EPA-600/2-75-062
December 1975
Environmental Protection Technology Series
psKs^s^Sf^!)^!??*^^
^m'^^
^^
:OMBINED SEWER OVER FLOW REGULATOR
unicipal Environmental Research Laboratory
-------
• lRe^search''regbrts of the office of Research an3 Development,
tf.i;S."'Environmental'/?^ SgencyJ "Gave Been grouped" Jn"t0"
" five' "series' These five broad"' categorTeis were e"s taoTSCined to
facilitate further development and application of environmental
techno logy"!1' '" 'El^ina'tion' 0*'"f" 'TtraSit" iona 1 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
4. 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.
iiwill in1" IIPl1!11 Hi nil
i mi! ii nil nil iiiiii|iiiii Nim iiiiiiiiiiiii i it i iiiiii i in m i iiiiiiiiiiiiii n ill it i in wnini i iii'iii inn111 111 niii in ill
This document is available to the public through the National
Technical Information Service, Springfield, Virginia 22161.
it i, i vi .r *:•' Ki""11!1!.; ,,'1'! I'ltiti v; kit. '• .,,;';,;,'<-. iiasrii n-E'ts.! i-i' iiiiM11
i!l!":' i '!,;l:::i ^ :€'.: ;C; S; P"i:*^^^ iiMIIR^^^^^^^^^^^^^^ !«ii:i!!!ilH^^^^^^^^^^^^^
-------
EPA-600/2-75-062
December 1975
THE HELICAL BEND COMBINED SEWER OVERFLOW REGULATOR
By
Richard H. Sullivan
Ralph R. Boericke
Morris M. Cohn
George Galina
Carl Koch
Fred E. Parkinson
T. M. PrUs-Chacinski
James E. Ure
American Public Works Association
Chicago, Illinois 60637
Contract No. 68-03-0272
Project Officer
Richard Field
Storm and Combined Sewer Section (Edison, N.J.)
Wastewater Research Division
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45268
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
-------
DISCLAIMER
This report has been reviewed by the Municipal Environmental
Research Laboratory, U.S. Environmental Protection Agency, and
approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the U.S.
Environmental Protection Agency, nor does mention of trade names
or commercial products constitute endorsement or recommendation
for use.
ii
-------
FOREWORD
Man and his environment must be protected
from the adverse effects of pesticides, radiation,
noise and other forms of pollution, and the unwise
management of solid wastes. Efforts to protect the
environment require a focus that recognizes the
interplay between the components of our physical
environment — air, water, and land. The National
Environmental Research Centers provide this
multidisciplinary focus through programs engaged
in
• studies on the effects of environmental
contaminants on man and the biosphere, and
• a search for ways to prevent contamination
and to recycle valuable resources.
This report on the Helical Bend Combined
Sewer Overflow Regulator presents the basis of
design for an effective device to limit pollution of
receiving waters from combined sewer overflows.
Improvement of the quality of the overflow while
regulating the quantity is an important
performance specification. The use of a
nonmechanical device utilizing fluid dynamics is
particularly valuable in light of the importance of
energy conservation.
111
-------
ABSTRACT
A design procedure and method to calculate
settleable solids retention efficiency has been
prepared for a combined sewer overflow regulator,
using the principle of developing helical flow in an
enlarged, curved extension of a sewer. A curved
side overflow weir is used to draw off the clarified
combined sewer overflow.
Hydraulic and mathematical model studies
were used in developing the helical flow concept
and the design procedure. The reports of each
model study are included.
The helical bend principle was originally
investigated by Dr. Prus-Chacinski of London,
England. A second generation regulator was
constructed in 1971 in Nantwich, England. The
present study modified the design to conform to
American wastewater conditions and practices.
It was found that the helical bend combined
sewer overflow regulator is capable of higher
removal efficiencies with less hydraulic head loss
than the swirl concentrator regulator, although the
overall length of the helical unit appears to make it
more expensive than the swirl concentrator.
The helical bend regulator requires the use of
only a mechanical outlet gate and cleaning
facilities; otherwise it is essentially non-mechanical.
This report is submitted by the American
Public Works Association in partial fulfillment of
Contract No. 68-03-0272, between the U. S.
Environmental Protection Agency and the
American Public Works Association.
IV
-------
TABLE OF CONTENTS
Page
Abstract iv
Section I Conclusions, Recommendations and Overview of the Studies 1
Section II The Study 5
Section III Design Factors for Helical Bend Regulator Separator Facilities 18
Section IV Implementation 46
SectionV Glossary of Pertinent Terms — Helical Bend Report 47
Section VI References : 50
Appendix A Hydraulic Model Study 51
Appendix B Mathematical Model Study 81
Nomenclature 114
Appendix C Background Information on the Helical Bend 116
TABLES
Page
1. Velocities in Transitions 24
Helical Bend Regulator (Design Example) 28-32
2. Helical Bend Regulator Dimensions 33
3. Site Dimensions and Areas for Helical Bend
and Swirl Concentrator Regulators 35
4. Typical Head Losses in Helical Bend and Swirl
Concentrator Regulators 37
5. Construction Cost of Helical Bend Regulator 40
6. Swirl Concentrator Dimensions ".....' 41
7. Construction Cost - Swirl Concentrator 42
8. Comparison of Construction Costs — Helical Bend-
and Swirl Concentrator Regulators . 44
9. Recovery Results — Modifications 1-8 57
10. Recovery Results-Modifications 9, 10, 12, 14-18 59
11. Recovery Efficiency at Various Bend Radii 114
-------
FIGURES
Page
1. Isometric View of Helical Bend Regulator 3
2. Helical Bend Regulator, 1967 7
3. Photograph of Nantwich, England, Helical Bend Regulator 8
4. Helical Bend Regulator — Form 3 (Model Layout) 9
5. Discharge Measuring Weirs 10
6. Prototype Gradation for Grit and Settleable Organic Material 12
7. Particle Settling Velocities for Solids in Still Water 13
8. Gradation Curves for Gilsonite® and Petrothene® Used in Model 14
9. Prototype Grit Sizes Simulated by Gilsonite and Petrothene in Model 15
10. Prototype Settleable Organic Material Sizes Simulated
by Gilsonite and Petrothene in Model 16
11. Predicted Prototype Grit Recovery vs Design Flowrate Ratio 18
12. Predicted Prototype Settleable Organic Material Recovery vs Design Flowrate Ratio . 18
13. Recommended Transition Profile 19
14. Effect of Transition Slope 19
15. Design Flowrate vs Inlet Diameter 21
16. Recommended Plan Layout 22
17. Water Level in Regulator Above Weir 23
18. Recommended Cross Sections 25
19. Spillway Channel Profile 27
20. Site Requirements 34
21. Typical Cross Section — Helical Bend Regulator 38
22. Estimated Construction Costs — Helical Bend
and Swirl Concentrator Regulators 43
23. Predicted Separation Efficiency vs Settling Velocity
at Several Flowrates 45
24. Downstream View of Model 52
25. Upstream View of Model 52
26. Solids Injection Vibrator 53
27. Top and Bed Flow Angles 54
28. Floor Flow Angle Measuring Equipment 54
29. Bed Angle Relationships for Straight-Through Flow 55
30. Modification 6 - Tests 23-29 56
31. Modification 4 - Tapered Outlet 58
32. Modification 5 - Narrow Inlet 2D Wide 58
33. Modification 5 - Tapered Bend 58
34. Minimum Width Inlet, l.SDWide 59
35. Narrowest Bend, l.SDWide 59
36. Modification 9 - Tests 38-39 60
37. Modification 10-Tests 40-41 60
38. Modification 12-Tests 46-47 60
39. Modifications 14 & 15-Tests 53-55 60
40. Petrothene Recovery in Model as Function of Bend Channel Width 61
41. Modifications 17 & 18-Tests 60-61 61
42. Inlet Configurations Tested 62
43. Transition lODLong 62
44. Petrothene Recovery in 60° Bend for Various Inlet Configurations 63
45. Transition 15D Long 64
VI
-------
FIGURES (Continued)
Page
46. Scum Board Locations Tested 64
47. Petrothene Recovery in 50° Bend for Various Scum Board Locations 65
48. Petrothene Recovery in 60° Bend for Various Scum Board Locations ....... 65
49. Floor Flow Angles with Scum Board D/2 Deep 65
50. Floor Flow Angles with Scum Board D/6 Deep . 66
51. Cross Section of Offset Weir in Bend 66
52. 60° Bend with Offset Weir 67
53. Upstream View of Scum Board on Offset Weir 67
54. Downstream View of Bend and Offset Weir 67
55. Scum Board on Offset Weir 67
56. Petrothene Recovery in 60° Bend with Offset Weir
and Various Inlet Configurations 68
57. Proving Tests Layout ; 69
58. Solids Recovery in Model 70
59. Velocity Contours on 0° Cross Section 70
60. Velocity Contours on 10° & 20° Cross Sections . 71
61. Velocity Contours on 30° & 40° Cross Sections 72
62. Solids Concentration Sampling Jig 73
63. Simultaneous Filling of Solids Sampling Bottles 73
64. Suspended Solids Concentrations on 0° Cross Section 74
65. Suspended Solids Concentrations on 10° & 20° Cross Sections 75
66.. Suspended Solids Concentrations on 30° & 40° Cross Sections 76
67. Distribution of Solids Which Escape Over Weir 77
68. Floor Flow Angles 78
69. Comparative Average Floor Angles for Recommended Layout 80
70. Cylindrical Coordinate System 82
71. Definition of Surface Shape in Channel Cross Section 83
72. Coordinate Transformation 85
73. Mathematical Representation of Channel Cross Section . 87
74. Channel Cross Section in Cartesian Coordinates 88
75. Transformation of Channel Cross Section to Rectangular Region . . , 89
76. Rotation of Velocity Components '. 90
77. Computational Grid in Transformed Space 91
78. Fluid Flow Solution Summary 92
79. Location of Computational Grid Points for
Concentration Field Calculation 95,
80. Particle Flow Solution Summary 97
81. Comparison of Measured and Predicted Velocity Profiles at 0° 103
82. Comparison of Measured and Predicted Velocity Profiles at 20° 104
83. Comparison of Measured and Predicted Velocity Profiles at 40° 105
84. Comparison of Measured and Predicted Flow Angles on Bottom
Along Channel Centerline 106
85. Measured Values of Relative Petrothene Concentration at 0° 107
86. Comparison of Measured and Predicted Relative
Petrothene Concentration at 20° 108
VII
-------
FIGURES (Continued)
Page
87. Comparison of Measured Values of Relative
Petrothene Concentration at 40° 109
88. Mass Flux Over Weir as a Function of Angular Position Ill
89. Cumulative Mass Flux Over Weir as a Function of Angular Position Ill
90. Comparison of Predicted and Measured Recovery Efficiencies at Discharges
Greater than the Design Value 0.85m3 /sec (QD =30 cfs) 11.2
91. Predicted Separation Efficiency versus Settling Velocity
at Several Flow Rates 113
92. Alternative Design for Future Investigation 121
via
-------
ACKNOWLEDGEMENTS
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 U. S. Environmental Protection
Agency.
PROJECT DIRECTOR
Richard H. Sullivan
CONSULTANTS
Dr. Morris M. Cohn, P.E., Consulting Engineer
Paul B. Zielinski, P.E.
C. H. DOBBIE & PARTNERS
Dr. T. M. Prus-Chacinski
ALEXANDER POTTER ASSOCIATES, CONSULTING ENGINEERS
Morris H. Klegerman, P.E.
James E. Ure, P.E.
LA SALLE HYDRAULIC LABORATORY, LTD.
F. E. Parkinson
George Galina
GENERAL ELECTRIC COMPANY
Dr. Ralph R. Boericke
Dr. Carl Koch
U. S. ENVIRONMENTAL PROTECTION AGENCY
Richard Field, P.E., Project Officer, Chief, Storm & Combined
Sewer Section (Edison, New Jersey)
IX
-------
AMERICAN PUBLIC WORKS ASSOCIATION
Board of Directors
Herbert A. Goetsch, President
Ray W. Burgess, Vice President
Erwin F. Hensch, Immediate Past President
Robert D. Bugher, Executive Director
Jean V. Arpin
John T. Carroll
Donald S. Frady
Lambert C. Mims
James J. McDonough
Robert D. Obering
John J. Roark
James E. McCarty
Kenneth A. Meng
Frank R. Bowerman
Wesley E. Gilbertson
Rear Admiral A. R. Marschall
APWA RESEARCH FOUNDATION
Board of Trustees
Samuel S. Baxter, Chairman
Ross L. Clark, Vice Chairman
Robert D. Bugher, Secrtary-Treasurer
Richard H. Sullivan, General Manager
Fred J. Benson
John F. Collins
Jean L. DeSpain
Richard Fenton
W. C. Gribble
John A. Lambie
James E. McCarty
Marc C. Stragier
-------
SECTION I
CONCLUSIONS, RECOMMENDATIONS AND OVERVIEW OF THE STUDIES
Conclusions
1. A helical flow device has been
developed and demonstrated, as an expanded
section of a combined sewer line, for the dual
purpose of removing settleable suspended
solids from combined sewer overflows, and to
serve as an overflow spill weir regulator for
the discharge of clarified effluent to receiving
waters or to retention and/or treatment
facilities.
2. The helical bend regulator can operate
efficiently as a flow-through, nonmechanical
channel bend device in removing settleable
solids and, thereby, reducing the pollutional
impact of periodic overflow incidents.
3. The solids removed from the combined
sewer flows may tend to shoal in the deep
invert section of the helical bend chamber
during storm flow conditions.
4. Model tests showed that these deposits
remain dormant during such high-flow periods
and are then moved or self-scoured out of the
invert by dry-weather flows and discharged,
via a foul sewer outlet, to the interceptor
sewer and downstream wastewater treatment
works. Similar conditions should prevail in
prototype helical bend installations but the
scale representation of combined sewer solids
is not confirmed and the self-scouring action
experienced in the model studies must be
demonstrated under prototype operations.
(Note: A prototype unit in Nantwich,
England has not experienced the buildup of
solids during operation.)
5. Washing or flushing facilities, and
regular maintenance procedures should be
provided in prototype helical bend
installations until the removal of solids
deposits by dry-weather scouring action has
been confirmed.
6. Uniformity of flow as it enters the helical
bend section of the regulator-concentrator
facility is of utmost importance to the
successful operation of the secondary flow
actions induced in the chamber. .
7. A straight section of conduit, ahead of
the helical bend section, is required to assure
effective solids recovery rates. This straight
section length should be five times the
diameter of the inlet sewer (5D).
8. If no straight section is provided, the
recovery rates for organic solids in the helical
bend will be reduced approximately 10
percent below the efficiency attained with the
5D straight approach line.
9. Beyond this 5D straight approach
length, greater lengths will have minimal
effect on solids removal efficiencies. A 10D
straight section will further improve removals
by less than five percent.
10. Grit recoveries will not be greatly
affected by changes in the length of the
straight approach section.
11. The straight horizontal transition
length from the inlet pipe diameter, out to
the full helical bend channel width of three
times the inlet diameter, should be at least 15
times the inlet, diameter.
12. The transition section must be roofed
or covered to provide the proper flow
conditions for secondary motion and helical
action in the bend section. The cover or roof
should rise from the crown of the inlet pipe
to the hydraulic gradient at the end of the
transition section.
13. The drop through the structure can be
confined to the slope of the incoming sewer;
although greater slopes to encourage
self-scouring should not present any
problems.
14. The length of the bend is determined
by the inlet diameter. A radius of 16D should
be used.
15. A 60 degree segment is adequate to
develop the full effects of the helical flow
principle.
16. Most of the floatable solids entering
the helical bend regulator will be retained in
the chamber by the scum board or dip plate,
located ahead of the overflow weir, during
storm flow conditions. As the discharge rate
decreases and the surface of the combined
-------
flow in the helical chamber recedes, the
floatables will drop with the flow level and be
removed with the channel bottom deposits
during dry-weather flow.
17. A design procedure has been
developed for use in dimensioning the
geometrical configuration of full-scale
prototype applications having specific flow
rates, solids characteristics, and percentages of
dry-weather flows diverted to interceptor
sewers and downstream treatment facilities.
The design criteria are based on a maximum
flow of three times dry-weather flow through
the foul sewer outlet at the end of the bend
section.
18. Mathematical techniques have been
developed for computing the particle and
liquid flowfields in open channel bends.
Recommendations
1. The hydraulic model studies and the
computer-mathematical simulation of the
helical bend combined sewer overflow
regulator indicate that this flash method of
solids removal, without use of mechanical
appurtenances, can produce excellent
efficiencies with reasonable size units in
combined sewer systems. The results are so
promising that they should be confirmed in a
full-scale prototype installation at the earliest
possible opportunity.
Such an installation in the field will
provide confirmation of the pattern of solids
deposition in the deeper channel portion of
the helical bend, located along the inner
circumference of the bend section, and of the
ability of dry-weather flows in this restricted
deep channel to self-scour the deposited solids
into the foul sewer outlet.
The full-scale field prototype installation
should be fully instrumented to record
performance under actual combined sewer
conditions. Facilities should be provided for
sampling the stratified bed load of the inlet
flow and the overflow by means of vertical
arrays of sampling probes. The flow over the
weir should be sampled at several locations to
determine the distribution of solids lost with
the overflow, as a function of position along
the side weir length. A full regimen of
laboratory control studies could be planned
and instituted to explore the helical flow
patterns created in the prototype unit under
normal service conditions. Out of such a pilot
prototype investigation will come operating
experience that can assist in the application of
this promising and economical device to meet
the 2 Q challenge of effective
regulator-overflow control — control of both
quantity and quality of combined sewer
discharges to receiving waters.
Overview
A study1 conducted by the American
Public Works Association (APWA) Research
Foundation in 1969-70, Problems of
Combined Sewer Facilities and Overflows,
disclosed that combined sewer
regulator-overflow devices on the American
continent did little to improve the quality of
liquid spills from these facilities into receiving
waters. The environmental impact of these
discharges into the nation's waters was
characterized as a pollutional paradox in view
of current concern over the secondary
treatment and even higher degrees of
purification of sewage and industrial
processing wastewaters.
The findings of the 1969-70 investigation
have catalyzed subsequent studies on how
economical and efficient devices can be
utilized to eliminate part of the suspended
solids contained in admixed sewage storm
flows in combined sewers prior to the
wasting of major volumes into surface water
sources. In short, the endeavors have been
aimed at making such regulator-overflow
facilities perform two functions: Control the
flow rate of combined sewer overflows and
improve the quality of such spill volumes.
A study2 conducted by APWA, The Swirl
Concentrator as a Combined Sewer Overflow
Facility, described the development and
demonstration of a nonmechanical swirl
concentrator as an economical means of
removing suspended solids from combined
sewer overflow wastewaters.
To supplement the search for workable
means of accomplishing the clarification of
combined sewer overflows, and thereby
-------
INLET
CHANNEL FOR
OVERFLOW
WEIR
OUTLET TO
STREAM
TRANSITION SECTION
15D
STRAIGHT
\ SECTION
5D
NOTES:
1. Scum baffle is not shown.
2. Dry-weather flow shown in channel
OUTLET TO PLANT
FIGURE 1 ISOMETRIC VIEW OF HELICAL BEND REGULATOR
reducing the pollution load imposed by such
periodic discharges, the current study has
investigated the feasibility of achieving the
removal of solids from combined sev/er flows
by means of a helical bend incorporated into
an expanded section of such a sewer system.
This device would utilize the secondary flow
patterns produced by helical hydraulic
phenomena to deposit solids in the invert of a
helical channel section, adjacent to the inner
curve of the conduit, and to allow a clarified
effluent to overflow a side spill weir for
discharge to receiving waters or to retention
and/or treatment facilities.
Figure 1. Isometric View of Helical Bend
Regular, shows the important elements of
the facility. The device may require only one
mechanical part, a control on the outlet to
allow a predetermined rate of flow to the
interceptor sewer if this advanced type of
positive control is desired.
Hydraulic model studies carried out at
the LaSalle Hydraulic Laboratory at
Montreal, Canada, and mathematical
model-computer studies performed by the
Re-entry and Environmental Systems Division
of the General Electric Company at
Philadelphia, Pennsylvania, have resulted in
the development of a helical
regulator-separator device. Searching
investigations of the liquid and solids flow
patterns through a helical bend section have
been carried out, preceded by a roofed- or
covered-transition section length 15 times the
inlet sewer diameter, expanding the
flow-through conduit to a diameter three
times that of the inlet sewer followed by a
straight-flow section ahead of the helical bend
channel having a length of ten times the inlet
pipe diameter.
The studies have demonstrated the
efficacy of the helical bend principle in
achieving a flash separation of solids from the
combined sewer flow and the diversion of a
foul flow of up to three times the dry-weather
flow into the interceptor sewer and thence to
downstream treatment facilities.
Investigations have shown the ability of the
-------
helical separator to act as a nonmechanical
overflow regulator by means of a side weir
overflow arrangement along the outer radius
of the treatment chamber.
The results of helical flow patterns for
these purposes have been gratifying. They
confirm and augment previous findings
described by Dr. T. M. Prus-Chacinski in a
thesis at the Imperial College of Science,
London, England;3 demonstrated in a
prototype installation at Nantwich, England;
and outlined in a consulting report to APWA
by Dr. Prus-Chacinski as part of his advisory
services in connection with the current study.
As a result of hydraulic and mathematical
studies, basic design data have been evolved
for use by designers in applying the helical
regulator-separator to prototype installations
in combined sewer systems.
-------
SECTION II
THE STUDY
The study was designed to investigate the
efficiency of pipe and channel bend
configurations in separating suspended solids
in combined sewer flows and diverting such
concentrated solids to the fraction of the
volume which is carried by the interceptor
line to wastewater treatment facilities. The
studies investigated the solids separation
patterns induced by the helical motion
established in the flow-through bend sections
of pipe or channels, and the consequent
clarification of the overflows from the helical
device into receiving waters or into holding or
treatment facilities for the overflow volumes.
The investigative procedures covered both
hydraulic model configurations and results,
and mathematical model evaluations.
Dr. T. M. Prus-Chacinski reported4 at a
1967 Symposium on Storm Sewage Overflows
sponsored by the Institution of Civil
Engineers on the results of a study he had
conducted utilizing secondary motions in a
bend to separate solids from the moving flow
of sewage. In recent years, Dr. Prus-Chasincki
and the firm with whom he is associated, C.
H. Dobbie and Partners, designed a combined
sewer overflow regulator for the City of
Nantwich, England. A hydraulic model study
was conducted by the Mersey and Weaver
River Authority. Financing of the
construction was, in part, by the Construction
Industry Research and Information
Association.
At the initiation of this study, C. H.
Dobbie and Partners were engaged to develop
an initial design for the hydraulic model
which would incorporate the tentative
findings from the operation of the Nantwich
unit and adapt the design to United States
practices, i.e., to provide a maximum of three
times dry-weather flow to downstream
treatment facilities. Appendix C. Background
and Preliminary Design, is the C. H. Dobbie
and Partners report which established the
essentially third generation configuration for
the hydraulic and mathematical model tests.
The flow pattern phenomenon utilized in
the helical bend . principle involves
liquid-solids separation which occurs when
flow moves around a bend and creates
secondary currents which tend to move the
water surface toward the outside of the bend
and to induce bottom current angles which
move to the inside of the curve. This
separation principle is well known in river
sections where the deepest part of the channel
is usually scoured on the outside of any bend
and finer material is lifted by the bottom
currents and deposited along the inside
shoreline.
The hydraulic model developed for the
present studies was intended to impose the
opposite geometry from that experienced in a
natural stream; the deepest section of the
helical bend line was located at the inside
circumference. The intent was to provide the
deepest part of the bend cross section where
the solids removed by the secondary flow
would have opportunity to settle out and be
swept by the bottom flow to the outlet end
of the bend and thence to downstream
wastewater treatment facilities.
Appendix C reviews the established facts
about helical motion in single bends, the areas
where uncertainty exists, and the basis for the
initial design of the hydraulic model.
This study confirmed the findings outlined
by Dr. Prus-Chacinski in a preliminary report
to the American Public Works Research
Foundation on the model of helical combined
sewer overflow regulators. Selected points
from Dr. Prus-Chacinski's report follow. They
are of significance in the translation of the
hydraulic and mathematical model findings
into practical design guidelines. They are used
to preface the design factors evolved by both
the hydraulic and mathematical study personnel.
1. All bends investigated to date (1973)
have not been longer than 180°.
2. It has been established that in such bends
in rectangular channels prominent helical
motion exists in the form of one helix, in
which the direction of flow, about
one-third of the depth near the bottom, is
toward the inner wall; and in another,
about two-thirds of the depth near the
top is toward the outer wall.
-------
3. The angle between the circumferential
direction and the direction of the
transverse flow is very much greater near
the bed than near the surface; therefore,
the resulting helix is assymetric and very
much flattened toward the free surface.
4. In such a helix the strength of the helical
motion in a rectangular channel is
proportional to the angle of the direction
of flow next to the bed.
5. Such a single helix changes the velocity
distribution, both in vertical and in
horizontal along the bend; around 60° to
80° of the bend the slow bed water is
upturned to the top. There the velocity
distribution is different than in a normal
straight open channel: the maximum
velocity occurs in the lower half of the
depth.
6. Around the same region the pattern of
helical flow changes (at least in a
rectangular channel) and a second helix in
the opposite direction starts to form at
the outer wall. This second helix
gradually grows towards the end of the
bend 180° long.
7. Around the same region the area of
maximum velocity across the channel (at
least in a rectangular channel), which
almost from the beginning of the bend is
at the inner wall, shifts to the outer wall
and remains there up to the end of a
180°longbend.
8. The maximum strength of the primary
helix occurs at about 40° of the bend and
decreases very slowly to the end of the
180° long bend.
9. The described pattern of the helical
motion in a rectangular channel can exist
only if the flow at the entry to the bend
is completely free of any transverse
currents. This is a fundamental
requirement.
10. The strength of the helix is relatively
insensitive to the velocity distribution
across the channel at the entry to the
channel (at least in a rectangular
channel).
11. The strength of the initial helix is much
more sensitive to the velocity distribution
in the vertical at the entrance to the
bend. The initial strength can be
increased by artificially distorting the
vertical velocity distribution at the entry
to the bend in such a way that the
velocity near the surface is increased.
12. The initial strength can be decreased by
artificially depressing the maximum
velocity in the vertical at the entry.
13. Such changes of the strength of the
helical flow disappear around 60° to 80°
of the bend; from there on, the motion
returns to normal helical motion.
14. Introduction of an artificial helical flow
at the entry to the bend can produce an
infinite variety of patterns of helical
motion. The strength of one helix can be
slightly increased or decreased.
Introduction of more than one helix at
the entry to the bend can result in
patterns of two or three helices. Such
pattern persists for at least 45° along the
length of the bend and probably for a
greater length.
15. Helical flow similar in shape has been
experimentally documented in the bends
of rectangular channels with
depth-to-width ratio from about 0.12 to
about 1.0; triangular channel with the
symmetrical apex and with the apex near
to the outer wall; trapezoidal channels;
parabolic channels.; eliptical channels;
semicircular channels; and rectangular
channels with semicircular bottom. The
strength of a primary single helix is
probably the greatest in semicircular
channels.
Figure 2, Helical Bend Regulator - Form
1, as investigated by Dr. Prus-Chacinski,5 was
presented at the 1967 Symposium. Figure 3,
Helical Bend Regulator - Form 2, as
investigated by the Mersey & Weaver River
Authority is a photograph of the facility
designed for Nantwich, Figure 4, Helical Bend
Regulator - Form 3, as investigated by
American Public Works Association, is the
configuration chosen for the initial model
tests. A review of these three figures reveals a
change to simplicity of shape and an
improved method of takeoff to the
interceptor sewer to prevent the outlet from
being plugged by rags and debris.
Starting with the configuration in Figure
4, concurrent hydraulic and mathematical
model studies were conducted.
-------
The basic structural features of
significance in the helical bend model are: the
inlet from the entrance sewer section to the
device; the transition section from the inlet to
the expanded cross section of the straight-run
section ahead of the bend; the overflow side
weir and scum board, or so-called dip plate;
and the foul outlet for the concentrated solids
removed in the secondary flow pattern,
together with the means for controlling the
amount of this underflow going to the
treatment works.
The hydraulic model was constructed at
the LaSalle Hydraulic Laboratory.
Configuration changes and internal auxiliary
flow control and effluent improvement
modifications, as well as detailed studies of
the helical flow patterns developed and the
suspended solids removal efficiencies
achieved, were -studied. The report of the
hydraulic model studies is presented as
Appendix A to this report.
The mathematical model and computer
simulation of the device was conducted by
the General Electric Company. The report of
the mathematical model study is presented as
Appendix B to this report.
The ultimate purpose of both studies was
to correlate and confirm findings by both
hydraulic and mathematical means and to
develop design criteria which will enable
engineers to utilize the helical flow principle
for solids removal from combined sewer flows
and to properly regulate the overflow of
clarified wastewater to receiving waters or
points of retention and/or treatment. The
design basis is presented in Section III.
Hydraulic Model Studies
The transition from the sewer line to the
overall helical system was made of Plexiglas,®
20 diameters (20D) long to assure proper flow
deceleration. This transition section was
followed by a straight-flow Plexiglas section
of 1OD length to carry the flow to the start of
the bend. It was built of Plexiglas, using a
2.44 m (8 ft) radius from the extension of the
inlet pipe centerline. Since the model was
developed to demonstrate the basic principles
of the secondary motions created in the
helical bend, the curvature was originally
carried around through an angle of 120°. Side
channels were provided on each side to
accommodate the clear overflow discharge
from either the inside or outside
circumference of the bend. Control of either
Channel for normal
flow and heavy solids
Overflow weirs
with dip plates
Siphonic slots
to remove
heavy solids
Pipe for solids to
foul sewer or tank
for first flush
SECTION A-A
Flume
Control
pipe -
SECTION B-B
Overflow wey-s
with dip plates
Control
pipe
SECTION B-B
inlet
Flow.carried
forward to works
Courtesy of Dr. Prus-Chacinski
FIGURE! HELICAL BEND
REGULATOR, 1967
as presented in 1967 at the Symposium in
London, England sponsored by the
Institution of Civil Engineers
-------
Courtesy of C.H. Dobbie and Partners
FIGURE 3 PHOTOGRAPH OF NANTWICH, ENGLAND,
HELICAL BEND REGULATOR
-------
100
120
TYPiCAL SECTION IN BEND
CROSS-SECTION
IN STRAIGHT
Locoted 5m(l5.2')[A;rt
Upstreom of
Transition
Note: location of perforated slide
gate varied from 60° to 120
INLET PIPE
I5.acm(6")
FLOW
FIGURE 4 HELICAL BEND REGULATOR - FORM 3 (Model Layout)
-------
the entire flow through the bend, or just the
small foul outflow was provided by a
perforated slide gate at the 120° position.
The basic floor cross section inside the
transition section, the straight section and the
bend was constructed of polished cement
mortar, as shown in Figure 4. The original
layout could accommodate simple
modifications of the Plexiglas overflow
weirs for the purpose of changing their
positions horizontally or their crest levels.
Similar variations in scum board location and
depth could be provided.
Unmeasured water flows entered the
helical bend complex through the supply pipe
which was fitted with a discharge control
valve and equipment with which to inject
predetermined amounts and types of solids
whose removal characteristics and
performance were to be studied. The overflow
water was diverted to a calibrated Rehbock
weir basin where water levels could be read
and the rate of discharge determined.
Similarly, the foul outflow from the bottom
of the bend channel, containing the deposited
solids, was diverted to a second basin for
measurement over a small 90° V-notch weir.
These control devices are shown in Figure 5,
Discharge Measuring Weirs.
Injection of Process Black ink on the
floor of the bend, applied with hand syringe,
produced clearly defined traces of the bottom
or floor flow angles which could be measured
by means of a protractor. These trace tests
demonstrated the presence of the anticipated
helical secondary flow patterns.
Tests for the efficiency of solids
separation in the helical flow pattern were
performed in accordance with recognized
standard methods. One liter of the selected
model solids was introduced into the water
supply via the supply line. This solids material
entered the bend flow and was exposed to the
separation process. Any solids that were
swept over the overflow weir were captured
on a screen in the measuring basin. The
balance normally was retained as a deposit in
the bend and recovered in the diversion basin
when it was flushed from the bend section.
Any solids contained in the foul outflow
FIGURES DISCHARGE MEASURING WEIRS
during the model run were also captured and
retained in the collection chamber.
The volumes of the two fractions — the
solids passing over the overflow weir and the
solids contained in the foul outflow — were
measured to determine if any material had
been lost. The recovery rate, or efficiency of
solids separation, was computed as the ratio
of, the solids retained in the bend compared
with the original 1-liter input, expressed as a
percentage.
The model scale selected for comparison
with a rational prototype size was 1:6. The
pertinent scale relations were:
Scale
Time
Discharge
1:6
1A/6, = 1/2.45
1/65/2 = 1/88
The prototype combined sewer overflow
in the corresponding 91.5 cm (3 ft) sewer was
computed at 0.85 m3/sec (30 cfs) flowing
full, which would correspond to 9.1 I/sec
(0.339 cfs) in the model. To simplify
operations in the model, a discharge of 10
I/sec (0.354 cfs) was used, giving a storm
discharge of 0.88 m3/sec (31.1 cfs). Selected
discharges in the model were 10, 7.5, 5, and
10
-------
2.5 I/sec (0.354, 0.265, 0.177 and 0.088 cfs),
corresponding to 0.88, 0.66, 0.44 and 0.22
m3/sec (31.1, 23.3, 15.55 and 7.78 cfs) in the
prototype. Dry-weather flow (dwf) was
defined as one percent of the storm flow, or
on the model 0.1 l/sec(0.004 cfs), and in the
prototype 8.81 I/sec (0.31 cfs). The basic
decision was made that during storm flows, 3
dwf would be withdrawn continuously
through the foul outlet at the end of the
helical bend section — 26.4 I/sec (0.93 cfs).
As stated, the preliminary studies of
secondary flow patterns and solids removal
results were carried out with the original
model, as shown in Figure 4. Subsequently,
modifications were made in the bend
configurations and internal ancillary
structural details. In all, the LaSalle Hydraulic
Laboratory report, Appendix A, covers 16
modifications and 59 test runs, involving
various changes in the body of the bend and
other variations in length of transition and
straight-flow sections ahead of the bend
structure.
Over and above the basic structural
configurations of the helical bend composite
provided for the studies, the LaSalle
investigations placed great stress on the
introduction of the proper solids materials
into the inflow water to simulate in a
prototype installation actual combined
sewage.
SOLIDS SIMULATION
In defining the pollutant materials to be
removed from the regulated overflows, two
categories were considered: grit, with specific
gravity of 2.65 and settleable organics with-
specific gravity of 1.2. Details of the
simulation procedures are given below:
Grit
The prototype gradation of the grit
material in sewage which is to be removed in
the helical structure was chosen as shown in
Figure 6, Prototype Gradation for Grit and
Settleable Organic Material. The outside
grain-size limits of 0.2 and 2.0 mm (No. 70
and No. 10 sieve) represent medium and fine
sand as defined by the Unified Soil
Classification System. The specific gravity of
the grit was assumed as 2.65, and the
straight-line grain-size distribution was
selected as a representative average of grit-size
data reported for existing raw sewage influent
at treatment plants. Concentration was
considered as being from 20 to 360 mg/1.
Particle sizes smaller than about 1 mm
(No. 18 sieve) are known to remain
suspended and transported in flowing water
according to equations of the type reported
by Meyer-Peter and Muller,5 or H. A.
Einstein.6
Between 1 mm and 0.2 mm (No. 18 and
No. 70 sieve) the particles are in the transition
zone between the above equations and the
Stokes relation. Since the particles involved in
both prototype and model extended into
both ranges, across the transition zone, the
above equations could not adequately
describe the scale relations.
It was necessary, therefore, to use curves
of particle settling velocities as .shown in
Figure 7, Settling Velocities for Solids in Still
Water. For a given grit size with specific
gravity 2.65 in prototype, the settling velocity
was determined from Figure 7. Based on
Froude's law of similitude, this was divided
by the square root of the scale being
considered to find the required model settling
velocity. By referring to Figure 7 with this
model settling velocity, the model particle
sizes were found for the simulating materials
— Gilsonite or Petrothene.
The physical relations used here can be
expressed as follows:
Model scale = \ = Lp/Lm
where Lp andXm are corresponding lengths
in the prototype and the model respectively.
From Froude's Law, the velocity
simulation is expressed by the equation:
Ys. -
v
m
and
For example, for the scale ratio of
prototype to model of 6:1, the settling
velocity in the prototype should be divided
by the square root of 6, or 2.45. From Figure
7, the settling velocity of prototype grit of
11
-------
U.S. STANDARD SIEVE NUMBERS
34 6 8 IO 16 20 3O 40 50 70 100 140
€
1
\
> A
\
\
OF
\
GANI
V
\
\
\
\
/
cs-^
SG 1.20
\*
\
\
- X
•**"
\
\
\
\
\
\
f»
3.
s
\
\
k
G 2
\
\
\
65
V
\
^\
2 1 O.6 O.4 O2 0.1-
Grain Size in mm
U.S. SIEVE SIZE
4
10
20
40
50
70
417 C *MH»
ol^c mm
5.0
2.0
0.84
0.42
0.3O
0.20
% FINER. BY WEIGHT
GRIT
100
100
63
31
18
0
ORGANICS
100
53
31
17
14
10
IOO
A/N
9O
o^\
8O
-fr\
f\i
•H
&f\ "S*
DO .51
0)
>.
J2
ert %:
il
S?
jtf\
4O
^IA
3vJ
or«
iCVJ
1 A
IO
FIGURE 6 PROTOTYPE GRADATION FOR GRIT
AND SETTLEABLE ORGANIC MATERIAL
12
-------
Reference: Hydraulique et Granulats - J. Larras.
10
0
0
o
o>
1
CO
0.1
/
L/
3
i
y/
_$L
u
XI
•»•
£ &
0.01
0.01
0.1 1
Particle Diameter, mm
1O
FIGURE 7 PARTICLE SETTLING VELOCITIES FOR SOLIDS IN STILL WATER
13
-------
U.S. Standard
8 10
numbers
50 70 100 140
100
FINE
GRAVEL
COARSE
VJ 1 U 1 II O lit III II
MEDIUM
i in
FINE
SAND
FIGURE 8 GRADATION CURVES FOR GILSONITE
AND PETROTHENE USED IN MODEL
0.2 mm (70 mesh) size is 2.2 cm/sec (0.86
in./sec). The model settling velocity is then
0.90 cm/sec (0.35 in./sec). Thus, in the
model, the grit of 0.2 mm size (70 mesh) can
be simulated by 0.70 mm (0.27 in.) Gilsonite,
or 2.1 mm (0.83 in.) Petrothene.
The Gilsonite and Petrothene available
for test work in the laboratory had the grain
size distributions shown in Figure 8,
Gradation Curves for Gilsonite and
Petrothene Used in Model. Practical limits
represented on these curves were chosen
between 0.5 and 3.0 mm (0.02 in. and 0.12
in.) (No. 35 and 6 sieves), and the
corresponding prototype grit sizes simulated
were calculated. The results are shown in
14
-------
1/4 1/6 1/8 1/12 I/IS 1/20 1/24
Model Scale X
Petrothene
Gilsonite
FIGURE 9 PROTOTYPE GRIT SIZES SIMULATED BY
GILSONITE AND PETROTHENE IN MODEL
Figure 9, Prototype Grit Sizes Simulated by
Gilsonite and Petrothene in Model.
This figure shows that for smaller scales,
up to about 1/16, the Gilsonite did;not
cover the larger prototype particle sizes.
However, it was reasoned that if the structure
under study showed a particular recovery rate
for these scales, the larger particles not
simulated would have settled equally as well.
Conversely, the range covered by the
Petrothene includes all of the Lower
Prototype Limit, and drops down to much
finer particles. In fact, as was demonstrated
later, the Gilsonite settled out completely
for all cases tried, so the Petrothene was
used exclusively for the development tests,
and all comparisons are for Petrothene
recovery. This means that the figures quoted
15
-------
are a severe evaluation of the structure; all the
grit in the defined range was removed, and the
comparisons are for even finer particles.
Organics
The settleable organic material desired to
be removed from the flow in the prototype
was assumed to have a specific gravity of 1.2,
and a grain-size distribution as shown in
Figure 7. The same Froude model scale-up
procedure was followed, and the limits
simulated by the Gilsonite and Petrothene
were calculated as shown in Figure 10,
Prototype Settleable Organic Material Sizes
Simulated by Gilsonite and Petrothene in
Model.
The upper limits offered no difficulty; all
the larger sizes were very easily covered by
the Gilsonite. However, there remained a
small section of the lower limit which was not
covered by the Petrothene for scales smaller
than about 1/10. This portion might be
ro.o
1/4 1/6 1/8 1/12 1/16 1/20
Model Scale X
1/24
Petrothene — —
Gilsonite
FIGURE 10 PROTOTYPE SETTLEABLE ORGANIC MATERIAL SIZES
SIMULATED BY GILSONITE AND PETROTHENE IN MODEL
16
-------
considered as lost but, at most, it actually
represents only 10 percent of the prototype
settleable organics at the smallest scales.
Floatables
Only brief tests were carried out to
simulate floating pollutants which were
assumed to have a specific gravity between
0.9 and 0.998, and a size range between 5 and
25 mm. Concentrations of 10 to 80 mg/1 were
assumed. In the model studies, uniformly
sized polythene particles 4 mm in diameter
and a specific gravity of 0.92 were used.
Mathematical Model Studies
The mathematical studies were carried
out on a theoretical model, as shown in
Figure 4. The mathematical model provided
for the same general features as the hydraulic
model, namely, a fixed inlet diameter, a
transition section, a straight section, and a
helical bend that comprised a 60° section.
The configuration of the bend cross section
provided a deeper area at the inner curve, a
set overflow-weir and scum board for
overflow purposes, and an overflow collection
trough. Underflow from the separator was
provided at the 60° location at the end of the
bend.
The mathematical computer-simulation
studies involved detailed numerical
calculation of the liquid flowfield based on
the equations of motion, together with
appropriate boundary and initial conditions.
The velocity field for the solid particles was
approximated by superimposing the settling
velocity on the calculated liquid velocity
flowfield. The spatial variations m the particle
concentration throughout the bend were then
calculated numerically from the mass
conservation equation with turbulent
diffusion. Mathematical relations governing
the scaling of the liquid flow and particle flow
were evolved from the governing equations.
Of final significance was the
mathematical development of comparisons of
calculated mathematical model results with
test data. This phase of the mathematical
model-computer evaluation study compared
the calculated flowfield with test data and
correlated calculated concentration field
findings with the results developed with the
hydraulic model. The findings of the
mathematical model studies were translatable
into design techniques for the development of
prototype installations of the helical bend as
an overflow regulator and as a solids separator
to improve the quality of overflow
wastewaters from combined sewers.
17
-------
SECTION III
DESIGN FACTORS FOR HELICAL BEND REGULATOR SEPARATOR FACILITIES
The hydraulic studies yielded data which
can be utilized to develop full-scale design
values for reasonable prototype dimension.
The LaSalle Hydraulic Laboratory
investigations were on prototype inlet sewer
0.915 m (3 ft) in diameter. The design
discharge QD, was found by taking a nominal
flood flow velocity in the range of 1.20 - 1.50
m/sec (4 tp 5 ft/sec). For the design discharge
actually simulated in the test procedures, 0.88
m3 /sec (31.1 cfs), the flow velocity would be
1.3 5 m/sec (4.4 ft/sec).
Design Guidelines
The designer should use the following
figures for designing the helical separator.
These figures are:
Figure 11 Predicted Prototype Grit
Recovery vs Design
Flowrate Ratio
Figure 12 Predicted Prototype
Settleable Organic
Material Recovery vs
Design Flowrate Ratio
Figure 13 Recommended
Transition Profile
Figure 14 Effect of Transition
Slope
Figure 15 Design Flowrate vs Inlet
Diameter
(Recovery % \
a a o 1
0 0 g |
j-
-
"""""•
\
•5
-__
O.SQD 0D I.5Q0 2QD
Design Flowrate Ratio
Figure 16 Recommended Plan
Layout
Figure 17 Water Level in Regulator
Above Weir
Figure 18 Recommended Cross
Sections
The first step is to determine the design
flowrate. This might be based on a storm
flow expected to occur with a frequency of 5
or 10 years, or some other period, depending
on the local design criteria. Usually larger
flows than the selected design discharge may
occur, depending on the capacity of the sewer
system when surcharged. Figure 11 indicates
that the grit recovery will decrease to 97,
percent with a flow equal to 1.5 times the
design flowrate, and to 93 percent with a flow
equal to 2 times the design flowrate. Hence,
the efficiency of grit removal is not greatly
affected by flows up to twice the design
flowrate.
Similarly, Figure 12 indicates the decrease
in recovery of organic matter with increase in
flow. Thus, for 1.5 times design flowrate, the
efficiency decreases to about 87 percent; and
for 2 times design flowrate, the efficiency
decreases to about 75 percent.
0.5QD QD 1,5 00
Design Flowrate Ratio
Note:
Organic material as defined on Figure 6
FIGURE 11 PREDICTED PROTOTYPE
GRIT RECOVERY VS
DESIGN FLOWRATE RATIO
FIGURE 12 PREDICTED PROTOTYPE
SETTLEABLE ORGANIC
MATERIAL RECOVERY VS
DESIGN FLOWRATE RATIO
18
-------
Inlet Diameter *1D'
Note: For Profile C-C Location
See Figure 16
FIGURE 13 RECOMMENDED TRANSITION
PROFILE
From the foregoing, it would appear that
a considerable increase in flow above the
design flowrate can occur without greatly
affecting the operating efficiency of the
helical separator.
Transition Slope
As shown in Figure 13, the recommended
transition has a length of 15 D and a height ot
D at the inlet and 2 D at the outlet. In the
laboratory model the invert of the transition
was level. In practice this is not desirable
because this would cause deposition of solids
on the invert during periods of minimum
flow. Therefore, the invert should have some
slope. To prevent any surcharge at the inlet,
the top of the transition should be kept level
and the invert given a slope. The slope should
be either the slope of the inlet, or the slope that
will satisfy the hydraulic slope S in the
Manning Equation, whichever is greater.
The resultant hydraulic conditions either
with the invert level or the top level is shown
in Figure 14, Effect of Transition Slope. The
transition with the level top has the following
Hydraulic grade line
Water surface
• Velocity head
2D
T
Velocity Head
Transition loss
D
Transition 15D
Profile with Level Invert
Hydraulic Grade line
• Water surface
• Velocity head
Velocity head
Transition loss
2D
Profile with Level Top
FIGURE 14 EFFECT OF TRANSITION SLOPE
19
-------
advantages: (1) The sewer is not surcharged
upstream of the transition except for loss of
head in the transition, which may be minor;
and (2) the slope will increase the velocity
through the helical separator as the storm
flow subsides which may aid in flushing
deposits out of the helical section. The chief
disadvantage of providing too great a slope in
the transition is that the outlet pipe to the
stream from the helical separator may be
lowered so much that the extension of the
existing sewer cannot be utilized for this
purpose. Therefore, each situation must be
evaluated before selecting the slope. Again as
a minimum, the transition should have the
same slope as the incoming sewer.
Transition Length
The transition length as given in Figure
13 is 15 D. The value of D is selected from
Figure 15, Design Flowrate vs Inlet Diameter.
Assume the designer selects a D of 1.83 m (6
ft) from Figure 15 as appropriate for the
design flowrate. Then the recommended
transition length is 27.4 m (90 ft). However,
assume the existing sewer has a diameter of
1.52 m (5 ft) rather than 1.83 m (6 ft). The
problem is how to effect the connection from
the existing sewer to the transition. The most
logical way would be to extend the transition
to meet the existing sewer while reducing the
area at the same rate as occurs in the
transition. The area of the transition at the
entrance would be 0.785 D2 and at the exit
4.70 D2. These areas are equivalent to squares
with a side of 0.885 D at the entrance and of
2.16 D at the exit. Accordingly, the slope of
the side of the transition would be equal to
1.28 D divided by 30 D, or 0.0426. This slope
has an angle of 2 degrees 26 minutes. Thus, if
the diameter of the existing sewer is 0.30 m
(1 ft) smaller than the selected D, the
transition should be extended by 3.5 m
(11.6 ft).
It would also seem logical to reduce the
length of the transition by a similar process if
the area of the existing sewer is larger than
the area of the transition inlet selected from
the design charts.
Transition Inlet Size
All dimensions of the helical separator are
related to D, the diameter of the transition
inlet. After determining the design flowrate,
the designer should select the inlet diameter,
D, from Figure 15, which shows the simple
scaled-up values according to the Froude Law,
for the design discharge, QD, as well as 1.5
QD and 2 QD . These have been computed
covering the likely range of applicable flood
discharges and pipe sizes that will be
encountered in any prototype installations.
Seldom will the value of D be that of a
standard pipe size. Hence, the designer should
select the nearest D corresponding to a
standard pipe size. If the indicated D falls
between two pipe sizes, the larger D will give
a separator with greater efficiency than the
smaller D. For instance, if the design flowrate
is 2.83 m3/sec (100 cfs), the indicated D will
be 1.45 m (4.75 ft). The designer can select a
D of 1.52 m (5 ft) which is equivalent to a
design flowrate of 3.11 m3/sec (110 cfs), or a
D of 1.37 m (4.5 ft), equivalent to a design
flowrate of 2.40 m3/sec (85 cfs). If the latter
capacity is chosen, the design flowrate will be
18 percent larger than the separator capacity.
From Figure 11, the grit removal efficiency
will be reduced to 99 percent of the total
gtitload. From Figure 12, the settleable
organic removal will be reduced to about 96
percent.
If, in the example given above, the
existing sewer should have a diameter equal to
one of the possible D selections, then it would
be logical to select the D which matches the
existing sewer size. Otherwise, the transition
should be extended as discussed previously.
The overall length of the helical separator
is approximately 37 D including the transition
and straight sections, as shown in Figure 16,
Recommended Plan Layout. If a D of 1.37 m
(4.5 ft), is selected, the length will be 50.9 m
(167 ft), whereas if a D of 1.52 m (5 ft) is
selected, the length will be 56.4 m (185 ft). A
third possibility, assuming the existing sewer
is 1.37 m (4.5 ft) and the D indicated by the
chart is 1.4 m (4.75 ft), would be to base all
dimensions on the indicated D and to extend
the transition according to the method
explained previously. In this case, the
transition would be extended an amount
equal to one-half the difference in diameters,
divided by 0.0426 or 0.91 m (3 ft). The
overall length in this case would be 37 times
D plus 0.91 m (3 ft), or 5.45 m (179 ft).
20
-------
. 12
10
Q
1
a>
.S
Q 4
Jj
"c
10
20 30 40 50
3.5
3.0
2.5
2.0
1.5
2
5
o>
I
Q
;-,
-2
I
.3
Q
i.o
0.5
IOO 20O 300 400500 100?)-cfs
i i I i i i i I I I t
0.5
2345
Design Flowrate
10 15 2O 25 m3/s
FIGURE 15 DESIGN FLOWRATE VS INLET DIAMETER
21
-------
Scum Board
Weir
Note:
See Figure 18 for
sections A-A & B-B
See Figure 13 for
Profile C-C
Inlet Diameter -
-D-
FIGURE 16
RECOMMENDED
PLAN LAYOUT
Thus, the designer is faced with the
choice of three lengths - either 50.9 m (167
ft), 56.4 m (185 ft) or 54.5 m (179 ft).
Obviously the largest helical separator will
provide the most efficient operation.
Velocities in Transition
As a matter of interest the velocities at
the inlet and outlet ends of the transition
were computed for five values of D, from
Figure 17. The D values selected were 0.91,
1.22, 1.52, 1.83 and 2.13 m (3,4,5,6, and 7
ft). The results are shown in Table 1,
Velocities in Transitions. These data indicate
an outlet velocity from the transition ranging
from 0.22 m/sec (0.71 fps) to 0.36 m/sec
(1.17 fps). This compares with the usual
criteria of velocities between 0.23 m/sec (0.75
fps) and 0.38 m/sec (0.75 fps) and 0.38 m/sec
(1.25 fps) in a rectangular grit channel with
velocity control. In general, the outlet
velocities are about one-sixth the inlet
velocities. All velocities are based on the
sections flowing full.
Channel. Slope
In the laboratory model the channel of
the helical separator was level. In practice the
channel should be given enough slope to
maintain a self-cleansing velocity of 0.61
m/sec (2.0 fps) with DWF (average
dry-weather flow).
Assume the following:
D = 0.91 m (3.0 ft)
Design flowrate = 0.85 m3/sec (30 cfs)
DWF = 1 percent of design
flowrate
= 0.008m3/sec (0.3 cfs)
Peak DWF = 0.025 m3/sec (0.9 cfs)
From a chart showing hydraulic
properties of circular sections when the
flowrate is one percent of the full section,
the depth is seven percent of the full depth
and the velocity is 31 percent of the velocity
of the full section. The desired slope is that of
a section when flowing full at a velocity of
0.61 m/sec (2.0 fps), divided by 0.31, or 1.98
m/sec (6.5 fps). From a nomograph of flow for
Manning n = 0.013, the required slope of the
channel for a diameter of 0.91 m (3.0 ft) is
0.48 percent. If the peak dry-weather flow is
3 times DWF the following data prevail:
When slope is 0.48%
Q = 0.025m3/sec (0.90 cfs)
d =0.11 m (0.36ft)
v =0.5 8 m/sec (2.0 fps)
The foregoing assumes a circular section
in the channel when flow is 1 percent and 3
percent of design flowrate. From a visual
comparison of a large-scale section of channel
with a, circular section it is evident that flow
conditions in a circular section will prevail for
the depths of flow considered above. The
foregoing indicates that peak dry-weather
flows should cause no deposition in the
channel.
22
-------
1.2
1.0
0.9
0.8
£ 0.7
1
^ .
'3
g 0.6
< 0.5
(U
0>
3:
0.4
0.3
0.2
O.I
20 30 40 50
1 1 i
0.5
100 200 300 400 500 1000 cf s
-i I I I I 1 I I I I II _
1
2345
FSowrate
10 15 20 25 m/s
Note: Divide Flow/rates
for D = 0.61 m (2 ft)
Curve by 100
FIGURE 17 WATER LEVEL IN REGULATOR ABOVE WEIR
23
-------
TABLE 1
VELOCITIES IN TRANSITIONS
Inlet Design
Diameter Discharge
0.91m
(3ft)
Area
Velocity
Inlet
1.22m
(4ft)
1.52m
(5ft)
1.83m
(6ft)
2.13m
(7ft)
0.85 m3 Is
(30 cfs)
1.84m3/s
(65 cfs)
3.11m3/s
(110 cfs)
4.96 m3/s
(175 cfs)
7.65 m3 Is
(270 cfs)
0.65 m2
(7.0 sf)
1.17m2
(12.6sf)
1.82m2
(19.6 sf)
2.63 m2
(28.3 sf)
3.58 m2
(38.5 sf)
Note: Inlet Area = 0.785 D
Outlet Area = 4.70 D when depth is 2D.
Weir Discharge
Previous research on side overflow weirs
indicates that with a relatively high weir, as
proposed in the helical separator, the usual
weir discharge equations provide a reasonable
basis of design. The usual equation is as
follows:
Q = CLH3/2
where
Q
c
L
H
The
whether
flowrate in m3/sec (cfs)
coefficient
length of weir in m (ft)
head on weir in m (ft)
coefficient C varies depending on
the weir is sharp crested or broad
crested and depending on the head and width
of the weir.
In the laboratory model the weir was
made of Plexiglas and maintained in level
position. The heads on the weir were
measured at the 35 degree position. The heads
on the weir for various values of D and
flowrates are shown in Figure 17. Heads were
obtained from this figure for various flowrates
and the value of C was computed in the weir
equation. The results indicated a range of C
(based on use of U.S. customary units) from
3.3 to 3.7, with most values being 3.4 or 3.5.
Such values are usually associated with
sharp-crested weirs.
Outlet
3.93 m2
(42.3 sf)
6.98 m2
(75.2 sf)
10.9 m2
(117 sf)
15.7m2
(169sf)
21.4m2
(230 sf)
Inlet
1.31 m/s
(4.3 fps)
1.58 m/s
(5.2 fps)
1.71 m/s
(5.6 fps)
1.89 m/s
(6.2 fps)
2.13 m/s
(7.0 fps)
Outlet
0.22 m/s
(0.71 fps)
0.26 m/s
(0.86 fps)
0.29 m/s
(0.94 fps)
0.30 m/s
(1.0 fps)
0.36 m/s
(1.17 fps)
In practice a sharp-crested weir would be
made of a steel or fiber glass plate. The only
advantage of such a weir over a broad-crested
weir is that it is easier to make adjustable.
However, this is considered of minor
importance.
Experience in Great Britain, where side
overflow weirs have been used more widely
than in the United States, favors the use of a
weir with a semicircular shape. This shape
seems preferable for the helical separator.
The coefficient of a broad-crested weir
varies with the width of crest and head on the
weir. For the widths and heads likely to occur
in the helical separator the value of C (for
U.S. customary units) may range from 2.8 to
3.3. The use of a C value of 3.0 (for U.S.
customary units) for design purposes is
suggested. An example follows:
Design flowrate = 0.85 m3 /sec (30 cfs)
D = 0.91m (3.0 ft)
L (weir length) = 18.83 D
= 17.2m (56.5 ft)
Assume flow to plant = 0.028 m3/sec(1.0 cfs)
Q (over weir) = 0.82 m3 /sec (29.0 cfs)
In English units Q = CLH3/2
If C = 3.0 then H = 0.095m (0.32 ft)
The weir height is 1-5/6 D from Figure
18, Recommended Cross Sections. Therefore:
24
-------
Section A-A
m
Note: For Section Locations
See Figure 16
Typical Section B-B
FIGURE 18 RECOMMENDED CROSS SECTIONS
Weir height = 1.68 m (5.50 ft)
Head on weir = 0.095 m (0.32 ft)
Water depth = 1.77m (5.81 ft)
However, to meet the laboratory
demonstrated requirements that the transition
be flowing full, the.water depth should be 2D
or 1.83 m (6.0 ft). Therefore, in this case the
weir height should be a minimum of 1.73 m
(5.68 ft) so that the transition outlet is
flowing full when design flowrate occurs.
Outlet Control
Various methods of controlling the flow
from combined sewer overflow regulators are
discussed in an EPA report.7 This report
indicates that close control of the outlet flow
requires the use of a sluice gate controlled by
a float and actuated by either water power or
an electric motor. On smaller structures where
the use of such devices is not justified, one
method of control is by use of a manually-
operated gate. The intent is to- only operate
such gates to clear them 'of debris or to
change the opening size.
The use of such gates may result in
considerable variation in the flow diverted to
the treatment plant. This may not be serious
when this flow is only a small percentage of
25
-------
the total flow tributary to the plant. To
indicate the possible range in flow, the
following example is based on the use of a
manually-operated gate on the outlet to the
treatment plant. The minimum size gate used
should be 0.20 m (0.67 ft) square but a gate
with a minimum size of 0.30 m (1.0 ft) square
is preferable.
Legend
A = Cross-sectional Area
D = Diameter
V = Velocity
d = Depth of flow
Q = Quantity of flowrate
b = Width of opening
C = Coefficient
DWF = Average dry-weather flow
g = 9.81 m/sec2 (32.2 ft/sec2)
Pertinent Data
DWF = 0.008 m3 /sec (0.30 cfs)
Peak DWF = 0.025 m3 /sec (0.90 cfs)
Try sluice gate 0.30 m (1.0 ft) square
Assume opening 0.10 m (0.33 ft) high
Then A = 0.03 m2 (0.33 sf)
Determine depth upstream of gate when:
Q = 0.025 m3/sec (0.90 cfs)
Q = C A V 2gH
0.025m3 /sec (0.9 cfs)
= 0.7 x 0.031 m2 (0.33 sf) x
4.43 (8.03) x V H
H = 0.21 m (0.69 ft) on center line of orifice
Depth of flow is H, plus one-half height
of orifice, or 0.26 m (0.86 ft). This is much
greater than the normal depth of flow at the
peak dry-weather flow of 0.11 m (0.36 ft)
computed previously. Therefore, the velocity
will be much less than the 0.58 m/sec (2.9
fps) computed previously and may cause
deposition of grit at peak dry-weather flow.
Determine flow to the treatment plant
when the water level is at weir crest.
Depth of flow in chamber is 1.83 m (6.0 ft)
Head on center of orifice is 1.77 m (5.83 ft)
Q = C AV2gh
= 0.7 x 0.03m2 (0.33sf) x 4.43 (8.03)
1.33m (2.41 ft)
= 0.127 m3 /sec (4.46 cfs) = 15 DWF
Hence, the flow to the plant will exceed
15 DWF during periods of design discharge if
there is no further restriction to flow
downstream of the sluice gate. One way to
restrict the flow is to design a sewer between
the sluice gate manhole and the interceptor in
such a way that it will convey the peak
dry-weather flow without surcharge but will
become surcharged when the flow exceeds the
peak dry-weather flow. This procedure is
described and illustrated by an example in
an EPA report.7
Spillway Channel
The side channel in the helical section
which conveys the overflow from the weir to
the outlet sewer leading to the stream should
be designed for the maximum flow expected
to pass through the separator. The maximum
flow will depend on the storm frequency for
which the combined sewer is designed, as well
as on the extent to which the combined sewer
can be surcharged by storm flows greater than
the design flow. It should also be assumed
that the pipe outlet to the treatment plant is
not in use either by design or by accident. On
this basis it is possible for the maximum flow
to exceed the design flowrate by 50 to 100
percent.
As an example, assume that the design
flowrate is 0.85 m3/sec (30 cfs) and the
maximum flow is 1.27 m3/sec (45 cfs). The
side channel can be designed as a lateral spillway
channel with the weir discharge spilling into it
throughout its length. To aid in self-cleaning,
it is desirable to set the downstream end of
the channel above the invert of the outlet
pipe and to provide a slope in the channel so
that at low depths of flow the velocity will
.exceed 0.31 m/sec (1.0 fps).
The channel should be designed large
enough so that the upstream water surface
will not cause submergence of the weir.
The general equation for determining the
depth of flow in a lateral spillway channel is
the following:8
h0 =
(hl -1/3U)2 -2/3H
hi
where
26
-------
h,
z
/
and
where
= upstream water depth
= critical depth
downstream water depth
when flow is submerged
= slope of channel
= length of channel
gb
- width of channel
Entrance loss =
2g
Elevation invert
outlet pipe
Elevation weir
Elevation water
at entrance
Length of channel =
length of weir, less
outlet diameter
= 0.29m (0.96ft)
= 0.00m (0.00ft)
= 1.83m (6.00ft)
1.21 m (3.96 ft)
= 16.3m (53.5ft)
The factors in the foregoing equation are
depicted in Figure 19, Spillway Channel
Profile. Actually, only 17.83/18.83, or 95
percent of the maximum flow discharges
directly into the spillway channel. In the
following example, however, it is assumed
that all the maximum flow is conveyed by the
channel.
Assume the following data:
Design fiowrate = 0.85 m3 /sec (30 cfs)
Q(side channel) = 1.27m3 /sec (45 cfs)
Outlet pipe diameter = 0.91m (3.0ft)
Weir height = 1.83 m (6.0 ft)
Then
Outlet velocity = 1.95 m/sec (6.4 fps)
Initial computation indicated that a
channel 1.83 m (6.0 ft) deep and 0.31 m (1.0
ft) wide would cause submergence of the
weir. For maintenance purposes a minimum
width of channel of 0.61 m (2.0 ft) is
considered desirable.
Preliminary computation with zero slope
and the downstream end of the channel at
elevation 0.0 indicated a water depth at the
upstream end of the channel of 1.49 m (4.9
ft).
The effect of submergence on
broad-crested weirs is surprisingly small. If
necessary the fall in the water surface over the
weir can be limited to 50 percent of the head on
weir without affecting the discharge over the
18.83D
Freeboard •
D = Transition inlet diameter
Figure assumes .that outlet
sewer has same diameter
FIGURE 19 SPILLWAY CHANNEL PROFILE
27
-------
HELICAL BEND REGULATOR
Design Example
Straight Pipe
Assume pipe designed so that at DWF the velocity is about 2 fps
D = 3.0 ft
Q full = 45 cfs
S = 0.44 %
v = 6.5 fps
n = 0.013
For Q design = 30 cfs
.Qi = 30 = o.67
Q2 45
—l = 0.6 from chart
d2
di =0.6x3.0= 1.8ft
-1 = 1.07 from chart1
V2
v, =1.07x6.5 = 7.0 fps
For Q DWF = 0.3 cfs
OIL = Qi3= 0.007
Qa 45
^=0.06
d2
£>-= 0.29
d, =0.06x3 = 0.18 ft
vi =0.29x6.5= 1.9 fps
OK almost 2.0 fps
For Q3(Peak DWF) = 0.9 cfs
QL, QJ = Q.02
Q2 45
^^ 0.1
dt =0.1 x3 = 0.3 ft
v2
= 0.4
= 0.4 x 6.5 = 2.6 fps
28
-------
Helical Bend Regulator, Design Example (continued)
Straight Pipe D = 3 ft
i = 0.3 ft
j =0.18 ft
Q = 0.9 cfs
Q = 0.3cfs
Helical Bend Regulator
0.3ft
Q = 0.9 cfs
At 3 DWF the area will only be slightly larger in separator than in 3 ft diameter
pipes. Assume velocity the same
v = 2.6 fps
Exit Pipe — Assume 1.0 ft diameter
S = 0.44 %
Q = 2.4 cfs
Qi = PJU
Q2 = 2.4
dj- = 0.42
d2
XL = 0.92
v = 3.0 fps
di = 0.42 ft
v, = 0.92 x 3 = 2.8 fps
i = 0.42 ft Q = 0.9 cfs
I
Lower invert of outlet pipe 0.12 ft below invert of separator so as not to raise water surface
Determine outlet design
when Q = 30 cfs
so that Q outlet - = 0.9 cfs
Weir Length
Angle = 60° . D = 3 ft
29
-------
Helical Bend Regulator, Design Example (continued)
Weir Radius =
Head on Weir
Weir Length =
Q per ft
Use Rehbock K
Q
JJ3/2.
H
Depth of Water
1-5/6 D
Head on weir
Total water depth
Assume short tube exit
oo
16D + 2.5D + D/3
(16) (3)+ (2.5) (3)+1
56.5 ft
60
360 V~"7 6
59ft
-3-0- = 0.51 cfs
M-
KLH3/2 = 3.41 (1)H3/2 =0.51
0.15
0.28 ft
ii- (3) = 5.50ft
/eir
>th
D
A
=
=
1.0ft
- TrD2
0.28
5.78 ft
- n 7«
4
CAV 2gH
(0.7) (0.785) (8.03)vr5T28~
10.1 cfs
Too large
0.12
Outlet Design
Determine orifice area for
Q
0.9
A
A
D
CA V 2gH
(0.7) (A) 8.03
6.9 * 12.9 =0.07
30
-------
Helical Bend Regulator, Design Example (continued)
Orifice should be greater than 0.67 ft. If orifice is made this size so that only 0.9 cfs or
3DWF would pass when tank is full, then it is apparent that the tank would fill up whenever
3DWF occurs which might be the peak daily flow.
To prevent deposition of solids on the separator floor and to prevent cleaning the separator
in dry weather periods, the separator and outlet should pass up to 3 DWF without raising
levels in separator to weir levels.
Try throttle pipe on outlet
00
Assume free fall
Outlet Design
Use 8-inch pipe as minimum
Use s
For n
For
0.4% as minimum
0.013
QDWF
QL
Q= 0.75 cfs
v = 2.2 fps'
2g
= 0.08ft
0.3 cfs
0.3
0.75
= 0.4
If discharge ratio is 0.4, then depth is 44% and velocity 94%
Assume
For
d = .44 D
v = .94 V
L
Q3DWF
v
Entrance & exit loss
Slope hydraulic gradient
Actual pipe slope
Water surface above top pipe
Water surface in tank
Depth water in tank
0.44 x 0.67
0.94 x 2.2
100ft
0.9 cfs
2.5 fps
1.5x0.1
100x0.5%
= 0.3ft
= 2.1 fps
H= 5.78-0.67
si = o.i
2g
0.15
= 0.50
0.65
0.40
= 5.11ft
s = 0.5%
0.25
JL61
0.92 ft
31
-------
Helical Bend Regulator, Design Example (continued)
Determine Q max when tank is full
Assume entrance and exit loss =
slopeH.G _-
Q max
1.6cfs
1.2ft
100+0.4 = 4.3%
v = 7.2 fps
2g
= 0.
Thus with 8 in. throttle pipe 100 ft long the maximum Q will be 1.6 cfs or about
5 times DWF.
Try other lengths of pipe
Lft 5%HG Qcfs vfps -^- Q DWF
200
300
400
600
2.45
1.9
1.45
1.2
1.8
1.6
1.4
1.3
5.4
4.7
4.0
3.8
2g
0.5
0.4
0.3
0.2
6
5.3
4.7
4.3
A length of 400 ft should be the maximum for an 8 in. sewer. Therefore it is obvious
that if the discharge is to be limited to 3 DWF some type mechanical device should be
used to close the outlet opening as the water level rises in the separator.
Determine depth of water in tank with throttle pipe 400 ft long, when Q = 0.9 cfs
Required 5 = 0.5% (See previous page)
400 x 0.5% = 2.0 ft
Slope sewer 400 x 0.4% 1.6
0.4ft
Entrance & exit loss 1.5— 0.15
2g
Head on top of pipe 0.55 ft
Diameter pipe 0.67
Depth of water in tank 1.22 ft
weir. As computed previously the head on the
weir is 0.095 m (0.32 ft) and little elevation
can be gained by assuming a submerged weir.
Therefore design can be based on no
submergence of weir. It is also desirable to
locate the downstream end of the discharge
channel above the outlet pipe invert to
prevent deposition in the channel. Therefore
the downstream end of the channel was set at
elevation 0.30 m (1.0 ft) and the channel
slope set at 0.005. The resultant freeboard of
0.18 m (0.6 ft) indicated that the channel
could have been raised an additional 0.18 m
(0.6 ft). The final data are as follows:
Elevation downstream
invert of channel 0.3 m (1.0 ft)
Rise in channel 0.09 m (0.3 ft)
Elevation upstream
invert of channel 0.40 m (1.3 ft)
h0 1.25m (4.1ft)
Elevation upstream
water surface 1.65 m (5.4 ft)
Elevation weir 1.83 m (6.0 ft)
Freeboard 0.18m (0.6 ft)
32
-------
In the foregoing example, it was assumed
that the outlet pipe was located at the end of
the channel. If the outlet pipe were located at
the center of the side channel this would
result in a lesser rise of the water surface in
the spillway channel.
Typical Dimensions
For the purpose of comparing the helical
separator with the swirl concentrator, three
design flows were selected as follows: 1.42
m3/sec (50 cfs), 2.83 m3./sec (100 cfs), and
5.66 m3/sec (200 cfs). The dimensions of the
helical separator are based on Figures 15, 16,
18, and on Profile with Level Top, in Figure
14, Effect of Transition Slope. The resultant
dimensions are tabulated in Table 2, Helical
Bend Regulator Dimensions. The dimensions
of the swirl concentrator are based on Figures
7, and 11 through 18, of Report
EPA-670/S-74-039, Relationship Between
Diameter and Height for the Design of a Swirl
Concentrator as a Combined .Sewer Overflow
Regulator. (July 1974) The resultant
dimensions - are shown in Table 6, Swirl
Concentrator Dimensions.
It should be noted that the helical
separator sized in Table 2 will remove 100
percent of grit, whereas the swirl concentrator
sized for the same discharge in Table 6 will
remove only 90 percent of grit. This is
because the published design charts for,the
swirl concentrator provide for 70, 80, and 90
percent recovery (or removal) of grit. Later in
this section, under the heading "Comparison
of Costs," a method is developed to indicate
the possible cost of a swirl concentrator to
remove 100 percent of grit.
TABLE 2
HELICAL BEND REGULATOR DIMENSIONS
Design Discharge
Inlet Diameter
Transition Length
Straight Section - Length
Radius
Width
Minimum Wall Height
Channel to Top Weir
Height End of Transition
Scum Baffle Height
Distance from Weir to
Bottom of Baffle
Weir Height
Distance Wall to Weir:
Max
Min
m3/s
(cfs)
D-m
(ft)
15D-m
(ft)
5D-m
(ft)
16D-m
(ft)
3D-m
($)
2.5D - m
(ft)
1-D - m
6 (ft)
2D-m
(ft)
D m
3 (ft)
D m
12 (ft)
D m
3 (ft)
1.42
(50)
1.07
(3.5)
16.0
(52.5)
5.33
(17.5)
17.1
(56.0)
3.20
(10.5)
2.67
(8.75)
1.95
(6.4)
2.13
(7.0)
0.36
(1.2)
0.09
(0.3)
0.36
(1.2)
2.83
(100)
1.52
(5.0)
22.9
(75.0)
7.62
(25.0)
24.4
(80.0)
4.57
(15.0)
3.81
(12.5)
2.77
(9.1)
3.05
(10.0)
0.52
(1.7)
0.13
(0.4)
0.52
(1.7)
4.67
(165)
1.83"-
(6.0)
27.4
(90.0)
9.14
(30.0)
29.3
(96.0)
5.49
(18.0)
4.57
(15.0)
3.35
(11.0)
3.66
(12.0)
0.61
(2.0)
0.15
(0.5)
0.61
(2.0)
D m
3 (ft)
D m
6 (ft)
0.36
(1.2)
0.18
(0.6)
0.52
(1.7)
0.26
(0.85)
0.61
(2.0)
0.30
(1.0)
33
-------
11.8D +30.5m (100 ft)
D2 +31.1m (102 ft)
Notes:
1.
2.
3.
4.
Swirl Concentrator
If D< 0.76 (2.5ft)
the length is 16.9 D +
30.5m (100 ft)
Or 15.2m (50 ft)
whichever is greater
D = Diameter of
Transition inlet
D2= Inside diameter
of Swirl Concentrator
FIGURE 20 SITE REQUIREMENTS
Site Requirements
The size of the buffer or protective zone
required around the helical separator will
depend to a large extent on the environment
of the neighborhood. In any locality, a buffer
zone at least 15.2 m (50 ft) wide would be
desirable. Therefore, the site requirements
given herein are based on a 15.2 m (50 ft)
buffer zone around all open or above-ground
parts of the facility. Because the transition is
below the surface, no buffer zone is required
for that part of the structure; however, it is
assumed that all of the transition section is
located on the site.
On the foregoing basis, the site
requirements for both the helical separator
and the swirl concentrator are shown in
Figure 20, Site Requirements. The required
lot dimensions and areas for three sizes of
each facility are shown in Table 3, Site
Dimensions and Areas for Helical Bend and
Swirl Concentrator Regulators. As explained
previously, the site dimensions are based on a
helical separator to remove 100 percent of
grit .and a swirl concentrator to remove 90
percent of grit.
It is evident from Table 3 that the site
requirements for the helical bend are greater
than for the swirl concentrator and that the
larger the design flow the greater the
difference. For the design flows of 1.42
m3/sec (50 cfs), 2.83 m3/sec (100 cfs) and
5.66 m3/sec (200 cfs), the helical bend
requires a site 49 percent, 106 percent, and
137 percent greater, respectively, than the
swirl concentrator.
34
-------
TABLE 3
SITE DIMENSIONS AND AREAS FOR HELICAL BEND
AND SWIRL CONCENTRATOR REGULATORS
Capacity
Relative Area
Capacity
Site Size
Site Area
Relative Area
Swirl
Concentrator
1.42m3/s(50cfs)
Site Size
Site Area
Relative Area
Capacity
Site Size
Site Area
38.0 mx 38.0m
(124.5 ft x 124.5 ft)
1,440m?
(15,500sf)
1.00
2.83m3/s(100cfs)
40 m x 40 m
(131.5 ft x 131.5 ft)
1,600m2
(17,300 sf)
1.00
4.67m3/s(165cfs)
42 m x 42 m
(138 ft x 138 ft)
1,770m2
(19,000 sf)
1.00
Helical
Separator
43.0m x 54.6 m
(141 ft x 179 ft)
2,340 m2
(25,200 sf)
1.63
48.5 mx 71.5m
(159 ft x 234 ft)
3,460 m2
(37,200 sf)
2.15
52.0 m x 82.8 m
(171 ft x 272 ft)
4,300 m2
(46,500 sf)
2.45
Comparison of Hydraulic Head
Losses in Helical Bend and
Swirl Concentrator Regulator
The available head at a specific site may
be a critical factor in the choice of the
specific type of combined sewer regulator to
be used. The head loss must be considered for
two - conditions: (1) For periods of
dry-weather flow, and (2) for periods of
wet-weather flow. The available head during
dry-weather flow will depend on the
difference in elevation between the combined
sewer and the interceptor that will convey the
flow to the wastewater treatment plant. The
available head during wet-weather flow will
depend on the difference in elevation between
the combined sewer and the water surface of
the receiving stream. A further consideration
in the latter case is whether the existing
combined sewer is to be used to convey the
overflow from the regulator to the receiving
stream or to any holding or treatment
facilities involved.
In periods of dry weather there will be
open channel flow through the regulator, and
hence the drop in invert and hydraulic
gradient will be similar from the regulator
inlet to the foul outlet. In wet-weather
periods there may be a considerable
difference between the drop in invert and the
drop in hydraulic gradient from the regulator
inlet to the clear outlet.
The usual practice is to design combined
sewers to run full at design discharge, i.e., the
hydraulic gradient is at the top of the pipe. In
special -cases, due to topography or for other
reasons, it may be possible to design the sewer
to be surcharged, i.e., the hydraulic gradient is
above the top of the sewer. Both cases are
considered below. To simplify the discussion,
the slope of the channel in the regulator to
maintain a dry-weather flow velocity that will
prevent solids deposition has not been
included in the required drop in the invert.
In the following comparisons, the head
losses are given as a multiple of the inlet
35
-------
dimension: D, the inlet diameter of the
helical separator; and Dt the side of the
square inlet of the swirl concentrator. To
show that D and DI are approximately the
same for the same discharge, their values for
three discharges are given, as follows:
Design
Discharge m3/sec 1.42 2.83 5.66
(cfs) (50) (100) (200)
D
m
(ft)
m
(ft)
1.07
(3.5)
0.90
(3.0)
1.52 1.98
(5.0) (6.5)
1.52 1.83
(5.0) (6.0)
First, consider the case where there is to
be no surcharge on the inlet during design
discharge.
In the helical separator the transition will
have a level top as shown in Figure 14. The
drop in the invert of the transition will be 1.0
D. Therefore, the drop in the invert from the
inlet to the foul outlet will be 1.0 D
(neglecting the slope of the channel through
the regulator). The loss in the hydraulic
gradient will also be 1. O D. The invert of the
clear outlet will be at approximately the same
elevation as the invert of the separator, as
explained previously in the discussion of the
weir overflow spillway channel. Therefore,
the drop in the invert between the inlet and
the clear outlet will also be 1.0 D. The loss in
the hydraulic gradient may be the same as the
drop in the invert or it may be slightly
different depending on outlet design.
The dimensions of the swirl concentrator
as a Combined Sewer Overflow Regulator are
given in Figure 11, General Design Details, of
Report EPA-670/2-74-039, Previously cited.
The general construction details are shown in
Figures 12, 13, and 14 of EPA Report
R2-72-008, titled "The Swirl Concentrator as
a Combined Sewer Overflow Regulator
Facility." (Sept. 1972)
If there is to be no surcharge on the inlet
sewer, the crown must be at a distance above
the invert of the chamber equal to H! (the
height of weir above the chamber invert), plus
the head on the weir. The drop in the invert
of the sewer will be this distance less D! , the
dimension of the inlet. The foul outlet is
located below the chamber bottom. Assuming
a foul outlet diameter of 0.31 m (1.0 ft) and
concrete cover over the outlet to the same
amount, the distance from the chamber invert
to the outlet invert is 0.61 m (2 ft).
Excluding the channel slope through the
concentrator, the drop in the invert from the
inlet to the foul outlet is, therefore, 0.8 Dt to
1.5 DI, plus 0.6 m (2.0 ft). The foul outlet
pipe diameter may exceed 0.31 m (1.0 ft)
diameter for larger flows, thus increasing the
total drop somewhat. The hydraulic gradient
will have a similar drop.
The clear outlet is also located below the
chamber floor and, if a 0.31 m (1.0 ft)
concrete cover is provided over the outlet, the
vertical distance from the chamber invert to
the invert of the clear outlet will be 1.0 Dt,
plus 0.31 m (1.0 ft). Combining this with the
entrance drop of 0.8 D! to 1.5 D! , will result
in a total drop in the invert from the inlet to
the clear outlet of 1.8 Dt to 2.5 Dt, plus 0.31
m (1.0 ft). The drop in the hydraulic gradient
in this case will be different. The circular weir
is set a distance equal to the head on the weir
below the top of the inlet sewer. If there is no
submergence of the weir then the loss in the
hydraulic gradient will be equal to this head.
Trial computations indicate the head on the
weir is about 0.2 D! . Allowing for friction
losses in the outlet pipe and some freeboard
downstream of the weir, the drop in hydraulic
gradient is about 0.4 D! .
When the inlet sewer is surcharged
different hydraulic conditions will exist in the
helical separator. If the inlet is surcharged an
amount equal to D, the transition invert will
be level, as shown in Figure 14. The drop in
the invert from the inlet to the foul outlet
will be zero (neglecting the channel slope
through the separator). The drop in hydraulic
gradient will also be zero. Likewise, the drop
in the invert from the inlet to the clear outlet
will be zero. However, the loss in hydraulic
gradient for this case will be 1.0 D.
In the case of the swirl concentrator, if a
surcharge of Dt is permitted then the crown
of the sewer can be set a distance of D, below
the water surface of the chamber. The drop
from the chamber invert to the foul outlet
will be 0.61 m (2.0 ft), as previously
computed. Therefore, the drop in the invert
from the inlet to the foul outlet will be 0 to
0.5 D1; plus 0.61 m (2.0 ft). The drop in
36
-------
TABLE 4
TYPICAL HEAD LOSSES IN HELICAL BEND
AND SWIRL CONCENTRATOR REGULATORS
Helical Swirl
Separator Concentrator
Dry Weather Flow — Drop in Invert
Helical Separator
Transition invert level
Transition roof level
Swirl Concentrator
Wet Weather Flow
Helical Separator
Transition invert level
Hydraulic grade
Drop in invert
Transition roof level
Hydraulic grade
Drop in invert
Swirl Concentrator
Hydraulic grade
Drop in invert
Note: Friction losses not included in above Table.
hydraulic gradient will be the same. The drop
from the chamber invert to the clear outlet
invert will be 1.0 Dt, plus 0.31 m (1.0 ft), as
before. Therefore, the total drop from the
inlet invert to the clear outlet invert will be
1.0 D, to 1.5 D, plus 0.31 m (1.0 ft). The
drop in hydraulic gradient will be about 0-4
DI as computed previously.
The data relative to the foregoing
discussion are shown in Table 4, Typical Head
Losses in Helical Bend and Swirl Concentrator
Regulators.
From the Table, it is apparent that the
drop in the invert is always greater in the swirl
concentrator than in the helical separator.
When the inlet sewer is not surcharged, the
drop to the foul outlet is only slightly greater
but the drop to the clear outlet is about twice
as great. When the inlet sewer is surcharged an
amount equal to D or D! , the drop in the
invert is zero in the helical separator,
compared to the minimum drop of 0.61 m
(2.0 ft) to the foul outlet and of 1.0 Dt, plus
0.31 m (1.0 ft) to the clear outlet in the swirl
concentrator. For dry-weather flows, the drop
None
1.0 D
1.08 D to 1.33 D
1.0 D
None
1.0 D
1.0 D
0.58 D
2.1 D
in hydraulic gradient is similar to the drop in
the invert. For wet-weather flows, the drop in
hydraulic gradient from the inlet to the clear
outlet in the-swirl concentrator is about
one-half that for the helical separator.
Construction Details
Means of access must be provided to the
curved section of the separator for
maintenance purposes, including possible
washing down after each storm event. The
provision of a superstructure over this section
is desirable for safety and esthetic reasons,
and for confining possible odors. The type of
superstructure used will depend on the
character of the locality. As a minimum and
for purposes of this report, the walls are
assumed to be of concrete block and the roof
of precast concrete units. For roof spans
exceeding about 8.5 m (28 ft), it will be
necessary to provide structural steel framing.
A cross section of the helical separator
with a superstructure is shown in Figure 21,
Typical Cross Section, Helical Bend
Regulator. In this Figure, for cost estimating
37
-------
s?
£
r*
E
(0
CO
CO
Q
CM
s/Stf/
1 Precast Concrete Roof
• J
!v~V
—
r
^_
*'•'
• \
Vr
H
*.<•
.#
•'''i.
•'.77
-'4
«'
**t
;-iS.-4:<' '.'A:'.\':-'i'-A.'
^ Concrete block walls -^_^_^
Stainless steel rail — — »
>^ \
f 4
4' Concrete walk jl 1
| \
Concrete beam __ || \
7 II \
|WiSf»»jsSjMS>»{*Sk:{
Fiber glass baffle ^
r5fl
/^°iJ r
Flushing pipe ^^ ;
(i
*- 'i'?'f
•f t ^t
"<5 ^^r'N.a . i/;
CM ^^sa--"' " '••
• ^f^: «
V 5 ^^' .4:?
:*fi;\ 0 ^<"->i' "'<'--
V«t\ ^f-;- • Y • i-..
,'v-r ;K^ ,___^^ ' ^
_j,
*. —
'•'.V
K15
't.(
f;'A'
"V* '
;4f
M
1 ..«
;-'f^
y/
J " •
\t
**> t * . " <4'« »• *^*« • »rf^ i •• •*•&*/
' ' • — r^ '— '
'\
1.3D
wrT . „ te.
-^ Approximately 4.1 D
>,»
i ,
* *
oo c;
E E
•* «*?
•* o
CM c-
I
^\--4^\V. ^
<_Min.0.3m. (1 ft)
Spillway
Channel
0.67 D
_L
A
f
u
T
t:
CM
£
r—
CO
FIGURE 21 TYPICAL CROSS SECTION - HELICAL BEND REGULATOR
purposes the width of structure is indicated as
4.1 D and the width of spillway channel as
0.67 D. For any specific case the width and
elevation of the spillway channel may vary
from that shown in Figure 21, Typical
Cross-Sectional Helical Separator, as
explained previously.
The hydraulic conditions require that the
transition section be provided with a roof.
These conditions do not apply to the straight
section, having a length of 5 D, preceding the
curved section. It is not apparent from the
model studies that this section will require the
same maintenance as the curved section.
Accordingly, there appears to be no need to
make this section accessible.
For purposes of this report it has been
assumed that the straight section will have
walls 2.5 D high and will be provided with a
concrete roof at that elevation.
Other construction details considered
necessary or desirable are as follows:
38
-------
a. Provide concrete walls with a minimum
thickness of 0.3 m (1 ft), extending above
grade a minimum height of 0.3 m (1 ft).
b. Provide a concrete walk 1.2 m (4.0 ft)
wide.
c. Provide a stainless steel railing on each
side of the walk.
d. Provide a fiberglass scum baffle hung
from the beams or supported from the
weir.
e. Provide a flushing water pipe on the
channel side of the scum baffle and hung
from the beams. Connect this line to the
public supply with a backflow device, if
this is permitted by local code. If this is
not permissible, provide a storage tank to
store overflow from the weir and -a
submersible pump to use for washing
down. The usual criteria of 3.1 1/s (50
gpm) at 28,120 N/m2 (40 psi) for
flushing purposes at treatment plants
should be applicable to the helical
separator facility. Hose connections
should also be provided in case the stream
from the wash water pipe is not effective.
f. Provide concrete block walls with a
height of 2.4 m (8.0 ft).
g. Provide a precast concrete roof.
h. Provide adequate electric lights.
i. Provide roof ventilators,
j. Provide doors at both ends of the
structure for ventilation and access.
Cost estimates of the helical separator
were made for two purposes: (1) to indicate
the probable construction cost of the facility;
and (2) to compare its costs with that of the
swirl concentrator used as a combined sewer
regulator.
The cost estimates are considered to be
reasonable engineers' estimates. However,
during periods of economic inflation, it is not
unusual for contractors' bids to materially
exceed engineers' estimates.
In making a choice between the helical
separator and the swirl concentrator, it is
possible that other factors related to the
specific site of the facility may be of greater
importance than the difference in
construction costs.
Quantity Basis
The estimated quantities are based on the
following:
a. The transition will be constructed with a
drop in the invert equal to D as shown in
Figure 14, so that the sewer upstream of
the transition will not be surcharged.
b. The straight section preceding the curved
section will have walls 2.5 D high and
concrete roof.
c. The superstructure over the curved
section will be as shown in Figure 21.
d. The width of the curved section is
assumed to be 4.1 D; the width of the
spillway channel is assumed to be 0.67 D.
e. The .cover on the sewer at the transition
inlet will be 2.44 m (8.0 ft).
f. The ground is level and the subsurface is
earth with no groundwater problems. -
g. All concrete walls will have a minimum
thickness of 0.3 m (1.0 ft), except the
weir.
h. Sheet piling will be required about 0.6 m
(2.0 ft) outside the structure.
i, Transverse concrete beams will be
required at 4.5 m (15 ft) intervals with
the cross section 0.45 m (1.5 ft) square.
j. The continuous concrete walk will be
1.22 m (4.0 ft) wide and 0.20 m (0.67 ft)
thick.
Cost of Helical Separator
The costs are based on the following:
a. The Engineering News-Record
Construction Cost Index average for the
United States is 2,100
b. Unit prices are as follows:
Steel Sheer Piling $ 86/m2 $ 8/sf'
Excavation $ 16/m3 $ 12/cy
Reinforced Concrete $326/m3 $250/cy
Concrete Block Walls $107/m2 $ 10/sf
Roof $150/m2 $ 14/sf
c. Miscellaneous costs are assumed to be 25
percent of the foregoing items and to
include a manual sluice gate and manhole,
handrail, flushing water facilities, scum
baffle, electrical work, roof ventilators
and doors.
d. The estimated cost of the bypass sewer
during construction is based on providing
a sewer of the same diameter as a
transition inlet around the proposed
separator, plus an allowance for
temporary connections at each end.
e. Contingent and engineering costs will be
25 percent of the foregoing items.
39
-------
The resultant costs are shown in Table 5,
Construction Cost of Helical Bend Regulators.
Cost of Swirl Concentrator
Typical dimensions for three sizes of the
swirl concentrator are given in Table 6, Swirl
Concentrator Dimensions, based on Figures 7
and 11 of Report EPA-670/2-74-039. The
cost estimates are based on these dimensions
and on the construction details shown in
Figures 12, 13, and 14 of Report
EPA-R2-7 2-008.
TABLE 5
CONSTRUCTION COST OF HELICAL BEND REGULATOR
Capacity 1.42 m3 /s (50 cfs)
ITEM
Sheet Piling
Excavation
Reinforced Concrete
Concrete Block Walls
Roof
Miscellaneous Costs
Bypass Sewer
Contingent & Engineering Costs
Capacity 2.83 m3/s dOO cfs)
ITEM
Sheet Piling
Excavation
Reinforced Concrete
Concrete Block Walls
Roof
Miscellaneous Costs
Bypass Sewer
Contingent & Engineering Costs
Capacity 4.67 m3 /s ( 1 65 cfs)
ITEM
Sheet Piling
Excavation
Reinforced Concrete
Concrete Block Walls
Roof
Miscellaneous Costs
Bypass Sewer
Contingent & Engineering Costs
420m2
950m3
250m3
114m2
85 m2
QUANTITY
(4,550 sf)
(l,240cy)
( 330 cy)
(1,230 sf)
( 910 sf)
Sub Total
25%±
Sub Total
Total
QUANTITY
710 m2 (7,700 sf)
2,200m3 (2,800 cy)
475m3 ( 620 cy)
160m2 (l,740sf)
170m2 (l,800sf)
Sub Total
25%±
Sub Total
25%±
Total
QUANTITY
950m2 (10,200 sf)
3,200 m3 (4,180 cy)
679 m3 ( 888 cy)
200m2 (2,130sf)
250 m2 (2,700 sf)
Sub Total
25%±
Sub Total
25%±
Total
AMOUNT
$ 36,150
15,200
81,500
12,200
12.750
$157,800
39,450
20.000
$217,250
54.000
$271,250
AMOUNT
$ 61,050
35,200
154,850
17,150
25.500
$293,700
73,300
39.000
$406,000
102.000
$508,000
AMOUNT
$ 81,700
51,100
221,350
21,400
37.500
$413,150
103,850
56.000
$573,000
143.000
$716,000
40
-------
TABLE 6
SWIRL CONCENTRATOR DIMENSIONS
Design Discharge
Diameter of Chamber
Diameter at Inlet
Height No. 1
1-5/6 D + 2.74 m
(1-5/6 D 2 2.74m
Height No. 2
Floor to Weir dr
Head on Weir for 150%
Design Discharge
Clearance to Walk
Headroom
Total
Use for Height
Note: Height is from invert to
' • m3/3
(cfs)
D2 m
(ft)
D! m
(ft)
m
(ft)
m
(ft)
m
(ft)
m
(ft)
m
(ft)
m
(ft)
m
(ft)
underside of roof.
1.42
(50)
6.85
(22.5)
1.15
(3.75)
4.55
(14.9)
1.71
(5.6)
0.27
(0.9)
0.30
(1.0)
2.44
(8.0)
4.72
(15.5)
4.72
(15.5)
2.83
(100)
9.0
(29.5)
1.50
(4-92)
5.18
(17.0)
2.26
(7.4)
0.40
(1.3)
0.30
(1.0)
2.44
(8.0)
5.40
(17.7)
5.40
(17.7)
4.67
(165)
11.0
(36.0)
1.83
(6.00)
5.79'
,(19.0)
2'. 74
(9.0)
0.55
(1.8)
0.30
(1.0)
2.44
(8.0)
6.03
(19.8)
6.03
(19.8)
The height of the structure from the
invert of the chamber to the underside of the
roof is based on the following criteria:
Criteria 1: The clearance between the
top of the walk and the water surface is 0.31
m (1.0 ft) when the discharge is 150 percent
of design discharge and the foul outlet is not
functioning. The head on the weir is
determined from Figure 11, Head Discharge
Curve for Circular Weir, in Report
EP A-R 2-72-008. It is assumed that the
emergency weir starts overflowing when
inflow to the chamber reaches the maximum
design discharge for the facility.
Criteria 2: The headroom: above the walk
is 2.44 m (,8.0 ft). The depth of the structure
below the ground surface was based on the
following criteria:
Criteria 3: The cover on the crown of the ..
sewer is 2.44 m (8,0 ft).
Criteria. 4: To prevent surcharge on the
inlet sewer, the crown of the inlet sewer shall
be the same elevation as the water surface at
design discharge. :
As shown in Table 6, the depth below the
ground surface, based on Criteria 3 and 4, is
less than the interior height, based on Criteria
1 and 2; therefore, the height is adequate to
provide a structure with a roof above the
ground surface. If the roof slab is assumed to
be 0.25 m (0.83 ft) thick, then the top of
roof is about 0.61 m (2 ft) above the ground
surface, as shown in Table 6.
Additional assumptions for estimation
purposes aie as follows:
a. The walls are 0.30 m (1.0 ft) thick.
b. The roof is of poured concrete, about
0.25 m (0.83 ft) thick, with two beams
0.92 m (3.0 ft) by 0.46 m (1.5 ft).
c. The bottom concrete slab is 0.61 m (2.0
ft) thick.
d. The concrete walk is 1.22 m-(4.0. ft) wide
and supported on concrete beams.
e. The superstructure is 3.96 m (13.0 ft)
long by 1.52 m (5.0 ft) wide, by 2.44 m
(8.0 ft) high.
The unit prices used were the same as
those used for the helical separator.
The miscellaneous cost is taken as 25
percent and is intended to include stairs,
handrail, scum baffle, circular weir, flushing
water system and pipes, a manual sluice gate
and manhole, electrical work, ventilating
work and doors.
41
-------
The cost of the bypass pipe is assumed to
be 50 percent of the bypass pipe for the
helical separator.
Contingent and engineering costs are
taken as 25 percent of the foregoing.
The costs of the three selected sizes of
swirl concentrators, designed for 90 percent
removal of grit, are shown in Table 7,
Construction Cost — Swirl Concentrator.
Comparison of Costs
The estimated costs are shown graphically
in Figure 22, Estimated Construction Costs —
Helical Bend and Swirl Concentrator
Regulator. As explained previously, although
the two structures are sized for the same
TABLE 7
CONSTRUCTION COST - SWIRL CONCENTRATOR
Capacity
1.42m3/s fSOcfs)
Item
Sheet Piling
Excavation
Reinforced Concrete
Concrete Block Walls
Roof
Outlet Pipes
Downshaft and Plate
Miscellaneous Costs
Bypass Sewer
Contingent & Engineering Costs 25%±
Capacity 2.83 m3 Is (IQOcfs)
Item
Sheet Piling
Excavation
Reinforced Concrete
Concrete Block Walls
Roof
Outlet Pipes.
Downshaft and Plate
Miscellaneous Costs
Bypass Sewer
Contingent and Engineering Costs 25%±
Capacity
4.67 m3/s <165cfs>
Item
Sheet Piling
Excavation
Reinforced Concrete
Concrete Block Walls
Roof
Outlet Pipes
Downshaft and Plate
Miscellaneous Costs
Bypass Sewer
Contingent & Engineering Costs
Quantity
200m2
(2,160 sf)
460 m3
(600 cy)
98m3
(128cy)
27m2
290 sf)
6m2
(65 sf)
Sub Total
25%±
Sub Total
Total
Quantity
290 m2
(3,120 sf)
900m3
(l,180cy)
156m3
(204 cy)
27m2
(290 sf)
6m2
(65 sf)
Sub Total
25%±
Sub Total
Total
Quantity
375m2
(4,030 sf)
1,360 m3
(1.780cy)
216m3
(282 cy)
27m2
(290 sf)
6m2
(65 sf)
Sub Total
2S7r±
Sub Total
25#±
Total
Amount
S 17,200
7,360
31,948
2,889
900
1,300
2.000
S 63,597
15,403
10.000
S 89,000
22.000
5111,000
Amount
S 24,940
14,400
50,856
2,889
900
3,000
3.000
S 99,985
24,515
19.500
$144,000
36.000
5180,000
Amount
S 32,250
21,760
70,416
2,889
900
4,000
5.000
5137,215
34.785
28.000
5200,000
50.000
5250,000
42
-------
10-
<=>.
§
Notes:
A
d
o
Helical Separator
100% Grit Removal
Swirl Concentrator
100% Grit Removal
Swirl Concentrator
90% Grit Removal
Helical Separator
100% Grit Removal
Swirl Concentrator
100% Grit Removal
Swirl Concentrator
90% Grit Removal
50 100
150
200
Discharge — CFS
FIGURE 22 ESTIMATED CONSTRUCTION COSTS - HELICAL BEND
AND SWIRL CONCENTRATOR REGULATOR
discharge, the helical separator will remove
100 percent of the grit compared to 90
percent for the swirl concentrator. The use of
90 percent removal is based on Report
EPA-670/2-74-039, dated July, 1974, in
which design curves are presented for 90, 80,
and 70 percent recovery (or removal) of grit.
An earlier report on the swirl concentrator,
Report EPA-R2-72-008 of September, 1972,
includes Figure 22, Separation Efficiency
Curve, in Appendix 1 thereof. This curve
indicates that a swirl concentrator designed
for 90 percent removal of grit will remove
100 percent of grit when the discharge is 60
percent of the design discharge. Therefore, to
remove 100 percent of the grit the structure
should be sized for a discharge equal to 167
percent of the design discharge. Using this
method, the costs of swirl concentrators to
remove 100 percent of grit were estimated
and the results shown in Figure 22.
The summary of all the estimated costs is
shown in Table 8, Comparison of
Construction Costs — Helical Bend and Swirl
43
-------
TABLE 8
COMPARISON OF CONSTRUCTION COSTS - HELICAL
BEND AND SWIRL CONCENTRATOR REGULATORS
Capacity
1.42m3/s(50cfs)
2.83m3/s(100cfs)
4.67m3/s(165cfs)
Note: Land costs not included.
Swirl
Concentrator
$111,000
180,000
250,000
Concentrator Regulators. The results indicate
that, for the sizes used in the Table, the
helical separator will cost 1.7 to 2.5 times as
much as a swirl concentrator designed for 90
percent grit recovery and 1.5 to 1.6 times as
much as one designed for 100 percent grit
recovery.
Alternate Design — Solids Removal Efficiency
Further design techniques and the
rationale based on mathematical data were
evolved as a result of the model studies
carried out by the General Electric Company.
The procedure for designing a helical flow
separator for a given discharge flowrate and
specific suspended material is as follows:
Step 1: Characterize the settling
properties of the suspended solids. A study9
(see reference section) has emphasized the
variability of the settling properties at
different geographical locations. Once the
cumulative distribution of settling velocities
has been determined from column settling
tests, the distribution should be broken down
into 10 or more fractions, and the
performance calculations outlined below
should be repeated for each settling velocity
fraction. Thus, assume that 10 percent of the
material settles at a velocity lower than w2
etc. The performance for each settling
velocity is then determined and the overall
recovery efficiency is computed as the
weighted average of the recovery for the
individual fractions.
Helical
Separator
$271,000
508,000
716,000
Step 2: Determine a scale factor, S, as
the ratio
in which Q^ is the design discharge rate and
Q, is a selected flowrate within the range of
the laboratory experiments 0 to 0.85m3 /sec
(0-31.1 cfs). Selecting Q! near the lower end
of the range will give better recovery
efficiencies, but will also require a larger unit.
The selection of Q! can be iterated, as
described in the subsequent step.
Step 3: Determine a rough estimate of
the prototype performance by calculating
first an equivalent settling velocity we from
= w
.5
where ws is the median (50%) settling
velocity from the cumulative distribution
determined in Step 1. The initial estimate of
efficiency can then be found by entering
Figure 23, Predicted Separation Efficiency
Versus Settling Velocity at Several Flowrates,
with settling velocity we, and interpolating
for the recovery efficiency at the selected
flowrate QA. If this estimated efficiency is
lower than about 80 percent, it is probably
desirable to select a lower value of Q{ (to
provide a larger unit), and repeat steps 2 and
3. Conversely, if the estimated efficiency is
greater than 95 percent, a smaller unit will
probably suffice, and a larger Q, can be
selected.
44
-------
Step 4: A refined estimate of the
recovery efficiency can be obtained by
calculating an equivalent settling velocity for
each settling velocity fraction w,- of step 1 .
w
The recovery efficiency for each of these
fractions is then determined from Figure 23
as in Step 3. The overall recovery efficiency is
the weighted average of the results for each
individual fraction.
Step 5: The inlet diameter, D, should ,
then be
D = 0.95 s (ft)
or
D = 3 S (meters)
The inlet dimensions are given in terms of
D as described in the preceding paragraphs.
100
95
s?
8
0)
cc
85
80
Qi
= 0.1**
I III
0.1
1.0
Settling Velocity, w (cm/sec)
FIGURE 23 PREDICTED SEPARATION EFFICIENCY VERSUS
SETTLING VELOCITY AT SEVERAL FLOWRATES
45
-------
SECTION IV
IMPLEMENTATION
Use of the helical bend combined sewer
overflow regulator should be considered
where there is a requirement to improve the
quality of the combined sewer overflow, or
where there is insufficient hydraulic head to
allow construction of a swirl concentrator.
Table 4 indicated the typical hydraulic head
losses in both the helical bend and swirl
concentrator regulators. The helical bend
regulator, because of its length, can be expected
to have a higher construction cost than the
swirl concentrator. Removal of floatable solids
should be of the same order.
An important difference in the operation
of the two units, however, is that the solids
removed from the overflow by the helical
bend regulator may be expected to be
released to the interceptor sewer at the end of
the storm — the first flush will be at the end
of the storm. This characteristic may result in
less shock loading and more efficient
operation at the treatment facility.
The helical bend regulator is essentially
linear and, thus, construction should be
possible within existing street rights-of-way.
The essential features of the device are as
follows:
Inlet: The inlet is the collector sewer of
any shape.
Transition Section: The helical bend can
curve to the right or left, depending on the
direction of flow in the interceptor sewer or
the available right-of-way. The transition
section flares from the inlet to a width of 3D
in a distance of 15D. The section also deepens
to a depth of 2.0D. The section is covered to
facilitate the development of uniform flow
conditions.
Straight Sectibn: A 5D straight section
with the same configuration as the remainder
of the structure is required to fully control
the flow and eliminate cross currents.
Bend: A 60 degree bend of a radius is
selected on the basis of the design used. The
floor of the bend should be smooth.
Weir: A side-spill, curved weir along the
outside of the bend is used to draw off the
clarified overflow.
Scumboard: A scumboard is set 1 /6D to
1/3D in from the weir, with a minimum
submergence depth, to trap floatables.
Outlet: The outlet should be sized to
allow 4.5 to 5 times the dry-weather flow to
pass without activating the regulation
characteristics. This will allow passage of peak
dry-weather flows. However, maximum flow
to the wastewater treatment plant during
storm events is limited to 1 to 3 times its
dry-weather flow. Thus, a mechanical gate
controlled by the flow in the interceptor is
desirable. The outlet should be either 30.4 cm
(12 in.) or of a size capable of being cleaned
very easily in order that rags and other debris
will not clog the opening.
The helical bend regulator can be
constructed of concrete or any other
appropriate material. Ordinarily, it will be
desirable to construct the regulator within a
chamber in order that maintenance may be
readily performed.
Normal requirements for such chambers,
such as ventilation, lighting, safe access and
other features must be provided.
46
-------
SECTION V
Glossary of Pertinent Terms
Helical Bend Report
Combined Sewer — A pipe or conduit which
collects and transports sanitary sewage, with
its component commercial and industrial
wastes and inflow and infiltration during
dry-weather conditions, and which, in
addition, serves as the collector and conveyor
of stormwater runoff flows from streets and
other sources during precipitation and thaw
periods; thus, a pipe or conduit which handles
all of these waste waters in a single or
"combined" facility
Dip Plate — A vertical plate or baffle which is
partially immersed in flowing liquid in a
manner that will prevent the discharge of
surface or floating materials over an outlet
weir; in the helical bend studies, a baffle plate
placed near the overflow weir, at a
predetermined distance therefrom and with a
predetermined depth of "dip" or immersion,
to prevent the overflow of floating solids with
the clarified effluent
DWF (Dry-Weather Flow) - The flow
through the helical bend during periods when
no stormwater runoff is collected and
transported by the combined sewer which
discharges through the helical bend section
Equation of Motion - A mathematical
equation which expresses the hydraulic
patterns of flow occurring in any vessel,
chamber, conduit or other appurtenant
structure in which fluid flow is occurring
Foul Sewer - The sewer connected to the
foul outlet of the helical bend, through which
the solids slurry deposited in the bottom of
the helical section is discharged to a
downstream wastewater treatment facility or
to any other predetermined point of disposal
Floatables - The lighter-than-water solids,
including congealed floating materials which
rise to the surface of the wastewater flowing
through the helical bend regulator, and which
must be intercepted and prevented from
discharging with the clarified effluent flowing
over the outlet weir; the material retained by
a dip plate or scum board
Floor Flow Angle - The angular pattern of
the flow of wastewater and solids as it
traverses the bottom or floor of the helical
bend separator as part of the helix form of
liquid movement through the device; in this
study, the floor flow angles were disclosed by
the pattern of movement along the bend floor
of Process Black ink injected at appropriate
points along the floor.
Gilsonite® - Synthetic solid material utilized
in the helical bend studies to simulate the grit
particles which will be contained in combined
sewer flows to be handled in prototype units
in actual field practice; material having a
specific gravity of 1.06 and a size range of 0.5
to 3 mm
Grit — Heavier and larger-sized solids
contained in stormwater flows in combined
sewers, or in dry-weather flows, which
because of their size and specific gravity settle
in a helical bend separator more readily than
organic materials contained in the flow;
material having a specific gravity of 2.65,
more or less, and an effective size of 0.2 mm.
Helical Bend - A physical configuration of a
pipe or open channel which results in a bend
or radius through which a liquid flow occurs
in a manner that produces helical, or
secondary flow phenomena, inducing the
rapid separation of solids from the liquid and
the deposition of the solids along the inner
diameter of the radius; in the study, the total
helical bend assembly consisted of a transition
section, a straight section, and the bend
section
Helical Flow — The pattern of liquid flow
induced by the helical bend, characterized by
a helical configuration, or secondary motion,
created in the liquid flow
Hydraulic Head Loss — The lowering of the
hydraulic flow line through a pipeline, device,
chamber or other facility, due to dynamic
conditions which produce friction, turbulence
or other conditions that are translated into
loss of pressure, or head, or free water
gradient surface level
47
-------
Mass Flux — The rate of flow of the total
body of liquid and solids flowing through any
device or facility, such as a helical bend; the
flow energy in the total fluid body in the
device or facility; a measure of the strength of
a field of force in a given area, such as in any
part of a helical bend section, in the case of
the study reported herein
Organic Solids — Solids of a non-grit or
light-weight nature, contained in a sewer flow,
which are subject to decomposition and
consequent oxygen-consumption in receiving
waters into which stormwater overflows from
combined sewers discharge, and which impose
pollutional oxygen-demand loadings on such
water resources; the function of a helical flow
regulator is to control the volume of overflow
wastewaters and to remove grit and organic
solids from the effluent.
Petrothene® — A synthetic plastic material
which has a specific gravity of 1.01 and was
used in the helical separator studies to
simulate the lighter organic materials
contained in combined wastes handled by
prototype helical bend regulators in actual
field practice
Prototype — A full-scale replica of the
laboratory test model (in this case, of the
helical bend model), designed in scaled-up
proportion to the test model, for use in actual
field installations; the study provided design
criteria for the dimensioning of various sizes
of full-scale installations to handle
predetermined volumes of combined sewer
flows
Recovery — The percentage of solids
introduced into the helical bend
separator-regulator with the combined
wastewater flow that will settle in the bend
chamber and be drawn off from the bottom
via the foul outlet and the foul sewer; the
measure of the efficiency of the helical bend
device hi clarifying the overflow effluent and
thereby reducing the pollutional effect of the
overflow incidents on receiving waters
Regulator — Any device in a combined sewer
system which regulates or controls the
amount of concentrated wastewater diverted
to interceptor sewers and downstream
treatment facilities and, consequently, the
amounts of effluent discharged to receiving
waters, or holding or treatment facilities
Scum Board — A vertical plate or baffle which
is partially immersed in the flow liquid and
partially above the flow line, in order to
capture and retain floating scum solids and
prevent their discharge over an overflow weir
with the clarified effluent; in this study, a
scum board and a dip plate have similar
functions
Solids Simulation — The use of test solids in
the model, of a weight and size which
simulate, in scale-down, the composition and
character of solids materials in actual
combined sewer flows to be handled in
prototype devices — in this case, in prototype
helical bend systems in combined sewer lines
Straight Section — The part of the helical
bend structure which precedes the bend
section and delivers the flow uniformly and
without velocity interferences into the helical
section; in the studies of the helical bend
principle, it was determined that the straight
section having a length of five times the
diameter of the sewer pipe will be required
for effective solids recovery in the helical
bend system
Spillway Channel — The channel or conduit
which receives the overflow effluent from the
helical bend weir section and delivers it to a
pipe or conduit leading to receiving waters, or
facilities for the retention and/or treatment of
the clarified wastewater discharge
Swirl Concentrator — A cylindrical chamber
in which hydraulic flows experience
swirl-type liquid flow patterns that induce
relatively rapid separation of solids from the
flow, and, thereby, produce a clarified
effluent which is discharged from the
chamber, freed from solids which are
collected in the bottom of the swirl chamber
and discharged via a foul sewer outlet; in this
study, the helical separator was intended to
perform the same general function as a swirl
concentrator used as a combined sewer
regulator
Transition Section — That portion of the
helical bend composite which carries the
48
-------
combined sewer flow from the entering sewer
pipe section and delivers it to the straight
section and thence to the bend section; the
transition section in the studies had a length
of at. least fifteen times the inlet sewer
diameter and expanded the flow cross section
to three times the inlet diameter
WWF (Wet-Weather Flow) - The flow in the
combined sewer during periods of
precipitation or thaw runoff, composed of the
dry-weather flow plus the storm runoff
volume
The following are registered trademarks:
Gilsonite
Petrothene
Perspex
Plexiglas
49
-------
SECTION VI
REFERENCES
1. Problems of Combined Sewer Overflow
FWPCA - WP-20-11, December, 1967.
2. Swirl Concentrator as a Combined
Sewer Overflow Regulator Facility, EPA —
R2-72-008, September 1972. PB-214 687.
3. The Secondary Flow in a Meandering
Channel, by T.M. Prus-Chacinski,
Unpublished, PhD Thesis, University of
London, 1955.
4. Secondary Motion Applied to Storm
Sewage Overflows, by T.M. Prus-Chacinski
and J. W. Wielogorski, Symposium on Storm
Sewage Overflows, Institute of Civil
Engineers, London, 1967.
5. Formulas for Bed-Load Transport by E.
Meyer-Peter and R. Muller, Proceedings IAHR
Second Meeting, Stockholm, 1948.
6. The Bed-Load Function for Sediment
Transportation in Open Channel Flows by H.
A. Einstein, U.S. Department of Agriculture,
Technical Bulletin No. 1026, September
1950.
7. Combined Sewer Regulation and Man-
agement — Manual of Practice, FWQA —
11022 DMUO, July 1970.
8. Water Supply and Waste Water Disposal,
by G. M. Fair and J. C. Geyer - John Wiley
& Sons, Inc., New York, 1954.
9. Physical and Settling Characteristics of
Particulates in Storm and Sanitary Waste--
waters, by Robert J. Dalrymple, Stephen L.
Hodd, and David C. Morin, EPA-670/2-75-011,
April 1975.
50
-------
APPENDIX A
HYDRAULIC MODEL STUDY
This report covers the hydraulic studies
of the helical bend application to the
separation of solids from combined sewer
flows as carried out at the LaSalle Hydraulic
Laboratory, Montreal, Quebec, Canada.
The most complete investigation of the
helical bend principle, as applied to the
current investigation, was carried out by Dr.
T. M. Prus-Chacinski, as reported in his 1955
thesis at Imperial College of Science, London,
titled The Secondary Flow in a Meandering
Channel.2 He augmented his 1955 thesis with
further studies as a Partner of C. H. Dobbie
and Partners, Consulting Engineers, London,
at the University of Surrey and the Mersey
River Authority Hydraulic Laboratory in
Warrington, near Liverpool. These studies led
to the construction of a prototype at
Nantwich, Cheshire, England, for research on
behalf of the Construction Industry Research
and Information Association.
As flow proceeds around a bend,
secondary currents develop, with the upper
volume tending to move toward the outside,
while the bottom current angle is directed
toward the inside of the bend. Actual trace
studies made of this secondary motion show
that it describes a spiral or helical pattern.
This phenomenon is well known in rivers
where the deepest section of the channel is
usually scoured on the outside of any bends,
and the fine sand has been buoyed up by the
bottom currents and deposited at the inside.
In the present study of the bend
principles, the object was to impose just the
opposite geometry from that of a natural
stream — i.e., to have the deepest point at the
inside of the bend. In this manner, the
pollutants would be carried by the helical
flow down into the deepest section where
they would have optimum opportunity to
settle out. Furthermore, the flow velocities in
the study were to be controlled in the
transition and straight sections so the solids
would begin to concentrate in the lower
stratum of the flow. The combined effect of
these two phenomena would be to settle the
solids out of the liquid flow, and to
concentrate them in the deepest section of
the chamber, where they could be delivered,
via a foul sewer, to the treatment plant. The
major part of the liquid flow would then be
clarified and could be discharged over a weir
for discharge to the receiving stream, or to
subsequent holding or treatment processes.
Starting with a basic structure layout
established by Dr. Prus-Chacinski, the object
of the study was to evaluate the effects of
changes in width, depth, length of approach
channels, and discharge and conduit
configurations on solids separating efficiency.
The inlet pipe to the model was selected
as a 15.2 cm (6 in.) diameter P.V.C. pipe.
Based on the agreed geometric proportions to
start the study, this first dimension
established the model layout as shown on
Figure 4 of the foregoing report, Helical Bend
Regulator—Separator, Form 3 (Model Layout),
and as depicted in Figure 24, Downstream
View of Model, and Figure 25, Upstream
View of Model.
Unmeasured water flows were delivered
through the supply pipe, which was fitted
with a discharge control valve and solids
injection equipment, shown in Figure 26,
Solids Injection Vibrator. The original
structure began at the entrance to the
transition section; this was made of Plexiglas®
and was 20 diameters (20D) long to ensure
adequate flow deceleration. Following this, a
straight length of 10 D, also constructed of
Plexiglas, carried the flow to the start of the
bend.
The bend itself was built of Plexiglas,
using a 2.44-m (8 ft) radius from the
extension of the inlet pipe centerline. Since
the model was intended to demonstrate the
basic principles of the secondary motions
being .studied, the bend was carried around
through an angle of 120°. Side channels were
provided on each side to accommodate the
clear overflow spill from either the inside or
the outside of the bend. Control of either the
whole flow or just the small foul outflow was
provided by a perforated slide gate at the
120° position.
51
-------
FIGURE 24 DOWNSTREAM VIEW OF MODEL
FIGURE 25 UPSTREAM VIEW OF MODEL
52
-------
FIGURE 26 SOLIDS INJECTION VIBRATOR
The basic floor cross section inside the
transition, straight sections, and the bend was
made of polished cement mortar, as shown in
Figure 4 of the foregoing report. Simple
modifications to the Plexiglas overflow
weirs could be made to either change their
positions horizontally or their levels.
Flow spilling over the side weir was
directed to a calibrated Rehbock weir basin,
where the water levels could be read and the
discharge determined. Similarly, the foul
outflow was taken to a second basin for
measurement over a small 90° V-notch weir,
as was shown in Figure 5, Discharge
Measuring Weirs.
Injections of Process Black ink were
introduced on the floor of the bend. They
created clearly defined trace patterns which
could be read with a protractor to measure
the angle of the flow along the floor.
Tests ^involving solids recovery were
performed, using a standard procedure. One
liter of the selected model solids was injected
at a predetermined rate into the supply pipe.
The material entered the structure in the
flow, and was subjected to the helical
separation process. Any of the solids that
went over the weir were caught on a screen in
the measuring basin. The rest normally
remained as a deposit in the bend, and were
recaptured after the test by means of a screen.
The volumes of the two fractions were
measured to determine that no material had
been lost. The recovery rate, or efficiency,
was then computed as the ratio if the solids
retained in the be'nd with respect to the
original 1-liter input, expressed as a
percentage.
The model scale selected for comparisons
to a reasonable prototype was 1/6. The
pertinent scale relations are:
Scale =1/6
Time = 1/^/6 = 1/2.45
Discharge = 1/6 5/2 = 1/88
The prototype storm discharge with the
pipe flowing full in the corresponding
prototype 91.5-cm (3-ft) sewer was computed
as 0.85 m3/sec (30 cfs) which would
correspond to 9.6 I/sec (0.339 cfs). In fact, to
simplify operations on the model, a discharge
of 10 I/sec (0.354 cfs) was used, giving a
storm discharge of 0.88 m3/sec (31.1 cfs).
Dry-weather flow (dwf) was defined as
being one percent of the storm flow, or on
the model 0.1 I/sec (0.004 cfs), and in the
prototype 8.8 I/sec (0.31 cfs) through the
foul outlet, to the interceptor sewer and the
treatment works.
The methods used for solids simulation
were presented in Section II.
The first tests were carried out with the
model as shown on Figure 4, and overflow
spill over the full 120° bend, for discharges of
5, 10, 15 and 20 I/sec (0.177, 0.354, 0.531
and 0.708 cfs, respectively). The helical
motion was found to be very well defined.
Measurements were made of the floor flow
angles at the 35° position for straight-through
flow, i.e., no spill over the weir, as shown on
Figure 27, Top and Bed Flow Angles. The
method for determining the angular flow
along the floor of the helical bend is shown in
Figure 28, Floor Flow Angles Measuring
Equipment.
The resulting angles were treated,
following Dr. Prus-Chacinski's equation, in
the form: _ . ' ,
, Tana0= Cl Wr.Rll*
where: ' c "
&o = floor angle
Ci= coefficient
W = wetted perimeter
rc = central radius of
bend
Rn = Reynolds number
and plotted on a partial copy of Figure 28
from his thesis, and included here as Figure
53
-------
- Surface flow direction
- Bottom flow direction
FIGURE 27 TOP AND BED FLOW ANGLES
29, Bed Angle Relationships for
Straight-Through Flow. The preliminary test
points fell just below Dr. Prus-Chacinski's
work for rectangular and semi-circular
channels, but they were fairly close to those
for triangular channels with the deepest point
at the outside of the bend.
The fact that the points were lower than
the Prus-Chacinski findings would normally
indicate that the flow angle on the floor was
less, from which it would be deduced that the
helical action was weaker. However,
observation in the model indicated just the
opposite. Although the angle was perhaps
lower, the helical flow was very strong, and
the angular flow was acting over the full
width of the floor. Brief tests with shredded
Petrothene ® showed the model to be very
efficient in concentrating the settleables
toward the inner wall of the bend.
Further tests were performed, using
various discharges up to 20 I/sec (0.708 cfs),
first with spill over the full 120° bend. At this
maximum discharge, deposits containing
about 70 percent of the injected material
appeared in the 60° to 70° range. A
temporary wall was placed at the 60° position
and Petrothene® was introduced again. About
60 percent of the material was deposited
between the 30° and 50 ° points. From these
first results, it appeared that careful attention
should be paid to moving the solids through
the structure to the foul outlet during a storm
FIGURE 28 FLOOR FLOW ANGLE
MEASURING EQUIPMENT
so as to prevent a build-up of so large a
deposit that the dry-weather flow might be
unable to move it out of the helical bend
section.
Scale Selection and Discharges
As a result of the preliminary tests
described above, the most likely acceptable
discharge range had been defined in the
model, so a firm scale was selected for further
testing. This was taken as 1/6, meaning that
the prototype inflow pipe would be 91.5-cm
(3 ft) diameter. The selected discharges in the
model were 10, 7.5, 5, and 2.5 I/sec, (0.354,
0.265, 0.177 and 0.088 cfs), corresponding to
0.88, 0.66, 0.44, and 0.22 m3/sec (31.1, 23.3,
15.55 and 7.78 cfs) in the prototype.
The dry-weather flow (dwf) was specified
as being one percent of the storm'flow, or 8.8
I/sec (0.31 cfs) in the prototype. This would
normally flow through the structure at a
shallow depth along the invert, and discharge
through the foul outlet to the treatment
plant. It was further decided that during any
storm event, three times the dry-weather flow
(3 dwf) would be discharged through the foul
outlet - i.e., 26.4 I/sec (0.93 cfs).
A series of rapid modifications were made
in the model and tested in an attempt to
determine the importance of the geometric
54
-------
5.0
4.0
3.O
£
^
$ 2-°
c
£
l.O
<#>
V
-%*
Or-1
°C
^?
OQC
<
«L_J
Vi
6
o
•> o
p —
£
30C
O
'A'
e
1
o
V*
0
?!
c
tJ
0
A
1 °
o n o
^&1° o<
^§3^1^
ooo~^
A 0 <^
e*9«
-^^H
«••
p^fec
£?c§
0 ^
3 a
-^
345 JO 20 30 40 50 607080
Rnx I0~3
o Rectangular Section (Prus)
j&. Triangular Section (Prus)
^p Semi-circular Section (Prus)
*• LHL Tests
FIGURE 29 BED ANGLE RELATIONSHIPS FOR STRAIGHT-THROUGH FLOW
variables. All four discharges were run for a
few tests, but it quickly became evident that
only the 0.88 m3/sec (31.1 cfs) should' be
used for comparisons, or at times, the 0.66
m3/sec (23.3 cfs). Petrothene was used as the
settleable material for most tests, with only
one or two check runs using Gilsonite.
Data given in Table 9, Recovery Results
— Modifications 1-8, show the recovery
results for the first series of modifications
tested. All cases shown are for the 0.88
m3/sec (31.1 cfs) overflow discharge and 26.4
I/sec (0.93 cfs) foul outflow, with
Petrothene used as the test material. All
values are for prototype dimensions.
From the outset it was obvious that the
long transition and straight sections formed a
very efficient settling chamber. With
Modifications 1 and 2, it was noted that all
the Petrothene was deposited on the floor in
the bend, so changes were made in an effort
to cause the material to flow through to the
foul outlet. This pattern seemed difficult to
achieve with a short bend, so the full 120°
length was tested. (Test 9) with the bleeder at
55°.
The recovery efficiency was reduced so
much that this approach was given no further
consideration. The bleeder was a
small-diameter discharge pipe located as
shown in Figure 30, Modification 6 — Tests
23-29.
The taper in Modification 4 induced
much stronger helical motion, to such a
degree as to cause an upflow and to carry
more material up over the weir. The change is
55
-------
Foul
Outflow
Underflow
Bleeder
SECTION A-A
FIGURE 30 MODIFICATION 6 - TESTS 23-29
56
-------
TABLE 9
RECOVERY RESULTS - MODIFICATIONS 1-8
Modification
Number
1
2
3
Orig.
4
5
6
7
8
Ref.
Fig.
9
9
9
1
10
11
12
13
14
Test
No..
1
4
7
9
13
16
17
20
22
23
28 ,
30
32
34
Bend
Length
60°
50°
40°
120°
60°
60°
60°
60°
60°
60°
60°
50°
60°
60°
Weir
Length
60°
50°
40°
120°
10° -50°
10° -50°
60°
15° -60°
60°
60°
60°
50°
60°
60°
Weir Height
m. ft.
1.64(5.38)
1.64(5.38)
1.64(5.38)
1.64(5.38)
1.26(4.13)
1.64(5.38)
1.64(5.38)
1.64(5.38)
1.33(4.38)
1.33 (4.38)
1.64(5.38)
1.64(5.38)
1.64(5.38)
1.39(4.55)
Recovery
%
100
85
82
50
( through bleeder at 55°)
90
90
75
60
60
65
70
(through bleeder at 55°)
85
85
83
shown in Figure 31, Modification 4 -
Tapered Outlet. Li spite of this increased
secondary flow, the Petrothene recovered
was still all on the floor of the bend, most of
it ahead of .the 35° position. Weir height and
length changes did not have much apparent
effect.
Modification 5 was the first attempt to
enter the bend at a higher velocity so the
Petrothene would be carried through to the
foul outlet. The layout is shown in Figure 32,
Modification 5 - Narrow Inlet, 2D Wide; and
Figure 33, Modification 5 — Tapered Bend.
The recovery rates dropped slightly, but the
bottom deposits had moved along to the 35°
to 55° position. The outstanding feature of
this layout was the surface eddy which
formed at the end of the helical bend near the
60° position. At times it entrained material
from the bottom, causing it to upsurge to the
surface and to be carried over the overflow
weir.
Narrowing the end of the bend in
Modification 6 did not result in carrying the-
material any further toward the foul outlet.
Test 28, with the bleeder at 55° operating,
produced a slight improvement.
Shortening the bend to 50° in
Modification 7 gave encouraging results, with
an increased recovery. Modification 8 was
tested as a means of having a simpler,
parallel-sided bend: Recoveries were good, but
no improvement over the tapered format was
evident.
Although slightly less Petrothene was
recovered in a 1.83 m-wide (6 ft) channel (2
D) than the 2.745 m (9 ft) channel (3 D), it
was investigated to see if there was any merit
in achieving a narrower structure. (Gravity
and dynamics of motion provide removal, not
the structure). The channel was finally
reduced to a 1.372 m (4 ft - 6 in.) width (1.5
D), to check on the minimum reasonable
dimensions. This configuration is shown in
Figure 34, Minimum Width Inlet, 1.5 D Wide;
and Figure 35, Narrowest Bend. 1.5 D Wide.
Tests were carried out for the 0.88
m3/sec (31J cfs) and 0.66 m3/sec (23,3 cfs),
cases in each instance For both total
discharges, the foul discharge was maintained
constant at 26.4 I/sec (0.93 cfs), or 3 dwf.
Results of these tests are given in Table 10,
57
-------
•:*•••-•*
•; h
•":: '» • ,„:!' » •— t,: attaLfa :s safl a • "jwitntt ta»!ta 4 sti rtiii '.iiiutfMte
: ii'j"1!" iijTB, !!Ji;\jiii!i:ii;iijiiii!!:i;:^liji;!M:i7i!ii;iJ|ii|!!!i;7 r'i'J!!!1'^ "'Bfiis uf^jjiii:*!1^!;;):!
FIGURE 31 MODIFICATION 4 - TAPERED OUTLET
FIGURE 32 MODIFICATION 5 -
NARROW INLET 2D WIDE
FIGURE 33 MODIFICATION 5 -
TAPERED BEND
58
-------
FIGURE 34 MINIMUM WIDTH INLET,
1.5DWIDE
FIGURE 35 NARROWEST BEND,
1.5DWIDE
Recovery Results, Modifications 9, 10, 12,
14-18.
Figure36, Modification 9 - Tests 38-39,
shows that the bend was shortened to 50°.
The object was to attempt to eliminate the
deposition of material on the sloping floor
between 45° and the end of the bend. In Test
32, this deposit was considerable. Test 38 was
only partially successful in eliminating the
material.
A truncation was made at the end of the
channel in Modification 10, as shown in
Figure 37, Modificiation 10 - Tests 40-41.
This, too, was insufficient to prevent the
deposit. It did, however, slightly reduce the
back-eddy in the end zone.
Figure 38, Modification 12 - Tests
46-47, shows that a Z-shaped partition was
provided to allow flow over 60° of the weir,
with the foul outlet placed at 50°. This offset
arrangement aggravated the back-eddy to the
extent that all material reaching beyond 45°
was uplifted and carried over the weir
immediately without any chance of settling.
At this stage, the first tests of shortening
the inlet transition were tried, as shown in
TABLE 10
RECOVERY RESULTS - MODIFICATIONS 9, 10, 12, 14-18
Modification
Number
9
10
12
14
15
16
17
18
Ref.
Fig.
15
16
17
18
18
19
21
21
Test
No.
38
40
46
53
55
57
59
60
Bend
Length
50°
50°
60°
60°
60°
60°
60°
60°
Channel
Width
m
183
183
183
183
183
1.372
1.372
1.372
ft.
(6)
\6)
(6)
(6)
(6)
(4.5)
(4.5)
(4.5)
Recovery
Q=0.85 I/sec
(30 cfs)
87
88
82
65
63
65
Q=0.64 I/sec
(22.5 cfs)
100
100
96
77
89
85
85
70
59
-------
Foul
Outflow
SECTION A-A
FIGURE 36 MODIFICATION 9 -
TESTS 38-39
Foul
Outflow
SECTION A-A
Sloping Triangle In Corn<
Foul
Outflow
SECTION A-A
FIGURE 37 MODIFICATION 10 -
TESTS 40-41
FIGURE 38 MODIFICATION 12 -
TESTS 46-47
FIGURE 39 MODIFICATIONS 14 & 15 -
TESTS 53-55
60
-------
Figure 39, Modification 14 and 15 — Tests
53-55. This reduced the transition to 10D, or
9.15m (30 ft) prototype. There was no roof
in Modification 14 to guide the flow, as
shown on Figure 39. Test 53 showed a sharp
drop in recovery — i.e., 65 percent as
compared to 85 percent in Test 32. In the
model, it was visually evident that the flow
entering the transition did not expand
efficiently, so that at the 0° position entry to
the bend, considerable turbulence and lack of
flow uniformity across the section were
experienced.
A sloping roof was placed in the
transition for Modification 15. This change
was still insufficient to guide the flow, and
too much irregularity remained at the 0°
position. It can be concluded that with the
asymmetrical entrance, 10 D is an insufficient
length for expansion from the 0.915
m-diameter (3 ft) inlet pipe, D, to the 1.83 m
(6 ft) channel, 2 D wide.
At this stage, it was decided that there
would be insufficient economical justification
for providing a narrower channel. Once the
excavation is made for a particular structure,
the cost difference between a channel 2 D and
3 D wide would be minimal. This reasoning
led to resumption of studies of a wider
section.
However, before reverting to a wider
section, a few brief tests were carried out with
the section narrowed down even further to
1.5 D, or 1.372 m (4.5 ft) prototype. The
same shortened inlet was retained, and flow at
the 0° position appeared to be fairly evenly
distributed. Of course, the flow rate was
much faster than in the preceding tests. The
recovery rates of 65 percent for 0.88 m3/sec
(31.1 cfs) and 85 percent for 0.66 m3/sec
(23.3 cfs) seemed to conform well when
compared with the wider channels, as shown
on Figure 40, Petrothene Recovery in Model
as Function of Bend Channel Width.
Even with this narrowed channel, most of
the material recovered was in the form of
deposits on the bend floor. Two minor
changes were investigated in an effort to move
this material along to the foul outlet. The first
was a series of corner blocks 15.2 cm (6 in.)
high and 22.95 cm (9 in.), projecting out
Inlet Pipe
Diameters
Q=O.66n
3/s (23.3
*'•'
0.88 m% (31.1 cfs)
D ISO i.0
BEND CHANNEL. WIDTH
FIGURE 40 PETROTHENE RECOVERY IN
MODEL AS FUNCTION OF
BEND CHANNEL WIDTH
from the side wall, as shown in Figure 41,
Modifications 17 and 18 - Tests 60-61. Only
the 0.66 m3/sec (23.3 cfs) case was tested; it
Floor Deflectors Tried
in Modification 18
(with Blocks Removed)
'liu0.1" High Corner Blocks
\o I
FIGURE 41 MODIFICATIONS 17 & 18
TESTS 60-61
61
-------
gave an 85-percent recovery. This represented
practically no change from the configuration
without the corner blocks. Next, the blocks
were removed, and a series of floor baffles
7.62 cm (3 in.) high were installed, as shown
in Figure 41.
These baffles generated so strong a
secondary current, that the Petrothene
deposits, were re-suspended and carried over
the weir. The recoveries dropped to 50
percent and 70 percent.
The preceding studies resulted in
resumption of interest in the bend with the
full 3 D or 2.745-m (9 ft) width originally
built in the model. The studies showed that
this bend, 60° long, when supplied through
the original inlet configuration shown on
Figure 42, Inlet Configurations Tested,
recovered 100 percent of the Petrothene for
feat
Outflow
D =
FIGURE 42 - INLET CONFIGURATIONS
TESTED
FIGURE 43 TRANSITION 10D LONG
a 0.88-m 3/sec (31.1 cfs) discharge.
Therefore, tests were undertaken to see how
much the inlet length could be reduced and
still retain an acceptable rate of recovery. No
scum boards were used in these tests.
As shown on Figure 42. Alteration A
consisted of advancing the 0.915 m-diameter
(3 ft) inlet pipe 9.15 m (30 ft), providing the
transition out to the 2.745-m (9 ft) width in
9.15 m (30 ft), or 10 D, and retaining a 9.15
m (30 ft) straight section as depicted in
Figure 43, Transition 10 D Long. It was
evident that the flow jet did not expand well
in this short transition and significant
turbulence entered the bend, disturbing the
helical secondary flow. Recoveries for 0.66
m3/sec (23.3 cfs), and 0.88 m3/sec (31.1 cfs),
respectively, were 95 percent and 89 percent,
as shown on Figure 44, Petrothene
Recovery in 60° Bend for Various Inlet
Configurations.
62
-------
100
£
>l
o
I 90
«
Q:
0
w
JC
% 80
a.
j>
V,
\
-x
i ^
r^
\ /-
X ^/^
"x
V ^
V
\
, Q _ O.S6m3/3
P (23.3 cfs )
I
Q 0.88 m3/s
""" (31.1 cfs)
I
Original ABC
Inlet Configurations- Ref. See Fig 22
Jote: Bend Width- 3D= 2.74m (9-0")
FIGURE 44 PETROTHENE RECOVERY IN 60° BEND
FOR VARIOUS INLET CONFIGURATIONS
Alteration B, Figure 42, provided the
start of the transition from the same point,
but it expanded over 13.73 m (45 ft) or 15 D
to reach the 2.745-m (9 ft) width. This is
shown in Figure 45, Transition 15 D Long.
Just 4.58 m (15 ft) of straight line remained
ahead of the bend. Flow through this
configuration was much improved; it
expanded smoothly to fill the cross section
effectively before entering the bend. As
shown in Figure 44, the recoveries for the
0.66 ma/sec (23.3 cfs) and 0.88 m3 /sec (31.1
cfs) discharges rose to 98 percent and 93
percent, respectively. Compared with the-
original long transition and straight sections,
the flow ebtering the bend now was slightly
more turbulent, but helical motion was still
generated.
Since the transition in Alteration B
appeared to be operating well, it was moved
forward so it reached its full width just at the
bend entrance. This was Alteration C, shown
in Figure 42. The turbulence entering the
bend was too strong in this case; Figure 44
shows the drop in recoveries.
The obvious recommendation was to
retain Alteration B, and this was used for the
following tests with scum boards. The
reasoning for this choice was based on the
fact that it resulted in only a seven percent
drop in recovery from the original case, with a
structure that is 9.15 m (30 ft) shorter.
Implicit in this configuration is the
requirement for a transition 15 D long to
provide satisfactory deceleration of the flow
while expanding to the 3 D channel width in
the straight section. A flat sloping roof covers
the transition, starting at the height D and
rising to 2 D over the 15 D length.
As shown on the cross section in Figure
46, Scum Board Locations Tested, the scum
board was tested at four different depths of
immersion and at three distances out from the
weir lip. For each of these locations, the
Petrothene recovery was determined for the
0.88-m3/sec (31.3 cfs) discharge, with both
the 50° and 60° bends. Figure 47.
Petrothene Recovery in 50° Bend for
Various Scum Board Locations, and Figure
48, Petrothene Recovery in 60° Bend for
Various Scum Board Locations, show the test
results.
63
-------
FIGURE 45 TRANSITION 15D LONG
It was immediately evident that the
deepest scum board locations, 45.8 cm (18
in.), or D/2, below the weir lip, seriously
disturbed the helical flow. Figure 49, Floor
Flow Angles with Scum Board D/2 Deep,
shows the bottom flow pattern. The
recoveries fell off sharply, as well, and brief
tests with Process Black ink showed that the
floor angles were severely modified, even
rising toward the weir at some points.
There was some improvement when the
scum board immersion was reduced to 30.4
cm (1 ft) below the lip, particularly for the
60° bend length.
When the Scum board was just 15.2 cm
(6 in.) below the lip, the recoveries rose
significantly. In the 50° bend length, it
reached about 84 percent, whereas, for the
free overflow case — i.e., with no scum board
— the recovery was 87 percent, the optimum
in these tests. Figure 50, Floor Flow Angles
With Scum Board D/6 Deep, shows the effect;
of deep immersion.
In the 60° bend length, recoveries with
the scum board reached 85 percent, but the
free overflow performance was 93 percent,
leaving a wider gap in performance. On this
basis, the scum board was raised to just 7.6
cm (3 in.) below the lip. However, instead of
I
;a
{J£
•in
o
oo
«
e -
_ o
5
o
o
ro
O
in
-------
Hot.: Bw« WMr» - 30. 1.74,, illtt
0* O.tSm'/t (SI. let.)
... *««•> »oor.] Dipt*
x No Sn. I««M /Strew tNk Up- endn)
•<
£•0
i
t
J70
•O
\
/ f
-i
>^ — ^^
— ^^^^
r-t-
^--wa (•>
X4S«(«)
^
-------
r
FIGURE 50 FLOOR FLOW ANGLES WITH SCUM BOARD D/6 DEEP
Water Level for 0.88 rtiYs (3l.lcfs)
FIGURE 51 CROSS SECTION OF OFFSET WEIR IN BEND
Weir; Figure 53, Upstream View of Scum
Board on Offset Weir; in Figure 54,
Downstream View of Bend and Offset Weir;
and in Figure 55, Scum Board on Offset Weir.
Tests run with this cross section and a
60° bend showed that the scum board did not
adversely affect the recovery rates. At this
stage, therefore, a series of tests was carried
out using various inlet configurations.
Earlier studies had shown that the
transition length had to be 15 D to give
adequate flow deceleration. This form was
retained, and it was tested for a discharge of
0.88 m3/sec (31.1 cfs), first with no straight
section, as shown in Alteration C in Figure
42, then with straight sections 5D and 10D
long (Alterations B and D on Figure 42). The
corresponding Petrothene recovery rates are
66
-------
FIGURE 52 60° BEND WITH OFFSET WEIR
FIGURE 53 UPSTREAM VIEW OF SCUM
BOARD ON OFFSET WEIR
FIGURE 54 DOWNSTREAM VIEW OF BEND
AND OFFSET WEIR
FIGURE 55 SCUM BOARD ON OFFSET WEIR
67
-------
100
8
S" so
>
o
o
0)
DC
-------
FIGURE 57 PROVING TESTS LAYOUT
on Figure 52, the plan dimensions in Figure
57, Proving Tests Layout, were related for
detailed testing over the range of discharges in
the model. Both Gilsonite and Petrothene
were used in these tests and the results are
shown on Figure 58, Solids Recovery in
Model.
In predicting the prototype recoveries
expected with grit, reference was made to
Figure 9 showing the sizes simulated by the
Gilsonite and Petrothene materials used in
the model. It appeared that over practically
the whole range of scales, the Gilsonite
represented the grit satisfactorily. Figure 11,
Predicted Grit Recovery for All Scales, was
then prepared, using the Gilsonite recovery
rate appearing in Figure 58.
Using Gilsonite to simulate prototype
organic material in the model as shown on
Figure 10 covered the major portion of larger
particle sizes. The upper portion appearing in
Figure 10 for each given scale was multiplied
by the Gilsonite recovery rates from Figure
58 for QD , 1.5 QD and 2 QD , and taken as
the prototype recovery for the particle sizes
in that zone.
The particle sizes lying below the dm =
0.5 mm line for Gilsonite in Figure 10 were
assumed to be entirely represented by the
Petrothene. Similarly, this portion for each
scale was multiplied by the Petrothene
recovery rates from Figure 61 for QD, 1.5
QD, and 2 QD, and taken as the prototype
recovery for the lower zone. '
These two prototype recoveries simulated
by Gilsonite and Petrothene in the model
were added together and presented on Figure
12, Predicted Prototype Settleable Organic
Material Recovery.
It is, therefore, possible to find the
predicted recovery rates for grit and organic.
materials as defined in Figure 6, for any scale
of prototype structure by using Figure 11,
and Figure 59, Velocity Contours on 0° Cross
Section.
It was found during the development
testing that the solids materials recovered
were normally in the form of deposits on the
floor of the bend. Only traces, normally less
than two percent, were carried through the
foul outlet during the storm flow incidents.
For most tests, the Petrothene and Gilsonite
were deposited or shoaled in the bend
between the 15° and 60° locations. A fair
proportion of the Gilsonite settled to the
floor in the straight section, but it was
subsequently moved into the bend.
As the discharge was reduced in the
model, as it returned to dry-weather flow,
most of the depostis were scoured out and
discharged through the foul outlet. However,
it is possible that this self-scouring
phenomenon during dry-weather flow in the
model simualtion may not take place in any
prototype installation, so provision should be
made in design for some form of wash-down
facility or for some other form of regular
maintenance.
69
-------
100
90
80
70
55 60
|50
I 40
cc
30
20
10
0'
Gils
Pe
, .^_
mite on Model —
rothene on Mod
\ y
y"x
»l ^ ^
*— — — .
Iv
X
X
\^
^
1
5 10 V 15 20 1/s
Model Discharge —^CT
, > ,
0-1 0.2 0.3 0.4 0.5 0.6 0.7
111!
cfs
0 0.5QD Q0 1.5 QD 2.0Q0
FIGURE 58 SOLIDS RECOVERY IN MODEL
NOTE: Velocities in ft/sec (to get cm/sec , multiply by 30.5)
Discharge = 0.88 mVsec (31.1 cfs )
FIGURE 59 VELOCITY CONTOURS ON 0° CROSS SECTION
70
-------
10°
NOTE: Velocities in ft/sec (to get cm/sec , multiply by 30.5)
Discharge = 0.88 m3/sec (31.1 cfs )
FIGURE 60 VELOCITY CONTOURS ON 10° & 20° CROSS SECTIONS
71
-------
30
NOTE: Velocities in ft/sec (to gel cm/sec,multiply by 30.5)
Discharge = 0.88 mVsec (31.1 cfs)
FIGURE 61 VELOCITY CONTOURS ON 30° & 40° CROSS SECTIONS
72
-------
FIGURE 62 SOLIDS CONCENTRATION SAMPLING JIG
fj£r*~
FIGURE 63 SIMULTANEOUS FILLING OF SOLIDS SAMPLING BOTTLES
73
-------
NOTE: Concentrations given in relative terms only
FIGURE 64 SUSPENDED SOLIDS CONCENTRATIONS ON
0° CROSS SECTION
74
-------
NOTE: Concentratrations given in relative terms only
FIGURE 65 SUSPENDED SOLIDS CONCENTRATIONS ON
10° & 20° CROSS SECTIONS
75
-------
30'
NOTE: Concentrations given in relative terms only
FIGURE 66 SUSPENDED SOLIDS CONCENTRATIONS ON
30° & 40° CROSS SECTIONS
76
-------
Q)
Q.
O
U
U>
Ul
O
CO
0>
(T
10 20 30 40
Position Along Weir
50
20 Sections
J
60 Degrees
FIGURE 67 DISTRIBUTION OF SOLIDS WHICH
ESCAPE OVER THE WEIR
77
-------
Floor flow angles for
120° bend with no
overflow
Floor flow angles for
60° bend, free overflow
by offset weir
Floor flow angles for
60° bend with scum
board on offset weir
FIGURE 68 FLOOR FLOW ANGLES
78
-------
Another approach would be to provide
sufficient slope from the inlet to the foul
outlet of the structure to induce all deposited
solids to be scoured out and flushed away
with the dry-weather flow. The model invert
had no slope in any of the tests.
Testing the Performance of the
Recommended Layout
Utilizing the model forms shown in
Figures 51 and 57, final proving tests were
carried out to define the structure's flow
characteristics, to serve as guidance for the
work being carried out on the mathematical
model.
First, the .tangential flow velocities in the
bend were measured with a midget propeller
current meter for the discharge of 0.88
m3/sec (31.1 cfs). Readings were taken at 14
points on each of the cross sections, at the 0°,
10°, 20°, and 40° positions. The prototype
velocities found were plotted at the
corresponding points, and contours of even
velocity values were drawn as shown on
Figures 59, 60, and 61, Velocity Contours on
0°; on 10° and 20°; and on 30° and 40° Cross
Sections.
The same cross section locations were
used for installing a special suspended solids
sampling device, as depicted in Figure 62,
Solids Concentration Sampling Jig. Twelve
6.4-mm (1/4 in.) I.D. Plexiglas sampling
tubes were fixed on a frame, directed
upstream to intercept the flow. A flexible
tygon tube ran from each sampling tube to a
wooden stand, under which 1-liter sampling
bottles could be introduced, as shown in
Figure 63, Simultaneous Filling of Solids
Sampling Bottles.
With the model subjected to clear water
only, each of the tubes was primed and they
were all adjusted to provide the same
discharge. Petrothene injection was begun by
means of the vibrator, and as soon as the
cloud of suspended material reached an
equilibrium state at the cross section being
tested, the bottles were slipped under the 12
tygon tube discharges. This system provided
simultaneous samples of the suspended solids
in the flow at all 12 points.
Results of these tests are shown in
Figures 64, 65, and 66, Suspended Solids
Concentration Contours on 0°; on 10° and
20°; and on 30° and 40° Cross Sections.
The length of the overflow weir in its
offset position was 302 cm (118.8 in.). A
catch screen was fitted outside the weir and
divided into 19 sections, each 15.2 cm (6 in.)
long, with the twentieth being just 12.2 cm
(4.8 in.) long. The standard Petrothene
injection procedure was followed, and the
particles escaping over the weir were caught in
the corresponding sections on the screen. The
corresponding fractions in each section were
measured and plotted as shown on Figure 67,
Distribution of Solids Which Escape Over
Weir. '
Using the special Process Black ink, the
floor flow angles (a0 on Figure 68) were
measured at six points across the cross
sections at 10°, 20° and 35°, for each of three
separate layouts:
1.
2.
120 bend with straight through flow
60 bend with offset weir, but no scum
board
3. 60° bend with offset weir and scum
board.
The averages of these readings were
computed and plotted in Figure 69,
Comparative Average Floor Angles for
Recommended Layout. The floor flow
phenomena are shown in Figure 68, Floor
Flow Angles for 120° Bend With No
Overflow; for 60° Bend. Free Overflow by
Offset Weir; and for 60° Bend With Scum
Board on Offset Weir. The average of floor
angles is plotted in Figure 69, Comparative
Average Floor Angles for Recommended
Layout.
79
-------
30°
120
Straight
Through
No
Scum Board
60°
Scum
Board
FIGURE 69 COMPARATIVE AVERAGE FLOOR ANGLES FOR
RECOMMENDED LAYOUT
80
-------
APPENDIX B
MATHEMATICAL MODEL STUDY
This report describes the development of
a mathematical model and computer
simulation of an open channel bend with a
side overflow weir for the separation of grit
and organic solids from combined sewer
overflows. A companion, hydraulic laboratory
investigation was conducted by LaSalle
Hydraulic Laboratory of Montreal.
The general features of the helical bend
device are illusrated in Figure 4, Helical Bend
Regulator - Form 3 (Model Layout) in
Section It The dimensions shown are for a
prototype designed for a nominal peak flow
of 0.85 m3/sec, (30 cfs). The flow from the
circular inlet sewer passes through a straight,
rectangular transition section designed to
spread the flow uniformly across,the larger
cross section of the device.
The flow then proceeds through a 60°
bend, with cross section as shown in Figure 4.
The clean overflow is withdrawn via a side
weir located along the outside of the bend,
while the concentrated solids are withdrawn
via a foul sewer orifice in the end plate at the
60° position. Downstream control is used to
limit the amount of flow discharged to the
wastewater treatment plant to three times the
dry-weather flow, or 0.025 m3 /sec, (0.9 cfs),
for the nominal prototype design. The
remainder of the inlet flow is discharged to
receiving waters over the side weir, or to any
holding or treatment facility which is
intended to handle the overflow liquid.
The usefulness of this device for
separating grit and organic solids from
combined sewer overflows is enhanced by the
secondary flow patterns which develop in the
bend. These secondary flows form a clockwise
spiral or helical flow pattern, in the direction
of flow. The helical flow tends to sweep the
bedload to the inside of the bend, so that
relatively clearer liquid is discharged over the
side weir. These secondary flow patterns have
been studied extensively by many
investigators, most notably by Dr. T. M.
Prus-Chacinski,1 who served as consultant on
the present study. His report, Appendix C,
contains an extensive bibliography of the
previous work in this field. •
The application of open channel bends to
separation of solids from storm and combined
sewer overflows has also been studied
experimentally by Dr. Prus Chacinski,2.3 and
a prototype device shown in Figure 3 in the
foregoing report, Photograph of Nantwich,
England, Helical Bend Regulator, has been
constructed by C. H. Dobbie and Partners,
Consulting Engineers, under a research
contract from the Construction Industry
Research and Information Association,
London. The objective of the present study
has been to refine and extend this previous
work in accordance with American conditions
and practices.
LIQUID FLOW CALCULATION
The secondary flow which develops in a
curved channel is of definite significance in
determining the separation performance of
the helicaLbend separator. The helical flow
pattern tends to sweep the bedload to the
inside of the bend, thereby reducing the
amount of solids which pass over the weir,
with the clarified combined sewer flow.
The helical secondary flow is induced by
the vertical velocity profile at the entrance to
the bend. An element of fluid near the center
of the channel experiences an outward
centrifugal force proportional to v2 /r, where v
is the longitudinal velocity and r is the radius.
This centrifugal force tends to raise the
surface level at the outer radius of the bend,
and .lower it at the inside of the bend. Near
the center of the channel, the centrifugal
force is, therefore, balanced by internal
pressure gradients caused by the slope of the
water surface. However, near the bottom
where the longitudinal velocity is lower, the
pressure gradient overbalances the smaller
centrifugal force, and the fluid near the
bottom is accelerated toward the inside face
of the bend. Conversely, at the surface where
the longitudinal velocity is greatest, the
centrifugal forces overbalance the pressure
gradient so that water at the surface is
accelerated toward.the outside of the bend.
8.1
-------
This results in a basic clockwise spiral flow
pattern. For large angle bends, the
redistribution of fluid by the secondary
motions can lead to situations where the
longitudinal velocity no longer increases
monotonically from the bottom - to the
surface. Under these conditions, multiple
helices may develop. However, even under
these conditions, the acceleration of the fluid
is controlled by the local balance of the
centrifugal force (v2 //•) and the pressure
gradient caused by the slope of the surface.
The important point in the preceding
discusssion is that the secondary motion is
essentially an inviscid flow phenomenon. The
action of viscosity is important in establishing
the vertical velocity profile in the flowing
liquid at the entrance to the bend. However,
given the initial vertical variations in velocity,
the development of the helical secondary flow
depends upon the balance of the centrifugal
and pressure gradient terms.in the equations
of motion. The complex flow in the channel
bend can, therefore, be adequately described
without including viscous terms in the
equations of motion.
This approach was adopted by Fox and
Ball4 in their computer model for the
secondary flow in bends with no side weir.
The present formulation represents an
extension of this work to include discharge
over a side weir, a more general channel cross
section, and calculation of the resulting
particulate concentration field and separation
efficiency.
Equations of Motion
The basic equations for steady state flow
of an incompressible fluid are the momentum
and continuity equations:
Momentum V • (VV) + I Vp = 0 (1)
Continuity V • V = 0,
where
(2)
V = velocity vector
p = fluid density
p = pressure
Consider first a curved rectangular
channel. Any point in the channel can be
located by the cylindrical coordinates (r, Q, z)
,as shown in Figure 70, Cylindrical Coordinate
System.
Corresponding respectively to the coordinates
(r,Q ,f) are the velocity components (u, v, w),
also shown in Figure 70. The general
momentum and continuity equations (1) and
(2) may be written in cylindrical coordinates:
Momentum "Ui- +
(3)
u 9v
dr
__
r 30
uv
r
-
Continuity f- + f + -J- f + f - 0 (5)
/' XN^
s' 4
p
\
\
\
\
?
/ CHA
CRO,
SEC1:
FIGURE 70 CYLINDRICAL COORDINATE SYSTEM
82
-------
Here, the original pressure gradient terms
have been replaced with derivatives off, which
represents slight variations in the fluid surface
elevations. 3f/3/- is a positive quantity
resulting from the fact that centrifugal force
causes the surface elevation at the outside of
the channel to be slightly higher than the
elevation at the inside of the channel. The
pressure gradient term of gd$/dr balances the
radial acceleration v2 jr. The factor 9f ,/3 e is
also positive due to the slight rise in surface
elevation caused by the channel blockage.
This factor has the effect of slowing the fluid
(decreasing average v) as the channel blockage
is approached.
For computational purposes, equations
(3), (4), and (5) are rewritten as follows:
|| = . _/• L 3« . _£ + w|«
oO v \ dr r az
3r
30 "y ' "~ +— +
^ +-S.3II
3z r 3flj
w = -
JF+f + ff]^
(6)
(7)
(8)
A simplified summary of the computational
procedure is as follows: At an angle 0,
suppose that at discrete points in r and f'
values are known for z4>,0,?), v(r,8 £), and
w(>,0,f)- The quantities on the right hand
sides of (6) and (7) can be calculated, and
values for 3«(r,0,f)/0 and dv(R,6,{/de
follow. Then, u and v can be projected
through an incremental angle A0 to the 0 +
A0 plane:
ufr, 0 +&B,zJ=u(r, 0, z) +(du/d6JAe (9)
vfr.e +&e,zj-v(re,z)+(dv/de]Ae (10)
These new values in the 0 + A0 plane are
then applied to Equation (8) from which
w(r, 0 + Af) follows. With this the cycle is
completed.
Radial Surface Slope
The terms on the right hand sides of
equations (6), (7), and (8) can all be evaluated
knowing u, v, and w in a given 6 plane, but
the terms df /dr and 3f/80 are not as obvious
as the rest. Figure 71, Definition of Surface
Shape in Channel Cross Section, shows a
channel cross section, still represented by a
rectangle, with an enlarged surface slope
component.
f
f.
J
ti
h ^
±^
y
''
_^<"~§
•— ^ ,
f^^\
\f^— j
V»j
^VX'VVVVVxV/C'/'X////
r
o
z
C (r, 6)
§
^
•4 »-r
f2
/
/
y
W/xxxxx
IN CHANNEL CROSS SECTION
Define q(r, 0) to be the lateral discharge
across a line of constant radius r:
h
qfr,8J = | u(r,e,z) dz
-f
(11)
Velocity components u(r0, 0, z) are
illustrated in Figure 71. It is realistic to
assume that the rate of lateral discharge does
not vary with angle 0, so 90 = 0, or
r h
90
The.Slope 3J/90 is very small, so
h
« dz =
dz
= 0
(12)
(13)
83
-------
However, (3zi/90) is known from Equation
(6), so,
h
**
\~_ru _du + „ _ ny 1" _I2 1£~] cfz = 0,
from which
_
iu u
v dr
v ,
(15)
All of the terms on the right hand side of this
expression follow directly from the
knowledge of u, v, and vv, so the resulting
g9f/9r may be substituted into Equation (6).
This technique for obtaining the radial surface
slope, 9f /9r, was developed by Fox and Ball.4
Longitudinal Surface Slope
The fluid flow solution is treated
computationally as an initial value problem,
so only initial conditions at the upstream end
of the base are needed. However, in making
this simplification, there is no way that the
fluid can feel the presence of the dam at the
downstream end of the channel, so a
mechanism is needed to slow the average
longitudinal velocity as it proceeds around
the channel arc. The first possibility in-
vestigated involved artificially increasing the
surface ?(r, 0) with increasing angle 0 . The
integral of the surface slope, ?t (r, 0), can be
found from (3f/3r) in Equation (15):
(16)
where r! is the inner radius of the channel
bend. The average surface height is then:
(17)
where r2 is the outer radius of the bend.
The resulting surface elevation, ffr-,0), has
a zero average value:
To this zero mean surface, an average value,
increasing with angle 6 , was added. The result
was the desired slowing of the average
longitudinal flow, but at angles greater than
40° local backflows developed. These
backflows are not unrealistic, but are
incompatible with the formulation of the
initial value problem.
An alternative means for slowing the
longitudinal flow is to slightly decrease the
average longitudinal velocity at each
incremental angle 0 at which the velocities
are computed. ?(r,0) in Equation (18) is still
computed to evaluate 9f /90 which is needed
in Equation (8). If the inflow rate is Q6, and
the foul flow withdrawal rate is Qs , then a
flow rate equal to (Q0 - Qs) must flow over
the weir. Assuming a uniform discharge rate
over the weir over the arc length 0 m , the
discharge over the weir per radian is (Q0 —
Qs)/6m. So, at any angle 0<0<0m,the flow
rate in the channel must be:
0
(19)
However, if at any angle 0, vt (r,0(?) the
velocity is calculated from Equation (10), the
channel flow rate would be computed to be:
dz dr
(20)
The desired slowing effect will take place if
Vi(r,6 ,z) at each point is multiplied by (Qc
(9 )/Gc • (0) )• This will always be a positive
constant, very nearly equal to unity.
Calculated in this way, negative values, of v
(backflow) will not develop:
h(r)
(r,B,z) dz dr
(21)
84
-------
This approximation, therefore, allows
treatment of the flow as an initial value
problem, while still partially accounting for
the variation in longitudinal velocity, v, which
arises from the secondary fluid motion (u, iv).
Coordinate Transformation
For computational purposes, it is
convenient to deal with a rectangular array of
points in each 6 plane. If the channel cross
section were rectangular, Equations (6), (7),
(8), and (15) could be used directly. The
channel cross section is, however,
approximately a trapezoid so a
transformation is used to map the trapezoidal
cross section into a rectangular computational
space.
In Figure 72(a), Coordinate
Transformation, if at both r = r^, and r = rz,
the vertical sides are divided into the same
number of equally spaced intervals, the
intervals at r = r^ will obviously be greater
than at r = r2. But in Figure 73(b), the
intervals at R = R1 and R = R2 will be equal.
The transformation (r,d,$) -» (&©,£)
transforms the trapezoid into a rectangle. To
accomplish this transformation, define
Z = zlh(r)
0
-------
From the definition of the transformation:
ZfJl£ and Zz=^-.
h(r) h\r>
(29)
To summarize:
R =r
Z =
9 =
"57
9
3z
-2-
3_
3Z
0=0 S
9 =
30
Simplified Transformed Equations
When the transformed partial derivatives
in equations (26), (27), and (28) are applied
to Equations (6), (7), (8), and (15), the
results are as follows:
38
w
3u1
_
9Z
(30)
39 >'
h(r) 9Z
ae
(31)
w —
h(r) 9Z
.M.I 9v
"
(32)
---
Mr) 3Z
h(r)dZ
(33)
By referring to Figure 72(a) and noting that
in Equation (23) hb is the bottom slope, the
velocities u and w are related approximately
as follows:
^ = hbZ (34)
This shows that in any 0 plane, near the
bottom (Z = 1), the flow is parallel to the
bottom, and near the top (Z = 0), the vertical
velocity component approaches zero. When
this simplification is applied to Equations
(30), (31), and (33), the following equations
result in the form which is used for
computation:
30
dv =^R
30 v
w —
9v 4. uv 4. _£ 3?
9K "R R 9©
__
az R R a©
(35)
(36)
h(r)dZ
(37)
-™™,\ h(R)dZ
(38)
The channel cross section is described by
the radii TJ and r2 , height of sides HI and H2,
and overflow height and position B2 and Bl
as shown in Figure 73, Mathematical
Representation of a Channel Cross Section. If
Q° is the inflow rate, and Qs the foul flow
withdrawal flow rate, the fluid will flow over
the weir with a height ZO, given by the
standard weir formula:
-I 2/3
r Qo -Q,
zo =
3.33(r2)(0
n\
(39)
where ®m is the arc length of the flow
chamber. The coordinate system shown in
Figure 73 has its origin at the inner radius
and at the surface of the fluid. Along the
vertical surfaces, there is no radial flow
except at the overflow outlet, hence:
86
-------
r=r.
Bl + ZO
__£__r = r2
T
T
T
B2
z =H2 + ZO
z = Hl+ZO
FIGURE 73 MATHEMATICAL REPRESENTATION OF CHANNEL CROSS SECTION
u(r,e,z) - 0
r=r2, except oottet
(40)
The outlet has a height B2 and length r2@m ,
so the radial flow rate at the overflow outlet
is as follows:
and
fr
\_fBl +ZOJ < z
(43)
where:
p
k
y0
= bottom shear stress
- density
= von Karman constant
= length related to the
roughness height.
The term vrjp is the friction velocity, Vf,
which is given by:
(44)
where / is the Darcy friction factor from the
Manning equation
(45)
87
-------
In Equation (45), g is the acceleration of
gravity, n is Manning coefficient and H is the
hydraulic radius.
°lfj> Equation (43)
is equivalently written:
v = Cln (yly0) = C (In fy/h)+ln(h/y0)] ,
where h is the channel depth. For this
velocity distribution the average channel
velocity is:
Y = C j" [ln(y/h) + ln(h/y0) ] d(yjh)
)*l.} (46)
Then an equivalent expression for equation
(44) is:
v = V + C ( 1 + In (y/h) )
(47)
In this expression, V is the average channel
velocity, a function of flow rate and channel
cross-sectional area only. The second term is a
perturbation term which predicts slower
moving fluid near the bottom and faster flow
near the surface.
Now suppose that the channel is not
wide, so that the effects of the vertical walls
are felt. A functional form analogous to
Equation (43), taking into account bottom
and both walls is as follows:
v = Cln
in which a is the width of the channel.
Again, expressing the velocity in average
and perturbation terms, the result is
analogous to Equation (47):
= V + C
In ^y/h) fx/a) fij*- Tl
(49)
Finally, consider the channel cxos s
section shown on Figure 74, Channel Cross
Section in Cartesian Coordinates, in a
Cartesian reference frame.
1
*,.
, Y)
FIGURE 74 CHANNEL CROSS SECTION IN
CARTESIAN COORDINATES
Define Y as the height above the sloping
bottom:
Y = y - r^-f-k)* (50)
The appropriate form of the Prandtl-von
Karman law is as follows:
v = C In
[,
(
' '" J (5D
Again, in terms of average velocity, it can be
shown that this velocity distribution can be
written:
= V f Cln .
where the average velocity, F, is obtained by
dividing the total flow by the cross-sectional
area:
— 6
V ~ K(ni+hz )a (53)
This result, in an (x,y) plane, is easily
transformed into the r, z plane defined in
Figure 72(a) by using the following:
r = ri + x
z = hi - y
a = ra - /-!
(54)
88
-------
3. —
h(r)
f
*
(a)
FIGURE 75 TRANSFORMATION OF CHANNEL CROSS SECTION
TO RECTANGULAR REGION
Initial Values for the Cross-Flow Velocities
u and w
The initial values for the cross-flow
velocities describe the flow from the interior
of the channel over the weir at the entrance
to the bend, before the customary helical
flow pattern develops.
The u and w velocity components lie in
the © = 0 plane, and are, respectively, in the
radial (>) and vertical (z) directions. Figure
75(a), Transformation of Channel Cross
Section to Rectangular Region, shows the
channel cross section, while Figure 75(b)
shows a transformed cross section.
The ultimate goal is a velocity field in
Figure 75(a), where flow is parallel to both
the top (z = 0) and the bottom (z = h(r) ),
and no flow crosses the sides (r = r^ and r =
r2) except for a point sink at r = r2, and z = 0,
which represents the flow over the weir.
Several steps are required to reach this point:
(a) In Figure 75(b) a potential flow field
solution is derived which crosses and is
perpendicular to x =' 0 at a uniform rate on
0//=0 (57)
along with the boundary conditions:
y = 0 i// = 0
x = 0 \l> =
y - hi ty — Uoh-z
x = a \jj = U0/z2
where
(58)
(60)
(61)
(discharge/
unit length). (62)
89
-------
These boundary conditions are such that a
uniform flow crosses between y = 0 and
y = /z2 at x = 0. A point sink is located at
x - a, y = 0, while no other flow crosses y = 0,
y = h'-i, and x = a.
The solution of Equation (57), with the
above boundary conditions at points interior
to the boundary, is given by:
sink
where
2U0/z,
. . ,n7Ta
OT S/rtfc (-—
(63)
(64)
In practice, an infinite series cannot be
completely evaluated, so Equation (63)
includes all terms up to the point where:
2U0 h-> sink (rntxlh-,)
I nit sink (
<0.01
(65)
Now, suppose that the velocity
components u, and w, are rotated by a
variable angle so that u\ is parallel to the
channel top and bottom, as shown in Figure
76, Rotation of Velocity Components.
U
FIGURE 77 ROTATION OF VELOCITY
COMPONENTS
The angle 4> is chosen so that there is enough
rotation to make MI parallel to the bottom at
2 = h(r), while there is no rotation at z = 0:
0=74-, tan'1
h(r)
(66)
Then the corresponding velocities (w2,
) in the cylindrical coordinate system are:
= MI cos 0 + Wi sin 0
(67)
W2 = -u\sin 0 + M>I cos 0 (68)
These velocities must next be scaled by a
factor F, so that the same lateral discharge
exists for any value of /•, despite the variable
bottom depth h(r):
u3=F-u2 w3 = F- w2, (69)
where the scale factor, F, is chosen so that
F- [it 2 cos 0-w2 sin 0] dz
But
so
sin
U=~h(7j e
w =
Kr [-MI sin 0 +
'(76)
COS 0]
(77)
90
-------
At r = r2, the scale factor is unity. An
experimentally determined acceptable value
for the constant is Kr = 1.5.
These approximate initial values for u and
w describe the flow in the cross-flow (r, z)
plane at 0 = 0, which arises because the flow
upstream of 0 = 0 has already adjusted to the
presence of the weir. This flow generally
proceeds from the inside toward the outside of
the bend, and upward from the bottom. The
exact values of the velocities are not critical,
because the flow will re-adjust itself as the
computation proceeds downstream.
Numerical Method for Liquid Flow
The transformed space shown in Figure
72(b) is divided into a rectangular grid as
shown in Figure 77, Computational Grid in
Transformed Space. Grid points are spaced by
a distance AR radially, and AZ vertically.
Figure 77 is a plane in R and Z. A complete
flow field solution includes a number of these
planes separated by angular increments of A0-
The cross-flow velocities, u(R,®,Z) and
v(R,@,Z), are calculated from Equations (35)
and (36) by use of a predictor-corrector
scheme. In both stages of this two-stage
process, the right hand sides of these
equations must be evaluated.
R-
i-1, k
i, k-KL
1+1, k
•*>R
FIGURE 77 COMPUTATIONAL GRID IN
TRANSFORMED SPACE
The longitudinal surface slope 9f/9© is
evaluated in both stages as a backward
difference:
The. evaluation of d$/dR is the same in both
stages and is discussed in a subsequent
paragraph. Both u(R,®,Z)) and v(R,@, Z) are
calculated by the predictor-corrector process,
so it is sufficient to discuss only u(R,@,Z).
During the predictor stage, a predicted
value u(R,®,Z) is found from:
^(R, 0 + A0,Z) = u(R,Q,Z) + A0 --|^
d° (79)
Where 9u/9o is evaluated from Equation
(35) in which the terms du/dR is found as a
backward difference for^< 0.5(R1+R2):
du= u(R, 0, Z) -u(R -A.R. 0. Z)
_^R (8Q)
and a forward difference for R>0.5(Rl +
R2):
dji - u(R + A.R.0.Z) - u(R,6,Z)
dR A/? (81)
The new u(R,®,Z) is then the average of the
predicted u(R,® + A0, Z) and a correction
term:
u(R,6 + A0,Z) = I ^(^,0 + A0,Z)
(82)
Here, 3^/3 © is^ evaluated using the
predicted u and v", and the backward
and forward differences are reversed, so that
dH/dr is a forward difference for R< $ (R 1
+ RT), and a backward difference for
R>l/2 (Rl + RT). Both w(R,Z) and 3^/3^ in
Equations (37) and (38) must be calculated
after each predictor-corrector cycle, and both
contain the form:
f(Z)dZ
(83)
zi
90
(78)
This integral is approximated by the
trapezoidal rule:
Z2
/(Z)dZa
(84)
1,AZ)
91
-------
where
Zl =/l -AZ Z2 = -AZ
Within the integrand of Equation (37), 9v/90
is evaluated as a backward difference:
-v(R,0 -A0.Z)
A0
(85)
and the terms du/3R and 9u/9Zare evaluated
as centered differences.
A.R.0..Z) -
2A/?
(86)
JZ
2AZ
Liquid Flow Summary
The equations basic to fluid flow, the
momentum and continuity equations, are
presented as Equations (1) and (2). These
equations are transformed to an equivalent
set, Equations (3), (4) and (5), in cylindrical
coordinates to represent the curvature of the
channel. They are then expressed in
Equations (6), (7), and (8) in a form from
which the velocities (u,v,w), corresponding to
coordinates (r,6,z) can be calculated for a
channel of rectangular cross section.
A surface height, $(r, 6), is introduced to
represent the fact that the fluid surface is not
horizontal, but rises radially to counteract
centrifugal force. Equation (15) provides the
surface slope, 9f/9r, needed to calculate the
radial velocity u. Then fO'.fl) follows in
Equation (8) as the integral of (3f/3r) over r.
Since the problem is formulated as an
initial value problem, the channel blockage
cannot be felt. Longitudinal velocity scaling
in Equation (21) provides the necessary
average velocity reduction. A coordinate
transformation is made to account for the
non-rectangular channel cross section. The
simplified transformed equations needed to
solve for (u, v, w) appear in Equations (35) to
(38).
Boundary conditions define the channel
walls, bottom, fluid surface, and overflow. An
initial longitudinal velocity profile, v(R,Z), is
derived, based on the Prandtl-von Karman
universal-velocity-distribution law. An initial
velocity field for u and w in the plane of the
channel cross section is developed to represent
flow toward the overflow as a point sink.
Figure 78, Fluid Flow Solution
Summary, summarizes the computational
INITIAL VELOCITY v(R, 6= 0, Z)
EQ (52)
'
'
INITIAL VELOCITIES u(R, 6 = 0, Z),
w(R, 6 = 0, Z) EQS (76), (77)
3£
g T7
'
C (r, 6 )
•
EQ (38)
'
EQ (18)
^
VELOCITY COMPONENTS u AND v
BY PREDICTOR -CORRECTOR, EQS (35), (36)
'
r
u BOUNDARY CONDITIONS
EQS (40), (41)
1
w BOUNDARY CONDITION
EQ (42)
\
w (r, f), Z) EQ (37)
\
INCREMENT 6 BY A 6
NO SQ* ,
ST(
r
)m J>
YES
DP
FIGURE 78 FLUID FLOW SOLUTION
SUMMARY
procedure, and shows the equations used in
each step.
92
-------
Particle Flow Calculation
The calculation of the particle flow field
is carried out, based on the assumption that
the particle number density is low so that
particle interaction can be neglected. The
individual particle velocities at each grid point
can be accurately represented by
superimposing the particle settling velocity on
the calculated liquid velocities. The local
concentration of the particle cloud is then
calculated from the continuum continuity
equation. These calculations are performed
for a discrete particle size class, and are
repeated for various settling velocities in order
to represent the mixture of particle sizes to be
encountered in practice.
Particle Flow Equation
The solution of the particle flow problem
is carried, out as an initial value problem,
made possible by the assumption that there is
no diffusion in the longitudinal (0) direction,
and that no back-flow (negative v velocities),
occurs. Written in conservation form, the
following equation describes the steady-state
particle concentration (Q distribution:
=0 (88)
Vp is the particle velocity vector
comprised of the components (up,vpwp).
While u and v are those calculated in the
fluid flow problem, wp is the sum of the
component w from that solution, plus the
particle settling velocity, ws. Written in
cylindrical coordinates the equivalent
equation is:
9r
= e
90
N'
9C
9r
9z
72
902
9z2J
(89)
The eddy diffusivity has been assumed to
be constant. The assumption of no
longitudinal diffusion is equivalent to
assuming that (r2) 92C/902 is small with
respect to the other terms, and may be set to
zero. Having done this, and re-arranging the
factors, the equation becomes:
+
J (90)
The numerical solution basically follows the
same pattern as the solution for the liquid
flow. The right hand side of Equation (90) is
evaluated at grid points in a given 9 plane;
then, .
(vQr,6+&e,z=(vCr,8,z+ ^ \~W~ } r>d>z •
V '
and
(91)
A0,z) (92)
Transformed Equation
As is the case for the fluid flow solution,
the numerical solution of the concentration
equation is made easier by a coordinate
transformation. The transformation is
repeated here:
9 = JL + 7 _JL
R =r
br
0 = & ^- =
9
90
_ 9
90
Z =
where
9 -7
9F ~zz
(93)
(94)
(95)
(96)
(97)
Applying this transformation to Equation
(90):
d(vQ = _ I 9 (RUG) + z
-Zhb
h(r)
and
Z = 1
h(r)
-\-*-
dR
r dZ
9Z9.R
93
-------
+ Z,JK.
__
9Z
M
+ R
9Z
(98)
Boundary Conditions For Particle Flow
The boundary conditions for the particle
concentration field, (Equation 88), require
specification of the particle flux vector F
defined as:
F =
eVC
(99)
If ~n denotes the unit inward normal to one of
the bounding surfaces, then the particle flux
normal to this boundary is:
= n • F =
n - e
dC
dn
(100)
Along the vertical walls (except at the
overflow), the particle flux, normal to the
wall must be zero. Since the velocity normal
to the wall is zero, Vp.n = o, for these surfaces,
so that Equation (100) reduces to:
-|^- = 0 (for vertical surfaces). (101)
Through the open surface of the channel
there is also no particle flux. However, along
this free surface, the vertical velocity of the
liquid, w, is zero, but the particle velocity is
the settling velocity, ws . The rate at which
particles settle from the surface must,
therefore, balance the flux of particles toward
the surface by diffusion, or, from Equation
(100):
= 0 (open surface)
(102)
Along the bottom, it is possible to specify
either of two boundary conditions. The
particle flux through the bottom can be
assumed to be zero (F • "n = 0) in which case
all of the bed load remains in suspension
Alternatively, particles reaching the bottom
can be assumed to settle into a thin, highly
concentrated sediment layer external to the
computational mesh. The first boundary
condition — all bed load remains in
suspension — is probably somewhat closer to
reality and has been used in the present
model. However, some deposition of sediment
is known to occur and, by neglecting this, the
model will tend to under-predict the removal
efficiency. To correct for this tendency, the
eddy viscosity has been empirically calibrated
against laboratory data, as will be described to
reproduce the correct removal efficiency at
the design flow rate.
Initial Concentration Distribution
An analytical derivation of the
concentration in the 0=0 plane is not
as straightforward as the initial velocity
calculation. The actual particle concentrations
which exist at the entrance to the bend are
influenced by the design of the entrance
section. It was originally thought that the
vertical variations in concentration could be
obtained from the analytical solution for
sediment transport in a straight open channel.
However, the laboratory measurements
revealed significant lateral concentration
variations which could not be modeled with
this approach. For this reason, the initial
concentration distribution is based on
measured data at 12 points in the channel
cross section. Initial concentrations at each
computational grid point are calculated as a
linear two-dimensional interpolation of the
four measured values surrounding each grid
point. For grid points not surrounded by four
data points, the interpolation becomes an
extrapolation.
Numerical Method for Particle Flow
The numerical solution for C(.R,®,Z)
proceeds ahead in angle 0, according to
Equations (91) and (92). These require that
the right hand side of Equation (98) be
evaluated at grid points in R and Z at each ©
step. The points (o) at which C is calculated
lie midway between the points (x) at which u,
v, and w are calculated in the (R,Z) plane.
Figure 79, Location of Computational Grid
Points for Concentration Field Calculations,
shows the arrangement.
The boundary conditions for the particle flow
are built into the numerical procedure by
specifying the appropriate particle fluxes to
be zero at the solid surfaces and along the
open top.
94
-------
\
r
R
k
Z i
(i-1, k-1) (i-l, k) (i-1, k+1)
(i-1, k-1)
o
(i-1, k)
o
k-1)
(i, k+1)
(i, k)
O
AZ i o
1(1+1, k-1) (i+1, k) (i+1, k+1)
AR
FIGURE 19 LOCATION OF COMPUTATIONAL GRID POINTS FOR
FOR CONCENTRATION FIELD CALCULATION
The numerical calculation of each of the
eight terms in Equation (98) is described
below. In the first partial derivatives in the
first three terms, care is taken so that mass
flux is conserved.
Term 1
b(RuO = (Ru)n C0 - (Ru)m Cm
9R AK (103)
where
(Ru)p =
(Ru)m = >
i,k
and
= Citkfor(Ru)p>0
Cm = Ci,k-l f°r (Ru1
Cm = Ci,k f°r (^«)m<°
R(k) and Z(i), which will appear later, are
evaluated at the points (x).
Term 2
3( RuC) -
(ZrRu) =
where
(Z^?u)m =
and
Cp =
(104)
1, k
>0
Zr (i,k) and Zz(k) in the following
expression are evaluated at the points (o).
95
-------
TermS
Term 6
= 2
2A z
(105)
where
_ 1
2.
_ 1
(108)
wi
it k
and
Term 7
By substitution forZ,.,
~ ct. k for wp > o
Cm =
, k for
for wm
(109)
0
The diffusion terms, 4 through 8, all span
two increments in A/? or AZ as written in the
expressions to follow. However, when the
points (0) are adjacent to the channel
boundaries, only single spans in &.R or AZ
may be possible, in which case one-sided
ditrerences are used.
Term 4
- q fc) /AZ - z, (qfc - q.1;fc) / Az /A z
J
Term 8
Again, by substituting for Zz,
3C\ _ R 32C
(110)
RZ,
3Z
3Z2
(h(Rk)
(106)
+ R 1 /
^fc+i /. _j
+ h(R ))2
fc-t-i |—
AZ
TermS
9
Az
/AZ..
(in)
*-. i
/2AZ 1/2A.R
Finally, when integrating C(R,@,Z) ahead
in 0 by use of equations (91) and (92), the
velocity term, v, is evaluated as the average of
the four points surrounding each
concentration mesh point.
Particle Flux Calculations
The particle flux crossing the 0 = 0 plane
(107) is the integral of the product of concentration
96
-------
and longitudinal velocity over the cross
section:
v(r,e=o,z)dzdr
(112)
C(r,6 =o,$) dzdr
The flux over the weir is a function of the
radial velocity and concentration at that
point. The flux between angles ©i and ©2 is:
ft^ Bl +.B2 + Zo
(C(HJ J»M^C^
®n Bl + Zo
dzdd.
Then, the total flux over the weir is:
(CQW
W otal
= 6
(1 14)
The removal efficiency is, then, the ratio of
the material which did not pass over the weir
to the input flux.
-(.CQw)total
CQ0
(115)
Particle Flow Summary
The particle flow solution is treated as an
initial value problem, starting with
interpolated experimental data in the 0=0
plane. After each A0 increment where
velocity components u, v, and w are
calculated, the concentration is calculated at
points on a (r,z) plane grid. Equation (88) is
the basic relation describing the concentration
field. It is solved numerically in conservation
form for the product (vC) at each angle 6;
then, by dividing by v, the concentration C
results. Equations (90) to (92) describe this
process. In order to account for the
non-rectangular channel cross section, a
transformed equation for 9 (vC)/d6 is given in
Equation (98).
The numerical solution method is a
conservative upwind differencing scheme.
The numerical calculation of the
individual terms of Equation (98) is
described in Equations (103) to (111).
Finally, the particle flux calculations
needed to determine efficiency are presented
in Equations (112) to (115) Figure 80,
Particle Flow Solution Summary, shows the
overall flow and concentration calculation
procedure. Figure 78 portrays details of the
flow calculation.
INITIAL VELOCITIES u, v, w
\
r
INITIAL CONCENTRATION,
INTERPOLATED MEASURED DATA
\
r
INPUT FLUX CALCULATION
EQ. (112)
\
i
VELOCITY COMPONENTS u, v, w
CALCULATED (FIGURE (11) )
'
3 (vC)
se
t
<
EQ (48)
r
c (R, e, z)
EQS (91, 92)
i
>
INCREMENTAL OUTPUT
FLUX, EQ (113)
r
INCREMENT 6
BY Aft
N0 ^n -
flm ^>
|YES
EFFICIENCY
EQ (115)
t
STOP
FIGURE 80 PARTICLE FLOW SOLUTION
SUMMARY
97
-------
Approximate Solution for
One-Dimensional Flow
In a uniform, wide rectangular channel,
the suspended sediment tends to stratify, with
a higher concentration occurring near the
bottom, and lower concentration at the
surface. The degree of stratification is
influenced by the particle settling velocity
and the turbulence in the channel. The classic
analysis of bed-load stratification was
published by Dobbins6 in 1944. Dobbins
studied a simplified version of Equation (88)
in Cartesian coordinates in which the
longitudinal velocity, v, was assumed to be
constant, and u and w for the liquid were
taken as zero. As in the present study, the
longitudinal diffusion was neglected in
comparison to vertical diffusion, and the
particle velocity was approximated by
superimposing the settling velocity, ws, on the
liquid flow. In the rectangular coordinate
system shown in Figure 74 the simplified
equation becomes:
= e_9^ +
v dc
s by
(116)
Because the longitudinal velocity, V, is
assumed constant, Equation (116) can be
considered as a time-dependent problem in
which the time, t, is the liquid flow time
t =-4-
V
(117)
Dobbins obtained analytic solutions to
Equation (116) for the boundary condition of
no particle flux through the open surface at y
= h. Expressed mathematically, this boundary
condition is
'bC_
y=h.
(118)
in analogy with Equation (102). At the
channel bottom, Dobbins considered the
boundary condition:
•w.
A,
(119)
in which A is an arbitrary constant
representing the asymptotic bottom
concentration at t ->°°. For A=0, the
asymptotic concentration is zero, indicating
that all of the material has settled out of
suspension. The initial concentration
distribution was assumed to be of the
exponential form:
Cty.o) =C0e -by .
(120)
For the special case 5 = 0, Equation
(120) corresponds to an initially uniform
concentration. For this problem, Dobbins
obtained the analytical solution:
CG/,0 = Ae
Cne
n sin«B;T| ,
" J
(121)
where the constants, Cn, are evaluated from
2
in which
(122)
H = cosah +
W.,
sin oLnh .
(123)
The values of «„ are obtained as the solution
to the transcendental equation:
>wsh \
2 cot OL./Z =
2e
WL\ anh
ze
(124)
98
-------
For the boundary conditions studied by
Dobbins, it is necessary to specify the
asymptotic bottom concentration, A. In
practice, unless complete clearing of the flow
is anticipated (so that A = 0), it is difficult to
know what an appropriate value for A might
be. Consequently, Dobbins' solution was
rederived for the bottom boundary condition
of zero mass flux through the, bottom, or:
AC = r
3y y=Q L
•=o (125)
in analogy with Equation (102). This
boundary condition corresponds to that used
in the numerical model, and assumes that the
entire bedload remains in suspension. Under
this condition, it can be shown that the
solution to Equation (116) is:
-ws y -ws y
C(y,t) = Ae
2
46 2
_
n=\
where
A =
\\-e -Bh
' ~e~
' (126)
(127)
(128)
,and
Cn =-
(-ire
2e
2e
(129)
This new solution is closely analogous,
but somewhat simpler than that of Dobbins.
Furthermore, the value of the previously
unknown constant A, is now determined from
the requirement that the longitudinal mass
flux remain unchanged — i.e., all bed load
remains in suspension. Although these
solutions correspond to much simpler
geometry than the helical flow separator,
several useful insights into the more
complicated problem can be obtained from a
study of their analytical form. For example,
in both Equations (122) and (126), the
asymptotic vertical concentration distribution
is shown to be a negative exponential:
C(y, t-»»>)=A exp (-wsy/e), (J3Q)
which depends on the scale height "a"
defined by
a = e/ws. (131)
Thus, sediments with large settling
velocities, ws, will have small scale heights,
corresponding to a very rapid decay, in
concentration with distance above the
bottom. Furthermore, for a given settling
velocity, the scale height is directly
proportional to the eddy viscosity due to
turbulence, e. Thus, as the turbulence level is
increased, the vertical concentration
distribution tends to become more uniform,
with less stratification. In the discussion by
Camp''7'' of Dobbins' paper, the eddy
viscosity was evaluated as the vertical
averaged value corresponding to the universal
logarathmic velocity distribution as discussed
in Equation (43). The resulting expression for
e is:
€ = Thvv{- (132)
where h is the channel depth, Kis the average
velocity, and / is the Darcy friction factor.
This useful result has been retained in the
present analysis. The eddy viscosity increases
directly with the average velocity. Since the
recovery efficiency of the helical flow
separator depends on the degree of bedload
stratification, Equations (130) and (132)
indicate the desirability of reducing -the
average velocity as much as possible by using
a large channel cross section.
It was originally 'thought that the
asymptotic vertical concentration distribution
given by Equation (130) could be used
directly to model the initial distribution at
the entrance to the bend, by appropriate
correlation of the scale height, "a". However,
as noted, the laboratory results showed
99
-------
significant lateral variations which could not
be accounted for with this approach.
Additional useful insights can be obtained by
studying the relationship between time and
distance given by Equation (117). For a
channel with a side weir, the average
longitudinal velocity decreases in the
downstream direction, due to loss of fluid
over the weir. For uniform lateral discharge,
the average velocity is given by:
V = dx
dt
in which Q0
_ Qo -Qw
A "~ (133)
is the flow rate at the start of the
side weir, Qw is the total flow over a weir of
length L, and A is the cross-sectional area of
the channel. Equation (133) can be integrated
to give the following relation between
distance and time:
Q
?0-Q,
(134)
Since the degree of stratification (and hence
separator performance) which can develop
within the separator depends on time (as
shown in Equation 121 or 126), Equation
(134) indicates that better performance can
be achieved with longer retention times, T,
defined in the conventional manner:
. = vol „ LA
Q Qw ' (135)
By combining this result with the
analytical form appearing in Equations (121)
and (126), it can be concluded that a
significant non-dimensional parameter, 0,
affecting the separator performance is:
9 i~~ (136)
where ws is the settling velocity, T is the
retention time defined by Equation (135),
and e is the eddy viscosity. To increase
separator efficiency, 0 should be made as
large as possible, which implies large retention
times, T, and small longitudinal velocities, to
reduce e . Furthermore, since the
concentration decays exponentially with
distance from the bottom, and the clear flow
is withdrawn from the surface, it appears
desirable to achieve a given retention time
with a narrow, deep section, as opposed to a
shallow, wide one. This conclusion strictly
applies only to a straight channel. In the
proposed curved channel, the induced
secondary flows act to reduce the
concentration of particulates in the overflow.
The development of these secondary flows
would be suppressed with a deep, narrow
channel section.
Scaling of the Liquid Flow
The development of the secondary flow
in the bend depends primarily on the
distribution of the approach velocity at the
entrance of the bend. If it can be shown that
the non-dimensionalized inlet velocity profile
is the same in both the model and the
prototype, then maintaining the same Froude
number,
F=
-
Lg
(137)
in the model and the prototype will ensure
that the flow patterns will be the same
throughout the bend.
It was shown that the entrance velocities
for the non-rectangular cross section can be
represented by:
+ 1/2
h, +/z2
In
(138)
where "a" is the width of the separator, hi
and hi are the depths at the inner and outer
walls, and Y is the distance from the bottom.
This formula applies to both the prototype
and the model and, since all terms inside the
brackets are non-dimensional, each of these
terms will be identical if the model and
prototype are geometrically similar.
Consequently, the .same non-dimensional
values of velocity (v/V) will result for both
model and prototype if the term C/V is the
same for model and prototype.
The constant Cis given by:
C=l/k Vf, (139)
100
-------
where k is von Karman's constant, and Vf is
the friction velocity
v, (140)
and where / is the Darcv friction factor.
Therefore, the ratio ofC/Fwill. be the same in
model and prototype if:
(vTT)m = (V/V (Hi)
The friction factor, / can be determined
from the Manning Equation:
f= 0.453
#1/3
(142)
in which g is the acceleration of gravity
(ft2 /sec) n is the Manning coefficient (sec
ft-7/5) and H is the hydraulic radius. Typical
values of n are 0.009 for the model and 0.012
for the concrete prototype. Thus the ratio of
friction factors is:
Jttt f **w\ \ / •"• n \ ^/*^
~fp~ ~\^j (Hr») (143)
For a length scale of 1:6:
fm = (0.009\ 2 <-6W3 = i 025
-Jp— lo.012J (6) 1"025'
and so the ratio of CfV in model and
prototype will be:
=1.013,
(em.
which is very close to unity.
It can, thus, be seen that the lower model
velocities are offset by its smoother surface,
so that to a very close approximation the
non-dimensional entrance velocities, vf'y will
be the same as for the prototype.
The entire flow in the bend will then be
reproduced by maintaining the Froude
number constant between model and
prototype. Thus, if the prototype dimensions
are S times larger than the model, the
following relationship follow from Equation
(137):
Lp=SLm (144)
Vm =
v
(145)
(146)
Scaling of the Particle Flow
Equation (89) for the particle
concentration field applies to both the model
and the prototype. If the equation is
non-dimensionalized by '-'dividing-, the
concentration by the inlet concentration, C0,
dividing all lengths by the width of the
channel, "a", and dividing all velocities by the
average entrance velocity, V, there results:
:i_ _!_ (r 3£ ) + -L
- V
3ac
1
_ lev
,2
(147)
in which the tilde (-) denotes a non-dimen-
sional variable. This equation will be identical
for the model and. the prototype if the
non-dimensional eddy diffusivities are the
same:
ef
-
(148)
The equation used to represent the eddy
diffusivity is Equation (132):
e = -1 h V ^/Ji* ,
6
where Ji is the mean depth. Equation (148),
then, requires that:
h V2
VP)
p
(149)
As was shown previously, fm& fp, and since
the velocities and dimensions are related by
Froude number scaling (Equations 144-146),
p
.2
= s2
= s V
m '
so that the equality in Equation (149) is
preserved.
101
-------
As a consequence, Froude number scale
relationships between the model and
prototype will ensure duplication of the
non-dimensional concentration fields and,
therefore, the recovery efficiency. The
Froude scale relationship, Vp = vT~ Vm,
applies to all velocities, including the particle
settling velocity. Thus, to represent a given
class of prototype particles in the laboratory
model, the laboratory material must have a
settling velocity of S— 'A times the prototype
value, where S is the length scale.
Comparison of Mathematical Model
Results with Test Data
Figures 81-83, Comparison of Measured
and Predicted Velocity Profiles at 0°, 20°,
and 40° respectively, show comparisons of
calculated and measured longitudinal, (v),
velocities in cross sections at the indicated
angular positions. The test data were obtained
by LaSalle Hydraulic Laboratory in a
companion study, as part of this project. The
velocities shown are in ft/sec, prototype scale.
In Figure 81, the calculated velocity
contours are in good agreement with the
laboratory data. The predicted velocities at
this position were calculated from Equation
(52) applied to the prototype, for 0.85
m3/sec (30 cfs) inlet flow, with a Manning
coefficient n = 0.012 in Equation (45). As
was shown, the non-dimensional velocity
profile, (y/V), will be very nearly identical for
both the model and the prototype, hence all
calculation has been performed at prototype
scale.
Figure 82 shows significant shifts in the
longitudinal velocity at the 20° position. Due
to the secondary fluid motion, low energy
boundary layer fluid from the bottom is
swept up to the surface at the inner radius of
the bend, resulting in a low velocity region
there. This is clearly seen in the laboratory
data, but is not reproduced in the computer
simulation. This' deficiency in the
computational technique was also noted in
the results of Fox and Ball,4 and is a result
of incorrectly modeling the convective
acceleration term w3v/3z in Equation (34). In
the work of Fox and Ball this term was
neglected altogether. In the present model,
the ratio of w and u was assumed to be of the
form given Equation (34), which is correct
along the bottom and the surface, but does
not properly account for the upflow which
occurs at the inner radius of the bend. An
attempt was made to. resolve the discrepancy
by retaining all of the terms shown in
Equation (31). However, with the additional
terms, the computational technique became
unstable.
In Figure 83, the laboratory data shows a
separated (reverse) flow region near the inner
bend. This is evidenced by the zero velocities
in Figure 83 (a). Dye studies reveal very small
negative velocities in this region. The reverse
flow region is the consequence of the low
energy fluid being more rapidly decelerated
than the faster moving fluid. The original
technique used for calculating the
longitudinal surface slope did result in the
appearance of a reverse flow region in the
computer simulation. However, the predicted
reverse flow occurred further downstream
because the calculated longitudinal velocities
near the inner bend were greater than in the
model, due to the w9v/9f term discussed
above, and thus, took longer to decelerate.
In any event, the reverse flow region is
incompatible with the initial value problem
formulation and had to be eliminated in order
to proceed. The resulting discrepancies in the
longitudinal velocity field are not particularly
important in computing the concentraion
field. The differences in the longitudinal
velocity do result in further errors in the
cross-flow velocities u and w, which are
potentially more critical. However, the
principal effect of the reverse flow region is to
raise the longitudinal velocity near the outer
radius of the bend and to cause an eddy to
appear just upstream of the baffle at 60°. This
eddy causes a sudden uplift in the material
discharged over the weir near the end of the
bend, but the effect is very local.
Figure 84, Comparisons of Measured and
Predicted Flow Angles on Bottom Along
Channel Centerline, shows a comparison of
the measured and predicted flow angles along
the bottom centerline of the bed, with and
without flow over the weir. To obtain the
102
-------
(a) Measured Velocities
(b) Predicted Velocities
NOTE: Velocities are relative
FIGURE 81 COMPARISON OF MEASURED AND PREDICTED
VELOCITY PROFILES AT 0°
103
-------
I
(a) Measured Velocities
NOTE: Velocities are relative
(b) Predicted Velocities
FIGURE 82 COMPARISON OF MEASURED AND PREDICTED
VELOCITY PROFILES AT 20°
104
-------
0.0 0.1 0.2 0.30.4 0.45. 0.50
41
(a) Measured Velocities
NOTE: Velocities are relative
(b) Predicted Velocities
FIGURE 83 COMPARISON OF MEASURED AND PREDICTED
VELOCITY PROFILES AT 40°
105
-------
Bed Angle (degrees)
a LAB DATA, NO OVERFLOW
O LAB DATA, OVERFLOW
WITH SCUMBOARD
^CALCULATED, NO OVERFLOW
.^-CALCULATED, OVERFLOW
10
35 0 (degrees)
FIGURE 84 COMPARISON OF MEASURED
AND PREDICTED FLOW
ANGLES ON BOTTOM ALONG
CHANNEL CENTERLINE
laboratory results with no overflow, the
partition at 60° was removed so the flow
proceeded uninterrrupted for a full 120°.
With no overflow, the laboratory data
indicate a bed flow angle near 22° along most
of the bed, with 18° bed flow angle at the
10°position. This implies a very rapid initial
growth in the bed flow angle. In contrast, the
computer simulation indicates a continuous
growth in bed flow angle, reaching 22° only
at the 35° position. In this respect the present
results are in agreement with those of Fox
and Ball.4 They showed a similar steady
growth in bed angle in substantial agreement
with their test data, although their work was
for a flat bed.
The measurement of the bed flow angles
is performed by using Process Black ink,
placed along a radius at a given angular
position. The fluid shear along the bottom
causes threads of ink to extend downstream
from the inked line, and the angle of these
threads with respect to the Q direction are
measured with a protractor. The technique is
accurate only to (±3°), but the differences in
in the no overflow results shown in Figure 84
are too large to be explained as measurement
inaccuracies. The very rapid initial growth in
bed angle in the laboratory model is puzzling.
There is no obvious reason why the
laboratory and mathematical models should
not be in better agreement in this respect.
The results for the bed angle in the
presence of overflow are in much better
agreement. For this case, the laboratory
results indicate a slowly growing bed angle.
The computer simulation matches the
laboratory results at the 10° position and
then somewhat overpredicts the growth in
bed angle. However, the differences are less
than 5°. Both the laboratory model and the
-computer simulation indicate substantially
smaller bed flow angles in the presence of the
discharge over the weir. This indicates that
the helical secondary flow is largely destroyed
by the weir and scum board. The reason for
this is that the side weir at the outer bend
effectively controls the water level there and
prevents the development of a large radial
surface slope. The smaller radial surface slope
produces a smaller helical motion with smaller
bed flow angles, as observed.
Comparison of Calculated Concentration Field
with Laboratory Data
It was originally anticipated that the
simple straight channel theory could be
applied to the inlet transition section to
obtain the initial concentration field at the 0°
position. However, the laboratory data
revealed significant lateral variations in
concentration which could not be adequately
accounted for with the simplified theory.
Consequently, the initial conditions for the
mathematical model were obtained by
interpolating the measured concentration data
at the 0° position, shown in Figure 85,
Measured Values of Relative Petrothene
Concentration at 0°. The measured
concentrations are only applicable for
shredded Petrothene at the nominal design
discharge of 0.85 m3/sec, (30 cfs). At higher
flow rates or lower settling velocities, the
concentration distribution will be more
uniform in the vertical direction. Conversely,
at lower flows and higher settling rates, the
bed load will be more stratified. To account
for these differences, a correction was applied
to the laboratory data, based on the theory.
The steady state vertical concentration
distribution is of the form:
C_ =e
-(wsy)
e
(150)
106
-------
FIGURE 85 MEASURED VALUES OF RELATIVE
PETROTHENE CONCENTRATION AT 0°
where y is the distance above the channel
bottom, ws is the settling velocity, and e is
the eddy diffusivity. Consequently, at flow
rates or eddy viscosities, and settling velocities
other than the nominal ones applying to the
laboratory measurements (ws0, and eo), the
initial concentration data were taken as:
C(r,z) = C0 (r,z)
(151)
where Q, (r,z) is the measured concentration
field and h is the average depth. It is readily
apparent that if ws/e = s0/e0\i no alteration
results, whereas for a larger settling velocity
or smaller flow rate, the concentration near
the surface, z = 0, will be reduced, giving a
more stratified distribution. Conversely, at
lower settling velocities or higher flow rates,
the, concentrations near the surface are
increased, giving a more uniform distribution.
Figures 86 and 87, Comparison of
Measured Values of Relative Petrothene
Concentration at 20° and at 40°, show the
measured and predicted concentration fields
for the nominal case of shredded Petrothene
(prototype settling velocity of 1.22 cm/sec
(0.04 ft/sec) at the design discharge of
0.85m3/sec, (30 cfs). Figure 86 shows the
comparison at the 20° position. The measured
and predicted results are similar, having
essentially horizontal isopleths, but the
calculated results indicate a more highly
stratified bed load. The very high predicted
concentrations along the floor of the unit are
the result of assuming that the entire bed load
remains in suspension, where the laboratory
measurements do not reflect the sediment on
the : bottom. These differences can be
neglected. However, the calculated results also
indicate very low concentration near the
surface, whereas the laboratory results show
significant amounts of material there. This
discrepancy is caused by the large spread in
107
-------
(a) Measured Concentration
(b) Predicted Concentration
FIGURE 86 COMPARISON OF MEASURED VALUES OF
RELATIVE PETROTHENE CONCENTRATION
AT 20°
108
-------
(a) Measured Concentration
10.0
(b) Predicted Concentration
FIGURE 87 COMPARISON OF MEASURED VALUES OF
RELATIVE PETROTHENE CONCENTRATION
AT 40°
109
-------
the settling velocities of the Petrothene. The
simulation results were obtained for a single
settling velocity applicable to the mid-range
of the Petrothene size distribution. The
laboratory results indicate that a significant
fraction of the slower settling particles
remains near the surface.
Figure 87 shows a similar comparison at
the 40° position. Both the laboratory and the
simulation results indicate very little material
at the surface, although the laboratory results
still indicate a less stratified bed load, due to
the distribution of settling velocities. The
most important comparison between the
laboratory results and the computer
simulation is the relative rate at which
material is discharged over the weir. Figure
88, Mass Flux Over Weir as a Function of
Angular Position, shows the percent of the
original particles lost over the weir in each of
twenty 3° angular segments. Figure 89,
Cumulative Mass Flux over Weir as a Function
of Angular Position, shows the cumulative
percentage lost over the weir as a function of
angular position. The mathematical model
was calibrated to give the correct total
percentage material lost — 9 percent — for
this nominal case by adjusting the eddy
diffusivity constant, k, in Equation (132).
The selected value was 1.5, compared to a
theoretical value of 0.4.
Figure 88 shows that in the laboratory
model, the rate of material passing over the
weir is initially low, but increases rapidly to a
maximum at the 18° angular position.
Thereafter, the rate of material loss decreases
slowly. The initial transient rise in the
laboratory results is not duplicated in the
computer simulation, which indicates,
instead, a rapid continuous decrease from a
maximum at the 0° position. This significant
difference in behavior is a consequence of
incorrectly modeling the lateral flow over the
weir. In the computer simulation, the lateral
weir flow is assumed to be fully developed by
the 0° position, and is accounted for by the
initial distribution of the cross-flow velocities,
u and w. As the flow enters the bend, the net
lateral discharge, q, at each angular station is
unchanged from the initial distribution, as a
consequence of assuming 9^/90 = 0 in
Equation (12). In fact, the laboratory results
in Figure 88 indicate that the lateral discharge
is not fully developed until near the 19°
position.
The development of the lateral discharges
is controlled by the weir which reduces the
surface level at the outer bend radius, and
thereby accelerates the fluid laterally toward
the weir. Because of its inertia, a finite time is
required for the lateral discharge to fully
develop across the cross section, in contrast to
the instantaneous flow adjustment assumed in
the computer simulation. The reduction in
surface elevation at the outer bend also
inhibits the initial development of the helical
motion.
As a consequence, the bed flow angle
initially grows at a lower rate than indicated
by the computer simulation, as shown
previously in Figure 84. Several attempts were
made in the computer studies to resolve these
differences in flow behavior by properly
simulating the development of the lateral
discharge, q(r,@),along the channel. To do
this, the lateral surface slope must be
computed directly, instead of relying on
Equation (38) which is derived on the
incorrect assumption that 9
-------
0 6 12 18 24 30 36 42 48 54 60
ANGULAR POSITION (DEC.)
FIGURE 88 MASS FLUX OVER WEIR AS A FUNCTION OF ANGULAR POSITION
10
I
Hi
PS
£
SIMULATION
I
12 18 24 30 36 42
ANGULAR POSITION (DEC)
48
54 60
FIGURE 89 CUMULATIVE MASS FLUX OVER WEIR AS A FUNCTION
OF ANGULAR POSITION
111
-------
% RECOVERY
100
80
60
40
20
0
w = 0.04 FT/SEC
s
O MODEL
DATA
Q-,
1.5Q
D
2.0Q
D
FIGURE 90 COMPARISON OF PREDICTED AND MEASURED RECOVERY
EFFICIENCIES AT DISCHARGES GREATER THAN THE
DESIGN VALUE 0.85 M3 /SEC (QD = 30 cfs)
diffusivity was adjusted to give the correct
total amount of material discharge over the
weir for the nominal case, as indicated in
Figure 89.
Figure 90, Comparison of Predicted and
Measured Recovery Efficiencies at Discharges
Greater than the Design Value QD = 0.85
m3/sec, (30 cfs) shows the predicted and
measured recovery efficiencies at flow rates of
1.5 and two times the design flow rate of 0.85
m3/sec (30 cfs). It is apparent that the
computer simulation considerably
underestimates the drop in recovery at the
higher flows.
This is evidently the result of the poor
representation of the lateral discharge, which
becomes more critical as the flow rate is
increased. At these high flows, large values of
the radial velocity, u, are induced in the
central region of the cross section, thereby
sweeping a substantial amount of material
over the weir. The present method for
assigning the weir-induced cross-flow
velocities, u and w, does not adequately
account for these large cross-flows. Instead,
most of the weir flow is withdrawn from the
upper right-hand area of the cross section,
where the concentration is lower, resulting in
an under-estimate of the lost material.
At flow rates lower than the design
discharge, the computer simulation should be
substantially more accurate because the
weir-induced cross-flows are then relatively
less significant than the helical motion.
Calculated Results for Various Conditions
The computer model was exercised over a
range of settling velocities and flow rates, to
produce the parametric curves shown in
Figure 91, Predicted Separation Efficiency
Versus Settling Velocity at Several Flow
Rates. These results show improvements in
112
-------
100
95
90
85
80
14 M'
J I I I I I
0.1
1.0
SETTLING VELOCITY , w (CM/SEC)
s
FIGURE 91 PREDICTED SEPARATION EFFICIENCY VERSUS
SETTLING VELOCITY AT SEVERAL FLOW RATES
the recovery efficiency as the settling velocity
is increased and the flow rate is reduced.
Results for flow rates larger than the design
discharge of 0.85 m3/sec (30 cfs) are not
shown because the model does not give
reliable results at large flow rates, as explained
in the preceding section.
An attempt was made to reduce the
parametric curves in Figure 91 to a
single-performance curve, through the use of
an appropriate correlation. As has been noted,
a significant parameter derived from the
analysis for straight channels is the
non-dimensional function, , defined in
Equation (136):
in which r is the retention time.
LAS
T ~ -— , •
where
L is the arc length, As is the surface area, and
Qw is the weir flow. Substituting for e from
Equation (132), and noting that Qw = V.AC
where Ac is the cross-sectional area:
. w L As
(T)
1
hv^f/B (153)
For a fixed geometry, Equation (153)
suggests that the performance should vary
with the ratio of ws/V, which is the same
behavior predicted from the non-dimensional
settling parameter:
(154;
Equation (154) was used successfully to
correlate the results of the swirl concentrator
tests.8 This correlation also works for the
present case, but only if the non-dimensional
113
-------
inlet concentration distribution is used. Under
these conditions, the downstream
development of the vertical concentration
distribution — and hence the recovery
efficiency - is basically a balance between the
settling velocity and eddy diffusivity, as
implied in the use of Equation (153) or (154).
However, because of the long inlet transition
section, significant changes in the initial
concentration profile are expected as the inlet
velocity or the settling velocity is varied.
When these changes are incorporated,
correlation of the results with either Equation
(153) or (154) no longer results in a single
universal curve.
A further important point is that in the
swirl concentrator study,8 Equation (154)
was shown to represent the upper limit on
recovery efficiency, e, so that:
e<-
Q
(155)
In the present case, this result is not
applicable, and efficiencies greater than
indicated by Equation (155) can result,
especially at low flow rates and high settling
velocities. The reason for this is that the inlet
transition section also functions as a settling
chamber under these conditions.
Additional numerical experiments were
conducted to determine the importance of
the bend radius on the performance of the
helical separator. Using the same cross
section, the outer radius of 17.4 m (57 ft) was
increased by factors of two and ten. For these
runs, the weir length was maintained constant
by reducing the total angle of the bend, ®m,
to 30° and 6° for these two cases,
respectively. The results of these calculations
for the design flow rate of 0.85m3/sec (31.1
cfs) are summarized in Table 11, Recovery
Efficiency at Various Bend Radii.
TABLE 11
RECOVERY EFFICIENCY AT
VARIOUS BEND RADII
Radius Recovery
(Initial Radius) Efficiency
1 91%
2 89%
3 82%
These results show significant decreases in
performance efficiency as the bend radius
becomes larger. The decrease in recovery is a
direct result of the reduced helical motion
present in these configurations, since the
other parameters were maintained constant.
Design techniques have been summarized
in Section III.
NOMENCLATURE
A
a
B
C
e
F
F
/
g
H
Area; also constant used in
one-dimensional flow solution
Channel width
Constant used in one-dimensional flow
solution
Depth of scumboard below weir (Fig.
5)
Overflow height (Fig. 5)
Particle concentration
Efficiency
Froude number
Particle flux vector
Darcy friction factor
Acceleration due" to gravity
Head loss through orifice
h(r) intercept (Eq. 22)
h(r) slope (Eq. 23)
Channel maximum depth
/z2 Channel .minimum depth
h(r) Channel depth as a function of radius
k von Karman constant
L Weir length
n Manning coefficient
Irt Vector normal to channel wall
P Pressure
q Lateral discharge
Q0 Inflow rate
Qs Sludge withdrawal rate
R Transformed coordinate r
r Cylindrical radius coordinate
TI Channel inner radius
r2 Channel outer radius
S Scale factor
t Time
U<> Flow velocity at overflow
u Radial velocity component
114
-------
*V Velocity vector
v Longitudinal velocity component
P/ Friction velocity
Vp Particle velocity vector
w Vertical velocity component
we Equivalent settling velocity
ws Settling velocity
Y Vertical height above channel bottom
u0 Scale length related to the roughness
height
z Cylindrical vertical coordinate
ZO Fluid depth over the weir
Zr Zjr
Zz Z/z
AJR Incrementing
AZ . Increment in Z
A© Increment in 0
f Fluid surface elevation
© Transformed coordinate ©
e Cylindrical angular coordinate
@ra Channel angle maximum
p Density
T Retention time
P0 Bottom shear stress
REFERENCES
1. T. M. Prus-Chacinski, "Patterns of Motion
in Open-Channel Bends," Union of
Geodesy and Geophysics, Vol. 10, 9A,
1954, pp 311-318; also Proceedings, 6.
Institute of Water Engineering, London,
Vol. 10, Aug. 1956, pp 420-426.
2. T. M. Prus-Chacinski, and J. W. 7.
Wielogorski, "Secondary Motion Applied
to Storm Sewage Overflows," Symposium
on Storm Sewage Overflows, Institute of
Civil Engineers, London, 1967. 8.
3. J. G. Lloyd, "Report on the Model Tests
of the Nantwich Storm Sewage
Spiral-Flow Separator 5/14B,"
Unpublished report by Mersey and
Weaver River Authority, Warrington,
CIRIA, London.
4. J. A. Fox, and D. J. Ball, "The Analysis 9.
of Secondary Flow in Bends in Open
Channels," Proceedings, Institute of Civil
Engineering, London, Vol. 39, March
1968, pp 467-477.
5. V. T. Chow, Open Channel Hydraulics,
McGraw-Hill Book Company, New York
(1959), p 200.
W. E. Dobbins, "Effect of Turbulence on
Sedimentation," ASCE Transcript, Vol.
109, 1944, pp 629-656.
T. R. Camp, "Discussion of 'Effect of
Turbulence on Sedimentation' by W. E.
Dobbins," ASCE Transcript, Vol. 109,
1944, pp 660-667
R. R. Boericke, et al, "Mathematical
Model of the Swirl Concentrator as
Applied to Primary Separation of Sewage
and Combined Sewer Discharges," Draft
report submitted to American Public
Works Association, by General Electric
Co., June 15, 1974.
R. J. Dalrymple, et al, "Physical and
Settling Characteristics of Particulates in
Storm and Sanitary Wastewater," U.S.
EPA Report No. EPA-670/2-75-011.
115
-------
APPENDIX C
BACKGROUND INFORMATION ON THE HELICAL BEND
Report of C. H. Dobbie and Partners
by Dr. Prus-Chacinski
Experiments on the bends of open
channels during the last 20 years have
narrowed very considerably "the band of
uncertainty." Prior to the time the series of
experiments carried out at the Imperial
College in London between 1950 and
19561'16-18 and the Russian experiments
carried out about the same time6'7'13 were
completed, almost no information was
available on this hydraulic phenomenon.
Interest in the research on the bends of open
channels has been revived in recent years and
the experiments carried out in Karlsruhe are
of particular interest.2 •3 •'4
"The band of uncertainty" is however
still considerable. The Russian studies and the
most recent German studies were oriented
towards the erosion in the bends of natural
rivers and, therefore, the ratio of depth to
width not much less than unity was
experimentally investigated only in the
Imperial College studies, and later by the
studies oriented towards storm-sewage
overflows.1 9>2° Of interest have been recent
experiments on stratified flow5 where the
ratio of depth-to-width was unity. What to
date has not been achieved is a complete
investigaion of the series of bends with
different ratios of width-to-radius and with
varying ratio of depth-to-width. The Russian
studies are perhaps more complete in this
respect than any others, but for deep,.small
channels their results are not well
documented.
Considering the form of cross section and
the nature of previous hydraulic bend studies,
it would seem that virtually all forms of
simple cross sections were investigated with
the exception of the cross section with the
deepest part at the inside bend — the basic
form investigated by this (APWA) project.
Therefore, the present study, apart from its
value with regard to the design of combined
sewer overflows, will also fill at least one gap
in existing information on this subject.
Experimental or mathematical formulae
which would describe the pattern of helical
motion and its strength is open to
speculation. In a small, smooth rectangular
channel the expression which describes
accurately the value of the bed angle for the
fully-developed helical flow is one expressed
by Wadekar1 as:
tana0 =
(1)
where "C" depends on the value of the
secondary depth, that is the depth where the
transverse velocity is nil; i.e., where a. = 0. The
writer's equation:
tana0 =
R
(2)
is a "blanket" expression which seems to
provide a reasonable approximation for
smooth channels in a wide range of
depth-to-width ratio and of different cross
sections. It is very likely that the same
formula written in the form:
tan a0 =
wf/r
(3)
where "f' is the friction factor, may be the
best approximation which would also cover
rough channels. This has not yet been
established by any experiments. The Russian
approximation6:
tana0 =
(4)
may be valid for the natural channels; again, it
is a "blanket" expression covering many cross
sections but mostly with small depth-to-width
ratio. The Russian formula certainly
overestimates the value of "a0" in smooth
laboratory channels. The writer has observed,
however, during re-examination of his own
experimental data1 8 that in certain cases of
small rectangular channel bends, where the
bed was rough and "Re" reasonably large, the
116
-------
Russian formula is a good approximation. It
should be added that the Russian formula (4)
can be easily derived from either formula (2)
or (3): W = B + 2d. In shallow, wide channels,
the influence of "Re" or "f' will be small,
and as "B" (width) will tend to be constant, it
is obvious that formula (4) is a "blanket"
variation of formula (2) or (3).
Because the subject of helical flow is still
not very well known, care must be practiced
in accepting the published results of
experiments and, particularly, of their
interpretation. For example, it is difficult to
accept without further study the helix pattern
in the stratified flow at very low "Re," as
reported in reference 5, Mode A. This applies,
as well, to the statement in reference 2 and
reference 10 that the strength of helical
motion depends only on the ratio of
depth-to-width. Obviously it must also
depend on the ratio of width-to-central radius
and on the resistance to flow. In certain cases
control of the entry to the bend may be
suspected, resulting in unacceptable
experimental results. This is difficult to
establish in some published references. A
mathematical analysis has been
attempted1'6'7'9'12'13 but none of the
results so far achieved seem to be of much
help to the practical design. Recent studies on
turbulence21 by Yalin would seem to
demonstrate the origin of the existence of
helical motion in straight channels. The
existence of helical multicellular flow in
straight channels has been reported in several
references, not quoted here, for a long time.
Therefore, there has been some progress in
the mathematical analysis. On the other hand,
the general information on the behaviour of
liquids, and particularly of water, at the
molecular level, obviously most important in
the boundary layers phenomena, is still, to
say the least, incomplete. The recent opinions
of physicists with regard to the present
progress in this direction are rather
pessimistic.2 2
The Main Overflow Chamber
a) The shape of the main chamber, with
the deepest part at the inside wall is a novelty,
and to the writer's knowledge this shape has
never been investigated. Some Russian studies
included trapezoidal and triangular channels
but, because the research was oriented
towards the meanders of natural rivers, the
deepest part was always at the outside bend.
The triangular channel investigated by the
writer and described in his PhD thesis18 was
also deepest at the outside wall.
b) The reasons for adopting the novel
shape are as follows: It has been found by
Wadekar1 and confirmed by recent studies
carried out under Professor E. Mosonyi at the
University of Karlsruhe in Germany2'3 that in
a single bend the line of the maximum
velocity which at the entry to a curved
channel is at the inside wall, remains there
only up to about 40 degrees to 60 degrees of
the bend. Further, it crosses the channel and
remains at the outside wall up to 180 degrees
of the bend.
To the writer's knowledge, a bend longer
than 180 degrees has not yet been
investigated. Moreover, the region between 40
degrees and 60 degrees of the bend is where
the bottom slow water is already at the top.
In the writer's opinion, this region, in fact,
occurs a little further downstream, perhaps at
about 80 degrees of the bend. At the same
region, a second smaller helix forms at the
outer wall and grows bigger along the bend
downstream. This is now firmly established,
although there is still controversy with regard
to the ratio of width-to-depth which may
have an influence on the formation of the
second helix.2 In any case, at a region around
60 degrees of the bend the motion changes
from that of a free vortex to a composite
vortex. In the proposed novel,shape of cross
section, the line of maximum velocity will be
kept at the inside wall for a greater length of
the bend and so the upturning of the slow
bottom water will occur further downstream.
Therefore, the general condition of helical
flow should be stable for a longer distance
along the bend.
c) The relative strength of helical flow
was approximated by the writer as
S= 10tana0 %
where S = qs/ q or the ratio of the transverse
unit discharge to the forward unit discharge
and «0 is the bottom angle of flow at the
117
-------
center line of the rectangular curved channel.
The unit discharge is the discharge per unit
width at the center line of the channel.
The above-mentioned recent German
work carried out under Professor Mosonyi
(Ref. 3) has confirmed the writer's
approximation, except that S was integrated
across the channel and therefore Mosonyi's S
is only about 50 percent of the writer's S. Of
course,
-------
The Inlet
a) The inlet as now adopted is an open
channel transition 3.04 m (10 ft) long based
on an idea of a long diffuser of five degrees.
In the suggested design the open channel
diffuser is followed by 1.52 m (5 ft) length of
open channel of the same cross section as the
main overflow chamber.
b) To the writer's knowledge the
problem of stratification in storm sewage has
never been properly investigated. The solids in
storm water are seldom greater than 2,000
mg/1; the normal content is around 300 to
600 mg/1, or even less. BOD and ammonia are
linked to the solids in a very complex manner.
If the velocity in the incoming sewer is
around 1.82 m/sec (6 ft/sec) it is probably
not possible to say with any certainty
whether the flow is stratified or not; this will
depend on the content of solids and also on
their size. In addition, there is a problem of
flocculation; in fact, as far as the writer
knows, the subject is still obscure. However,
with a high content of solids it would be
surprising if there were no stratification.
c) The problem of waves of discharge is
further complicated by the well-known fact
that storm discharge is seldom uniform. It
occurs in the waves of high discharge lasting
five to ten minutes, which may be followed
by reasonably steady conditions of flow.
Often one incident of overflow demonstrates
two or even three waves. This means that the
hydrograph of storm runoff may be quite
complex. In long sewers the waves of the
runoff are attenuated, but never completely.
The result of these conditions is that the
content of solids is extremely variable because
each wave may contain more solids than in
steady flow.
d) The intended purpose of the inlet is to
decelerate the flow in a uniform manner and
to direct the region of the maximum velocity
to the inner wall of the main overflow
chamber. The straight section downstream
should result in reasonably steady conditions
with regard to any stratification.
e) The helical flow in open channel
bends with stratified liquids adds a further
complexity which has been described in
Reference 5. It has been found that the
helical flow in the bends of open channels
with two stratified liquids occurs in at least
three modes:
1. If stratification is complete and
velocity is low the heavy bottom
liquid is almost free of helical motion
and behaves as a false bottom. There
is then no helical motion in the
denser liquid but the helix in the
lighter liquid was observed to be of
the opposite nature than in the
normal flow, that is, the top
direction was towards the inner wall.
Such conditions may not be bad for
an overflow but probably they
seldom occur, if ever, in sewers. The
model observations carried out by
the Mersey River Authority
Hydraulic Laboratory have
demonstrated good results with salty
water at the bottom of the overflow
chamber but the Reynolds number in
the above experiments was always
greater than Re = 3500, as quoted in
Reference 5 for mode 1.
2. If the stratification is prominent and
the velocity is greater, the heavier
bottom liquid forms its own helix
which mixes only to a small degree
with the top helix of the lighter
liquid. The heavy liquid tends to
remain at the inner wall for at least
90 degrees of the bend. It is probable
that such conditions occur in the
storm water curved overflows if the
solids content is sufficiently large.
The lighter liquid may demonstrate
the presence of two helices after
about 60 degrees of the bend. It is
hoped that the model may provide
some information on this subject.
3. If the stratification is less prominent
or if the velocity is still higher, both
liquids will mix to a large degree and
only one helix occurs as in an
ordinary non-stratified flow. But
even then the heavier liquid is at the
inner wall for at least 45 degrees of
the bend. This case is probably
common in the curved stormwater
overflows if the content of the solids
is average.
119
-------
f) It is now an open question whether a
curved overflow should be designed for
conditions (2) or (3). The design for
conditions (3) would require a short side weir
starting at about five degrees of the bend and
finishing at about 55 degrees of the bend.
Design for conditions (2) would result in a
longer weir, up to 70 degrees or 80 degrees of
the bend. Again, experiments with the model
should result in a reasonable compromise
recommendation for the design. The model
investigated in Reference 5 was small; the
highest Reynolds number was only 9200.
Therefore, the question of stratification is still
far from being clarified.
g) The behavior of a model with steady
flow will not reproduce the effect of the
discharge waves. Such waves will invariably
disturb the helical motion and they will
decrease the efficiency of the overflow.
However, this problem is common to all the
types of stormwater overflow.
h) In view of the above discussion it is
possible that the proposed novel cross section
of the main overflow chamber may produce
better results than any other cross section;
this was an additional reason for the proposed
novel cross section. But it is evident that the
symmetrical cross section and the cross
section deepest at the inner wall should also
be investigated.
The Outlet
In British practice, a stormwater overflow
passes to the treatment works 6 to 7 DWF, or
sometimes even 8 DWF. It is, then, a
relatively simple matter to design an outflow
chamber in which the floating debris goes
over the end weir and the outflow is
controlled by the outflow sewer of such
dimensions as are dictated by the downstream
conditions. However, even with 7 DWF going
to treatment, variations in the outflow
discharge are observed, which are probably
caused by floating material accumulating in
the outlet chamber and temporarily
decreasing the capacity of the outlet sewer.
This, in turn, results in temporarily larger
overflows. This effect is not very large but it
does exist. The requirement of the APWA
Research Foundation is to pass 3 DWF to the
treatment works, and in such conditions the
effect may be more serious. The design of the
outflow chamber depends much on the
dimensions of the incoming sewer; for large
sewers it will be easier than for small sewers.
Alternative Design
The alternative design represented in
Figure 92, Alternative Design for Future
Investigation, may be an improvement as
compared with a simple overflow.-It would
seem to be possible, practical, effective, and
not particularly expensive.
The general concept is that, in addition to
the main chamber, the side weir and the end
outflow similar to those described already,
three side pipes should be installed at the
inner wall of the main chamber. These pipes
are connected into a side sewer of small
diameter which discharges into an end
manhole and which is closed by a flapgate.
The smallest flapgates obtainable in the
United Kingdom are 7.62 cm (3 in.) in
diameter.
A rough examination of discharges
demonstrates that such a design will work
safely if the inlet pipe is not smaller than
about 60.5 cm (2.0 ft) diameter. Then the
draw-off small sewer would be about 10.18
cm (4 in.) diameter and the off-take pipes
could be either 7.6 or 10.8 cm (3 or 4 in.)
diameter. The flapgate should then be
balanced in such a way that it would open
only if the inflow was almost 3 DWF, say 2.5
DWF. This would prevent the side pipes from
silting.
The actual design may be different than
that shown. For example, it would help if the
invert of the end or foul sewer passing to the
treatment works were approximately 15,24
cm (6 in.) lower than the invert of the main
overflow chamber. Also, the small diameter
side sewer could be straight, discharging
directly without a flapgate.
The main factor in the above alternative
is to avoid the silting up of the side pipes and
of the small diameter collecting sewer. The
flapgate should be balanced in such a way
that the velocity in the side pipes is. not
smaller than 60.5 cm/sec (2 ft/sec). The
alternative suggested in Figure 00 should be
easier to design for large than for small inlet
sewers. For example, if the inlet sewer were
120
-------
To treatment works .
FIGURE 92 ALTERNATIVE DESIGN FOR FUTURE INVESTIGATION
121
-------
90.5 cm (3.0 ft) diameter the draw-off sewer
would be about 20.32 cm (8 in.) diameter and
the side pipes could be 12.7 cm (5 in.)
diameter. It is possible that with the above
alternative, a simple symmetrical cross section
similar to that in the Nantwich overflow
might produce satisfactory results, but the
sharp edges should be eliminated. It is also
possible that the velocity in the main chamber
could be increased.
It is recommended that the above
possibilities should be investigated. It might
be sufficient to have only two side pipes. The
position of the side pipes and the position and
the length of the side weir should also be
investigated. The side pipes would discharge
directly to the side spill channel but some
means for collecting samples should be
provided.
Review of Laboratory Techniques
Known to the Writer
The list below is given in approximate
order of time when the reference was
published.
1. Shukry1 s has used the Pilot-sphere. Some
of his results are open to doubt because it
is evident that there was no proper
control of the entry to the channel bend.
2. Malouf16 used only the black dye —
Process Black — and the local velocity
was not measured.
3. Prus-Chacinski17'18 used Process Black
paint, small lighted floats, and the nylon
threads for direction measurements, using
an accurate protractor. Velocity was
measured by a pitometer.
4. Wadekar1 improved greatly on the
methods of (2) and (3). In addition to
Process Black paint he used droplets of
Meridian-unity oil (S G 1.002) as a tracer
for small velocities, and polystytene sand
(1 mm dia. SGI .06) as a tracer for larger
velocities. For the direction inside of the
channel, nylon threads and an accurate
protractor were used.
The surface direction and velocities were
measured by a sophisticated method of
photographing the surface wave patterns.
He was able to observe accurately the
direction of flow on the walls of his
rectangular channel because it was all
constructed of Perspex.®
5. The Russean researches known to
date6-7-13 have used methods similar to
those described under (2), (3) and (4). In
addition, the density flow effects were
investigated,13 demonstrating patterns, in
general, similar to those described in
Reference 5 case (3).
6. Fox and Bell8 used nylon thread as
direction indicators for velocity
measurement. They used a heat-transfer
recorder (not described) for velocities
smaller than 9.15 cm/sec 0.3 ft/sec), and
a multi-propeler or current meter with an
ultraviolet light recorder (not described)
for larger velocities.
7. Prus-Chacinski and Wielogorski19 used
Process Black paint and an accurate
protractor, plastic sand, orange colored (S
G 1.00), coal dust (particle size 0.1 to 1.0
mm), and polystyrene beads (S G 1.05)
for the bed patterns, and nylon thread for
direction inside of the channel. The
plastic sand also demonstrated the general
pattern of the helix in the body of the
flow. Perspex® shavings were used to
observe the surface flow direction. Local
velocities were not measured.
8. The Mersey River Authority, with the
cooperation of C. H. Dobbie and
Partners2 °, used the Process Black paint
and potassium permanganate. Potassium
permanganate was not satisfactory. The
threads were used, as already mentioned.
Local velocities were measured by a
mini-current meter. For surface flow
tracer, plastic beads were used. In addition
the density flow was investigated by
injecting the salty water colored by po-
tassium permanganate upstream of the
inflow. The results were most satisfactory
but only if the injection point was very
near to the bed. The analysis of overflow
was carried out, using the conductivity
meter.
9. Macagno and Alonso5 measured velocities
and densities with a constant temperature
hot-wire anemometer and electrical
conductometer, respectively. The signals
were processed through an IBM DACS.
122
-------
10. Francis and Safari9-10 used tracers and
sophisticated photographic and lighting
equipment. For laminar flow they used
TF.LCO powder (S G 0.9) with grain size
0.1 to 0.2 mm; turbulent flow droplets
(quite large) were formed by the mixture
of nitrobenzene, olive oil,,and water (S G
1.0). The rectangular channel had glass
windows in the walls. Local velocities
were not measured. It is possible that the
entry to their experimental channel was
not free from helical motions.
11. Mosonyi and- Gotz and Siebart and
Musers2'! 4used the hot-film anemometer
and a fibre-wire probe for -the local
velocity and local direction
measurements. This procedure seemed to
produce excellent results.
SYMBOLS USED
rc central radius of the bend in a
rectangular channel
Re Reynolds Number
C constant dependent upon depth
K constant to describe strength of helical
flow
W wetted perimeter
f friction factor
<*0 bed angle of
s strength of helical flow
qs/q forward unit discharge
B width of rectangular channel
d depth of rectangular channel
REFERENCES
Only a short list of references which introduce some new observations will be quoted below.
Otherwise, a long list of references is contained in the writer's PhD Thesis and in his paper
(together with Wielogorski):
Secondary motions applied to Storm Sewage Overflows
Symposium at the ICE, London, 1967
1. G. T. Wadekar, Secondary Flow in
Curved Channels, Unpublished PhD
Thesis, Imperial College, London, 1956.
2. Emil Mosonyi and Werner Gotz,
Secondary Currents in Subsequent Model
Bends, International Association for
Hydraulic Research, International
Symposium on River Mechanics,
Bangkok. January 1973.
3. E. Mosonyi and G. Meder, Effects of
Scale Distortion on Flow Properties in
Model Meanders, The Rehbock
Laboratory for River Improvement,
University of Karlsruhe, Germany, 1973.
4. P. Ackers, A Theoretical Consideration of
Side Weirs as Storm-Water Overflows,
Proceedings, Institute of Civil
Engineering, London, Febraury 1957.
5. E. O. Macagno and C. V. Alonso,
Two-layer Density-Stratified Flow in an
Open Channel Bend, International
Association for Hydraulic Research,
Proceedings of 14th Congress IAHR,
Paris, 1971
6. I. L. Rozovskii, Flow of Water in Bends
of Open Channel, (Translated from
Russian), The National Science
Foundation, Washington, D. C., 1967
(The Russian original, Kiev, 1957).
7. A. K. Ananyan, Fluid Flow in Bends of
Conduits, (Translated from Russian),
Israel Programme for Scientific
Translations, Jerusalem, 1965. (Russian
original, Erevan, 1957).
8. J. A. Fox and D. J. Bell, The Analysis of
Secondary Flow in Bends in Open
Channels, Proceedings, ICE, London,
March 1968.
9. J. R. D. Francis and A. F. Asfari,
Velocity Distributions in Wide, Curved
Open Channel Flows, Journal of Hyrauh'c
Research No. 1, 1971.
10. J. R. D. Francis and A. F. Asfari,
Visualisation of Spiral Motion in Curved
Open Channels of Large Width, Nature,
London, February, 1970.
11. Yoshio Muramoto, Secondary Flows in
Curved Open Channels, International
Association for Hydraulic Research,
Proceedings, 12th Congress IAHR, Paris,
1967.
123
-------
-------
tfc"..
------- |