. Samples were taken first in the box
upstream from the chlorine injection device to determine the initial
coliform concentration, then from sampling point Z, and finally from
sampling point 1. Samples for the determination of chlorine residuals
were taken. The coliform samples were dechlorinated as quickly as
possible with 0, 5 m-0 of a 10% solution of sodium thiosulfate. The
bacteriological analyses were performed by the Sanitation and Radiation
Laboratory, California State Department of Public Health in a mobile
laboratory located at the plant site. All bacteriological determinations
were made on the basis of four dilutions, using five tubes for each
dilution, and following the procedure outlined in Standard Methods.
After samples were taken with the first device, the flow was stopped,
the box was de-watered with two gasoline powered pumps provided by
Sacramento County, the grid was installed or removed, and the flow
was started again. When the flow rate became constant, the sampling
procedure was repeated using the other initial mixing device.
Each day a 6-hr composite sample of the unchlorinated secondary
effluent was collected. This sample was kept under refrigeration and
135
-------
\ \ \ \
r
«
:-'? ::-.'. /-;.'.:~-?.>?.?:»'.):'''*;.
WEIR CREST
EXISTING
DIFFUSER
d = 27 in.
A = 3. 98 ft2
SAMPLING
POINT i
FLOW = 2. 2 to 2. 5 mgd = 3. 65 cfs
VELOCITY = 3. 65/3. 98 - 0. 92 fps
PIPE LENGTH = 184 ft to sampling point 1. t[ =
PIPE LENGTH = 622 ft between points 1 and 2. T2 =
184
0. 92 x 60
622
0. 92 x 60
= 3. 3 min
= 11.3 min
rp ,
t = 14. 6 min
SAMPLING
POINT 2
FIGURE 3. SCHEMATIC DRAWING OF RANCHO CORDOVA CHLORINATION SYSTEM
-------
transported at the end of the day to the Sanitary Engineering Research
Laboratory at the Richmond Field Station of the University of California.
Determinations were made of the ammonia nitrogen, organic nitrogen,
COD, volatile suspended solids, and total suspended solids. The
analytical procedures used were those recommended by Standard
Methods.
RESULTS
The physical and chemical analyses of the unchlorinated secondary
effluent are shown in Table 1. The coliform and fecal coliform sur-
vival ratios and the operating parameters are summarized in Table 2.
Each bacterial density shown (MPN per 100 mi) representes the log
mean of four replicate samples
TABLE 1
ANALYSES OF UNCHLORINATED SECONDARY EFFLUENT
Run
1
2
3
4
NH3 -N
mg/i
12. 3
10. 8
13. 0
12. 5
Org-N
mg/i
3. 1
3. 8
2. 8
3. 0
SS
mg/4
9-0
4. 0
3. 0
6.0
vss
mg/i
8. 0
0. 0
0. 0
0. 0
COD
mg/i
54
51
57
46
Temp
°C
--
17. 0
18. 0
17. 5
PH
Unchlor.
--
7.4
7. 4
7. 4
Chlor.
--
7. 1
7. 0
7. 1
The results are plotted in Figures 4 and 5. The coliform (Figure_4)
and fecal collform (Figure 5) survival ratios are plotted against Rt, the
total chlorine residual in mg/i times the contact time in minutes. These
figures show that the multiple-source grid did not improve process
performance as was expected. Possible reasons for this are discussed
in the next section. A positive result of the experiment is the fact that
the slope of the lines in Figures 4 and 5 can be taken as minus 3 on
log-log paper. This is the same decay rate that Selleck[ 57] found
for non-backmixed reactors using a primary effluent.
137
-------
TABLE Z
OPERATING PARAMETERS AND BACTERIAL SURVIVAL RATIOS
Run
1
2
3
4
Initial
Mixing
Device
Grid
Diffuser
Grid
Diffuser
Grid
Diffuser
Grid
Diffuser
Calc.
Contact
Time
min
0
3. 2
13.9
0
3. 3
14. 5
0
3. 0
13. 3
0
2. 98
13
0
2.9
12. 5
0
3.0
12. 8
0
2. 8
12.8
0
3.0
13.3
Flow
mgd
2. 3
2. 3
2. 3
2. 2
2. 2
2. 2
2.4
2.4
2.4
2.45
2.45
2.45
2. 55
2. 55
2. 55
2. 5
2. 45
2. 5
2.6
2. 6
2. 5
2.4
2.4
2.4
Chlorine
Residual
mg/t
0
3.65
3. 55
0
4. 2
4.0
0
4. 7
4. 55
0
5.05
5.05
0
5. 55
5. 70
0
5. 90
5. 75
0
1. 60
1. 80
0
2.5
1.85
Coliform
Bacteria
MPN/100 mt
y &c y
0
1. 6 x IO6
<4. 7 x IO3
3. 0 x IO2
1. 1 x IO6
-
<4. 0 x IO2
7. 05 x IO5
7. 3 x IO2
1. 2 x IO2
1. 17 x IO6
2. 45 x IO3
1. 25 x IO2
1. 3 x IO6
1. 04 x IO3
1. 6 x IO2
2. 64 x IO6
1. 02 x IO3
4. 09 x IO2
2.01 x IO6
5. 28 x 10s
3. 34 x IO4
2. 6 x IO6
3. 41 x IO5
7. 7 x IO3
y/y0
1. 0
<2. 9 x IO"3
1.9 x IO"4
1.0
-
<3. 6 x IO"4
1. 0
1.04 x 10"3
1. 66 x 10"*
1. 0
2. 1 x IO"3
1. 07 x 10"4
1.0
8. 0 x 10"*
1. 23 x IO"4
1. 0
3. 9 x IO"4
1. 6 x IO"14
1. 0
2. 62 x 10"1
1. 66 x IO"2
1. 0
1. 33 x IO"1
2. 96 x 10"3
Fecal
Coliform
Bacteria
MPN/100 ml
n &c n
o
2. 5 x 10s
<2. 0 x IO3
<2. 0 x 10Z
<2. 38 x 10s
-
-
2. 64 x IO5
<2. 0 x IO2
<25
2. 86 x 10s
<2. 38 x 102
<25
4. 5 x 10s
20
<20
4. 5 x IO5
<32
<20
3. 06 x 10s
5. 67 x IO4
<4. 45 x IO2
8. 58 x IO5
3. 84 x IO4
<2. 0 x IO2
n /n
o
1.0
<8 x 10"3
<8 x IO"4
1.0
-
-
1.0
<7. 6 x 1Q-1
<9. 5 x IO"5
1.0
<8. 3 x IO"4
-------
i, 0
2. 3
10
-i
-I
CO
o
O
u
10
-2
10
-3
10
-4
10
-5
10
-6
y/y = [ VOTT9 Rt]
LEGEND:
O GRID
DIFFUSER
MLESS THAN OR EQUAL TO
JTHE VALUE INDICATED
I
0. 1
i. 0 10
Rt, mg/f-min
FIGURE 4. COLIFORM SURVIVAL RATIO IN AN ACTIVATED SLUDGE
EFFLUENT - EFFECT OF INITIAL MIXING
139
-------
cn
o
o
u
w
1. 6
1.0
10
-1
o
H 10-2
10
-3
10
-4
10
-5
10
-6
o
n/n = [ VOT39 Rt]"3
o
LEGEND:
O GRID
^ DIFFUSER
01 LESS THAN OR EQUAL TO
A (THE VALUE INDICATED
I
I
0. 1
1. 0 10
Rf, mg/jf-min
102
103
FIGURE 5. FECAL COLIFORM SURVIVAL RATIO IN A CHLORINATED
ACTIVATED SLUDGE EFFLUENT - EFFECT
OF INITIAL MIXING
140
-------
CONCLUSIONS
The results of this field experiment, coupled with.the previous and
subsequent pilot-scale experiments, have led to the conclusions
discussed in Appendix A. Specifically, while different rates of initial
mixing in a non-backmixed reactor may initially produce different
levels of disinfection, at sufficiently long contact times similar to
those found in practice the results from the various times of initial
mixing are the same.
These experiments have shown, however, that while the colifdrm sur-
vival ratio in the effluent of a tubular reactor cannot, in practice, be
improved as it had been hoped, it has been found that a tubular reactor
is superior to a backmixed reactor for two reasons. First, as noted
by Selleck, Collins, and White [ 56], backmixlng apparently results
in a chlorine residual with poorer bactericidal effectiveness because
of reaction of the chlorine entering the reactor with residuals pre-
viously formed. Second, short-circuiting, or the presence In the
effluent from the reactor of fluid particles with a very short chlorine
contact time, can greatly affect overall performance. A tubular
reactor prevents this.
141
-------
APPENDIX C
COMPARISON OF RESULTS WITH THOSE OF GIBSON
143
-------
APPENDIX C
COMPARISON OF RESULTS WITH THOSE OF GIBSON [ 11, 26]
Gibson used a square-mesh biplane grid with 1/8-in. grid bars and
tracer orifices placed halfway between the grid bar intersections on
the upstream side of the bars. This configuration is very similar to
that used for one run of this study (see Figure 28, Section VI.) The
grid bar diameters were essentially the same and upstream injection
was used in both instances. The scaJLar decay rate should therefore
be the same. The values of ns and A.were different for the two
experiments, but it should be possible to relate the results through
use of the mixing model developed in Section VI. NaCl solution-was
used as the tracer in both studies. A more complete comparison of
the parameters of the two experiments is given in Table 1.
The results of the two experiments are shown in Figure 1, with (a'ns)
/(Ao'1') plotted against x/d. Within the accuracy of the measurements,
the points for both experiments can be said to fall along the same line.
The value of a*11 and a for this line are 50-in.~E and 0. 86, respectively.
In his determination of the scalar decay rate, Gibson obtained a
value of a = 0. 69- If Gibson's data points were considered separately,
a value of a-" much lower than the given value of 50 would result.
This, as noted previously, is the result of a-'1 being very sensitive
to slight changes in the slope of the line drawn through the data
points.
The fact that the results of the two studies agree to a reasonable
extent is important for two reasons. First, it seems to indicate
that the probe used in the present study was not excessively large
and that a reasonable approximation of the "true" rms values was
obtained. It should be noted that the results of both studies may be
low; Gibson's because of an inability to measure low wave number
components of the spectrum, and those of the present work because
of the large probe diameteri.
Agreement between the two experiments also serves to further confirm
the usefulness of the mixing model developed in Section VI. It was
concluded that for a given grid bar diameter and tracer injection.
system, the results should follow the equation
a'M , % -a
s ' ,
~A
144
-------
TABLE 1
PARAMETERS FOR MIXING EXPERIMENTS
M, in.
d, in.
M/d
Solidity
Tracer Source
Diameter, d , in.
Reactor Cross-
Section, in. 2
Tracer Source
Density, M , in. ~2
S J
A-p, mg/S.
A, m.g/1
Probe Diameter,
d , microns
o
Tracer Injection
System
Present Study
0. 500
0. 125
4. 0
0. 45
0. 0135
3. 14
7. 9
850, 1700, 2550
50, 000
47. 5
75
**
Gibson
0. 625
0. 117
5. 33
0. 34
0. 012
36. 0
5. 0
1,910
58,000
16. 6
.
«
Not listed. Probe size varied from 10 to 50 microns
in Gibson's experiments.
* *
Tracer injected upstream through sources in grid bars
placed halfway between bar intersections.
where #'' and a are constants. In Section VI the results of several
experiments -were compared. In all instances downstream injection
was used. Now, reasonable agreement has been found for two ex-
periments which were made in independent studies.
145
-------
0. 1
. 08
.06
. 05
. 04
. 03
. 02
K
. oi
. 008
. 006
. 005
. 004
. 003
0. 002
20
a" = 50 in.
a = 0. 86
-2
a = 0. 69
FROM PRESENT WORK
FROM GIBSON [ 11]
I I
I
J_
30
40 50 60
80
100
x/d
150
200 300 400 500
FIGURE 1. SCALAR DECAY DOWNSTREAM FROM A GRID:
COMPARISON OF RESULTS FROM PRESENT STUDY
WITH RESULTS FROM GIBSON'S STUDY
146
-------
APPENDIX D
PREDICTION OF MIXING FOR LARGER GRIDS
147
-------
APPENDIX D
PREDICTION OF MIXING FOR LARGER GRIDS
Although a completely satisfactory method of predicting the time of
mixing which can be expected from larger grids has not been developed,
it is possible to use the results of the present mixing studies and
Corrsin's theory to estimate what the scalar decay curve will be for
such grids. Corrsin's equation is
u
da1
du{
7 + M
NSc
0(3 2/3 ( Ls}2/3 , 53/2 log NSc
2 Lf 3 NRe
54)
Assuming Batchelor;s turbulence decay law holds (u1 ax1), the
right-hand side of the above equation is equal to a, the scalar decay
rate. NSC - 700 for sodium chloride, and NRe, = 45, the average
value for the present work. Putting in these values, Equation (54)
becomes
Z
a =
2/3
+ 0. 63
As mentioned in Section VI, L depends on the method of tracer
injection (e. g. , either upstream or downstream) and Lf is proportional
to the grid bar diameter. If it is assumed that L /L does not vary
as the mixing progresses, it is possible to obtain a value of Ls/L-f for
an experimentally determined scalar decay curve. With this known,
the value of Ls/Lf for larger grids can be estimated and a scalar
decay rate can be calculated.
The result of such calculations are shown in Figure 1. The experi-
mental curves for d = 1 /4 in. and d = 1/8 in. were taken from Figure
31. From the experimental curve for d = 1/4 in- , scalar decay
curves were predicted for d = 1/8, 1/2, and 1 in.
For d = 1/8 in. the experimental value of a was 0. 4. The predicted
value is 0. 54. Because of the extensive scatter, a line with a = 0. 54
would fit the data almost as well as the line which was used in Figure
31. However, the as sumption that a" is constant places the predicted
curve somewhat lower than the experimental curve. A similar calcula-
tion using u'a x~ 5'7as proposed by Frenkiel gave slightly poorer
agreement.
148
-------
1. 0
0. i
K
0. 01
PREDICTED FROM
DATA FOR d = 1/4 in.
EXPERIMENTAL
DATA
I
J I
I
I
10 20 40 60 100 200
x/d
400 600 1000
FIGURE i. PREDICTION OF SCALAR DECAY CURVES FROM
EXPERIMENTAL DATA FOR d = 1/4 in.
-------
As no tests were done with grid bars i/Z or 1 in. In diameter, it is
impossible to know how accurate the predicted curves are. However,
this graph may be used to estimate the time of mixing to be expected
from prototype grids.
150
-------
SECTION X
GLOSSARY
Symbol Definition
A "Point" tracer concentration, mg/&; coefficient in
Equation (31); coefficient in Equation (44); reactant in
Equation (63); cross-sectional area of conducting medium.,
Aj Coefficient in Equation (30)
A Mean component of "point" tracer concentration, rag/I
A Average concentration of tracer mixed with portion of flow
P during wake-mixing
a Fluctuating component of "point" tracer concentration,
scalar decay rate
a' rms concentration fluctuation, mg/f.
a1 Initial rms concentration fluctuation, mg/-2
a1 Initial rms concentration fluctuation of isotropic scalar
1 field, mg/.£
B Distance from spherical probe which represents volume
within which 90% of the total resistance exists, coefficient
in Equation (42), reactant in Equation (63)
C Coefficient in Equation (32), coefficient in Equation (46),
Reaction product in Equation (63)
Q
D Drag coefficient
c Coefficient in Equation (34)
C(r) Scalar correlation function
i Diffusion coefficient of i-fold particles
ij Combined diffusion coefficient of i-fold and j-fold particles
m Molecular diffusivity, ft2/sec
151
-------
Symbol Definition
d Grid bar diameter, in.
o Probe diameter, microns
E Three-dimensional energy spectrum function, voltage
E! One-dlmens lonal energy spectrum function
p«
e Universal three-dimensional energy spectrum function
p-
1 e Universal one-dlmens lonal energy spectrum function
T£
s Scalar spectrum function
F Fractional completion of reaction
f(r) Longitudinal correlation function
G rms velocity gradient, sec"1
g Acceleration due to gravity, ft/sec2
g.(r) Lateral correlation function
g(x) Function defined by Equation (66)
jj
Ij Collision frequency of l-fold and j-fold particles In
turbulent flow
L Head loss through grid, In.
ij Collision frequency of l-fold and j-fold particles due
to Brownian motion
s Intensity of segregation
ij Collision frequency of i-fold and j-fold particles due to
laminar flow
jr
A Aggregation rate coefficient
rs
B Breakup rate coefficient
152
-------
Symbol
K
c
KL
K
K
w
k*
L
g
L
s
M
MPN
N
NT
Re,
N
Re
N
Sc
n
n.
Definition
Conductivity cell constant
Head loss coefficient for grid
Cross -sectional area near each orifice with which the
tracer is mixed during wake-mixing
Coefficient in Equation (92)
Wave number, ft'1
One -dimensional wave number, ft
1/4
Batchelor wave number (k = (e/vD 2) )
rJ m
Kolmogoroff wave number(k-r = (e /v3 )1' 4)
Distance between two electrodes
of a conductivity probe, in.
Longitudinal integral scale
Lateral integral scale
Scalar integral scale
Center-to-center spacing of grid bars, in.
Most probable number of coliform organisms per 100 ml
Paddle rotation speed in flocculator, rpm
Microscale Reynolds number
Grid bar Reynolds number
Schmidt number (Nc = v/D )
oc m
= u1 X I v)
= V d/v)
Frequency of fluctuations, sec
Number concentration of primary particles
Number concentration of i-fold particles
153
-------
Symbol Definition
n Number concentration of primary part icles entering
flocculator
n Number concentration of primary particles in m
1 compartment of flocculator
P Power Input to flocculator
Q Flow through flocculator, gpm
M Mainstream flow rate through tubular reactor, gpm
Q Flow with which tracer Is mixed during wake-mixing
T Tracer Injection flow rate, gph
R Resistance, ohms; chlorine residual,
R Resistance measured by a spherical electrode In an
CO
Infinite conducting medium, ohms
R Resistance measured by probe, ohms
R1 Resistance In parallel with probe, ohms
R^ R'R /(R1 + R ), ohms
T P P
R. Radius of l-fold particles
R.. Combined radius of i-fold and j-fold particles
o Radius of single electrode conductivity probe, microns
*
r A vector
S Grid solidity, I. e. , fraction of tubular reactor cross-
section covered by grid bars, dlmenslonless
T Flocculatlon chamber residence time, min
T
m Flocculation chamber .residence time per compartment,
min
t Time
t Mean chlorine contact time, min
154
-------
Symbol Definition
[ Instantaneous velocity in i direction in Cartesian
coordinates, fps (i ='i,2,3)
U. Mean velocity in ith direction, fps (L = i, 2, 3)
dU !
V elocity gradient, sec
X
X.
i Fluctuating component of velocity in i direction (i = i,2,3)
u1, u! rms velocity fluctuation in isotropic turbulence, fps
V
M Mainstream velocity in tubular reactor, fps
V V
' r Reactor volume, ft *
v Kolmogoroff characteristic velocity (v = (v &) 1'4 )
x Distance downstream from grid, in.
b Apparent origin of rms velocity fluctuations, in.
i Cartesian component of coordinate (i = i, 2, 3)
x A vector
y Most probable number of coliforrn organisms per 100 rrd
after disinfection
^o Most probable number of coliform organisms per 100 mi
before disinfection
Z Impedance, ohms
a Coefficient in Equations (45a) and (86)
cx1 Coefficient in Equation (45)
<*' Coefficient in Equation (89)
a" Wake-mixing coefficient in general mixing model,
Equation (97)
j3 Ratio of amount of reactant present to the stoichiometric
amount
155
-------
Symbol Definition
£ Rate of energy dissipation
£ Rate of scalar "dissipation"
T| Degree of mixing, Kolmogoroff characteristic length
scale
f Longitudinal microscale
g Lateral microscale
s Scalar microscale
H- Viscosity lb-sec/ft2
v Kinematic viscosity, ft2/sec
| Voltage
p Resistivity, ohm-ft
cr Conductivity, mhos /ft
156
-------
SECTION XI
REFERENCES
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15. Van der Hegge Zijnen, B. G. "Measurement of the Intensity,
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28. Corrsln, S. "Simple Theory of an Idealized Turbulent Mixer, "
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29. Beek Jr. , John, and R. S. Miller. "Turbulent Transport In
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30. Gibson, C. H. , and W. H. Schwarz. "Detection of Conductivity-
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31. Argaman, Yerachmiel, and W. J. Kaufman. "Turbulence and
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33. Fair, G. M. , and J. C. Geyer. Water Supply and Wastewater
Disposal. New York: John Wiley and Sons, 1967.
34. Langelier, W. F. , and H. F. Ludwig. "Mechanisms of
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35. Rich, L. G. Unit Proces ses of Sanitary Engineering, New York:
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36. Kirrij Wonsuk, H. F. Ludwig, and W. D. Bishop. "Cation
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37. Stumm, W. , and C. R. O'Melia. "Stoichiometry of Coagula-
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38. Packham, R. F. "The Coagulation Process A Review of
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39. Black, A. P. and Ching-Lin Chen. "Electrokinetic Behavior
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40. Hahn, H. H. , and Werner Stumm. "Coagulation by Al(III); The
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42, LaMer; V. K. "Coagulation Versus the Flocculation of Colloidal
Dispersions by High Polymers (Polyelectrolytes), " Principles
and__Applications of W_at;_c_r__Ch_emistry, S. D, Faust and J. V. Hunter,
(Eds, ) John Wiley and Sons, 1965.
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Brownsche Molekular Bewegung und Koagulation von Kolloidteilchen,
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44, _. "Versuch einer Mathematischen Theorie der
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Work in Fluid Motion, " J. Bos. Spc, Civ. Engrs. , 30_:219, 1943.
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Orthokmetic Flocculation, SERL Report No. 68-5, Sanit. Eng.
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Flocculation in Water Purification, " Proc. ASCE, JSED, 9^:95,
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50. Saffman, P. G. , and J. S. Turner. "On the Collision of Drops
in Turbulent Clouds, " J. of Fluid Mechanics, J: 1 6, 1965.
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istics of Biological Floes in Turbulent Regimes, Sanit. Eng.
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52. Vassilatos, G. , and H, L. Toor. "Second Order Chemical
Reactions in a Non-Homogeneous Turbulent Fluid, " A. I. Ch. E.
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Sewage. V Mixing of Chemicals and Coagulation, " Sewage
Works Journ. . 1:547, 1936.
55. Selleck, R. E. , and H. F. Collins. "Di sinfect ion in Wastewater
Reuse, " Paper presented at the Second Annual Univ. of Calif,
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56. Selleck, R. E. , H. F. Collins, and G. White. "Kinetics of
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1970.
58. Riddick, T. M. "Zeta Potential and Polymers, " JAWWA,
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59. Vrale, L. , and R. M. Jorden. "Rapid Mixing in Water
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60. Wilson, G. Work done at Sanit. Eng. Research Lab. ,
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161
. GOVERNMENT PRINTING OFFICE:1972 514-149/104 1-3
-------
SELECTED WATER
RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
/. Report No.
4. Title
INITIAL MIXING IN COAGULATION PROCESSES
7. Author(s)
Stenqulst, R. J. , Kaufman, W. J.
9. Organization
California Univers Lty, Berkeley
Sanitary Engineering Research Laboratory
3. Accession No.
W
5. Report Date March 1972
6.
8. Performing Organization
^MRL 72-2
10. Project No.
11. Contract!Grant No.
17030-DLX-(5)NC
13. Type of Report and
Period Covered
12. Sponsoring Organization
15. Supplementary Notes
Environmental Protection Agency report
number EPA-R2-72-053, November 1972.
16. Abstract
This investigation was undertaken with the objective of determining the importance
of the initial mixing step in water and wastewater treatment processes and deter-
mining whether increasing the rapidity of the initial mixing could improve process
performance. The principal process considered was alum coagulation-flocculation
of a kaolin suspension in water. The initial mixing device under consideration was
a biplane, square-mesh grid of bars placed in a turbulent flow, tubular reactor;
a 2-in. pipe was used in the present studies. Studies were made using a single
electrode "point" conductivity probe and NaCl solution tracer to determine what
parameters affect the mixing which occurs in the turbulent flow field downstream
from a grid, and from these results a general mixing model was developed. The
relation between initial mixing and process performance was studied by using two
of the grids from the mixing studies as initial mixing devices in coagulation of a
kaolin suspension.
17a. Descriptors
*Mixing, *Turbulence, *Coagulation, *Water treatment, Conductivity,
Chlorination, Flocculation
17b. Identifiers
Initial mixing, Conductivity Probes
17c. COWRR Field & Group
18. Availability
05F, 05D
19. Security Class.
(Report)
20. Security Class.
(Page)
21. No. of
Pages
22. Price
Send To:
WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON. D. C. 20240
Abstractor
Institution
WRSIC 102 (REV. JUNE 197l)
SPO 913.261
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