FPA R? 79 flflfi
ENVIRONMENTAL PROTECTION TECHNOLOGY SERIES
September 1972
The Swirl Concentrator as a Combined
Sewer Overflow Regulator Facility
Office of Research and Monitoring
U.S. Environmental Protection Agency
Washington, D.C. 20460
-------
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
standards..
-------
EPA-R2-72-008
September 1972
THE SWIRL CONCENTRATOR
as a
COMBINED SEWER OVERFLOW REGULATOR FACILITY
Project 11023 GSC
Project Officer
Richard Field
Edison Water Quality Research Div.
National Environmental Research Center
Edison; New Jersey 0881?
Prepared for
OFFICE OF RESEARCH AND MONITORING
U.S. ENVIRONMENTAL PROTECTION AGENCY
. WASHINGTON; D.C. 201+60
and the
CITY OF LANCASTER; PENNSYLVANIA
For sale by the Superintendent of Documents, U.S. Government Printing Office
Washington, D.C,, 20403 - Price $2.26
-------
EPA Review Notice
This report has been reviewed by the
Environmental 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.
-------
ABSTRACT
A study was conducted by the American
Public Works Association to determine the
applicability of a combined sewer overflow
regulator which by induced hydraulic conditions
separates settleable and floatable solids from the
overflow. The device, called a swirl concentrator,
was originally developed in Bristol, England. The
present study was conducted through the use of a
hydraulic model test to determine swirl
concentrator configurations, flow patterns and
settleable solid removal efficiency. A mathematical
model was also prepared to determine a basis for
design.
Excellent correlation was found between the
two studies. It was found that at flows which
simulate American experience a vortex flow
pattern was not effective. However, when flows
were restricted, a swirl action occurred and
settleable solids were concentrated in the outflow
to the interceptor in a flow of two to three percent
as compared to the quantity of overflow through a
central weir and down shaft.
For a flow of 165 cfs, representing a five-year
frequency storm it was determined that a 36-ft
diameter tank, 9-ft deep with a 20-ft diameter weir
would have an efficiency of 85 percent of
maximum.
The swirl concentrator appears to offer a
combined sewer overflow regulator that effectively
regulates the flow and improves the quality of the
overflow, with few moving parts.
The complete hydraulic laboratory and
mathematical reports are included as appendices.
This report was submitted in fulfillment of the
agreement between the City of Lancaster,
Pennsylvania, and the American Public Works
Association under the partial sponsorship of the
Office of Research and Monitoring, Environmental
Protection Agency, in conjunction with Research
and Demonstration Project 11023GSC.
-------
APWA RESEARCH FOUNDATION
Project 70-7
Richard H. Sullivan, Project Director
SPECIAL CONSULTANTS
Dr. Morris M. Cohn
J. Peter Coombes
Bernard S. Smisson
Alexander Potter Associates, Consulting Engineers
General Electric Company, Re-entry and Environmental Systems Division
LaSalle Hydraulic Laboratory, Ltd.
APWA Staff*
R.H. Ball
Mona Jordan
Shirley M. Olinger
Oleta Ward
*Personnel utilized on a part-time basis
-------
AMERICAN PUBLIC WORKS ASSOCIATION
BOARD OF DIRECTORS
William W. Pagan, President
Erwin F Hensch, Vice President
Myron D. Calkins, Immediate Past President
Timothy J. O'Leary
Walter A. Schaefer
Donald S. Frady
Ray W. Burgess
Herbert Goetsch
Leo L. Johnson
John J. Roark
Lyall A. Pardee
Robert D. Bugher, Executive Director
Gilbert M. Schuster
Frederick J. Clarke
Wesley E. Gilbertson
John A. Bailey
APWA RESEARCH FOUNDATION
Samuel S. Baxter, Chairman
W. D. Hurst, Vice Chairman
Fred J. Benson
John F Collins
William S. Foster
F. Pierce Linaweaver
D. Grant Mickle
Milton Offner
Lyall A. Pardee
Milton Pikarsky
Robert D. Bugher, Secretary-Treasurer
Richard H. Sullivan, General Manager
VI
-------
CONTENTS
Page
Abstract . - • • "i
Foreword . - • .... . ix
Section I Conclusions, Recommendations and Overview . . .1
Section II The Study .... . . ... ... 5
Section III General Features .... ... . . 23
Section IV Design of Swirl Concentrator Facilities . . . . 29
Section V Implementation .... . .49
Section VI Potential Uses and Research Needs . . . .53
Section VII Acknowledgments . . . • 57
Section VIII Glossary of Pertinent Terms .... . . . .59
Section IX. References . . ........ .... . . 61
Section X Index to Tables and Figures in Appendices . . . . . .63,64
Appendix 1-Hydraulic Model Study . . . . . 65
Appendix 2-Mathematical Model of Swirl Concentrators . . . 125
TABLES
1 Determination of Combined Sewage Solids . . 13-15
2 Specific Gravity, Size and Concentration of Settleable Solids . . 15
3 Flow and Velocity at Lancaster ... ... . . 17
4 Effect of Weir Size on Concentrator Performance .... ... 25
5 Sample Calculation on Analysis of Pounds of Suspended Solids Lost
Due to Undersize Chamber, Storm 5 ... ... .32
6 Analysis of Six Storms, Lancaster, Pa . . 32
7 Head Discharge Data ... . . . 34
8 Combined Discharge Over Circular and Side Weir 34
9 Chamber Dimensions . .... .... 39
10 Design Example (from hydraulic model data) . . . .41-45
11 Design Example (from mathematical model data) . 48
FIGURES
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Swirl Concentrator Final Form . .
Preliminary Lancaster Flow Diagram
White Ladies Road — Vortex Regulator . .
Photograph of Model Setup
Photographs of Initial Hydraulic Test Model ...
Cross Section of Swirl Concentrator
Isometric View of Swirl Concentrator
Photograph of Final Form Surface Flow Condition . . .
Photograph of Final Form Floatables Handling . .
Flow and Suspended Solid Load for Six Storms . .
Head Discharge Curve for Circular Weir
Plan and Elevation — Roof Area . ....
Plan and Elevation - Below Roof
Plan and Elevation — Floor Area . . . .
Hydraulic Profile 3 cfs
Hydraulic Profile 8.6 cfs . ...
Hydraulic Head Requirements . .
. . . . 3
8
... 10
11
. 12
. . 21
24
. . 26
27
.30-31
... 35
36
37
.... 38
46
46
... 50
Vll
-------
FOREWORD
The report which follows presents the result of an
intensive study conducted by the American Public
Works Association Research Foundation concerning the
development and basic design of a new type of
combined sewer overflow regulator facility. The
regulator, although basically a static facility due to the
minimization of moving parts will, in addition to
controlling the rate of flow to the interceptor,
significantly reduce the amount of settleable solids in
the overflow. With proper design it will also maximize
insystem storage.
Although work was accomplished using a basic
configuration developed in England, modified to meet
American combined flow conditions, the study indicates
that high solids removal efficiency can be obtained from
relatively large flows in relatively small chambers. The
significance to local officials of the ability to
concentrate solids utilizing very short detention periods
and almost no mechanical equipment is very great.
The American Public Works Association was
fortunate to be able to utilize the services of three
outstanding companies in the development of the study:
Alexander Potter Associates, Consulting Engineers;
La S a lie Hydraulic Laboratories, Ltd. and General
Electric Company, Re-entry and Environmental Systems
Division.
The Association believes that the swirl concentrator
as a combined sewer overflow regulator may be very
useful in many communities in alleviating much of the
combined sewer overflow problem In addition, as a
pretreatment device in a sanitary sewage or industrial
wastes system it should allow treatment facilities to be
constructed and operated more efficiently and at less
cost.
As combined sewer systems are upgraded and
improved regulators constructed to reduce the
pollutional impact of overflows on receiving waters, we
believe that the swirl concentrator should be considered
wherever there is sufficient hydraulic head to allow its
dry weather operation.
Samuel S. Baxter, Chairman
APWA Research Foundation
IX
-------
SECTION I
CONCLUSIONS, RECOMMENDATIONS AND OVERVIEW
CONCLUSIONS
1. A practical, simple facility has been
developed which offers a high -degree of
performance in reducing the amount of
settleable solids contained in combined
sewer overflows as well as enabling the
quantity of flow to the interceptor to be
controlled, all with a minimum of moving
equipment.
2. The design of the swirl concentrator has
been developed for rapid calculation of
the different elements enabling ready
transferability to the regulation of various
quantities of flow.
3. The swirl concentrator is very efficient in
separating both grit and settleable solids
in their middle (>0.2 mm) and larger
grain size ranges. By weight, these
fractions represent about two-thirds of
the respective materials in the defined
combined sewage. Separation of the
smaller grain sizes was less efficient,
although still appreciable.
4. The concentrator appeared to exhibit
preferential limits of grain sizes separated
according to the elements being tested.
5. The floatables trap and storage
arrangements should capture most of the
lighter than water pollutants. Its
dimensions are such that oversize floating
objects would jam it, and tend to go over
the weir rather than stay in the chamber
to clog the foul outlet.
6. Both the floatables trap and foul outlet
are easy to inspect and clean out if
necessary, during dry weather flows.
7. Sufficient head must be available either
by depth to the interceptor sewer from
the collector or by provision for insystem
storage in the collector to allow operation
of the facility.
RECOMMENDATIONS
1. A demonstration facility should be
constructed of sufficient size to be totally
effective for flows of 103 cfs. The facility
should be monitored to verify the
hydraulic and mathematical modeling
which was accomplished in the study.
2. Research should be directed at narrower
grain size bands; for example, a chamber
which would separate only the fines
might do so with a much higher
efficiency.
3. Additional hydraulic and mathematical
modeling should be accomplished to
determine the effectiveness of the swirl
concentrator concept in the various
phases of primary sewage treatment. Such
research should also have application in
many industrial waste situations.
4. Further investigation should be made to
determine if better efficiency could be
obtained with two or more concentrators
operated in parallel or in series.
OVERVIEW
A report by the American Public Works
Association published in 1970 gave the results
of a study of combined sewer overflow
regulator facilities. Design, performance and
operation and maintenance experiences from
the United States and Canada, and in selected
foreign countries were reported. It was
evident that North American practice has
emphasized the design of regulators simply as
flow splitters, dividing the quantity of
combined sewage to be directed to the
treatment facilities, and the overflow to
receiving waters. Little consideration was
given to improving the quality of the overflow
waste water.
In the current study, hydraulic laboratory
tests and mathematical modeling strongly
indicate that it is possible to remove
significant portions of settleable and floatable
solids from combined sewage overflows by
using a swirl concentrator. The practical,
simple structure has the advantages of low
capital cost; absence of primary mechanical
parts should reduce maintenance problems;
and construction largely with inert material
should minimize corrosion. Operation of the
facility is automatically induced by the
inflowing combined sewage so that operating
problems normal to dynamic regulators such
as clogging will be very infrequent.
1
-------
The device, as developed, consists of a
circular channel in which rotary motion of
the sewage is induced by the kinetic energy of
the sewage entering the chamber. Flow to the
treatment plant is deflected and dischafges
through an orifice called the foul sewer
outlet, located at the bottom and near the
center of the chamber. Excess flow in storm
periods discharges over a circular weir around
the center of the tank and is conveyed to
storage treatment devices as required or to
receiving waters. The concept is that the
rotary motion causes the sewage to follow a
long spiral path through the circular-chamber.
A free surface vortex was eliminated by using
a flow deflector, preventing flow completing
its first revolution in the chamber from
merging with inlet flow. Some rotational
movement remains, but in the form o'f a
gentle swirl, so that water entering the
chamber from the inlet pipe is slowed down
and diffused with very little turbulence. The
particles entering the basin spread over the
full cross section of the channel and settle
rapidly Solids are entrained along the
bottom, around the chamber, and are
concentrated at the foul sewer outlet.
• Figure 1, Swirl Concentrator Final Form,
depicts the final hydraulic model layout
showing details such as the floatables trap,
foul outlet and floor gutters.
The swirl concentrator may have practical
applications as a degritter, or grit removal
device for sanitary sewage flows or separate
storm water discharges of urban runoff
waters. It may have capabilities for the
clarification of sanitary sewage in treatment
plants, in the form of primary settling or,
possibly, final settling chambers. It might be
used for concentrating, thickening, or
elutriating sewage sludges. It may be
serviceable in the separation, concentration
and recycling of certain industrial waste
waters, such as pulp and paper wastes or food
processing wastes, with reuse of concentrated
solids and recirculation of clarified overflow
waters in industrial processing closed circuit
systems.
In water purification practices, it ma>
find feasible applications in chemical mixing,
coagulation and clarification of raw water.
Other uses may prove to be realistic and
workable.
Complete reports describing the hydraulic
laboratory study and the mathematical
modeling are included as Appendices -1 and 2,
respectively. The body of the report details
the basis of the assumptions used to establish
the character and amount of flow to be
treated and the design of a swirl concentrator
based upon the hydraulic and mathematical
studies.
Although the study was performed for
the City of Lancaster, Pennsylvania, with a
specific point of application defined, all work
was accomplished in a manner which allows
ready translation application of the results to
conditions which might be found at other
installations and for other purposes.
-------
Floatables Trap
General Layout
Floor Gutters, Foul Outlet
and Deflector
Detail of Foul Outlet
Note Deflector
FIGURE 1
SWIRL CONCENTRATOR FINAL FORM
-------
SECTION II
THE STUDY
A national investigation of the means by
which municipal jurisdictions in the United
States and Canada regulate and control
overflows from combined sewer systems, and
of methods by which the pollutional effects
of these discharges into receiving waters can
be minimized, was carried out by the
American Public Works Association Research
Foundation in 1969-70, on behalf of 34 spon-
soring local governmental agencies and the
then Federal Water Quality Administration.
The in-depth studies of combined sewer
system regulation practices produced data on
the design, construction, operation, and
maintenance of various types of overflow
control devices and their abilities to cope with
the large amounts and the frequency of
combined sewer waste waters discharged into
receiving streams. Of major significance was
the finding that in American practice little or
no effort was made to improve the quality of
the overflow liquids and, thereby, to reduce
the pollutional impact on receiving waters. In
short, regulators were found to have, in
American practice, the sole function of
controlling the quantity of overflows; and
even this function has been carried out with
only limited success.
The report on the APWA studies1'2 of
this phase of sewer system management
emphasized, perhaps for the first time, the
possible "dual purpose" of combined sewer
regulator facilities: (1) to control the
frequency and duration of overflows to the
greatest extent possible; and (2) to improve,
by practical means, the quality of the
overflow waters by diverting the greatest
possible portion of the sewage and storm
runoff solids to the interceptor sewer system
and downstream treatment facilities. The
report coined the phrase, the "two Q's" of
overflow control to represent the two
functions of quantity control and quality
control.
The investigation disclosed that European
practices laid greater stress,'at least in some
measures, on improvement of the quality of
storm overflows from combined sewers by
various mechanical-hydraulic means. These
included types of screens or bar racks and
scum baffling and retention devices. One of
the promising methods of quality control in
combined sewer regulator overflows was the
so-called circular "vortex" device used in the
City of Bristol, England. Two such devices
were installed several years ago and have
functioned satisfactorily.
This circular chamber concept was
evolved in order to obtain adequate weir
length for overflow discharge without the
expense of constructing a long side-spill weir
for this purpose. At Bristol, laboratory studies
were carried out on this configuration to
ascertain its hydraulic characteristics and
performance, prior to construction of the
facilities in 1964. As a bonus, it was found
that this type of overflow control device was
able to concentrate combined sewage solids
by separation of the solids from the liquid
phase in the flow pattern and to divert as
much as 70 percent of these solids to the
"foul sewer" tributary to the sewage
treatment works. Thus, it was felt that this
type of hydraulic regulator facility, without
use of any moving parts, provided the "two
Q" principle ennunciated by the APWA in its
study and the report thereon.
In order to focus attention on the
dual-purpose function of regulators and to
emphasize the need for greater knowledge of
the hydraulic means by which quality control
can be enhanced, the APWA Report made the
following recommendation:
"Regulators and their appurtenent
facilities should be recognized as devices
which have the dual responsibility of
controlling both quantity and quality of
overflow to receiving waters, in the
interest of more effective pollution
control.
"Further research should be
sponsored by the FWQA to determine
the ability of new devices to induce
separation and interception of
concentrated pollutional solids and
liquors, and the decantation of dilute
storm water—sanitary sewage admixtures
to receiving waters; to determine
-------
practical applications of such devices and
systems; to demonstrate their
potentiality by means of mathematical
modeling; and to determine cost-benefit
relationships."
Reference in the recommendation of the
APWA study report was to "new devices;" the
device which offered the most promising
ability to separate solids from liquid and
produce the "two Q's" results appeared to be
the so-called "vortex" system researched and
used in the Bristol installations. Staff
members of the regulator research team
visited the Bristol units, conferred with
Bernard Smisson, Senior Engineering
Assistant, City Engineer's Office, and
reviewed his findings and reports on his
research of the rotary motion principle
involved in his units.
The British "Vortex": Solids Concentration
by "Swirl"Action
Longitudinal flows of combined sanitary
sewage and storm water tend to either hold
solids admixed with the liquid phase, due to
scouring velocities or agitation, or to allow
solids to settle out or stratify in the liquid
flows due to the influence of non-scouring
velocities on suspended materials that are
sufficiently heavier than water to react to
gravity influence. The principle of
sedimentation utilizes this phenomenon. The
removal of heavier grit in grit separation units,
and the eventual removal of lighter solid
fractions in settling chambers utilize gravity
solids-classification as the underlying means
of removing unwanted materials from
wastewater flows. Solid materials, or
solidified liquid fractions that are lighter than
water, become floating materials and are
removed in standard treatment practice by
means of intercepting baffle arrangements
and/or by manual or mechanical skimming
devices.
These removal processes are dependent
on settling characteristics of solid particles
and the time involved in producing the degree
of removal desired. This time element is of
great importance in the design of
solids-removal facilities because they
influence the size of charfibers that will
provide adequate volume for the lowering of
velocities and the deposition of wastewater
solids. The concept of removal of wastewater
solids by means of other forces rather than
vertical gravity phenomena, in relatively short
periods of time, and therefore, in facilities of
relatively small volumetric size and at greatly
reduced cost, lies behind the proposal to
utilize some form of concentric flow pattern
to achieve this result. The so-called "vortex"
principle utilized at Bristol, and discussed in
the APWA study report on combined sewer
overflow practices, utilizes this method of
producing the separation and concentration
of solids from such flows.
The "vortex" terminology used in Bristol,
England, and referred to in the APWA studies
was adequate to define and characterize the
original concept. However, the investigatory
work described in this report, working with
much larger flows in minimum-sized chambers
shows that a vortex flow pattern must be
avoided. A different hydraulic condition can
be developed which will still effectively
remove solids. The device involved in this
study for Lancaster, Pa., can be defined as a
swirl concentrator.
The purpose of this flow configuration is
to induce swirl action in the liquid and
liquid-borne solids and, thereby, to induce the
classification of the total flow into deposited
solids, as a concentrated slurry, in the
underflow; the discharge of clarified
supernatant liquid in the overflow; and
retention of floating solid fractions at the
upper surface of the clarified effluent. This
separation and concentration of the fractions
would then provide for the discharge and
transportation of the concentrated
solids-liquid underflow to interceptor
conduits and treatment works; the discharge
and transportation of the clarified liquid to
receiving waters, treatment devices, or to
holding chambers which are designed for
pump-back into the interceptor system during
periods of non-peak flows; and the disposal of
the entrapped floatables by whatever means
best applying lo such an installation.
This very simple description of the
liquid-solids separation and concentration
principle offers a restricted definition of the
-------
application of such devices and configurations
for the improvement of combined sewer
overflow wastewaters discharged through
regulator devices to receiving waters. If the
principle is valid, the applicability of this flow
configuration, and the geometries of the
structural chamber and its internal details to
induce this type of flow pattern, should be
applicable to many other processes and
procedures in the handling and treatment of
liquid-solids flows in the municipal and
industrial fields.
The Lancaster, Pa., Installation
An opportunity to supplement the work
carried out at Bristol, England, and to apply it
under American combined sewer conditions,
has been provided by the plan of the City of
Lancaster, Pa., to construct a new combined
sewer overflow storage-pump-back and
partial-treatment facility downstream of a
regulator installation. While specifically
motivated by the Lancaster plan, such
installations based on the swirl principle could
have practical applications in other
comparable combined sewer regulator-over-
flow problems.
A demonstration of the "two Q" dual
function of combined sewer overflow
regulators can be achieved at Lancaster by
installing a swirl concentrator regulator to
divert the greatest possible concentration of
solids slurry to the interceptor and sewage
treatment works. In Lancaster the regulator
will act to minimize flow of solids to a flow
equalization device (a deep silo). It will also
be evaluated as to its suitability as a treatment
device by itself. A flow sheet of the proposed
Lancaster installation, showing the
juxtaposition of the swirl concentrator, is
presented in Figure 2, Lancaster Flow
Diagram.
The Lancaster facility will provide a
demonstration or prototype swirl
concentrator which will receive the combined
sewer flow; a silo-shaped storage chamber for
the clarified overflow from the concentrator,
and a wet well and pumping station to deliver
the concentrate underflow slurry, via a "foul
sewer" connection, into the interceptor
sewer. The City of Lancaster plans to install a
grit chamber on the foul sewer to protect the
wet well and pumps. The silo will provide
mixing-aeration of the stop 1 liquid. The
supernatant liquid may then be passed
through a micro strainer and chlorinated
before being discharged into Conestoga River.
The contents of the silo, or any portion
thereof, can be pumped back into the
interceptor sewer during low-flow periods.
Flexibility of design will enable any of the
above storage and treatment devices except
the swirl concentrator to be by-passed in
order to demonstrate and evaluate their
individual characteristics and performances,
or the performances of any group of such
units functioning together. Thus, the
Lancaster installation will serve as a full-scale
demonstration of various types of combined
sewer handling methods, including the swirl
concentrator. Adequate monitoring-sampling
facilities and locations will be provided to
determine the two factors of quantity and
quality at various stages of combined sewer
flow and treatment.
The Lancaster installation could provide a
demonstration of the validity of the swirl
principle if it is preceded by carefully planned
and recorded hydraulic pilot studies and
supported by mathematical modeling which
would provide basic design criteria applicable
to the Lancaster project and, coincidentally,
to any other installation of comparable
nature. At one and the same time, this
procedure would confirm the original Bristol
work; provide engineering data to rationalize
modifications of the Bristol geometric
configurations and flow patterns to American
conditions; and develop design criteria
correlations which could be used for the
Lancaster swirl concentrator and be used by
designers for other projects in the combined
sewer field or any of the other applications
described above.
Study Plan
To accomplish this purpose, the
American Public Works Association, under
contract with the City of Lancaster, Pa., has
completed the research study. The scope of
the study was to investigate the use of vortex
storm sewage (combined sewer) separators,
-------
! Exist 60-in
Sewer
Block
jExist jO-in. San-Sewer
Exist 6-in. San-Sewer
Underflow
i Overflow
Disinfect
Mixing
Aeration
Device
1
j Exist. Outfall 6G-in.
Conestoga River
Silo Tank
Interceptor
42-in. ,
I——f
Wet
Wei!
—
. New Const. 1972; Not
Part of Demo. Project
Backwash
To Receiving Water
FIGURE 2
PRELIMINARY LANCASTER FLOW DIAGRAM
To South
.Treatment
-------
involving the development of studies by
"mathematical modeling correlated with
hydraulic laboratory modeling, to determine
the degree of efficiency which might be
associated with construction of such facilities
and design relationships."
The La Salle Hydraulic Laboratory Ltd.
(Laboratoire D'Hydraulique) La Salle,
Quebec, Canada, was engaged to conduct the
hydraulic modeling studies. The General
Electric Company, Re-entry and Environ-
mental Systems Division, Philadelphia, Pa.,
was retained to carry out the mathematical
modeling phase of the study.
In order to utilize the basic knowledge
and experience gained in the Bristol, England,
investigations of the so-called "vortex"
principles and the actual construction of two
such regulator-separator units, the innovator
and investigator of these developments,
Bernard Smisson, was retained as consultant.
Direct contacts with the American studies
were maintained by Mr. Smisson by means of
an on-site period of conferences and data
reviews at the La Salle Hydraulic Laboratory,
and by periodic exchange of data and other
correspondence.
Consultative services were arranged with
the firm of Alexander Potter Associates, New
York City, a consulting engineering firm
widely experienced in the hydraulics and
design field, and with experienced individual
engineers, to help guide modeling studies and
to correlate the findings in the course of the
hydraulic and mathematical modeling
investigations. Section VII lists the many
individuals whose efforts made this complex
study possible.
Underlying Assumptions of the Modeling
Studies
Before the hydraulic and mathematical
modeling work could be undertaken, it was
necessary to establish underlying assumptions
that would assure the investigators that their
.work and their findings would be in
consonance with recognized and expected
liquid flow and solids characteristics in
representative American combined sewer
wastewaters, and therefore applicable to the
Lancaster installation. These basic
investigative assumptions had to be grounded
in known principles of liquid flow and
particle flow characteristics and phenomena
under combined sewer conditions.
The following factors were accepted as
the basic assumptions for the investigations
by the technical consultative group and the
two developers of the mathematical and
hydraulic modeling data.
Configuration: The research work at
Bristol and the actual details of the so-called
"vortex" chamber installed at White Ladies
Road were utilized as the basic starting point
for the study of the swirl concentrator
covered by this report. Modifications of
dimensions, internal appurtenant structures
and flow patterns for concentrated underflow
solids, overflow liquid and floatables
entrainment and removal were made to
provide optimum performance of the "two
Q" functions of the hydraulic model and of
the mathematical confirmation of the
hydraulic conditions.
The White Ladies Road device as shown
in Figure 3, provided an 18-foot-diameter
chamber; an overflow weir; a scum ring for
retention of the floating material mounted on
the central column; and a "foul sewer" outlet
for the concentrated solids. Other essential
features in the chamber were provided. Flow
entered the circular chamber tangentially at
the floor level. The foul sewer outlet was
located on the floor of the chamber, near the
central column, at a point where it would
collect the solids deposited on the floor of the
chamber. The supernatant clarified liquid
overflowed the weir and was discharged to
receiving waters.
Figure 4 contains general photographs of
the model. Figure 5, Photograph of Initial
Hydraulic Test Model, shows the model being
operated at a simulated 165 cfs with and
without a deflector. Without the deflector, a
free vortex was formed which resulted in a
low solids separation efficiency.
No Moving Parts: One of the fundamental
advantages foreseen for the swirl concentrator
principle is the absence of any moving or
mechanical parts in the chamber, and its
self-cleansing of deposited solids by
-------
COMBINED SEWER
STORM SEWER
--INLET 36"DIA.
AFFLE
BRANCH INTERCEPTOR
TO TREATMENT PLANT
SECTION "A"-"A"
WHITE LADIES ROAD
FIGURE 3
WHITE LADIES ROAD - VORTEX REGULATOR
utilization of the flow patterns created by the
configurations of the device. This is in
contrast with standard facilities for removing
grit and lighter suspended settleable and
floatable solids from sewage and other waste
waters, which require some form of collection
and removal mechanisms to perform this
function.
The removal of such solids from the body
of liquid and from the swirl chamber is
induced by the liquid body itself as a result of
the flow patterns set up by the geometric
configuration of the unit. Absence of moving
parts, which was one of the important
assumptions established for the study of the
swirl concentrator principle, overcomes
hydraulic impedances caused by the intrusion
of mechanical collection equipment and the
sub-agitations caused by the movement of
collectors even at slow rates. Mechanical
breakdowns and the need for standby
equipment for use during repair shut-downs
are avoided in the swirl arrangement.
Corrosion of metallic parts could be avoided
by construction of a swirl chamber with inert
materials.
Particle Sizes of Solids in Combined
Sewer Flows: It was necessary to artificially
simulate the solids components used in the
hydraulic and mathematical model studies.
for the purpose of making the laboratory
investigations translatable into what might be
assumed to be a representative combined
sewer flow of admixed sanitary sewage and
storm water runoff. Since it was not possible
to use actual combined wastes in the
scaled-down hydraulic model investigations, it
was necessary to reproduce ranges of particle
10
-------
General Views of Model
Ltf.
Vibrator Solids Injection
System
Precision Point Gauge to Measure
Water Levels in Chamber
FIGURE 4
PHOTOGRAPH OF MODEL SETUP
sizes and specific gravity by simulation. It was
not possible to reproduce all size and gravity
ranges, nor was this essential to the accuracy
of the model studies because combined sewer
flows vary markedly in composition from day.
to day and from season to season in the same
system, and even more markedly from
community system to community system. As
a result, no single truly representative
combined sewage-storm water "analysis"
11
-------
FIGURE 5
PHOTOGRAPHS OF INITIAL HYDRAULIC TEST MODEL
could be set forth for the studies. In lieu of a
single agreed-upon solids size and specific
gravity composition for the hydraulic studies,
various ranges were investigated.
After intensive reviews of recorded
analytical data for representative flows from
various systems, and consideration of all of
the factors outlined above, an acceptable
"range" of particle sizes and specific gravities
was chosen for the studies. Decisions were
based on data provided by Alexander Potter
Associates, the Environmental Protection
Agency and the LaSalle Hydraulic
Laboratory. Due consideration was given to
information published on British practice and,
in particular, the work of Smisson,3 Ackers.
Harrison, Brewer,4 Prus-Chacinski and
Wielgorski.5
Table 1, Determination of Combined
Sewage Solids, presents the rationale used to
develop the combined flow solids particle
decisions on sizes, concentrations and specific
gravity. The table is intended as symbolic of
the distinctions made for the study between
grit, suspended solids and floatable solids.
From the solids particle studies for the
hydraulic-mathematical model studies it was
necessary to make a basic assumption of the
firm analytical data to be used. Table 2,
Specific Gravity, Size and Concentration of
Settleable Solids, indicates the settleable
solids characterization simulated in the
12
-------
hydraulic laboratory.
Simulation of these materials for use in where: V is settling velocity
the hydraulic model was based on settling d is particle diameter
velocities according to Stokes equation: M is water viscosity
pw is density of water
y -gd2 (p.-p.,,) Ps is density of solids
TABLE 1
Determination of Combined Sewage Solids
A. Sewage Composition
1. Average Composition of Domestic Sewage, mg/11 P 564
5-day,
State of Solids Mineral Organic Total 20 C BOD
(1). (2) (3) (4) (5)
1. Suspended 85 215 295 140
a. Settleable 50 130 180 65
b. Non-settleable 35 85 115 75
2. Dissolved ' 265 265 530 40
3. Total 350 480 825 180
2 Organic Matter:1 P563
40% nitrogenous matter
50% carbohydrates
10% fats
Settleable Solids: will settle to bottom of Imhoff cone in one hour.2
Non-settleable Solids: will not settle nor float to surface in period of one hour.2
3. Grit:1 613
Specific gravity 2.65
Size usually captured in grit chambers up from 2 x 10~2cm diameter
Amount collected: 1 to 12 (average 4) cu ft per million gallons
Daily maxima reported: 10-30 cu ft per million gallons and as high as 80 cu ft
per million gallons
4. Sewage Solids except Grit1 P 609
Specific gravity 1.0 to 1.2 on dry basis-1.001 on wet basis
Size up to several centimeters in diameter
Si/e of 10-1 cm will have settling velocity of 4.2 x 10~2 cm/sec
B. Suggested Synthetic Sewage — full size model
1. Grit
Specific gravity 2.65
cuft/mg lb/mga mg/lb
~ 1 100 12
From Fair1- 4 400 48
12 1200 144
30 3000
a) Assuming 100 Ibs per cf
b) Ib/mg -H 8.33
13
-------
TABLE 1 (continued)
2. Settleable Solids
Smisson
Ackers
Prus-Chacinski
Fair
Use
Velocity to settle in 10 foot tank in 2 hours
10x305 mm in 2 x 60 x 60 sec
= 3050 mm in 7200 sec
= 0.4 mm/sec
Quantity range from 200 to 800 mg/1
3. Floatable Solids
4.
(excluding grit)
Fall Velocity
rnm/sec
2.5 to 7. 5
613
0.4
for 1 mm size
0.4 to 2
sg
1.19
1.005
1.05
1.0 to 1.2
1.1
Size
mm
0.18 to 0.42
25
1.6 to 3.2
1 to 75
1 to 5 mm
Smisson
Prus-Chacinski
Akers
perspex chips
perspex chips
actual sewage
polythene
Rise Velocity
mm/sec
61
21
sg
0.995
Size
25 mm
2 mm
Quantity - assume 10% of settleable solids
Quantity 20 to 80 mg/1
Settleable Solids — excluding grit
Domestic
Suspended
Settleable
Grit say
Settleable sg 1.05
Settleable (sg 1.05) =
295 mg/1
180
25 i.e., 50% of mineral
155
x 100 = 52% of suspended,
say 50% of suspended
For domestic sewage settleable (excl. grit) =150 mg/1
From Journal WPCF Jan. 1968 p 122 Burm, Krawczk, Harlow, "Suspended
solids consisted generally of between 70 and 90% settleable solids in both
sewage systems." i.e., combined and separate storm.
14
-------
TABLE 1 (continued)
Maximum suspended solids from reports
11024FKN 11/69
Bucyrus, Ohio
11023 FDD 03170
Portland, Oregon
111023 EVD 06170
p 156
p 157
p 158
p 27
p 26-27
1700 to 500
1000 to 500
1000 to 300
325 to 70
mg/1
mg/1
mg/1
mg/1
498 to 21 mg/1
For combined sewage, settleable solids might range
from 70% x 300= 210 mg/1
90% x 1700= 1530 mg/1
Say, floatable = 10% of above
Use Floatable 20 to 150 mg/1
Use Settleable 200 to 1400 mg/1
Portland, Oregon Study4
Comparison of Combined Flow and Dry Weather Flow
Mean Min. Max. Mean Min. Max.
Settleable solids mg/1 3.1 1.5 5.0 4.8 2.5 7.0
Total suspended solids ml/1 146 70 325 129 50 244
Use of 165 mesh (105 micron opening) screen will remove 99% of floatable and
settleable solids, and 34% of total suspended solids.
Note: 105 micron = 0.105 mm
1 Fair, G.M. and Geyer, J.C., Water Supply and Waste-Water Disposal, (John Wiley and
Sons, Inc., New York, 1954).
2 Glossary—Water and Wastewater Control Engineering
3 0.2 ft/sec = 61 mm/sec
411023 FDD 03/70 Rotary Vibratory Fine Screening of Combined Sewer Overflows
Material
(1) Settleable Solids
excluding grit
(2) Grit
(3) Floatable Solids
TABLE 2
Specific Gravity, Size and Concentration of Settleable Solids
Specific Concentration Particle
Particle Size Distributed
Gravity
1.05
2.65
0.9 •*
-1.2
.998
(mg/1)
200-1550
20-360
10-80
Size
0.2
0.2
5-
-5
-2
25
mm
mm
mm
Particle size (mm)
% by weight
Particle size (mm)
% by weight
Particle size (mm)
.2
10
.2
10
5
.5
10
.5
10
10
1.0
15
1.0
15
15
2.5
25
1.5
25
20
5.0
40
2.0
40
25
% by weight
10 10 20 20 40
15
-------
The material most used in the hydraulic
testing program was gilsonite, a natural
hydrocarbon with a specific gravity of 1.06
and a grain size between 1 and 3 millimeters.
Following the Stokes relation at a scale of
1:12 —laboratory test unit to full-sized
prototype —this material reproduces grit
between 0.36 and 1.06 mm and settleable
suspended solids between 1 and 3 mm.
This grit range leaves a small part of the
fines unrepresented, as well as a wide part of
the coarser particles. The coarser end of the
scale was assumed to be covered, since any
larger particles would obviously settle out if
those represented in the chosen material had
settled. The fines at the lower end of the scale
in turn were simulated with Petrothene®, a
compounded plastic with grain sizes between
2 and 4 mm and a specific gravity of 1.01.
Similar reasoning was utilized in
establishing particle characteristics to simulate
settleable suspended solids. The large gilsonite
covered a significant part of the middle size
range and the larger particles were considered
to have been removed if the gilsonite settled.
On this basis, the large gilsonite represented
65 percent by volume of the settleable solids
in the specified prototype combined
sewage-storm water runoff. Two finer
fractions of ground gilsonite were tested to
cover the fines. The first, which passed
25-mesh and was retained on 30-mesh, had a
mean particle size of 0.5 mm The second,
retained on 50-mesh, had a mean particle
diameter of 0.3 mm, thereby approximating
the finer particles specified as 0.2 mm.
The rates of solids injection used in the
hydraulic pilot unit correspond to the 50-300
mg/1 range in the prototype flows.
Confirmatory tests at a later time increased
the settleable solids injection rate up to 1,550
mg/1 established for the upper limit of
combined wastewater in the Lancaster
prototype.
Tests for the removal of floatables were
carried out using uniformly sized polythene
particles of 4 mm diameter, with a specific
gravity of 0.92; and Alathon®, another plastic
compound with particle size of 3 mm
diameter and specific gravity of 0.96.
Injection rates for this material varied from
30 to 150 mg/1, at prototype scale.
Liquid Flow Characteristics: The size of
the proposed prototype swirl concentrator to
be constructed at Lancaster would, of course,
be dictated by the anticipated combined
sewer flow conditions in that community's
system. The flow information supplied by the
city and its consulting engineers, Meridian
Engineers, was as follows:
Peak sanitary dry-weather flow—2.9 cfs
(say 3 cfs)
Storm flow: (a) intermediate frequency—
100 cfs
Storm flow: (b) infrequent peaks—162
cfs
Storm flow: (c) gravity flow capacity of
system—450 cfs
An attempt was made to evaluate the
ratio of combined flow to sanitary sewage
flow and to ascertain flow and velocity
characteristics at Lancaster, by means of
theoretical computations. Table 3, Flow and
Velocity at Lancaster, estimates the flows at
the site.
It was decided to 'evaluate model solids
removal efficiencies in the ranges of grit,
settleable suspended solids and floatables at
not only the 165 cfs maximum range but also
at 15 50 and 100 cfs flow levels. A swirl
concentrator of the type proposed will have
to function with suitable solids removal
efficiencies under such widely varying flow
conditions. To meet these conditions the
chamber must function as a flow-through
device, without any need for solids
concentration, at dry-weather flow levels of 3
cfs—the same flow rate established as the
capacity of the foul sewer outlet at the
bottom of the chamber—and varying
wet-weather flow conditions greater than 3
cfs.
Scaling—from Theory to Model, to
Prototype: The study of the hydraulic model,
and the mathematical model which simulated
the scale size of the hydraulic laboratory unit,
was intended to give confirmatory evidence of
the flow patterns and solids behavior which
will be produced in the prototype swirl
concentrator at the Lancaster site, and other
comparable installations. The studies were
designed to develop specific design criteria for
16
-------
the scaling of all component dimensions of entrapment and removal details,
swirl facilities by consulting engineers and
municipal engineering officials, relating to
inlet features, overflow features, foul sewer
connection features, floatable solids
and
incidental internal flow control features.
It is evident that the behavior of the
liquid phase and solids phase of the
separator-concentrator device will be
TABLE 3
Flow and Velocity at Lancaster
Preliminary Estimate (Rationale used prior to metering of flows)
Ratio of combined flow to sanitary flow
1. Other Areas
Camp - Sewage and Industrial Wastes April 1959
For storms of frequencies from 5 years to 25 years ratio
of storm flow to average sanitary flow will be 50 to 200
Flow estimates for Staten Island by Alexander Potter Associates
Peak storm flow for 5-year frequency
Sanitary from residential area
Section
Area
Storm
1
8 (part)
8 (part)
Acres
393
100±
163
cfs
5 yr
827
212
305
Av. San.
cfs
3.2
1.2
1.7
Peak San.
cfs
10.7
3.63
5.0
2
Av
Ratio
Storm
Av. San.
258
176
180
614
205
Storm
Pk. San.
77
58
61
196
68
Assume density of 10 persons per acre and C = 0.3 instead of above
100
128
0.36
0.85
2.
355 150
From the foregoing the ratio of the 5-year flow to the average sanitary flow may
vary from 50 to 350.
Study Area
Study Area 130 acres '
Assume 40 persons per acre
100 gpcd sanitary flow and infiltration
Av. sanitary flow = 130 x 40 x 100 = 520,000 gpd = 0.81 cfs
Peak sanitary flow - 0.81 x 36 = 3 cfs
Peak storm flow = 200 x 0.81 = 162 cfs
Present combined sewer is 60-inch diameter
For Q= 162 cfs D = 60 in. n=.013
s = 4 ft/100 ft
v = 8.6 fps
For Q = 2.9 cfs
_ 2.9 = 16
~ 162 -18
d _
From chart 4 = 0.09,^ = 0.37
17
-------
dependent on the following parameters:
configuration and geometrical dimensions; the
ratio of influent flows to foul sewer
concentrated slurry flows; and particle sizes,
concentrations and specific gravity in the
influent flow. The proposal was to make
qualitative analyses of the relationships
between these basic factors in various
combinations, in order to achieve maximum
efficiency of solids removal and, thereby, to
produce the highest possible overflow quality
with the least adverse impact on receiving
waters.
Normal scaling laws were used to
establish the geometry of the hydraulic model
and, in turn, of the mathematical model used
in verifying the hydraulic findings. A ratio of
1:12 was used for converting the laboratory
model to actual prototype size.
The liquid mass, being water, remained
constant in both the model and the translated
prototype unit. Consequently, the solids
particles were scaled down in the model
studies to represent full-scale size and specific
gravity conditions that will be experienced in
the prototype unit. The expected solids
characteristics in the combined sewer flows
would thus be simulated in the hydraulic
laboratory work. Limitations in such solids
scale-downs were recognized, as outlined
previously. If the sizes of particles were scaled
down to simulate laboratory conditions, the
coefficient of drag of the particles imposed by
the liquid would cause the particles to behave
under different settling velocities than those
which will be passing through the full-scale
prototype installation. To reproduce
prototype conditions, settlement velocity
curves were developed and confirmed by both
hydraulic and mathematical modeling. This
involved relating particle size to specific
gravity, making it possible to follow the
Stokes equation in reducing the scale size to
one-twelfth of the proposed prototype size
and in altering the particle sizes and specific
gravities to reproduce the same velocity
settlement characteristics for any
combination of solids characteristics.
For example, gilsonite having a size of 1
to 3 mm and a specific gravity of 1.06
reproduced grit particles at the prototype
scale between 0.36 and 1.6 mm and a specific
gravity of 2.65. The greater laboratory-scale
size and the lower specific gravity reproduced
the expected combined sewage characteristics
having a smaller size and higher specific
gravity. This same settling efficiency was
duplicated in the hydraulic tests with lighter
settling solids having a size range from 1 to 3
mm and a specific gravity of 1.01 to 1.2.
Hydraulic scaling was applied to a limited
number of cases. Actual modeling was based
upon similitude of settling velocities, i.e., a
1-3 mm gilsonite particle will settle at the
same rate as suspended solid particles of
specific gravity 1.2 with a size range of
0.34-1.00 mm, as well as grit.
Translating Model Studies to the Bristol
Investigations
Reference has been made to the original
investigations of the swirl concentrator
principle (there referred to as the "vortex") at
Bristol, England, and to the actual
performance of this system at two locations
in that city. In essence, the Bristol
development was based on cut-and-try
procedures, with configuration modifications
made in model units to produce the desired
solids removal efficiencies. What was lacking
in the British experience was a mathematical
evaluation of the liquid and solids flow
patterns achieved in the chamber and the
conversion of this evaluation into specific
design criteria. The studies involved in the
current project were designed to provide these
missing facts.
The Bristol pioneering work, in that
sense, served as the preliminary phase of the
swirl chamber investigation. It provided the
guidelines for shaping and dimensioning the
American hydraulic model, subject to
mathematical confirmation of the geometric
patterns utilized and the subsequent changes
of configurations built into the model to
improve liquid-solids control, separation and
concentration.
As stated by the LaSalle Hydraulics
Laboratory in its final report, Appendix 1, on
its modeling investigations: "The general
principle which Mr. Smisson had developed
and utilized did not fit the definition of
18
-------
known laws of either vortex or simple gravity
settlement, but rather appeared to be a
controlled combination of the two Mr.
Smisson's publications covered his work up to
1967, and the first hydraulic tests served as a
verification of these principles. Since 1967,
his research has led him to modify the
geometry of the chamber in some degree.
"The main difference in the European
and North American conditions was in the
discharge/chamber volume ratio. The aim was
to use a similarly sized chamber as Mr.
Smisson utilized but to treat from four to six
times as much flow.
"The first model geometry selected for
the hydraulic studies was based on the latest
data from Bristol. It took the form of a
flat-floored chamber, with a central column
one-sixth of the chamber diameter,
supporting a flat weir plate about five-sixths
of the chamber diameter. A weir and weir
skirt were attached to the outer
circumference of the weir plate. The research
program investigated the importance of
chamber depth, the shape of the entrance to
the chamber, and different weir diameters to
obtain the optimum removal of settleable
solids through the foul sewer outlet.
"The latest Bristol work included the use
of an oblique entry to the chamber. With the
flow from the chamber wall toward the
central shaft, it had been proven possible to
trap floatables under the weir. It was found
that a skirt hanging below the weir would
retain the floatables under the weir plate.
When the water level dropped in the chamber,
these trapped, lighter-than-water solids
descended on the water surface and could be
evacuated through the foul sewer outlet.
"The skirt served the purpose of creating
a shear zone which effectively divided the
chamber into two water mass parts: an
exterior liquid mass in which the flow moved
relatively rapidly; and an interior liquid mass
which rotated more slowly. Proper
exploitation of these two zones could
enhance the ability of the chamber to
produce solids separation and concentration.
The longer trajectory of the outer mass would
allow sufficient time for heavier solids to
settle to the floor while the slower movement
in the inner mass would allow finer settleable
solids to settle out. Manipulation of these
research parameters was directed toward
organizing the flow in the chamber to pass
continuously through the two zones so as to
take maximum advantage of their respective
hydraulic characteristics."
The Hydraulic Model and Testing Procedures
The LaSalle Hydraulics Laboratory report
on various changes in its model and the
testing procedures used to determine the flow
patterns and solids removal characteristics of
all modifications is contained as Appendix 1
to this report.
The Mathematical Model
The methods utilized by the General
Electric Company in carrying out the
mathematical modeling work on the swirl
concentrator are described in its final report,
which is included as Appendix 2 to this
,, report.
The general objective of the mathematical
model study was to develop a representative
model and computer simulation of a swirl
chamber device to separate floatable solids,
grit and suspended solids from storm water
overflows and to produce, thereby, a higher
quality of supernatant wastewater for
discharge into receiving waters or into storage
and/or storm water overflow treatment
facilities. In conjunction with the hydraulic
laboratory studies carried out at the LaSalle
Laboratory, the analytical model was devised
and used to predict variations in performance
of the swirl concentrator under conditions of
variable design criteria and, thereby, to arrive
at an optimum configuration for the unit.
A prototype chamber was modeled in
hydraulic and mathematical studies and
specific calculations were performed for both
the laboratory model and the proposed
prototype unit to be installed at Lancaster,
Pa. Over and above the specificity of the
mathematical investigations of Lancaster
conditions, the results are applicable to a
broad range of chamber sizes, flow rates and
particle characteristics. This broad
applicability was achieved by developing a set
of scaling laws based on the necessary
19
-------
governing equations. With the scaling laws,
the results of the hydraulic studies and the
computer calculations can be extended to
chambers of other sizes and flow rates,
provided only that geometric similarity is
maintained.
The following information on liquid flow
calculations and particle flow calculations in
the mathematical modeling procedures has
been excerpted from the General Electric
Company report, to serve as an introduction
to this work.
"The general approach of this study has
been to calculate the liquid flow field within
the swirl concentrator, neglecting the
presence of the particles (i.e., assuming a
dilute mixture). This was accomplished by
using a relaxation procedure to numerically
solve the equations for turbulent
axisymmetric flow. A three-dimensional eddy
viscosity model was used to relate the local
turbulent Reynolds' stresses to the gradients
of the mean flow properties. Once the liquid
flow had been calculated, the particle flow
through the liquid was computed. At each
mesh point at which the liquid flow was
computed the three particle momentum
equations, and the equation of continuity
were solved to determine the particle
velocities and concentration. The equations
included turbulent diffusion terms, virtual
mass effects, gravity forces, and drag. The
equations were solved with a time-dependent
scheme, integrating forward in time until a
steady-state was achieved.
"The liquid flow calculation was
calibrated by adjusting the mixing length and
friction coefficient to provide the best match
with the experimental data. The agreement
was generally good, but limited by
non-axisymmetric flow effects in the physical
model due to the inlet and baffle plate
arrangements. Using the calibrated liquid
flow, particle flows were calculated for several
flow rates, particle sizes, and chamber sizes.
The results generally showed favorable
agreement with the laboratory data although
the model tended to over-predict the
separation efficiency.
Liquid Flow Calculation
"The calculation of the liquid flow field
within the swirl concentrator required making
several simplifying assumptions. The two
chief assumptions were that the flow was
axisymmetric, and that its turbulent character
could be modeled. The axisymmetric
assumption meant that the flow could be
described with only two independent
variables (r and z), and was independent of
the angular position. This assumption
required that the inlet flow which in the
actual device entered tangentially through a
square duct, be represented by a
circumferential region of the wall through
which the inflow occurred. The inlet flow
through the wall was assumed to have a cubic
velocity profile as illustrated in Figure 6,
Cross Section of Swirl Concentrator as
Represented in Axisymmetric Mathematical
Model, with the magnitude adjusted to give
the proper mass flow rate. The tangential
velocity of the incoming flow was assumed to
be constant, and equal to the mean velocity in
the entrance channel. These assumptions gave
the correct tangential velocity near the outer
wall. Also, since the inflow was spread over a
large area, the inflow velocity was small, and
did not differ appreciably from the actual
case in which the radial velocity vanished at
the wall.
"The axisymmetric model thus
approximated the average behavior of the
flow at most radial locations. The differences
were largest in the vicinity of the inlet, and,
of course, the model could not reproduce
non-axisymmetric behavior such as local
vortices observed in testing. Similarly, the
effect of the baffle plate at the inlet could not
be reproduced exactly. However, the chief
effect of the deflector baffle was to raise the
tangential velocity of the liquid under the
weir. This effect could be simulated in the
model by proper adjustment of the free
constants associated with the eddy viscosity
and the wall shear. This procedure gave good
agreement with the mean tangential velocity
profiles observed in the test program.
20
-------
Overflow Velocity
w
H
w
Inlet
Velocity
Foul Sewer Outlet
Velocity
CROSS SECTION OF SWIRL CONCENTRATOR
as Represented in Asymmetrical Mathematical Model
The actual turbulent flow was very
complicated, and many models could be used
to represent the effect of turbulence on the
mean motion. The art of turbulent flow
calculation is not far advanced, and even for
the simpler case of a boundary layer flow,
two different computational schemes can' give
results which differ by as much as 50 percent
in some respects. The present model used an
elementary eddy viscosity approach which
related the turbulence to the gradients of the
mean velocities through the use of a mixing
length concept. Such a crude approximation
could not hope to duplicate the details of the
turbulent, time varying flow structure.
However, the main features of the internal
flow were reproduced reasonably well, and
the results gave considerable insight into the
behavior of the streamlines within the swirl
chamber.
"In keeping with the axismmetric nature
of the model, the overflow velocities need to
be specified as uniform around the
circumference of the weir. This was
accomplished -by using smooth power series
profiles. This procedure represented the
overflow velocity fairly well except near the
inlet where disturbances due to the baffle
plate occurred. The underflow, however, was
in reality withdrawn through a single port in
the floor rather than uniformly through an
annulus as assumed in the mathematical
model. For small values of the underflow
fraction, the differences were not large. For
sizeable underflows, significant
non-axisymmetric effects could have been
anticipated.
"An additional detail of the actual swirl
chamber which could not be modeled, was
the skirt which hung below the weir to trap
floatables. The computational mesh used for
the present calculation was too coarse to
permit this detail to be modeled without
causing numerical instabilities.
Particle Flow Calculations
"The particle flow within the swirl
chamber was calculated, assuming that with
sufficiently low concentrations, particle
collisions and coalescence could be neglected.
The effect of the particles on the structure of
the liquid flow field was also neglected. For
21
-------
sewage concentration less than 1000 mg/1,
these were both reasonable approximations.
Additional approximations were required to
calculate the particle flow. The most
significant approximation concerned the
effect of turbulence. The turbulent fluc-
tuating liquid velocity induced fluctuations
in the particle velocities. In addition, and
more importantly, it also causes a diffusion
of particles away from the paths they would
follow for a laminar motion. The modeling
of this effect was crucial because in the
absence of turbulence, the particles in many
cases would sink directly to the bottom.
The turbulence, however, scattered the
particles into the vicinity of the weir where
they were entrained with the overflow.
For this study, the effect of the turbulence
was accounted for by adding the approximate
diffusion terms to the equations of motion
and continuity. The eddy diffusion coefficient
was modeled in the same way as the eddy
viscosity for the liquid flow."
liquid flow."
Based on' the comparispns discussed in
the full report, the model appeared to be
quite satisfactory in its mathematical form.
22
-------
SECTION III
GENERAL FEATURES
The swirl concentrator must be sized to
function efficiently at a design flow based
upon the capacity requirements of the
collector system. It will be subjected to
widely varying flow and solids content
conditions characteristic of combined sewer
networks. For an essentially static device to
perform efficiently under such conditions,
special attention must be given to the various
pertinent elements within the chamber as
learned from the modeling study.
Figure 7, Isometric View of Swirl
Concentrator, identifies the various special
features hereinafter discussed.
(a) Inlet Ramp—The inlet ramp was
designed to introduce the incoming flow at
the bottom of the chamber while preventing a
surcharge on the collector sewer immediately
upstream. The principal purpose of
introducing the inflow at the chamber floor is
to introduce the solids at as low a position as
possible. The slope of the ramp chosen in the
hydraulic model was 1:2. Greater efficiency
of separation can be expected as this slope is
decreased, making the inflow less turbulent.
Local conditions will govern as modifications
to the collector sewer upstream of the
chamber may be necessary to reduce the
slope, and the affected section of the
collector sewer would be surcharged during
overflow periods.
The floor of the inlet ramp should be
V-shaped to the center providing self-
cleansing capability during small storm flow
events or delay of the hydrograph and a
channel for the peak dry-weather flow. It is
recommended that the minimum crossflow be
one inch per foot.
It is essential that this ramp and its entry
port introduce the flow tangentially so that
the "long path" maximizing solid separation
in the chamber may be developed.
(b) Flow Deflector-The flow deflector is
a vertical free-standing wall which is the
straight line extension of the interior wall of
the entrance ramp extending to its point of
tangent. Its location is important, as flow
which is completing its first revolution in the
chamber strikes, and is deflected inwards,
forming an interior water mass which makes a
second revolution in the chamber, thus
creating the "long path."
Under the energy conditions normal to
combined sewer flows, rotational forces in the
chamber would quickly form a vortex of
negligible separating efficiency if the flow
deflector were not used.
The height of the deflector is the height
of the inlet port, thus ensuring a head above
the wall slightly greater than the weir height
during overflow events. This head passes over
the flow deflector after one revolution in the
chamber and acts as a damper on inflow thus
tending to keep incoming solids nearer to the
floor and clear liquid at overflow elevations.
(c) Scum Ring-The purpose of the scum
ring is to prevent floating solids from
overflowing. It, therefore, should extend a
minimum of six inches below the level of the
overflow weir crest and extend vertically
above the crest of the emergency weir. Its
diameter is such that its edge is located
vertically above the flow deflector, thus
further establishing a boundary between the
outer and inner flow masses. During overflow
events and because of the great difference in
volume of water overflowing and discharging
to the interceptor, the velocities of the outer
flow mass are much greater than those of the
inner flow mass, allowing solids in the inner
zone a greater opportunity to settle.
For large diameter scum rings-weir
configurations, the upward overflow velocity
component will be large. Any particles
entrained in this flow will be readily swept
out with the overflow. As the scum ring
diameter is decreased with constant weir
diameter the cross section area between the
scum ring and weir is decreased and the
upward velocity is increased.
(d) Overflow Weir and Weir Plate-The
optimum diameter of the overflow weir is not
totally dependent on the total design
overflow. The diameter must be such that an
underflow beneath the scum ring will not be
created that would allow floating solids to be
23
-------
inflow
overflow
Inlet Ramp
Flow Deflector
Scum Ring
Overflow Weir and Weir Plate
Spoilers
Floatables Trap
Foul Sewer Outlet
Floor Gutters
FIGURE 7
ISOMETRIC VIEW OF SWIRL CONCENTRATOR
24
-------
lost to overflow. Experiments in the hydraulic
laboratory indicated that the relation between
the wejr diameter and the scum ring diameter
should be 5:6.
The weir plate connects the overflow weir
to a central column, carrying the overflow
liquid to discharge. Its underside acts as a
storage cap for floating solids directed
beneath the weir plate through the floatables
trap. The vertical element of the weir is
extended below the weir plate to prevent
floating material escaping to overflow. The
weir should be extended a minimum of
eighteen inches below the weir plate, but not
lower than the top of the flow deflector.
The mathematical model studies
evaluated the efficiency of two weir sizes on a
36-ft diameter swirl concentrator. The results
are recorded in Table 4. This information is
valid when considering a device not equipped
with a scum ring. If floatables are to be
collected, the diameters mentioned in the
table are for the scum ring, and the ratio of
weir to scum ring is 5:6.
TABLE 4
Effect of Weir Size on Concentrator Performance
% Captured
Particle Settling Velocity 24-ft 32-ft
(prototype scale—ft/sec) Weir Weir
0.0275 31.2 27.6
0.717 63.1 51.6
0.212 93.2 79.4
0.432 100.0 90.3
The efficiency does not take into
consideration self-cleansing.
(e) Spoilers—Spoilers are radial flow
guides, vertically mounted on the weir plate
extending from the center shaft to the scum
ring. They are required to break up rotational
flow of the liquid above the weir plate, thus
increasing the capacity of the overflow
downshaft. These spoilers should extend in
height from the weir plate to a position
approximately six inches above the crest of
the emergency weir, thus ensuring efficient
and controlled operation of the swirl
concentrator well beyond the design flow and
preventing formation of a free surface vortex
under all loading conditions.
Figure 8, Photograph of Final Form
Surface Flow Condition, indicates the effect
of the spoiler in elementary vortex conditions
at low flows and the extreme turbulence
developed when vortex conditions are
reached.
(f) Floatables Trap-A surface flow
deflector extends across the outer rotating
flow mass and directs floating material into a
channel crossing the weir plate to a vertical
vortex cylinder located at the wall of the
overflow down shaft. Floating material is
drawn down beneath the weir plate by the
vortex and dispersed under the plate around
the down shaft. The trap and its deflector are
located at the point of least surface velocity
in the liquid mass outside the scum ring.
Location of the device in other positions
resulted in floating materials which were
collecting at the mouth of the channel being
swept under the deflector and scum ring, and
then over the weir to overflow. The depth of
the deflector should coincide with that of the
scum ring. If lower, eddy currents under the
deflector will increase the loss of floating
material into the overflow.
Figure 9, Photograph of Final Form
Floatables Handling, shows the handling of
floatables by the hydraulic model.
(g) Foul Sewer Outlet—The foul outlet is
the exit designed to direct peak dry-weather
flow and settled solids in the form of a
concentrated slurry, to the interceptor. It has
been positioned at the point of maximum
settlement of solids and is vortex shaped to
draw down the surface in dry-weather flow
thus improving the efficiency and reducing
the clogging problems of a horizontal orifice.
Its down draft velocities minimize deposited
solids in the vicinity and floatable materials
on the surface of the water at a depth of one
foot.
During the course of hydraulic laboratory
investigation, it was determined that the
optimum location of the floatables trap and
the foul sewer outlet were similar in plan
view. Consequently, they have been located in
vertical alignment so that these important
elements of the swirl concentrator can be
readily inspected from above the device.
25
-------
100 cfs Storm Overflow
3 cfs to Foul Sewer
162 cfs Storm Overflow
3 cfs to Foul Sewer
250 cfs Storm Overflow
3 cfs to Foul Sewer
350 cfs Storm Overflow
6 cfs to Foul Sewer
FIGURE 8
PHOTOGRAPH OF FINAL FORM SURFACE FLOW CONDITIONS
-------
Floatables Trap
Floatables Emerging Under
Weir Through Trap Cylinder
Polythene and Alathon Trapped
Under Weir After 100 cfs Test
Random Settlement of Floatables on
Floor After Storm
Note Vortex at Foul Outlet
FIGURE 9
PHOTOGRAPHS OF FINAL FORM FLOATABLES HANDLING
27
-------
(h) Floor Gutters—The primary floor
gutter is the peak dry-weather flow channel
connecting the inlet ramp to the foul sewer
outlet. Its location has been chosen to
eliminate shoaling of settled solids.
A secondary gutter follows the wall of
the overflow downshaft and aids the primary
gutter in the minimization of deposits.
Although rectangular shaped gutters were
used in the laboratory model, a semi-circle of
pipe section should prove more efficient in
minimizing shoaling of solids.
(i) Floor Shape—Under design flow
conditions, flat floors performed very well;
however, at low flow conditions and reduced
chamber velocities, settlement to the floor
and local shoaling becomes a problem.
Therefore, the floor should be sloped toward
the center. A minimum slope of one-quarter
inch per foot is desirable to permit the
chamber to be flushed out.
To facilitate flushing out the chamber a
ring water main should be installed around
the outer perimeter wall with radial jets to
flush the floor clean following storm water
runoff events. For greatest efficiency, this
flushing action should be activated by level
control sensors, timed to operate as the water
level, on draining, reaches the floor level at
the exterior chamber wall.
With respect to the general configuration
of the swirl concentrator, increasing the depth
or the width of the chamber will have the
effect of reducing the available energy for
transporting settled solids to the foul sewer
outlet which may result in shoaling problems
with coarse, or heavier solids. Reducing the
depth or the width of tne chamber will have
the converse effect, heavier material will be
directed to the foul sewer, shoaling will not
be a problem, but fine materials will not settle
and will be lost to overflow.
Small changes in the design of the
concentrator and its appurtenant elements
may produce wide variations in its operation
efficiency. In this regard, particular care must
be taken during design and construction to
avoid irregularities or intrusions in the walls,
floors, and elements of the device.
Efficiencies of solids separation noted in
this report relate to specific gravities, sizes,
and concentration mentioned in Section II.
Such conditions of size and specific gravity
may not reflect local conditions. If, for
example, grit is a problem in a particular
design area, scaling down of concentrator
dimensions established by the hydraulic
design should be considered. An examination
of the mathematical modeling design methods
in Appendix 2 will indicate necessary
adjustments for greater removal efficiency of
specific particle types.
28
-------
SECTION IV
DESIGN OF SWIRL CONCENTRATOR FACILITIES
Hydraulics
Three flow quantities must be considered
in the design: (1) the peak dry-weather flow;
(2) the design flow, i.e., the flow for which
the optimum treatment is desired and (3) the
maximum flow likely to occur through the
chamber.
The peak dry-weather flow should pass
through the chamber without delay while
being retained in the gutter. The diameter of
the foul outlet for the dry-weather flow
should be a minimum of 8 inches and
preferably be 10 or 12 inches. At low flow
rates, discharge through the outlet pipe may
occur as gravity flow while at higher flows
discharge will occur as in a pressure pipe. It is
difficult to size the pipe to act as a "throttle"
pipe to pass a specific peak dry-weather flow.
Therefore, it is recommended that a sluice
gate or other flow control device be installed
on the pipe in a manhole located outside the
chamber. The use of a gate will permit
adjustment of the opening and the discharge
rate; further, it will allow the use of larger size
pipe with less chance of clogging and, if
clogging occurs at the gate, the gate can be
opened to clear out the debris.
The use of a manually operated gate with
a fixed opening (between adjustments) will
result in considerable variation in the
discharge rate through the outlet sewer due tc
variation in water level in the chamber.
Less variation in the discharge will occur
if a tipping gate is used instead of a manual
gate. However, this alternate would require
the installation of two manholes to provide
access to the upstream side as well as
downstream side of the gate for maintenance
purposes.
If it is necessary to limit the variation in
flow of the foul sewage to a minimum, then a
motor or cylinder-operated gate should be
used. Such gates could be controlled by either
the downstream water level or the water level
in the chamber. Electrical power would be
required to operate the gate.
Tipping, motor-operated and cylinder-
operated gates are described in the EPA
Publication, Combined Sewer Regulation and
Management, A Manual of Practice, and are
not further considered in this report.
The size of the facility will depend upon
the flow for which optimum treatment is to
be provided. For the purposes of this study it
was decided that a flow representing an
infrequent peak flow (165 cfs) should have
settleable solids in its flow reduced' by about
85 -percent of maximum removal by the
device.' On this basis it was found that for an
intermediate frequency flow (100 cfs),
optimum settleable solids removal would be
provided. As the cost of the facility and the
hydraulic head loss for dry-weather flows
increase with the flowrate to provide
optimum solids removal, choice of the design
flow and degree of settleable solids removal is
very important.
The amount and rate of flow of settleable
solids is not directly related to the total flow.
The University of Florida, as a subcontractor
to the City of Lancaster, developed through
computer modeling both outflow
hydrographs and pollutographs, . i.e., a
representation of the amount of specific
pollutants. Information concerning six storms
was provided as shown in Figures lOa and
lOb, Flow and Suspended Solid Load for Six
Storms. The -peak suspended solids load for
these storms did not occur at the same time as
the peak discharges.
An analysis was made of storms 4-6 to
determine an estimate of the pounds of solids
which might be lost due to the chamber size
criteria used. Table 5, Analysis of Pounds of
Suspended Solids Lost, Storm 5, is a'sample
of the calculation technique utilized. From
the Table, it can be seen that perhaps 344
pounds of settleable solids, or 17 percent of
the total settleable solids, may be lost during
the ninety minutes that the flow rate
exceeded 100 cfs. Table 6, Analysis of Six
Storms, indicates that due to size limitations,
if the flow exceeds 250 cfs, perhaps 15-20
percent of the total suspended solids may be
lost. It should be remembered, however, that
self cleansing efficiency is improved at smaller
diameters because of the tendency of the
29
-------
Storm 1
a
160
140
120
100
80
60
40
20
140
120
100
o
a
60
40
20
Hour of max. intensity
0.81 in. rainfall.
Total rainfall—
1.21 in. in 5 hours
234567
Time* (x 10)
10
/»
/\
Storm 3
Hour of max. intensity
0.51 in. rainfall
Total rainfall—
0.82 in. in 7 hours
a
40
20
, 10
Key: Q cfs
— s.s. Ib/min.
/\
\
Storm 2
Hour of max. intensity
0.30 rainfall
Total rainfall—
0.60 in. in 7 hours
45678
Time*(x 10)
10
FIGURE lOa
FLOW AND SUSPENDED SOLID
LOAD FOR SIX STORMS
*Minutes from start of storm (i.e., 6 = 60 minutes)
30
-------
Storm 4
Hour of max. intensity 1.54 in.
1.54 in. rainfall
Total rainfall—
2.16 in. in 4.5 hours
Key Q cfs
— •— s.s. Ib/min.
Approx. 5 year storm
Hour of max. intensity
1.85 in. rainfall
Total rainfall—
1.85 in. in 1 hour
34567
Approx. 10 year storm
Hour of max. intensity 125
2.30 in. rainfall
Total rainfall-
2.3 in. in 1 hour
1234 56 78 9 10 11
Time*(x 10)
FIGURE lOb
FLOW AND SUSPENDED SOLID
LOAD FOR SIX STORMS
34567
Time*(x 10)
9 10 11
*Minutes from start of storm (i.e., 6 = 60 minutes)
31
-------
TABLE 5
Sample Calculation
Analysis of Pounds of Suspended Solids Lost Due to Undersize Chamber
Storm 5
Time
15-20
20-25
25-30
30-35
35-40
40-45
45-50
50-55
55-60 or 1:00
1:00-1:05
Av. Q
cfs
295.3
271.7
219.1
192.1
167.0
148.0
135.8
124.5
111.2
98.2
1 .... Av. SS1
Mm- Ib/min,
5
5
5
5
5
5
5
5
5
5
Total Ib
94.0
38.7
39.1
39.8
31.7
31.9
32.1
35.8
43.9
52.6
Eff. of2
Recovery
47.5
58
71
76
84
90
94
97
99
100
Total
suspended solids for storm
Suspended3
Solids Not
Recovered
246.7
81.2
56.7
48.0
25.3
15.9
9.6
5.4
9 i
-0-
491 Ib
2,869.7
Ib settleable solids lost = 491 x 70% = 343.7 Ib
% not received = 4 x 100 = 17%
1 From University of Florida
2 From LaSalle Hydraulic Laboratory
3 Assume suspended solids and settleable solids overflow in equal proportions
TABLE 6
Analysis of Six Storms-Lancaster, Pa.
(data from University of Florida)
Settleable Solids
- Ib lost due to
QMax. SSMax. Tot SS size of regulator
Storm No. (cfs) (lb/rnin.) (Ib) (70%ofss)
1 42.3 172.4 3036.8 -0-
2 20.6 63.8 2285.6 -0-
3 65.5 134.8 3264.3 -0-
4 250.4 94.8 30981 114
5 310.4 14.6 2869.7 491
6 346.7 148.9 2858 9 433
-0-
-0-
-0-
5
17
15.2
32
-------
solids to shoal at low rotational velocities.
The maximum flow will determine the
elevation of the chamber with respect to the
inlet sewer. An important consideration is
whether the inlet sewer can be surcharged
and, if so, to what extent. Having determined
the permissible water level at the inlet sewer,
the circular weir must be set below this level
so the weir discharge will equal the maximum
flow. Equations are not available for
determining the required head over the
chamber weir; therefore, data obtained from
the hydraulic model runs must be used. Stage
discharge curves based on laboratory data are
given in Figure 18 of the LaSalle Report,
Appendix 1, for a 20-foot diameter weir. Data
derived from Figure 18 are plotted on Figure
11, Head Discharge Curve for Circular Weir,
to indicate the discharge per linear foot of
weir.
The discharge over the circular weir is
compared tc the discharge of a straight
sharp-crested weir with no velocity of
approach in Table 7, Head Discharge Data.
Between heads of 0.5 feet and 3.0 feet the
discharge of the circular weir ranges from 74
percent to 28 percent of that for a straight
weir. At the higher heads the flow over the
circular weir was affected by submergence of
the weir.
Assuming the maximum flow is 300 cfs
and the circular weir length is 62.8 feet, the
discharge per foot of the weir would be 4.8
cfs. From Figure 8 this would indicate a head
of 3.0 feet. Neglecting entrance losses this
would require that the weir crest be set 3.0
feet below the allowable hydraulic gradient of
the inlet sewer.
In some cases it may be permissible to
provide a side overflow weir on the periphery
of the chamber to take part of the flow when
the flow exceeds the design flow based on the
minimum size necessary to acheive the desired
removal of suspended solids. For instance,
assume the design flow is 165 cfs, the
maximum flow 300 cfs, the circular weir 62.8
feet long and a side weir 28 feet long which is
set 1.2 feet above the circular weir. Then the
conditions shown in Table 8, Combined
Discharge Over Circular and Side Weir, would
result.
Thus with the use of a side weir on the
periphery of the chamber, the circular weir
could be set 2.0 feet below the maximum
hydraulic gradient for a flow of 300 cfs
instead of 3.0 feet as required if the circular
weir were to take the entire flow
In the foregoing example, it has been
assumed that the discharge-head relations
shown in Figure 11 are applicable to a side
overflow weir. While this may not be correct,
no better basis for estimating the flow is
available.
Sizing
The results of laboratory model studies
on open hydraulic structures can be used to
determine the size of the prototype if the
geometry is made similar and the Froudes
number for the circular weir discharge are the
same. On this basis the discharge ratio of the
prototype to the model will equal the
five-halves power of the scale ratio.
For any given design discharge the
diameter of the chamber may be determined
from Figure 20, Appendix 1, Storm Discharge
vs Chamber Diameter Design Curve. From
Figure 20, the chamber diameters are 29.5
feet for 100 cfs and 22.5 feet for 50 cfs.
The other dimensions of the chamber
should have the same ratio to the diameter as
those in the model. These ratios are shown in
Figure 21, General Design Detail, Appendix 1.
The location of the various dimensions are
shown in Figures 12, 13 and 14, Plan and
Elevation. On the basis of the foregoing the
dimensions for design discharges of 50, 100
and 165 cfs are shown in Table 9, Chamber
Dimensions.
The percent of solids diverted to the foul
sewer can be obtained from Figure 22,
Appendix 1, for any given discharge. Thus, at
design discharge the flow through the foul
outlet will contain 90 percent of grit larger
than 0.35 mm and of settleable solids larger
than 1.0 mm. Smaller percentages of finer
materials would also pass through the foul
outlet.
It should be noted that the dimension d2
is the vertical distance from the invert of the
inlet sewer to the bottom of the chamber.
This drop was used in the model to prevent
33
-------
H
Feet
0.5
1.0
1.5
2.0
•2.5
3.0
TABLE 7
Head Discharge Data
Discharge in cfs/ft
Circular
Weir
0.86
2.04
3.15
3.98
4.52
4.85
Straight
Weir1
1.17
3.33
6.12
9.42
13.16
17.30
Ratio of Circular Weir
Discharge to
Straight Weir Discharge
0.74
0.61
0.52
0.42
0.34
0.28
TABLE 8
Combined Discharge Over Circular and Side Weir
Head-Feet
Circular
Weir
1.2
2.0
3.0
Side
Weir
0.0
0.8
1.8
Foul
Outlet
3
3
3
Circular
Weir
162
248
304
Side
Weir
0
45
102
Total
165
296
409
the inlet sewer from being surcharged. This
arrangement is not critical. If there is no
objection to surcharging the inlet sewer then
the dimension d2 may be decreased.
Design Elements
The primary element is the circular
chamber which normally would be
constructed of reinforced concrete. However,
it is not necessary to make the interior wall
surface a perfect circle and the use of
two-foot-wide prefabricated steel forms is
considered permissible.
The use of a flat floor in the chamber is
permissible. However, for drainage purposes,
it is suggested the floor have a minimum slope
of 1/4 inch per foot from the wall toward the
center.
The layout of the gutter is extremely
critical in elimination of deposits on the floor.
The foul outlet should be located at the 320°
position. The floor should have a circular
depression around the outlet sewer with a
diameter of about 3 times the diameter of the
outlet sev/er. While the gutter in the model
was rectangular in shape the use of a
semi-circular shape is permissible and
considered preferable for moving solids in low
flow periods. The gutter should have
sufficient capacity for the peak dry-weather
flow.
The size of the outlet sewer will be
governed to a large extent by the required size
of sluice gate on the outlet pipe.
The inlet to the chamber must be aligned
so as to introduce the flow tangentially to the
outer periphery of the chamber. An
important element is the "flow deflector," a
free standing wall extending from the
entrance of the inlet sewer to the 0° position
of the chamber. The top of this wall is the
same level as the bottom of the weir skirt and
is not connected thereto. Storm water
entering the chamber is directed toward the
outside of the chamber by this deflector.
Storm water rotating in the chamber passes
34
-------
I
-a
Discharge cfs per Linear Foot
FIGURE 11
HEAD DISCHARGE CURVE FOR CIRCULAR WEIR
over the deflector wall and tends to cause the
entering solids to be directed downward in
the chamber.
It is important that the inlet sewer enter
the chamber with its invert at the same
elevation as the chamber bottom. Meeting this
criteria results in more rapid settling of solids
to the bottom. In the model studies a ramp
with a slope of 1 on 2 was used in the
approach to the chamber. If it is possible to
surcharge the inlet sewer then the chamber
can be raised the amount of the surcharge and
the drop in the ramp decreased accordingly.
It is suggested that the "clear water"
downshaft and the weir be constructed of
steel. The use of steel rather than concrete:
(1) makes the structure thickness similar to
those used in the model, (2) may be more'
economical, and (3) will make it possible to
make revisions if further model studies or
operation results indicate revisions are
needed. The downshaft supports a horizontal
circular plate. The outer edge of the plate has
a vertical plate welded to it which forms a
weir above and a skirt below the plate.
So-called "spoilers" are vertical plates located
on the circular plate to prevent vortex action
in the downshaft. At least four to eight
spoilers should be used extending from the
edge of the downshaft to the weir. To prevent
floatables from flowing over the weir, a scum
plate is set away from the weir with the lower
edge of the scum plate 6 inches below the
weir crest. This scum plate can be supported
by the spoilers or by separate brackets
extending from the weir to the scum plate.
Other studies in combined sewer
regulators have indicated there is less
collection of debris on broad-crested weirs
than on sharp-crested weirs. Therefore it is
suggested the weir be semi-circular in shape
with radius of two to four inches.
35
-------
Sluice gate stand
Flushing
wafer pump///
motor
Sidewalk door *
over floo fable \
deflector
LManhole over
floatable riser
Superstructure
for stairs
Entrance aoor->
ROOF PLAN
-Inlet
sewer
ELEVATION D-D
Wa/k
2'min.
SCALE sr-o"
FIGURE 12
PLAN AND ELEVATION - ROOF AREA
36
-------
Shear
gate
Wall
opening
PLAN BELOW ROOF
ELEVATION C~C SCALE I =
FIGURE 13
PLAN AND ELEVATION - BELOW ROOF
37
-------
-Flow
deflector
Flushing pipe
PLAN B-B
deflector
ELEVATION A-A
FIGURE 14
PLAN ELEVATION - FLOOR AREA
38
-------
TABLE 9
Chamber Dimensions
(all dimensions in feet)
Design Storm Discharge — cfs
Diameter of Chamber = D2
Diameter of Overflow and
Diameter of Inlet = D!
Diameter of Circular Scum Ring = D3
Diameter of Circular Weir = D4
Radius of Inlet Gutter (0-90°) = Rj
Radius of Inlet Gutter (90-180°) = R2
Radius of Secondary Gutter (90-270°) R3
Radius of Secondary Gutter (0-90°) = R4
Radius of Secondary Gutter (270-360°) = R5
Difference in Radius Between
Secondary and Circular Weir = bj
Offset Distance for Determining
Gutter Radii = b2
Distance Between Floor and Top of
Circular Weir = dj
Depth Invert to Bottom of Chamber = d2
Height of Circular Weir = hi
Height of Scum Ring = h2
(Fig. 20, Apdx. 1)
1/6 D2
= 4D,
3 1/3 D,
= 21/3D,
= - 1 1/2 D,
= 5/8 D,
1 1/8 DI
32/3D,
= 1/3 D,
- 1/6 D,
= 1 1/2 D,
= 5/6 D,
= 1/2 D,
- 1/3 Da
50
22.5
1.25
0.62
5.62
3.12
1.87
1.25
100
29.5
1.64
0.82
7.38
4.10
2.46
1.64
165
36.0
3.75
15.00
12.50
8.75
5.62
2.34
4.22
13.75
4.92
19.68
16.40
11.48
7.38
3.08
5.54
18.04
6.00
24.00
20.00
14.00
9.00
3.75
6.75
22.00
2.00
1.00
9.00
5.00
3.00
2.00
The floatable deflector consists of a steel
plate extending from the outer wall of the
chamber to the scum ring and having the same
dimensions as the scum ring. From the scum
ring two plates form a passage one foot wide
to the weir. From the weir two plates resting
on the horizontal plate form a passage to a
point near the center. At this point a cylinder
is provided through the horizontal plate.
Vortex action at this point carries the
floatables to the underside of the circular
plate. The floatable deflector should be
constructed as shown in Figures 16 and 17c of
Appendix 1. The vortex cylinder through the
circular plate should be located directly above
the foul sewer outlet.
Design Features
Plans and sections through a typical
chamber are shown on Figure 14.
The provision of a roof for the chamber is
not necessary for functional reasons but is
considered desirable for safety and esthetic
considerations. Several openings are required
in the roof. A manhole 24 to 30 inches in
diameter should be placed directly over the
vortex cylinder for the floatables. This will
permit rodding of the cylinder in case of
clogging. Since the cylinder is located directly
over the foul sewage outlet this manhole will
also permit rodding of the outlet pipe. A large
sidewalk door should be provided to permit
removal of large floating objects. The size of
the door should be related to some extent by
the size of the inlet sewer and the possible
size of floating objects.
Three types of entrance stairs are shown
in Figure 6.1.3 of the Combined Sewer
Overflow Regulator Manual of Practice. The
preferred access is the use of a 38-degree
stairway with 73/4-inch risers, and 10-inch
treads surmounted with .a superstructure with
exterior dimensions of 13 feet by 5 feet by 8
feet high. Minimum openings of 2 feet square
should also be provided in the sluice gate
manhole and the overflow manhole.
An inspection walk should be provided
39
-------
around the periphery of the chamber with a
minimum width of two feet. The walk should
be located so that the weir and scum plate can
be cleared of debris if required. A pipe
handrail 42 inches high should be provided on
the walk and stairs.
After each storm the chamber should be
inspected. It may be necessary following
storms to flush down the bottom of the
chamber to prevent subsequent nuisance
odors. During the model runs in the
laboratory the material used, to simulate the
floatables collected under the horizontal
plate. When the water level receded some
material had a tendency to remain attached to
the plate. Floatables in an actual structure
will be subjected to heads of up to five feet
and this may cause the floatables to adhere to
the horizontal plate as occurred in the model.
Therefore, it may be necessary to remove the
materials by flushing after each storm. In
cities with many regulators, several days may
elapse after a storm before each regulator can
be inspected. Hence it is suggested that
automatic cleansing of the chamber bottom
and horizontal plate be provided.
If water used for this purpose comes from
a potable supply there should be no physical
connection between the supply and the
flushing system. A more feasible source of
flushing water may be either the nearby
receiving waters to which the chamber
discharges or the storm water that passes
through the chamber. The use of receiving
water requires the construction of a sump and
pumps. The use of storm water requires the
construction of a reservoir adjacent to the
chamber to store the storm water during the
storm so that it can be used after the storm is
ended.
One suggested method of using storm
water for flushing the chamber is shown in
Figure 12. This comprises a 4-foot-square
manhole 9 feet deep adjacent to the sluice
gate manhole. The capacity is about 1,000
gallons. Storm water enters the manhole
through a 12-inch- square opening in the
chamber wall set with top of opening level
with the circular weir crest. The opening is
covered with 1/2-inch mesh to prevent solids
from entering. The velocity parallel to the
chamber wall should keep the screen from
clogging. A shear gate is installed in the
common wall between the two manholes so
that the storm water manhole can be emptied
into the sluice gate manhole after each storm.
A vertical wet pit non-clog pump is used to
pump the storm water into the flushing lines.
A 4-inch-diameter pipe is installed on the
underside of the horizontal plate adjacent to
the skirt. This pipe has eight 3/4-Inch nozzles
aimed upward at the bottom of the plate.
When the water level in the chamber has
fallen to some point below the plate the
pump will operate for 5 minutes, discharging
80 gallons per minute at 40 psi.
For flushing the bottom of the chamber
another 4-inch-diameter pipe is attached to
the chamber wall at about weir level with
sixteen 3/4 - inch nozzles pointed straight
downward. When the water level in the
chamber has fallen to below the chamber
bottom the pump will again operate for about
5 minutes. The foregoing flushing procedure
is suggested for use on a trial basis.
Hydraulic Design
Most combined sewer overflow regulators
are designed for use in connection with
existing combined sewers and either existing
or proposed intercepting sewers. The vertical
distance between the hydraulic grade lines in
the combined sewer and interceptor must be
great enough to permit installation of the
regulator. It may be necessary to run through
the hydraulic computations at any specific
location in order to determine if the swirl
concentrator can be used. Table 10, Design
Example, indicates the nature of the
computations required to illustrate the factors
that should be considered.
In the following computation the "foul
sewer" is the outlet pipe from the chamber to
the sluice gate manhole and the "branch
interceptor" is the sewer from the sluice gate
manhole to the interceptor.
As stated previously, some type of
control device should be provided on the foul
sewer where it leaves the chamber. In the
following computations the control is
assumed to be a manually operated sluice
gate. This type of control will result in the
40
-------
TABLE 10
Design Example (from hydraulic model data)
Sample Computations
L = Length in feet
A = Cross sectional area in square feet
D = Diameter in feet
V = Velocity in feet per second (fps)
d = Depth of flow in feet
Q = Discharge in cubic feet per second (cfs)
b = Width of opening in feet
g = Acceleration of gravity (32.2)
C = Coefficient
W.S. = Water Surface
H.G.L. = Hydraulic Grade Line
E.L. = Energy Line
n = 0.013 (Manning)
S = Slope (ft/ft)
di = Depth of swirl concentrator
Interceptor
D = 3.0; invert el. = 10.0; W.S. = 12.4
Combined Sewer
D = 6.0; invert el. = 19.14; S = 0.005
Peak Dry Weather Flow = 3 cfs
Design Flow = 165 cfs
Maximum Flow = 300 cfs
Invert H.G.L. E.L.
Interceptor
Assume 10 00 \2AQ
Branch Interceptor
L = 100ft., Q = 3 cfs
D = 1.0ft., S =0.007
V(full) = 3.8 fps
d/D = 0.8
V(0.8 full) = (1.14) (3.8) = 4.3
V2/2g = 0.28ft.
Set downstream end so flow line
is same as interceptor 12.40
Invert 12.40-0.8 11.60
Exit loss = 0.28; 12.4 + 0.28 12.68
Upstream end
Rise = (100) (0.007) = 0.70
11.60 + 0.70 12.30
12.40 + 0.70 13.10
12.68 + 0.70 13.38
41
-------
TABLE 10 (continued)
Invert H.G.L. EX.
Sluice Gate Manhole 12.30
Entrance lossvO.s) y- =0.14
13.38 + 0.14 13.52
Assume loss of velocity head in
manhole 13.52
Sluice gate
Use 12 inch by 12.inch gate
Assume opening 0.67 ft high
V " = 3/0.67 - 4.5 fps
V2/2g = 0.31ft
Exit loss = 0.31
13.52 + 0.31 13.83
Contraction loss at gate
0.3V2/2g = 0.09
13.83 + 0.09 13.92
Set gate invert at manhole invert 12.30
Use 1.0 ft square conduit
Top conduit 13.30
V = 3/1=3 fps
V2/2g = 0.14ft
13.92-0.14 13.78
Outlet Pipe
D=1.0 L=20 A = 0.785
Start pipe 1 ft upstream of gate 12.30
V = 3/0.785 = 3.8 fps
V2 /2g = 0.22 ft
Enlargement loss = (0.25) (0.22)
= 0.06
E.L. = 13.92+0.06 1398
H.G.L. = 13.98-0.28 13.70
L = 20ft S = 0.007
Rise = (20) (0.007) = 0.14
Upper end 12'.30 + 0.14 12.44
13.70 + 0.14 13.84
13.98 + 0.14 14.12
Use 90° C.I. bend
Length invert to bell 1.85 ft
Top of bell 12.44+ 1.85 = 14.29
Bend loss 0.25V2/2g = 0.06
E.L. = 14.12 + 0.06 14 18
H.G.L. = E.L. 14.18
H.G.L. is below top of bell at 14.29
42
-------
TABLE 10 (continued)
Invert H.G.L. E.L
Chamber Bottom
Gutter invert 14.29
Make gutter 0.75 ft deep
Chamber invert at center
14.29 + 0.75 15.04
Use transverse slope of 1 /4 in. per ft
Rise = (15) (1/4) = 3 3/4 in.
= 0.31 ft
Chamber invert at wall
15.04 + 0.31 15.35
Gutter
Try one-half 18-in. pipe
Length from end of ramp to foul
outlet = 64 ft scaled from Figure
16 (Appendix 1)
Total fall = (12) (1/4) = 3 in.
S = 0.25/64 = 0.004 " 0'25 ft
Q = 6^5 cfs (full pipe)
V = 3.7 fps (full pipe)
One-half pipe
Q = (0.5) (6.5) = 3.2 cfs > 3.0
OK
V = (1.0) (3.7) = 3.7 fps OK
Chamber Weir
For design flow of 165 cfs
dj = 9.0 (Table 9)
Weir crest 15.35 + 9.00 24.35
Weir diameter = 20 ft
Weir length = 62.8 ft
Weir discharge per ft
165 =2.6
Weir head = 1.2. (Figure 11)
H.G.L. for 165 cfs
24.35 + 1.2 25.55
Set emergency weir 28 ft long at
elevation 25.55
Determine W.S. for maximum flow
of 300 cfs
43
-------
TABLE 10 (continued)
By trial and error
H
Circular weir 2.0
Emergency weir 0.8
Foul outlet
Weir
H.G.L.
E.L.
Q
248
45
3±
296
Water surface 24.35 + 2.0
This is at 1 80° position
Assume same at 0° position
At 0° position area between
deflector and wall equals
(6)(9 + 2.0) = 66sqft
=4.6fps
V2/2g = 0.33ft
At 0° position
Inlet Pipe
D = 6ft A = 28.3sqft
V = 10.6
V2/2g= 1.74
Enlargement loss
(0.25) (1.74-0.33) =0.35
Required E.L
Required H.G.L.
Required invert so pipe is not
surcharged 25.29 - 6.0
Required vertical distance from
W.S. in interceptor to invert of
inlet sewer 19.29 - 12.40 = 6.89 ft
Determine flow to interceptor when
maximum flow is 300 cfs and W.S.
in chamber is 26.35
Assume 8.6 cfs
Interceptor
Assume W.S. as before
26.35
24.35
26.35
26.68
Invert
27.03
25.29
19.29
12.40
44
-------
TABLE 10 (continued)
Invert
H.G.L. E.L.
Branch Interceotor
D=hO;V= 11.0; V2/2g= 1.88
S = 0.06
Exit loss 1.88
Rise = (100) (0.06) = 6.00
Manhole
Entrance loss 0.5V2 /2g = 0.94
Sluice gate (from before)
A=0.67;V= 12.9 ;V2/2g = 2.58
Exit loss 2.58
Contraction loss (0.3) (2.53) = 0.77
Outlet Pipe
L=20 S = 0.06
Rise = (20) (0.06) = 1.20
Bend loss (0.25) (1.88) = 0.47
H.G.L. for 8.6 cfs
Actual H.G.L.
Therefore discharge thru foul outlet
will be about 8.6 cfs when maximum
flow of 300 cfs occurs.
greatest variation in flow to the interceptor
between dry and wet-weather periods. One
way to decrease the amount of the variation is
to design the branch interceptor to flow full
under peak dry-weather conditions. Increasing
the length of the branch interceptor will also
help to decrease the variation. Under these
conditions when wet-weather flows occur, the
flows will surcharge the sewer and the
hydraulic grade line will rise and limit the
discharge capacity.
If the variation in flow is too great, then a
tipping gate or motor or cylinder-operated
gate should be used instead of the manually
operated gate.
The hydraulic gradient and energy lines
for peak dry-weather flow should be
computed starting at the interceptor and
proceeding upstream through the sluice gate
manhole to the chamber. The quantity
diverted to the interceptor during storm
periods is determined in a similar manner by
14.28
20.28
21.22
23.80
24.57
25.77
26.24
26.24
26.35
trial and error method assuming various
discharges.
In the initial computation, the hydraulic
computations should start at the water
surface in the interceptor at peak dry-weather
flow. In subsequent trials it may be necessary
to raise the branch interceptor at its junction
with the main interceptor which will result in
flow at critical depth at the end of the branch
interceptor. In this case it may be necessary
to compute the backwater curve for the flow
in the branch interceptor to determine the
depth of flow at the upstream end. Figures 15
and 16, Hydraulic Profile for 3 cfs and 8.6
cfs, present the results of the design
computations for flow in the foul outlet.
Sizing from Mathematical Model
The sizing of the chamber in the
foregoing discussion is based on the results of
the hydraulic laboratory study as reported in
Appendix 1.
45
-------
h-
Chamber invert /$. O4 -
Buffer /nv&rf
Energy /me
12'fou/
<
12'Branch Interceptor
12.44
L'lOO O* /.O'
surface
FIGURE 15
HYDRAULIC PROFILE 3 cfs
fl2.40
-Weir crest 24,35
I i 2S.35 H.G.L. for 30OCF6
u I I r-2&.24 Energy line for &.G CFS in Foul Ouf/et
-*- ;
FIGURE 16
HYDRAULIC PROFILE 8.6 cfs
•12.40
46
-------
TABLE 11
Design Examples
(from mathematical model data)
Example No. 1
Design Q = 165 cfs
Remove 90% of settleable solids greater than 1 .0 mm (0.0394 inches) with specific gravity
of 1 .2. (To conform with Fig. 20, Storm Discharge vs Chamber Diameter Design Curve,
Appendix 1 ).
From Figure 30, Particle Settling Rates, Appendix 2:
Enter with particle diameter qf 0.039 inches and specific gravity of 1.2.
Then Vs = 0.145 fps
Then * = = __)5 = 2.57 x 106
From Figure 31, Scale Factor Diagram, Appendix 2:
Enter with * of 2.57 x 10s and
E of 90%
Then 9 = 0.16 and $ = 0.036
Use S = 16
ThenD= (16) (3) = 48 feet
This compares with 36 feet as determined from Figure 20, Storm Discharge,
Appendix 1.
Determine other dimensions of chamber from Figure 2 1 , Appendix 1 , General
Design Details.
Example No. 2
Increase size of settleable solids from 1 .0 mm to 2.0 mm
Design Q = 165 cfs
Remove 90% of settleable solids greater than 2.00 mm (0.078 inches) with specific gravity
of 1.2
From Figure 30, Appendix 2:
Vs = 0.28 fps
=* =9-59xl°4
From Figure 3 1 , Appendix 2 :
61=0.28 * = 0.078
°-4 -4
=12.8
S = -•
0.078
SayS=13
Then D = (13) (3) = 39 feet
47
-------
Concurrent with the hydraulic laboratory
iwork a mathematical model of the swirl
chamber was developed. This was the first
attempt to rationalize the design of such
devices to determine operating principles. A
method was developed for sizing the chamber
based on a given design flow and the desired
percentage removal of solids with a given size
and specific gravity. Hence, the applicaton of
this method is more universal than the
hydraulic laboratory model, which is based on
the removal of solids in a synthetic sewage.
The sizing of the chamber by the two
methods does not give exactly the same
results. This is primarily due to the difference
in interpreting the characteristics of the solids
used in the hydraulic laboratory model.
Hopefully the construction of the full size
chamber and the resultant testing thereof will
yield data which will confirm the design
methods.
For illustrative purposes the design
method developed in the mathematical model
is given in Table 11, Design Examples (from
mathematical model data)
From the Design Example based upon the
mathematical model for a solids size of 2.0
mm a chamber only slightly larger (39 vs 36
feet) will be required as compared to the
hydraulic model curve for a solids size of 1.0
mm. This is due, in part, to the different
interpretation of the relation of the gilsonite
size to the solid size in the prototype -
mathematical model deriving larger solids
sizes in the prototype for the gilsonite than
from the hydraulic model.
48
-------
SECTION V
IMPLEMENTATION
Consideration of the use of a swirl
concentrator as a combined sewer overflow
regulator facility requires an evaluation of
many factors which include:
1. hydraulic head differential between
the collector and interceptor sewers
and head available in collector sewer
to allow insystem storage;
2. hydraulic capacity of collector sewer;
3. design flow;
4. dry-weather flow and capacity of
interceptor sewer; and
5. amount and character of settleable
solids.
Although many of these items have been
mentioned in the preceeding sections of the
report, the importance of each will be
highlighted in order to emphasize the
importance of each point in a preliminary
evaluation of the use of the swirl
concentrator.
Hydraulic Head Differential. There must
be sufficient hydraulic head available to allow
dry-weather flows to pass through the facility
and remain in the channel. The total head
required for operation is shown in Figure 17,
Hydraulic Head Requirements. Determination
of the maximum elevation in the collector
sewer that can be utilized for insystem storage
and the differential elevation between the
collector and interceptor sewers is the total
available head.
The head required will vary directly with
flow and the outlet losses in the foul sewer.
If sufficient head is not available to
operate the foul sewer discharge by gravity,
an economic evaluation would be necessary to
determine the value of either pumping the
foul sewer outflow continuously, or pumping
the foul flow during storm conditions and
bypassing the swirl concentrator during
dry-weather conditions, perhaps with a fluidic
regulator.
Hydraulic Capacity of Collector Sewer
System. The facility must be' designed to
handle the total flow which might be
delivered by the collector system. Thus a
study of the drainage area must be made to
determine the limiting grade and pipe sizes
which control the quantity of flow. Solids
removal from a peak flowrate may not be
required. If the chamber is not designed for
such maximum flows, however, velocity
energies which could be developed at su'ch full
flow conditions should be avoided by
providing a bypass in the form of a side
overflow weir.
Design Flow. Selection of the design flow
for sizing the chamber should be
accomplished on the basis of a complete
hydrological study to determine frequency
and amount of precipitation which can be
anticipated as well as runoff hydrographs.
Computer models such as developed by the
University of Florida for USEPA can be of
assistance in determining the solids load
which may be associated with various
amounts and intensity of precipitation.
Provision of maximum solids removal for a
two-year frequency storm for the Lancaster,
Pennsylvania, Project was made on the basis
of engineering judgment and an evaluation of
local receiving water conditions. As the cost
of construction will increase in direct
proportion to design flow, an economic
evaluation should generally be used to select
the flow capacity. The efficiency curve for
the facility is rather flat over a wide range of
flows, resulting in perhaps large increases in
cost for marginal improvements in efficiency.
A major constraint in selecting large
design flows is the anticipated shoaling
problems of solids at low flow rates in large
facilities. Self cleaning is enhanced by reduced
diameters. This consideration may make it
desirable to design for lower flows,
particularly where some form of overflow
treatment is to be provided. Again the
computer model can be used to determine the
magnitude of the solids carry-over problem to
the secondary device.
A third consideration is the maintenance
of low-inflow velocities, with turbulence
minimized. At the design flow the inflow
velocity should be in the range of three to five
fps. The inflow velocity may require
49
-------
Maximum elevation-
of flooding in
collector sewer
Overflow weir (side)
Overflow weir (central)
Collector sewer
invert —
Foul outlet
height of flow
over weir
Interceptor
sewer inlet
| chamber depth
I—
losses due to outlet,
J gate, connecting
X sewer and flow
through chamber
hydraulic
head required
FIGURE 17
HYDRAULIC HEAD REQUIREMENTS
reduction by enlarged pipe sections or other
means to achieve this rate.
Dry Weather Flow and Capacity of
Interceptor Sewer. Sizing of the foul sewer,
the foul outlet and the gutter depend upon a
determination of the dry-weather flow In
addition, the capacity of the interceptor
sewer to handle the foul flow must be known.
The foul sewer must be large enough to
maintain and not be subject to
blockage—usually a minimum 12-in. diameter.
However, the head on the outlet during
overflow conditions will allow considerable
variations in the foul discharge if it is not
controlled.
The efficiency of the chamber is affected
by the ratio of foul flow to overflow-
although there appears to be a broad
operating range over which reasonable removal
efficiencies can be maintained.
Maximum advantage should be taken of
capacity in the interceptor system,
particularly during the period when the
chamber is being drawn down. Thus, sensing
of the flow in the interceptor and the use of a
control gate on the foul sewer appear
desirable to obtain maximum results from the
use of the chamber.
Amount and Character of Settleable
Solids. The sewer system must provide
capacity to handle the increase in settleable
solids which will be captured from the
combined sewer overflow and discharged to
the treatment plant. In the case of Lancaster,
Pennsylvania, this could amount to more than
a ton of solids from one device in a very short
period of time. Additional grit removal and
sludge processing equipment may be
necessary. Should the foul flow be pumped,
sumps and pumps should be designed to
handle the anticipated high solids content.
If the settleable solids which can be
anticipated in the combined sewer overflow
can be defined by the amount, specific;
gravity, and particle size, the mathematical
and the hydraulic model may be used to
determine the size of the chamber required to
achieve desired levels of solids removal.
Ordinarily this will not be feasible and the
flow criteria developed by the hydraulic
model will be used to design the facility and
predict removal efficiencies.
In order to evaluate the efficiency of the
chamber, facilities should be provided for
sampling the inflow, foul sewer flow and
overflow. Settleable solids should be
delineated in all these flows. The quantity of
inflow and foul sewer flow should also be
measured. Difficulties in obtaining
representative samples from any of the flows
may make evaluation difficult. However, the
treatment plant or combined sewer overflow
50
-------
treatment facility, if used, should provide an
excellent means of making a gross evaluation
as to the effectiveness of the chamber.
Provision of a means to measure the
depth of flow over the weir should act to give
a reliable measurement of the flow when
added to the quantity" of flow to the foul
sewer.
Data from many full-scale operations,
operating with various flow conditions and
solid loadings will be necessary to properly
evaluate the usefulness of the swirl
concentrator as a combined sewer overflow
regulator.
Cost of Facility. The cost of construction
of the swirl concentrator will vary with the
length of inlet pipe which must be
reconstructed, the depth of the chamber and
the nature of the material to be excavated,
the need for a roof, and the general site
conditions under which the work will be
conducted. The materials of construction will
usually be concrete and steel and elaborate
form work will not be required.
For the Lancaster, Pennsylvania,
application where a 36-ft-diameter chamber in
limestone is contemplated, the preliminary
estimate of cost was $100,000 in 1972 costs.
This cost estimate included a roof, foul sewer
outlet control and a wash-down system. Site
construction problems are minimized in as
much as the construction will be off of the
street right-of-way.
51
-------
SECTION VI
POTENTIAL USES AND RESEARCH NEEDS
POTENTIAL APPLICATIONS
The principle which has been
demonstrated in this study project should
have application to facilities (other than
combined sewer regulators) which are
involved in, and affected by, liquid flows and
the presence of solid particles of various
diameters and specific gravities which must be
concentrated and removed from the liquid
flowfield. In the sanitary engineering field,
this could relate to sanitary sewer flows,
storm sewer flows, primary treatment
requirements for sewage treatment plants, and
concentration of settleable solids from
industrial and commercial wastes.
Each of the above applications in the
sanitary engineering spectrum may involve
less arduous conditions of operation than the
combined sewer regulator application. Both
the hydraulic laboratory and the
mathematical model investigation have
indicated that greater efficiency of solids
separation may be experienced if the device
operates under steady flow conditions, and if
a specific range of solids size and specific
gravity is to be removed. The hydraulic
laboratory studies concluded that the device
appears to exhibit preferential limits of grain
sizes separated according to the elements
being tested.
Future research should be directed at
narrower grain size bands. For example, a
chamber which was designed to separate only
the fines might do so with much greater
efficiency than the regulator device which was
designed to remove grit as well. Similarly, the
mathematical investigation report states, "It is
not clear whether better efficiencies can be
achieved with two half-size chambers or one
full-size unit. With two units, one chamber
could be used for all flows lower than 100
cfs . . (at the site of the proposed
prototype regulator where 165 cfs was the
design flow). . . and the second would be
required if the storm flow exceeded that
value. This might provide better separation at
both higher and lower flow rates. This
example corresponds to operating two
chambers in parallel and the concept cai
readily be extended to an arbitrary number o
units. The possibility also exists of operatinj
units in series to improve, i.e., classify, th(
solids particles to be removed."
The following applications of the swir
concentrator are not proven, but appear to bf
rational in light of the experience of the
current studies, basic hydraulics, and available
information from water and wastewatei
systems.
Primary Treatment Plant Application. Ir
the primary sewage treatment process
floating, suspended settleable solids ir
untreated sewage are reduced by plair
sedimentation, or fine screening. Therefore
the principal elements of primary treatmenl
are devices which assist in the physical
separation of sewage solids from their flow
This is the specific purpose for which the
swirl concentrator is intended. The principal
elements of primary treatment facilities which
could be considered include grit chambers.
primary clarifiers, and sludge thickeners. In
each of these applications, the range of
material sizes and inflow variation can be
reduced, increasing the probability of
efficient performance.
Grit Chamber. In the application of the
swirl concentrator as a grit chamber, two
design features are desirable. First, the device
should separate grit only; second, it should be
self cleansing under design operating
conditions. As the specific gravity of grit is
2.65, the ratio of design inflow to the foul
sewer outflow would be greater than that of
combined sewer overflow regulator design, so
that rotational velocities in the chamber
would be sufficient to move all the heavier
denser material to the foul sewer, and so great
that all the lighter solids fraction would
overflow to further treatment devices. Based
on current laboratory experiments, the device
could be sized so that shoaling of grit would
not be a problem. No mechanical collection
and removal would be required.
The grit fraction removed from the
sanitary sewage would require dewatering.
53
-------
This could be achieved by using conventional
grit collectors of the screw or cleaning bucket
variety. The advantage of this application is
the speed with which the grit can be removed,
and the reduced size or quantity of
conventional grit collection devices required
at the plant. No attempt should be made to
recover floating solids in this operation; they
would overflow to further treatment.
Primary Clarifier. The primary clarifier is
a sedimentation basin which normally
operates on a continuous flow basis.
Considering that the grit has been removed, as
described above, the function of the swirl
concentrator as a primary clarifier is the
removal of organic suspended settleable solids
and floating solids.
Removal of settleable solids would be
accomplished by reducing the rotational
velocity in the chamber sufficiently to
promote their settlement to the bottom.
Floatables could be separated by using a scum
ring and floatables deflector, sized and
located as in the regulator application, with
the optimum point of collection and
concentration of floatables determined by
further studies. It may be advantageous to use
coagulant aids to assist in the removal of
particles in suspension.
In a prototype sized primary clarifier
being tested in England, one of the most
serious difficulties encountered has been how
to ensure the continuous removal of sludge.
The greater the separation efficiency in the
chamber, the more difficult this became. It
was virtually impossible to operate the
clarifier continuously with a low foul sewer
flow without mechanical cleaning in the
England application. Base scrapers had to be
used and they were vane driven by the
rotational flow of the sewage.
Data developed by Smisson in England
indicate that a solution to this problem may
be to operate two swirl concentrator clarifiers
in series with sludge thickeners of the same
type, and with a percentage of the overflow
returned to the inlet. A significant decrease in
sludge shoaling has been achieved with a
return flow of less than 25 percent.
The principal advantage of the use of the
swirl concentrator as a primary clarifier is the
great reduction in time required to effect the
settlement as compared to standard
sedimentation basins. The standard separation
time is 120 minutes. The swirl concentrator
should achieve similar separation efficiencies
in less than 15 minutes. Thus the size and
space requirement of the swirl concentrator
would be 12.5 percent of current needs. This
application would reduce the area of the
plant, the construction materials required,
and the mechancial equipment and energy
required to move and collect solids.
Consequently, the capital, operating and
maintenance costs of primary treatment
facilities would be similarly reduced.
Sludge Thickener. The object of this third
potential application of the swirl concentrator
principle in primary treatment is to separate
and concentrate all solids delivered from the
primary clarifier so that the volume to be
handled in the digestor or other sludge
disposal facilities will be reduced. The specific
gravity of sludge particles approaches unity,
and the purpose of sludge thickening is to stir
sludge for prolonged periods for the purpose
of agglomerating the mass to form larger and
more rapidly settling aggregates of sludge floe
with less water content. To achieve this
phenomena in a swirl concentrator, it will be
necessary to operate the device with a very
gentle rotary motion under steady flow
conditions, so that the floe will not be
broken. The advantage of this application of
the swirl concentrator is" that thickened sludge
at the foul outlet should be available in
considerably less than the hours normally
ascribed to the process of sludge thickening
by standard stirring methods, thus reducing
the size requirement of a comparable swirl
sludge concentrator. Although the need for
mechanical equipment may be reduced in the
device, the use of a bottom sludge collector
mechanism may be necessary.
OTHER APPLICATIONS
Other potential applications of the swirl
concentrator offer rational possibilities in
related liquid-solids handling in the hydraulic
sanitary engineering field.
Wash Water Clarifier-Water Treatment
Plant. Serious concern has been expressed
54
-------
over the pollutional effect of discharging
filtered wash water into watercourses. To
overcome this hazard, these wash waters must
be intercepted and treated. Concentration of
the wash liquor in a swirl concentrator of
appropriate design offers the possibility that
approximately 80 percent of the wash water
solids could be concentrated in three percent
of the wash water flow, and be directed to a
predetermined point of disposal. The balance
of the flow would be permitted to overflow
to the receiving water without creating a
shock loading on the receiving waters.
Storm Sewer Pollution. A report entitled
"Water Pollution Aspects of Urban Runoff,"
prepared by the American Public Works
Association for the Federal Water Pollution
Control Administration, concluded that the
coarse or crude materials in street litter have a
marked pollutional impact on receiving
waters. These suspended solids are washed
into street inlets of storm sewers and can
create objectionable conditions at storm
sewer outlets, where they float or shoal in
receiving waters. In addition, organic
materials may decompose and produce
tangible oxygen demand upon receiving
waters while the cost of reducing pollution of
surface drainage water from urban areas may
be very high, it may become necessary in
some areas to treat storm water runoff before
it is discharged into receiving waters.
In such case, the foul sewer discharge
could be directed into an available interceptor
sewer for treatment either by gravity or
pumping, as required.
Improvement in the quality of such
separate storm sewer discharges could be
accomplished by swirl concentrator facilities
much in the same manner used for combined
sewer flows as described by the current study.
Soil Conservation. Sediment carried by
erosion represents the greatest volume of
waste entering surface waters.6 The volume of
such suspended solids reaching watersources is
at least 700 times greater than the total of
sewage wastes. One estimate is that the
average siltation yield at construction sites
during rainstorms is about ten times that for
cultivated land, 200 times that for grass areas,
and 2,000 times that for forest areas,
depending on the rainfall, land slope and
exposure.
Many agencies now require that special
precautions be taken by developers during
subdivision construction and by road
construction contractors. In spite of these
regulations, erosion of silt and topsoil from
construction sites can infuse downstream
receiving waters with suspended and settleable
solids, and make it necessary for new
landscaping material to be hauled to the
construction site, increasing the cost of land
development and other projects.
In subdivision construction, installation
of storm water utility services is one of the
first phases of a project. A swirl concentrator
could be placed at the downstream end of a
drainage project. Silt and topsoil could be
trapped at the site and used in landscaping,
rather than being discharged to a receiving
stream. Even if it is a temporary installation,
its cost may represent a minor part of the
overall value of the development.
Similarly, mine tailing wastes, particularly
from strip mines, have been allowed to run
off to receiving streams creating excessive
dredging costs and endangering downstream
reservoirs because of siltation. These tailings
could be concentrated in a swirl concentrator
and rehandled for backfilling at the mine site.
RESEARCH NEEDS
In order to evaluate these and other
applications, it will be necessary to
demonstrate by pilot studies the value of the
swirl concentrator principle outside the
combined sewer regulator field. Because of
the limitations of the tests carried out in the
current combined sewer study, ranges of
particle sizes and their specific gravities,
which produce greater separation efficiencies
are unknown. The size limitations of the swirl
device for the suggested purpose are also
unknown. It is understood that different
rotational velocities produce maximum
separation efficiency of specific particle size
and specific gravity ranges, but the
relationships are not yet defined. It has been
demonstrated that the concentrator can
produce maximum efficiencies when
operating under steady flow conditions, but
55
-------
in the sanitary engineering field this hydraulic
condition is rarely possible. Consequently, it
will be necessary to determine by research
what fluctuation in flow can be tolerated to
achieve an acceptable level of efficiency and
what inlet to foul sewer outlet ratio produces
the greatest separation efficiency, consistent
with self-cleansing velocity and for what type
particle.
These criteria must be answered through
continuing research aimed at examining such
applications and developing of design
nomographs and simple parametric formula
which will enable designers to exploit the
swirl concentrator to its fullest potential.
56
-------
SECTION VII
The American Public Works Association is deeply indebted to the following persons and their
organizations for the services they have rendered to the APWA Research Foundation in carrying
out this study for the City of Lancaster, Pennsylvania, and the Environmental Protection Agency.
City of Lancaster
Lester R. Andes, Director of Public Works
Consultants
Dr. Morris M. Cohn, Consulting Engineer
J. Peter Coombes, Consulting Engineer
Bernard S. Smisson, Bristol, England
Alexander Potter Associates, Consulting Engineers
Morris H. Klegerman
James E. Ure
General Electric Company, Re-entry and Environmental Systems Division
Harold D. Gilman
Dr. Ralph R. Boericke
Carl M. Koch
LaSalle Hydraulic Laboratory, Ltd.
F. E. Parkinson
U. S. Environmental Protection Agency
Richard Field, Project Officer, Chief, Storm and Combined Sewer Technology Branch,
Edison Water Quality Research Divison, National Environmental Research Center
William A. Rosenkranz, Chief, Municipal Technology Branch,
Office of Research and Monitoring
Darwin R. Wright, Chief, System Control and Optimization Section,
Office of Research and Monitoring
Meridian Engineering, Inc.
T. R. Darmody
University of Florida
Dr. Wayne C. Huber
57
-------
SECTION VIII
GLOSSARY OF PERTINENT TERMS
(as applied to the report on the swirl concentrator)
Deflector-A plate or plane structure
which diverts and directs flows in a swirl
concentrator chamber into desired patterns
and thus prevent flow kinetic conditions
which would interfere with optimum swirl
motion.
Combined Sewer-A pipe or conduit
which collects -and conducts sanitary sewage,
with its component commercial and industrial
wastes and inflow and infiltration waters at all
times, and which in addition, serves as the
collector and conveyor of storm water runoff
flows from street and other sources during
precipitation and thaw periods, thus handling
all of these types of waste waters in a
"combined" facility.
Depth of Chamber—The vertical distance
between the floor level in the swirl
concentrator chamber and the crest of the
overflow weir at the central downdraft
structure.
Exterior Liquid Mass-The liquid induced
to flow in the outer zone of the circular swirl
concentrator chamber, by use of the skirt, wall
structural configuration or other built-in
devices, where the higher velocities of flow
produce a longer liquid trajectory which
allows adequate time for heavier solids to
settle to the floor of the chamber.
Floatable Solids—Solids and congealed
liquid matter which are lighter than water and
float on the surface of the waste water
flowing in the swirl concentrator chamber.
Floatables Trap—A device or structural
configuration in a swirl concentrator chamber
which intercepts floatable solids, prevents
them from overflowing from the chamber
with clarified waste water, and retains these
materials at a desired location until removed
and disposed of by predetermined means.
Foul Sewer—The sewer carrying the
mixture of combined sewage and
concentrated settleable solids to the
interceptor sewer.
Gn7-Heavier and larger solids which,
because of their size and specific gravity,
settle more readily to the floor of the swirl
concentrator chamber by the phenomenon of
gravity classification.
Gutter-A structural configuration in the
floor of a swirl concentrator chamber which
serves as a channel for the desired flow of
dry-weather sanitary sewage flow from the
inlet to the foul sewer outlet, and for
conducting any other waste water
components to predetermined points of
concentration and exit from the chamber.
Interior Liquid Mass—The liquid induced
to flow in the inner zone of the circular swirl
concentrator chamber-by use of the- same
skirt, wall structural configuration or other
built-in devices which induce exterior liquid
mass flows—where the lower velocity permits
lighter solids to settle out of the waste water
flow and to deposit on the chamber floor and
to be drawn to the foul sewer outlet. The
principle of the swirl concentrator is to
organize the flow patterns and cause the
liquid mass to pass through the exterior and
interior liquid mass zones to optimize solids
separation and removal.
Overflow Weir-The structural member of
the swirl chamber, which is built as a central
circular wall with a proper form of overflow
edge over which the clarified waste water can
discharge to the downdraft outlet leading to
receiving waters or to holding or treatment
facilities.
Regulator-A device or apparatus for
controlling the quantity and quality of
admixtures of sewage and storm water
admitted from a combined sewer collector
sewer into an interceptor sewer or pumping or
treatment facility, thereby determining the
amount and quality of the flows discharged
through an overflow device to receiving
waters, or to retention or treatment facilities.
Scaling—The principle of ascertaining
dimensions and capacities of hydraulic test
units and mathematical analysis systems to
59
-------
evaluate the performance of swirl
.concentrator chambers, and to up-scale such
sizes to provide actual field design and
construction criteria or parameters.
Scum Ring-A circular plate or baffle
encircling the overflow weir, located at a
predetermined distance from the weir and at a
depth which will serve to retain floating or
scum material and other floatables and
prevent them from passing over the effluent
weir with the overflow liquid.
Settleable So lids-That portion of the
solids contained in the waste water flow into
a swirl concentrator chamber which will
subside and be collected in the chamber due
to gravity and other liquid-solids kinetic
conditions induced by the controlled swirl
flow pattern. (Note: Not all suspended solids
are settleable solids, nor are so-called colloidal
solids or other finely dispersed solids
settleable solids.)
Spoiler (Energy Dissipating Baffle)—A
plate or structural plane constructed from the
scum ring to the weir plate in a swirl
concentrator chamber for the purpose of
preventing or dampening the development of
free vortex flow conditions and minimizing
agitation and rotational flow over the
discharge weir.
Static Regulator—A regulator device
which has no moving parts, or has movable
parts which are insensitive to hydraulic
conditions at the point of installation and
which are not capable of adjusting themselves
to meet varying flow or level conditions in the
regulator-overflow structure.
Storage Silo-A holding chamber,
constructed in the form of a "silo," for the
Lancaster, Pennsylvania overflow
management project, which will collect, store
and aerate overflow waste waters from the
combined sewer regulator facilities until these
liquids can be pumped back into the
interceptor sewer system or treated prior to
being discharged into nearby receiving waters.
Storm Frequency—The time interval
between major storms of predetermined
intensity and volumes of runoff for which
storm sewers and combined sewers, and such
appurtenant structures as swirl concentrator
chambers, are designed and constructed to
handle flows hydraulically without
surcharging and back-flooding; i.e., a
five-year, ten-year or twenty-year storm.
Swirl Concentrator—In the context
involved in this study and report, a device or
chamber with necessary appurtenant
structural configurations which will
kinetically induce a rotary motion to the
encering waste water flow from a combined
sewer, resulting in secondary motion
phenomena which will cause a concentration
of solid pollutional materials at a
predetermined location, from which it can be
diverted into the foul sewer, thereby
producing a partially clarified waste for
decantation or overflow into receiving or
storm overflow treatment facilities.
Vortex Separator—A device of general
structural configuration similar to the swirl
concentrator studied in the current project,
but which involves flow patterns that produce
less effective solids separation because of
turbulence and other uncontrolled
liquid-solids flow conditions.
Weir Plate—A plate or surface constructed
contiguous with the outlet overflow weir of a
swirl concentrator chamber, and a skirt
hanging below the weir, under which
floatables will be trapped and held until
released for removal from the chamber.
Weir Skirt—A plate hanging below the
swirl concentrator chamber overflow weir, to
assist in retaining floatable solids under the
weir plate and in inducing the shearing of the
chamber flow into an exterior liquid mass and
an interior liquid mass, thereby optimizing
the solids separation effectiveness of the swirl
concentrator principle.
60
-------
SECTION IX
REFERENCES
1. American Public Works Association,
Combined Sewer Regulation and Manage-
ment, 11022DMU 08/70, U.S. Environ-
mental Protection Agency, 1970, pp. 134.
2. American Public Works Association,
Combined Sewer Regulator Overflow
Facilities, 11022DMU 07/70, U.S. Envi-
ronmental Protection Agency, 1970, pp.
139.
3. Smisson, B., Design Construction, and
Performances of Vortex Overflows, [Pro-
ceedings, Symposium on Storm Sewage
Overflows, Institution of Civil Engineers,
May 4, 1967],pp. 99.
4. Ackers, P., Harrison, A.J.M., and Brewer,
A.J., Laboratory Studies of Storm Over-
flows with Unsteady Flovy, [Proceedings,
Symposium on Storm Sewage Overflows,
Institution of Civil Engineers, May 4,
1972], p. 37.
5. Prus-Chacinski, T.M., and Wielgorski, J.W.,
Secondary Motions Applied to Storm
Sewage Overflows.
61
-------
SECTION X
INDEX TO TABLES AND FIGURES IN APPENDICES
Appendix 1 - Hydraulic Model Study
Table 1 Test Removal Efficiencies Using Various Slot Widths .... 84
Table 2 Comparative Volumes of Gilsonite Recovered .... .97
Figure 1 Model Layout ... . 66-69
Figure 2 Whiteladies Road Configuration . . . 72-73
Figure 3 Model Simulation of Prototype Solids ... ... . 74-75
Figure 4 Stage I Modifications . . 76-77
Figure 5 Stage II Development . . . . .... 80-81
Figure 6 Stage III Development-Submerged Horizontal Slot Inlett .... .82-83
Figure 7 Stage III Development-Submerged Vertical Slot Inlet 86-87
Figure 8 Stage III Development-Submerged 6 ft x 6 ft Inlet 88-89
Figure 9 Velocity Contour Cross Sections for 100 cfs Overflow 90
Figure 10 Velocity Contour Cross Sections for 162 cfs Overflow . . 91
Figure 11 Floatables Trap Arrangements 92-93
Figure 12 Stage IV Proof Tests 94-95
Figure 13 15 cfs Hydrograph With the Stage IV Configuration ... .... 96
Figure 14 Deposition of Solids at Low Flows, Test 1 ... . 98
Figure 15 Deposition of Solids at Low Flows, Test 3 99
Figure 16 Recommended Configuration 100-101
Figure 17 Details of Special Structures Gutter Layout ... . . .102-104
Figure 18 Stage Discharges and Efficiency Curves . .106-107
Figure 19 Details of Weir, Scum Ring and Spoiler Assembly . . . . . . . 108
Figure 20 Storm Discharge vs Chamber Diameter . ... 112
Figure 21 General Design Details .113
Figure 22 Separation Efficiency Curve . .114
Appendix 2 — Mathematical Model Study
Table 1 Particle Sizes and Specific Gravity 148
Table 2 Effect of Weir Size on Concentrator Efficiency 159
Table 3 Effect of Chamber Depth on Concentrator Efficiency 163
Table 4 Effect of Foul Sewer Fraction on Concentrator Performance 168
Table 5 Sample Calculation of Concentrator Performance for a
Specified Particle Size Distribution 174
Figure 1 Cross Section of Swirl Concentrator 119
Figure 2 Comparison of Predicted Particle Settling Rates With
Measured Settling Rates 126
Figure 3 Illustration of the Method of Characteristics 130
Figure 4 Tangential Velocities, 0° Position 138
Figurr 5 Tangential Velocities, 0° Position '138
Figure 6 Tangential Velocities, 180° Position 139
Figure 7 Tangential Velocities 270°-Position 139
Figure 8 Effect of Skin Friction Coefficient on Streamlines 140
Figure 9 Effect of Skin Friction on Velocity Profiles 141
63
-------
Figure 10 Effect of Mixing Length Constant on Streamlines . . . . 143
Figure 11 Effect of Mixing Length Constant on Velocity Profiles 144
Figure 12 Comparison of Predicted Mathematical Model Velocities
Profile with LaSalle Data . ... . . . 145
Figure 13 Streamline Patterns for Base Case . 146
Figure 14 Details of Special Structure . . . . 147
Figure 15 Photographs of Flow Direction Utilizing One-half Inch Threads in
Laboratory Model . .148
Figure 1 6 Comparison of Particle Flow Mathematical Model Results with
Test Data . . . .149
Figure 17 Predicted Performance of Prototype Swirl Concentrator Versus Flowrate 151
Figure 18 Particle Trajectories and Concentration Profiles at 100 cfs
For 2 mm Gilsonite Particles . . . . . .153
Figure 19 Particle Trajectory and Concentration Profiles at 100 cfs
For .25-in. Petrothene^ Particles .... .154
Figure 20 Particle Trajectories and Concentration Profiles at 100 cfs
For 0.5 mm Gilsonite Particles . . 156
Figure 21 Particle Trajectories and Concentration Profiles at 100 cfs
For 0.3 mm Gilsonite Particles . . . . 157
Figure 22 Comparison of Crossflow Streamlines for 24-ft and 32-ft Weir . 160
Figure 23 Comparison of Velocity Contours for 24-ft and 32-ft Weir . ... .161
Figure 24 Effect of Weir Diameter on Overflow Velocity Profile 162
Figure 25 Comparison of Crossflow Streamline Patterns for Different Tank Depths 164
Figure 26 Comparison of Velocity Contours for Different Tank Depths .... 165
Figure 27 Comparison of Velocity Contours for Different Foul Sewer Fractions . .166
Figure 28 Comparison of Crossflow Streamline Pattern for Different
Foul Sewer Fractions ... ... 167
Figure 29 Effect of Underflow Sewer Fraction on Removal Efficiency . .169
Figure 30 Particle Settling Rates . . ... . 170
Figure 31 Scale Factor Diagram . . : . . . 171
Figure 32 Efficiency Curve for Prototype Scale . . . .172
Figure 33 Cumulative Distribution of Settling Velocities for
Prototype Stormwater Particles . . . . 175
64
-------
APPENDIX 1
HYDRAULIC MODEL STUDY
The hydraulic model study described in
this appendix was undertaken with the object
of developing the basic geometry for a swirl
concentrator best adapted to North American
conditions. Guidance was provided in this
work by earlier research carried out in Bristol,
England, by Mr, Bernard Smisson.
PRINCIPLES AND SCOPE OF STUDY
The general principle which Mr. Smisson
had developed did not fit into the definition
of known laws of either vortex or simple
settlement separation, but rather appeared to
be a controlled combination of the two.
Basically, his approach consisted of
introducing the combined sewer flows into a
cylindrical chamber, so that a rotational flow
was created in the chamber. A significant
portion of the heavier solid particles settled to
the floor, then migrated toward the center of
the chamber. The foul sewer outlet was
located to intercept this concentration of
pollutant materials, so that they could be
directed to the interceptor and thence to the
treatment plant. The clearer liquid overflowed
a central circular weir, to the outfall and
receiving waters.
Mr. Smisson's publications covered his
work up to 1967, and the first tests served as
a verification of these principles. Since 1967,
his research led him to modify slightly the
chamber geometry. The test program was laid
out to carry on from there, adapting his
principles to North American requirements.
The main difference in European and
North American conditions was the
discharge/chamber volume ratio. The aim was
to use a similarly sized chamber as Mr.
Smisson, but to treat from four to six times as
much flow.
The first model geometry selected was
based on the latest Smisson test data. This
was a flat floored chamber with central
column one-sixth the chamber diameter
supporting a weir approximately five-sixths of
the chamber diameter. A weir and weir skirt
plate were attached to the outer
circumference of the weir plate. The research
program investigated the importance of
chamber depth, shape of the entrance to the
chamber, and various weir diameters to obtain
the optimum recovery of settleable solids
through the foul outlet.
Mr. Smisson's latest work had also
included use of an oblique entry to the
chamber. With the flow directed across the
chamber from the chamber wall toward the
central shaft, it became possible to trap
floatables. He found that a skirt hanging
below the weir would retain the floatables
under the weir plate. When the water level
dropped in the chamber, these trapped
floatables descended on the water surface to
be evacuated through the foul sewer outlet.
The skirt also served the purpose of
creating a shear zone which effectively
divided the chamber into two parts; an
exterior liquid mass in which the flow moved
rapidly, and an interior mass which rotated
slowly Optimum separation could be
obtained by the proper exploitation of these
two zones; the longer trajectory in the outside
section would,allow sufficient time for larger
particles to settle to the floor, and the slower
movement in the interior mass would permit
settling of finer material. Manipulation of
these research parameters was directed toward
organizing the flow in the chamber to pass
continuously through the two zones so as to
take maximum advantage of their respective
characteristics.
Dimensioning of the model and scale-up
were based partly on the White Ladies Road
project1 in Bristol, with the object of using it
in a project being built in Lancaster,
Pennsylvania. At the same time all the testing
and results were treated as being applicable to
other installations at other locations, on the
basis that this type of device would be
adaptable, over a wide range of scale-up
ratios, to amenable projects anywhere.
Model Description
The swirl concentrator took the form of a
vertical cylinder 36 inches in diameter and 40
inches high, made of 1/2-inch plexiglass as
65
-------
Cleor outflow settling basin
Calibrated V- notch weir
A
Clear water overflow
outlet pipe - 4" plexiglass
Foul outflow settling basin
FIGURE 1
MODEL LAYOUT (Plan 1)
Foul outletpipe I tygon
flexible tubing
66
-------
Chamber Cylinder - '
plexiglass 36"
Small water supply
for solids injection
FIGURE 1
MODEL LAYOUT (Plan 2)
Water supply from
pumping station
67
-------
Foul outletpipe l" tygon
flexible tubing
Discharges returned
to pumping Station
Foul outflow settling basin
Calibrated V- notch weir
Clear outflow settling basin
FIGURE 1
MODEL LAYOUT (Section 1)
shown in Figure 1, Model Layout. The inlet
was a six-inch diameter polyvinyl chloride
(PVC) pipe, set at an arbitrary level with
respect to the chamber, and at a slope of
1:1000. A vibrating solids injection system
was placed on this supply pipe, nine feet
upstream of the chamber. Water supply to the
model through the pipe was taken directly
from the constant level tank in one of the
laboratory permanent pumping stations.
A movable one-inch diameter tygon tube
was placed inside the cylinder, beneath the
floor of the test chambers to pick up the foul
flow. The tube was led out the bottom of the
cylinder, and its free end could be raised or
lowered at will to control the discharge drawn
off through the foul outlet.
The overflow water outlet came up from
the base, on the centerline of the cylinder in
the form of a six-inch-diameter P.V.C. pipe.
Its level could be changed easily either by
adding or removing elements of the same
68
-------
Solids Hopper
Chamber Cylinder - 'A"
plexiglass — 36"
-------
inlet pipe with its round cross section was
built undeviatingly to the circular chamber
wall, directing flow around the chamber peri-
phery as shown by Figure 2, White Ladies Road
Configuration. A later modification provided
a wider and deeper enclosure in which
variations to the entrance form could be
fitted and tried.
Solids Simulation Relationships
Project consultants specified the materials
in prototype combined sewage that were
desired to be removed with the swirl
concentrator:
Solids Specific Diameter Concentra-
Gravity (mm) tion (-mg/1)
Grit 2.65 0.2-2.0 20-360
Setteable
Solids 1.2 0.2-5.0 200-1150
Floatables 0.9-0.998 5-25 10-80
A further definition was provided for the
organic settleable solids material with specific
gravity 1.2, by specifying its grain size
distribution as follows and as shown on
Figure 3, Model Simulation of Prototype
Solids:
Diameter-(mm) 0.2 0.5 1.0 2.5 5.0
Cumulative
Total -% 10 20 35 60 100
Simulation of these materials on the
model was considered on the basis of settling
velocities according to Stokes equation:
v = 3rf (as_aw)
where: V = settling velocity
d = particle diameter
H = water viscosity
3w = specific gravity of water
3s = specific gravity of solids
The material most used in the testing was
gilsonite, a natural hydrocarbon with specific
gravity 1.06 and grain sizes between one and
three mm. Following the Stokes relation at
1/12 scale, this material reproduces grit
between 0.36 and 1.06 mm, and settleable
solids between one and three mm.
Reference to Figure 3 indicates that this
grit range leaves a small part of the fines
unrepresented, as well as a wide part of the
coarser particles-. The coarser end of the scale
was assumed to be covered, since any larger
particles would obviously settle out if those
represented had settled. The fines at the lower
end were simulated with Petrothene®, a
compounded plastic with grain sizes between
two and four mm and specific gravity of 1.01.
Similar reasoning was followed
concerning the settleable solids. The large
gilsonite covered much of the middle size
range, and the larger particles were assumed
to have better settling characteristics than the
gilsonite. Therefore the large gilsonite
represented 65 percent by volume of the
settleable solids in the specified prototype
combined sewage. Two finer fractions of
ground gilsonite were tested to cover the
fines. The first, which passed 25 mesh and
was retained on 30 mesh, had a mean particle
diameter of 0.5 mm. The second, retained on
50 mesh had a mean particle diameter of 0.3
mm, thereby practically attaining the finest
particles specified of 0.2 mm.
The rates of solids injection normally
used corresponded to the 50-300 mg/1 range
in prototype for the development tests.
Proving tests later raised the solids injection
rate up to 1,550 mg/1, protciype.
Tests for removal efficiency of floatables
were carried out using uniformly sized
polythene particles 4 mm in diameter with
specific gravity 0.92 and Alathon®, another
plastic compound, with particles 3 mm in
diameter and specific gravity of 0.96.
Injection rates were varied from 30 to 150
mg/1 at prototype scale.
Testing Procedures
Although the basis for utilization of a
swirl concentrator involves its operation with
a continuously varying discharge over a storm
hydrograph, for testing purposes, quantity
steady state discharges were used. The
maximum discharge for which an appreciable
degree of solids removal could be attained for
the Lancaster application was taken as 165
70
-------
cfs. Optimum solids removal for flows of 103
cfs was desired at an actual flow of 0.32 cfs.
A few control tests were also carried out for
50 and 15 cfs. The development tests
consisted of putting the particular chamber
form on the model, then running steady
discharges simulating i 00 cfs and 165 cfs. A
few control tests simulated flood passage with
variable discharge hydrographs.
Two forms of measurement were used to
provide quantitative means of comparison
betwee-n the succeeding chamber
modifications. These were solids separation
and rotational flow velocity in the chamber.
Solids Separation Efficiency
The first measurements used various light
specific gravity solids which were selected to
simulate as nearly as possible the settleable
solids in combined ^ewers. This allowed
observation of the particle flow path within
the chamber, at the same time giving a
definite measure of the amounts of the
material which overflowed or were deposited
on the chamber floor, or were taken out the
foul sewer outlet. Observations on several of
the earlier configurations indicated that the
separating process was not always uniform in
time, indicating that measuring solids
concentrations was not a complete form of
measurement.
A system using a constant volumetric
measurement was devised. This consisted of
ejecting, at a predetermined rate, one liter of
the solid material into the given steady state
discharge. The test was continued until all
solids had been removed from the water in
the chamber; solids had either passed over the
weir, through the foul sewer outlet, or had
been deposited on the chamber floor.
Measurements were then made of the removal
efficiency which was defined as the total
quality of the solid material by volume which
was separated to the bottom foul sewer
outlet, plus all that deposited on the chamber
floor, the total expressed as a percentage of
the original full liter introduced.
Rotational Velocity Measurement
The second form of comparison was
measurement of the rotational velocity in the
outer, faster moving flow section of the
chamber. Only three points were taken
regularly-at the surface, in the middle and at
the bottom of the flow on a vertical line in
the center of the annular section between the
weir and the chamber wall at the 180°
position (see Fig. 2).
Study of these velocities served as an
indication of any tendencies to approach the
higher velocity ranges which had been found
earlier to cut down the removal efficiency.
Once the acceptable geometry of the chamber
had been developed, detailed velocity
contours were measured on four predeter-
mined radii. All velocity measurements were
made using a small propeller current meter.
DEVELOPMENT PROGRAM
The testing procedures described in this
chapter follow the various steps through
which the different chamber characteristics
were 'investigated, leading up to the final
optimum structure. Each basic form that was
tested is discussed, along with the various
alterations that were tried. Observations and
comments on each of these intermediate steps
are also included in order to aid future
researchers. Throughout the following
discussion, the flow given is the clear overflow
volume.
A . White Ladies Road
Configuration-The layout shown on Figure 2
was adapted from Mr. Smisson's 1967
publication of a project he had built in
Bristol, England. Tests were carried out first
without any deflectors in the chamber, and
gilsonite with specific gravity 1.06 and
particle sizes between one and three mm was
used.
Visual observation of flows in the
chamber immediately classed the conditions
as a free vortex. Velocity measurements
indicated velocities in the chamber in excess
of that at the inlet for the 100 cfs case, with
practically undisturbed rotational flow lines.
Very few gilsonite particles settled to the
bottom to be drawn off through the foul
sewer outlet; the rest remained in suspension
in the rotating water mass for several turns
before overflowing.
71
-------
FIGURE 2
WHITE LADIES ROAD CONFIGURATION (Plan)
72
-------
Deflector
T
18'
12'
Foul Outlet
A-A
Deflector
FIGURE 2
WHITE LADIES ROAD CONFIGURATION (Sections)
73
-------
ORGANIC SETTLEABLE SOLIDS SG = 1.2
4.0
Porticle size -mm
MODEL MATERIALS (a)
AND SIZE (b)
SIMULATIONS AT (c)
PROTOTYPE SCALE (d)
Particle size—mm
Gilsonite 1-3 mm SG=1.06
Gilsonite on 30 mesh SG = f.06
Gilsonite on 45 mesh SG = 1.06
Petrothene 2-4 mm SG = 1.01
FIGURE 3
MODEL SIMULATION OF PROTOTYPE SOLIDS
Also shown on Figure 2 is the location of
the flow deflector which was put into the
chamber adjacent to the inlet. The flow
conditions were vastly changed immediately,
with the free vortex being eliminated. Some
rotational movement remained, but in the
form of a gentle swirl, such that water
entering the chamber from the inlet pipe was
slowed* down and diffused with very little
turbulence.
This effect was particularly evident when
gilsonite was injected into the flow As
particles entered the basin, they spread over
the larger cross section of the chamber and
settled rapidly. Particles were entrained along
the bottom around the chamber and
concentrated by two secondary vortices
located under the lip of the weir, at
approximately positions 200° and 290° from
the inlet point. Foul sewer outlets at each of
these positions did not draw off all the
gilsonite: the greater part remained in
deposits on the chamber floor, out from the
central shaft. Volumetric measurements of
the total gilsonite recovery from both the foul
outlet and the floor deposit, for three tests
yielded the following results:
Storm Discharger Gilsonite Removal
Efficiency
50 cfs 97%
100 cfs 87%
162 cfs 65%
74
-------
o>
•3
100
50
o
PROTOTYPE GRIT SG = 2.65
0.5
1.0
1.5 2.0
Particle Size mm
MODEL MATERIALS
AND SIZE
SIMULATIONS AT
PROTOTYPE SCALE
(a) Gilsonite 1-3 mm
(b) Petrothene 2-4 mm
SG= 1.06
SG= 1.01
FIGURE 3
MODEL SIMULATION OF PROTOTYPE SOLIDS
Mr. Bernard Smisson reviewed the two
tests described, and indicated that these
findings agreed entirely with his own earlier
work. He also pointed out the direction his
most recent research was following and
proposed a means by which he felt the study
could be advanced rapidly.
Mr. Smisson had found that large
diameter weirs, with horizontal undersides
but no deflector walls gave light solids
removal efficiency even better than the
smaller diameter, sloping'underside weir with
deflector wall, as used in our second test
series. He also suggested that a smaller
diameter storm water down shaft would
improve efficiency.
In order to advance development as
rapidly as possible, full advantage of Mr.
Smisson's experience was taken, including
adoption of the following criteria:
• use a 6-ft-diameter central shaft
• use a spiral gutter from the inlet
sewe-r to the foul outlet for
dry-weather flow
• concentrate on flat, large diameter
weirs without any deflectors
underneath
• try to avoid drowning the inlet sewer
• test flat bottomed chamber
B. Stage I Modifications—As the first
departure from the original layout, the central
shaft was reduced to six feet in diameter. On.
the model it was made up of stacked elements
to allow for easy changing of the weir
elevations, ^and the original sloping floor was
retained, as shown on Figure 4, Stage I
Modifications.
Operating with this bask shape, tests
were carried out on three different weir
elevations, but with only the 24-ft-diameter
75
-------
Raised Flow
Guide — to simulate gutter
FIGURE 4
STAGE I MODIFICATIONS (Plan )
76
-------
A-A
B-B
FIGURE 4
STAGE I MODIFICATIONS (Sections)
77
-------
weir, and various floor configurations to
simulate a spiral gutter placed above the
existing floor.
Observations of the various tests, using
one to three mm gilsonite representing grit
between 0.3 and 1.1 mm, led to the following
conclusions:
« need more depth in chamber;
® put spiral gutter in floor, below floor
level, i.e., avoid any projections above
floor level;
• inflow sewer should be directed along
bottom of chamber;
» flat floor in chamber probably as
good as sloping floor; and
® with greater depth and bottom inlet,
try larger diameter weirs.
C. Stage II Modifications—As shown on
Figure 5, Stage II Development, tests carried
out in this series were concerned with the
chamber depth, weir diameters, and elevations
with respect to the inlet.
1. Chamber 13.75-15.75 Feet Deep-For
the first tests, the chamber floor was
dropped to a point nine feet below the
inlet pipe invert. The inlet itself was not
modified because of the importance of
the relative levels of the weir lips with
respect to the inlet and the chamber
floor.
The 24-ft weir was first set +1.75 feet
above the pipe center line (depth = 7.75
ft) giving free surface flow in the inlet
pipe for 100 cfs, and just submerged for
162 cfs. The flow impinged directly on
the weir periphery, and the resulting
turbulence combined with the low water
surface level (relative to the inlet) allowed
a higher portion of the gilsonite rise and
spill over the weir. Recovery of gilsonite
through the foul sewer outlet dropped to
75 percent for 100 cfs and 60 percent for
165 cfs.
Following this finding, the weir was
raised two feet (depth 9.75 ft) and the
gilsonite recovery efficiencies were 100
percent for 100 cfs and 75 percent for
165 cfs. At this new elevation, the 32-ft
weir was tested and found to give slightly
less efficiency at 100 cfs (95%), but more
at 162 cfs (87.5%). Deposits remained on
the chamber floor, so different positions
of the foul outlet were tested to try to
intercept more of the material as it
settled; 290° seemed to be the best
position.
2. Chamber 10 75-12.75 Feet
Deep—Tests were run for the 12-ft-deep
chamber, using both the 24-ft and
32-ft-diameter weirs, placed at the higher
levels, submerging the pipe inlet. A spiral
gutter was placed in the chamber floor to
give some indication of its effect, as
shown in Figure 5.
3 Chamber 7 75-10. 75 Feet
Deep—Exactly the same series of tests
was carried out with the chamber nine
feet deep.
Observations at this stage were:
a. Relative to each other, the weir must
be above the inlet and shielded from
the direct inflow. Tests should be
made on a submerged inlet
configuration which would leave free
surface flow in the pipe upstream. In
this approach, floatables should be
caught under the weir, and settleables
will reach the floor of the chamber,
and thus migrate more directly to the
foul outlet.
b. The greater depths of chamber, down
to 15 feet, gave only marginal, even
questionable, increases in gilsonite
recovery. Therefore, consideration
should be given to depths only to 12
feet for the inlet modification tests.
It should be noted" that with the
submerged bottom inlet, the weirs
would be lowered to give free surface
flow in the pipe. This means that the
water volume in the 12-ft chamber
corresponds approximately to the
water volume in the 9-ft chamber in
the previous tests.
c. The 32-ft diameter weir was better
for the 15-ft deep chamber only;the
24-ft weir was better for the others.
It would be desirable to check a 28-ft
weir as well in the next series of tests.
d. Grit sizes of solids carried toward
the foul outlet just as well on the flat
chamber floor as on the sloping floor.
78
-------
The spiral gutter must be placed
below the floor level.
e. The spiral gutter below floor level is a
valuable element in generating and
maintaining the circular motion in
the chamber; it aids in clearing the
grit deposits.
D. Stage III Developments-Modifica-
tions as shown in Figure 6, Submerged
Horizontal Slot Inlet, include:
• a plexiglass enclosure at-the entrance
into the chamber in which various
inlets could be fitted, and
• the floor of the chamber was set flat
at a level of five feet below the invert
of the inflow sewer
Working to this basic set of
characteristics, different inlet shapes and weir
diameters were tested, and their performances
evaluated with the usual two clear water
overflow discharges—100 and 162 cfs. At all
times the foul outflow discharge maintained
at three cfs.
Submerged Inlet Three Feet x Nine
Feet-No Skirt on 24-ft. Weir-All of the
previous tests had indicated that this
form of inlet should solve most of the
problems. However, as soon as it was put
in operation, it became evident that it
was disturbed by the rotating mass
already in motion, and the ensuing
turbulence rolled the incoming jet up the
chamber wall. The gilsonite, which
entered the chamber along the floor, rose
into the upper layers of flow due to
turbulence. From this position, a large
proportion of it went over the weir
before it had completed half a turn in the
chamber.
Several different flow deflectors and
ramps were tried in order to shield the
incoming flow from the exterior liquid
mass. The most efficient was the ramp
shown shaded on Figure 6. This
arrangement, with the 24-ft. weir
produced 90-percent removal efficiency
with 100-cfs clear flow, and 60 percent at
162 cfs. These figures in themselves were
not as good as previous results, however,
these were the first tests where all the
material removed exited through the foul
sewer outlet. There were no deposits left
on the chamber floor.
Submerged Inlet Three Feet x Nine Feet
with One and One-Half-Foot Skirt Below
the Weir—Adding a skirt below the weir
as suggested by Mr. Smisson's tests
represented an effort to induce a flow
pattern similar to that obtained with the
ramp in the preceding tests. The results
were most disappointing; for the 100-cfs
clear flow discharge, both the 24-ft and
32-ft weirs gave 90 percent recovery
efficiency of gilsonite, and both left
significant portions deposited on the
chamber floor.
The evaluation at this stage did not
incriminate the skirt below the weir; to
the contrary, it seemed to be working
well. However, it was evident that efforts
to direct" the flow under the weir in order
'to trap floatables was the source of the
problem. The flow entering the chamber
obliquely, moved across under the weir,
struck the opposite chamber wall and
welled up to the surface and over the
weir.
Once this problem was recognized, a
series of brief tests were carried out
trying different forms of vertical wall
deflectors as shown in dotted lines on
Figure 6. Use -of these deflectors resulted
in better removal efficiencies as the flow
was brought back to a tangential entry.
This constituted the first major
departure from Smisson's work. He had
found he could use oblique inflows to
great advantage to trap floatables under'
the weir and control the rate and location
of deposition of the settleable solids.
However, the fact that this was not
reproduced can be easily explained by
comparing discharges. The maximum
discharge that Mr. Smisson ha*d used, was
25 cfs, meaning that the LaSalle unit had
to handle between four and six times as
much energy in its chamber.
Vertical Slot Free Surface Inlets—In
proposing the inlet forms shown on
79
-------
B
Different Foul Outlet
Positions Tried
Dry Weather Flow Gutter
90'
FIGURE 5
STAGE II DEVELOPMENT (Plan)
80
-------
32
24'
Foul Outlet
3'9"
/
A-A
FIGURE 5
STAGE II DEVELOPMENT (Sections)
B-B
81
-------
Romp Deflector
il
m 11 \
/ i i /
Dry Weather Flow
Gutter 2' wide , I1 deep
FIGURE 6
STAGE III DEVELOPMENT
Submerged Horizontal Slot Inlet (Plan)
82
-------
.'el
Skirt Added
Below Weir
32'
24'
I--1
I
I
I — h
el
3-:
I /
rL3"
.FIGURE 6
STAGE III DEVELOPMENT
Submerged Horizontal Slot Inlet (Sections)
A-A
B-B
83
-------
Figure 7, Vertical Slot Inlet, the
following characteristics were being
sought:
* bring the flow into the chamber
tangentially,
* keep free surface flow for ease of
maintenance access,
• disregard floatables recovery, and
» avoid physical intrusion in the
chamber.
Slot widths of two and one half,
three, three and one-half and four feet
were tried as a means of evaluating the
importance of the inlet velocity. Brief
preliminary tests quickly eliminated the
24-ft and 32-ft weirs, since the 28-ft. weir
gave markedly better recovery
efficiencies. Table 1 presents the
pertinent results from these tests, using
the 28-ft weir, with the one and
one-half-foot skirt below it:
TABLE 1
Test Removal Efficiencies Using Various Slot Widths
Slot Vm at Gilsonite Floor
Width Discharge 180° Recovery Deposit
ft. (cfs) (ft/s) Efficiency
2 1/2 100 4.8 100% 10%
162 7.2 90% 5%
3 100 4.4 93% traces
162 7.0 83% none
3 1/2 100 4.3 82% 35%
162 6.1 80% 30%
4 100 3.9 97% 37%
162 6.7 75% 20%
The two and one-half-foot-wide slot
gave very good separation of the gilsonite.
The settlement to the floor immediately
upon entry to the chamber, combined
with concentration of the particles
against the wall further around drew the
gilsonite toward the foul outlet in two
revolutions. However, the high velocity of
rotation once again approached a vortex
form of flow.
The wider slots appeared to offer
smoother flow conditions in the chamber,
but their gilsonite recovery efficiency fell
off considerably.
Submerged Inlet, Six Feet x Six
Feet—This final inlet shape was chosen as
the means to combine the best
characteristics from the preceding tests.
First runs using the 28-ft weir with skirt,
and without any deflector in the
chamber, gave removal efficiencies of 95
percent and 75 percent for 100 and 162
cfs. These were encouraging results, but
they both left significant deposits on the
chamber floor—50 percent and 35
percent, respectively.
The 24-ft weir, with skirt but no
deflector, was tested. This produced
gilsonite removal efficiencies of 100
percent and 90 percent for 100 cfs and
162 cfs respectively; the first left 15
percent deposit, and the second left only
traces in the chamber after the test.
Tests were then performed using
Petrothene® granules, measuring between
two and four mm with a sg of 1.01. These
granules correspond in the prototype to
grit in the 0.2 to 0.3 mm range, and to sg
of 1.2 for material in the 1.5 to 2.5 mm
range, as indicated by Figure 3.
With the 100 cfs discharge, and no
deflectors in the chamber, 45 percent of
the Petrothene® was recovered through
the foul sewer outlet. After modifications
were made as indicated by Figure 8,
Submerged Six-ft x Six-ft Inlet, with a
six-ft-high deflector, 65 percent removal
efficiency was obtained.
Tests were then undertaken using
ground gilsonite. The first fraction tested
passed 25 mesh sieve and was retained on
30 mesh; i.e., a mean grain size of 0.5 mm
corresponding in prototype to 0.2 mm
grit or 0.5 mm material of sg = 1.2. Two
successive tests with this fraction at 100
cfs gave 35 percent and 42 percent
removal efficiency through the foul sewer
outlet; deposits were five percent and ten
percent respectively. Simulating 50 cfs
gave an 80 percent removal efficiency,
with 60 percent remaining in the form of
a deposit.
The second gilsonite fraction passed
the 30-mesh sieve and was retained on 45
mesh. The mean particle size of 0.3 mm
corresponds to about 0.1 mm grit and 0.3
mm •particles at sg = 1.2 in prototype.
With a discharge of 50 cfs, 50 percent of
84
-------
the material was evacuated through the
foul outlet, with 38 percent as a deposit.
At a discharge of 100 cfs, 28 percent of
the material was removed, with six
percent in the form of a deposit.
A series of point velocities was taken
for the 100 and 162 cfs cases and the
velocity contours drawn for the four
selected cross sections as shown on
Figures 9 and 10, Velocity Contour Cross
Sections for 100-cfs Overflow and 162
cfs.
Velocity Contour Cross Sections for 100
cfs and 162 cfs Overflow—An effort was
made to show the flow direction
deviations from the purely tangential by
means of thread tracers. A wire grid with
one-inch squares was placed across the
chamber at the 90° section. Thread
tracers two inches long were tied to the
wire intersections and photographed from
three positions—from downstream normal
to the flow, vertically down on the
section and looking radially inward along
the section. The threads were cut back to
one inch long and photographed again.
All photographs were taken with 100 cfs
clear discharge and 3 cfs foul sewer
discharge.
Scum Ring and Floatables Trap
The chamber layout as it had been
developed at this stage was acceptable in its
treatment of grit and settleable solids, but it
had no means of separating floatables. All
tests using an oblique entrance to the
chamber had been unsuccessful in trapping
floatables under the weir. Therefore, tests
were performed with a scum ring 28 feet in
diameter; this left two feet clear between the
weir and the scum ring, and four feet between
the scum ring and the chamber wall.
Polythene® grains four mm in diameter and
with sg = 0.92 were used as a test material.
Tests were carried out with the scum ring
alone, first with its lower edge at the same
level as the weir crest, then six inches lower.
When the scum ring was at the same level as
the weir, much of the Polythene® was drawn
under the ring, escaping over the weir crest.
With the ring six inches lower, the
Polythene® was held outside the ring at first,
but gradually was drawn under after several
revolutions in the chamber.
Two concepts of floatables traps were
tried. The first had a deflector across the
annular channel outside the scum ring, and
deflected the floating material through a hole
cut in the exterior wall of the swirl chamber
as shown in Figure 11, Floatables Trap
Arrangements. The floatables were retained in
the small ante-chamber on the model, while
the excess water was evacuated through a low
'level opening back into the swirl chamber.
This system worked well, but left the problem
of what to do with the trapped floatables
without adding a mechanical device.
As a second concept, the deflector was
placed to bring the material into a 1-ft-wide
channel cut through the scum ring and the.
weir. This channel arrived tangentially in a
2-ft-diameter vertical cylinder whose open
bottom was cut through the weir disc as
shown in Figure 11. As the floatables arrived,
they were pushed by the flow along the
deflector, through the channel, then were
swept around in the vortex that formed in the
cylinder and were drawn down under the weir
disc. Two forms of this arrangement were
tried; one with the vortex cylinder beside the
weir crest, and the second with the cylinder
half way between the crest and the clear
water downshaft. Repeated tests with the
second gave Polythene® recovery in the order
of 80 percent for 100 cfs, and 40 percent for
162 cfs. The first worked equally as well for
trapping the material, but allowed some tq
escape later. The second cylinder location, set
at the 225° position in the chamber appeared
desirable.
When the storm discharge was turned off,
the floatable solids under the weir dropped
with the receding water surface. The floor,
gutter and vortex foul sewer outlet shown in
Figure 11 were developed as an efficient
means of drawing off the floatables from the
surface while there was still about one foot of
water in the chamber. This did not remove
all the floatables, and some remained scattered
at random after draining.
85
-------
Different
Slot
Widths
Tried
Double Gutters
Each 2' wide by
I1 deep.
FIGURE 7
STAGE III DEVELOPMENT
Submerged Vertical Slot Inlet (Plan)
86
-------
Foul Outlet
A-A
Approximate Spillway
Ogee Form
B-B
FIGURE 7
STAGE III DEVELOPMENT
Submerged Vertical Slot Inlet (Sections)
87
-------
Open Topped Vortex
Foul Outlet
Double Gutters
FIGURE 8
STAGE III DEVELOPMENT
Submerged 6 ft x 6 ft Inlet (Plan)
Deflector
6'High
-------
B-B
FIGURE 8
STAGE III DEVELOPMENT
Submerged 6 ft x 6 ft Inlet (Sections)
89
-------
370° POSITION
FIGURE 9
VELOCITY CONTOUR CROSS SECTIONS FOR 100 cfs OVERFLOW
Later tests on the recommended
configuration showed that the 225° position
for the floatables trap was disturbing the
settleable solids movement on the chamber
floor. Successive changes moved the floatables
trap around to the 320° position. This was
the location finally retained. It offered good
floatables recovery (80% for 100 cfs),
introduced a minimum of disturbance for the
rest of the flow, and provides direct vertical
access to the foul outlet, which could be a
distinct advantage for visual inspection or
maintenance. In the final arrangement, the
vortex cylinder was moved in nearer the
downshaft, to be concentrically located above
the foul outlet.
Final Proof Tests-Stage IV Development
The 28-ft scum ring and floatables trap
placed on the 24-ft weir had modified the
flow conditions significantly, so a final series
of tests was carried out to check the
structure's overall operation.
A slope was put on the floor of the
chamber, dropping one foot along a radius in
the 15-feet distance from the chamber
periphery to the central downshaft. The
outside wall level was retained at the same
position as in the preceding tests; i.e.', five feet
below the inlet sewer invert, and nine feet
below the weir crest. This change was
incorporated in an effort to improve the
self-cleansing of remaining solids following a
storm.
90
-------
180° POSITION
270° POSITION
FIGURE 10
VELOCITY CONTOUR CROSS SECTIONS FOR 162 cfs OVERFLOW
Observation of the settleable solids
trajectories in the flow led to trying the
modified floor gutter layout shown in fine
dotted lines on Figure 12, Stage IV Proof
Tests; this proved to be inadvisable and after
several further changes, the optimum layout
was selected as shown in heavy solid and
dotted lines.
Tests were run injecting Polythene®,
Petrothene® and the large gilsonite. It was
immediately evident that the gilsonite was
settling out into significant deposits on the
chamber floor, for the most part outside the
gutters between the 90° and 270° positions.
Analysis of the results indicated that the
presence of the 28-ft scum ring was causing
flow conditions the same as the 28-ft weir,
which had been eliminated in earlier tests.
Attempts were made to get back to the
efficiencies of the 24-ft weir alone by cutting
off the skirt below the weir. A weir skirt of
one foot deep produced the best test results,
however, with this, a deposit of 15 percent of
the solids remained at 100 cfs and 30 percent
at 162 cfs.
In later tests the scum ring acted as the
limit between the interior and exterior flow
masses. Then the weir skirt could be lowered
to three feet without adversely affecting flow
characteristics in the chamber. The depth
provided greater floatables recovery.
These tests indicated the desirability of a
smaller diameter weir. The scum ring
submerged to a depth only six inches below
the weir crest imposed flow conditions similar
to that for a solid skirt extending to three feet
91
-------
Flootobles Deflector
Toward Outside
Floatabies Deflector
Toward Inside
FIGURE 11
FLOATABLES TRAP ARRANGEMENTS (Plan)
92
-------
Chonnel
Cylinder
B-B
FIGURE 11
FLOATABLES TRAP ARRANGEMENTS (Sections)
93
-------
FloatoMes
Deflector
FIGURE 12
STAGE IV PROOF TESTS (Plan)
94
-------
Flow Deflector
Foul Outlet
A-A
Flow Deflector
FIGURE 12
STAGE IV PROOF TESTS (Sections)
B-B
-------
- 9
4hr
NOTE:
—Read all discharges on left hand ordinate scale
—Read chamber water level on right hand scale
FIGURE 13
15 cfs HYDROGRAPH WITH STAGE IV CONFIGURATION
below the weir around the scum ring
diameter. Therefore, since the optimum weir
alone from the earlier tests had been found at
24-ft diameter, a 20-ft-diameter weir and
24-ft-diameter scum ring were tested. [
Confirmatory tests on this configuration
showed flow conditions very similar tb those
for the 24-ft weir alone, and the large
gilsonite recovery for 100 cfs was 100
percent, leaving just traces in the gutters, and
for 162 cfs, 85 percent recovery with no
deposit at all.
Short - Duration, Low - Discharge Storm
Hydrograph Passage
Three tests were performed to reproduce
the storm hydjograph relations shown on
Figure 13, 15 cfs Hydrograph with the Stage
IV Configuration. Gilsonite injection rates
were used to reproduce an approximate
prototype settleable solids concentration of
200 mg/1.
All these tests showed remarkably similar
characteristics. Each test was different,
although each adhered to the same general
pattern.
As the discharge began rising from 1.5 to
3.0 cfs, all the gilsonite passed quickly
through the chamber with the flow cohtained
in the main gutter. As soon as the flow
exceeded the capacity of the foul outlet, and
began to extend out and cover the floor, the
gilsonite movement slowed down quickly.
With one foot depth in the chamber, gilsonite
96
-------
was deposited in the gutter between the 60°
and 90° positions. Through a depth of five
feet, the gilsonite flowed into the chamber
but was deposited in the vicinity of the inlet.
All of the gilsonite was deposited in the
supply pipe as the level in the chamber rose
from five feet up to the weir crest level at
nine feet. The mass in the chamber was very
quiescent, with only a very gentle rotation.
This same characteristic continued until the
flood peak had passed and the level began
dropping.
As the flow went down, when the
chamber level reached 5.5 feet, large slugs of
gilsonite started coming out of the pipe, and
before the 5.0-feet-level was reached, a large
rush of gilsonite poured out of the pipe. The
mass was carried as far as the inlet ramp, and
was then redeposited. As the depth was
lowered, the agitation of the 1.5-cfs discharge
coming down the inlet gutter swept most of
the gilsonite deposit down underwater.
When the water surface was at 1.3 to 1.0
foot, the three tests showed divergent results.
The general pattern was for the incoming flow
to stir up and carry the gilsonite around in the
main gutter to the foul outlet. A large portion
of the discharge also spilled out of the main
gutter running across the chamber floor
toward the secondary gutter, carrying along
much of the gilsonite.
As the level dropped to the point where
all of the discharge could be carried by the
main gutter, the spill qver the floor toward
the secondary gutter was cut off, leaving
significant deposits on the floor. The volume
and location of these deposits differentiated
the individual tests. Table 2, Comparative
Volumes of Gilsonite Recovered, indicates
amounts of gilsonite recovered through the
foul outlet.
TABLE 2
Comparative Volumes of Gilsonite Recovered
Test Rising Natural Flush Manual
Hydrograph Falling Washout
Hydrograph of Model
1 26 18 56
2 22 56 22
3 26 26 48
The data for Tests 1 and 3 should be
considered as most representative, since Test
2 was artificially altered by temporary
blockage of the main gutter just as the final
flush was occurring. Figures 14 and 15,
Deposition of Solids at Low Flows, show the
deposits for Tests 1 and 3.
The tests showed that significant deposits
may remain after low flow discharges. An
automatic wash-out system should be
incorporated in the chamber design, with jets
directed to flush the inlet, the chamber
perimeter walls and the floor, including the
inside of the main gutter to minimize
maintenance following operation of the
concentrator.
It appeared that deposition in the sloping
inlet ramp area could be avoided if the floor
sides were sloped in toward the central gutter.
Another solution might be to have a
semi-circular lower half-pipe down the ramp
and flaired into the chamber floor. Neither
was tried on the model, but they could be
accepted as a design detail for prototype
construction.
7.5-Foot Deep Chamber Tests
As an added check to determine the
necessity of the nine foot depth (measured
from the weir crest to the floor level at the
perimeter wall), two tests were run with the
weir lowered to 7.5 feet.
The two standard steady flow discharges
of 100 and 162 cfs were run with the 1-3 mm
gilsonite injected at about the prototype 200
mg/1. rate, and Polythene® grains representing
floatables.
For the 100 cfs tests, 90 percent of the
gilsonite was recovered through the foul
outlet, and 70 percent of the Polythene® was
retained under the weir. With 162 cfs, only 60
percent of the gilsonite was recovered, and 50
percent of the Polythene® was trapped.
These efficiencies are less than the
performance with a nine foot depth. The
general impression gained from observation of
the flows was that the turbulence for both
discharges was greater, and more gilsonite and
Polythene® were* churned up into the upper
layers and discharged over the weir crest.
97
-------
>.
FIGURE 14
DEPOSITION OF SOLIDS AT LOW FLOWS, TEST 1
RECOMMENDED CONFIGURATION
Structural Layout
As shown on Figure 16, Recommended
Configuration, the recommended layout
incorporated a 36-ft diameter for the
chamber, a 20-ft-diameter weir, a 1.5-ft weir
skirt and a 224-ft-diameter scum ring, set so
its lower edge is just six inches below the weir
crest. The 6-ft x 6-ft-square submerged inlet
was retained as well as a two gutter floor
arrangement. Details of the open vortex foul
sewer outlet are shown on Figure 17, Details
of Special Structures, as well as the floatables
trap and vortex cylinder. If desired, the web-
skirt could be increased to as much as three
feet to maximize floatables storage capacity.
98
-------
FIGURE 15
DEPOSITION OF SOLIDS AT LOW FLOWS, TEST 3
Figure 16 also indicates the 1-ft slope
across the chamber radius. This slope appears
desirable from a maintenance standpoint.
Expected Efficiencies
In the normal procedure for the model
tests, a given volume of solids was introduced
.to a steady flow, and the recovery efficiency
specified in terms of the original volume.
Prototype operation will always be in the
form of a hydrograph passage, with varying
discharges and solids concentrations. In,
forecasting efficiencies for the prototype, a
simple system similar to that used on the
model was followed. Removal efficiencies are
expressed in percentages, representing the
amount of the various materials going out the
foul sewer outlet with respect to the total'
-------
Row
Deflector
Floatables
Deflector
o.A
Doubte Gutter, each 1-6" wide
0'- 9" deep
FIGURE 16
RECOMMENDED CONFIGURATION (Plan)
100
-------
Foul Outlet
A-A
24V Scum Ring
20'0 Weir
Flow Deflector
B-B
FIGURE 16
RECOMMENDED CONFIGURATION (Sections)
101
-------
Note Both gutters
|'-6" wide by 9" deep
Secondary gutter
goes down on h4 slope
to 9" depth below chamber
floor.
90°
FIGURE 17a
DETAILS OF SPECIAL STRUCTURES
GUTTER LAYOUT
amount entering the chamber over the storm
flow period.
1. Floatables: Specific Gravity 0.9-0.96.
Particles sizes between five and 50 mm.
The chamber should remove between 65
and 80 percent;
2. Grit: Specific Gravity 2.65. For
particles larger than 0.3 mm, removal
should be 90 to 100 percent with the
possibility of some minor deposits
confined to the gutters. Progressing
towards smaller particles, the efficiency
would drop, so that at 0.2 mm it would
be about 75 percent, and at 0.1 mm,
probably less than 50 percent;
3. Settleable Solids: Specific Gravity 1.2.
For particles larger than J mm, the
recovery efficiency should be between 80
and 100 percent. As shown on Figure 3,
this fraction represents 65 percent of the
102
-------
Gutter ond Outlet 9" deep
FIGURE 17b
DETAILS OF SPECIAL STRUCTURES
DETAILS OF OPEN VORTEX FOUL OUTLET
total amount of settleable solids in the
design solids concentration. Progressing
towards the finer particles, removal
efficiency would fall off so that for 0.5
mm, it would be about 30 percent and
for 0.3 mm, probably less than 20
percent.
Operation With Higher Discharges
It was proposed at a later stage in the
study that discharges far exceeding the
original design maximum of 162 cfs would be
considered. Tests with higher discharges were
carried out with both the 24-ft weir alone,
and the 20-ft weir with 24-ft scum ring.
The stage-discharge curves are shown on
Figure 18, Stage Discharge and Efficiency
Curves. The ends of the curves in the 320-350
cfs range indicate the flow limits found for
the model as it was constructed; the water
level was just splashing over the top of the
chamber. The water surface was very
irregular, with rotating waves, but a free
surface vortex was not developed due to the
dampening effect of vertical 'baffles (spoilers)
constructed on the weir plate which acted as
energy dissipators.
Spot checks were carried out dn
separation efficiency by using the large
gilsonite. The separating flow characteristics
in the chamber remained remarkably steady
up to about 250 cfs in each case, then they
seemed to break up. The separation
efficiencies, however, seemed to drop more
consistently as shown on Figure 18.
Comments on Model Test Results
Evaluation of the experience gained on
the model study of the swirl concentrator
chamber strongly supports the validity of tEe
basic principles of its operation. As was
pointed out earlier by Mr. Smisson, the flow
inside the chamber must not be allowed to
accelerate to the point where vortex forces
take control of the particle movements. The
particles must be allowed to settle either
through the water or along the perimeter wall
onto the chamber floor, and to be drawn
along by the swirl or the gutters towards the
foul outlet.
103
-------
Floatables Deflector
Floatables Trap
1/2" = r o"
0'6" i
Section A-A
1/2" = r o"
2'6"
FIGURE lie
DETAILS OF SPECIAL STRUCTURES
FLOATABLE TRAPS
104
-------
Other chamber configurations may exist
which could provide the required flow
characteristics, but that selected in this study
appeared the most practical as well as offering
high recovery rates for solids.
The following comments are offered on
the various elements in the chamber which
were studied. Similar remarks appear from
time to time in the Appendix, and in some
cases the views which follow may contradict
the earlier statements. This situation has been
retained purposely to show the evolution of
knowledge of the structure's operation, and it
is always the latter opinion which indicates
the latest state.
1. Inlet Port:
• must introduce the flow tangentially;
• with submerged inlets, top of inlet
must be either at same level or below
the lowest part of the scum ring;
• the square inlet was retained on the
model, but a round inlet with
diameter equal to the square side,
giving smooth, evenly distributed
flow would also be acceptable;
• inlet invert should come in on the
floor of the chamber so solids tend to
stay down and not be swirled up;
• on the model, flow arrived at the
inlet after dropping down a 1:2
slope, designed to keep free surface
flow in the sewer upstream, this
arrangement is not critical—what is
required is smooth even flow; if a
longer section at the lower level,
which would be submerged under
storm flows, can be provided, it
would be better. for the chamber's
operation; the least possible
turbulence in supply gives better
concentration of solids near the
bottom before entry to the chamber;
• the narrow vertical slot entrance 2
1/2-ft wide showed much promise,
and should be kept in mind for
further development if a completely
free surface flow system would be
desired;
• the inlet has a six-ft nominal
dimension, either square or round, in
the 36-ft-diameter chamber; it was
arrived at through the testing
program;
• this six-ft inlet can be independent of
the combined sewer diameter; if this
latter is a different size, a transition
would be necessary to introduce the
flow into the chamber, evenly
distributed through a six-ft inlet; and
• in scaling up prototype sizes, this 1:6
ratio between the inlet dimension
and the chamber diameter must be
adhered to.
2. Chamber Depth'
• the nine-ft depth retained in the final
structure was based partly on
performance criteria, partly on
practical considerations;
• the two shallower chambers tested
showed a slight drop off in solids
removal efficiency; and
• greater depths gave only marginally
better removal, and that was not
always consistent; these
unpredictable advantages were judged
so small that they did not justify the
extra expense for the deeper
construction.
Note: Chamber depth is the difference in
elevation between the nominal floor and
the overflow weir crest.
3. Chamber Diameter
• the diameter was not varied,
however, extrapolation of the depth
studies indicates that greater
diameters should give more efficient
solids separation.
4. Weir Diameter (Without Scum Ring)
• 32-ft-diameter weir was eliminated
early as it created a very quiescent
inside mass of water and deposits
covered much of the chamber floor;
• all inlet forms created jet impingment
on weir or skirt, causing turbulence
in the outer ring, allowing more
solids rise to go over weir;
• 28-ft weir had the same
characteristics as the 32-ft, but to
lesser degree;
• only exception was with 2
1/2-ft-wide vertical slot, with the
narrow slot; the 28-ft weir showed
105
-------
STAGE DISCHARGE CURVES
5.0-
I 4.0-
£
o
.!=
I
3
•o
o
20' Weir with 24* Scum Ring
3,0
2.0-
1.0 -
Sharp Crested Weir Formula Applied to
Developed Length of 20' 0 Weir
100
150
200
250
300
350
Clear Overflow Discharge - cfs.
FIGURE 18
STAGE DISCHARGES AND EFFICIENCY CURVES
promise;
if further research considers the
vertical slot, the 28-ft weir should be
investigated further;
24-ft weir when operating alone (i.e.,
no scum ring) offers optimum solids
separation and good settling
characteristics with still enough
velocity to entrain particles to- the
foul sewer outlet;
when used with 28-ft scum ring, the
24-ft weir reverted to conditions
found for 28-ft weir, i.e., serious
deposits on floor; and
20-ft weir in combination with 24-ft
scum ring gave optimum solids
separation, similar to the 24-ft weir
alone, as shown in Figure 19, Details
of Weir Scum Ring and Spoiler
Assembly.
5. Weir Crest Shape
• only two crest shapes were tested in
this study; the first had a sharp outer
edge created by a horizontal cutoff
of the 45° rising underside of the
cone on the White Ladies Road
configuration as shown in Figure 2;
the second was the simple
flat-topped vertical plate wrapped
around the weir disc for all other
tests;
• this latter form corresponded to a
flat section 1 1/2 inches across on the
prototype; with its vertical sides, this
could be considered as a sharp
crested weir;
• the stage-discharge curves for this
weir crest on the two last weir
diameters tested on the model are
shown on Figure 18; also shown for
106
-------
GILSONITE RECUPERATION EFFICIENCY
100-
^ 90
.£ 80
g
60
50
O 40
0
cc
«. 30
c
0)
« ao
10
20' Weir with 24' scum ring
24' Weir Alone
100 200 300 400
Clear Overflow Discharge - cfs.
FIGURE 18
STAGE DISCHARGES AND EFFICIENCY CURVES
comparison is the curve for a straight
sharp crested weir, 62.8 ft long, this
being the perimeter length of the
20-ft weir;
• this crest shape could be made round
topped for practical construction or
operating reasons without affecting
the chamber's separating
characteristics; and
• more refined weir crest shapes were
not investigated in the present study;
they were considered of secondary
importance as compared to the
overall flow patterns in the chamber,
but could be the subject of more
detailed research.
6. Flow Deflector
• fundamental approach to study was
aimed at avoiding any auxiliary
appurtenances in chamber; in spite of
this, flow deflector was found
necessary;
tests run without deflectors showed
build-up of rotational velocity and
reduction of solids separation;
the flow deflector was devised to be a
continuation of the inlet, and serves
two purposes; (1) it shields the
incoming flow from the rotating mass
in the chamber, hence avoids
turbulence which would make the
solids rise; (2) it guides the flow into
the inner zone;
deflector must terminate at height of
incoming channel to allow liquid
mass in chamber to pass over
incoming flow; this reduces tendency
for upward incoming velocity;
107
-------
24' Scum Ring
A <—» Pour flow spoilers
^^ I used on model
i I
6' 0 Cleorwoter
Oownshaft
12
10'
I'6"
I'6"
K
Spoiler
A-A
FIGURE 19
DETAILS OF WEIR, SCUM RING AND SPOILER ASSEMBLY
108
-------
• in the final form, the deflector does
not touch the weir, so must be
free-standing, six feet high,
reinforced at its base to withstand
the thrust of guiding the rotating
water into the interior water mass;
and
• the downstream end of the deflector
on the model was cut off square—it
could be rounded or parabolic in plan
if desired.
7. Scum Ring
• only one location of scum ring tried;
i.e., two feet outside overflow weir;
• when rings were placed at same
elevation as weir crest, serious loss of
floatables occurred under ring, then
over weir;
• when rings placed six inches below
weir crest elevation, good retention
of floatables was obtained up to 100
cfs with some losses at 162 cfs;
• depth six inches below weir is
acceptable; and
• scum ring is subjected to irregular
hydrodynamic forces; head
variations equivalent to three or four
inches of water should be considered
in designing structure that would
remain rigid in place during operation
and afford some measure of safety
from large floating objects.
8. Floor Gutter Layout
• extremely critical in reducing
deposits;
• plan shown was optimum evolved in
this program of tests, and its layout
should be adhered to with care and
model studies should be conducted
on any variations; for example, the
primary gutter shown dotted on
Figure 12 was laid out to follow the
predominant solids trajectory along
the floor: it proved very inefficient,
causing serious deposits beyond the
foul outlet, and stirring up the solids
so more went over the weir;
• gutter cross section 1.5-ft wide and
nine-in. deep retained as adequate to
"pass dry-weather flow.
9. Foul Sewer Outlet
• the position shown on the final
configuration at 320° resulted from
successive changes during the tests;
• at times it appeared desirable to
move back towards 270°, but when
this was done, deposits remained on
the floor against the downshaft
between 270° and 360°;
• first tests performed with horizontal
opening at end of gutter, one-ft x
two-ft were judged not as efficient,
and more subject to blockage, and
more difficult for visual inspection or
maintenance;
• open vertical outlet intercepted more
solids moving along floor and
provided easy visual and access
maintenance;
• vortex shape developed to draw
surface down with dry-weather flow;
also, after storm, floatables on
surface would be drawn down while
still about one foot of water
remained in chamber; and
• diameter of outlet should be capable
of permitting twice the sanitary flow
to prevent shoaling of deposits on the
chamber floor; the actual discharge
should be controlled by a gate.
10. Floatables Trap
• bottom of the floatables deflector
across exterior annular channel
placed at same level as scum ring for
best floatables diversion and
minimum flow disturbance;
• simple vertical deflector best, curved
as it crosses annular channel to meet
exterior wall; deflector should not
extend more than one inch below
water- surface to prevent eddy
currents from sweeping floatables
under the deflector and scum ring;
• canal and trap envisaged as simple
shop fabricated unit, possibly of
1/4-in. steel plate;
• location of vortex cylinder, which
passes down through weir disc, is
important; if too close to weir, loose
floatables would flow in current out
109
-------
under skirt; position as shown on
Figure 16 was efficient in keeping
floatables under weir and provided
access to foul sewer outlet;
« location at 320° for floatables trap
selected as optimum; and
• similar deflector approach possible to
divert floatables out through exterior
chamber wall; this was not pursued in
this test program but would merit
attention in any future studies if it
were desired to retain them.
11. Floor Shape
« flat floors performed perfectly
acceptably when flows are constant
or operating; and
• 1-ft slope toward center across radius
used to help clear floatables after
storm introduces effect of directing
some of the flow upward off the
deflector.
12. Spoilers
• from the beginning, tests showed that
discharge through the vertical
downshaft was seriously reduced if
rotational flow was allowed to build
up on the weir plate;
• spoilers, or radial flow guides were
constructed on the weir plate to
dissipate the rotational energy
components of the flow and to direct
the flow to the center outlet;
• in the final form, four 3-ft. spoilers
were adequate to control discharges
up to 250 cfs as shown in Figure 19,
Details of Weir Scum Ring and
Spoiler Assembly; and
• no limiting number of spoilers was
found on the model, but it would
seem likely that a practical limit
would be six to eight.
13. Prototype Construction Standards
• in the model, plexiglass and finished
concrete were used to reproduce the
chamber—they produce a Manning's
of approximately 0.008.
• scaling up from this to a prototype
12 times larger would give "n" =
0.013;
« this degree of smoothness would
correspond to a concrete finish inside
the chamber, using either smooth
wood forms or steel forms;
• care should be taken to avoid
projections into the flow period.
DESIGN CRITERIA
The model separation chamber used in
the present study had a diameter of three
feet, and was operated according to Froude's
scaling relations. Froude's law states that the
discharge between two geometrically similar
structures varies according to the five-halves
power of the linear scale between the two
structures:
QaX5/2
The design peak discharge used on the
model was 0.322 cfs, so the scale-up relation
between the chamber diameter, D2 , and the
peak discharge, Qd , can be expressed as:
This equation was used to draw the curve
shown on Figure 20, Storm Discharge vs
Chamber Diameter, and is presented as a
design curve for determining chamber sizes.
The design procedure is as follows:
1. The hydrological study for the given
application would be carried out
independently of this report. Resulting
from that study would be a storm
hydrograph giving the possibility of
runoff from various sized storms.
2. Take either the peak discharge from the
above hydrograph or determine from an
economic study the flow which can
economically be considered, say a two,
five or ten year storm, and consider it as
the Design Storm Discharge, Qd .
3. Find this discharge, Qd , on the abcissa of
the graph on Figure 20., then move
vertically upward to the design curve.
4. From this point, move horizontally to the
left to read the corresponding Chamber
Diameter, D2 , on the ordinate scale.
5. Using the D2 , go to Figure 21, General
Design Details, first to find D( , then to
calculate the dimensions of the other
110
-------
chamber elements.
6. The dry weather sanitary flow was taken
as two percent of Qd in the present
model study. The same value was
maintained as the foul outflow during
storm operation. In practical design, this
same order or ratio, two percent times
Qd, should be retained, and the main
gutter designed to carry it through the
chamber to the foul outlet during dry
weather.
Figure 21 presents in simplified symbolic
form the dimensions for the various internal
elements of the separation chamber. Although
the chamber diameter, D2, is the basic
dimension taken off the design curves on
Figure 20, advantage was taken of the 6:1
ratio between this and the inlet dimension,
D,, and this latter was selected as the unit
dimension. The resulting symbolic relations
given on Figure 21 are:
DI = inlet dimension = unit
D2 = diameter of Chamber = 6Dj
D3 = diameter of scum ring = 4Di
D4 = diameter of overflow weir 3 1/3 Dj
h, = height of overflow weir = 1/2 DI
h2 = height of scum ring = 1/3 Dt
th = distance between scum ring and overflow
weir= 1/3D!
b2 = offset distance to determine locations of
gutter = 1/6D!
dj = depth from weir plate =1 1/2 Dj
dz = distance from inlet invert to bottom of
chamber = 5/6 D,
Rj = radius of gutter 0-90° = 2 1/3 Dj
R2 = radius of gutter 90-180° = 1 1/2 D,
R3 = radius of inner gutter 90-270° = 5/8 D!
R4 = radius of inner gutter 45-90° =1 1/8 D!
R5 = radius of inner gutter 315-45° = 3 2/3
DI
For a chamber dimensioned on the basis
of Qd as shown on Figures 20 and 21, the
efficiency of solids recovery over a storm
period is given by the curve on Figure 22,
Separation Efficiency Curve. Solids recovery
is the volume of solids- taken out through the
foul outlet, divided by the total volume of
solids entering the chamber during the
complete storm hydrograph period, expressed
as a percentage.
The solids described by the curve o'n
Figure 22 are those which were represented
by the 1-3 mm gilsonite on the model. It
follows by reasoning that if that material was
recovered, any larger particles would also
settle. Therefore, Figure 22 may be used to
include either all grit larger than 0.35 mm or
all settleable solids larger than 1.0 mm. There
would be less but still significant recovery of
finer particles of both materials, but not
enough data were taken in the present model
study to allow its definition for generalized
design use.
In following this scale-up procedure,
considerable liberty has been taken in
interpreting the model results. The structure
dimensioning has been done simply on the
basis of the Froude law. This procedure is
categorically correct as concerns the hydraulic
flow characteristics.
The grain size dimensioning, on the other
hand, was developed following Stokes law, on
the basis of settlement velocities. Over as wide
a range of particle specific gravities and sizes,
and scale-up ratios which have been suggested,
it is certain that the limits of this law would
be exceeded in some manner or another.
However, it should be pointed out that the
absolute definition of the operating laws still
lies in the field of advanced fundamental
particle movement research, hence, far
beyond the scope of the present study.
Therefore, in referring to the separation
efficiencies given on Figure 22', it should be
borne in mind that they are an attempt to
give a useful, practical guide to the design
engineer, rather than a presentation of
clinically precise research data.
The abscissa scale on Figure 22 has been
graduated non-dimensionally as a function of
the Design Storm Discharge, Qd. If a storm
with peak discharge equal to Qd occurs, 90
percent of all the grit and settleable solids
larger than the sizes shown on the curve
111
-------
60 —i
50 —
-£ 40 —
-a
8
cd
b
IM
x:
E
ca
30 —\
20 -
10 -
r
400 500
Qd= Design Storm Discharge - c.f.s.
FIGURE 20
STORM DISCHARGE VS CHAMBER DIAMETER
DESIGN PROCEDURE
1. Select the peak discharge from the desired probability storm
hydrograph and use this as the Design Storm Discharge, Q
2. Enter the graph with Qj, go up to the curve then read the corres-
ponding chamber Diameter, D2, on the ordinate scale at left.
3. Using this D?, go to Fig. 18 to find first Dj, then calculate the
dimensions 01 the other chamber elements.
112
-------
Inlet. Chamber Diameters
Weir, Scum Ring Diameters
hi
d2
R4
= unit
= Di/2
= 5/6 D
= 1 1/8
D2
h2
= Dj/3
= 2 1/3 Dj
32/3D!
D3
^ 4D,
Di/3
= 1 1/2
= Di/6
D4 = 3 1/3 D
dj = 1 1/2 D
R3 = 5/8 D,
r_
,
Weir. Scum Ring Details
Cerrterline Secondary Gutter
Inlet Detail
Centerline Primary Gutter
FIGURE 21
GENERAL DESIGN DETAILS
113
-------
100
90 J
-d
o
I
1
70,
60 »|
-g 50-
fc
-------
would be recovered through the foul sewer
outlet. For storms with peak discharges
greater or smaller than Qd, the solids recovery
over each particular storm period can be
determined as a function of the ratio of the
actual storm peak divided by Qd. For
example, for a storm peak equal to 1.5 Qd,
enter the curve on Figure 22 on the abscissa
with this value. Move vertically upward to the
curve, then horizontally to the left to read 62
percent on the ordinate scale. The chamber,
would therefore recover through the foul
sewer outlet 62 percent of the solids larger
than the sizes shown arriving in the chamber.
over the sterm hydrograph.
DESIGN EXAMPLE
The hydrological study of a given urban
area shows a peak storm discharge, Qd, of 400
cfs. If it is desired to effectually treat this
entire flow, reference to Figure 20 gives a
chamber diameter of 52 feet. From Figure 21,
the following main dimensions can be found:
a. Inlet Dimension, D! = D2 =8 ft-8 in.
for practical design, eight feet six inches
or nine feet would be acceptable.
b. Weir Diameter, D4 = 3 1/3 D, = 28 ft 10
in.
for practical design, take 29 ft
c. Scum Ring Diameter, D3 = 4 D, = 34 ft 8
in.
for practical design, take 35 ft
d. Chamber Depth (weir crest to floor), d, =
1 1/2 D, = 13ft
With a structure built to these
dimensions, reference to Figure 22 will show
what efficiencies to expect. If the design
storm discharge of 400 cfs occurred, 90
percent of all the grit and settleable solids
larger than those mentioned previously would
be removed from the clearer overflow. For
flows of 240 cfs or less the concentrator
would operate at maximum efficiency.
If a storm with peak of 500 cfs occurred,
this would be:
500 = i ?so
4~00~ '""^
Going into Figure 22 with this value on
the abscissa, moving up to the curve, then to
the left on the Recovery scale, would indicate
that 78 percent of the solids would still be
removed.
115
-------
APPENDIX 2
MATHEMATICAL MODELING OF SWIRL CONCENTRATORS
INTRODUCTION
The objective of this study was to
develop a mathematical model and computer
simulation of a swirl concentrator device to
separate grit and settleable solids from storm
water overflows. The general features of the
device were described in Appendix 1., Figure
12. The flow enters tangentially, setting up a
swirling motion. Settleable solids sink to the
bottom, and are carried by a secondary liquid
flow to the center of the chamber where they
are withdrawn, along with a fraction of the
liquid flow to the foul sewer. Most of the
flow proceeds over the circular weir mounted
on the central standpipe. This clarified
effluent (the overflow) is withdrawn through
the central standpipe.
As described in Appendix 1, a deflector
plate was installed parallel to the inlet flow as
shown in Figure 12. The deflector plate forces
the high energy liquid at the periphery of the
tank to flow into the center, thus raising the
tangential velocities under the weir. An
additional effect of the deflector is to help
scour the deposited particles and direct them
into the foul sewer.
Near the conclusion of the present study,
additional changes were introduced in the
laboratory model in order to trap floating
material. The changes included a vertical scum
ring between the weir crest and the outer tank
wall. Material floating to the surface between
the scum ring and tank wall are thereby
prevented from flowing over the weir. A
surface deflector located at station 320°
directs these floating particles into a channel
across the weir and into a small vortex drain
through the weir plate. The particles are
drawn through this drain and are stored in the
low velocity area under the weir. Due to
schedule limitations, the mathematical model
does not include the effects of the scum ring.
The swirl concentrator was first proposed
by Smisson1 in Bristol, England, and has since
been further investigated by Smisson and
other investigators.2"4 This study is the first
attempt to rationalize the design of such
devices through development of an analytical
model to predict the operating principles. In
conjunction with the laboratory tests described
in Appendix 1, the analytical model has been
used to predict the variation in performance
with the principal design variables, and so
arrive at a valid configuration.
The present results are aimed specifically
at optimizing the design of a unit to be
installed at Lancaster, Pennsylvania, as part of
a demonstration grant. In this application, up
to 440 cfs flowrates may occur, with a
nominal design value of. 165 cfs. The
laboratory unit is referred to as the model
chamber. Although specific calculations were
performed for the model and prototype
chambers, the results are applicable to a broad
range of chamber sizes, flowrates, particle sizes
and specific gravities. This broad applicability
is achieved through a set of scaling laws based
on the governing equations. With the scaling
laws, the results of the lab tests and the com-
puter calculations can be extended to chambers
of other sizes and flowrates, provided that
geometric similarity is maintained.
The general approach of this study has
been to calculate the liquid flowfield within
the swirl concentrator, neglecting the
presence of the particles (i.e., assuming a
dilute mixture). This is accomplished by using
a relaxation procedure to numerically solve the
equations for turbulent axisymmetric flow. A
three-dimensional eddy viscosity model is
used to relate- the local turbulent Reynolds
stresses to the gradients of the mean flow
properties. Once the liquid flow has been
calculated, the particle flow through the
liquid is computed. At each point at which
the liquid flow was computed, the three
particle momentum equations, and the
equation of continuity are solved to
determine the particle velocities and
concentration. The equations include
turbulent diffusion terms, virtual mass effects,
gravity forces, and drag. The equations are
solved with a time dependant scheme,
integrating forward in time until a
steady state is achieved.
117
-------
The liquid flow calculation has been
calibrated by adjusting the mixing length and
friction coefficient to provide the best match
with the experimental data. The agreement is
generally good, but limited by
non-axisymmetric flow effects in the physical
model due to the inlet jet and deflector plate.
Using the calibrated liquid flow, particle flows
were calculated for several flow rates, particle
sizes, and chamber sizes. The results generally
show favorable agreement with the laboratory
data for prototype overflow rates up to 162
cfs on a 36-ft diameter computer model.
ANALYSIS SUMMARY
Liquid Flow Calculation
The calculation of the liquid flowfield
within the swirl concentrator requires making
several simplifying assumptions. The two
chief assumptions are that the flow is
axisymmetric, and that its turbulent character
can be modeled as described in the following
section. The axisymmetric assumption means
that the flow can be described with only two
independent variables (r, radius and z, depth),
and is independent of the angular position.
This assumption requires that the inlet flow,
which in the actual device enters tangentially
through a square duct be represented by a
circumferential region of the wall through
which the inflow occurs. The inlet flow
through the wall is assumed to have a quartic
velocity profile as illustrated in Figure 1,
Cross Section of Swirl Concentrator, with the
magnitude adjusted to give the proper mass
flowrate. The tangential velocity of the
incoming flow is assumed to be constant, and
equal to the mean velocity in the entrance
channel. These assumptions give the correct
tangential velocity near the outer wall. Also,
since the inflow is spread over a large area, the
radial inflow velocity is small, and does not
differ appreciably from the actual case in
which the radial velocity vanishes at the wall.
The axisymmetric model thus approximates
well the average behavior of the flow at most
radial locations.
There are three principal
non-axisymmetric effects in the physical
model:
a) The tangential velocity near the
center of the tank is increased due to the
deflection of the outer flow under the weir by
the deflector plate.
b) A local vortex is created above the
foul sewer outlet by the deflector plate.
c) The inlet flow exhibits a jet-like
behavior.
The first of these effects has been
simulated in the mathematical model by
adjusting two arbitrary constants (mixing
length and wall skin friction coefficients) to
match the average' observed tangential
velocities under the weir. The second of the
effects listed is very important in determining
the scouring properties of the chambers. The
location of the foul sewer outlet has been
carefully adjusted in the physical model to
take advantage of the scouring properties of
the local vortex induced by the deflector.
Without the local vortex, the separated solids
may remain as -deposits on the floor of the
chamber. An auxiliary device (mechanical
scraper or flushing jet) is then required to
cleanse the chamber after a storm. In the
mathematical model, however, all particles
hitting the bottom are assumed to eventually
be withdrawn through the foul sewer. The
mathematical model does not determine
whether these particles form deposits or are
swept into the foul sewer outlet. This
distinction is not required to predict the
overall separation efficiency because the local
vortex does not appreciably affect the
separation ability of the chamber, only its
self-cleaning capability.
The third non-axisymmetric effect
(jet-like inlet flow) is most important at high
flowrates. At low flowrates (100 cfs or lower
in the present case), the inlet jet has largely
diffused vertically and laterally before the
liquid reaches the 90° station, without
creating serious non-axisymmetric distortions.
At these low flowrates, the water surface
appears relatively smooth and axisymmetric.
At high flowrates (250 cfs and above), the
entrance jet persists further into the chamber
and tends to surface as a plume, creating
waves.and turbulence at the surface. Since the
mathematical model is limited to
axisymmetric flow, there is a gradual
breakdown in its ability to describe the
118
-------
Weir
//////////////
u
ft/1
'-l
1-1, k
U
1, k+
Velocity
1+1,
Computational Grid
Inlet
Velocity
///////// // ////////a
Foul Sewer Outlet
Velocity
W f-*\
FIGURE 1
CROSS SECTION OF SWIRL CONCENTRATOR
physical flow above 100 cfs. At high
flowrates, the mathematical model will
overestimate the separation efficiency because
the transport of particles to the surface by the
entrance jet and by excess turbulence has not
been accounted for.
Even at low flowrates where the
axisymmetric approximation applies, the flow
is turbulent and quite complex. The art of
turbulent flow calculation is not far advanced,
and even for the simpler case of a boundary
layer flow, two different models can give
results which differ-by as much as 50 percent
in some respects. The present model uses an
elementary eddy viscosity approach which
relates the turbulence to the gradients of the
mean velocities through the use of a mixing
;length concept. This approximation cannot
duplicate the finer details of the turbulent,
time varying flow structure. However, at low
flowrates, the main features of the internal
flow are reproduced reasonably well, and the
results give considerable insight into the
behavior of the streamlines within the swirl
concentrator.
Also, in keeping with the axisymmetric
nature of the model, the outflow velocities
are specified as uniform around the
circumference of the weir. This is
accomplished by using smooth power series
profiles, as illustrated in Figure 1. This
procedure represents the overflow velocity
fairly well, except near the inlet where
disturbances due to the deflector plate occur.
The overflow velocity is specified along a
horizontal line at the same height as the
underside of the weir, as shown in Figure 1.
This procedure is used in order to maintain a
rectangular computational mesh. The actual
depth of liquid in the tank is higher by about
1.5 ft (prototype scale) due to the projection
of the weir crest above the weir plate. For
consistency with the hydraulic model report,
the depths in this report refer to the distance
from the bottom of the chamber to the weir
crest, even though the computational region
did not extend beyond the underside of the
weir plate.
The foul sewer flow is also represented as
an annular discharge in the mathematical
119
-------
model. In reality, the foul sewer flow is
withdrawn through a single port in the
bottom of the concentrator. For small values
of the foul sewer fraction, the differences
resulting from the annular approximation will
not be large. For sizeable foul sewer flows,
significant non-axisymmetric effects could be
anticipated.
An additional detail of the actual swirl
concentrator which could not be modeled,
was the skirt which hangs below the weir to
trap floatables. The computational mesh used
for the present calculation was too coarse to
permit this detail to be modeled without
causing numerical instabilities. However, the
present results seem satisfactory without the
complication. The ultimate test of the
reasonableness of this and the other
approximations discussed previously, is how
well the mathematical model predicted the
actual behavior of the concentrator. Based on
the comparisons to be discussed later, the
model appears to be satisfactory in its present
form at overflow rates up to 162 cfs.
Equations of Motion
The basic equations for the steady-state
flow of a viscous incompressible fluid in
tensor notation are5
Continuity:
U/y = 0
Momentum:
where
,. y + UA/)
(1)
(2)
(3)
To _obtain equations for the mean
motion, \J{, in the presence of fluctuations in
velocity and pressure U',-, and p') whose
averages are zero, one can substitute
u, = u, + u;
p = p + P'
into Equations (1) and (2) and perform an
averaging in time. The result is the
well-known Reynolds equations for the mean
motion: _
U'',,- (4)
In Equation (5) the viscous shear term
(5)
(6)
is due to the viscosity of the fluid, whereas
the Reynolds stress
Ty - pu't
(7)
arises from the correlation between the
fluctuating velocities «',- and u'j.
For this project, the Reynolds stress
terms have been modeled by relating the local
stress to properties of the mean flow,
retaining the proper tensor character of the
equation.5 In particular
where e is an eddy viscosity defined by
(8)
(9)
in which fi is a mixing length, and $ is the
local dissipation function
= >/2 S'7 Sl7
where
(10)
(11)
Written in the cylindrical coordinate
system of Figure 1, Equations (4) and (5)
become, for axisymmetric flow:
dtt
r
9u'
-^^ - o
u du + ^- _O_;L - i! - -1
3r 3r '' p dr
(e+v)
I 9f, _
r W
23;;
fbw
(w
(13)
120
-------
~dr
1 9v
oz r
= (e
9T"1
~> V \ 9e
- ~ 7 / 9r
(14)
\br2
r dr
p
9z / dr
8e
97
(IS)
Following the technique of Reference 6,
Equations (12)-(1'5) are put in a more
convenient form for computation as outlined
below. The continuity equation (Eq. 12) is
identically satisfied by introducing a stream
function, i// such that
r 9z r dr (16)
The pressure is then eliminated by
differentiating Equation (13) with respect to
z, and Equation (15) with respect to r, and
then 'subtracting one from the other. The
results are then written in terms of the
non-dimensional variables
r =z/s
% = r/s
G = ^-
n=^-
du
9z
VV = W/C05
(17a)
(17b)
(17c)
(17d)
(17e)
(17f)
(17g)
where 5 is a reference length (chosen equal to
the concentrator depth), and a; is a reference
frequency (chosen to be Q/r0 A where Q is the
inlet flowrate and A is the area of the inlet
channel).
The final equations are as follows:
(18)
TF~ 9P
£ 9?
i[("-f)tM"-i
'/A A \
_ 1 I 9u _ 9_vv \
~?V9? 9fy
ML
9?
iL 9JL _ 9G2
I at 9r
1 31
(19)
92G +92G + 3 9G
9G
9?
+ ^-j,
co 5
(20)
(21a)
(21b)
(21c)
The eddy viscosity e is computed from
the mean motion with Equation (9). The
quantity $ in Equation (9), expanded in
axisymmetric cylindrical coordinates
becomes, in non-dimensional variables.
121
-------
=
and from Equation (17c)
3GY*
a? /
(22)
The mixing length is assumed to be of the
form
-!/ (23)
so that £ vanishes at all boundaries. The
constant H is chosen to give the best match
with test data.
Boundary Conditions
In keeping with the axisymmetric
approximation to the flow the inlet region is
treated as a porous wall rotating at the mean
inlet velocity. Thus the flow is assumed to
enter uniformly around the circumference at
the mean tangential velocity of the entrance
pipe as illustrated in Figure 1. In the overflow
and foul sewer outlet shown in Figure 1, the
vertical velocity of the flow leaving the
concentrator is specified, and the tangential
velocity is obtained by extrapolation from the
interior region, assuming no tangential shear
stress to act in these regions. On the solid
boundaries, the two velocity components
parallel to the surface are obtained by setting
the local shear stress at the wall equal to an
average skin friction coefficient times the
local dynamic pressure. The skin friction
coefficient is selected to give good agreement
with test data.
Translated into equations for the
non-dimensional stream function (f), vorticity
(ft), and tangential velocity (G), on the
boundaries, these conditions are expressed as
follows:
a) Inlet
u0 (f) and v0 (£) are specified. Then from
Equation (2la)
(25)
To obtain a boundary condition for ft, the
stream function is expanded into a third order
Taylor Series, and the required derivatives are
evaluated from the specified velocity, and
from Equation (18) which defines ft. This
procedure is substantially as outlined in
Reference 2, modified to allow for the inflow
of fluid. The resulting equation for ft on the
boundary at the inlet region is
5 AJ
3 5
ft
b + l
(26)
where the subscript "b" refers to the value on
the boundary, while "b + 1" refers to the
point immediately interior.
b) Overflow and Foul Sewer Outlet Flow
In the overflow region, w0 (£) is
specified. Then from Equation (21b), we
obtain
(24)
(27)
which defines / in the overflow region, and a
similar equation applies to the foul sewer
outlet.
The boundary value of G is obtained by
noting that for zero tangential shear stress,
|°- = 0 so that
Gb = Gb+i- (28)
As in the inlet region, the boundary
122
-------
condition for n is found by the procedure
given in Reference 2. The result is
"„ = 3
Af2
(29)
with a similar equation for the foul sewer
outlet.
c) Solid Boundaries
On solid boundaries, the expression for
the wall shear stress in terms of the skin
friction coefficient, C^, and dynamic pressure
is
Te = $ ( \ pv2) (30)
For a Newtonian fluid, the shear stress
can also be expressed in terms of the velocity
gradient. For example, on the bottom
(31)
Combining Equations (30) and (31), and
rewriting the result in terms of the
non-dimensional tangential velocity function,
G, the resulting boundary condition is
Gh =
~v
(32)
Similar expressions can be found for G on
the top and sides.
The boundary condition for n is of a
simpler form than used in Reference 6. For
example, on the bottom, the radial
component of shear is
-ju-
(33)
From the definition of n (Equation 17a),
on the bottom where
•r = 0, we have
_ s du
ur dz
(34)
For small values of u/v, the radial shear
can also be written in terms of the tangential
shear
.a ^re =M C;|-i,
(35)
-i
i
J
,-o/c\
(36)
Combining (33) to (35) and using
Equation (2 la) gives for the vorticity on the
bottom , r-
0 _ Cf_ G_b _ , A fin - /h+i
"b - 2 (^/cJP) «[_ Af
Numerical Method
Equations (18), (19) and (20), together
with the auxiliary equations (21)-(23) and
boundary conditions defined above, are
solved numerically on a uniform grid,
subdividing the cross section of the swirl
concentrator as shown in Figure 1 . Each of
the principal equations is of the general form
T
?
?
of
0 +D=0
(37)
where 0 represents f,n or G in Equation (18),
(19) and (20) respectively. By writing
centered finite difference approximations for
the derivatives, i.e.,
d ~(
of
l, k)
2Af
and
(38)
(39)
Equation (37) can be solved for 0,-jfc in
terms of the surrounding four points. The
numerical procedure consists of sweeping
through the mesh repeatedly, replacing each
value of 0,-;fc with an updated value found
from Equation (37). In performing this
calculation for fi the new-found value is
averaged with the previous value to provide
additional stability. This relaxation process is
repeated until successive changes in the
function are less than some preassigned value.
In performing the numerical calculation,
it was found that numerical instability
occurred whenever the kinematic viscosity
appearing in Equation (21) was made too small.
With a mesh spacing of 1/2 inch (model
123
-------
scale), these difficulties occurred at about v -
4 x 10"* ft 2/sec , whereas the viscosity of
water is 1 x 3O5 ft2 /sec. This is a common
difficulty in viscous flow calculation, and
occurs when the Reynolds number based on
mesh spacing and kinematic viscosity
becomes too large. The problems can be solved
by using a smaller mesh spacing (thereby
lowering the Reynolds number). However this
is a' costly solution. To use the viscosity of
water (1 x 1OJ ft2 /sec) would require that
the mesh spacing be reduced by a factor of 40
in each direction, with a consequent large
increase in the computer storage and
computational time.
The numerical difficulties arise near the
walls where the turbulent eddy viscosity e
vanishes (note that the mixing length, Eq. 23,
is zero at all boundaries), leaving only the
kinematic viscosity contribution to e (see Eq.
21c).
Away from the walls, the eddy viscosity is
several orders of magnitude larger than the
kinematic viscosity and the Reynolds number
is correspondingly small. The mesh therefore
needs to be refined only near the walls.
However, this requires a non-uniform mesh
and presents considerable complications in
the program logic. For the present study, the
kinematic viscosity was simply maintained
large enough to avoid instability, and the
resulting inaccuracy near the wall was
considered acceptable. All of the results were
obtained with v - 4 x 10 ~4 ft2 /sec or 8 x
10'4 ft2 /sec. These results therefore exhibit a
higher viscous laminar-like flow behavior in
the immediate vicinity of the wall. However,
two or more mesh points away from the wall
where the eddy viscosity is dominant, the
results are unaffected by these boundary
effects.
Liquid Flow Summary
The equations developed in the
preceeding section makes it possible to nu-
merically compute the turbulent axisymmetric
flow within the swirl concentrator. The turbu-
lence in the flow gives rise to local fluctuations
in the velocities which cause apparent stresses
(Reynolds stresses) similar to those induced
by viscosity. In the present study an eddy
viscosity model is used to relate these
Reynolds stresses to gradients of the mean
flow properties through the use of a mixing
length concept.
For the numerical calculation, a stream
function is introduced to satisfy the
continuity equation, and the vertical and
radial momentum equation are combined to
give a single equation for the vorticity, £1. By
assuming axial symmetry, the dependance of
the flow on angular position is eliminated and
the number of independant variables is
reduced to two: the non-dimensional radial
coordinate £, and the non-dimensional radial
coordinate f.The final result is three partial
differential equations for the stream function,
/, the vorticity, tt, and the tangential velocity
function, G(Eq. 18, 19, and 20, respectively).
These three principal equations are
supplemented by auxiliary relations for
computing the non-dimensional velocities u
and w (Eq. 2la, 21b) and eddy viscosity (Eq.
21 c, 9, 22, and 23). These equations and
appropriate boundary conditions are solved
with a numerical relaxation procedure.
The ability of the mathematical model to
describe the actual flow phenomena is limited
by the approximate eddy viscosity model, and
by non-axisymmetric flow effects in the
physical model. At low flowrates, the
mathematical model should give reasonably
good agreement with the physical model,
within the limits of the eddy viscosity
approximation. The mathematical model
results are independent of the angular
position, and thus represent the average
behavior of the flow of any cross-section. At
these low flowrates, the chief
non-axisymmetric effect of the laboratory
model deflector is to increase the velocity of
the liquid under the weir. The velocity
increase is simulated in the model by
adjusting the mixing length and skin friction
coefficients to give results in agreement with
laboratory data. The local vortex induced by
the deflector cannot be duplicated in the
124
-------
axisymmetric approximation. However, the
local vortex affects primarily'the self-scouring
ability of the concentrator, and is not critical
to the overall separation efficiency.
At high flowrates (250 cfs), large
asymmetries appear in the physical flow due
to the jet-like behavior of the inlet flow
Turbulence and waves are visible on the
surface. The axisymmetric model cannot
duplicate these phenomena, and so the
usefulness of the numerical results is
restricted to flows lower than 250 cfs for the
tested configuration.
Particle Flow Calculations
The particle flow within the swirl
concentrator is calculated assuming
sufficiently low concentrations so that particle
collisions and coalescence can be neglected.
The effect of the particles on the structure of
the liquid flowfield is also neglected. These
assumptions are both valid for particle
concentrations less than 1,000 mg/1 as
demonstrated by data on settling rate versus
concentration given by Camp.7 Additional
approximations are required to calculate the
particle flow. The most significant
approximation concerns the effect of
turbulence. The turbulent fluctuating liquid
velocity induces fluctuations in the particle
velocities. In addition, and more importantly,
it also causes a diffusion of particles away
from the paths they would follow for a
laminar motion.7'8 The modeling of this
effect is crucial because in the absence of
turbulence, the particles in many cases would
sink directly to the bottom. The turbulence,
however, scatters the particles into the
vicinity of the weir where they are entrained
with the overflow For this study, the effect
of the turbulence was accounted for by
adding the approximate diffusion terms to the
equations of motion and continuity (see
following section for details). The eddy
diffusion coefficient was modeled in the same
way as the eddy viscosity for the liquid flow 8
In addition to turbulence, the following
factors also contribute to uncertainties in the
particle motion:
non-spherical shape
offset center of gravity and/or buoyancy
acceleration effects
Magnus effects
previous motion history
The non-spherical shape of both the
actual sewage particles and the simulated
sewage used in the laboratory tests introduces
uncertainties into the particle's drag, although
the differences due to the shape are small at
the low settling rates involved.7'9 The
uncertainty in the drag was minimized by
measuring the settling velocities of the test
particles. The measured velocities are
compared in Figure 2, Comparison of
Predicted Particle Settling Rates with
Measured Settling Rates, to the values
calculated for spherical particles of various
diameters and specific gravities. The
differences are not large, but the data shows
considerable scatter.
The effect of offset center of gravity or
center of buoyancy is to induce oscillations in
the particle orientation. For non-spherical
particles, the changing orientation will cause
variations in ithe particle trajectory due to lift
forces perpendicular to the trajectory. Even
for spherical particles only a very small center
of gravity offset can cause wandering from
the nominal trajectory due to asymmetric:
vortex shedding.10-11 The ultimate effect of
the center of gravity offset is to introduce
additional uncertainties into the trajectory of
a given particle. Statistically, this is equivalent
to having a larger dispersion, and the effect
can be included in the eddy diffusion
coefficient. The Magnus effect can also be
accounted for in this way. The Magnus effect
is the lift perpendicular to the trajectory
associated with a spinning particle.9'12 The
classic example is the baseball pitcher's curve
ball. Since the sewage particles are moving
through a highly rotational liquid flow, the
fluid shear will cause some particles to spin,.
and thus increase their dispersion.
Studies have also shown that the drag of
an accelerating sphere is not the same as the
drag of the same sphere at constant velocity.
The difference is believed due to asymmetric
125
-------
10-1
u
w
in
10
-2J
g §
10 --J
o
e
10 ^j
ho'
10
-3
Data
(LaSalle Lab SG - 1.06)
Curve Fitted to
Gilsoaifce Data by LaSalle
Petrotheoe Data
(Measured by GE)
Theore&isal Settling
Curves for SG - 1.01, 1.06
10 (inches)
10
-1
10 (Centimeters) io"1
PARTICLE DIAMETER
FIGURE 2
COMPARISON OF PREDICTED PARTICLE SETTLING RATES
WITH MEASURED SETTLING RATES
126
-------
shedding of vortices behind the particle.1' At
very low Reynolds number (creeping motion),
there is also an influence due to the previous
history of motion.8 This unsteady viscous
effect appears to represent a drag due to
momentum transfered back to the particle as
a "shear wave" from fluid previously
accelerated.13 Both of these effects are
relatively small, and their influence on drag
has been neglected in the present study.
Another area of uncertainty in the
particle flow calculation is the behavior of
particles near solid boundaries. Heavy
particles, for example, sink rapidly to the
bottom. However, a detailed study of the
interaction of the particle with the boundary
layer is required to determine whether the
particle actually hits the bottom or is deflected
and carried away by the secondary flow. If
the particle does hit the bottom, it may form
a deposit, or it may subsequently be either
re-entrained by the flow, or rolled along the
bottom to a new location. In the physical
model, all of these mechanisms are at work,
but modeling them properly is a very difficult
task, requiring a detailed description of the
flow on the bottom. In fact, an accurate
analysis of the scouring and re-entrainment
phenomena would require a description of the
non-axisymmetric local vortex induced by the
deflector plate. This vortex cannot be
modeled with the present axisymmetric liquid
flow model.
Rather than attempt a detailed local
boundary layer analysis, the present particle
flow model assumes that particles hitting the
bottom simply pass through it and out of the
chamber (in computing the separation
efficiency, all such particles are assumed to be
entrained in the foul sewer flow). The particle
concentration at the bottom is therefore the
same as at the adjacent interior points, and no
deposits build up. Since the deposition and
re-entrainment of particles are not accounted
for, the particle concentrations near the
bottom will be underestimated. For .very
shallow chambers the particle concentrations
near the overflow may also be lower than
they should be, and the model will therefore
tend to underestimate the number of particles
entrained in the overflow (thereby
overpredicting the efficiency). This effect is
minimized with deeper chambers, and does
not appear to be a problem with the nominal
9-ft. depth.
Particle Equations of Motion
The time-dependant equations of motion
for spherical particles can be written in tensor
notation as:
Continuity: L + (Nv):. = 0
(40)
Momentum:
(Sg+n) ( + V v/>;) =
V-U
(V, - U,)
(41)
In Equation (40), N is the local number
density o_f particles with volume vp, moving at
velocity V in liquid which is moving with the
(different) velocity U. In Equation (41), the
left hand side represents the mass times
acceleration of the particle. On the right hand
side are the various forces acting on the
particle. The first term is the integrated effect
of pressure acting over -the surface of the
particle where p2 is the pressure, as obtained
from the liquid flow solution, but without the
hydrostatic term. The latter has been included
in the third term. The second term on the
right is the "induced mass" effect, which
arises from the acceleration of surrounding
fluid in response to alterations in particle
motion. The coefficient of virtual mass, 77,
depends on the particle shape, and is equal to
112 for a sphere. The third term on the right
is the buoyancy force, and the last term is the
viscous drag due to relative motion between
the particle and liquid. The drag coefficient,
CD, is a function of the Reynolds number for
flow over the particle, based on the difference
between particle and liquid velocities. This
dependence can be adequately represented for
spheres by the empirical relation14
+ 0.34
(42)
127
-------
Equations (40) and (41) are modified for
turbulent flow with fluctuations v,- in particle
velocity, ut in liquid velocity, and n in
number density by substituting
V; = V,. + v,
U,-= U..+W,-
N = N +72
(43)
and taking a time average. This is essentially
the same procedure as followed in deriving
the Reynolds equation for liquid flow as
previously described. As before, the
correlation between the fluctuating velocities
vf Vj, and_between the velocity and number
density nVj appear as additional terms in the
equation for the mean motion. Neglecting the
effect of turbulent fluctuations on the mean
value of the drag, the result of this averaging
process is
+ V'Vt/+(v
v-u
(V.--U,)
(45)
As in the case of the liquid turbulent
fluctuation, the correlations between the
fluctuating quantities are modeled with an
eddy viscosity/mixing length approach. Thus,
it has been assumed that
v.Vj =-ep (V,-f/ + Vy.,-) (46)
^ =-aep (V^ + Vy,,) (47)
and
nvi=-£p*& (48)
The constant, a, represents the ratio of
the rms fluctuation in the liquid velocity, to
that of the particle, i.e.,
a=l«l
I" I
(49)
For large, heavy particles, one would
expect small fluctuations in particle velocity
so |v|<.|w|. However for small particles with
specific gravities near that of water | v\ ^ \u\
and thus for all the calculations in this report
a = 1 is used. Substituting these
approximations into (44) and (45), and
rearranging yields for the mean particle flow
quantities
NV'),,- = (*„!§)„• (50)
ar
The pressure gradient is found from the
solution of the liquid equations of motion.
For the calculations of this study, it is
assumed that ^the eddy viscosities for the
particles were identical with those computed
for the liquid. This assumption is believed
valid for the present case, especially for
particles close to water in specific gravity.
This point is discussed further by Hirfze in
Reference 8. It is important to note that
Equation (51) reduces to the liquid flow
equation for the special case of a small
particle with specific gravity of unity. In that
case the gravity term vanishes, and both the
drag and the virtual mass terms drop out if, as
supposed V-»U. Then, since a = 1, Equation
(51) becomes formally identical with
Equation (5) for steady flow, provided ep = e
+ v.
Equations (50) and (51) can be expanded
for axismmetric flow in cylindrical
coordinates. The resulting form of the
equations, dropping the overbars for mean
quantities, is:
,, 3N
UW
3N _
~
-+-L
1 3N
r 3r
3N
3N_
dr
az
(52)
128
-------
du _ y2 + J— Numerical Method for Particle Flow
9z r ss+r> Equations (52) to (55) all contain the
same directional derivative on their left-hand
side. This fact makes the method of charac-
L r P teristics a natural choice for integrating these
equations. The method of characteristics
consists of integrating each equation along
this characteristic direction at each mesh
point for each time step, and evaluating
the right-hand side from the known for
initially assumed) solution at the previous
time step. Thus, for example, assume that the
solution (N,u,v,w) is known at each mesh
(53) point at time t0 ; and it is desirable to find the
solution at mesh point 1 at time t0 + A t
[corresponding to point 6 of Figure 3].As an
w ~ = '~ + (s~^~ ) initial guess, the quantities (N, u, v, w) at
g point 6 are assumed equal to the
corresponding values at point 1. (This will be
exactly true in the steady state). The
"Characteristic" line —(it e r+w e z) shown
dotted in Figure 3, Illustration of the Method
of Characteristics, is then extended back from
time plane (t0 + A t)] to time t0, where it
intersects at point 5. Since all the functions
3r r I 3~7"~ ' are known at time t0, the right hand sides of
(52) to (55) can be determined at point 5 by
interpolation. Each equation can then be
integrated forward in time using the finite
difference approximation
3w =
A V
Ri
(54) 6 =05 + A?[RHS]S (56)
where 0 represents any of the functions
(N,«,v, or w), and [RHS] s refers to the right
= (S .j^) side of the appropriate equation evaluated at
8 point 5. The entire process described above is
then repeated with the updated values for u
and w averaged with those at point 5, to
determine the characteristics direction.
Equation (52) through (55) can be
integrated forward in time to provide a
-wiL) + (% + 0 - a)i?) time-dependent history of particle number
density, N, and velocity (n,v, and w) for
, g 32 \ / a 3 \ a particles with diameter, dp, at each mesh
^ 7 "37" + 1)P/ +\97~ + dz)~dr^+ point for which the liquid flow has been
determined. These equations must be resolved
for each particle size of interest. For steady
liquid flow and constant boundary conditions
a steady state is reached in which N, u,v, and
w remain constant. This is the desired
(55) solution to the problem.
129
-------
k + 2
i + 1
FIGURE 3
ILLUSTRATION OF THE METHOD OF CHARACTERISTICS
Boundary Conditions for Particle Flow
The procedure previously outlined serves
to determine the values of N,u,v, and w at all
interior mesh points. At the boundaries of the
mesh, special conditions must be applied, and
these boundary conditions are not so
straightforward as those for the liquid flow
The boundary conditions given below were
found to be reasonably successful.
The number density of particles in the
incoming flow can be specified arbitrarily as a
function of the vertical coordinate, z. Since
no interaction between particles is considered,
the actual concentration is unimportant and
only the relative concentration need be
determined. Therefore the number density
was set equal to unity over the entire inlet
region. Stratification of the sediment near the
bottom of the inlet channel could be readily
simulated but was not attempted for this
study. The velocities of particles at the inlet
were assumed to be the same as those of the
liquid.
The boundary conditions on the vertical
sides (except in the inlet region) were set so
that the derivative of the number density
normal to the wall was always zero, as
evaluated from a second order Taylor series
expansion. Thus, the number density at the
wall was taken as
Nb=4Nb + 1-Nb+2
3
(57)
where Nb is the number density on the
boundary, Nb + j is the next point inward, etc.
The particle velocity normal to the wall was
held at zero, and the velocity parallel to the
wall was set to the local liquid velocity, plus
the particle settling velocity.
At the underside of the weir plate,
particle velocities are always downward for
particles with a specific gravity greater than
one. Any particles which exist at the
underside of the weir, thus fall away towards
the center of the chamber. Therefore, the
number density is zero on the underside of
the weir and also across the overflow at those
points where the settling velocity exceeds the
liquid outflow velocity. At such points, the
particle velocities were set so that
"p
Vr
and
- UL
= vL
+V.C
130
-------
At points along the overflow where the
settling velocity was less than the local
outflow velocity (so that particles were
leaving the concentrator), the solution was
found from the method of characteristics
procedure. The method of characteristics was
also used to determine the solution at all
points on the bottom boundary, because the
particles always flowed into the bottom, and
not upward through it. All particles hitting
the bottom were assumed to pass along it
and out of the concentrator. This assumption
is required in order to achieve a steady-state
solution without having the number density
grow indefinitely large due to deposition. In
practice, this assumed boundary condition is
closely matched due to the removal of
particles on the bottom by the inward
secondary flow .
The separation efficiency of the swirl
concentrator for a given particle size can be
readily determined from the numerical
solution of Equations (52)-(55), by integrating
the mass flux entering and leaving the
concentrator. For this purpose, all particles
hitting the bottom of the concentrator were
assumed to be entrained in the underflow.
The various particle fluxes, in units of number
of particles per second are :
N0
/ro + & ri
• „„..„„, .^rN (r-Zma^Wp (r,z
(58)
(59)
(60)
The units of these particle fluxes, QPin,
QPo, and Qpt>,are "number of particles per
second," for an inlet concentration of one
•particle per cubic foot (because the number
density has been normalized to unity at the
entrance). For actual concentrations greater
than one particle/cu ft, the particle fluxes are
simply scaled up in direct proportion. The
influx, QPin, is positive for particle inflow.
The other fluxes above are positive for an
outward flux of particles.
In principle, the sum of the particle
fluxes hitting the bottom and leaving through
the overflow should equal the total influx,
Qpjn However, due to numerical inaccuracies,
this was not always the case. Consequently
the chamber efficiency was always defined in
terms of the actual sum of QPo and QPb The
fraction of particles removed is thus
PO + QPb
Particle Flow Summary
The equations developed for the particle
flow provide a numerical solution for the
particle concentration N and the three
particle velocity components u, v, and w at
each mesh point. From these velocities and'
concentrations, the flux of particles leaving
the concentrator in both the overflow and in
the foul sewer flow are calculated, in order to
determine the separator efficiency. Since the
concentrations and velocities are different for
each particle size and specific gravity, the
equations must be resolved for each particle
class of interest.
The particle flow equations include the
effects of turbulent diffusion, virtual mass,
gravity, and drag. The turbulent diffusion is
modeled in the same way as in the liquid flow
calculation, assuming that the eddy diffusion
coefficient is numerically equal to that of the
liquid. The effect of turbulence is to scatter
particles from regions of high concentration
into regions of low concentration. The
turbulence tends to decrease the concentrator
performance because particles which might
otherwise sink directly to the bottom are
instead scattered to the top of the chamber
and become entrained in the overflow.
As in the liquid flow case, the particle
flow is assumed to be axisymmetric. The
results are therefore accurate only at
flowratf.s below 250 cfs whe're the
axisymmetric approximation is reasonable.
The particle flow equations also neglect
interactions between particles, and therefore
apply only to low concentrations (less than
1000 mg/1). At higher concentrations,
agglomeration of particles and the interaction
131
-------
between the particles and the liquid flow
become important.
Scaling Laws
The governing equations for both the
liquid and particle flow must be examined to
deduce appropriate scaling laws. There are
two aspects to the scaling problem. One is to
determine what approximations are involved
in representing the prototype concentrator
chamber by a smaller scale laboratory device.
The other aspect is to derive relationships for
scaling the calculated results to the prototype
system. By using these scaling laws, the results
calculated for a few special cases can be
extended to other flowrates, chamber sizes,
particle diameters, and particle specific
gravities. Scaling,therefore,greatly reduces the
amount of computation to be performed and
extends the usefulness of both the
mathematical and physical model results.
Scaling of the Liquid Flow
Equations (18)-(20) for the liquid flow
are in non-dimensional form, such that all
lengths are referred to the reference length
",$," and velocities to the product of the
reference frequency, co, and length, s, etc.
Therefore, the same equations apply to any
combination of flowrate and concentrator
size. A solution to these equations for any
special case can therefore represent the
solution for other flows and sizes, provided
that:
(a) boundary conditions on /, $7, and G
must be the same
(b) the eddy viscosity, e, must be the
same.
Condition (a) is ensured by maintaining
geometric similarity and a given overflow
fraction. Condition (b), however, can only be
satisfied approximately. From Equation
(21c), (9), (22), and (23), the
non-dimensional viscosity is:
e =
1/2
(6:
The first term on the right is the eddy
viscosity arising from the Reynolds stresses
while the second term represents the
molecular viscosity. For the model chosen,
the eddy viscosity is independent of scale size
and flowrate since neither GJ nor s appear
explicitly in the first term. Thus, as the size of
the chamber is increased, or the flowrate, the
turbulence level increases so that the same
non-dimensional eddy viscosity results. The
second term on the right however, depends on
both the flowrate and size. This term is the
inverse of a Reynolds number based on
reference length s, reference velocity (w s),
and liquid kinematic viscosity v. Since this
molecular viscosity term is very much smaller
than the eddy viscosity term (provided the
flow remains turbulent) it can be neglected
for practical purposes, permitting scaling of
the liquid flow calculation. It is noted, how-
ever, that as the concentrator size becomes
very small (small s), or the flowrate becomes
very small (low reference velocity, ws), that
this term can no longer be neglected, thus
restricting the range of sizes and flows which
can be represented by a single solution.
In practice, if the size of the chamber or
flowrate is low enough to result in laminar
flow, the turbulent flow solution will no
longer apply. For the present case, interest is
primarily focused toward scaling the results
for the laboratory scale model to larger
prototype sizes. Provided that the scale model
has turbulent flow, upward scaling is feasible
within the accuracy of the eddy viscosity
model.
In summary, the non-dimensional
equations show that two swirl concentrators
of the same shape but of different sizes and
flowrates will nevertheless have identical
flowfields if a) all dimensions are divided by a
reference dimension (the depth of the
concentrator for example) and, b) if all
velocities are divided by a reference velocity
V = cos (the inlet velocity for example).
It is important to observe that the
gravitational term does not appear in the
liquid flow equations. Gravity will not affect
the calculated flow velocities, but it will
influence the pressure. The actual pressure
p(r, z) can be written
P(r,z) = pgz
(r,z)
(63)
132
-------
where p2(r,z) is the pressure determined from
solving the liquid flow equations. Thus, the
hydrostatic term is not needed in calculating
the internal liquid flow, but it can be added
later if necessary. However, the action of
gravity (through both the hydrostatic pressure
and the weight) is crucial to the particle flow,
and hence the separation efficiency of the
concentrator, as will be discussed further. The
effect of gravity is also important in
determining the shape of the free surface at
the overflow, although this effect has not
been modeled in the present study. The
importance of gravity dictates that the
Froude number
be used as a scaling parameter between the
model and prototype swirl concentrators. For
a fixed size relationship (smodel/ sprototype),
the flowrate in
adjusted so that
the model must then be
V
'model
prototype
— /_^jnodel
\J ^prototype
(64)
Maintaining the same Froude number in
model and prototype ensures that the ratio of
gravitational and inertial effects remains
unchanged. Using the Froude number to
determine the velocity ratio from Equation
(64), the results calculated for the laboratory
model can be applied to the prototype case
equally well by scaling the results with
S ~~ S prototype
CJ - CO mo<}el
s prototype
s model
in equations 17 and 21.
The effect is to give larger dimensions
and higher velocities, but the identical flow
pattern. As an example, the present
laboratory model represents the prototype
swirl concentrator on a 1:12 scale. To
represent the prototype concentrator
operating at 100 cfs, the scale model
velocities were reduced by:
v = v
~ m v n
Since flowrate is proportional to v?2, the
laboratory model was operated at a flowrate
°f Q = Q
Vm Vp
= 0.20037 cfs
Equations (18)-(20) for the liquid flow
condition were solved for the flowfield
within the 'laboratory model, resulting in
specific values for f,fi, and G at each mesh
point-. To determine the actual flow velocities
at any point, the non-dimensional variables
were scaled according to Equation (17). Thus
the tangential velocity at a general point (i,k)
is
"i,fc = "s?fc G i,fc (65)
The reference length, s, is taken as the
chamber depth, and the reference frequency
is taken as (v0/r0) where v0
tangential entrance velocity
radius rn.
is the average
at the outer
s =9 ft.
and
= Q
r0
100
eft
(6 ft x6 ft) (18 ft)
= 0.154 sec.'
Here A is the area of the 6-ft.- square
entrance channel. If at point (i,k), G/ k =
0.500 and £fc = 0.800, then the tangential
velocity in the prototype at that location is,
from (65),
(Vi,k )P =(0.154) (9) (0.8) (0.5)
= 0.556 ft/sec
The same calculated solution
can also be applied to the model by altering s
and to. For the model
s = 9/ 12 = 0.75 ft
j VQ O
and co — -^—
= 0.200./, =0535 sec -1
(0.5ftx0.5ft)(1.5Jt)
The tangential velocity in the model at
133
-------
point (z,/c) is then
(vi,k) model = (0.535 sec-1 ) (0.75 ft) (0.8) (0.5)
= 0.1605 ft/sec.
Note that from this numerical example
("i.fc) prototype _ Q.556 = 347
(vi,k)model 0.165
so that these velocities are in proportion to
X/TT as demanded by the Froude number
scaling (equation (64)).
Scaling of the Particle Flow
Equations (50) and (51)-for the particle
flow can be put in non-dimensional form by
'dividing all number densities by a reference
value, N0, all velocities by Vn and all lengths
by s. If the pressure, p2 is normalized by ew
V0 s2, and time by s/V0, the resulting
equations with non-dimensional variables
denoted with a caret are
(66)
The solution to Equations (66) and (67)
in terms of the non-dimensional variables V, 'x
etc., will be identical for all cases for which
the following dimensionless groups are the
same:
/ApCpj
'\ VP
(68)
The particle eddy viscosity, ep, is
assumed to be equal to the liquid eddy
viscosity, which is independent of scale size
and velocity, as has been discussed. Therefore,
ep will be the same for all flows within
geometrically similar swirl concentrators.
The quantity r\ is the virtual mass
coefficient, which is the same for all particles
of the same shape. The coefficient 77 depends
on orientation for non-spherical particles, but
in this study an average value has been used to
avoid the necessity to calculate the
orientation. The effect of using an average
value will be small, and within the accuracy of
the other assumptions, 77 has a numerical
value of 0.5 for a sphere and generally lies
between zero and one.
The coefficient (Sg-1) gs/V20 is the
inverse of the square of the Froude number,
modified by the factor (Sg-1 ). As noted in the
previous section, the Froude number
represents the ratio of inertial to gravitational
forces, and must be maintained constant to
properly model the liquid flow.
For a fixed particle shape, the remaining
dimensionless group
is equivalent to the simpler form
d
where d is a characteristic particle dimension.
This group must be constant to insure that
the drag forces are of the same magnitude
(relative to the inertia, buoyancy, and
gravitational forces) in the model and full size
chambers. The drag coefficient, CD , is a
function of the particle shape and Reynolds
number, as given in Equation (42).
Exact simulation of the prototype
performance with a scale model is possible,
provided that all of the dimensionless
quantities mentioned
,nd
are held constant. However, this is in general
not possible if gravity and the liquid
properties are not varied. There is no
difficulty with e p , because this quantity
is automatically properly scaled with
the size and flowrate. But, if the specific
gravity and Froude number are held constant,
then the remaining ratio sCD /d must also be
constant. However, the drag coefficient is a
134
-------
function of the Reynolds number which is
proportional to the product of the scale
velocity and particle size, Vd. If the particle
size, d, is adjusted to give the proper
Reynolds number at the scaled velocity, V,
then the drag coefficient, CD, will have the
same value in model and prototype, but the
grouping
(sCj
\ d
will not be correct. Similarly, if the ratio s/d
is held constant, then the particle Reynolds
number, and hence CD will be wrong.
It is possible to arrive at an approximate
scaling procedure by assuming that the
particles always move at their equilibrium
settling velocity with respect to the fluid.
Then, it is always possible to vary the particle
diameter, d, or specific gravity, Sg to obtain
the proper scaled settling -velocity. In fact, an
infite varity of combinations of Sg and d will
give the proper settling velocity. Scaling of
the settling velocity is only valid, however, so
long as the principal mode of separation is the
settling of particles under the influence of
gravity. This will be the case, provided the
particle accelerations due to motion within
the chamber are much smaller than the
acceleration of gravity, so that the inertial
terms in Equation (67) are negligible
compared with the drag and buoyancy.
To determine the applicability of scaling
the settling velocity in the present case, the
magnitude of the inertial accelerations
appearing in Equations (53) to (55) can be
estimated. Because changes in velocities occur
smoothly over the chamber cross section,
terms such as
r..i
u 4" can be approximated by max
dr fo
where c is a constant of order one.
Furthermore, in solving these equations for
the swirl concentrator, it is found umax and
wmax are smaller than vmax, the inlet
tangential velocity. Therefore the largest
inertial acceleration term in (53)-(55) is the
centrifugal acceleration li
r
for the prototype chamber operating at 100
cfs, this acceleration is approximately
ft/sec2
L 36/f^
Since this acceleration is two orders of
magnitude smaller than the gravitational
acceleration, its effect on the particles should
be negligible, and scaling the settling velocities
is justified.
Summary of Scaling Laws
The liquid flow velocities (from either the
mathematical model or physical model) for a
swirl concentrator of size s^, can be scaled to
represent the flow in a geometrically similar
concentrator of size s2 using Froude number
scaling. This requires that velocities and
dimensions in the two concentrators be
related so that
*->/?F
A.S a corollary, since the flowrate is
proportional to the velocity and to the
reference length squared, the flowrates in
these two concentrators are related by
5/2
For example, the flow in a swirl concentrator
36 ft. in diameter with an entrance velocity of
3 fps (corresponding to an inlet flowrate of
108 cfs in a 6-ft x 6-ft entrance channel), is
equivalent to the flow in a swirl concentrator
only three ft in diameter with an entrance
velocity
= Q.866fps
The corresponding flowrate in the second
concentrator is
Qa=Qi ()5/2
At this flowrate, the fluid motion and the
balance between the gravitational and inertial
forces will be identical in both concentrators.
However, the foul sewer flow fraction must
be the same in both cases.
135
-------
The equations of motion also show that
the flow velocities at any point in a given
concentrator are proportional to the flowrate
provided the fraction of flow in the foul
sewer is maintained constant. For the
example given above if the flowrate in the
36-ft concentrator is halved to 54 cfs, the
entrance velocity will be half of its original
value or 1.5 fps. While it is obvious that this
rule applies to the entrance velocity, the
equations show that the velocity at every
point in the concentrator also scales in the
same fasion. At very high flowrates, however,
the equations are no longer applicable, due to
the increasing importance of
non-axisymmetric effects. Therefore the
proportionality between local velocities and
flowrate is only valid below about 250 cfs.
This restriction does not limit the
applicability of Froude number scaling. Since
Froude scaling preserves the balance between
gravitational and inertial forces, exactly the
same non-axisymmetric effects will appear in
both model and prototype concentrators.
The analysis of the particle flow
equations discussed under the Scaling of the
Particle Flow shows that it is not possible to
reproduce in the laboratory the three-way
balance between inertial, gravitational, and
drag forces in the full size swirl concentrator.
However, the inertial forces are shown to be
much smaller than the gravitational and drag
terms. By neglecting the inertial forces
altogether, representation of the full scale
particle flow in the laboratory is possible by
preserving only the balance between gravity
and drag forces. To achieve this balance it is
only necessary to scale the particle settling
velocities according to the Froude number, as
for the liquid velocities. The separation
efficiency of the concentrator will be the
same for all combinations of particle size and
specific gravity which give the same settling
velocity.
Using the example above, suppose it is
desired to represent in the scale model the
behavior of 0.1 inch (0.254 mm) particles
with specific gravity of 1.05 moving in the
36-ft chamber. These particles have a settling
rate of 0.145 ft/sec (see Fig. 30). They can be
represented in the 3-ft laboratory concentrator
by particles with settling velocity Vs2 scaled
by the Froude number:
(0.146)V~J^ = 0.0420 ft/sec
This scaled settling velocity can be achieved
with 0.034-in. particles with specific gravity
1.05, or 0.080-in. particles with specific
gravity of 1.01, or any other combination of
diameter and specific gravity yielding the
same settling velocity. The movement and
separation efficiency of these scaled particles
in the laboratory scale concentrator will
duplicate closely the movement and
separation efficiency of the full size particles
in the full size concentrator.
In >a similar fashion, once the separation
efficiency for particles with a settling velocity
of 0.0420 fps is measured in the laboratory,
the same efficiency applies to all particles
with a settling rate of 0.146 ft/sec in the
36-ft-diameter concentrator. The same
measurement can also be applied to other
concentrator sizes (say 20 ft.) by scaling the
flowrate and settling velocity according to the
Froude number.
RESULTS
Comparison of Mathematical Model With Test
Data for Nominal Case
A detailed comparison has been made of
the mathematical model results with data
from LaSalle Hydraulics Laboratory. The
comparison was made for the "nominal"
concentrator configuration. This laboratory-
scale concentrator is nine inches deep, 36
inches in diameter, and has a square 6-in. x 6-
in. inlet channel at floor level. Due to
schedule limitations, the results for the final
laboratory model configuration which
included the scum ring, could not be used in
this comparison. However the performance of
this final configuration is nearly identical to
the performance of the nominal case. As will
be described, the mathematical model was
exercised using a range of mixing length and
skin friction coefficients. These results were
then compared with the measured velocity
profiles. The final values for these two
136
-------
constants were selected to give the best match
between the mathematical and physical model
velocity profiles for the nominal concentrator
configuration at 100 cfs and 162 cfs. In this
fashion, therefore, the mathematical model
was "calibrated" against the laboratory scale
concentrator. Additional calculations for both
the liquid and particle flowfields were then
carried out, retaining these values for the
empirical constants.
Comparison of Predicted Liquid Flowfield
with Laboratory Data
The velocity contours obtained from the
LaSalle Hydraulics Laboratory model were
used to calibrate the mathematical model
liquid flowfield solution. These velocities
were measured, in the laboratory at four tank
cross sections, corresponding to angles of O°,
90°, 180°, and 270°, as measured from the
inlet point. Measurements were made at two
inlet flowrates corresponding to prototype
overflow rates of 100 and 162 cfs. Thus, eight
velocity profiles were available for calibration
of the mathematical model liquid flowfield
solution.
At this point it is important to note the
geometric dissimilarities between the LaSalle
Hydraulic model and the mathematical
configuration. Due to the axisymmetric
approximation, the mathematical model
assumes that the inflow is introduced
uniformly around the circumference of the
chamber. Consequently, only minor local
alterations in the liquid flowfield are imparted
by the inflow In the axisymmetric
mathematical model, therefore, the velocity
contours are identical for any cross section.
The LaSalle Hydraulics Laboratory
velocity profile data on the other hand, was
obtained for a configuration which included a
deflector plate at the inlet to direct the flow
under the weir at the 360° location. The
inflow was also given a downward direction to
force the inflow beneath the overflow weir.
These physical modifications resulted in a
non-axisymmetric flow pattern as indicated
by the differences in the velocity profiles
between the 0°, 90°, 180°, and 270° cross
sections shown in Figures 4-7, Tangential
Velocities for 0°, 90°, 180°, and 270°
Position.
For example, the location of the 0.8-fps
velocity contour varies from one to three feet
from the standpipe at the 90° (Fig. 5) cross
section to seven feet from the standpipe at
the 270° position. (Fig. 7) This variation in
the velocity profiles between sections
necessitates that an average profile be used to
compare with the predicted axisymmetric
mathematical model solution. Since the 180°
section represents a situation somewhere
between the other cross sections it was used
for the data comparison. The 180° cross
section also is located the fartherest away
from the deflector plate, and as such should
provide the closest approximation to the
axisymmetric case.
The velocity profiles obtained for the
180° cross section were redrawn to the same
scale utilizing the same velocity contours that
were plotted by the mathematical model, Fig.
• 12, Comparison of Predicted Mathematical
Model Velocity Profile With LaSalle Data.
This yielded simplified velocity comparisons
since the laboratory data could be
superimposed directly upon the computer
output plots.
As a result of the eddy viscosity and skin
friction assumptions which have been
discussed, the mathematical model contains
two empirical constants which must be
determined from the laboratory data. One of
these is the skin friction coefficient which
determines the velocity slip at the wall. The
other constant is the mixing length which
determines the scale of turbulence.
The effect of the skin friction constant in
the velocity and streamline functions can be
noted in Figures 8 and 9, Effect of Skin
Friction Coefficient on Streamlines and
Effect of Skin Friction Coefficient on
Velocity Profiles. In Figure 8, the streamline
patterns are plotted for the cases which are
identical in every respect except for the value
of the skin friction coefficient. For the
lower skin friction coefficient the 50 percent
and 60 percent streamlines are not as close
to the bottom wall. This is a result of
the relaxation of the velocity constraint along
the wall imparted by the lower friction term.
This effect is even more pronounced in
137
-------
0° POSITION
FIGURE 4
TANGENTIAL VELOCITIES IN HYDRAULIC MODEL OF APWA SWIRL
SEPARATION CHAMBER, 0° POSITION, FEET PER SECOND
Clear Overflow Discharge:
Foul Bottom Outflow:
100 cfs (prototype)
3 cfs (prototype)
90° POSITION
FIGURE 5
TANGENTIAL VELOCITIES IN HYDRAULIC MODEL OF APWA SWIRL
SEPARATION CHAMBER, 90° POSITION, FEET PER SECOND
138
-------
18
I
180° POSITION
FIGURE 6
TANGENTIAL VELOCITIES IN HYDRAULIC MODEL OF APWA SWIRL
SEPARATION CHAMBER, 180° POSITION, FEET PER SECOND
Clear Overflow Discharge: 100 cfs (prototype)
Foul Bottom Outflow: 3 cfs (prototype)
270° POSITION
FIGURE 7
TANGENTIAL VELOCITIES IN HYDRAULIC MODEL OF APWA SWIRL
SEPARATION CHAMBER, 270° POSITION, FEET PER SECOND
139
-------
Axis STANDPXPE
Skin Friction = 0.0025
COVER PLATE , OVERFLOW
o .' 3 .' . . ,
O
O 1 1 T . L
««,'333lj:rj"'«I
> 0 o ?, S 1 £ ' I 1 O
FOUL SEWER OUTLET
Axis STANDPXPE
Skin Friction = 0.005
COVER PLATE
OVERFLOW
• Q V Q 1
O H D 7
$ SOI
° I D T
L L>
H
FOUL SEWER OUTLET
CODE
O
X
D
5% of 1
10% of Inflow
20% of Inflow
30% cf Inflow
40% of Inflow
U
0
50% of Inflow
60% of Inflow
707 cf Inflow
80% of Inflow
9C% of Inflow
FIGURE 8
EFFECT OF SKIN FRICTION COEFFICIENT ON STREAMI INFS
140
-------
Skin Friction = 0.0025
Axis STANDPIPE
/
COVLK FLATE OVERFLOW
*
,»":.'>••
* ,
t •? , •
* t H r
• » * o
' * 0
• V I O
* » I O
» I 0
* T « O
T %
f
FOUL SEWER OUTLET
Axis STANDPIPE
/
Skin Friction - 0.005
»••*-
o
%
0
0
0
e
I CODE
FOUL SEWER OUTLET
+ - 0.18 ft/sec
Y - 0.35 ft/sec
D - 0.71 ft/sec
X - 1.06 ft/sec
o - 1.77 ft/sec
. - 2.83 ft/sec
FIGURE 9
EFFECT OF SKIN FRICTION COEFFICIENT ON VELOCITY PROFILES
141
-------
the velocity profiles in Figure 9. The
0.71-ft/sec velocity contour is shifted toward
the center of the chamber as a result of the
lowering of the skin friction coefficient. This
is a result of increasing the velocities at the
wall due to the velocity slip along the wall.
The skin friction constant, therefore, tends to
control the position of the velocity contours
while maintaining the general shape of the
streamline contours intact.
The effect of the mixing length constant,
K, is illustrated in Figure 10, Effect of Mixing
Length Constant on Streamlines, and Figure
11, Effect of Mixing Length Constant on
Velocity Profiles. Figures 10 and 11 represent
flows with values of the mixing length
constant differing by a factor of two with all
other factors the same. Figure 10 illustrates
how the general pattern of the streamlines is
markedly affected by the mixing length. A
higher mixing length constant increases the
scale of turbulence, giving a more viscous
solution. As a result of the greater shear
stresses, the streamlines are shifted toward the
outer chamber walls, and do not penetrate as
far under the weir.
This effect can also be observed in the
velocity contours in Figure 11. For the
lower value of the mixing length constant
the velocity contours more closely follow the
direction that was imparted to them along the
wall. For the higher mixing length case, the
effect of the viscous shear along the wall is
more rapidly damped out and the velocity
contours take on a vertical orientation as they
reflect the turbulence-dominated shear.
The mixing length, thus, tends to control
the shape of the individual streamline and
velocity contours.
The values of the mixing length constant
and eddy viscosity coefficient were adjusted
to provide the best fit of the mathematical
model with the 100-cfs LaSalle data.
A mixing length constant of 1.0 and a
skin friction constant of 0.0025 provided the
best fit. The mathematical model was then
operated for a flow of 162 cfs and the
velocity profiles were compared to the
LaSalle data at the higher flowrate, for the
same 180° cross section. Figure 12
summarizes the results of these velocity
comparisons for both 100 and 162 cfs.
The velocity profiles compare quite
closely, especially under the degree of
variation in the LaSalle data observed
between the four sampling sections. The
discrepancy between the predicted profiles
and the observed profiles near the wall can be
partially attributed to the higher viscosity
near the wall in the mathematical model
required to stabilize the computational
procedure. In theory, the velocities must
decline toward the walls as depicted by the
mathematical model in order to satisfy the
boundary conditions. However, the distance
over which this occurs is smaller than
indicated by the calculated results and would
not be observed in the laboratory data.
Furthermore, the laboratory data itself are not
reliable at the walls as a result of limitations
in the measuring equipment. Velocities were
measured in the laboratory with a 1.5-in.
diameter turbine meter which can only be
placed at a minimum distance from the wall
of about 0.75 in.
Another factor which could contribute to
discrepancies in the velocity profiles near the
upper wall is the presence of the skirt around
the overflow weir. This structural detail could
not be modeled with the relatively coarse
computational grid of the present model.
Comparison with the laboratory velocity
profiles near the outer wall was not attempted
due to large variations in the contours at the
various cross sections indicated by the LaSalle
data. However, the average velocities observed
in this region are of the same order of
magnitude as predicted.
The crossflow streamline pattern for the
selected baseline case (100 cfs) is shown in
Figure 13, Streamline Pattern for Base Case.
For the present choice of eddy viscosity
model, the flow patterns are independent of
flowrate. The flowfield at 162 cfs can be
obtained by scaling up the velocity profiles
for 100 cfs. The accuracy of this scaling
procedure is demonstrated by the previous
comparison with laboratory data (Fig. 12).
The crossflow streamline pattern shown in
Figure 13, therefore, applies to both flowrates.
It is interesting to compare the
streamlines predicted by the mathematical
142
-------
Mixing Length =1.0
Axis STANDPIPE
Axi
Foir
s STANDPI
. / .
UUVtK FLATt;
o
(P
0° ^
O
. * p° *
' . * rf> ^ » ' * L ^i
/ ,/ oc°°°,> ', •' , ' LL; ;
cP " ° '' ' .' /*.••
o ior*» *.TT
o • T _ '
0 I0'«« • . i o ;
. * " % °° /' ,;; .*•...-•]' *o\'\ •
FOUL SEWEI
EFFECT OF 1
nirrr.KT CODES
i
<
L
o
. - 5% of Inflow + - 50% of Inflow
o - 10% of Inflow * - 60% of Inflow
X - 20% of Inflow L - 70% of Inflow
,D - 30% of Inflow U - 80% of Inflow
Y - 40% of Inflow 0 - 90% of Inflow
FIGURE 10
MIXING LENGTH CONSTANT ON STREAMLINES
143
-------
Mixing Length =1.0
Axis STANDPIPE
COVER PLATE
OVERFLOW
°0
FOUL SEWER OUTLET
Mixing Length = 0.5
Axis STANDPIPE
* 1 >
IjUVJitf. CLitt.J-Cj UVC.K-TJjUW
-4 to ^ ^
r o
« ,T O I O o
« t* o « o o
• •* » I 0 0)
• ' e « o
• »T tfi » o
« T S I 0
• t 0*0
T
T O » 0
/ «> t S
T e f
t D » g
T O V O
o
r DM o
o * o
°° 0 D . *«,,.. • ' - o o o . -"'
— . . to. POHF
J
1
r<
1
FOUL SEWER OUTLET + - 0.18 ft/sec
Y - 0.35 ft/sec
D - 0.71 ft/sec
X - 1.06 ft/sec
o - 1.77 ft/sec
. - 2.83 ft/sec
FIGURE 11
EFFECT OF MIXING LENGTH CONSTANT ON VELOCITY PROFILES
144
-------
Overflow Discharge • 100 cfs
Foul Sewer Flow « 3 cfs
Weir Diameter • 24 ft
Overflow Discharge - 162 cfe
foal Sewer Flow - 3 cfs
Weir Diameter • 24 ft
LEGEND:
GE Predicted Velocities
LaSalle Observed Velocities
FIGURE 12
COMPARISON OF PREDICTED MATHEMATICAL MODEL VELOCITY PROFILE
WITH LASALLE DATA
145
-------
Axis STANDPIPE
COVER PLATE
OVERFLOW
»/*'••
* ' 3 ,' •' •
O r 3 »
O I
0 1 3 T
i « O '
/ 3 T
I 3 T
;•; ! n i i I rl * ?'•
H
FOUL SEWER OUTLET
(THE PERCENTAGE OF FLOW PASSING TO THE LEFT OF EACH STREAMLINE IS
INDICATED BY THE CODE BELOW)
CODE
o
X
D
Y
5% of Inflow +
10% of Inflow *
20% of Inflow L
30% of Inflow U
40% of Inflow 0
50% of Inflow
60% of Inflow
70% of Inflow
80% of Inflow
90% of Inflow
FIGURE 13
STREAMLINE PATTERNS FOR BASE CASE
model (Fig. 13) with photographs of the flow
patterns observed by the laboratory. The
LaSalle Laboratory performed two
experiments in which a wire grid with threads
attached was placed across the 90° cross
section of the chamber. It was intended that
the direction taken by the string would
provide an approximation of the streamline
pattern. Figures 14 and 15, Details of Special
Structures and Photograph of Flow Direction
Utilizing One-Inch Threads in Laboratory
Model, illustrate the results of these
experiments for both 1/2-in. and 1-in. long
threads. LaSalle noted that the tests were
complicated by violent fluctuations in the
string position as a result of the high
turbulence. The pictures are also distorted
towards the outer chamber wall as a result of
the chamber curvature.
Nevertheless, a few observations can be
made. In Figure 15. toward the outer wall
at points 1 and 2, toward the top of
the chamber, the threads are directed up-
ward. At point 3 in the same vertical line
but toward the bottom of the chamber, the
threads are directed downward. In Figure 13,
the mathematical model indicates that toward
the outer wall, the streamlines above the inlet
will be directed upward while those below the
inlet will be directed downward. Thus there is
general agreement between the laboratory
data and the mathematical model close to the
outer wall. According to Figure 13. 70
to 80 percent of the flow never passes
under the weir, thus to the left of the
weir the flow is predominately in the
146
-------
FIGURE 14
DETAILS OF SPECIAL STRUCTURES
tangential direction so that attempts to
measure the streamlines would be
complicated by the low radial velocities. At
the weir (see Figs. 14 and 15) the threads are
directed in an upward direction. This is also in
agreement with the mathematical model. A
more refined comparison of Figure 13 with
Figures 14 and 15 is not warranted because of
the high degree of uncertainty in the thread
position as a result of the violent fluctuations
in these positions observed by LaSalle.
Comparison of Mathematical Model Particle
Flow With Test Data
Particle calculations were made for the
five particle size and specific gravity
combinations given in Table 1, Particle Sizes
and Specific Gravity. Particle numbers one,
three, four and five were chosen to represent
gilsonite with specific gravity of 1.06, having
equivalent spherical diameters of 2 mm 0.5
mm, 0.3 mm and 0.019 mm, respectively.
Particle number two was selected to represent
Petrothene® with specific gravity of 1.01, and
diameter of 3.175 mm. These particle sizes
give settling velocities which span the range of
interest. Test data were available from LaSalle
Hydraulics Laboratory for particle numbers
one through four at 50 cfs, 100 cfs, and 162
cfs. The results for particle number five were
used to establish trends at very low settling
rates.
147
-------
FIGURE 15
PHOTOGRAPH OF FLOW DIRECTION UTILIZING 1/2-INCH THREADS IN
LABORATORY MODEL (provided by LaSalle Laboratory)
Particle flow calculations for all five
particles were made for 100 cfs flowrate. The
res-ults are presented in Figure 16,
Comparison of Particle Flow Mathematical
Model Results with Test Data, as a graph
depicting the percent of removal through the
foul sewer outlet as a function of settling
velocity. A smooth curve has been drawn
through the five calculated points. The appli-
cability of the scaling laws was tested next, by
calculating a flowfield for particle number
three at a flo\vrate of 162 cfs. This calculation
was compared with a prediction made by scal-
ing the 100-cfs results. Thus, particle number
three, with settling velocity of 0.0717 fps
(prototype scale), is separated with an
1. Gilsonite
2. Petrothene®
3. Gilsonite
4. Gilsonite
5. Gilsonite
TABLE 1
Particle Sizes and Specific Gravity
Particle Diameter Sg
0.0787 in. (2mm) 1.06
0.125 in. (3.175 mm) 1.01
0.0197 in. (0.5mm) 1.06
0.0118 in. (0.3mm) 1.06
0.0075 in. (0.019mm) 1.06
Settling Velocity (fps)
Model Scale Prototype Scale
0.1248
0.06112
0.0207
0.00795
0.00347
0.432
0.212
0.0717
0.0275
0.0100
148
-------
100,
0.01
0.1 (FT/SEC)
1.0
1.0
(CM/SEC)
10.0
PROTOTYPE SCALE SETTLING VELOCITY
FIGURE 16
COMPARISON OF PARTICLE FLOW MATHEMATICAL MODEL RESULTS
WITH TEST DATA
efficiency of 63.4 percent at 100 cfs. The
separation efficiency for this particle at 162
cfs should be the same as for a particle with
settling rate
VS2=VS)
(Qi)
Q2
= (0.0717)
1 62
=0.0442/pi
at 100 cfs. From the 100 cfs curve in Figure
16 this efficiency is 46 percent.
The mathematical model calculation for a
particle with settling velocity of 0.0717 fps at
162 cfs, gave an efficiency of 46.2 percent,
which is within the accuracy with which
Figure 16 can be read. With the accuracy of
the scaling procedure established, the
separation efficiency results calculated for
100 cfs were scaled to 50 cfs and 162 cfs
flowrates. The results are also shown as
smooth curves in Figure 16.
The test data from LaSalle Hydraulics
Laboratory have also been plotted in Figure
16 for comparison with the mathematical
model results. The spreader bars shown on the
Petrothene® and 2 mm gilsonite data indicate
the range in settling velocities corresponding
to the spread in particle sizes. At the two
smaller sizes, the gilsonite was screened to
reduce the range of particle sizes. Two data
points are shown for 0.5 mm gilsonite at 100
cfs, which gave separation efficiencies of 35
and 42 percent in two successive tests. This
difference of seven percent is probably
149
-------
indicative of the scatter to be expected in the
remaining data. The settling velocities of all
particles in Figure 16 have been scaled up to
the prototype chamber size (a factor of A/IT
times their actual settling velocities).
The calculated efficiency curves generally
agree very well with the test data at both high
and low settling velocities, but they overesti-
mate the measured efficiencies at intermediate
settling rates. For 0.3 mm gilsonite, the
agreement is very good at all three flowrates.
The calculated results slightly overestimate
the actual efficiency by three percent at 50
and 100 cfs, and by five percent at 162 cfs. In
the limit of very small settling velocities, all of
the calculated curves correctly approach a
lower limit of three percent removal
efficiency, corresponding to the fraction of
liquid withdrawn through the foul sewer
outlet.
At the highest settling rates tested, the
calculated results correctly indicate where
100 percent removal efficiency will occur. At
100 cfs, both calculations and tests show 100
percent removal efficiency is obtained with
two mm gilsonite. At 162 cfs, the calculated
separation efficiency is 96 dercent for two
mm gilsonite. The measured efficiency at 162
cfs was 90 percent, but this test included finer
particles as indicated by the spreader bars.
The calculated curve crosses these spreader
bars a little to left of center, just as it does at
100 cfs.
At t'he intermediate settling rates
corresponding to 0.5 mm gilsonite and 3.175
mm Petrothene®, the calculated efficiencies
are substantially larger than those measured at
100 and 162 cfs, for example, the
mathematical model predicts 80 percent
recovery for the Petrothene® whereas the
tests gave only 35 to 45 percent removal
efficiency. The agreement is somewhat better
at 100 cfs, with calculated removal efficiency
of 93 percent compared with a measured
removal efficiency of 65 percent. The reasons
for these discrepancies are not clear, but
several suggestions are offered.
First, it is surprising that the measured
removal efficiency for Petrothene® is so
much lower than for the gilsonite because the
unsieved gilsonite contains some particles
whose settling rates are in the same range as
that of the Petrothene® (note the overlap in
the spreader bars shown in Figure 16).
Probably these fine particles are lost in the
gilsonite tests without appreciably affecting
the measured removal efficiency.
Nevertheless, the very sharp decrease in
performance attained with Petrothene® is
surprising. One explanation lies in the possible
non-uniformity of the Petrothene® particles.
With a nominal specific gravity of only 1.01,
very small changes in the composition could
drastically affect the settling rate, which
varies in proportion to (Sg-1). In fact, in some
simple tests performed at General Electric, 12
to 20 percent of the particles were found to
float, even after soaking overnight in a
detergent solution. In the LaSalle tests, these
floating particles were removed from the test
mixture. Nevertheless, the presence of these
floating particles indicates a larger range in
settling velocities than shown in Figure 16.
During testing, adhered gas bubbles may also
cause some particles to rise and be entrained
in the overflow. For these reasons, the
observed removal efficiency with Petrothene®
may have been influenced by the loss of
particles with lower settling velocities than
those for which the calculations were made. It
is doubtful, however, whether the entire
discrepancy can be attributed to this cause,
because a large number of lightweight
particles would be required to explain the
difference.
An additional source ef disagreement
between the mathematical model and test
results lies in the non-axisymmetric nature of
the laboratory model, which must differ
appreciably from the computed axisymmetric
flow at the inlet and near the baffle. In fact,
it could be expected that the jet created by
the inlet channel could readily carry particles
to the surface, a condition not accounted for
in the mathematical model. It is reasonable
that the smoother flow in the mathematical
model (produced by smoothly spreading the
inlet flow over the entire circumference),
would give better removal efficiencies. This
explanation also confirms the observation that
agreement is better at 100 cfs than at 162 cfs.
At the higher flowrate, the turbulence and
150
-------
100
20
100
FLOWRATE - CFS
1000
FIGURE 17
PREDICTED PERFORMANCE OF PROTOTYPE SWIRL CONCENTRATOR VS FLOWRATE
(36 ft Diameter)
non-axisymmetric effects are accentuated.
Furthermore, at the lowest flowrate,
agreement is quite good even at the
intermediate settling rates. Thus, the
predicted removal efficiency for 0.5 mm
gilsonite at 50 cfs is 83 percent, whereas the
measured removal efficiency was 80 percent.
In summary, it appears that the
mathematical model correctly predicts the
removal efficiency at the upper and lower
ends of the efficiency curve. At intermediate
settling rates, the model predicts the
performance well at 50 cfs, but the agreement
deteriorates at higher flows, probably due to
non-axisymmetric flow effects.
Results for Nominal Case
The performance of the concentrator for
several settling rates over a wide range of
flowrates was determined through use of the
scaling relationships. The results are shown in
Figure 17. Predicted Performance of
Prototype of Swirl Concentrator Versus
Flowrate. The scaling of the calculated results
to new flowrates requires that the flow
patterns remain unchanged although the
velocities increase in magnitude. The liquid
flowfield will scale properly in this manner,
provided the fraction of flow withdrawn
through the foul sewer outlet is held constant.
Therefore, Figure 17 applies to cases where
the foul sewer flow is three percent of the
total inflow. Because the foul sewer flow is so
small, the results should also apply
approximately to cases where the foul sewer
fraction is still smaller or slightly larger. With
151
-------
a different foul sewer fraction, the asymtotic
lower limit of the separator performance will
be altered from three percent to the new foul
sewer value.
The results given in Figure 17 do not
account for non-axisymmetric flow effects, or
for changes in the flow pattern which may
occur at high flowrates. Some evidence of
non-axisymmetric effects is evident in the
laboratory data at 100 and 162 cfs, and these
effects may become more pronounced at still
higher flows. Similarly, at the very large
flows (250 cfs and higher) the nature of the
flow could be altered due to the increasing
restriction of the overflow weir and to the
jet-like behavior of the inlet flow. The
predicted results at large flowrates may,
therefore, not be reliable and should be used
cautiously. Within the range of the laboratory
data (50 cfs-162 cfs) the scaling procedure has
been shown to reliably predict the
concentrator performance. The results should
also be accurate at lower flows.
The physical mechanisms operating
within the swirl concentrator are illustrated in
Figures 18-21, Particle Trajectories and
Concentration Profiles at 100 cfs for 2 mm,
0.25 mm, 0.5 mm and 0.3 mm Particles. Each
of these figures shows the particle
concentration (number density) profiles and
typical particle trajectories for a given settling
rate. The settling rates are 0.432 fps, 0.212
fps, 0.0717 fps, and 0.0275 fps respectively.
In Figure 18, the very large settling rate
results in high particle concentrations along
the bottom, which decreases gradually toward
the underside of the weir. These
concentrations have been normalized by the
inlet concentration and thus vary generally
from zero to unity, with some local regions
having concentrations greater than unity. The
distortion of the concentration profiles by the
upflow velocity near the overflow is
interesting. The upflow increases the local
concentration as evidenced by the lifting of
the constant concentration lines in this
region. Thus, at a given depth, the
concentration is greater right under the
overflow region than on either side, due to
the transport of particles by the upward flow.
The particle trajectories in Figure 18
show very rapid fallout toward the bottom,
with only slight deviations caused by the
secondary liquid flow along the bottom. The
trajectories were calculated for particles
arbitrarily started at selected points in the
flowfield as shown in Figure 18. It is not
possible to determine concentrator
performance by tracing particle paths from
the inflow region alone, as one can for-the
liquid flow. For the case shown in Figure 18,
for example, all the particles entering the
concentrator at the periphery hit the bottom
to the right of point B. Yet both the
laboratory and mathematical model results
show that particles in fact reach the inner
region of the concentrator, as evidenced by
the number density contours shown in Figure
18. The explanation of this seeming
discrepancy lies in the turbulence of the flow
The calculated trajectories only represent the
mean particle motion. The liquid turbulence
will cause the actual trajectories to differ
randomly from those shown, thereby
scattering particles from regions of high
concentration into the low concentration
regions.
As the particle settling velocity is
decreased, the particle trajectories and
concentration profiles change drastically. In
Figure 19, Effect of Underflow Sewer Fraction
on Removal Efficiency, particles with settling
velocity of one-half those in Figure 18 show
much more influence due to the secondary
liquid flow in the chamber. This is evidenced
by the large lateral excursions of the particles
near the center, which move first outward and
then inward as they fall. All particle
trajectories shown, however, still reach the
bottom indicating a very high efficiency
(actually 93% for this case which represents
the Petrothene®). The concentration profiles
in Figure 19 indicate a much larger region
with a concentration near unity. The N = 1
profile (marked by the symbol Y) is
irregularly shaped, and generally covers the
bottom two-thirds of the chamber. The
random appearance of this profile is due to
small variations in concentration about a
nominal value of unity. Thus, adjacent points
may have concentrations of 0.99 and 1.01
respectively The computer plotting
152
-------
Axis STANDPIPE
I. / .1.
a) Concentration Profiles
COVER PLATE
OVERFLOW
-------
a) Concentration Profiles
Axis STANDPIPE
COVER PLATE
OVERFLOW
>-4-
;
M
f
FOUL SEWER OUTLET
CODE A
- N/N.n = 0.2 D - N/N. = 0.8
N/N.n = 0.4 Y - N/N,'" = 1.0
N/N. =06
b) Trajectories for particles
started at 5 vertical positions
Axis STANDPIPE and 6 equi-spaced radial locations
/
UUV.&.K. rjjAJ.ii uvtiKriiUW
': i X "\ i >
• 0. 0 O. f> -°
• 0- •„ Q « ••
« 0. . 0 « * i° .'
* 0. « • if 0 • j, * .0 ,*
» «• * ? « « • c» -° ,
! °- " £**'**£*
S S' .* o »* c' -' *,' o '
^ £ ° ?**%%^^' ' •'' •ct^^lo"0,,,*'' ,•" » •
h* , JZ ^f'.5»_ • ' .T^VlViDOOO.^Sd^, j,0 T'
< ^ TOPE B
t-
6
hi
tr
c
Particle starting position (from bottc
FOUL SEWER OUTLET
. - 0.6 ft D _ 4.2 ft
o - 1.8 ft Y - 5.4 ft
X - 3.0 ft
FIGURE 19
PARTICLE TRAJECTORY AND CONCENTRATION PROFILES AT 100 cfs FOR 25-INCH
PETROTHENE® PARTICLES (prototype scale settling velocity of 0 212 fps)
154
-------
procedure interpolates between these values
to find the location of the N = 1 line.
However such small variations are not
physically significant, and the actual shape of
this contour is not meaningful. What is
significant is the volume of the chamber in
which the concentration is near unity. For
example, comparison of Figure 18 and 19
reveals that in the former case the N = 1
concentration profile is regular shaped, and
confined to the region of the chamber near
the bottom, due to the rapid settling rate. In
contrast, the slower settling particles in Figure
19 are almost uniformly distributed (at the
Met concentration) over the entire bottom
2/3 of the chamber. The concentration
gradient near the underside of the weir is also
much greater in Figure 19, as evidenced by
the closer spacing of the concentration
profiles under the weir. As in Figure 18, the
distortion due to the upward flow in the
overflow region is evident in the
concentration profiles of Figure 19.
Similar changes are evident in Figure 20,
which corresponds to 0.5 mm Gilsonite. The
concentration profiles show the particles are
spread uniformly over most of the chamber,
with a very steep gradient at the underside of
the weir. The particle trajectories now
indicate that a significant number of particles
leave by the overflow. Some of the particles
entering at the periphery are brought to the
bottom by the downward flow, and are then
dragged inward toward the center by the
secondary liquid motion. As these particles
reach the quiescent inner region they fall to
the bottom and leave by the foul sewer outlet.
It is noted that particles which are scattered by
turbulence into the inner region near the
standpipe, settle more or less straight to the
bottom. A little further toward the outside,
however, particles which start to settle to the
bottom are entrained in the upward liquid
flow and are carried out the overflow. The
behavior of the particles near the top of the
inlet region in Figure 20 is also interesting.
These particles are brought to the surface by
the upward liquid velocity, but then they
settle again toward the bottom About half
way down to the bottom, they are again
re-entrained with the upflow and are carried
out the overflow.
Finally, in Figure 21, which represents
the very slow settling 0.3 mm gilsonite, the
limit of the concentrator performance is quite
evident. The concentration is essentially
uniform over the cross section, and almost all
of the particle trajectories exit by the
overflow. Near the inner quiescent region by
the standpipe, some settling is evident, but
most of these particles are later entrained in
the upflow. Some of the particles which reach
the central region near the bottom are
entrained in the liquid flow leaving the foul
sewer outlet.
Taken together, Figures 18-21 provide a
graphic illustration of the swirl concentrator
operating mechanisms. The concentration
profiles show clearly that particles are
scattered into low concentration regions, and
the trajectories illustrate the average motion
of particles of different sizes within the
concentrator. These average trajectories
provide valuable insights into the
concentrator operation which are not always
possible with the physical model. In the
laboratory tests, for example, turbulence and
the rotational motion make it difficult to
follow individual particles. And if an
individual particle is tracked, its statistical
significance is uncertain, because another
particle started at the same location will
follow a different path due to the influence of
turbulence.
Effect of Scale Size on Concentrator
Performance
Probably the most important use of the
mathematical model is to predict how the
prototype scale swirl concentrator will differ
in performance from the laboratory model.
This is a vital piece of information which
cannot be obtained in the laboratory without
constructing a full size unit. Usually, the
answer cannot be obtained from field studies
either, due to the difficulty of performing a
controlled experiment under field conditions.
Some differences are expected because it is
impossible to correctly model all of the terms
in the particle equations of motion in the
laboratory. Consequently, the mathematical
model was exercised for two cases: the
nominal 100 cfs flow in the prototype scale
concentrator, and the scaled flowrate of
155
-------
a) Concentration Profiles
Axis STANDPIPE
COVER PLATE
OVERFLOW
OD 00000000000°
T f
T T
-aB_
«« fr
FOUL SEWER OUTLET
CODE A
. - N/Njn = 0.2 D- N/N. =0.8
o - N/NJn = 0.4 Y - N/N!" 1.0
X - N/N. = 0.6
b) Trajectories for particles
started at 5 vertical positions
and 6 equi-spaced radial locations
Axis STANDPIPE
/ COVER PLATE
»•-*-
*--*-
OVERFLOW
o.
0.
•
.o/ fo
.0. »o .
n
'&
/:'
00
FOUL SEWER OUTLET
.CODES
Particle starting position (from bottom)
. - 0.6 ft D - 4.2 ft
FIGURE 20 x I 1 o ft Y ~ " "
PARTICLE TRAJECTORIES AND CONCENTRATION PROFILES AT 100 cfs FOR 0.5 mm
GILSONITE PARTICLES (prototype scale settling velocity of 0.0717 fps)
156
-------
Axis STANDPIPE
. / .1.
a) Concentration Profiles
COVER PLATE
-»+*-
OVERFLOW
i. ', t,
FOUL SEWER OUTLET
o - N/N. = 0.4
X - N/N!" = 0.6
CODE A
0.2 D
Y
N/Njn = 0.8
N/N. =1.0
b) Trajectories for particles
started at 5 vertical positions
and 6 equi-spaced radial locations
Axis STANDPIPE
COVER PLATE
OVERFLOW
FOUL SEWER OUTLET
CODEB
Particle starting position (from bottom)
. - 0.6 ft D - 4.2 ft
o - 1.8ft Y - 5.4ft
X - 3.0 ft
FIGURE 21
PARTICLE TRAJECTORIES AND CONCENTRATION PROFILES AT 100 cfs FOR 0.3 mm
GILSONITE PARTICLES (prototype scale settling velocity of 0.275 fps)
157
-------
0.20047 cfs flow in the model concentrator.
Both calculations were performed for particle
number 3 (Table 1) which represents 0.5 mm
Gilsonite with settling velocity of 0.0207 fps
on the model scale. The corresponding
prototype scale settling velocity is
V, = (0.0207)^/12 = 0.0717 to
which was obtained by using an 0.0238-in.
particle with specific gravity of 1.2 (see Fig.
30). The results of these calculations are
summarized as:
Model Scale Prototype Scale
Particle flux-
Overflow (Qp0) 0.0819 sec"1 40.83 sec'1
Particle flux-
Bottom (Qpb) 0.1414 sec'1 70.66 sec"1
Efficiency Qpb
(Qpb + QPO) 63.3% 63.3%
The equations from which Qpo and Qp^
are calculated have been given previously
(Equations 59 and 60). The units are
number of particles per second for an inlet
concentration of one particle per cubic foot.
The fluxes for higher inlet concentration are
obtained by scaling them in direct proportion
to the actual inlet concentration. Since both
Qpo and Qpb are scaled by the same factor,
their ratio (and hence the efficiency) does not
change with inlet concentration.
This numerical experiment demonstrates
that the assumed scaling procedures are valid,
and that the prototype concentrator
performance can, in fact, be accurately
predicted by adjusting the particle specific
gravity and size so as to yield the proper
scaled settling velocity. This conclusion is, of
course, only valid to the extent that the liquid
flow pattern is the same in the model and
prototype. For the assumed eddy viscosity
representation, this similarity is very close in
the mathematical model. However, if the
prototype scale were to be very much larger
than the model (say a factor of 100 rather
than 12 as in the present instance), it is
possible for different flow effects to appear,
which are not accounted for in the present
mathematical model, specifically calibrated
against the laboratory scale device.
It is noted that the scaling procedure only
preserves the balance between the drag and
the buoyancy if the particle motion relative
to the fluid has exactly the settling velocity.
At other relative velocities, this balance will
be different for the model and prototype
scales. Furthermore, the inertial acceleration
terms are all multiplied by the specific
gravity. Since different specific gravities have
been used in the model and prototype
calculations, these terms will not be correctly
scaled. The fact that essentially the same
results were obtained in both calculations
demonstrates that the inertial terms in the
equations of motion are, in fact, negligible
compared with drag and buoyancy.
The results also indicate that, to a very
good level of approximation, the particle
velocities can be found by superimposing a
uniform settling rate on the velocities
obtained from the liquid flowfield. For
example, at the randomly selected point i = 7,
k = 17, in the model scale calculation, the
following results were obtained:
Radial Velocity
Tangential Velocity
Vertical Velocity
Flow Velocities (fps)
Liquid Particle
0.02630 0.02620
0.3130 0.3130
-0.04979 -0.02827
The differences between the liquid and
particle velocities are negligible for the radial
and tangential components. For the vertical
component, the difference is
VF Y! = (- 0.02878) -(-0.04979)
= 0.02101 fps
which is very close to the calculated settling
velocity of 0.0207 fps. Therefore, subsequent
calculations for other cases were made with
the particle velocities obtained by
superimposing the settling rate on the liquid
flow velocities as calculated for the given case.
Influence of Geometric Variables on
Separator Performance
Weir Diameter
To determine the effect of the diameter
of the overflow weir on the liquid flowfield
and the particle removal efficiencies, the
158
-------
mathematical model was operated at the same
conditions of 100 cfs inflow and 3 cfs foul
water outflow for two different weir sizes
(24-ft diameter and 32-ft diameter, prototype
scale).
The effect of the weir diameter on the
liquid flowfield is summarized in Figures 22
and 23, Comparison of Crossflow Streamlines
and Velocity Contours for 24-ft and 32-ft
Weirs. It should again be emphasized that
although the flowfields depicted in Figures 22
and 23 apply to any chamber cross section for
the mathematical model, as a result of the
axisymmetric approximation, they only
predict conditions at the 180° cross section
for the laboratory model. This is a
consequence of the calibration of the
mathematical model for the 180° laboratory
cross section. Figure 22 shows the effect of
the weir diameter on the crossflow
streamlines. For the larger weir diameter,
the streamline pattern is compressed near
the surface of the chamber. This is a result
of the smaller annular cross section through
which the flow must pass. The streamlines
toward the bottom of the chamber, on the
other hand, retain the same position for both
weir sizes.
This effect is also evident in the velocity
contours for the two weir sizes depicted in
Figure 23. As a result of the compression of
the streamline pattern for the larger weir
diameter, high velocities are experienced
towards the outer wall of the swirl
concentrator. The higher vertical velocities at
the wall also cause the crossflow velocity
contours to shift towards the outer wall. The
net result of the larger weir diameter is
therefore to cause larger vertical flow
velocities towards the walls of the swirl
concentrator.
The effect of the weir diameter on the
particle removal efficiency is given in Table 2,
Effect of Weir Size on Concentrator
Efficiency.
The larger weir diameter yielded poorer
removal efficiences for every particle settling
velocity. The difference in the efficiency of
the two weir sizes was lowest at both very
high and very low particle settling velocities
and largest at the settling velocity of 0.212
TABLE 2
Effect of Weir Size on Concentrator Efficiency
Particle Settling Removal Efficiency %
Velocity 24-ft 32-ft
(Prototype Scale ft/sec) Weir Weir
0.0275 31.2 276
0.0717 63.1 51.6
0.212 93.2 79.4
0.432 100 90.3
ft/sec. These results are in agreement with the
tests performed by LaSalle. The Laboratory
performed tests on 24, 28, and 32-ft
(prototype scale) overflow weirs, and
concluded that the 24-ft weir yielded the best
removal efficiency. Recent tests performed by
the Laboratory on a 20-ft weir with a 24-ft
scum ring indicated removal efficiencies of
the same order of magnitude as the 24-ft weir.
Since both the mathematical and physical
models predict better separation efficiencies
for a 24-ft diameter weir than for a 32-ft one,
it is possible that a still smaller weir diameter
would give improved performance. The
performance changes with weir diameter are
related to the changing overflow velocity
profile as illustrated in Figure 24, Effect of
Weir Diameter Overflow Velocity Profile. For
large weir diameters (Fig. 24a), the overflow
velocity contains a high peak. Any particles
entrained in this upflow will be readily carried
out the overflow. As the weir diameter is
decreased, the peak is reduced as a result of
the increase in cross-sectional area through
which the flow must pass (Fig. 24b). At this
lower upward velocity, fewer particles will be
carried out the overflow. In general, the lower
the upflow velocity, the better the separator
performance. Also, by withdrawing the flow
nearer the center, more of the particles may
be scattered by turbulence into the quiet
region under the weir, from which they can
settle to the bottom. As the weir diameter is
reduced still further, as illustrated in Figure
24c, the peak upflow velocity may not be
decreased any further because there is no
upflow near the outside of the tank, and the
smaller weir circumference demands a greater
local velocity over the weir. Decreases in weir
diameter below this point may reduce
159
-------
Axis STANDPIPE
a) 24' Weir
COVER PLATE
OVERFLOW
O / * ' • • I. I/ * "0
f I 3 1 ' • 1. U
0 « J ' • • L
O « 3 f • • L
O « 3 ' • • I
a « o ' « • i
O / 3 T . •
8 I 3 ' • •
S • o
., ,
o'? s rn 11"; •
FOUL SEWER OUTLET
Axis STANDPIPE
b) 32' Weir
COVER PLATE
OVERFLOW
*•-*-
O JOT . .LU.
O O t
O rOT**LU«
5 > 0 • :.t«
O T • • I
* '
FOUL SEWER OUTLET .
o
X
D
Y
5%
10%
20%
30%
40%
CODE
of Inflow
of Inflow
of Inflow
of Inflow
of Inflow
+ - 50% of Inflow
* - 60% of Inflow
L - 70% of Inflow
U - 80% of Inflow
0 - 90% of Inflow
FIGURE 22
COMPARISON OF CROSSFLOW STREAMLINES FOR 24-FT AND 32-FT WEIR
160
-------
Axis STANDPIPE
'
FOIT
a) 24' Weir
COVER PLATE
t
'
•
•
•
,
.
.
•
.
•
L SEWEE
Axis
5 STANDPI1
>E
*
t
*
*
,
,
*
*
*
*
*
•
FOUL SEWER
COMPARISON OF
T 3 3 J
,3 -
*' » 1
* 3 «
- 3
' 11
' 1
• «
" I
' I
T .
T |
T 1
3 •
L OUTLET
b) 32' Weir
COVER PLATE
T T l
» t
.' f
_ -O
f ff
f
""
TT * C
OUTLET
FIGURE 23
OVERFLOW
*
O
O
Q
•
o
o
«
°° o 0
O O v *
»°0 > *"
• o
X O
o
0
o
e
o
o
o
0
V O
• o
+
Y
D
X
o
•
O I
o >
H
§
S
s;
OVERFL
» 0
* O
•
OW
•
H
JH
f
§
CODE
- 0.18 ft/sec
- 0.35 ft/sec
- 0.71 ft/sec
- 1.06 ft/sec
- 1.77 ft/sec
- 2.83 ft/sec
VELOCITY CONTOURS FOR 24 *r AND 32-FT WEIR
161
-------
4/-L
a) High peak velocity due to narrow overflow annuLud
b) Lower peak velocity with wider overflow annulus
c) No additional reduction in peak velocity with further
widening of annulus
FIGURE 24
EFFECT OF WEIR DIAMETER ON OVERFLOW VELOCITY PROFILE
162
-------
removal efficiencies by reducing the size of
the low velocity region beneath the weir in
which much of the particle sedimentation
occurs. The recent tests performed in the
laboratory with a 20-ft weir and with a 24-ft
scum ring indicated removal efficiencies
approximately the same as those with the
24-ft weir. Thus 20 feet may be near this
lower limit for improving efficiency by
reducing weir diameter, although this
conclusion is speculative and not supported
by calculations or data. Further reduction in
weir diameter would also have the undesirable
effect of reducing the storage area available
for floating solids.
Depth to Width Ratio
The effect of the depth to width ratio on
the liquid flowfield and particle removal
efficiency was determined by operating the
mathematical model for two different
chamber depths, with all other parameters
held constant. The effect of the chamber
depth on the liquid flowfield is shown in
Figures 25 and 26.
Figure 25, Comparison of Crossflow
Streamline Pattern for Different Tank Depths,
illustrates the effect on the chamber crossflow
streamlines. Although there is some difference
in the position of a few of the streamlines
between the 9-ft depth (7.5 ft to bottom of
weir plate) and 10.5-ft depth (9.0 ft to
bottom of weir plate), the general pattern and
degree of penetration of the majority of the
streamlines remain unchanged. This trend can
also be noted in the velocity contours
illustrated in Figure 26, Comparison of
Velocity Contours for Different Tank Depths.
As in the case of the streamlines, there is no
marked difference between the general shape
and location of the velocity contours.
With regard to the removal efficiencies,
the mathematical model predicts a marginal
improvement in the removal efficiencies for
the larger tank depth as indicated in Table 3,
Effect of Chamber Depth on Concentrator
Efficiency. It should be emphasized that the
results indicated in Table 3 are based upon
the mathematical model and have not been
verified by testing of the final laboratory
configuration. However, laboratory tests
TABLE 3
Effect of Chamber Depth on Concentrator
Performance
Particle Settling
Velocity
Removal Efficiency
9.0 Ft Depth 10.5 Ft Depth
(prototype scale ft/sec) 0.25 depth/diameter, 0.29 depth/diameter
0.0275
0.0717
0.212
0.432
31.2
63.4
93.2
100
35.8
67.1
96.0
99.5
utilizing earlier concentrator configurations,
indicated that "marginal, even questionable,"
increases in performance were observed at
depths down to 15 feet.
Foul Sewer Fraction
The 100 cfs nominal case was operated at
three different foul sewer fractions to'
ascertain the effect of the foul sewer fraction
on concentrator performance. Figures 27 and
28 depict the velocity contours and the
crossflow streamlines for foul sewer fractions
of 10 and 20 percent. The base case at a foul
sewer fraction of three percent (see Fig. 26
for velocity profile and Fig. 25 for
streamlines) provides a third point for
comparisons.
The effect of the doubling of the foul
•sewer fraction from 10 to 20 percent is to
move the ten percent streamline so that it
provides for the increased flow out of the foul
sewer outlet (Fig. 27, Comparison of Velocity
Contours for Different Foul Sewer Fractions).
The ten percent streamline for the higher foul
sewer takes on the same shape as the five
percent streamline for the lower foul sewer
fraction. The remaining streamlines (for
example the 60% streamline) are identical for
both cases.
This localized change in the liquid
flowfield is also evident in velocity profiles in
Figure 28, Comparison of Crossflow
Streamline Patterns for Different Foul Sewer,
Fractions. The velocity profiles near the outer
wall are essentially unchanged for the two
foul sewer fractions, while the velocity
contours near the standpipe are shifted
towards the foul sewer outlet. This effect is
most pronounced for the 0.71 streamline
which has a sharp deflection toward the base
163
-------
Axis STANDPIPE
•<—
a) 9.0' Depth
COVER PLATE
OVERFLOW
U y U u
w
0 « ^ T » • L
O « 3 * * • L
0 «
0 • 3 » * ^ i
O » O T « • [.
wo
UO
U 0
FOUL SEWER OUTLET
Axis STANDPIPE
-*-
b) 10.5' Depth
COVER PLATE
OVERFLOW
-»-H-
o M
8
AUJ
•
L>u>
- o >* e f
•' « MOT
O > O T
e I o T
f
» t
L V •
O
e
o
e
o
.
; o o o o
88888
FOUL SEWER OUTLET
CODE
. - 5% of Inflow +
o - 10% of Inflow *
X - 20% of Inflow L
D - 30% of Inflow U
Y - 40% of Inflow 0
- 50% of Inflow
- 60% of Inflow
- 70% of Inflow
- 80% of Inflow
- 90% of Inflow
FIGURE 25
COMPARISON OF CROSSFLOW STREAMLINE PATTERNS FOR DIFFERENT TANK DEPTHS
164
-------
Axis STANDPIPE
a) 9.0' Depth
< / .
COVER PLATE OVERFLOW
, ' ' 3 3 3 J * ' ' '" -
/ •' ,' '- .' ' 0 0 .
' •
1 3 * 0
' I • »
• 10.
• » I
• t •
• » I
*
• T •
' I
« T f
»
' . 3 3 3 « . °° 0 • -
2
1
|
Axis STANDPIPE
FOUL SEWER OUTLET
b) 10.5' Depth
COVER PLATE |
->-•*-
OVERFLOW
_£—Q n « ^
FOUL SEWER OUTLET
CODE
+ - 0.18 ft/sec
Y - 0.35 ft/sec
D - 0.71 ft/sec
X - 1.06 ft/sec
o - 1.77 ft/sec
. - 2.83 ft/sec
FIGURE 26
COMPARISON OF VELOCITY CONTOURS FQR DIFFERENT TANK DEPTHS
165
-------
Axis STANDPIPE
_/_
a) Foul Sewer Fraction = 10%
COVER PLATE OVERFLOW
<• •
- o
a « e
o > «
• * •
o * »
DM O
O
01 n
O * «
01 e
0
e
° °
e
•
' I
o » ",
FOUL SEWER OUTLET
b) Foul Sewer Fraction = 20%
Axis STANDPIPE
4
(jUVJin. rj.iAJ.ri uvurvrijuw
<,rf"">°°"""/'-' : .-•••;
o i e •
o
a i :
0 i
i
a i
0 «
a i
* •
a i
' °"° * • *
^ , . .» CO!
1
1
DE
M
>3
Q
^
FOUL SEWER OUTLET + '_ °Q'™ ££^
D - 0.71 ft/sec
X - 1.06 ft/sec
o - 1.77 ft/sec
. - 2.83 ft/sec
FIGURE 27
COMPARISON OF VELOCITY CONTOURS FOR DIFFERENT FOUL SEWER FRACTIONS
166
-------
Axis STANDPIPE
-» 1-
a) Foul Sewer Fraction = 10%
COVER PLATE
OVERFLOW
» 0 T .
I «»'.
_
t t
* » I U»
• u
•III*
tl.ll>
' f
• 0 « *
???•;•, i ? IS! Sgj-t*-
FOUL SEWER OUTLET
Axis STANDPIPE
b) Foul Sewer Fraction = 20%
INFL
COVER PLATE OVERFLOW
; : : v-5-'^:
• • u
0° o» i* o r • • i. u •
0 0
O O f O 9 « • I U 9
8 • /-/'•'
• 10'.* •.
I ft f .. - • .
i o .; . ;
* «. % • ' f °
• • S "o ',-...,' ° '
CODE ' '
tr1
FOUL SEWER OUTLET
. - 5% of Inflow +
o - 10% of Inflow *
X - 20% of Inflow L
D - 30% of Inflow U
Y - 40% of Inflow 0
50% of Inflow
60% of Inflow
70% of Inflow
80% of Inflow
90% of Inflow
FIGURE 28
COMPARISON OF CROSSFLOW STREAMLINE PATTERN
FOR DIFFERENT FOUL SEWER FRACTIONS
167
-------
of the chamber to account for the higher
foul sewer velocity.
The removal efficiencies for the three
foul sewer fractions are summarized in Table
4, Effect of Foul Sewer Fraction on
Concentrator Performance.
It is apparent from Table 4 that the
mathematical model predicts increased
removal efficiencies for larger foul sewer
fractions. The increased removal efficiencies
can probably be attributed to the reduction in
the vertical velocities at the overflow, thus
allowing more particles to settle into the foul
sewer outlet. Figure 29, Effect of Underflow
Fraction on Removal Efficiency, represents a
plot of the data from Table 4.
DESIGN RECOMMENDATIONS
The purpose of this section is to show
how the results of the mathematical model
can be utilized for designing a swirl
concentrator from the model results. To
illustrate the approach, a hypothetical design
example will be used. Assume that a
concentrator is to be designed for 80 percent
removal of 1/4-in. particles having a specific
gravity of 1.05 for a design storm which
produces a chamber inflow of 200 cfs. The
first step is to determine a design settling
velocity of the particles from the particle size
and specific gravity data. The settling velocity
can be calculated by conventional methods,
or from a graphical analysis such as Figure 30,
Particle Settling Rates. Figure 30 was
generated .from Equation (42), which is valid
for Reynolds numbers less than 104. Entering
Figure 30 with a particle diameter of 0.25
in. and the Sg = 1.05 curve, a settling
velocity of 0.3 ft/sec is obtained. If several
particle sizes and specific gravities are
involved, engineering judgment must be used
to determine the design settling velocity for
the particle mixture.
After determination of the particle
settling velocity, the next step is to estimate
the size of the required concentrator. This can
be done by using a curve of the type shown in
Figure 31, Scale Factor Diagram The
constants 9, i//, and
-------
100
3% Foul Fraction
10% Foul Fraction.
20% Foul Fraction.
(FT/SEC)
10
-1
. , . , , , 1
1.0
(CM/SEC)
' ' ' 1
10.0
PARTICLE SETTLING VELOCITY
FIGURE 29
EFFECT OF UNDERFLOW SEWER FRACTION ON REMOVAL EFFICIENCY
For the hypothetical case, a value of S =
11.1 was obtained from either equation. An
average scale factor of 11 will be used for the
design example. The size of the chamber can
now be determined by multiplying the
dimensions of the LaSalle model concentrator
by a factor of 11. Thus the 3-ft model
concentrator diameter will result in a 33-ft
design diameter. Likewise, the other model
concentrator dimensions can be scaled up in a
similar fashion.
The boxed region in Figure 31 indicates
the model flowrates and particle settling
velocities tested by La Salle Hydraulic
Laboratory. Similarly the dotted i// lines
represent the scaling of the laboratory data to
169
-------
iocH
10
-3
10
'-2
(inches)
10
10
'-2
'-1
(centimeters) 10
PARTICLE DIAMETER
FIGURE 30
PARTICLE SETTLING RATES
170
-------
(FT/SEC)
FIGURE 31
SCALE FACTOR DIAGRAM
171
-------
100 1
0.01
0.1
(FT/SEC)
I
1.0
I
(CM/SEC) 10.0
PROTOTYPE SCALE SETTLING VELOCITY
FIGURE 32
EFFICIENCY CURVE FOR PROTOTYPE SCALE (12:1)
other concentrator sizes. Only the regions
within the dotted lines therefore represent
laboratory verified testing. The use of Figure
31 in any other region involves extrapolation
of the laboratory results beyond the range of
parameters tested and must therefore be
. applied with cognizance of this fact.
With an estimation of the design size of
the swirl concentrator, the removal efficiency,
E, at flowrates other than the design flows
and for particles sizes other than the design
particles can be determined. This can best be
accomplished by calculating the removal
efficiency versus settling velocity for the 200
cfs design flow. This curve can be created
from either the prototype efficiency curve
fitted to the LaSalle data or the prototype
efficiency curve determined by the
mathematical model.
Consider the prototype curve shown in
Figure 32, Efficiency Curve for Prototype
Scale. This curve represents the prototype
efficiencies as predicted by the mathematical
model. To use this curve to extract
information representing the 200 cfs flowrate
for the design example, it is first necessary to
determine the scale factor relating the two
cases. Since the prototype curve represents a
scale factor of 12 relative to the LaSalle
Laboratory model, and the scale factor of the
172
-------
design example represents a scale factor of 11
relative to the laboratory model, the scale
factor of the design relative to the prototype
case is equal to 11/12 or 0.915. To adjust the
prototype curves shown in Figure 32, it is
therefore necessary to adjust the flowrates
and particle settling rates for the design
example by the following factors:
Qw= T
/17 \ 5/2
= (\Y ) QDS= 1.24Qu,
v = I a
Vpps I -
V =
v nnr
1/2
"pps
=v/3j vpD, = 1.04
Where
QD s = Flowrate for design scale
Qps = Flowrate at prototype scale
VpDs = Particle settling velocity at design scale
Vpps = Particle settling velocity at protoscale
SDs = Design scale factor relative to model
Sps = Prototype scale factor relative to model
Multiply the design flow by 1.24, (1.24 x
200 = 248) and the design particle settling
velocity by 1.04 (1.04 x 0.3 = 0.312), and
enter Figure 32 with these values to obtain
the design removal efficiency of 80 percent.
This compares with the initially specified 80
percent design value.
The removal curves for the prototype
flowrate, Qp§ = 248 were created by shifting
the given 100 cfs curve by a factor of
(248/100) V along the settling velocity axis,
(i.e., V2 = 2.48 Vi). The effect of different
flowrates and particle settling velocities can
also be determined on the design example.
For instance, for a particle settling rate of
0.05 ft/sec, by entering Figure 32 at a Qps of
248 ft3/cfs and a settling velocity of (1.04)
(0.05) = 0.052 ft/sec, the designer obtains the
removal efficiency of 23 percent, representing
a particle having a settling velocity of 0.05
ft/sec at the design flowrate. The scaling laws
can thus be used to generate a set of
efficiency curves describing the predicted
performance of the swirl concentrator design.
To illustrate how the efficiency curves
can be used to predict the concentrator
performance for a particular sewage—storm-
water mix, a sample computation has been
performed. A typical source mixture in which
particle sizes and specific gravity are distribu-
ted as indicated in Figure 33, Cumulative
Distribution of Settling Velocities for
Prototype Storm Water Particles, was assumed.
The settling velocities in Figure 31 were
computed by entering the settling velocity
curve shown in Figure 30 with each of the
specific gravities and particle diameters
comprising the waste water composition. The
100 cfs prototype curve in Figure 32 was then
utilized to determine the removal efficiency
for each settling velocity. This assumes that
the scale factor of 12:1 applies for this
example since the settling velocities and
flowrates shown in Figure 32 have been
adjusted using the prototype scale factor. The
fifth column in Table 5, Sample Calculation
of Concentrator Performance for a Specified
Particle Size Distribution, represents an
efficiency obtained from Figure 32, for the
settling velocity indicated in column 4. The
efficiencies can then be adjusted by the
weight fraction of particles exhibiting that
settling velocity and summed to determine
the overall removal efficiency. Thus, the
overall removal efficiency of the particles
with a specific gravity of 1.2 will be 85
percent. In a similar manner, removal
efficiency of 90 percent for the 1.5 specific
gravity and 97 percent for the 2.65 specific
gravity were obtained. The scaling laws
therefore make it possible to predict the
performance of any chamber design for a
waste water mixture.
CONCLUSIONS
Many important conclusions can be
drawn from the results obtained with the
mathematical model of the swirl
concentrator. In this section, the most
significant findings and their importance are
summarized.
173
-------
TABLE 5
Sample Calculation of Concentrator Performance for a Specified Particle Size Distribution
D-Particle Size
(mm)
3.0
2.5
1.0
0.5
0.2
Specific
Gravity
1.2
1.2
1.2
1.2
1.2
Percent Particle
of Size D
40
25
15
10
10
Settling Velocity
from Figure 30
(ft/sec)
0.385
0.33
0.145
0.058
0.0108
Percent Recovery
for Particle Size D
from Figure 32
100
99
84
57
22
(Total recovery for mixture of particle sizes of specific gravity 1.2 is 85.2 percent)
Percent of Total
Particles Removed
(3)X(S)
40.0
24.7
12.6
5.7
2.2
a) For flowrates up to 165 cfs, the
mathematical model provides a
reasonably accurate description of the
liquid flowfield, within the limitations of
the axisymmetric assumption, as
demonstrated by comparisons with
laboratory data. Above 250 cfs,
significant non-axisymmetric effects arise
due to the jet-like behavior of the inlet
flow. These effects cannot be accounted
for in the axisymmetric mathematical
model.
b) The mathematical model correctly
predicts trends in concentrator efficiency
due to variations in flowrate, size, settling
velocity, geometric changes, and
underflow rate. None of the geometric
alterations calculated gave better results
than the baseline design.
c) The predicted separation efficiencies are
very close to those measured for very
slow and very fast settling particles. The
mathematical model over-predicts the
performance at intermediate settling
rates, probably because of
non-axisymmetric flow effects in the
physical model. The agreement between
mathematical model and physical model
is very good at 50 cfs, and becomes
somewhat poorer at 100 and 162 cfs, as a
-result of non-axisymmetric flow effects.
At still higher flows, the mathematical
model will markedly over-predict the
concentrator performance since the
jet-like behavior of the inlet flow has not
been modeled.
d) The mathematical model demonstrates
that the performance of the prototype
scale device can be accurately predicted
from the laboratory scale tests. This is
especially important because the particle
flow cannot be completely simulated in
the laboratory. The mathematical model
confirms that the most important effects
are properly simulated and the laboratory
results are representative of the prototype
performance.
e) The equations developed for the
mathematical model have been used to
derive scaling relationships for the liquid
and particle flows. The accuracy of these
scaling laws has also been verified by
detailed computer calculations, the
scaling laws permit either the laboratory
results, or the mathematical model results
to be extended to flowrates, chamber
sizes, particle sizes and particle' specific
gravities other than those for which
laboratory results or calculations are
available. The mathematical model or
laboratory .test results can be scaled to
any reasonable chamber size, using
Froude number scaling to relate the
flowrate to the size (Q~ s 5 /2 ).The results
can also be scaled approximately to other
flowrates, within the accuracy of the
axisymmetric approximation (up to 162
cfs with a 36-ft. diameter chamber.) The
usefulness of the laboratory and
mathematical model results are thereby
greatly increased.
174
-------
10Q
o
w 80
H
U
7. PARTICLES WITH SETTLING VELO
to *• o<
o o p
0
Crushed Gilsonite Gilsonlte
0.3 mm 0.5 mm 1 mm 2 mm 3 ran
Petrothene
2 mm 3 ran 4 mm
SG = 1.2
SG - 1.5
0.2 mm 0.2 ran 0.2 mm SG - 2.65
1 1
II!
0.5 mm 0.5 mm 0.5 mm
1 I '
i ;
1.0 mm 1.0 mm 1.0 mm
i !
i i
1 x1,.
1 .' ™
2.5 mm 2.5 mm
3.0 mm 3.0 mm 2.0 mm
.01 (FT/SEC) 0.10 1.0
1.0 (CM/SEC) 10.0
SETTLING VELOCITY (V0)
FIGURE 33
CUMULATIVE DISTRIBUTION OF SETTLING VELOCITIES FOR
PROTOTYPE STORMWATER PARTICLES
f) The operating principles of the swirl
concentrator are clearly demonstrated by
the mathematical model. The details of
the liquid and particle flow streamlines
and velocities are shown in
computer-generated plots. The separation
mechanism is shown to be gravitational,
with the liquid secondary flow serving to
sweep the particles on the bottom into
the center where they can be drawn off.
The effect of turbulence is clearly
demonstrated. Without turbulence, the
particles would settle directly to the
bottom. The effect of turbulence is to
scatter particles from regions of high
concentration near the bottom, into
175
-------
regions of lower concentration at the top,
where they can be drawn into the
overflow.
g) Finally, and most importantly, the
mathematical model results confirm that
the swirl concnetrator as presently
designed, is capable of achieving useful
improvements in* the quality of combined
sewer overflows. This improvement is
possible with reasonable size units (36 ft
in dia x 9 ft deep) for overflow rates up
to 162 cfs.
RECOMMENDATIONS
Based on the successful results from this
study, the following recommendations are
made for future work in the area of storm
water overflows.
First, it would be desirable to predict the
transient performance of the swirl
concentrator for a typical storm sewer
hydrograph. The present results, of course,
apply only to steady state operation at a given
flowrate and inlet concentration. In order to
predict the total waste matter discharged,
consideration should be given to time varying
inlet concentration (due to the first flush
effect), and to the accumulation of particles
within the concentrator as it is charged and
emptied. It should be possible to construct
from the present results, a method for
simulating the dynamic operation under
varying inlet flowrates and concentrations.
Using this simulation, studies could be carried
out to determine the optimum concentrator
size relative to typical hydrographs for a given
area, and to predict the reduction in
discharged waste matter for a typical year's
operation.
The second area which deserves further
study is the application of swirl concentrators
to typical design requirements. For example,
it is not clear whether better efficiencies can
be achieved with two half-size concentrators
or one full-size unit. With two units one
chamber could be used for all flows less than
100 cfs and the second chamber would be
needed only if the storm flow exceeded this
preset value. This might provide better
separation at both higher and lower flows
because the unit can be tailored to a smaller
range of flowrates. This example corresponds
to operating two units in parallel, and the
concept can readily be extended to an
arbitrary number of units. The possibility of
operating units in series to improve the overall
separation efficiency should also be
examined. Other questions which could be
answered in such an application study include
optimum inlet pipe configurations to avoid
settling during low flow conditions; methods
for controlling the foul sewer flowrate; means
of predicting head losses; use as a flow
regulator as well as particle separator; design
recommendations for areas where head loss is
critical; and design charts for preliminary size
selection as a function of sewer hydrograph
data.
176
-------
NOMENCLATURE
A Area
CD Drag coefficient
C/ Skin friction coefficient
dp Particle diameter
E Efficiency
~eg Unit vector in direction of
gravitational force
"tf^z Unit vectors in radial and axial
directions, respectively
/ Non-dimensional stream function
defined in Equation (17e)
g Gravitational acceleration
g/fc Metric tensor
G Non-dimensional tangential velocity
function defined in Equation (17c)
S. Mixing length
N Concentration (number density)
72 Fluctuation in number density
p Pressure
p2 Pressure less the hydrostatic term
Q Volume flowrate
Qp Particle flowrate—number of particles
per second
Re Reynolds number
r Radial coordinate
S Scaling factor
Sjj Deformation tensor defined by
Equation (11)
Sg Specific gravity
x Reference length
TIJ Reynolds stress tensor defined by
Equation (7)
t Time
U Liquid velocity
u Fluctuation in liquid velocity, or
radial velocity component
V Particle velocity
Vs Settling velocity
v Fluctuation in particle velocity, or
tangential velocity component
vp Particle volume
w Vertical velocity component
x> General coordinate direction
component
z Axial coordinate
X Mixing length constant
a Ratio of rms velocity fluctuations in
liquid to those of particle
e Eddy viscosity
f Non-dimensional axial coordinate
Virtual mass coefficient
Constant used in design calculations
Molecular viscosity
Kinematic viscosity
Non-dimensional radial coordinate
Density
Shear stress
Dissipation function defined by
Equation (10)
Constant used in design calculations
Stream function defined by Equation
(16), or constant used in design
calculation
Reference frequency (taken
Non-dimensional vorticity
defined by Equation (17d)
as
function
SUBSCRIPTS
b Boundary value, or bottom
b + i Value at point adjacent to boundary
i Inner standpipe
in Inlet
L Liquid
m Model scale
o Overflow outer boundary
P Prototype scale, or particle
w Water
SUPERSCRIPTS
A Denotes non-dimensional quantity
— Denotes mean value
-1- Vector quantity
Denotes fluctuating quantity, or
differentiation with respect to
argument
TENSOR NOTATION
U,- Co-variant form of the vector, U ^
U' Contra-variant form of the vector.U
U,- j Denotes co-variant differentiation of
the vector; the result is tensor of order
two, and is equivalent to writing v U
U'_(- Repeated index appearing once as
superscript and once as subscript
denotes summation. Thus this form is
equivalent in Cartesian coordinates, to
dy
177
-------
REFERENCES
1. Smisson, B., Design, Construction, and
Performance of Vortex Overflow, 8.
Symposium on Storm Sewage Overflows;
Institution of Civil Engineers, 1967, (pp.
99).
2. Ackers, P., Harrison, A.J.M., and Brewer, 9.
A.J., Laboratory Studies of Storm
Overflows with Unsteady Flow,
Symposium on Storm Sewage Overflows.
Institution of Civil Engineers, 1967 (p.
37).
3. Anonymous, Final Report-Technical
Committee on Storm Overflows and The
Disposal of Storm Sewage, London: Her 10.
Majesty's Stationery Office, 1970.
4. Zielinski, P.B., The Vortex Chamber as a
Grit Removal Device for Water
Treatment, Project No. A-019 sc, 11.
supported by U.S. Department of the
Interior, Office of Water Resources, at
Clem son University, Clemson, South 12,
Carolina.
5. Donaldson, O duP., Calculation of
Turbulent Shear Flows for Atmospheric
and Vortex Motions. AIAA J.. Vol. 10, 13.
No. 1, January, 1972.
6. Dorfman, L.A. and Romanenko, Yu.B.,
Flow of a Viscous Fluid in a Cylindrical
Vessel with a Rotating Cover, I/v. An
SSR. Mekhanika Zhidkosti i Gaza. Vol. 1, 14,
No. 5, pp. 63-69, 1966.
7. Camp, T. R.,Sedimentation and the
Design of Settling Tanks, ASCE Proc.
April, 1945, pp. 895-959.
Hinze, Vo., Turbulence, McGraw Hill
Book Co., Inc., New York, 1959. (esp
Chapter 5, "Transport Processes in
Turbulent Flows").
Torobin, L.B. and Gauvin, W.H.,
Fundamental Aspects of Solids-Gas
Flow Part IV: The Effects of Particle
Rotation, Roughness and Shape, The
Canadian Journal of Chemical
Engineering, October 1960, pp. 142-153.
Other parts of this survey appear in Aug.,
Oct., and Dec. 1959, and Dec. 1960.
Viets, H. and Lee, D.A., Motion of Freely
Falling Spheres at Moderate Reynolds
Numbers, AIAA J.. Vol. 9, No. 10, pp.
2038-2042.
Viek, H., Accelerating Sphere-Wake
Interaction, AIAA J.. Vol. 9, No. 10,
Oct., 1971, pp. 2087-2089.
Maccoll, J.W., Aerodynamics of a
Spinning Sphere, Royal Aeronautical
Society Journal. Vol. 32, No. 213, pp.
777-798, September 1928.
Lumley, J.L., Some Problems Connected
with the Motion of Small Particles in
Turbulent Fluid, Ph.D. Dissertation John
Hopkins University, Baltimore, Md.,
1957.
Fair, G.M. and Geyer, J.C., Water Supply
and Waste-Water Disposal, (John Wiley
and Sons, Inc., New York, 1954).
«U.S. GOVERNMENT PRINTING OFFICE: 1972 514-148/63 1-3
179
-------
1
Accession Number
w
5
2
Subject Field 61, Group
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
American Public Works Association
Title
The Swirl Concentrator as a Combined Sewer Overflow Regulator Facility
Authors)
American Public Works Association
1 JL Project Designation
Demo Project 11023GSC, APWA 70-7
2] Note
22
Citation
Environmental Protection Agency report
number EPA-R2-72-008, September 1972.
Descriptors (Starred First)
*Regulation, *Overflow, design
OC Identifiers (Starred First)
"Combined sewers, solid separation, quantity of overflow, quality of overflow
27
A study was conducted by the American Public Works Association to determine the applicability of a combined
sewer overflow regulator which by induced hydraulic conditions separates settleable and floatable solids from the
overflow. The study used a hydraulic model to determine swirl concentrator configurations flow patterns and settleable
solid removal efficiency. A mathematical model was also prepared to determine a basis for design.
Excellent correlation was found between the two studies. It was found that at flows which simulate American
experience a vortex flow pattern was not effective. However, when flows were restricted, a swirl action occurred and
settleable solids were concentrated in the outflow to the interceptor in a flow of two to three percent as compared to
the quantity of overflow through a central weir and down shaft.
The swirl concentrator appears to offer a combined sewer overflow regulator that effectively regulates the flow and
improves the quality of the overflow, with few moving parts.
The complete hydraulic laboratory and mathematical reports are included as appendices.
This report was submitted in fulfillment of the agreement between the City of Lancaster, Pennsylvania, and the
American Public Works Association under the partial sponsorship of the Office of Research and Monitoring,
Environmental Protection Agency, in conjunction with Research and Demonstration Project 11023GSC.
Abstractor
Richard H. Sullivan
Institution
American Public Works Association
WR:102 (REV JULV 1969)
WRSI C
SEND, WITH COPY OF DOCUMENT,
TO: WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON. D. C, 20240
------- |