CORMIX1 AN EXPERT SYSTEM FOR MIXING ZONE ANALYSIS OF
CONVENTIONAL AND TOXIC SINGLE PORT AQUATIC DISCHARGES
by
Robert L. Doneker and Gerhard H. Jirka
DeFrees Hydraulics Laboratory
Department of Environmental Engineering
Cornell University, Ithaca, New York 14853
Cooperative Agreement No. CR813093-01-0
Project Officer
Thomas 0. Barnwell, Jr.
Assessment Branch
Environmental Research Laboratory
Athens, Georgia 30613
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30613
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FOREWORD
The information in this document has been funded wholly
or in part by the United States Environmental Protection
Agency under Cooperative Agreement number CR813093 to Cornell
University. It has been subjected to the Agency's peer and
administrative review, and it has been approved for publication
as an EPA document.
11
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Table of Contents
Abstract iv
List of Tables vii
List of Figures viii
Acknowledgements x
Chapter I Legal Background and Introduction 1
l.A History of the Clean Water Act 1
I.A.I The Federal Water Pollution Control
Act of 1972 3
l.A. 2 The Clean Water Act of 1977 4
l.B Development of Mixing Zone Concept 8
l.C Special Mixing Zone Requirements for Toxics 12
l.D The NPDES Permit System 12
l.E Need for Regulatory Assessment Tools .... 13
l.F Justification for Expert Systems Approach . 14
l.G CORMIX1 Summary 17
Chapter II Hydrodynamic Background on Mixing Processes . 18
2.A Analysis of Subsurface Flow Regions .... 18
2.A.I Description of Turbulent Jets and
Plumes 20
2.A.2 Elements of Dimensional Analysis of
Buoyant Jets 20
2.A.2.1. Simple Jet in Stagnant
Environment 21
2.A.2.2. Simple Plume in
Stagnant Environment 23
2.A.2.3 Generalizations: Jet/Plume
Interactions and Effects of Crossflow 25
2.A.3 Length Scales for Buoyant Jets With or
Without Crossflow 25
2.A.3.1 Discharge Length Scale .... 25
2.A.3.2 Jet/Crossflow Length Scale . . 27
2.A.3.3 Plume/Crossflow Length Scale . 27
2.A.3.4 Jet/Plume Length Scale .... 27
2.A.4 Typical Regimes of Buoyant Jets ... 28
2.A.4.1 Weakly Deflected Jet in
Crossflow (mdnf) 28
2.A.4.2 Strongly Deflected Jet in
Crossflow (mdff) 29
2.A.4.3 Weakly Deflected Plume in
Crossflow (bdnf) 30
2.A.4.4 Strongly Deflected Plume in
Crossflow (bdff) 31
2.A.4.5 General Behavior in Unbounded
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Crossflow 31
2.B Flow Interaction With Free Surface 38
2.B.I Flow Classification of Near-Field
Regions 38
2.B.2 Analysis of Surface Interaction
Processes 38
2.B.2.1 Near Horizontal Surface
Approach 44
2.B.2.2 Near-Vertical Surface
Impingement With Buoyant Upstream
Spreading 44
2.B.2.3 Near-Vertical Surface
Impingement With Full Vertical Mixing 48
2.B.2.4 Near-Vertical Surface
Impingement With Unstable
Recirculation, Buoyant
Restratification, and Upstream
Spreading 48
2.C Analysis of Far-Field Mixing Process .... 50
2.C.I Buoyant Surface Spreading 50
2.C.2 Passive Diffusion 52
2.C.3 General Behavior in the Far-Field . . 54
Chapter III CORMIX1 Program Structure 56
3.A Discussion of Logic/Ml Elements 58
3.A.I DATIN 59
3.C.2 CLASS 63
3.C.3 SUM 64
3.C Discussion of Hydrodynamic/Fortran Elements 65
3.C.I PARAM '" 65
3.C.3 HYDRO 65
Chapter IV Data Comparison and Validation 69
4.A Near Field Flows (sub-surface regions) ... 69
4.B Near Vertical Surface Impingement With
Buoyant Upstream Spreading 72
4.3 Unstable Surface Impingement With Buoyant
Upstream Spreading . 79
4.4 Summary 79
Chapter V Design Case Studies 81
5.A Case 1: AB CHEMICAL CORP., WEST VIRGINIA ... 81
5.A.I The Problem Statement 81
5. A. 2 CORMIX1 Analysis 82
5.B Case 2: SAN ONOFRE UNIT 1 85
5.B.I The Problem Statement 85
5.B.2 CORMIX1 Analysis 87
Chapter VI Conclusions and Recommendations 89
References
91
VI
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APPENDIX A (Vol. II) 95
A.I DATIN (Vol. II) 96
A.2 CLASS (Vol. II) 138
A.3 SUM (Vol. II) 178
A. 4 PARAM (Vol. II) 200
A. 5 HYDRO (Vol. II) 216
APPENDIX B (Vol. II) 304
B.I AB Chemical Co. Analysis (Vol. II) 305
B.2 San Onofre Analysis (Vol. II) 329
VII
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- List of Tables
Table 1.1 Key Federal Water Pollution Control Laws
Table 1.2 Examples of Conventional, Nonconventional,
and Toxic Pollutants
Table 1.3 Examples of Technology-Based Effluent
Limitations Under The Clean Water Act of 1977 7
Table 1.4 State Legal Mixing Zones 10
Table 2.1 Trajectory and Dilution Relations 32
Table 2.2 Trajectory and Dilution Constants 33
Table 2.3 Flow Transition Rules 37
Table 3.1 Hydrodynamic Simulation Modules 67
Table 3.2 Hydrodynamic-Simulation Protocols 68
Vlll
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List of Figures
Figure 2.1 Illustrative Near Field and Far Field of Submerged
Buoyant Discharge 19
Figure 2.2 Pure Jet in Stagnant Environment 22
Figure 2.3 Simple Plume in Stagnant Environment 24
Figure 2.4 Examples of Combined Effects of Momentum Flux,
Buoyancy Flux and Crossflow on Flow Behavior 26
Figure 2.5 General Behavior for Buoyant Jets in Unconfined
Crossflow 35
Figure 2.6 Flow Classification System 39
Figure 2.7 Four Major Conditions of Flow Interaction with
Water Surface 40
Figure 2.8 Buoyant Surface Spreading 51
Figure 2.9 Passive Diffusion Process 53
Figure 3.1 System Elements of CORMIX1 57
Figure 3.2 Schematization of Discharge Configuration . . 60
Figure 4.1 Fan's Buoyant Jet Trajectory, Expr. 20-12, R = 1270
Figure 4.2 Fan's Buoyant Jet Trajectory, Expr. 40-4, R = 4 71
Figure 4.3 Fan's Buoyant Jet Dilution, Expr. 20-12, R = 12 73
Figure 4.4 Fan's Buoyant Jet Dilution, Expr. 40-4, R = 4 .74
Figure 4.5 Wright's Buoyant Jet Trajectory, Expr. 2-2 ... 75
Figure 4.6 Flatten and Keffer, 9o = 60.0" 76
Figure 4.7a Simulation of Stable Surface Impingement/Upstream
Spreading 77
Figure 4.7b Plan View of Surface Impingement/Upstream
Spreading 78
Figure 4.8 Plan View Comparison of San Onofre Prediction and
Field Data 80
Figure 5.1 Schematization of Cross-section 83
IX
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Figure 5.2 Plot of CORMIX1 AB Chemical Co. Predictions . . 86
Figure 5.3 San Onofre Longitudinal Cross-Section 87
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Acknowledgements
This study was conducted at Cornell University in
cooperation with the Environmental Research Laboratory,
Athens, Georgia. The authors want to extend their
appreciation to Dr. Thomas O. Barnwell, Jr., project officer,
who provided the initial stimulus and further guidance
throughout the study.
The authors also acknowledge the assistance given by Dr.
Anil Nerode, Chairman, Department of Mathematics, Cornell
University, in the development of expert system structure and
logical elements. Dr. Joseph H.-W. Lee, University of Hong-
Kong, helped in the formulation of trajectory laws for the
submerged jet phases during his sabbatical stay at Cornell
University -
The work was carried out using the computer facilities of
the DeFrees Hydraulics Laboratory. Mr. Cameron Willkens,
electronic technician, assisted in computer hardware and
software problem solutions.
XI
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Chapter I
Legal Background and Introduction
l.A History of the Clean Water Act
Prior to 1948, States, local, and regional agencies were
primarily responsible for controlling water pollution. After
the realization in the mid-1800's of the role of contaminated
water in the transmission of disease, State Boards of Health
were formed to administer water pollution control programs.
Most early pollution control programs focused on water-borne
infectious diseases like typhoid and cholera (Ortolano,1S84).
Table 1.1 outlines key federal water pollution control
legislation since 1943. The 1948 Water Pollution Control Act
was designed to provide technical services to the States to
strengthen their water pollution control programs. The 1948
Act focused on the primacy of the State role in water quality
management. Federal action against polluters could only be
taken with the consent of the State from which the pollution
was alleged to originate.
The Federal Water Pollution Control Act (FWPCA) of 1956
expanded the federal role in controlling water pollution. The
Act provided a program of subsidies for municipal treatment
plant construction, strengthened powers of enforcement against
polluters, increased funding for State water pollution control
efforts, and provided new support for research and teaching.
Each of these programs were included in the many
amendments to the Act in the 1960's and 1970's.
The Water Quality Ace of 1965 set new requirements for
States to establish ambient water quality standards and
increased the level of federal funding. Water quality
standards were designed to protect designated water uses
within a stretch of river. The Act required that State
agencies set water quality criteria to meet these standards.
Criteria established the suitability of water for different
activities. If the uses of water within a stretch of river and
the criteria designed to protect those uses were known,
ambient water quality standards could be set.
I.A.I The Federal Water Pollution Control Act of 1972
Prior to the 1972 Federal Water Pollution Control Act
(FWPCA) only States had power to develop ambient water quality
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Table 1.1 Key Federal Water Pollution Control Laws
Source: Ortolano, 1984
Year
Title
Selected New Elements
of Federal Strategy*
1948
Water Pollution
Control Act
1956
Federal Water
Pollution Control
Act (FWPCA)
1965
Water Quality Act
1972
FWPCA Amendments
1977
Clean Water Act
1981
Municipal Waste
Treatment
Construction
Grants Amendments
Funds for State water
pollution control
agencies
Technical assistance to
States
Limited provisions for
legal action against
polluters
Funds for water pollution
research and training
Construction grants to
municipalities
Three stage enforcement
process
States set water quality
standards
States prepare
implementation plans
Zero discharge of
pollutants as a goal
BPT and BAT effluent
limitations
NPDES permits
Enforcement based on
permit violations
BAT requirements for
toxic substances
BCT requirements for
conventional pollutants
Reduced federal share in
construction grants
program
* The table entries include only significant new
changes established by the law.
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standards applicable to interstate or navigable waters. Water
quality standards depended upon intended use -agricultural,
industrial, or recreational.
Enforcement of water quality standards was only possible
if water quality fell below standards. This hampered
enforcement efforts because proof of causation was difficult
in waters receiving wastes from various polluters. State
water quality standards could be lowered to attract industry
away from States with more stringent water quality standards.
Congress decided to take rigorous action in 1972 with the
FWPCA amendments. The Act established a uniform system of
water quality standards, permits, and enforcement. The
"goals" of the legislation were to produce fishable, swimmable
water by 1983 and a total elimination of water pollution by
1985 (Findley and Farber, 1983) .
Major changes in the FWPCA of 1972 included i) national
water quality goals, ii) technology-based effluent
limitations, iii) a national discharge permit system, and iv)
federal court action against sources in violation of permit
conditions (Ortolano, 1984).
Congressional intent in passing the FWPCA was to rule out
arguments of assimilative capacity of receiving waters.
Congress wanted uniformity of standards and enforcement.
Ambient water quality standards were intended to be "more
stringent" than effluent standards. The aim of the 1972
amendments was to restore and maintain "the chemical,
physical, and biological integrity of the nation's waters"
(Weyerhauser Co. v. Costle 590 F.2d 1001).
The 1972 amendments gave broad powers to the federal
Environmental Protection Agency (USEPA) administrator to
define pollutants and to determine and promulgate effluent
limitations. Effluent limitations were set according to
industry through the National Pollution Discharge Elimination
System (NPDES) permit system. These discharge limits were set
independent of the particular context in which the pollution
discharge occurs. Dischargers in violation of NPDES pollution
limits were subject to enforcement action.
The Act contained ambient water quality standards that
supplemented federal discharge standards for point sources.
Point sources were defined as "any discernable, confined, and
discrete conveyance .... from which pollutants are, or may be
discharged."
The 1972 FWPCA required that industry dischargers meet
"best practicable control technology currently available"
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(BPT) standards by 1977 and "best available technology
economically achievable" (BAT) standards by 1983.
The Act required public sources of pollution to use
secondary treatment by 1977 and use "best practicable waste
treatment over life of the works" by 1983.
Specific sections of the Act include:
Section 301 of the Act set standards for point sources
that were not publicly owned treatment works (POTW). It
requires dischargers to reduce emissions using "best
practicable control technology currently available" (BPT) by
1977 and "best available technology economically achievable"
(BAT) by 1983.
Section 302 of the Act set ambient water quality
standards. Ambient water quality standards were to comply
with State or federal law, whichever was more stringent to
achieve ambient water quality goals.
Section 306 of the Act pertains to new sources. This
section required such facilities to meet standards equivalent
to 1983 BAT standards.
Section 307 covers toxic water pollutants. It requires
that standards be developed for toxic water pollutants based
on public health and welfare and not technical feasibility.
Section 402 of the Act empowers the federal government to
create a National Pollution Discharge Elimination System
(NPDES). This pollution permit system empowers the USEPA to
set national effluent standards and grants States, with USEPA
approval, the responsibility of administering the program.
NPDES applies to any discharge to receiving waters. NPDES
permits had to incorporate applicable limitations under
sections 301, 302, 306, and 307 of the Act, including
enforcement to meet 1977 and 1983 deadlines.
Section 505 of provides the right of citizen suits to
enforce provisions of the Act. States have the primary
responsibility to enforce the provisions of the Act, but the
Federal government has the right to step in and enforce any
provision of the Act.
1.A.2 The Clean Water Act of 1977
In 1977 the FWPCA was amended by congress. These
amendments are known as the Clean Water Act (CWA). Five
general categories of pollutants covered in the Act are;
i) conventional, ii) nonconventional, iii) toxics, iv) heat.
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and v) dredge and fill spoil. The Act distinguishes between
new and existing source for setting effluent standards. Table
1.2 lists examples of the first three pollutant catagories.
Pollutants designated as "conventional" would be "as
defined by the administrator in compliance with the Act as
amended, generally those pollutants that are naturally
occurring, biodegradable, oxygen demanding materials and
solids. In addition, compounds which are not toxic and which
are similar in characteristic to naturally occurring,
biodegradable substances are to be designated as conventional
pollutants for the purposes of the provision" (Congressional
Research Service-, 1977) .
Pollutants designated as "nonconventional" would be "those
which are not toxic or conventional." (Congressional Research
Service, 1977). Table 1.3 illustrates the kinds of effluent
standards set by USEPA under the 1977 amendments.
A new class of effluent standards called "best
conventional pollution control technology" (BCT) were created
for conventional pollutants. Cost consideration could be
taken into account by USEPA in determining BCT effluent
regulations for conventional pollutants, but not for
nonconventional pollutants or toxics.
Congress modified BAT standards in the Clean Water Act of
1977. This action was in response to criticism the original
BAT effluent limitations required too high a percentage
removal of pollutants and the cost of reduction in these
residuals would be much greater than the benefits. BAT
standards apply to unconventional and toxic pollutants.
A variance provision for BAT standards for nonconventional
pollutants is contained in section 301(g) of the Act. It
allows the USEPA along with State approval to modify effluent
standards for nonconventional pollutants if this did not
interfere with water quality standards or public health.
All river segments within States are classified as water
quality limited or effluent limited under section 303 (e) of
the Act. Effluent limited segments are defined as those
stream reaches for which ambient water quality standards can
be met in 1977 by application of best practicable control
technology currently available (BPT) to industry and secondary
treatment to publicly owned treatment works (POTW). When
ambient water quality standards can not be met by BPT for
industry and secondary treatment for POTW, these reaches are
classified as water quality limited.
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Table 1.2 Examples of Conventional, Nonconventional,
and Toxic Pollutants
Source: Technical Guidance Manual For The Regulations
Promulgated Pursuant to Section 301(g) of the CWA 1977
Conventional
Nonconventional
biochemical
oxygen demand
(BOD)
PH
total suspended
solids(TSS)
fecal coliform
bacteria
chemical
oxygen demand
(COD)
chlorine
aluminum
barium
zinc
cyanides
toluene
benzene
asbestos
oil and grease
ammonia
copper
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Table 1.3 Examples of Technology-Based Effluent
Limitations Under The Clean Water Act of 1977
Source: Ortolano, 1984.
Publicly Owned Treatment Works:
Requirements for 85% BOD removal, with possible case-
-by-case variances that allow lower removal
percentages for marine discharges.
Industrial Discharges (bases for effluent limitations)
Toxic pollutants - BAT
Conventional pollutants - BCT; in determining required
control technology, USEPA is directed to consider ''the
reasonableness of the relationship between the costs of
attaining a reduction in effluent and the effluent
reduction benefits derived."
Nonconventional pollutants - BAT, but with possible
case-by-case variances that allow for lower degrees of
treatment.
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l.B Development of Mixing Zone Concept
The concept of a mixing zone is defined as an "allocated
impact zone" where numeric water quality criteria can be
exceeded as long as acutely toxic conditions are prevented. A
mixing zone can be thought of as a limited area or volume
where the initial dilution of a discharge occurs (Water
Quality Standards Handbook,1982). Water quality criteria
apply to the boundary of the mixing zone, not within the
mixing zone itself. EPA and its predecessor agencies have
published numerous documents giving guidance for determining
mixing zones such as the National Academy of Science Water
Quality Criteria 1968 (Green Book), EPA publications Quality
Criteria for Water 1976 (Red Book), and Guidelines for State
and Area Wide Water Quality Management Program. Guidance
published by EPA in Water Quality Standards Handbook (Oct.
1982) supersedes these sources.
In setting requirements for mixing zones, USEPA requires
that the size be "the area or volume of an individual zone or
group of zones be limited to an area or volume as small as
practicable that will not interfere with the designated uses
or with the established community of aquatic life in the
segment for which the uses are designated" and the shape be "a
simple configuration that is easy to locate in the body of
water and avoids impingement on biologically important
areas.... shore hugging plumes should be avoided." Within the
mixing zone USEPA requires "any mixing zone should be free of
point or nonpoint source related:
(a) Material in concentrations that will cause acute
toxicity to aquatic life;
(b) Materials in concentrations that settle to form
objectionable deposits;
(c) Floating debris, oil scum and other matter in
concentrations that form nuisances;
(d) Substances in concentrations that produce
objectionable color, odor, taste or turbidity; and
(e) Substances in concentrations which produce
undesirable aquatic life or result in a dominance of
nuisance species."
(USEPA, Water Quality Standards Handbook, 1982) .
The proposed rules for mixing zones recognizes the State
has discretion whether or not to adopt a mixing zone and to
specify its dimensions. USEPA allows the use of a mixing zone
in permit applications except where one is prohibited in State
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regulations. State standards require that water quality
criteria be met at the edge of the regulatory mixing zone 1)
to provide a continuous zone of free passage that meets water
quality criteria for free-swimming and drifting organisms and
2) to prevent impairment of critical resource areas (USEPA,
Technical Support Document for Water Quality-based Toxics
Control, 1985). A review of individual State mixing zone
policies shows that 48 out of 50 States make use of a mixing
zone in some form and can be seen in Table 1.4
For discharges into streams, 17 of the 31 States that
propose a mixing zone specify that the mixing zone shall not
exceed 1/4 of the cross-sectional area and/or volume of the
stream flow, and the remaining 3/4 of the stream shall be
maintained as a zone of passage for swimming and drifting
organisms.
The remaining States have varying requirements allowing
dimensions of the mixing zone to be as low as 1/5 of the
cross-sectional area (Ohio) to as much as 3/4 of the cross-
sectional area (South Dakota). West Virginia is the only
State that specifies a length dimension for mixing zones. The
length of the mixing zone must be less than 10 times the
average width of the stream or less than 5 times the average
width of the stream for warm water and cold water streams,
respectively.
In States which specify a mixing zone for lakes,
dimensions for the mixing zone vary from 10% of the surface
area of the lake to 300-1000' radial limits around the
discharge point.
Pennsylvania and Arizona are the two States that do not
make reference to a mixing zone. Therefore the USEPA does not
recognize any mixing zone for these States and water quality
criteria must be met at the point of discharge unless the
applicant and the State develop a mixing zone on a case by
case basis.
With the exception of West Virginia, the length of the
mixing zone is not specified. Usually, the size of the mixing
zone is determined on a case-by-case basis taking into account
the critical resource areas that need to be protected. Mixing
zones should be used and evaluated in cases where mixing is
not complete within a short distance of the outfall. EPA
recommends careful evaluation of mixing to prevent zones of
chronic toxicity that extend for miles downstream because of
poor mixing. (USEPA, Technical Support Document for Water
Quality-based Toxics Control, 1985).
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Table 1.4 State Legal Mixing Zones
Source: Draft Technical Guidance Manual for the
Regulations Promulgated Pursuant To Section 301(g]
State
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
D.C
Georgia
Florida
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Lake
Minnesota
Mississippi
Missouri
Montana
Nebraska
New Jersey
New Hampshire
New Mexico
New York
Water Body
0
river , streams
lakes
NR
large streams
0
0
streams
streams
lakes
estuary
0
streams , rivers
lakes, estuaries
0
0
all
streams
streams
streams
streams
streams
streams
streams
0
0
streams
Michigan
streams
0
streams
0
0
streams
streams
streams
streams
Dimensions
0
<= 1/3 CS
<= 10% SA
NR
<=l/4 CS
0
0
<=l/4 CS
<=l/3 CS
<=10% SA
<=10% SA
0
<=800 meters
<=10% total length
<=125,600 m**2
(600' radius)
<=10% SA
0
0
<=600' radius
<=l/4 CS
< = l/4 CS
<=l/4 CS
<=l/4 CS
<=l/3 CS
<=l/4 CS
<=l/4 CS
0
0
<=l/4 CS
<=1000' radius
<=l/4 CS
0
<= 1/4 CS
0
0
<=l/4 CS (thermal)
<=l/4 CS
<=l/4 CS
<=l/2 CS (thermal)
10
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Table 1.4 (Continued;
Nevada
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
S. Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
W. Virginia
streams
0
streams
receiving
watercourse
mouth of
receiving
streams
0
NR
streams
0
streams
0
streams
0
streams
0
0
warm water
fish streams
cold water
fish streams
Wisconsin
Wyoming
Guam
Puerto Rico
lakes
streams
0
0
streams
IMZ
FMZ
Virgin Islands streams
Where:
<=l/3 CS
0
<=l/4 CS
<=l/3 CS
<=l/5 CS
<=l/4 CS
0
NR
<=l/4 CS (thermal)
0
<=3/4 CS or
100 yds of streams width
0
<=l/4 CS
0
<=l/4 CS
0
0
<=33% CS, length
<=10*width
<=20% CS, length
<=5*width
<=300' any direction
<=l/4 CS
0
0
<=l/4 CS
<= 400 '
<= 4000 '
< = 1/4 CS
CS = cross-sectional area
NR = no reference
IMZ = initial mixing zone
SA = surface area
0 = not listed
FMZ = Final mixing zone
11
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l.C Special Mixing Zone Requirements for Toxics
In order to prevent lethal concentrations of toxics in the
regulatory mixing zone, regulations can prohibit lethal
concentrations in the pipe itself, or require that a
concentration known as the criterion maximum concentration
(CMC) be met within a short distance from the outfall. The
CMC is a concentration that prevents lethality or acute
affects in tested species. If dilution of the toxic discharge
in the ambient environment is allowed, this requirement, which
will be defined here as a toxic dilution zone (TDZ), is more
restrictive than the legal mixing zone for conventional and
nonconventional pollutants. In order to provide turbulent
mixing that will minimize organism exposure time to toxic
material, the outfall structure must meet the following
requirements for a TDZ (USEPA, Toxics, 1985):
-The CMC must be met within 10% of the distance from the
edge of the outfall structure to the edge of the
regulatory mixing zone in any spatial direction.
-The CMC must be met within a distance of 50 times the
discharge length scale in any spatial direction. The
discharge length scale is defined as the square-root of
the cross-sectional area of any discharge outlet. This
restriction will ensure a dilution factor of at least 10
within this distance under all possible circumstances,
including situations of severe bottom and surface
interaction.
-The CMC must be met within a distance of 5 times the
local water depth in any horizontal direction. The local
water depth is defined as the natural water depth
(existing prior to the installation of the discharge
outlet) prevailing under mixing zone design condition
(e.g. low flow for rivers). This restriction will prevent
locating the discharge in very shallow environments or
very close to shore, which would result in significant
surface and bottom concentrations.
l.D The NPDES Permit System
Any discharge into a navigable watercourse must have a
National Pollution Discharge Elimination System (NPDES)
permit. The permit is designed to insure that the discharge
meets all applicable standards. The permit is granted either
by USEPA, or, if the State has a USEPA approved program, the
State. The applicant must supply the reviewing agency with
all data needed to grant the permit. Data required in the
application include:
Name and exact location of facility
12
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- Nature of business engaged at a facility, including what
is or what will be manufactured
- The manufacturing process and maximum production levels
- Schematic of water flow through the facility
- Exact location, 'flow rates, flow frequencies, and
chemical composition of each facility discharge
- The waste-water treatment currently or to be employed
for each waste stream
- Pollutant test data
l.E Need for Regulatory Assessment Tools
Implementation of the mixing zone policy in the NPDES
permitting process requires that the applicants and regulators
predict the initial dilution of the discharge and the
characteristics of the mixing zone. If the discharge is
toxic, the CMC value must be determined for the discharge and
special requirements for a TDZ must be met within the mixing
zone. Given the large number of possible ambient
environments, discharge configurations, and mixing zone
definitions, the analyst needs considerable training and
experience to conduct accurate and reliable effluent mixing
analysis.
Dilution of the effluent in the receiving water is caused
by different mechanisms along its path. In the "near field"
of the source, dilution is caused mainly by jet induced
entrainment. Further away, in the so-called "far field" the
jet velocity decreases and ambient diffusion becomes the
primary mechanism of effluent dilution.
The most direct way of determining pollutant concentration
downstream is by physical measurement. Non-polluting tracers
can also be injected to give indications of effluent dilution.
Such field studies require considerable time and effort, and
field personnel need specialized training to perform studies
reliably. Field studies are in many cases impractical and
expensive. For example, if in situ observations are used they
must represent conditions that are present during critical
dilutions, not merely a typical dilution (Draft 301 (g)).
Field studies for analysis of dilution for toxic discharges is
patently unacceptable, so simulation must be used to determine
dilutions.
13
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Because of the complexity of the physical mixing process,
permit writers are increasingly relying on mathematical models
to analyze the fate and transport of pollutants (Tait, 1984).
The difficulty with many present models is that they tend to
become specialized and give accurate results only for a
particular type of outfall. The user must be careful to use a
model that was intended to make prediction under the
conditions with which he is concerned (Draft 301 (g)).
USEPA has developed a number of models to predict the
initial dilution of discharges. A few these are PLUME,
OUTPLM, DHKPLM, MERGE, and LINE. Applicants are not required
to use these models in analysis, but must be able to prove
that the methodology chosen gives reasonable estimates of
initial dilution.
l.F Justification for Expert Systems Approach
In determining the characteristics of the mixing zone, the
analyst, either the NPDES applicant or regulatory authority,
may choose from a wide variety of predictive models. The
models range in complexity from simple analytical formulae to
highly intricate numerical solutions to differential
equations. Although the USEPA has prepared assessment manuals
and actually endorsed certain models in specific situations,
the average user has little reliable guidance on which model
is appropriate for a particular situation, or which is
actually best (Mullenhoff, et. al., 1985). Examples of "model
abuse" are ubiquitous. Often unnecessarily complicated models
are employed, creating a needless burden for both regulators
and dischargers.
Even when a particular model is appropriate for a given
discharge, the model may not give reliable results over a wide
range of conditions. Model developers often fail to
explicitly specify limits of applicability, or model users may
simply overlook important restrictions to model applicability.
An example of a frequent error in the application of the USEPA
plume models is the violation of the assumption of the
infinite receiving environment. In reality, the plume may
attach to the bottom or may become vertically fully mixed,
possibilities which may occur due to changes in the ambient
environment such as low flow conditions. Consequently,
analysts have reported model "predictions" in which the plume
diameter exceeds actual water depth!
Once the correct choice of model is assured, the analyst
often faces the considerable task of assembling the required
design data base. This can be a frustrating and cumbersome
task for the unexperienced analyst who has little guidance on
what design base to choose, where to obtain data, which data
14
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is crucial to the analysis, and which data may simply be
estimated. Because of these difficulties, a large investment
in time is required for the analyst to become fully familiar
and proficient with the use of at least one model, or more
likely, a group of models. The analyst in reality must become
highly skilled or an "expert" in the use and interpretation of
number of simulation models. Such expertise in model use
requires expensive training and is rare. This is the reason
for the development of expert system tools for the analyst.
In essence expert systems mimic the way an expert or
highly experienced person would solve a problem. An expert
system is a structured computer program that uses knowledge
and inference procedures obtained from experts for solving a
particular type or class of problem called a "domain". This
knowledge is encoded into a "knowledge base" which enables
inexperienced personnel to solve complex problems by using the
same basic reasoning process that an expert would apply. The
knowledge base includes a set of "objective" or widely
accepted facts about a general problem area. This includes
the set of parameters or data an expert would seek in order to
characterize a specific problem. The inference procedures are
"subjective" rules of judgement which the expert might use
when analyzing the problem. The inference procedures provide
the rules for selecting an appropriate solution to the problem
from the knowledge base. The inference procedures allow the
expert system user to search rapidly and systematically
through the knowledge base to obtain a solution to the given
problem. This element uses structured search techniques based
upon mathematical logic.
The development of an expert system for mixing zone
analysis promises significant advantages compared with
existing conventional simulation techniques for water
pollution control and management:
-it assures the proper choice of model for a given
physical situation.
-it assures that the chosen model is applied methodically
without skipping essential elements.
-it guides the acquisition or estimation of data for
proper model prediction.
-it allows a flexible application of design strategies for
a given point source, screening of alternatives, and if
necessary, switching to different predictive models thus
avoiding rigid adherence to a single model.
15
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-it flags borderline cases for which no predictive model
exists, suggesting either avoidance of such designs or
caution by assigning a degree of uncertainty.
-it allows a continuous update of the knowledge base as
improved predictive models, experimental data, and field
experience with particular designs become available.
-it provides a documented analysis listing the knowledge
and decision logic that have lead to the problem solution.
Thus, unlike conventional programs or computer algorithms
an expert system is not a "black box".
-it provides a common framework whereby both regulators
(Federal or State), applicants, and the scientific
community can arrive at a consensus on the state-of-the-
art hydrodynamic mixing and pollution control.
-finally, and perhaps most importantly, it provides a
teaching environment whereby the initially inexperienced
analyst through repeated interactive use gains physical
insight and understanding about initial mixing processes.
Expert systems are a technology that has enormous
potential utility to solving problems in environmental
science. At the present time, several preconditions must be
satisfied before this technology can be applied successfully,
such as (Barnwell et al. , 1986):
-The problem domain must be narrow, e.g. restricted to
a particular well defined problem area.
-Expertise to solve the problem must exist; Expert
Systems cannot create expertise, they can only document,
disseminate, and enhance it.
-Formalization of concepts involved must be available in a
format compatible with the tool used.
If these preconditions can be satisfied, Expert systems
appear to be a powerful addition to the analyst's repertoire
of solution faculties. The analysis and simulation of the
discharge of pollutants into water courses meet these
preconditions. Experts in hydrodynamic mixing exist. It is a
well defined problem area, the problem being too complex for
glib analysis, but not too large to codify the knowledge
needed to solve the problem nor intractable to the novice if
expertise is available. Mixing zone analysis appears ideally
suited for exploiting Expert Systems technology.
16
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l.G CORMIX1 Summary
The problem addressed is to develop a tool for the
analysis and design of submerged single-port continuous
buoyant discharges into a non-stratified aqueous environment.
The expert system will be labeled CORMIX1, for Cornell Mixing
Zone Expert System, Subsystem :L. CORMIX1 is a subsystem of
CORMIX, to be developed, which will include stratified
environments, negatively-buoyant discharges, and bottom
attachments. CORMIX1 is primarily intended for applications
to flowing ambients(such as rivers or estuaries), although the
limiting cases of non-buoyant discharges and stagnant
environments are included. The emphasis of CORMIX1 will be on
discharge geometry and characteristics of legal mixing zone
(LMZ) requirements, including the toxic dilution zone (TDZ).
CORMIX1 will summarize dilution characteristics of the
proposed design, flag undesirable designs, give dilution
characteristics at legally important regions if specified, and
will have the capability to recommend design alterations to
improve dilution characteristics.
The subsequent chapters in Volume I are Chapter II
Hydrodynamic Background on Mixing Processes, Chapter III
CORMIX1 Program Structure, Chapter IV Data Comparison and
Validation, Chapter V Design Case Studies, and Chapter VI
Conclusions and Recommendations. Chapter II contains
discussions of the hydrodynamic analysis used to simulate the
jet mixing process. Chapter III details CORMIX1 program
structure, logic programming, and FORTRAN simulation
programming. Chapter IV presents a validation for the
hydrodynamic simulations by comparison with field and
laboratory data. Chapter V contains two typical design
examples demonstrating the use of CORMIX1 for mixing zone
analysis. Chapter VI outlines conclusions of CORMIX1
performance and recommendations for future improvements.
Volume II contains the CORMIX1 source code listings and
the output from an interactive session using the design
examples presented in Chapter V of this volume.
17
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Chapter II
Hydrodynamic Background on Mixing Processes
The hydrodynamics of a buoyant effluent continuously
discharging into a receiving body of water can be
conceptualized as a mixing process occurring in two separate
regions. In the first region, the initial jet characteristics
of momentum flux, buoyancy flux, and outfall geometry
influence the jet trajectory and mixing. This region will be
referred to as the "near field", and encompasses the jet
subsurface flow and surface impingement. In this region,
designers of the outfall can affect the initial mixing
characteristics through appropriate manipulation of design
variables.
As the turbulent plume travels further away from the
source the characteristics of the issuing source become less
important. Conditions existing in the ambient environment
will control trajectory and dilution of the turbulent plume
through buoyant surface spreading and passive diffusion. This
region will be referred to here as the "far field".
The hydrodynamic analysis treats the near field and far
field regions separately. An illustration of the near field
and the far field of a subsurface plume rising to the surface
and traveling downstream appears in Figure 2.1.
The strategy for analysis will be to first present the
mechanics of subsurface near field properties for pure jets
and pure plumes in stagnant ambient environments, extend these
results to ambient crossflows, and finally to generalize the
analysis to flows containing momentum and buoyancy. The
general results will be extended to include non-vertical
trajectories and transitions between flow regions. The
effects of flow surface interaction will then be discussed,
followed by a discussion of the far field mixing process.
2.A Analysis of Subsurface Flow Regions
A release with no buoyancy is referred to as a "nonbuoyant
jet" or "pure jet" . A release of buoyancy only (no initial
momentum) is called a "pure plume". A release containing both
momentum and buoyancy is designated a "buoyant jet" or
"forced plume". For simplicity, a region within the actual
pure jet, pure plume, or buoyant jet or forced plume will
often be referred to as a "flow".
-------
Plan View
u.
Side View
Near Fied
Far Field
Figure 2.1 Illustrative Near Field and Far Field of Submerged Single Port
Discharge
19
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For a buoyant jet in a stagnant unstratified environment,
List and Imberger (1973) propose three flow regions where
buoyant jet behavior is determined by different effects. In
the first region, near the issuing source, the geometry of the
discharge is important. In the second region, initial
kinematic momentum flux of the discharge predominates. In the
third and ultimate region, yet further away from the source,
buoyancy flux of the initial discharge becomes important.
Characterizing the flow by the predominating mechanism
controlling the flow within a region is the essence of
"asymptotic analysis" which will be pursued herein.
The effects of momentum and buoyancy thus can be
considered separately to reduce the number of independent
variables under consideration. For example, the solution for
a pure jet in a crossflow can be applied as an approximate
solution to that portion of . buoyant jet flow where jet
momentum dominates the flow. Likewise the results for a pure
plume can be applied to the buoyancy-dominated regions for the
buoyant plume.
Additional factors, such as crossflow velocities, can also
be treated within the framework of asymptotic analysis as
shown by Wright (1977).
2.A.I Description of Turbulent Jecs and Plumes
Most people are familiar with the sight of smoke rising
from a smokestack into the atmosphere. The smoke plume rises
and spreads narrowly; rising near vertically at first and
eventually bending over as it is carried away by the ambient
wind. The smoke plume is an example of a turbulent plume, the
discharge contains both momentum and buoyancy. The buoyancy
is produced by the lower density of the heated air with
respect to the cooler ambient air.
The discharge of a fluid such as sewage into the ocean
behaves in a similar fashion. The sewage has momentum from
being injected through the discharge orifice. The sewage has
the density of freshwater and thus is buoyant with respect to
the greater density of the ambient saltwater.
Turbulent jets are characterized by a long narrow
turbulent zone. Following release from a nozzle, the jet flow
becomes unstable at its boundary and breaks down into the
turbulent motion. Typically, the size of the turbulent eddies
increases with increasing distance along the trajectory
(Holley and Jirka, 1986) .
2. A.2 Elements of Dimensional Analysis of Buoyant Jets
Several assumptions are made in order to reduce the
independent variables under consideration. Only fully
-------
turbulent jets are considered so the effects of viscosity can
be neglected. The Boussinesq approximation is assumed;
density differences between the jet and the ambient
environment are small and are important only in terms of the
buoyancy force.
The three variables used to describe buoyant jet
characteristics in crossflow are the kinematic fluxes of mass,
Qo = (n/4)D2u0 , momentum Mo = Uo Qo , and buoyancy Jo = gi Qo ,
where D is the diameter of the orifice, uo is the exit
velocity, ua is the crossflow velocity, and gi is the reduced
gravitational acceleration caused by the density difference
between the jet and ambient environment. This term is defined
as g'0 = g (pa - PO)/PJ where g is the gravitational
acceleration and pa and po are the ambient and jet discharge
densities, respectively.
For the case of a buoyant jet discharged into a flowing
environment, dimensional analysis proceeds as follows. A
general dependent variable, ij>, such as local centerline jet
velocity, can then be expressed as a function of the various
independent variables:
<|> = f (Qo ,Mo , Jo , ua , s) (1)
where s is the distance along the jet trajectory. A function
is then empirically created by grouping the independent
variables on the right hand side of Eq. (1) together. The
created function has to be dimensionally consistent with the
desired dependent variable-
First, the following paragraphs present the details of
dimensional analysis for the simple case of a pure jet and a
pure plume in a stagnant environment. Then, the general case
of a buoyant jet in crossflow is presented. The jet and
ambient flow variables can be combined into various length
scales that measure the relative forces affecting a flow
within a particular trajectory distance.
The asymptotic approach will provide solutions that are
valid only within certain specified regions and furthermore
require experimentally determined coefficients. The
individual solutions, however, can be linked by appropriate
transition conditions to provide an overall prediction which
can be considered a first order approximation to the complete
problem.
2.A.2.1. Simple Jet in Stagnant Environment
Consider a pure jet in a stagnant ambient fluid (Figure
2.2). Initially as the flow exits the orifice the velocity
profile is near uniform. After a short distance s along the
21
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a. Instantaneous appearance
ENTRAPMENT
VELOCITY
Uo, po • pa, c0
CONCENTRA TION
PROFILE
AMBIENT DENSITY pa
• ZONE OF
FLOW ESTABLISHMENT
b. Time-averaged conditions
Figure 2.2 Pure Jet in Stagnant Environment (Ref. Holley and
Jirka, 1986)
22
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jet trajectory, the velocity distribution is assumed to be
gaussian. The region where this velocity distribution
transformation occurs is called the zone of flow establishment
(zofe). The details of the zofe will not be considered in any
of the following analysis; i.e. the jet is assumed to come
from a point source.
The maximum velocity uc occurs along the trajectory
centerline and a similarity profile is assumed for the
velocity distribution. Similar conditions pertain to the
centerline concentration cc of pollutant mass. The jet
centerline velocity uc decreases with distance s from the
orifice as the jet entrains the stagnant ambient fluid.
However, the momentum flux M at any section along the
trajectory is conserved. The magnitude and variation of the
jet centerline velocity depend primarily upon the initial
kinematic momentum flux and the distance along the trajectory,
Uc = (Mo , s) . Using techniques of dimensional analysis, the
result implies that ucs/Mo1/2 = constant
Uc = cMo ! / 2 s- i (2)
where c is a constant.
The width b of the jet at trajectory distance s can also
be expressed as b = (Mo,s). The only possible dimensionally
consistent equation is b/s = constant
b = bis (3)
where bi is a constant.
The dilution S at any cross-section along the jet is
defined by S = Co/cc , where Co is the concentration at the
exit nozzle. From the mass conservation equation CoQo =
ccUcb2 , and dilution S as a function of s
S = siMo i /2 s/Qo (4)
where si is a constant.
2.A.2.2. Simple Plume in Stagnant Environment
A pure plume rises vertically and has an increase in
vertical momentum flux with distance z above the source
(Figure 2.3). The buoyancy flux is constant for any cross-
section of the plume as it rises. For the pure plume, the
centerline velocity is a function of the buoyancy flux and
distance z, uc = 4>(Jo,z). The centerline velocity of the jet
can be obtained from dimensional reasoning
Uc c(Joz)1/3 (5)
23
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a. Instantaneous appearance
£NTRAINUENT ^
VELOCITY
AMBIENT
DENSITY pt
CONCENTRATION AND
BUOYANCY PROFILE
VELOCITY PROFILE
b. Time-averaged conditions
Figure 2.3 Simple Plume in Stagnant Environment (Ref. Hollev
and Jirka, 1986)
24
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The width b of the plume at trajectory distance z is
expressed as b = (Jo >z) , leading to
b = b3 z (6)
where ba is a constant.
Dilution S for the pure plume is given by mass continuity
equation as was shown in Eq. (4) for the pure jet. Noting
that buoyancy flux is conserved in the pure plume, the
dilution for the pure plume can expressed by the buoyant
acceleration g' which decreases with distance z as the plume
rises and becomes diluted by the ambient fluid. The decrease
in g' is directly proportional to the amount of ambient fluid
entrained in the plume, so S = gd/g'. Using the continuity
equation for buoyancy flux, dilution can expressed S =
4>(Jo,Qo,z) as g' z5 / 3 /Jo 2 ' 3 = constant
S = S3 Jo1 /3 z5 /3 /Qo (7)
2.A.2.3 Generalizations: Jet/Plume Interactions and Effects of
Crossflow
If additional parameters influence the flow field, then a
general asymptotic solutions for the whole flow field can not
be found. However, there may be individual regions where
specific asymptotic solutions of the type developed in the
preceding sections may still apply. The next section presents
the analysis for the discharge of the simple jet or plume into
a uniform ambient crossflow ua. As the jet or plume rises it
will be deflected by the ambient current as illustrated in the
several examples of Figure 2.4.
As can be seen in Figure 2.4 there are still specific
regions where the flow exhibits certain simple behavior.
These regions are separated by the transition zones which are
described by length scales (labeled IM, 1m, lb in Figure 2.4).
The development of these important length scales which specify
the spatial distribution of the asymptotic regimes of general
buoyant jets in crossflow is presented in the next section.
2.A.3 Length Scales for Buoyant Jets With or Without Crossflow
In general, functional relationships in the form of length
scales are sought which describe the relative importance of
discharge flux to momentum flux, momentum flux to buoyancy
flux, and discharge to crossflow in controlling flow behavior.
The length scales will describe the distance over which the
dynamic quantities in Eq. (1) control the flow.
2.A.3.1 Discharge Length Scale
Initially as the jet exits the port in the zone of flow
25
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Transition
Discharge
ua=0
Plume-like
like
a) Buoyant Jet in Stagnant Environment
\Transition
Ur
Jet
Deflected Jet
b) Pure Jet in Crossflow
u,
// ) Strongly Deflected Plume
/Weakly Deflected Plume
c) Pure Plume in Crossflow
Figure 2.4 Examples of Combined Effects of Momentum Flux
Buoyancy Flux and Crossflow on Flow Behavior
26
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establishment, port geometry controls the flow. The distance
over which the port has effect on the flow can be
characterized as a discharge length scale. Momentum controls
the flow initially for the buoyant jet. The discharge length
scale IQ relates the mass flux to momentum flux, and from
dimensional reasoning
= Qo /Mo1 /2
(8)
which is proportional to the diameter D of the orifice for a
round jet. For distances less than IQ the flow will be in the
zone of flow establishment. Thus for s/le « O(l) the source
geometry will have a significant effect on the flow behavior,
but for S/!Q » O(l) the effect of the initial geometry is
lost to jet momentum or buoyancy which will control the flow
behavior.
2.A.3.2 Jet/Crossflow Length Scale
The presence of a crossflow ua will deflect the jet as
shown in Figure 2.4b. The behavior of the pure jet in
crossflow depends on the relative magnitude of the crossflow
to jet momentum. The distance to the position where the jet
becomes strongly affected (i.e. deflected in the case of an
oblique discharge) by the ambient crossflow is given by a
jet/crossflow length scale 1m
1m = Mo1 /2 /Ua . (9)
Thus for s/lm « O(l) the initial jet momentum will
dominate and crossflow is of secondary importance, and for
s/lm » O(l) ambient velocity will have the most important
influence on jet behavior.
2.A.3.3 Plume/Crossflow Length Scale
Arguments presented for the effect of crossflow on the
pure plume flow are in analogy for the jet in crossflow. The
plume/crossflow length scale It for the pure plume rising to
be deflected by the crossflow as shown in Figure 2.4c is
determined through dimensional reasoning
lb
= Jo /Ua3
do:
Thus for z/lb « 0(1) the initial jet buoyancy will
dominate and crossflow is of secondary importance, and for
z/lm » 0(1) ambient velocity will have the most important
influence on plume behavior.
2.A.3.4 Jet/Plume Length Scale
Most flows contain both momentum and buoyancy. Because of
the buoyant acceleration, any jet containing buoyancy will
27
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have a momentum flux continually added to it. When a flow
contains both momentum and buoyancy, momentum controls the
flow initially until the buoyant acceleration overcomes the
effect of initial momentum and ultimately controls the flow.
The distance from momentum dominated to buoyancy dominated
flow for a buoyant jet in a stagnant environment is
characterized by a jet/plume length scale IM (See Figure
2.4a). Dimensional analysis suggests the functional
relationship
IM - Mo3/4/Jo1/2 (11)
So for Z/!M « 0(1) flow behavior will be controlled by
momentum and for z/ln » 0(1) flow behavior will be controlled
by buoyancy, i.e. approach that of a vertically rising-plume.
In the rare case that IM < IQ, there will be no momentum
dominated flow and the flow will be entirely plume-like expect
for the region very near the issuing source.
The ratio of IQ/!M is proportional to the reciprocal of
the usual discharge densimetric Froude number Fo = uo/(g6D)1/2
which relates the momentum forces to buoyancy within the
plume. The theoretical pure plume has a Froude number of 0(1)
and a pure jet Fo -> ».
2.A.4 Typical Regimes of Buoyant Jets
This section presents analytical results for jets and
plumes issued vertically upward from a point source,
perpendicular to the crossflow.
2.A.4.1 Weakly Deflected Jet in Crossflow (mdnf)
For a relatively weak crossflow, the jet would behave the
same as if it were in a stagnant environment, except that it
is slightly advected by the ambient current (Figure 2.4b).
This region is defined for z/lm « O(l).
Considering a jet issued perpendicular to the crossflow,
after the region of flow establishment the vertical relation
would be similar to Eq. (2) and the kinematic relationship
for a jet moving horizontally with the crossflow velocity
dx/Ua = dz/Uc (12)
Substitution for the vertical velocity given in Eq. (2) and
integrating gives the trajectory relationship for the weakly
deflected jet flow (Wright's (1977) "momentum-dominated near
28
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field", or mdnf1) expressed in terms of the jet/crossf low
length scale
Z/lm = tl (X/lrc)1 /2 (13)
where ti is a trajectory constant.
This relation holds in the region z/lm « 0(1). Eq . (13)
is valid for small values of lg /lm . In the rare case that
lc /1m is large, the effect of geometry is important and Eq .
(13) can not assumed to be valid.
Jet width b is similar to the jet issued in a stagnant
environment and is given by Eq. (3) .
The dilution S is similar to Eq . (4), and is expressed in
terms of IQ
S = si ( z/le ) (14)
where si is the dilution constant for the mdnf flow.
2.A.4.2 Strongly Deflected Jet in Crossflow (mdff)
For z/lm » O(l) the ambient flow will have a more direct
effect on the flow pattern. For a strongly deflected jet the
vertical velocity has decayed to less than the value for the
ambient crossflow; thus ambient crossflow will have
significantly deflected the jet as shown in Figure 2.4b.
The behavior of the bent-over jet is assumed to be roughly
equivalent to that of a cylindrical line impulse located at
the same vertical rise. Scorer (1954) describes a line
impulse as an instantaneous release of nonbuoyant fluid along
a horizontal line source. The characteristic variables are
the momentum impulse, M1(defined as the kinematic momentum
flux per unit length for an infinitesimal period of time),
vertical rise, and time. Applying dimensional analysis
M't/z3 = constant (15)
1 In the following the abbreviated descriptions for
subsurface flows (mdnf, mdff,bdnf and bdff) as suggested by
Wright (1977) will be used for convenience since they are
frequently used in the literature. Care must be exercised in
their interpretation so as to avoid confusing them with the
designation "near-field" and "far-field" as used in this
study (See introductory comments at the beginning of this
Chapter).
29
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To apply this analogy to the pure jet, Mo/ua is
substituted for M' and x/ua replaces t in Eq. (15). The
trajectory relation for the strongly deflected jet flow (i.e.
Wright's (1977) "momentum-dominated far field", mdff) is then
expressed in terms of the jet/crossflow length scale
Z/ln, = t2 (Z/lm )1 /3 (16)
where t2 is a trajectory constant.
Similar to Eq. (3) jet width b is proportional to position
z
b = b2 z (17)
where b2 is a constant for the mdff flow.
The continuity equation is used to determine the dilution
at any position z, CoQo=cb2ua . In terms of the jet/crossflow
length scale the dilution
S = s2 (z2 /1m IQ ) (18)
where 32 is a dilution constant for the mdff flow.
2.A.4.3 Weakly Deflected Plume in Crossflow (bdnf)
For a relatively weak crossflow, the pure plume would
behave the same as if it were in a stagnant environment,
except that it is advected with the ambient current (Figure
2.4c) .
For values of z/lc « O(l), the flow will behave as plume
in a ' stagnant environment but will be advected with the
crossflow. Proceeding in analogy to the mdnf flow (Section
2.A.4.1) the trajectory equation for the weakly deflected
plume flow (i.e. Wright's (1977) "buoyancy-dominated near
field", bdnf). The relationship in terms of the buoyant
length scale
z/lb - t3 (x/lb )3/4 (19)
Plume width b is similar to the plume issued in a stagnant
environment and is given by Eq. (6).
The dilution S is similar to Eq. (7), and is expressed in
terms of lb, IQ, and 1m
S = S3 (Ib^'z3 '3 ) /{lei- ) (20)
where 33 is the dilution constant for the bdnf flow.
30
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2.A.4.4 Strongly Deflected Plume in Crossflow (bdff)
For z/lb » O(l) the ambient flow will have a pronounced
effect on the flow pattern. When strongly defected, theplume
vertical velocity has decayed to less than the value for the
ambient crossflow; so ambient crossflow will have
significantly deflected the plume as shown in Figure 2.4c.
For z/lb » 0(1), the plume should behave as a thermal, an
instantaneous release of buoyancy-driven fluid along a line
source. Again, note the analogy to the mdff flow (Section
2.A.4.2) caused by the line impulse M1. The important
variables are J', the buoyant weight per unit length, vertical
rise, and time. Dimensional reasoning implies
J't2/z3 = constant (21)
Substituting x/ua for t and replacing J1 by Jo/ua in Eq. (21)
yields the trajectory relationship for the strongly defected
plume flow (Wright's (1977) "buoyancy-dominated far field",
bdff) expressed in terms of length scales
z/lb = t4 (x/lb)2'3 (22)
where t4 is a constant.
Plume width b is analogous to Eq. (6)
b = b4 z (23)
where b4 is a constant for the bdff flow.
The continuity equation is used to determine the dilution
at any position s, coQo=cb2ua. In terms of the jet/crossflow
length scale the dilution
S = s< z2 / (lc1m ) (24)
where Si is a dilution constant for the bdff flow.
The various trajectory and dilution relationships
presented in the previous sections are summarized in Table
2.1; Table 2.2 lists tentative constants proposed for
simulation studies for CORMIX1. These values are to be
further determined in future work.
2.A.4.5 General Behavior in Unbounded Crossflow
The general case of the trajectory and dilution for a flow
containing both momentum and buoyancy is considered next. The
correct choice of flow regions depends on relative importance
of the various length scales associated with a particular
discharge (Figures 2.4b and 2.4c).
31
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Table 2.1 Trajectory and Dilution Relations for
Submerged Flows
Source: Wright, -(1977)
Flow Region Trajectory Dilution
mdnf z/lm=ti (x/lm ) l ' 2 S = si(z/lg)
mdff Z/l»=t2 (X/lm )i /3 S = S2 (Z2 /Imlo )
bdnf z/lb=t3 (x/lb )3/4 S = s3 (It,1/3 z5/3 ) / do 1m )
bdff Z/lb=t4 (X/lb )2/3 S - S4Z2/(lQlra)
Where :*
mdnf = weakly deflected jet
"momentum dominated near field"
mdff = strongly deflected jet
"momentum dominated far field"
bdnf = weakly deflected plume
"buoyancy dominated near field"
bdff = strongly deflected plume
"buoyancy dominated far field"
* Designations in quotes according to Wright, (1977)
32
-------
Table 2.2 Trajectory and Dilution Constants
mdnf : ti =2 . 65
mdff: t2=1.44
bdnf: t3=2.36
bdff: t«=1.15
si =0.42
S2=0.38
s3=0.42
S4 =0.41
bi =0.34
b2 =0.34
b2 =0.34
b2 =0.34
33
-------
The possibility of flow attachment to the bottom is not
included in the analysis. Future work on CORMIX1 will include
the effect of bottom attachments.
a) Possible Transitions
If the buoyant jet is discharged into an unbounded
cross-flow, the ratio of lm/Ib will indicate which of the
regions (i.e. mdnf, mdff, bdnf, and bdff) occur for a
particular flow. Provided that lm and lb are both
substantially larger than IQ (generally true in practice) two
possible transitions can occur (See Figure 2.5).
Case I) For lm/lb » 0(1) the buoyancy in the plume is
relatively weak compared to momentum, and a large distance is
required for the buoyancy to generate additional momentum to
control flow characteristics. Therefore the flow will develop
as: mdnf -> mdff -> bdff.
Case 2) If lm/lb << O(l), the buoyancy force is much
stronger and the flow will be a weakly deflected jet when
buoyancy forces begin to dominate. Therefore the flow will
develop as: mdnf -> bdnf -> bdff.
b) Coordinate Systems for Oblique Discharges:
In CORMIX1 a global cartesian coordinate system (x,y,z) is
placed at the bottom of the water body with the origin (0,0,0)
directly below the center of the discharge orifice. The
height of the discharge orifice above the bottom is ho . The
positive x-axis is located at the bottom and directed in the
downstream direction following the ambient flow. The positive
y-axis is located at the bottom and points to the left, normal
to the ambient flow direction (x-axis). The positive z-axis
points vertically upward. The angle between the discharge
axis y* and its projection on the horizontal plane (i.e. the
discharge angle above horizontal) is 60 . The discharge-
crossflow angle ao is the angle between the projection of y*
on the x-y plane and the x-axis (ao = 0.0° for co-flowing
discharges, ao = 180" for counter-flowing discharges).
A primed coordinate position, (x1,y',z'), within a given
flow region is specified with respect to the virtual source
for that flow region. A virtual source is needed for each
flow region because the previous asymptotic analyses assume a
point discharge source, which is physically unrealistic. The
primed coordinate system is related to the global coordinated
by
(x,y,z) = (x',y',z') + (xv,yv,Zv) (25)
where (xv,yv,zv) is the global position of the virtual source
for that flow region. The position of the virtual source
34
-------
Transition)
2 = 0
a) Em» Eb ; Momentum Dominates
Transition
z=0
b)
", Buoyancy Dominates
Figure 2.5 General Behavior for Buoyant Jets in Unconfined
Crossflow (Assuming Near-Vertical Discharge)
35
-------
(Xv,yv,zv) is computed by taking the known flow solution at
the transition, as given from the previous flow region, and
back calculating the source position using the equations for
the given flow region.
In general, the analysis is extended to non-vertical 3-D
trajectories within the ambient crossflow. A supplementary
transverse coordinate 45.0- (26)
xt = C(l) IM ro < 45.0° (27)
where C(l) is a constant of the order of 1, and ro is the
angle defined by the discharge axis y* and the crossflow (x-
axis).
The dilution and size of the plume will be constant at the
transitions while a slight discontinuity in the centerline
velocity profile will occur.
A complete list of all transition rules used in CORMIX1,
included those for bounded flows, appears in Table 2.3. All
constants of the order 1, C{1), are assumed to be 1 in
CORMIX1. Future work plans include further refinement of
these constants with experimental data.
36
-------
Table 2.3 Flow Transition Rules
Trans . Current Next
Rule Flow Flow
Module Module
0 01 11
21
34
1 11 21
2 11 22
' Relation
Zf =
ro > 45°
ro < 45°
ro > 45°
ro < 45°
ho
ti=C
x/=C
ff=c
X/-C
(1) IM
(DIM
(Dim
(l)l,n
3
4
5
6
7
Module
01
11
16
22
31
32
33
34
41
61
21 22 Zf1
16 22 £j=C(
22 31
16 31 Zf
11 33
21 32 Zf
41 62 xr =xi +(2/3) (
( [ (S.Olbhi )
=C(l)lb
=H
=0.8H+0.2ho
bl a/ 2 /lbi 72 )
/(Si flmlQ ) ]3/2-l|
= zone of flow establishment (zofe)
= weakly deflected jet (mdnf)
= strongly deflected jet (mdff)
= strongly defected plume (bdff)
= near-horizontal surface approach
= near-vertical surface impingement with
buoyant upstream spreading
= near-vertical surface impingement with
vertical mixing
= near-vertical surface impingement, upstream
spreading, vertical mixing, buoyant
restratification
= buoyant surface spreading
= passive diffusion
37
-------
2.B Flow Interaction With Free Surface
The preceding section assumed a turbulent plume rising
with a crossflow in an infinitely deep water body. No
boundary effects of the flow meeting the surface were
considered. This section analyzes the boundary effects of a
flow interacting with the water surface within the near field.
The interaction of the flow with the water surface will be
characterized by the local ambient water depth H. The ratio
of the water depth length scale H to the length scales
discussed previously is used to characterize the flow
interaction with the surface.
2.B.I Flow Classification of Near-Field Regions
The flow classification system appears in Figure 2.6. The
flow classification system uses the ratio of 1m/H to
characterize the discharge as "deep water" or "shallow water"
based on the momentum of the flow as it contacts the surface.
A deep water discharge will have relatively weak momentum as
the flow contacts the surface, while a shallow water discharge
will have relatively strong momentum as the flow impinges on
the surface.
Ratios of lb/H and IM/H are used to further classify the
properties of the flow as it contacts the surface in both deep
and shallow water.
Discharges can be classified as "stable" or "unstable".
Flows with strong vertical momentum at surface contact tend to
be unstable. In this case the jet is deflected downward by
the surface and an unstable recirculation zone occurs around
the jet as it entrains the fluid deflected down from
the surface. In a stable discharge, buoyancy tends to have a
stabilizing effect on the flow as contacts the surface,
causing the flow to form a stratified layer on the surface.
2.B.2 Analysis of Surface Interaction Processes
Four major possible flow regions exist (Figure 2.7) for
the flow interaction with the surface; i) near-horizontal
surface approach, ii) near-vertical surface impingement with
upstream spreading, iii) near-vertical surface impingement
with full vertical mixing, and iv) near-vertical surface
impingement with unstable recirculation, buoyant
restratification, and upstream spreading. As shown in Figure
2.6, each of these four possible flows can be defined by
combinations of the ratio of the length scales !„, , lb , and IM ,
with the local water depth H.
A control volume approach is used for the following
38
-------
90*<#0<45*
(Near) Vertical
Deep
Water
with
Weak
Momentum
lb-
the flow is minf-^> mdff-> bdff), are included in CORMIX1 but for simplicity
are omitted in Figure 2.6.
-------
Cross-section
f (rectangular)
'i (round) width bh
width b
a) Surface Approach (Near-Horizontal)
Figure 2.7 Four Major Conditions of Flow Interaction with
Water Surface (i indicates inflow values in control volume and
f outflow values)
40
-------
Side View
u,
Plan View
Stagnation
Point
Inclined Front
y
b) Surface Impingement with Buoyant Upstream Spreading
Figure 2.7 (continued)
41
-------
Side View
c) Surface Impingement with Full Vertical Mixing
Figure 2.7 (continued)
42
-------
d) Surface Impingement with Buoyant Upstream Spreading,
Full Vertical Mixing, and Buoyant Restratification
Figure 2.7 (continued]
43
-------
sections. When the plume contacts the surface, bv and bh are
defined as the vertical depth and horizontal width of the
subsequent flow, respectively. The variable subscripts "i"
(initial) and "f" (final) (e.g. bi , Sf ) denote control volume
inflow and outflow quantities, respectively.
2.B.2.1 Near Horizontal Surface Approach
In this surface approach condition, the bent over flow
approaches the water surface near horizontally at impingement
angle 81 < 45° (Figure 2. la). The flow is advected with the
ambient velocity field at a rate equal to ua . This situation
occurs for weakly buoyant and deep water cases, hence the flow
will be strongly deflected when it contacts the surface. This
type of surface interaction occurs for flow classifications VI
and V2 which are defined as deep water with weakly buoyant
discharge (for 1m /H < O(l) and lb /H < O(l), respectively).
Experimental evidence (Jirka and Harleman, 1973) suggests
that within a short distance after surface impingement the
concentration distribution for a 2-D flow changes from the
assumed gaussian distribution to a top-hat or uniform
distribution (Figure 2. la). Using a control volume approach
the initial centerline dilution is related to the final bulk
dilution, and a bulk mixing process is assumed with Sf =
21/2Si (Fan 1967). An equivalent cross-section aspect ratio
for the outflow section of 2:1 is assumed. The continuity
equation for the control volume in Figure 2.7a
Uabi 2 TT = Ua 2bh f * bv f (28)
where bi is the initial dilution and half-width, bv f is the
final flow vertical width, and bh f is the final flow
horizontal half-width. This is evaluated as
bvf =bh f =bi
2.B.2.2 Near-Vertical Surface Impingement With Buoyant
Upstream Spreading
In this surface approach condition, the weakly bent flow
impinges on the surface at a near-vertical angle 61 (Figure
2.7b), where 81 > 45°. After impingement the flow spreads
more or less radially along the water surface as a density
current. In particular, the flow spreads some distance
upstream against the ambient flow, and laterally across the
ambient flow. This spreading is dominated by the strong
buoyancy of the discharge.
The stabilizing effects of buoyancy are greater than the
destabilizing forces of jet momentum and the crossflow, thus
this is classified as a stable discharge condition. This type
44
-------
of surface interaction occurs in flow classifications V3, V5,
H3 and H5 and is defined for strongly buoyant discharges (lb/H
> 0(1)) in both deep water (lm/H < 0(1)) and shallow water
(lm/H > 0(1)). For deep water discharges, lm <• lb implies
IM/H < 1, so the flow will be weakly deflected plume at
surface approach. For shallow water cases, to insure that the
flow is a weakly deflected plume, the additional requirement
will be that 1M/H < 1.
The lateral spreading of the flow in the surface
impingement region is driven by both the flow momentum and
buoyancy force. Of interest is the upstream intrusion length
Is , dilution S, horizontal width bh, and vertical depth bv of
the density current at surface impingement.
The analysis of this flow region follows results presented
by Lee and Jirka, (1981), and Jones, et al., (1983). Lee and
Jirka analyze the properties of a buoyant subsurface discharge
in stagnant water including the effects of recirculation and
buoyant restratification. Jones, et al. presents a methodolgy
to predict the upstream spreading of a buoyant radial
discharge in crossflow. The strategy for solution will be to
use the results of Lee and Jirka to provide initial conditions
for the methodology of Jones, et al. for predicting buoyant
upstream spreading and horizontal width.
A length scale IN representing the turbulent mixing action
of the horizontal momentum flux versus stability effect of
buoyancy force is given by
IN = (defected horizontal momentum flux)3/4/Jo1' 2 (29)
For the weakly deflected plume, Holley and Jirka, (1986) give
an expression for the vertical momentum of a plume
M s 0. 85Jo2 /3s4/3 (30)
Where, s (= H) is the distance along the plume trajectory.
Substituting appropriate values into Eq. (29), the length
scale for a weakly deflected plume at impingement
IN = 0.367H(l-cos6i) (31)
where the factor (l-cos8i) accounts for the deflected
horizontal momentum flux, in analogy to the vane equation in
classical fluid mechanics.
Jones, et al. defines an intrusion length scale li, by
relating the interaction of the buoyancy force with the
crossflow force
45
-------
li = Jo / 2rrCD ua 3 (32)
where CD is a drag coefficient of O(l).
Thus, for a weakly deflected plume at surface approach,
the ratio of length scales obtained from Eqs . (31) and (32)
li /1N = 0.54(lb /H) (I/ (l-cos0i ) ) (33)
which describes the relative importance of buoyancy to
momentum forces at surface impingement.
The upstream intrusion length Ls is found from observing
the Figure 5-14 in Jones, et al.,
Ls/li - 4.2(li/!N)-2/3 for li /!N < 3.3 (34a)
Ls /li = 1.9 li /!N > 3.3 (34b)
Noting that li = lb/5 with CD = 1 and since the flow is a
weakly deflected plume at surface approach, the upstream
intrusion length Ls in Eq. (34a) can be expressed
Ls = 1.261b ( (l-cos(8i ) )/(It/H) )2/3 (35a)
for lb/H < 6.11(1-cos (9i )) , and in Eq. (34b)
Ls = 1.91b (35b)
for lb/H > 6.11(1-cos (61 ).
To calculate the dilution in this region, first note that
Jones, et al. in Figure 7-8 gives the dilution for a radial
surface discharge
S/Fs = 1.6(li /!N J1 /3 (36)
where Fs is a radial surface spreading Froude number. This
Froude number is defined
Fs = ur / (g1 lo )1/2 (37)
where 10 is a characteristic length scale defined
lo = (2Trnhi M/2 (38)
where n and hi are the radius and depth of the buoyant radial
surface spreading flow, respectively.
Now the results of Lee and Jirka are used to evaluate the
surface spreading Froude number Fs , so the dilution S from Eq.
46
-------
(36) can be found. In this analysis, the initial radial
surface spreading region uses a simplified control volume to
relate the properties of the vertically buoyant jet at the
entrance of the surface impingement region to the
characteristic parameters of the horizontal axisymmetric
buoyant surface jet at the exit of this region.
Lee and
impingement
Jirka define the Froude
number at surface
Fi =
/ (g' hi
where ur is the radial surface spreading velocity and hi is
the depth after impingement. For large values of H/D, the
value Fi = 4.62 and the value hi/H = 0.0775.
The radius of the flow n is n = eH, where e = 0.11. By
substituting these asymptotic values into Eq. (38), the
characteristic length scale 10 from Jones, et al. becomes
lu = 0.23H
;4o:
which when combined with asymptotic values for Eq. (39) gives
Fs - Fi (hi /lo )> /2 =2.65 (41)
indicating that the flow in this region is jet-like- Finally,
note that the radial surface spreading Froude number Fs can be
expressed as in terms of the discharge flux variables as
Q/ (Mo3/ 4 /Jo 1 /2 ) -
This result can be then used to determine a bulk dilution
at the end of the region St . From Eqs. (36) and (41) the
expression for final dilution in the surface impingement
region
Sf - 3.49Si (lb/H)1 ' 3 (1-cos(81
1 / 3
42!
The geometry of the surface flow as revealed by Jones, et
al. will be used to determine the width and depth within the
region. From Jones, et al . Figure 7.1, the width, bi, t , at
impingement is assumed to be 2.6 times larger that L3 :
bh
= 2.6Ls
The typical depth of the flow in the upstream intrusion region
hs , is found using the vertical length scale from Jones, et
al. where
= CD ua 2 /g'
44:
47
-------
with CD = 0.8. Noting that g'= go/Si, where Sf is the total
bulk dilution, using the continuity equation ua2Qo/Jo =
ua3 Qo Mo * ' 2 / (Jo Ua Mo 1 i 2 } = Iglm/lb the stagnation flow thickness
hs
hs = 0 . 8Sf 1m IQ /lb (45)
The final depth bvf (at x=0) is found using the continuity
equation, bvf (x=0) = QoSf/(bvfua), and the previous equation
bv f = Ibhs / (0. 8bh f ) (46)
2.B.2.3 Near-Vertical Surface Impingement With Full Vertical
Mixing
In this case, the weakly bent flow impinges on the water
surface at a near-vertical angle (Figure 2.7c). This case is
defined by shallow water ( 1/H > 0(1) ) and weak buoyancy (
lb/H < O(l) ). Given the shallow ambient water depth and the
weak buoyancy of the discharge, the flow becomes unstable
after impingement. This occurs in flow classifications V4 and
H4, and results in a recirculation region immediately
downstream that extends over the full water depth. The
recirculation region causes the flow to entrain ambient fluid
from the flow itself causing dilution within the plume to
decrease. Because of unstable recirculation, the centerplane
dilution decreases to Sf = St/R, where R is a recirculation
factor. Experimental data indicate R ranges from 1.0 to 2.0,
and an average value of 1.5 will be assumed. The final flow
width, bhf , is found from the continuity equation
bh f = Sf 1m lo / (2H) (47)
and final outflow location Xf is approximated as
Xf = xi + 2H (48)
where xi is the plume position at the beginning of the region.
The distance 2H accounts for the typical length of a
recirculating zone (Holley and Jirka, 1985).
2.B.2.4 Near-Vertical Surface Impingement With Unstable
Recirculation, Buoyant Restratification, and Upstream
Spreading
In this surface approach region, the flow rises near
vertically and impinges on the water surface (Figure 2.7d).
After impingement the mixed flow recirculates over the limited
water depth and becomes partially re-entrained into the flow.
This surface interaction occurs in flow classification V6 and
is defined by shallow water (lm/H > O(l) ), strongly buoyant
48
-------
(Ib/H > O(l) ), as well as momentum dominated (Ix/h > 0(1) ).
Both momentum and buoyancy are strong, but momentum dominates
in the near field. The degree of recirculation and hence the
overall mixing in this region is controlled by
restratification of the flow at edge of the recirculating
region. The restratified flow spreads along the water
surface. In particular the flow spreads some distance
upstream against the ambient current, and laterally across the
ambient flow.
The analysis of the flow is based on the work of Lee and
Jirka, (1981) which was originally developed for stagnant
conditions. The final dilution Sf is given by
Sf = 0.76H3/3/ (lM2/3Ic ) (49)
The dilution is controlled by buoyancy forces only, the
effects of momentum become dissipated by the turbulent mixing
action. This result can be understood if the values of IM
and IQ are replaced in Eq. (49) by their respective efflux
definitions, the results show that dilution is a function of
the buoyancy flux only.
The surface buoyant spreading properties after the
unstable recirculation are analyzed similar to the development
for the near-vertical surface impingement with buoyant
upstream spreading presented in section 2.B.2.2. In
particular, for the unstable case, the limit of li/lu -> » is
of interest, so that Eq. (34b) applies.
Since the near-field momentum is dissipated, the length of
the upstream intrusion Ls is found from Jones, et al. (1984),
Figure 5-14. This figure plots Ls/li vs. li/!N and is a
constant line of Ls/li = 1.9 for li/!N -> ». Recalling li =
lb/5 from Eq. (32) for shallow ambient conditions and noting
that, the relationship for upstream intrusion length Ls
Ls = 0.151b (50)
The upstream intrusion thickness hs is found in analogy from
Section 2.B.2 . 2
hs - 2St lmlc/lb (51)
The final half-width bhf , is found from the continuity
equation
bv f = Ibhs / (2bbf ) (52)
The region is assumed to extend downstream a distance equal to
2H as in Eq. (48).
49
-------
2.C Analysis of Far-Field Mixing Process
After the flow interacts with the water surface as
described by the previous sections, the far field mixing
begins (Figure 2.1). This region consists of one or two
regions, depending on discharge characteristics. In the
general case, the flow contains sufficient buoyancy and there
will be a buoyant surface spreading region followed by a
passive diffusion region. The surface spreading region is
characterized by dynamic horizontal spreading and gradual
vertical thinning of the flow after interacting with the
surface (Roberts, 1979, Koh and Brooks, 1975). Boundary
interaction may occur, and in bounded sections the flow may
become laterally fully mixed. In the passive diffusion
region, the dilution is controlled by the turbulent mixing
action of the flowing ambient water body. Again, boundary
interaction may occur, and the flow may become both laterally
and vertically fully mixed in this region. If the flow is
non-buoyant or weakly buoyant there is no buoyant surface
spreading region, only a passive diffusion region.
2.C.I Buoyant Surface Spreading
In this region the buoyant surface plume spreads laterally
along the water surface while it is being advected by the
ambient current (Figure 2.8). The plume behaves as a density
current and entrains some ambient fluid in the "head region"
of the current. The mixing rate is usually relatively small.
Furthermore, the surface plume may interact with a nearby bank
or shoreline. The plume depth may decrease during this phase.
The analysis of this region is based on arguments presented by
Jones, et. al. (1985).
The continuity equation for the density current
uaah/ax + a(vh)/ay = we (53)
where we is the net velocity across the interface. Benjamin
(1967) has derived an equation for the spreading velocity VB
ve2/(g'h) - C (54)
where h is the density current thickness and C is a
coefficient that depends on the relative depth h/H and is of
order O (1 to 2). Combining the Eqs. (53) and (54) and
integrating gives
Uad(hb)/dx = qe (x) (55)
where qe (x) is the localized head entrainment.
50
-------
Front
Plan View
u,
— I
-*- l^-Initial A
Condition
Cross-section A-A
Frontal Zone
••
Figure 2.8 Buoyant Surface Spreading
51
-------
The localized head entrainment is qe (x) = PVB h where p is
a constant O(0.15 to 0.25) (Simpson and Bitter, 1979; Jirka
and Arita, 1987). The constant p will be set equal to 0 25 in
CORMIX1.
The flow half-with b is obtained for any downstream
distance x by using the boundary condition for the streamline
(vB=Uadb/dx) and integrating Eq. (53) (for the unattached
case )
bh = (bi3/3 + 3/21b1/2(x - xi))2/3 (56)
where xi is the downstream distance at the beginning of the
buoyant spreading region. The 2/3 power law of plume
spreading is in agreement with the previous work of Larsen and
Sorensen, (1968) .
The vertical plume width bv for any bh in the region is
given by integrating Eq . (54) to obtain
bv = bv i (bh /bh i ) (56)
where p represents the additional dilution caused by
entrainment at the head of the density current.
The bulk dilution S given by co/c, is equivalent to go' /g'
as is Eq. (7). Buoyancy conservation in the density current
(analogous to momentum conservation) can be expressed
uaa(g'h)/3x + a(g'veh)/ay = 0 (57)
Integrating Eq. (57) and noting that PVB h=pua h (db/dx) gives
the expression for dilution S
S = Si (bv /bv i ) P (58)
2.C.2 Passive Diffusion
In this region the background turbulence in the ambient
shear flow becomes the dominating mixing mechanism (Figure
2.9). The mixed surface flow is growing in depth and in
width. The flow may interact with the channel bottom and/or
banks .
The analysis of this region follows classical diffusion
theory (e.g. Fischer, et al. 1979). The standard deviation o
of a diffusing plume in crossflow can be written in terms of
the transverse turbulent diffusivity E
a2 = 2Ex/ua (59)
52
-------
Plan View
Possible Bonk Interaction
Plume
Centerline
•Initial Conditions
Side View
Possible Bottom Interaction
Figure 2.9 Passive Diffusion Process
53
-------
In open channel flow the eddy diffusivity can be related to
the friction velocity u* and the channel depth H
Ez = 0.2u*H (60a)
for vertical diffusivity, and
Ey = 0.6u*H (60b)
for horizontal diffusivity- Due to some anisoptropy in a
typical channel flow, the diffusivity in the horizontal
transverse direction is larger than the diffusivity in the
vertical direction. The friction velocity is given by u* =
(f/8)ua where f is the Darcy-Weisbach friction factor.
Solution of Eq. (59) gives the global coordinate system
expressions for flow width bv and depth bi, at any downstream
distance x
bv = ( (2Ey /ua ) (x-Xi ) + bv i 2 M/2 (61)
bh - ( (2EZ/ua ) (x-xi ) + bhi2)1/2 (62)
where xi, bvi, and bti are the distance, width, and depth of
the flow, respectively, at the beginning of the surface
spreading region. This assumes that the above lengths are
expressed in terms equal to one standard deviation, or bv = oy
and bh = az .
The continuity equation applied to a plume in crossflow
ua , oy o2 =SQ0 yields the dilution S
S = ay a2 / (lu,lQ ) (63a)
In the case that when the plume is vertically fully mixed
S = oy H/ (Imlg ) (64b)
2.C.3 General Behavior in the Far-Field
a) Boundary Interaction
If buoyant surface spreading occurs, the process will
continue until either the transition to passive turbulent
diffusion occurs (as described in the next section 2.C.3 part
b)) or the flow attaches to both banks in bounded sections,
whichever occurs first.
The end of the passive turbulent diffusion region occurs
when the plume becomes both vertically and laterally fully
mixed and no change in dilution occurs with increasing
downstream direction. In unbounded sections, the plume will
54
-------
never become laterally fully mixed, so the simulation
terminates at some large downstream distance preset by
CORMIX1.
b) Transition Between Surface Spreading and Passive Diffusion
A flux Richardson number, Rf , defined locally as the ratio
of buoyant energy flux to shear energy production will be used
as a stability criterion for the transition from the buoyant
surface spreading to the passive diffusion flow. Written in
terms of the eddy diffusivity convention (Tennekes an Lumley,
1972)
Rf= -gKa (dp/dz) / (pKM (du/dy)2 ) (63)
in which KM , KH = eddy diffusivity for momentum and for a
scalar (heat ), (KB =KM ) respectively; p(y) = local density; and
u(y) is the local velocity.
A critical value of Rf c = 0.10 to 0.20 has been suggested
by Monin and Yaglom, (1971) and Turner, (1973) . Above this
value, turbulence is damped and a stable profile can be
maintained and the density current flow continues; below this
value, turbulence erodes the stable density profile and
turbulent diffusion then controls the flow.
For the buoyant surface spreading region Jirka (1979)
suggests the appropriate Richardson number is of the form
Rf = K2 (go'H/u*2 ) (1/S) (h/H) (64)
where K is von Karman constant (S0.4). The ratio of h/H in
Eq . (64) is a length scale representing depth of the density
current to overall channel depth.
Noting that Si , bv i , and xi are the dilution, initial
depth, and downstream distance at the start of the buoyant
surface spreading flow, the distance to transition, xt , to the
passive spreading flow
xt = Xo + (2/3) (bi 3/2 /Ib1 / 2 ) { [ (Slbho ) / (fSi IO.IQ ) ]3/2 -1) (65)
If the plume is attached to one boundary Ib is replaced with
21b .
55
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Chapter III
CORMIX1 Program Structure
The Cornell Mixing Zone Expert System Subsystem 1.
(CORMIX1) is a series of software subsystems or elements for
the analysis and design of conventional or toxic single port
submerged buoyant or nonbuoyant pollutant discharges into
unstratified watercourses, with emphasis on the geometry and
dilution characteristics of the initial mixing zone. It is
designed as an analysis tool for regulators, dischargers, (and
students of hydraulics).
The user supplies CORMIX1 with information about the
discharge and ambient environment. CORMIX1 returns
information detailing the hydrodynamic mechanisms controlling
the flow, dilution, geometric information concerning the shape
of the pollutant plume or flow in the ambient water body, and
design recommendations allowing the user to improve the
dilution characteristics of the flow. If specified by the
user, CORMIX1 also presents information about the legal mixing
zone dimensions and dilution, toxic mixing zone requirements,
and zone of interest characteristics for the flow. The
minimum hardware configuration for CORMIX1 is an IBM-PC/XT
with a printer for hardcopy output.
The purpose of CORMIX1 is to obviate for the novice
analyst the need for detailed hydrodynamic understanding and
experience. A general environmental science or engineering
background at the BS level appears to be minimum educational
requirement needed to compile and supply relevant data,
interpret the system information, and ultimately learn and
become knowledgeable about hydrodynamic mixing through
repeated interactive use. Two working days appears to be the
minimum time needed for a first time user to gain initial
facility with system requirements, limitations, and
interpretation of results.
Figure 3.1 shows the system elements of CORMIX1. During
system use the elements are loaded sequentially by the user.
CORMIX1 is implemented in the programming language Fortran,
and M.I (Teknowledge, Inc.), an expert systems "shell".
M.I is an expert systems programming language, or more
precisely, a shell. A shell is a self-contained inference
engine that does not contain the knowledge base, but has
56
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M.I
DAT IN
User Input
Iteration
Alternatives
Corrections
file. CXD
Fortran
PARAM
Parameter
Computation
file. CXP
M
CLASS
Flow
Classification
file. CXI
file.
CXC
Fortran
HYDRO
Prediction/Simulation
Program
file. CXO
SUM MJ
Summary
Evaluation
Recommendations
(Legal/Engineering)
Figure 3.1 System Elements of CORMIX1
57
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facilities for both forward and backward reasoning, debugging
aids, consistency checking, input and output menus, and
explanation facilities.
Two programming languages are used to exploit their
respective strengths while avoiding their respective
weaknesses. M.I, as a knowledge base language, is very
efficient in knowledge representation and symbolic reasoning;
however it is relatively weak in numerical computational
ability. On the other hand, Fortran is ideal for computation
of mathematical functions (Fortran stands for formula
translator) but is poorly suited for the tasks associated with
symbolic reasoning. Thus M.I is employed to implement the
knowledge acquisition, model selection, and analysis of the
hydrodynamic simulation portions of the expert -'system.
Fortran is used for the computation of various length scales
and in the hydrodynamic flow simulation models.
It is interesting to note that the entire system could
have been programmed in a language such as Fortran, or even
assembly language; the real issue is one of programming
efficiency. For instance, a routine written in 5 lines of
Fortran code might take 100 lines of assembly level source
code. Since M.I was developed to encode and manipulate
symbolic logic, it does so with great efficiency, allowing the
programmer to write in 5 lines of code what might take 100
lines in Fortran or 1000 lines of assembly. In essence the
selection of M.I as the language for the symbolic reasoning
tasks gives the programmer significant leverage.
3.A Discussion of Logic/Ml Elements
The M.I elements of CORMIX1 are DATIN, CLASS, and SUM.
M.I is very similar in structure to PROLOG (PROgramming
LOGic). PROLOG was developed in Europe and is designed to
manipulate logical expressions(Clocksin and Mellish, 1984).
An M.I program is built from statements containing facts and
if-then rules about facts. This is called the knowledge base.
The knowledge base is supplied by the user corresponding to a
problem domain, in this case buoyant submerged jets and
hydrodynamic mixing processes.
M.I programs are driven by a "goal" which the program
tries to validate by searching the knowledge base to construct
a "proof" by using the facts and rules in the knowledge base
needed to deduce the goal as a valid hypothesis. The
following section gives a more detailed explanation of how
this is accomplished, using the CORMIX1 module DATIN as an
illustrative example.
58
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3.A.I DATIN
DATIN is an M.I program for the entry of relevant data and
for the initialization of the other program elements. The
user executes DATIN by typing "DATIN". DATIN then prompts the
user for needed information.
CORMIX1 deals with submerged buoyant single port
discharges into an unstratified water body. The system
assumes a schematic rectangular cross-section bounded by two
banks - or by one bank only for coastal or other laterally
unlimited situations. The user receives detailed instructions
on how to approximate actual cross-sections that may be quite
irregular to fit the rectangular schematization. The
representative schematization with all relevant hydrodynamic
variables that DATIN gathers, appears in Figure 3.2.
Even in this simple schematized ambient geometry, there
remains a tantalizing amount of geometric and dynamic detail:
the discharge location in relation to the bottom and the
shoreline; the discharge orientation may be with the flow,
against the flow, or vertically upward across the flow, or at
some arbitrary angle, the water depth may be deep or shallow;
the ambient flow may be stagnant or fast and highly diffusive;
and the discharge flow may be non-buoyant or highly-buoyant;
with high or low efflux velocity.
The purpose of DATIN is to specify completely the physical
environment of the discharge, as well as legal or regulatory
specifications. The following data groups need to be entered:
general site and case identifer information, ambient
conditions (geometry and hydrography), discharge conditions
(geometry and fluxes), and information desired including legal
mixing zone definitions and toxic dilution zone criteria.
DATIN provides consistency checks, and gives advice for input
parameter selection.
DATIN tries to satisfy the goal creating a valid parameter
input file for the other CORMIX1 elements. The goal is the
statement that drives the execution of DATIN. This is written
in M.I as
goal = param_input_file. [1]
Here the goal is to satisfy or find a valuation for the
expression "param_input_file".
All rules in M.I are stated as: if (expression(s) or
clauses called the "premise" or "head" of the rule) - then
(an expression or clause called the "conclusion" or "tail" of
the rulel statements. The premise of a rule in M.I can
contain more than one expression connected by and/or
59
-------
PLAN VIEW
W
CROSS-SECTION
42
H
D.
///////////// / s /
Nearest bank
Flux quantities: 00= discharge
M0= U0Q0= momentum flux
J0 = ( A/OO//DQ) g 00 = buoyancy flux
-M
Figure 3.2 Schematization of Discharge Configuration
, C,
60
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statements but the conclusion of the rule can contain only one
expression. M.I will try to satisfy the goal (here the
expression "param_input_file") by searching for a rule in the
knowledge base whose conclusion contains the expression
"param_input_file = (valuation)".
A -rule in DATIN that has "param_input_file = known" in its
conclusion is (a separate line for each expression in the
premise of the rule^ has been added to improve readability) :
if site_description = found and
ambient_conditions = found and
discharge_parameters = found and
zone = found
then param_input_file = known. [2]
Here, in the conclusion of the rule the expression
param_input_file is assigned the valuation "known".
First, a explanation is given on how M.I uses information
contained within if - then rules to assign valuations to
expressions. M.I always tries to satisfy a valuation in the
conclusion of rule by proving its premise. Thus, M.I tries to
satisfy all expressions in the premise of the rule, beginning
in statement [2] with the first expression "site_description =
found". If the valuation of the variable in first clause is
satisfied, i.e. the expression site_description does indeed
have the valuation ''found", then M.I tries to satisfy the
second expression, "ambient_conditions = found". If this
valuation is satisfied, M.I will try to satisfy the remaining
expressions in the premise of the rule. Whenever in the
premise the valuations for all expressions are satisfied, the
rule succeeds or ''fires". When the rule fires, the expression
in the conclusion the rule can be given a valuation and added
to the facts known in the knowledge base.
So how does M.I know the expression "site_description"
has the valuation "found"? Because there is another rule in
the knowledge base which is
if site_name = SN and
discharger_name = DN and
pollutant_name = PN and
design_case = DC and
grid_interval = NSTEP
then site_description = found. [3]
This statement is invoked by statement [2] in DATIN when it
tries to find a valuation for the first expression
"site_description". Since there is no present valuation for
the expression "site_descriptibn", M.I locates statement [3]
61
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with the expression "site_description" in its conclusion. If
all expressions in the premise of statement [3] can be
assigned valuations, then the expression site_description is
assigned the valuation "found". All capitalized values in
statement [3] (SN, DN, PN, DC, and NSTEP) are variables in
M.I. Variables in M.I are only assigned a valuation when
considered within a rule. M.I will try to find a valuation
for site_name, the first expression in statement [3]. Within
the DATIN there is another rule
question(site_name) ="Enter a descriptive name for the
discharge location". [4]
This rule is a treated as a "fact", and M.I prompts the user
for a valuation of "site_name" with the message within the
quotes of statement [4]. The user enters a value which is
bound to the variable SN, giving the expression "site_name"
the valuation of SN. M.I continues to find valuations for the
remainder of the expressions in statement [3] in a similar
manner. When all expression in the premise of statement [3]
are assigned a valuation, the conclusion "site_description =
found" is added as a fact to the knowledge base, which will
allow M.I to return to statement [2] to seek a valuation for
the expression "ambient_conditions".
Thus, as was shown with the previous example, the
knowledge base DATIN is built from rules which contain
expressions that force M.I to seek valuations from other
rules. The process of seeking valuations of expressions
continues either until all the valuations are found or the
rule base is exhausted without finding a valuation. M.I will
never assign a valuation which is in contradiction within a
rule, so we are assured whatever valuations we conclude are
taken from a rule within the knowledge base. Care must be
taken in program structure however, since the search strategy
of M.I may not consider all rules needed to find a valuation
for a given expression. In general, the rule base should be
programmed in a "tree" structure, with the most general and
independent rules at the beginning of the program, and rules
which depend on valuations from other rules following in the
program. The most dependent and nested rules should occur
last in the knowledge base.
When a valuation for a clause in the premise of a rule is
found not agree with the valuation given for that clause
within the rule, e.g. the expression discharge_parameters in
statement [2] is found to have the valuation "unknown", then
the rule fails, no valuation can be assigned to the expression
"param_input_file" from that rule. M.I will stop trying to
satisfy the remaining expressions in the premise of that rule.
M.I will continue to try to satisfy the expression
62
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"param_input_file" by looking for another rule in the
knowledge base with "param_input_file" in the conclusion of a
rule.
The actual rule corresponding to statement [2] in DATIN
contains additional clauses that control the manner in which
intermediate conclusions are stored in memory, messages are
displayed on the monitor, and other statements which create
and manipulate external files for use in other CORMIX1
modules.
When the rule in DATIN corresponding to statement [2]
fires, the "cache" of DATIN is written to an external DOS
file. The cache is a list of all expressions within DATIN
that have been assigned a valuation. This cache file is read
by the next sequential element in CORMIX1, the Fortran program
PARAM. At its termination, DATIN directs the user to exit the
M.I environment and execute PARAM.
A complete program listing of the DATIN knowledge base
appears in Appendix A.I. Appendix B contains the output of an
interactive session using DATIN for the design examples in
Chapter V.
3.C.2 CLASS
CLASS is an M.I program that classifies the given
discharge into one of the many possible flow configurations,
e.g. a simple jet or plume, an unstable vertically mixed case,
or mixing controlled by ambient flow. The user executes CLASS
by typing "CLASS".
Only one flow classification can be selected for a
particular discharge configuration from the many possible flow
classifications explained in Section 2.B.I and shown in Figure
2.6.
The goal of CLASS is to find a valuation for the
expression "flow_class" from the flow classification scheme
appearing in Figure 2.6. Each of the 17 possible flow
classification has an alphanumeric label(eg. VI, V2, H3,
etc.). CLASS inputs a cache created by PARAM that contains the
length scales and other dynamic variables needed for flow
classification, and uses the knowledge base rules to assign
the appropriate classification to the flow. A rule
corresponding to flow case V2 would appear in simplified form
for illustration purposes as
if vertical_angle = THETAO and
THETAO > 45.0 and
THETAO <= 90.0 and
63
-------
1m/H < 1 and
'Ib/H <1 and
IM/H > 1
then flow_class = V2. [5j
When the appropriate flow classification rule fires, a
detailed hydrodynamic description of the flow is provided to
the user. This detailed output includes a description of the
significant near field mixing processes, or the hydrodynamic
mixing zone (HMZ). The HMZ is the region where the particular
design of the outfall can have effect on initial dilution.
The HMZ is defined to give additional information as an aid to
understanding mixing processes and to distinguish it from
purely legal mixing zone definitions. CLASS also creates a
cache output file that supplies the next CORMIX1 element, the
Fortran hydrodynamic simulation program HYDRO, with
instructions for running the appropriate simulation. At its
termination CLASS directs the user to exit the M.I environment
and execute HYDRO.
The complete knowledge base for CLASS appears in Appendix
A. 2. The interactive output from CLASS appears in Appendix B
as discussed in the design examples Chapter V.
3.C.3 SUM
SUM is an M.I program that summarizes the hydrodynamic
simulation results for the case under consideration. SUM is
executed by the user by typing "SUM". SUM comments on the
mixing characteristics, evaluates how applicable legal
requirements are satisfied, and suggests possible design
alternatives to improve dilution. Thus, SUM may be used as an
interactive loop to guide the user back to DATIN to alter
design variables.
The output of SUM is arranged in four groups; site
summary, hydrodynamic simulation summary, data analysis, and
design recommendations. The site summary gives the site
identifier information, discharge and ambient environment
data, and discharge length scales. The hydrodynamic
simulation summary will list conditions at the end of the
hydrodynamic mixing zone, legal mixing zone conditions, toxic
dilution zone conditions, region of interest criteria,
upstream intrusion information, bank attachment locations, and
a passive diffusion mixing summary, depending if the preceding
conditions are specified or occur. The data analysis section
gives further details on toxic dilution zone criteria, legal
mixing zone criteria, stagnant ambient environment
information, and region of interest criteria. Finally the
design recommendations section gives design suggestions for
improving initial dilution. Factors effecting initial
64
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dilution are the discharge momentum flux, discharge angle,
outfall location, discharge buoyancy, bank attachment, and
ambient environment conditions.
The listing of the SUM knowledge base appears in Appendix
A.3. The interactive listing of SUM appears in Appendix B and
is discussed in the design examples Chapter V.
3.C Discussion of Hydrodynamic/Fortran Elements
The FORTRAN elements of CORMIX1 are PARAM and HYDRO. These
element are programmed in FORTRAN because of the limitations
of M.I for computing mathematical expressions. PARAM and
HYDRO are executed after the user has successfully completed
DATIN and CLASS, respectively.
3.C.I PARAM
PARAM is a Fortran program that computes relevant physical
parameters for the given discharge situation. This includes
the various length scales; IQ , 1» , lm , It. , fluxes and other
values needed by the other CORMIX1 elements. PARAM is
executed by the user by typing "PARAM".
PARAM also computes the maximum value for each specified
mixing or interest zone for each of the possible hydrodynamic
simulation termination criteria, i.e. maximum downstream
distance, plume area, or plume cross-section. At the
termination of PARAM the user is directed to execute the next
CORMIX1 element, CLASS.
A complete listing of the program PARAM appears in
Appendix A.4. Appendix B provides the interactive output of
PARAM using the design examples presented in Chapter V.
3.C.3 HYDRO
HYDRO is a Fortran program that runs the hydrodynamic
simulation program for the flow classification program
specified in CLASS. The simulation program elements are based
on the similarity theory presented in Chapter II.
HYDRO consists of control programs or "protocols" for each
hydrodynamic flow classification (V1,V2,H3, etc.) as specified
by CLASS. Each protocol executes a series of subroutines or
"modules" corresponding to the flow phenomena (e.g. Wirght's
(1977) mdnf, mdff, bdnf, bdff; surface interaction modules,
etc.) which may occur in that flow classification. Thus HYDRO
assembles the appropriate simulation from the modules are
which are arranged like "pigeon holes".
65
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Table 3.1 lists all modules called by the protocols for a
hydrodynamic simulation. The "type" column indicates whether
the analysis was based on a continuous or control volume
approach. Table 3.1 lists the flow classification as given in
CLASS and the protocols for assembling the simulation modules
corresponding to that flow classification. In Table 3.2, the
protocols list the simulation modules to be called in order,
from left to right, to complete the hydrodynamic simulation.
HYDRO creates a tabular output file of the simulation
containing information on geometry (trajectory, width, etc.)
and mixing (dilution, concentration). The user executes HYDRO
by typing "HYDRO".
After HYDRO has executed, the user may view the tabula
output file, giving detailed information on the trajectory and
dilution of the hydrodynamic flow simulation. The program
listing of HYDRO appears in Appendix A.5 and the interactive
output appears in Appendix B as discussed in the design
examples chapter V.
66
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Table 3.1 Hydrodynamic Simulation Modules
MODULE
(MOD)
NAME
TYPE
01
11
16
21
22
31
32
33
34
41
61
zof e
mdnf
mdf f
bdnf
bdff
surface approach
surface impingement
upstream spreading
surface impingement
full vertical mixing
surface impingement
unstable near-field
buoyant spreading
passive diffusion
Control Volume
Continuous
Continuous
Continuous
Continuous
Control Volume
Control Volume
Control Volume
Control Volume
Continuous
Continuous
67
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Table 3.2 Hydrodynamic Simulation Protocols
Flow Classification: VI, HI
Modules: 01 11 21 22 31 41 61
Transition Rule: 013507
T
End of HMZ
Flow Classification: VIP,HIP
Modules: 01 11 16 22 31 41 61
Transition Rule: 024507
T
End of HMZ
Flow Classification: V2,H2
Modules: 01 11 16 31 41 61
Transition Rule: 02507
T
End of HMZ
Flow Classification: V3, H3
Modules: 01 11 21 32 41 61
Transition Rule: 01607
T
End of HMZ
Flow Classification: V4, H4
Modules: 01 11 33 61
Transition Rule: 050
T
End of HMZ
Flow Classification: V5, H5
Modules: 01 11 21 22 31 41 61
Transition Rule: 013507
T
End of HMZ
Flow Classification: V6, H6
Modules: 01 34 41 61
Transition Rule: 007
T
End of HMZ
68
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Chapter IV
Data Comparison and Validation
In this chapter the predictions of CORMIX1 will be
compared with laboratory and field data. This chapter is not
meant to be an extensive validation of CORMIX1 predictions for
all possible flow classifications, but rather a limited test
of key CORMIX1 elements. Future work plans for CORMIX1
include additional calibration and validation with both
available laboratory and field data.
The comparison of CORMIX1 predictions will focus on the
near field flows, the unstable surface impingement process,
and the near vertical impingement with buoyant upstream
spreading module and buoyant surface spreading.
4.A Near Field Flows (sub-surface regions)
To validate the near field flows, CORMIX1 predictions were
compared with laboratory data from Fan (1967), Wright (1977),
and Flatten and Keffer (1971) .
Figures 4.1 and 4.2 show two cases of Fan's (1967)
trajectory data plotted with CORMIX1 projections. Fan
released a dyed salt solution into uniform ambient flow within
a 40.Oxl.10xO.61 m flume. Fan did not include the effects of
surface impingement in his analysis. Photographs recorded
trajectory and concentrations were measured with conductivity
probes.
Figure 4.1 shows an experiment 20-12 with a jet injected
perpendicularly (8 = 90.0° ) into crossflow (velocity ratio R
= uo/ua= 12) and a Froude number Fo = 20 representing a weakly
deflected forced plume. In this experiment, CORMIX1 predicts
a VI classification with a mdnf -> mdff -> bdff flow. CORMIX1
appears to slightly under predict Fan's observed trajectory by
about 20%. This discrepancy could be accounted for by Fan's
method for defining the plume centerline as the intersection
of lines of equal concentration within the plume cross-
section, and not location of maximum concentration within the
plume. CORMIX1 assumes a maximum concentration along the flow
centerline.
Figure 4.2 illustrates experiment 40-4 where the effect of
a larger crossflow with (R = 4.0) a less buoyant jet (Fo =
69
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0.40 -
o
LjJ
X
n 0.20 H
0.00
• = Fan. 1967
Uo = 0.174 m/s UO = 0.20B m/s
Froude No. = 20.0
Run No. 20-12
- = CORMIX1
I I I I I I I I I | I I I I I I I I I | I I I I I I I I I | M I I I I I I I | I I I I I I I I I |
0.00 0.20 0.40 0.60 0.80 1.00
DISTANCE X (m)
Figure 4.1 Fan's Buoyant Jet Trajectory, Expr. 20-12, R = 12
70
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0.40 -
n 0.20 H
0.00
Fan, 1967
Uo = 0.408 m/s UO = 1.63 m/s
Froude No. = 40.0
Run No. 40-4
CORMIX1
0.00 0.20 0.40 0.60 0.80
DISTANCE X (rn)
1.00
Figure 4.2 Fan's Buoyant Jet Trajectory, Expr. 40-1, R = 4
71
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40.0) where the flow becomes significantly deflected soon
after emerging from the discharge nozzle. In this experiment,
CORMIX1 predicts a VI classification with a mdnf -> mdff ->
bdff flow. CORMIX1 trajectory predictions appear to agree
well with Fan's data.
Dilution predictions from CORMIX1 that correspond with the
experiments in Figures 4.1 and 4.2 are presented in Figures
4.3 and 4.4, respectively. In both cases, dilution
predictions are in close agreement with Fan's results. It
should be noted that all CORMIX1 near field predictions are
continuous, the apparent "kink" in Figure 4.4 (and Figures 4.5
and 4.6) is due to the chosen step size and could be
eliminated by a higher resolution.
Figure 4.5 shows CORMIX1 trajectory predictions for
laboratory experiment 2-2 by Wright, (1977). Wright conducted
his experiments in a 8.7x0.61x0.61 m towing tank. Figure 4.5
shows an experiment with R - 37 and Fo =67. As can be seen,
CORMIX1 predictions appear to be in strong agrement with
Wright's data. Unfortunately, no dilution data was available
for this experiment.
Figure 4.6 shows the effect on a nonbuoyant jet of
changing the angle between the axis of the discharge to the
horizontal plane from 80 = 90°, as in the previous examples,
to 9o = 60°. This experiment by Flatten and Keffer was
conducted with air in a 2.44 x 1.22 m wind tunnel. CORMIX1
predictions appear to be in good agreement near the source,
but tend to deflect more strongly. No dilution data was
available for this experiment.
4.B Near Vertical Surface Impingement With Buoyant Upstream
Spreading
Field data for a deep wastewater outfall off the
California coast was obtained by the Allan Hancock Foundation
(1964); (see also Chen, 1980). In this case, a strongly
buoyant discharge with gd = 0.225 (Ap/p = 0.025) was released
16.8 m below the surface through a 2.0 m diameter outfall into
the ocean with an ambient current of 0.175 m/s. CORMIX1
predicts a flow classification of V5, indicating a stable
discharge configuration with buoyant upstream spreading after
surface impingement. The results of the CORMIX1 simulation
and the actual data appear in Figures 4.7a and 4.7b. Figure
4.7a shows a side view of the discharge as predicted by
CORMIX1. Unfortunately, no field data is available to compare
with these subsurface predictions. Field data is limited to
photographic observation of the surface plume. Figure 4.7b
shows a plan view of the CORMIX1 prediction with field data
available from this remote sensing evidence (Chen, 1980).
CORMIX1 predicts an upstream intrusion of 91 m with a flow
72
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CM
o-
z:
o
Fan, 1967 - = CORMIX1
Ua = 0.174 UO = 2.08 (m/s)
Froude No. = 20.0
Run No. 20 - 12
i 1—i i i i 111 1 1—r i i i 111 1 1—i i i i 111
10 ~2 10 ~1 1 10
DISTANCE ALONG TRAJECTORY s1 (m)
Figure 4.3 Fan's Buoyant Jet Dilution, Expr. 20-12, R = 12
73
-------
o-
Fan, 1967 - = CORMIX1
Ua = 0.408 UO = 1.63 (m/s)
Froude No. = 40.0
Run No. 40-4
10 -1
DISTANCE ALONG TRAJECTORY s1 (rn)
Figure 4.4 Fan's Buoyant Jet Dilution, Expr. 40-4, R = 4
74
-------
0.40 -J
£
M
LJ
X
0.00
0.00
Wright, 1977
Ua = 0.046 m/s UO
Froude No. = 67
Run 2-2
CORMIX1
1.720 m/s
i | i I i I I i I l l | r~~]i i i
0.40 0.80
DISTANCE X (m)
Figure 4.5 Wright's Buoyant Jet Trajectory, Expr. 2-2 R = 37
75
-------
o
6
LO -
o O
UJ
X
O -
Flatten and Keffer, 1971
THETAO = 60.0 deg SIGMAO 0.0 deg
Ua = 1.58 m/s UO = 9.99 m/s
Froude No. = infinity
- = CORMIX1
(I I I (I I I I j I TTlllIII[1III
I I I I I I I I I I I I I I I
0.00
0.05 0.10 0.15
DISTANCE X (m)
0.20
Figure 4.6 Flatten and Keffer, 9o = 60.0
76
-------
••20m
J0.98m
^
u0=O.I75 m/s
-75
-50
-25
\
\
9*
\\
25
50
75m
Figure 4.7a Simulation of Stable Surface Impingement/Upstream
Spreading
77
-------
Hancock data
CORMIX1
Figure 4.7b
Spreading
Plan View of Surface Impingement/Upstream
78
-------
half width at impingement of 237 m. The actual data indicate
an upstream intrusion of about 90 m and flow half-width at
impingement of about 75 m. No dilution or flow depth data
were available. CORMIX1 has good agreement with upstream
spreading, but over predicts flow width. Possible sources of
error in the prediction might be a caused by weak density
gradients which can be expected in such ocean depths. Future
work for CORMIX1 includes the consideration of density
stratification. Overall agreement appears to be satisfactory
in this test case.
4.3 Unstable Surface Impingement With Buoyant Upstream
Spreading
Fischer et al. (1979), presents field data for the San
Onofre nuclear power plant. The San Onofre Unit 1 discharge
is a thermal discharge from a 4.3 m diameter outfall located
5.0 ~R
m below the surface water off the California coast. The
ambient current in the vicinity of the outfall is about 0.14
m/s and the discharge velocity is 1.45 m/s. The temperature
difference between the ambient current and the discharge is
11.1'C giving rise to a buoyant acceleration of go ' = 0.032.
CORMIXl predicts a flow classification of V6, representing an
unstable shallow water discharge with buoyant upstream
spreading. This case is further discussed as a design example
in Chapter V.
Figure 4.8 shows the CORMIXl results compared with actual
field results obtained with a scanning infrared radiometer
(Figure 5.3 presents the cross-section predicted by CORMIXl).
CORMIXl predicts an upstream intrusion of 37 m with a flow
half-width of 95 m at surface impingement. The data show an
upstream intrusion and half-width at surface impingement of
about 30 m and 85 m, respectively. The unstable near field
impingement is a highly complicated hydrodynamic process, and
the results of CORMIXl appear to be in excellent agreement,
although the width of the density current may be somewhat
over-predicted with increasing downstream distance.
4.4 Summary
Overall CORMIXl predictions appear to be in good first
order agreement with available observations in the field and
laboratory. CORMIXl can predict buoyant upstream spreading,
where other available models (e.g. PLUME) would have failed
entirely.
Although limited data are available for both field and
laboratory experiments, further efforts will be made to
compare model predictions and adjust parameters in the flow
classification system.
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CORMIX1 Plume Front Prediction
Grid Interval =30.5m
Figure 4.8 Plan View Comparison of San Onofre Prediction and
Field Data (Corresponding cross-section in Figure 5.3)
-------
Chapter V
Design Case Studies
The purpose of this chapter is twofold; i) to give an
overview of the significant features of CORMIX1 in discharge
evaluation and design, and ii) to illustrate the flexibility
of CORMIX1 in highly divergent design conditions. The first
case presented represents a small hypothetical industrial
discharge into a slowly flowing river, and the second case is
an actual large cooling water discharge into the ocean.
5.A Case 1: AB CHEMICAL CORP., WEST VIRGINIA
This is a hypothetical example of a discharge in a bounded
section. The CORMIX1 output appears in Appendix B.I. This
buoyant discharge represents a complex 3-D trajectory subject
to three legal mixing criteria; a toxic dilution zone, a plume
cross-sectional area criteria on a legal mixing zone, and a
downstream region of interest. The analyst seeks pollutant
concentrations at these locations.
5.A.I The Problem Statement
AB Chemical discharges an industrial effluent into the
Ohio River through a submerged pipe outfall. The discharge
flow is 0.2 m**3/s and contains 0.5 miCi/m**3 of Cesium 134.
Cesium is considered toxic, and has a criterion maximum
concentration (CMC) value of 0.0005 miCi/m**3 (hypothetical).
For the critical summer conditions the discharge temperature
is 35.0'C.
At the discharge site the Ohio River is dammed as a run-
of-the-river reservoir. The cross-section is approximately
trapezoidal with a bottom width of 240 m and bank slopes of 1
in 3. The river depth is 8.5 m. Due to gate operation at the
dam the river velocity varies between 0.1 m/s (near-stagnant)
and 0.6 m/s. Typical summer temperatures are 22.0'C. The
river roughness conditions are given by a Manning's n of
0.024.
The outfall is located 50 m from the berm line near the
left bank. The right bank is under the jurisdiction of the
State of Ohio. The port is pointing directly offshore (normal
to the ambient flow) and is angled 20° upward above the
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horizontal. The round port has a diameter of 30 cm and its
center lies 0.5 m above the river bottom.
The mixing zone limitations of the State of West Virginia
have to be considered. These stipulate that the mixing zone
have a maximum dimension of 33% of the cross-sectional area
and a length equal to 10 times the stream width.
5.A.2 CORMIX1 Analysis
The first step in the analysis would be to schematize
the bounded cross-section as shown in Figure 5.1. Stream
cross-sections are usually highly irregular; the trapezoidal
cross-section represents an initial approximation of the
actual stream cross-section. CORMIX1 assumes an equivalent
rectangular cross-section as shown in Figure 5.1, which the
analyst would approximate.
Using DATIN, the site parameters are specified. One of
the advantages of logic programming is the "transparency" of
the rule base to the user. For example, DATIN seeks
information concerning the distance from the outfall to the
nearest shore. During the session, DATIN prompts:
What is the distance from the nearest bank or shore to the
effluent discharge point (m)? [1]
If the user wants to know why this information is needed,
he could determine the rule in the knowledge base that DATIN
is trying to evaluate simply typing "why", to which DATIN
responds:
M.I is trying to determine whether the following rule is
applicable in this consultation:
kb-33:
if bounded_section = 1 and
distance_bank = YB and
stream_width = BS and
BS*0.5 >= YB and
location_bank = NBANK
then nearest_bank = found
The following entries are also under consideration:
kb-29 (a rule)
kb-4 (an initialdata) [2]
The user can conclude that the question in expression [1] is
asked because DATIN is seeking a valuation for the expression
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Cross-section View
50m
W. Vo.
Ohio
Plan View
+ 0.5
m
8.5m
240m
262.75m
37.5m
t
uo =
t t t
O.I m/s
t t
f
D = 0.3m
-r'20'
0.5m
Detail of Discharge
Figure 5.1 Schematization of Cross-section
83
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"nearest_bank" in "kb-33". The flag "kb-33" is a label
created by DATIN for this rule.
If the user is interested in why DATIN is seeking a
valuation for "nearest_bank" in kb-33, expression [2] also
lists that kb-29 and kb-4 are also under consideration. Thus
the user can conclude that kb-33 was invoked by another rule,
kb-29; and kb-29 was invoked by kb-4 an "initialdata" (similar
to a "goal") statement. The user can see kb-29 by typing
"list kb-29" to which DATIN responds (simplified here, for
full printout, see appendix B.I)
kb-29:if depth_at_discharge = H and
nearest_bank = found and
ambient_velocity_field = found and
then ambient_conditions = found [3]
to which the user can conclude that "ambient_conditions" for
the discharge were being sought, when the rule in expression
[2] for "nearest_bank" was invoked.
Another advantage to logic programming is in error
handling. It is simple to write rules that reject
contradictory data. For example, when schematized as a
rectangular cross-section, the stream width is 262.75 m and
the distance to the nearest bank (W. Va.) is 37.5 m. If the
user made an error and responded to expression [1] by entering
the distance to the Ohio shore of 225.25 m, DATIN would
respond:
The distance to nearest bank is in error.
The value must be less than half the stream width.
Recheck and re-enter a value less than or equal
to 131.375 (m). [4]
and the user is given another chance to enter the correct
value of 37.5 m. This result can be explained as follows.
The rule kb-33 in expression [2] would fail when evaluating
the "BS*0.5 >= YB" clause (stream width = BS = 226.75) in the
premise. Since kb-33 failed when DATIN was seeking a
valuation for the expression "nearest_bank" it will
automatically seek another rule in the knowledge base with
"nearest_bank" in its conclusion. Error handling advice is
placed in the next rule that has "nearest_bank" in its
conclusion. Thus the message shown in expression [4] comes
from the next rule in the knowledge base with "nearest_bank"
in its conclusion.
After completing DATIN, the analyst executes PARAM,
followed by CLASS. In CLASS the analyst is advised of the
intermediate conclusions reached; i.e. the discharge is a near
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horizontal "H" case, 1m/h = 0.885 indicating deep water with
weak momentum, ID/H = 0.923 showing weak buoyancy, and finally
ln/h =0.864 concluding that buoyancy dominates at surface
impingement. CLASS assigns a flow classification of HI,
specifying the flow simulation will consist of mdnf -> bdnf ->
bdff -> surface approach -> buoyant surface spreading ->
passive diffusion.
Viewing the output of HYDRO shown in Figure 5.2, the plume
attaches to the left bank at x = 650 m downstream. The plume
meets the legal criteria of 33% of the stream cross-sectional
area at x = 850 m downstream of the orifice, S = 395, c =
0.0014 miCi/m**3. At x = 1200 m the effluent is fully mixed
within the cross section with c = 0.00053 miCi/m**3.
In SUM, the analyst is alerted that the assumed criterion
maximum concentration (CMC) value for the toxic discharge is
not met within the legal restrictions. The user is advised to
improve dilution by changing the exit velocity, decreasing the
discharge angle Go , locating the port in a deeper section of
the cross-section, or by orienting 'the discharge so it does
not attach to the left bank first.
5.B Case 2: SAN ONOFRE UNIT 1
While the previous case represented a hypothetical small
stable deepwater discharge, San Onofre is an existing large
cooling water outfall located on the coast of California.
Large cooling water outfalls are typically unstable,
characterized by strong momentum and relatively weak buoyancy.
The CORMIXl session appears in Appendix B.2. The output
includes all available help a user could request during the
consultation.
5.B.I The Problem Statement
The San Onofre Nuclear Generating Station, Unit 1, is
operated by Southern California Edison Company. It has a power
output of 450 MW. The cooling water from unit 1 is discharged
about 1000 m offshore at a local water depth of 5.0 m. The
bathymetry is sloping approximately linearly from the
shoreline.
The discharge port is round with a diameter of 4.3 m and
extends about 0.2m above the surrounding bottom. The cooling
water is discharged vertically at a flowrate of 21 m**3/s. The
design ambient temperature is 24.0°C and the condenser
temperature rise is 11.1'C (20°F).
The site is characterized by weak currents along the shore
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Cross-section
AB Chemical Co.
a) Close-Up Side View of Near Field
W.Va.
Plan View
Ohio River
Ohio
b) Overall Plan View
Figure 5.2 Plot of CORMIX1 AB Chemical Co. Predictions
86
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of 6 cm/s in the southerly direction. The bottom is smooth and
sandy with an estimated Darcy-Weisbach friction factor of
0.015 (Fischer et al., 1979, Lee and Jirka, 1981).
5.B.2 CORMIX1 Analysis
The representative cross-section in this case would place
the discharge 500 m from shore in 5.0 m of water.
Class assigns a flow classification of V6, indicating an
unstable discharge, characterized by strong momentum and
relatively weak buoyancy. The interactive session of CORMIX1
appears in Appendix B.2.
Figure 5.3 plots the cross-section of the CORMIX1
predictions. The plan view of this simulation is shown in
Figure 4.8.
SUM alerts the analyst to the upstream buoyant intrusion,
and the possible plume bank attachment. Again the analyst is
advised to improve dilution by some of the same options
outlined in section 5.A.2..
87
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-30 -20 -10
5.0m
10 20 30 40m x
Figure 5.3 San Onofre Longitudinal Cross-Section (Vertical
Distortion = 6, See Corresponding Plan View in Figure 4.8)
88
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Chapter VI
Conclusions and Recommendations
U.S. water quality policy allows for a mixing zone as a
limited area or volume of water where the initial dilution of
a discharge occurs. Water quality standards apply at the edge
and outside of the mixing zone. Toxic discharges have
additional regulatory restrictions, which require additional
dilution analysis. The implementation of this policy in the
National Pollution Discharge Elimination System (NPDES)
permitting process places the burden of prediction of initial
dilution on both regulators and dischargers. Given a myriad
of possible discharge configurations, ambient environments,
and mixing zone definitions, the analyst needs considerable
training and expertise to conduct accurate and reliable mixing
zone analysis. An expert system, CORMIX1, was developed as an
analysis tool for regulators and dischargers.
CORMIX1 predicts the dilution and trajectory of a single
buoyant discharge into a unstratified ambient environment with
or without crossflow. CORMIX1 uses knowledge and inference
rules obtained from hydrodynamic experts to classify and
predict buoyant jet mixing. CORMIX1 gathers the necessary
data, checks for data consistency, assembles and executes the
appropriate hydrodynamic simulation models, interprets the
results of the simulation in terms of the legal requirements
including toxic discharge criteria, and suggests design
alternatives to improve dilution characteristics.
The results of the hydrodynamic simulation are in good to
excellent agreement with field and laboratory data. In
particular, CORMIX1 correctly predicts highly complex
discharge situations involving boundary interactions and
buoyant intrusions, a result not predicted by other currently
available initial mixing models.
However, simulation models of complex phenomena, such as
the hydrodynamics of jet and plumes described here, should
always be given with a caveat. The analyst is forced to make
many assumptions when modeling the complex mechanisms
controlling buoyant jet flow.
In reality, many physical processes which occur in the
environment are difficult to simulate or control for in
laboratory experiments. If the basic assumptions within the
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methodology are violated in the analysis of a discharge, the
resulting analysis will be tenuous at best. For example,
CORMIX1 assumes a uniform velocity field in a uniform cross-
section. This is a good first order approximation for many
simple discharges. But the extreme case represented by a
discharge into a cross-section that is highly variable with
downstream distance, characterized by strong velocity
fluctuations within the flowfield (such as a discharge into
stream section with rapids), would be beyond the scope of
CORMIX1.
What has been attempted here is to place a modestly
complex hydrodynamic simulation methodology within the
framework of a rule based expert system. Many of the common
pitfalls to model use - incomplete or contradictory data,
choice of appropriate simulation model, and faulty
interpretation of results - appear to be mitigated within the
context of an expert system methodology.
CORMIX1 educates the user to the important hydrodynamic
processes controlling the flow. It will give 3-D discharge
trajectory and dilution. It will alert the user to where
significant legal criteria apply to the discharge. It
predicts buoyant upstream spreading, which presently no other
model can simulate. It allows for a rapid evaluation of
design alternatives, and gives the user suggestions for
improving dilution characteristics of the discharge. Overall
CORMIX1 appears to be an excellent first cut tool for the
analyst.
As stated in Chapter IV, further work should be done to
determine the constants in the flow classification system and
all other constants within the model. More research should be
devoted to the concepts involved in the design recommendations
in SUM. The existing data base is limited for conducting
rigorous validation studies indicating a need for additional
field and laboratory data.
The problem domain of CORMIX1, single port positively
buoyant discharges into a uniform density field, should be
extended to include near field boundary attachments,
negatively buoyant discharges, and density stratified
environments. The application of computer generated graphics
to plot simulation results would enhance user understanding of
simulation results.
Future work plans for CORMIX1 are: further calibration of
model constants, consideration of dynamic jet boundary
attachment, analysis of negatively buoyant discharges, and the
effects of density stratified environments.
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Reterences
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(1964) , "Final Report on an Investigation on the Fate of
Organic and Inorganic Wastes Discharge into the Marine
Environment and Their Effects of Biological Productivity",
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Phenomena", J. Fluid Mechanics, Vol. 31, pt. 2.
Barnwell, T. O.,Brown L. C., and Marek, W., (1985).
"Development of a prototype expert advisor for the enhanced
stream water quality model QUAL2E", Internal Report,
Environmental Research Laboratory, Office of Research and
Development, U.S.E.P.A., Athens, Georgia, September, 1985.
Briggs, G. A. (1969). Plume Rise, U.S. Atomic Energy
Commission, Division of Technical Information, Oak Ridge,
Tennessee.
Congressional Research Service, (1977). "Legislative History
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Chen, J. C., (1980). "Studies on Gravitational Spreading
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Control Association, vol. 20., No.33, pp. 6818-6835.
Findley and Farber (1983), Environmental Law in a Nutshell,
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Fischer, H. B. et al . (1979). Mixing in Inland and Coastal
Wat_ers , Academic Press, New York.
Gaschnig, J., Reboh, and J. Reiter, (1981). "Development of a
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Palo Alto, Calif. ~~
Holley, E. R., and Jirka, G. H. (1986). "Mixing in Rivers",
Technical Report E-86-11, U.S. Army Corps of Engineers,
Washington, B.C.
Jirka, G. H. and D. R. F. Harleman (1973). "The Mechanics of
Submerged Multiport Diffusers for Buoyant Discharges in
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Structures Design Manual, E. Naudascher, Ed., Vol 10.
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"Theoretical and Experimental intermediate Field Dynamics of
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Jones, J. M., G. H. Jirka, and D. A. Caughey, (1985).
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Stratified Flow Problems, with an Application to the
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Koh, R. C., and Brooks, N. H. (1975). "Fluid Mechanics of
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List, E. J-, and Imberger J., (1973). "Turbulent Entrainment
in Buoyant Jets", Proc. ASCE, J. HydraulicsDivision,99,
1461-1474.
Morton, R. B. (1959). "Forced Plumes," Journal of Fluid
Mechanics, vol 5, pp 151-163.
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Muellenhoff, W. P., et. al . , (1985). "Initial Mixing
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KH-R-35, W. M. Keck Laboratory of Hyydraulics and Water
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Roberts, P. J. W., (1979). "Line Plume and Occ-an Outfall
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Rodi, W . ed, (1932). Turbulent Buoyant Jets and Plumes ,
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based Toxics Control", Office of Water, Washington, B.C.,
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Bensity Stratif icaticm_gn the Characterise i c _ B e h ay i o r q f R o u n d
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APPENDIX A
Appendix A contains the code listing for all programs
within CORMIX1. The M.I programs are presented first followed
by the Fortran programs. Section A.I has the listing for
DATIN, the M.I data entry module. Section A.2 shows the M.I
listing for CLASS, the flow classification program. Section
A.3 lists SUM, the M.I program that summarizes the
hydrodynamic simulation output. Section A.4 is the Fortran
program PARAM which computes the length scales used in the
flow classification system. Section A.5 contains the Fortran
listing for the hydrodynamic simulation program HYDRO.
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