&EPA
United States
Environmental Protection
Agency
Environmental Research
Laboratory
Athens, GA 30613
EPA 600-3-90/012
Feb 1990
Research and Development
Expert System for
Hydrodynamic Mixing
Zone Analysis of
Conventional and Toxic
Submerged Single Port
Discharges (CORM1X1)
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EPA/600/3-90/012
February 1990
EXPERT SYSTEM FOR HYDRODYNAMIC MIXING ZONE
ANALYSIS OF CONVENTIONAL AND TOXIC SUBMERGED
SINGLE PORT DISCHARGES (CORMIX1)
by
Robert L. Doneker and Gerhard H. Jirka
DeFrees Hydraulics Laboratory
School of Civil and Environmental Engineering
Cornell University
Ithaca, New York 14853
Cooperative Agreement No. CR813093
Project Officer:
Thomas 0. Barnwell, Jr.
Assessment Branch
Environmental Research Laboratory
Athens, Georgia
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30613
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DISCLAIMER
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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FOREWORD
As environmental controls become more costly to implement
and the penalties of judgment errors become more severe, en-
vironmental quality management requires more efficient manage-
ment tools based on greater knowledge of the environmental
phenomena to be managed. As part of this Laboratory's research
on the occurrence, movement, transformation, impact, and control
of environmental contaminants, the Assessment Branch develops
state-of-the-art mathematical models for use in water quality
evaluation and management.
Special water quality regulations have been proposed to
limit lethal acute concentrations of toxic pollutants to a
spatiallly restricted toxic dilution zone. Predictive mathe-
matical models are used to establish the initial dilution of a
given discharge and the characteristics of its mixing zone. To
assist the analyst in choosing the appropriate models, deter-
mining the limits of applicability, and establishing data needs,
an expert system has been developed. The structured computer
program uses knowledge and inference procedures that would be
used by water quality experts. Operated on a personal computer,
the program appears to be a highly flexible tool for regulatory
analysis that is adaptable to the evaluation of alternatives
in engineering design.
Rosemarie C. Russo, Ph.D.
Director
Environmental Research Laboratory
Athens, Georgia
111
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ABSTRACT
U.S. water quality policy includes the concept of a mixing
zone, a limited area or volume of water where the initial dilution
of a discharge occurs. Water quality standards apply at the edge
and outside the mixing zone. The implementation of this policy
in the permitting process places the burden of prediction of ini-
tial dilution on both regulators and dischargers. Dischargers of
aqueous toxic substances are subject to additional mixing zone
requirements. Give 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.
The Cornell Mixing Zone Expert System (CORMIX1) was developed
to predict the dilution and trajectory of a submerged single port
discharge of arbitrary density (positive, neutral, or negative)
into a stratified or uniform density ambient environment with or
without crossflow. CORMIX1 uses knowledge and inference rules
based on hydrodynamic expertise to classify and predict buoyant
jet mixing. CORMIX1 gathers the necessary data, checks for data
consistency, assembles and executes the appropriate hydrodynamic
models, interprets the results of the simulation in terms of the
legal requirements including toxic discharge criteria, and sug-
gests design alternatives to improve dilution characteristics.
CORMIXl, with its emmpasis on rapid intitial mixing, assumes
a conservative pollutant discharge neglecting any physical, chem-
ical, or biological reaction or decay process. The predictive
results can be readily converted, however, to adjust for first-
order reaction processes.
The results of the hydrodymanic simulations are in good to
excellent agreement with field and laboratory data. In particular,
CORMIXl correctly predicts highly complex discharge situations
involving boundary interactions, dynamic bottom attachments, in-
ternal layer formation, and buoyant intrusions--all features that
are beyond the predictive capabilities of other currently avail-
able initial mixing models.
This report was submitted in partial fulfillment of Coopera-
tive Agreement No. CR813093 with Cornell University under the
sponsorship of the U.S. Environmental Protection Agency. This
report covers a period from July 1986 to July 1989, and work was
completed as of July 1989.
IV
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CONTENTS
Abstract iv
Acknowledgments xv
Chapter I
INTRODUCTION AND LEGAL BACKGROUND 1
1.1 Introduction 1
1.2 Overview of U.S. Water Quality Policy 2
1.2.1 The Federal Water Pollution Control Act of
1972 4
1.2.2 The Clean Water Act of 1977 6
1.3 The Concept of Mixing Zones 9
1.3.1 Mixing Zones: Development and Regulations .... 9
1.3.2 Special Mixing Zone Requirements for
Toxic Substances 13
1.4 Regulatory Assessment of Discharges and the
Permitting Process 14
1.4.1 The NPDES Permit System 14
1.4.2 Need for Regulatory Assessment Tools 14
1.4.3 Motivation for Expert Systems Approach .... 15
1.5 CORMIX1: An Expert System for Mixing Zone
Analysis of Submerged Single Port Aquatic
Discharges 18
1.5.1 Scope and Objective 18
1.5.2 Results of an Earlier Feasibility Study .... 19
1.5.3 Summary of Present Study 19
Chapter II
HYDRODYNAMIC ELEMENTS OF MIXING PROCESSES 21
2.1. Buoyant Jet Mixing Processes 23
2.1.1 Description of Turbulent Jets and Plumes ... 23
2.1.2 Dimensional Analysis of Buoyant Jets 24
2.1.2.1 Simple Jet in Stagnant Uniform
Environment 25
2.1.2.2 Simple Plume in Stagnant Uniform
Environment 27
2.1.2.3 Generalizations: Jet/Plume Interactions,
Crossflow Effects, and Stratification Effects . . 29
2.1.3 Length Scales 32
2.1.3.1 Discharge Length Scale 32
2.1.3.2 Jet/Crossflow Length Scale 32
2.1.3.3 Plume/Crossflow Length Scale 33
v
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2.1.3.4 Jet/Plume Length Scale 33
2.1.3.5 Jet/Stratification Length Scale 33
2.1.3.6 Plume/Stratification Length Scale 34
2.1.4 Typical Flow Regimes of Unconfined Buoyant
Jets 34
2.1.4.1 Weakly Deflected Jet In Crossflow 35
2.1.4.2 Strongly Deflected Jet In Crossflow 36
2.1.4.3 Weakly Deflected Plume in Crossflow 37
2.1.4.4 Strongly Deflected Plume in Crossflow .... 37
2.1.4.5 Horizontal Jet with Vertical Buoyant
Deflection 38
2.1.4.6 Vertical Plume with Horizontal Momentum
Deflection 39
2.2.4.7 Vertical Jet in Linear Stratification .... 40
2.2 Buoyant Spreading Processes 41
2.2.1 Buoyant Surface Spreading 41
2.2.2 Buoyant Bottom Spreading 44
2.2.3 Buoyant Spreading at Pycnocline 44
2.2.4 Buoyant Spreading at Terminal Level 44
2.3 Passive Ambient Diffusion Processes 46
2.3.1 Diffusion in Unbounded Channel Flow 46
2.3.2 Horizontal Diffusion in Unbounded Channel
Flow 48
2.3.3 Vertical Diffusion in Stratified Shear Flow . . 49
2.4 Interaction Processes: Surface or Bottom
Boundaries, and Internal Layer Formation .... 49
2.4.1 Near-Horizontal Surface Approach 50
2.4.2 Near-Vertical Surface Impingement with
Buoyant Upstream Spreading 54
2.4.3 Near-Vertical Surface Impingement with
Full Vertical Mixing 57
2.4.4 Bottom Interaction Processes 57
2.4.4.1 Wake Attachment 58
2.4.4.2 Coanda Attachment 60
Chapter III
HYDRODYNAMIC FLOW CLASSIFICATION 61
3.1 Ambient and Discharge Data: Geometry and Flow
Variables 61
3.1.1 Ambient Geometry and Flow Conditions 61
3.1.2 Ambient Density Stratification 62
3.1.3 Discharge Parameters 64
3.2 Near-field Flow Classification 66
3.2.1 General Procedure 68
3.2.2 Flow Classes S for Linear Ambient
Stratification 75
3.2.3 Flow Classes V or H for Buoyant Discharges
into Uniform Ambient Layers 76
3.2.4 Flow Classes NV or NH for Negatively
Buoyant Discharges in Uniform Ambient Layers . . 77
3.2.5 Flow Classes (..)A for Bottom Attached
vi
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Flows 78
3.3 Far-Field Flow Behavior 79
Chapter IV
EXPERT SYSTEM CORMIX1: GENERAL FRAMEWORK 81
4.1 Background on Expert Systems and Logic
Programming 82
4.2 Structure of CORMIX1 85
4.2.1 Data Input Element: DATIN 85
4.2.2 Parameter Computation Element: PARAM 89
4.2.3 Flow Classification Element: CLASS 89
4.2.4 Hydrodynamic Simulation Element: HYDRO .... 91
4.2.5 Hydrodynamic Simulation Summary Element: SUM . 91
Chapter V
CORMIX1: FLOW PROTOCOLS AND SIMULATION MODULES ... 93
5.1 Flow Protocols 93
5.1.1 Flow Protocols for Buoyant Discharges into
Uniform Ambient Layers (Flow Classes V and H) . . 96
5.1.2 Flow Protocols for Negatively Buoyant
Discharges into Uniform Ambient Layers (Flow
Classes NV and NH) 101
5.1.3 Flow Protocols for Discharges Trapped in
Linearly Stratified Ambients (Flow Class S) . . . 101
5.1.4 Flow Protocols for Bottom Attached Flows
(Flow Classes (..)A) 107
5.2 Hydrodynamic Simulation Modules 107
5.2.1 Simulation Modules for Buoyant Jet Near-Field
Flows 110
5.2.1.1 Introductory Comments 110
5.2.1.1 Discharge Module (MOD01) Ill
5.2.1.2 Weakly Deflected Jet In Crossflow (MOD11,
mdnf) 112
5.2.1.3 Weakly Deflected Wall Jet in Crossflow
(MOD12, mdnf-wj) 113
5.2.1.4 Near-Vertical Jet in Linear Stratification
(MOD13, mdls-v) 113
5.2.1.5 Near-Horizontal Jet in Linear Stratification
(MOD14, mdls-h) 114
5.2.1.6 Strongly Deflected Jet In Crossflow
MOD16, mdff) 114
5.2.1.8 Strongly Deflected Wall Jet in Crossflow
(MOD17, mdff-wj) 115
5.2.1.4 Weakly Deflected Plume in Crossflow (MOD21,
bdnf) 115
5.2.1.9 Strongly Deflected Plume in Crossflow
(MOD22,bdff) 115
5.2.2 Simulation Modules for Boundary Interaction
vii
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Processes 116
5.2.2.1 Near-Horizontal Surface/Bottom/Pycnocline
Approach (MOD31) 116
5.2.2.2 Near-Vertical Surface/Bottom/Pycnocline
Impingement with Buoyant Upstream Spreading
(MOD32) 117
5.2.2.3 Near-Vertical Surface/Bottom/Pycnocline
Impingement with Full Vertical Mixing (MOD33) . . 118
5.2.2.4 Near-Vertical Surface/Bottom/Pycnocline
Impingement with Unstable Recirculation, Buoyant
Restratification, and Upstream Spreading
(MOD34) 118
5.2.2.5 Stratified Terminal Layer Impingement with
Buoyant Upstream Spreading (MOD36) 118
5.2.2.6 Stratified Near-Vertical Surface Injection
with Upstream Spreading (MOD37) 119
5.2.3 Simulation Modules for Buoyant Spreading
Processes 119
5.2.3.1 Buoyant Surface/Bottom Spreading (MOD41) . . 119
5.2.3.2 Buoyant Terminal Layer Spreading (MOD42) . . 120
5.2.4 Simulation Modules for Attachment/Detachment
Processes 120
5.2.4.1 Wake Recirculation (MOD51) 120
5.2.4.1 Lift-Off/Fall-Down (MOD52) 120
5.2.5 Simulation Modules for Ambient Diffusion
Processes 120
5.2.5.1 Passive Diffusion in Uniform Ambient
(MOD61) 121
5.3.5.4 Passive Diffusion in Stratified Ambient
(MOD62) 121
5.3 Transition Rules, Flow Criteria and Coefficient
Values 121
5.3.1 Transition Rules 122
5.3.2 Flow Classification Criteria 122
5.3.3 Terminal Layer Expressions 128
5.3.4 Model Coefficient Values 128
Chapter VI
SYSTEM EVALUATION AND VERIFICATION 133
6.1 Buoyant Jets in Unconfined Ambient 134
6.1.1 Comparison With Experimental Data 134
6.1.1.1 Stagnant Ambient 134
6.1.1.2 Flowing Unstratified Ambient 137
6.1.1.2.1 Pure Jets In Crossflow 137
6.1.1.2.2 Buoyant Jets in Crossflow 141
6.1.1.2.3 Negatively Buoyant Jets in Crossflow . . . 141
6.1.1.2.4 Buoyant Jets with Three-Dimensional
Trajectories 141
6.1.1.3 Buoyant Jet in Stratified Stagnant Ambient . 147
6.1.2 Comparison of Predictions With Jet Integral
Models 150
viii
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6.1.2.1 Buoyant Jet in Uniform Crossflow 150
6.1.2.2 Buoyant Jet in Stratified Crossflow 150
6.2 Complex Flows With Boundary Interaction 153
6.2.1 Jet Flows in Shallow Receiving Waters 153
6.2.2 Strongly Buoyant Jets in Shallow Receiving
Waters 153
6.2.3 Flows with Wake Interaction 156
6.2.4 Negatively Buoyant Flows With Upstream
Spreading Along Bottom 158
6.3 Summary and Appraisal 158
Chapter VII
APPLICATIONS OF CORMIX1 . 161
7.1 AB Chemical Corporation 161
7.1.1 The Problem Statement 161
7.1.2 CORMIX1 Analysis 162
7.2 MN Municipal Treatment Plant 169
7.2.1 The Problem Statement 169
7.2.2 CORMIX1 Analysis 169
7.3 PQ Power Company 174
7.2.1 The Problem Statement 174
7.3.2 CORMIX1 Analysis 176
7.4 Comments on the Application of CORMIX1 179
7.4.1 Limitations of CORMIX1 179
7.4.2 Hints for CORMIX1 Use in Extreme
Conditions 181
7.4.2.1 (Near-)Surface Discharges 181
7.4.2.2 Elevated Discharges 182
7.4.3 Application to Non-Dimensional Coordinate
Systems 182
7.4.4 Adaptation to First-Order Reaction
Processes 183
Chapter VIII
CONCLUSIONS AND RECOMMENDATIONS 184
REFERENCES 186
Appendix A
STABILITY OF STRATIFIED AMBIENT SHEAR
FLOWS 192
Appendix B
ON-LINE USER ADVICE FOR DATA INPUT (DATIN) 194
B.I Introductory Advice 194
ix
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B.2 Ambient Advice 196
B.3 Density Profile Advice 199
B.4 Discharge Advice 199
B.5 Mixing Zone Advice 200
B.6 Design Advice 201
APPENDIX C
FLOW CLASSIFICATION DESCRIPTIONS 204
C.I V-Flow Classes 204
C.2 H-Flow Classes 210
C.3 S-Flow Classes 217
C.4 NV-Flow Classes 222
C.5 NH-Flow Classes 228
C.6 Attached Flow Classes 233
Appendix D
HYDRO OUTPUT FILE EXAMPLE 238
Appendix E
CASE SUMMARY AND DESIGN RECOMMENDATION
EXAMPLE 244
x
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List of Tables
Table l.l 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 . . 8
Table 1.4 State Legal Mixing Zones 11
Table 3.1 Flow Classification Variables and Length
Scales 67
Table 3.2 Near-Field Flow Classification Procedure . 73
Table 4.1 CORMIX1 Program File Directories 87
Table 5.1 Flow Prediction Modules of CORMIX1 .... 94
Table 5.2 Flow Protocols for Buoyant Discharges into
Uniform Ambient Layers 98
Table 5.3 Flow Protocols for Negatively Buoyant
Discharges into Uniform Ambient Layers 102
Table 5.4 Flow Protocols for Discharges Trapped in
Linearly Stratified Ambients 105
Table 5.5 Flow Protocols for Bottom Attached Flows . 108
Table 5.6 Transition Rules 123
Table 5.7 Coefficients Used in Transition Rules . . . 125
Table 5.8 Flow Classification Criteria 126
Table 5.9 Stratified Terminal Height Expressions . . 129
Table 5.10 Module Constants 130
XI
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List of Figures
Figure 2.1 Illustrative Near-Field and Far-Field
Regions of Submerged Positively Buoyant
Discharge . 22
Figure 2.2 Pure Jet in Stagnant Environment .... 26
Figure 2.3 Simple Plume in Stagnant Environment . . 28
Figure 2.4 Examples of Combined Effects of Momentum
Flux, Buoyancy Flux, Crossflow, and Density
Stratification on Flow Behavior 30
Figure 2.5 Buoyant Surface Spreading Process .... 42
Figure 2.6 Density Perturbation of Ambient
Stratification Leading to Buoyant Spreading
Processes 45
Figure 2.7 Passive Ambient Diffusion Process .... 47
Figure 2.8 Flow Interaction Process with Water
Surface 51
Figure 2.9 Near-Field Attachment Processes .... 59
Figure 3.1 Definition Diagram for Single Port
Discharge Geometry in Ambient Channel with
rectangular Cross-Section ... 63
Figure 3.2 Representative Stable Density Profiles
(Four Stratification Types) 65
Figure 3.3 Sub-Classification: Assessment of Ambient
Density Stratification and Different Flow Classes
for Internally Trapped Discharges 69
Figure 3.4 Sub-Classification: Behavior of Positively
Buoyant Discharges in Uniform Ambient Layer ... 70
Figure 3.5 Sub-Classification: Behavior of Negatively
Buoyant Discharges in Uniform Ambient Layer ... 71
Figure 3.6 Sub-Classification: Dynamic Bottom
Attachment of Discharge Due to Wake or Coanda
Effects 72
Figure 4.1 System Elements of CORMIX1 86
Figure 5.1 General Behavior for Buoyant Jet in
Unconfined and Unstratified Crossflow 97
xii
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Figure 6.1 Horizontal Buoyant Jet Trajectory in
Stagnant Ambient 135
Figure 6.2 Horizontal Buoyant Jet Trajectories in
Stagnant Ambient Over a Range of Froude Numbers . 136
Figure 6.3 Horizontal Buoyant Jet Dilution in
Stagnant Ambient 138
Figure 6.4 Non-buoyant Jet Trajectory in Uniform
Crossflow 139
Figure 6.5 Non-Buoyant Jets at Various Discharge
Angles in Uniform' Crossflow 140
Figure 6.6 Buoyant Jet Discharging Vertically into
Weak Crossflow 142
Figure 6.7 Buoyant Jet Discharging Vertically into
Strong Crossflow 143
Figure 6.8 Buoyant Jet Discharged Vertically into
Weak Crossflow (Logarithmic presentation) .... 144
Figure 6.9 Negatively Buoyant Jet Discharging
Obliquely Upward in Uniform Crossflow 145
Figure 6.10 Three-Dimensional Trajectory of
Transverse Horizontal Buoyant Jet in Weak
Crossflow 146
Figure 6.11 Three-Dimensional Trajectory of
Transverse Horizontal Buoyant Jet in Strong
Crossflow 148
Figure 6.12 Buoyant Jet Trajectories in Stratified
Stagnant Ambient 149
Figure 6.13 Comparison of CORMIX1 Predictions with
Integral Buoyant Jet Models in Uniform Crossflow 151
Figure 6.14 Comparison of CORMIX1 Predictions with
Integral Buoyant Jet Models in Stratified
Crossflow 152
Figure 6.16 Cooling Water Outfall from San Onofre
Nuclear Power Plant (Unit 1) 154
Figure 6.17 Strongly Buoyant Plume in Crossflow . . 155
Figure 6.18 Interaction of Negatively Buoyant Jet
with Bottom Boundary 159
Kill
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Figure 7.1 AB Chemical Company: Schematization of Cross-
Section at the Discharge Site 163
Figure 7.2 AB Chemical Co. Design Case No. 1: Predictions
(bottom attached jet) 165
Figure 7.3 AB Chemical Co. Design Case No. 2: Close-up
View of Unattached Buoyant Jet Near
Discharge 167
Figure 7.4 AB Chemical Co. Design Case No. 2: Overall
Appearance of Discharge Plume 168
Figure 7.5 MN Treatment Plant: Typical Density Profiles
for Summer and Winter Conditions ... 170
Figure 7.6 MN Treatment Plant Summer Design Case:
Internal Flow Trapping Caused by Pycnocline
Density Jump 172
Figure 7.7 MN Treatment Plant Summer Design Case: Far-
Field Behavior of Internally Trapped Flow .
173
Figure 7.8 MN Treatment Plant Winter Design Case: Plume
Surface Interaction 175
Figure 7.9 PQ Cooling Water Outfall in Low Current Design
,Case: Near-Field Plume Behavior .... 177
Figure 7.10 PQ Cooling Water Outfall High Current Design
Case: Near-Field Plume Behavior .... 178
Figure 7.11 Parameter Range of CORMIX1 Applicability
180
xiv
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Acknowledgments
This study was conducted at the DeFrees Hydraulics
Laboratory, Cornell University, in cooperation with the
United States Environmental Protection Agency, Environmental
Research Laboratory, Athens, Georgia. The authors want to
extend their appreciation to Dr. Thomas 0. Barnwell, Jr.,
project officer, who provided the initial stimulus for the
project and further guidance throughout the study.
The authors acknowledge the assistance given by Dr. Anil
Nerode, Director of the Mathematical Sciences Institute at
Cornell University, in the development of expert system
structure and logic elements. Professor Douglas A. Haith,
Department of Agricultural Engineering, Cornell University,
provided valuable review and criticism. Mr. Paul Akar,
Graduate Research Assistant at Cornell University, was
instrumental for the timely completion of the project
through evaluation of the computer code and knowledge base
and the execution of numerous test cases. Mr. Gilbert
Jones, Graduate Research Assistant, assisted in final report
preparation and system evaluation.
The work was carried out using the computer facilities
of the DeFrees Hydraulics Laboratory. Mr. Cameron Willkens,
Electronics Technician, generously assisted with solutions
for computer hardware and software problems.
This report was submitted with essentially similar
contents by Robert L. Doneker, Graduate Research Assistant,
to the Graduate School of Cornell University in partial
fulfillment of the requirements for the degree of Doctor of
Philosophy. Dr. Gerhard H. Jirka, Professor of Civil and
Environmental Engineering, was project supervisor.
xv
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Chapter I
Introduction and Legal Background
1.1 Introduction
Consider the numerous liquid waste streams emanating
from industrial, municipal, agricultural, and domestic
activities that are routinely discharged into water bodies.
The size and flow characteristics of receiving water bodies
vary widely they may be small streams, large rivers,
reservoirs, estuaries, or coastal waters. The water body
may be deep or shallow, stagnant or flowing, and may exhibit
ambient density stratification of various degree. Also, the
discharge type and configuration can be highly variable.
The flow may contain pollutants ranging from conventional
to toxic substances, vary greatly in magnitude ranging from
low flowrates for a small sewage treatment plant to the
substantial cooling water flows for a large stream-electric
power plant, issue with high or low velocity, be denser or
lighter than the ambient, be located near shore or far
offshore, and exhibit various geometric details ranging from
single port submerged discharges to multiport submerged
diffusers to surface discharges.
Given this diversity of both discharge and ambient
environmental conditions, a large number of possible flow
patterns will develop as the discharge waste stream mixes
in the ambient water. These flow patterns will determine
the configuration, size, and intensity of the mixing
process, and any impact of the discharge on the water body
surface, bottom, shoreline, or other areas.
All aqueous discharges located within the United States
are subject to Federal and/or state regulation. A key
aspect of these regulations is the concept of mixing zones.
The mixing zone is a legally defined spatial quantity that
allows for the initial mixing of the discharge. Legal
criteria specify the mixing zone shape and effluent
concentrations that must be maintained outside and at the
edge of the mixing zone. The mixing zone is an allocated
impact zone where more stringent ambient water quality
standards may be exceeded locally. Current mixing zone
regulations are a descendant of Federal water quality
legislation commencing in 1948.
More recent regulations on discharges of aqueous toxic
substances define additional subregions within the usual
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mixing zone. The intent of these regulations is to require
rapid mixing of toxic releases to limit exposure of toxic
materials to aqueous flora and fauna.
The mixing behavior of the discharge is dependent on
the depth of the ambient water body, the momentum and
buoyancy of the discharge, the spatial orientation of the
discharge, and the effects of many other factors. Detailed
engineering analysis is necessary to provide estimates of
discharge dilution within the mixing zone.
This work describes the development and implementation
of an engineering tool in the form of a micro-computer
based expert system for the analysis of submerged single
port discharges into water bodies with variable and complex
ambient conditions. The purpose of the expert system is to
provide reliable and accurate predictions of the mixing
characteristics of such discharges within the framework of
the applicable legal requirements.
1.2 Overview of U.S. Water Quality Policy
Prior to 1948, states, local, and regional agencies were
primarily responsible for controlling water pollution.
After the realization in the mid-1800s 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,1984).
Table 1.1 outlines key federal water pollution control
legislation since 1948. 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.
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 was
included in the many amendments to the Act in the 1960s and
1970s.
The Water Quality Act of 1965 set new requirements for
states to establish ambient water quality standards and
increased the level of federal funding. 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 Strategy8
1948
Water Pollution
Control Act
1956
1965
1972
Federal Water
Pollution Control
Act (FWPCA)
Water Quality
Act
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
aThe table entries include only significant new changes
established by the law.
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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.
1.2.1 The Federal Water Pollution Control Act of 1972
Prior to the 1972 Federal Water Pollution Control Act
(FWPCA) only the states had power to develop ambient water
quality standards applicable to interstate or navigable
waters. Water quality standards depended upon intended use,
whether 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. A state
could lower its water quality standards to attract industry
away from states that had 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) a provision for 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
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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"
(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.
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Section 505 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.
1.2.2 The Clean Water Act of 1977
In 1977 the FWPCA Act was amended by Congress. These
amendments are known as the Clean Water Act (CWA). The five
general categories of pollutants covered in the Act are; i)
conventional, ii) nonconventional, iii) toxics, iv) heat,
and v) dredge and fill spoil. The Act distinguishes between
new and existing sources for setting effluent standards.
Table 1.2 lists examples of the first three pollutant
categories.
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 that 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.
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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,
USEPA, 1984.
Conventional
solids(TSS)
fecal coliform
bacteria
Nonconventional
Toxic
biochemical
oxygen demand
(BOD)
pH
total suspended
chemical
oxygen demand
(COD)
fluoride
aluminum
chloroform
lead
f luorene
nickel
sulfide
selenium
oil and grease
ammonia
benzidine
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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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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 cannot be met
by BPT for industry and secondary treatment for POTW, these
reaches are classified as water quality limited.
1.3 The Concept of Mixing Zones
1.3.1 Mixing Zones: Development and Regulations
The 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, 1984). Water quality criteria apply at
the boundary of the mixing zone, not within the mixing zone
itself. USEPA 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), USEPA publications Quality
Criteria for Water 1976 (Red Book) , and Guidelines for State
and Area Wide Water Quality Management Program. Guidance
published by USEPA in Water Quality Standards Handbook
(1984) supersedes these sources.
In setting requirements for mixing zones, USEPA (1984)
requires that "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," and "shore hugging plumes should be
avoided."
Within the mixing zone USEPA requires "any mixing zone
should be free of point or nonpoint source related:
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(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, 1984).
The proposed rules for mixing zones recognize that the
state has the discretion to adopt 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 regulations. State standards require
that water quality criteria be met at the edge of the
regulatory mixing zone i) to provide a continuous zone of
free passage that meets water quality criteria for free-
swimming and drifting organisms and ii) 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 (Table 1.4).
The mixing zone dimensions vary from state to state as
shown in Table 1.4. The mixing zone can be defined as a
downstream distance, cross-sectional area, or volume of
water. Discharge concentrations of pollutants such as
nitrogen, phosphorus, or toluene, are limited to certain
numerical values at the edge of the mixing zone.
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.
10
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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)
(USEPA 1984)
State
Water Body
Dimensions
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
D.C.
Georgia
Florida
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
New Jersey
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
Lake Michigan
streams
0
streams
0
0
streams
New Hampshire streams<=l/4 CS
New Mexico streams
New York streams <=l/2
<= 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
< = 1 / 4 C S
(thermal)
<=l/4 CS
CS (thermal)
11
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Table 1.4
(Continued)
State
Nevada
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
S . Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
W. Virginia
Wisconsin
Wyoming
Guam
Puerto Rico
Virgin Islands
Water Body
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
lakes
streams
0
0
streams
streams
Dimensions
<=l/3 CS
0
<=l/4 CS
<=l/3 CS
<=l/5 CS
<=l/4 CS
0
NR
< = 1 / 4 C S
(thermal)
0
<=3/4 CS or 100
yds of stream's
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
IMZ<= 400 '
FMZ<= 4000 '
<= 1/4 CS
Where:
CS = cross-sectional area
NR = no reference
IMZ = initial mixing zone
SA = surface area
0 = not listed
FMZ = Final mixing zone
12
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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 that specify a mixing zone for lakes,
dimensions for the mixing zone vary from 10% of the surface
area of the lake to 300 to 1000 foot 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.
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.
1.3.2 Special Mixing Zone Requirements for Toxic Substances
For toxic discharges, USEPA recommends careful
evaluation of mixing to prevent zones of chronic toxicity
that extend for excessive distances because of poor mixing.
USEPA maintains two water quality criteria for the allowable
magnitude of toxic substances: a criterion maximum
concentration (CMC) to protect against acute or lethal
effects; and a criterion continuous concentration (CCC) to
protect against chronic effects (USEPA, 1985) .
The less restrictive criterion, the CCC, must be met at
the edge of the same regulatory mixing zone specified for
conventional and nonconventional discharges.
To prevent lethal concentrations of toxics in the
regulatory mixing zone, the restrictive CMC criterion must
be met within a short distance from the outfall or in the
pipe itself. 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. The technical support document
specifies a minimum exit velocity of 3 meters per second (10
feet per second), in order to provide sufficiently rapid
mixing that will minimize organism exposure time to toxic
material. In addition, the outfall design also must meet
three geometric restrictions for a TDZ (USEPA, Technical
13
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Support Document for Water Quality-based Toxics Control,
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 interaction 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 conditions (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.
1.4 Regulatory Assessment of Discharges and the Permitting
Process
1.4.1 The NPDES Permit System
Any pollutant 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, by 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
Nature of business engaged at the 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
14
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The waste-water treatment currently or to be
employed for each waste stream
Pollutant test data
1.4.2 Need for Regulatory Assessment Tools
Implementation of the mixing zone policy requires that
both applicants and regulators determine 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 also can 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, in many cases, are 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 (USEPA, Draft
301(g) 1984). Field studies for analyses of dilution for
toxic discharges are patently unacceptable, so simulation
must be used to determine dilutions.
Because of the complexity of the physical mixing
process, permit writers are increasingly relying on
mathematical models to analyze the transport and
transformation 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 predictions under the conditions
with which he is concerned (USEPA Draft 301 (g) 1984) .
USEPA has developed a number of models to predict the
initial dilution of discharges. A few these are known as
15
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PLUME, OUTPLM, UDKHDEN, MERGE, and LINE (Muellenhoff et al.
1985). Applicants are not required to use these models in
the analysis, but must be able to prove that the methodology
chosen gives reasonable estimates of initial dilution.
1.4.3 Motivation 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 (Muellenhoff, 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
(Muellenhoff, et al., 1985). In reality, the plume may
attach to the bottom or may become vertically fully mixed,
possibilities that may occur due to changes in the ambient
environment such as low flow conditions. Consequently,
analysts have submitted 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 are 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 a number of simulation models. Such
expertise in model use requires expensive training and is
rare. This is the primary reason for the development of
expert system tools to assist the analyst.
16
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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" that
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
that 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.
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
17
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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 hyclrodynamic mixing and
pollution control.
it gives pollutant concentration at the specified
regulatory mixing zones.
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.
1.5 CORMIX1: An Expert System for Mixing Zone Analysis of
Submerged Single Fort Aquatic Discharges
1.5.1 Scope and Objective
The Cornell Mixing Zone Expert System (CORMIX) is a
series of software subsystems for the analysis, prediction
and design of aqueous conventional or toxic pollutant
discharges into watercourses, with emphasis placed on the
geometry and dilution characteristics of the initial mixing
zone. Subsystem CORMIX1, described in this work, deals with
submerged single port discharges with arbitrary discharge
buoyancy (positive, negative, or neutral) into arbitrary
water bodies (shallow or deep, stagnant or flowing, uniform
or stratified) as may be representative for rivers, lakes,
reservoirs, estuaries, or coastal waters. CORMIX1 assumes
steady state flow conditions, both for the discharge and the
ambient environment. Another subsystem, CORMIX2, addresses
submerged multiport diffuser discharges (Akar and Jirka,
1989). CORMIX3, the third possible development, would be
for the analysis of surface discharges.
The objective of the expert system is to provide the
analyst with accurate and reliable predictions of discharge
mixing processes. The expert system should be easy to use,
and should allow for preliminary mixing zone analysis of a
typical design in perhaps 20 minutes if all necessary input
data is available. Emphasis is placed on the geometry and
initial mixing of the discharge, along with prediction of
concentration (or dilution) values and the shape of the
regulatory mixing zones. The expert system should provide
the analyst with detailed hydrodynamic information and
recommendations for discharge design, including sensitivity
studies.
18
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Since its emphasis is on initial mixing mechanisms with
their short time scales, CORMIX1 assumes a conservative
pollutant or tracer in the effluent. Thus any physical,
chemical, or biological reaction or decay processes are
neglected. However, if first-order processes are assumed
the predictive results can be readily adjusted to include
such processes (see Section 7.4).
It seems impossible, and probably unnecessary, to
develop a system that works reliably for every conceivable
mixing zone and discharge configuration. The present
philosophy, however, was to develop an expert system that
works for the large majority (better than 95%) of typical
discharges, ranging from simple to fairly complex cases.
The remaining cases may require separate analyses, perhaps
using sophisticated numerical modeling or a detailed
hydraulic model study.
1.5.2 Results of an Earlier Feasibility Study
A feasibility study (Doneker and Jirka, 1988) was
conducted to the test expert system methodology for the
analysis and design of submerged single-port continuous
buoyant discharges into a non-stratified flowing aqueous
environment. The objective was to test a prototype of the
hydrodynamic knowledge base and simulation model. This
simplified expert system did not include stratified
environments, negatively buoyant discharges, and bottom
attachments. The system was written in the expert system
shell M.I (Tecknowledge, Inc.) and in Fortran.
The results of the hydrodynamic simulation were found
to be in good to excellent agreement with available field
and laboratory data. In particular, the system proved
flexible and reliable in distinguishing among complex
discharge situations involving boundary interactions and
buoyant intrusion phenomena. Many of the common pitfalls
to model use incomplete or contradictory data, choice of
appropriate simulation model, and faulty interpretation of
results appear to have been mitigated within the context
of an expert system methodology. Because of the encouraging
results of the preliminary system, the more general
hydrodynamic problems of negative buoyancy, stratified
environments, and boundary attachments, along with more
sophisticated user elements, have been included in the
expert system described herein.
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1.5.3 Summary of Present Study
CORMIX1 uses the expert systems shell VP-Expert
(Paperback Software, Inc.) and Fortran. The following
chapters provide a detailed description of the expert system
CORMIX1. Chapter II provides a detailed review of basic
hydrodynamic processes of mixing in buoyant jets, buoyant
spreading, passive ambient diffusion, and boundary
interaction phenomena.
A hydrodynamic flow classification system is developed
in Chapter III. The classification system describes the
physical discharge/environment interaction processes
controlling near-field mixing for a discharge, and forms the
basis for the construction of the proper hydrodynamic
simulation model sequence.
Chapter IV presents an outline of the computer programs
in CORMIX1. This chapter describes the logic and Fortran
program elements of CORMIX1, their respective strengths and
weaknesses, and how they are applied to mixing zone
analysis.
Chapter V discusses the hydrodynamic model protocols
used to simulate a given discharge/environment condition.
The details of each simulation program element are also
presented.
Chapter VI is devoted to system evaluation and
validation. This chapter compares CORMIX1 results with a
wide range of laboratory and field data. Comparisons are
given with jet integral models that are widely used but are
limited to the initial subsurface buoyant jet processes.
Chapter VII presents design case studies to illustrate
the flexibility and power of the system to evaluate a wide
range of typical discharge/environment situations. Also
suggestions on extending the applicability of the system to
other possible discharge/environment conditions is given.
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Chapter II
Hydrodynamic Elements of Mixing Processes
The hydrodynamics of an 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 any surface or
bottom interaction, or in the case of a stratified ambient,
terminal layer interaction. In this region, designers of
the outfall can usually affect the initial mixing
characteristics through appropriate manipulation of design
variables.
As the turbulent plume travels further away from the
source, the source characteristics become less important.
Conditions existing in the ambient environment will control
trajectory and dilution of the turbulent plume through
buoyant spreading motions and passive diffusion due to
ambient turbulence. 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 simple positively buoyant subsurface
plume rising to the surface and traveling downstream appears
in Figure 2.1.
This chapter represents the basic hydrodynamic elements
of the several stages within typical mixing processes that
can occur in the water environment. In Section 2.1 the
mechanics of buoyant jet mixing are presented, starting with
the simple jet and plume. This analysis is extended to
include the effects of crossflows, combined sources of
momentum and buoyancy, and finally ambient density
stratification. Section 2.2 deals with buoyant spreading
processes in unstratified or stratified flowing ambients.
Passive diffusion, due to ambient turbulent mixing, is
summarized in Section 2.3. Finally various interaction
processes that provide a transition between buoyant jet
mixing and subsequent processes are presented in Section
2.4.
21
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Plan View
Side View
Near Field
o
Far Field
u,
Figure 2.1
Illustrative Near-Field and Far-Field Regions
of Submerged Positively Buoyant Discharge: An
Example of Unstratified Ambient Water and
Without Bottom Attachment
-------
2.1. Buoyant Jet Mixing Processes
A discharge 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 will
herein be referred to as a "flow". Positively buoyant flows
are defined as flows where the buoyancy force acts
vertically upwards against the gravity force; negative
buoyancy is defined as acting downwards in the direction of
the gravity force.
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 predominant 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 can be applied as an approximate solution to
that portion of buoyant jet in a crossflow where jet
momentum dominates the flow. Likewise the results for a
pure plume can be applied to the buoyancy-dominated regions
for the buoyant jet.
Additional factors, such as ambient crossflow and
density stratification, can also be treated within the
framework of asymptotic analysis as shown by Wright (1977),
and others.
2.1.1 Description of Turbulent Jets and Plumes
Most people are familiar with the sight of smoke rising
from a smokestack into the atmosphere. The smoke plume
first rises vertically and spreads narrowly, and eventually
bends over as it is carried away by the ambient wind. The
smoke plume is an example of a turbulent buoyant jet, the
discharge contains both momentum and buoyancy, and is
affected, at least in the final stages by the crossflow.
23
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The buoyancy is produced by the lower density of the heated
air with respect to the cooler ambient air.
The discharge of a liquid such as sewage into the ocean
behaves in a similar fashion. The sewage flow has momentum
from being injected through the discharge orifice. The
sewage may have the density of freshwater and thus is
buoyant with respect to the greater density of the ambient
saltwater.
2.1.2 Dimensional Analysis of Buoyant Jets
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) .
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 are the kinematic fluxes of mass, Q0 =
3~1 4"2
uQ [LT~], momentum M0 = u0Q0 [LT"] , and buoyancy J0
= <30 QQ. [L4"1""3]/ where D [L] is the diameter of the orifice,
u0 [LT 1] is the exit velocity, and g0' [LT~2] is the reduced
gravitational buoyant acceleration caused by the density
difference between the jet and ambient environment. This
term is defined as g0' = g(pa - P^/Pa where g is
gravitational acceleration and pa and pQ are the ambient and
jet discharge densities [ML"3] , respectively.
If the ambient water is flowing its velocity, ua [LT"1],
becomes an additional variable. Furthermore, when the
ambient density is not uniform, the density stratification
may be written in terms of a buoyancy gradient defined as
e = -g/P.(d/,a/dz) [T'2] (2.1)
where z is the vertical coordinate direction. Note that the
following assumptions are implicit in the above definitions:
a uniform exit velocity u0, a constant ambient velocity
(without shear) ua, and a linear density gradient with, at
least layer-wise, constant e.
24
-------
For the general case of a buoyant jet discharged into
a flowing stratified environment, dimensional analysis
proceeds as follows. Any dependent variable, *, such as
local centerline jet velocity, can be expressed as a
function of the various independent variables:
where s [L] is the distance along the jet trajectory. The
function on the right hand side of Eq. (2.2) has to be
dimensionally consistent with the desired dependent
variable.
The following paragraphs first present the details of
dimensional analysis for the simple case of a pure jet and
a pure plume in a stagnant environment. Then, the cases of
jets and plumes in a crossflow are presented. Finally the
effect of ambient density stratification on flow behavior
is presented. In each case, 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 require
experimentally determined coefficients. However, the
individual solutions can be linked by appropriate transition
conditions to provide an overall prediction for the complete
problem.
2.1.2.1 Simple Jet in Stagnant Uniform 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 jet trajectory, the velocity distribution is observed
to be bell-shaped (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 (Gaussian distribution)
may be assumed for the velocity distribution. Similar
conditions pertain to the centerline concentration cc of
pollutant (or tracer) 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 and
is equal to the initial momentum flux M0.
25
-------
a. Instantaneous appearance
ENTRAINMENT
VELOCITY
(Jo. po " p». c0
CONCENTRA TION
PROFILE
c
«T
AMBIENT DENSITY p,
ZONE OF
FLOW ESTABLISHMENT
b. Time-averaged conditions
Figure 2.2
Pure Jet in Stagnant Environment (Ref. Holley
and Jirka, 1986)
26
-------
The magnitude and variation of the jet centerline
velocity depends primarily upon the initial kinematic
momentum flux and the distance along the trajectory, uc =
s). Therefore, one can deduce on dimensional grounds
uc = cM
(2. 3) where c is a constant.
The width b of the jet at trajectory distance s can also
be expressed as b = f(M0,s). The only possible
dimensionally consistent equation is
b = cs (2.4)
where c is a another constant.
The centerline dilution S at any cross-section along the
jet is defined by S - CQ/C,., where cg is the concentration at
the nozzle exit. A mass conservation equation implies c0Q0
a ccucb2, so that the dilution S as a function of s can be
expressed as
S = cM01/2s/Q0 (2.5)
where c is a constant.
The various jet flow constants c in the above three
equations must be obtained from experimental data.
2.1.2.2 Simple Plume in stagnant Uniform Environment
A pure positively buoyant plume rises vertically and
experiences an increase in vertical momentum flux with
distance z from 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, uc = /(J0,z). The
centerline velocity of the plume can be obtained from
dimensional reasoning
uc= cCJo/z)1'3 (2.6)
The width b of the plume at trajectory distance z is
expressed as
b = cz (2.7)
where c is a constant.
27
-------
a. Instantaneous appearance
$»z
AMBIENT
DENSITY pa
EHTRAINMENT
VELOCITY
CONCENTRA TION AND
BUOYANCY PROFILE
9'
cc ' 9'c
VELOCITY PROFILE
u
U-
b. Time-averaged conditions
Figure 2.3
Simple Plume in Stagnant Environment (Ref,
Holley and Jirka, 1986)
28
-------
A mass conservation equation (similar to the approach
leading to Eq. (2.5)) provides the plume dilution
S = cJ01/3z5/3/Q0 (2.8)
All plume flow constants c in the above equations are
in general different from the jet flow constants and must
be evaluated from experiments.
2.1.2.3 Generalizations: Jet/Plume Interactions/ Crossflow
Effects/ and Stratification Effects
If several parameters influence the flow field, then a
general asymptotic solution for the whole flow field cannot
be found. However, there may be individual regions where
specific asymptotic solutions of the type developed in the
preceding sections still apply. This is illustrated in
Figure 2.4.
A buoyant jet in unstratified stagnant ambient (Figure
2.4a) is initially jet-like and affected by the initial
discharge orientation. After some distance the plume-like
behavior predominates, leading finally to a vertical rise.
The role of an unstratified crossflow is to deflect the
discharge flow downstream into the current direction.
However, there is always a region close to the source where
the flow is still jet-like (Figure 2.4b) or plume-like (Fig
2.4c). Beyond some distance the jet or plume becomes
strongly deflected and is advected by the ambient flow.
The role of ambient stratification, given by a
continuous linear distribution in the present case, is to
trap the flow at a certain level (trapping level or terminal
level). Prior to the trapping the flow may be either jet-
like (Figure 2.4d) or plume-like (Figure 2.4e). After
trapping the flow forms an internal density current with
moderate additional mixing, as discussed in Section 2.2.
Of course, multiple effects of the types sketched in
Figure 2.4 can all occur simultaneously in a given flow.
In every case it is possible, however, to identify dominant
flow zones and spatial regions. This identification is
possible by means of appropriate length scales that are
developed in the following sections. A rigorous flow
classification scheme on the basis of such scales is
described in Chapter 3.
29
-------
Transition
\
Discharge
ua=0
'0
Plume-like
Jet-like
a) Buoyant Jet in Stagnant Uniform Environment
\Transition
0(L
Strongly Deflected Jet
= 0 X\ Weakly Deflected Jet
b) Pure Jet in Uniform Crossflow
u.
^Transition
\
\
/ Strongly Deflected Plume
Weakly Deflected Plume
c) Pure Plume in Uniform Crossflow
Figure 2.4 Examples of Combined Effects of Momentum Flux,
Buoyancy Flux, Crossflow, and Density
Stratification on Flow Behavior
30
-------
Transition
7///7777T7
Density current
Jet-like
d) Pure Jet in Stagnant Stratified Ambient
ua =
Density current
e) Pure Plume in Stagnant Stratified Ambient
Figure 2.4 (continued)
31
-------
2.1.3 Length Scales
Length scales describe the relative importance of
discharge volume flux, momentum flux, buoyancy flux, ambient
crossflow, and density stratification in controlling flow
behavior. The length scales will describe the distance over
which these dynamic quantities control the flow.
2.1.3.1 Discharge Length Scale
Initially as the jet exits the port in the zone of flow
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. The discharge
length scale Lg relates the volume flux to momentum flux,
and from dimensional reasoning
LQ -
1/2
(2.9)
which is proportional to the diameter D of the orifice for
a round jet, Lg = (*r/4)1/2D. For distances s from the source
less than Lg the flow will be in the zone of flow
establishment. Thus if s/Lg is less than the order of
unity, or s/Lg « 0(1), the source geometry will have a
significant effect on the flow behavior, but for s/Lg »
0(1) the effect of the initial geometry is lost to jet
momentum or buoyancy which will control the flow behavior.
Similar to the flow constants discussed in Section 2.1.2,
the appropriate numerical value for the extent of this flow
region must be obtained form experimental data; this holds
for all the following "order of unity" statements.
2.1.3.2 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 jet momentum
to the crossflow. 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 1^
T TUT 1/2 /__ / O 1 rt \
LjT M0 /ua (2.10)
Thus for s/L^ « 0(1) the initial jet momentum will
dominate and crossflow is of secondary importance, and for
s/I^ » 0(1) ambient velocity will have a strong influence
on jet behavior.
32
-------
2.1.3.3 Plume/Crossflow Length Scale
Arguments presented for the effect of crossflow on the
pure plume flow are in analogy to those for a pure jet in
crossflow. The plume/crossflow length scale 1^ for the
deflection of a vertically rising plume as shown in Figure
2.4c is given by
Thus for z/I^ « 0(1) the initial jet buoyancy will
dominate and crossflow is of secondary importance, while
for z/L,., » 0(1) ambient velocity will have a strong
influence on plume behavior.
2.1.3.4 Jet/Plume Length Scale
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 1^ (See Figure
2.4a). Dimensional analysis suggests the functional
relationship
I* = M03/4/V/2 (2.12)
So for z/Ly, « 0(1) flow behavior will be controlled by
momentum and for z/Lj, » 0(1) flow behavior will be
controlled by buoyancy, i.e. approach that of a vertically
rising plume.
In the rare case that l^ « Lp, there will be no momentum
dominated flow and the flow will be entirely plume-like
except for the region very near the issuing source.
The ratio of I^/I^ is proportional^ to the usual discharge
densimetric Froude number F0 = UQ/(g0'D)1/2 which relates the
inertial forces to buoyancy forces within the plume, I^/I^,
= (4/*)1/4F0. The pure plume has a Froude number of O(l) and
the pure jet Froude number approaches infinity.
2.1.3.5 Jet/Stratification Length Scale
The effect of a linear ambient density stratification
on a pure jet is to counteract the momentum flux of the flow
as it travels away from the source. This is because the jet
discharging with upward orientation entrains fluid of a
greater density and carries it upwards where the ambient
fluid is less dense. A reverse condition holds for a
downward inclined jet. The jet/stratification length scale
is given dimensionally by
33
-------
V- (VO1A (2.13)
For a vertically discharging jet this length scale will be
a measure of the distance to the terminal level of the jet
flow. For a horizontally discharging jet L^' will be a
measure of the distance at which collapse of the jet flow
will commence, with increasing lateral spreading and damped
turbulent entrainment.
Thus for distance of s/L/ « 0(1) the effect of density
stratification will be negligible on jet behavior. For
distances of s/I^,' » 0(1) the effect of stratification will
be to terminate the jet motion and a density current will
then form at the terminal level.
2.1.3.6 Plume/Stratification Length Scale
As for the pure jet in stratification, the effect of a
linear ambient density stratification on a pure plume is to
modify both buoyancy and momentum fluxes of the flow as it
travels away from the source. The maximum height of rise
of a simple plume in linear density stratification will be
proportional to the plume/stratification length scale
V- J0V4A3/8 (2.14)
For a vertical distance of z/L^' « O(l) the effect of
density stratification on plume behavior will be negligible.
2.1.4 Typical Flow Regimes of Unconfined Buoyant Jets
This section presents a series of basic analytical
results for jets or plumes in a variety of ambient
situations. All of the results are perturbation solutions,
in the sense that a simple analytical solution (e.g. the
pure jet) is being perturbed by assuming a small effect of
an additional variable (e.g. a weak crossflow).
For the following development the simplest possible
assumptions are being made: a point source, either vertical
or horizontal orientation, and only one perturbing variable.
The results can be readily generalized to more complex
conditions (e.g. arbitrary orientation or multiple
influences). Indeed, such generalizations are implemented
in the predictive elements presented in Chapter V.
34
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2.1.4.1 Weakly Deflected Jet In Crossflow
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/I^, « 0(1), where z in
this section signifies the coordinate pointing across the
flow (e.g. vertically) .
In first order, the vertical velocity for this jet flow
would be similar to Eq. (2.3). In addition, a kinematic
relationship applies for a jet element moving horizontally
with the crossflow velocity in the direction x of the
crossflow
dx/ua = dz/uc (2.15)
Substitution for the vertical velocity given in Eq. (2.15)
and integrating gives the trajectory relationship for the
weakly deflected jet flow (Wright's (1977) "momentum-
dominated near-field", or mdnf1) expressed in terms of the
jet/crossflow length scale
(2.16)
where t1 is a trajectory constant.
Eq. (2.16) is valid for small source dimensions, i.e.
small values of L^/L^. In the special case that L^/I^ ^s
large, the effect of geometry is important and Eq. (2.16)
no longer holds.
Jet width b is similar to the jet issuing in a stagnant
environment given by Eq. (2.4) or
b = b,z (2.17)
where b, is the spreading constant.
The dilution S is similar to Eq. (2.5) , and is expressed
in terms of L,,
1In the following the abbreviated descriptions for
crossflow influenced 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).
35
-------
(2.18)
where s, is the dilution constant for the mdnf flow.
2.1.4.2 Strongly Deflected Jet In crossflow
For z/L^ » 0(1) the ambient flow will dominate the flow
pattern. For a strongly deflected jet the vertical velocity
has decayed to less than the value for the ambient
crossflow; thus the 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 from a horizontal line source. The characteristic
variables are the line impulse M'(defined as the kinematic
momentum flux per unit length for an infinitesimal period
of time), vertical rise z, and time after release t.
Applying dimensional analysis
M't/z3 = constant (2.19)
To apply this analogy to the pure jet, MQ/ua is
substituted for M' and x/ua replaces t in Eq. (2.19). The
trajectory relation for the strongly deflected jet flow
(i.e. "momentum-dominated far-field", mdff) is then
expressed in terms of the jet/crossflow length scale
z/^ = t^x/Lj173 (2.20)
where t2 is a trajectory constant.
The width b of the gradually rising jet element is
proportional to the height of rise z
b = b2z (2.21)
where b2 is a spreading constant.
The mass conservation equation is used to determine the
dilution at any position z, c0Q0 « cfb2ua. In terms of the
jet/crossflow length scale the dilution is expressed as
S = s2(z'/LA) (2.22)
where s2 is a dilution constant for the mdff flow.
36
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2.1.4.3 Weakly Deflected Plume in Crossflow
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/L,, « O(l) , the flow will behave as a
plume in a stagnant environment but will be advected with
the crossflow. Proceeding in analogy to the mdnf flow, the
trajectory equation for the weakly deflected plume flow
(i.e. "buoyancy-dominated near-field", bdnf) can be written
in terms of the plume/crossflow length scale
(2.23)
where t3 is a trajectory constant.
Plume width b is similar to the plume issued in a
stagnant environment and is given by
b = b3z (2.24)
where b3 is a spreading constant.
The dilution S is similar to Eq. (2.8), and is expressed
in terms of L^, L,,, and 1^
S = s3(Lb1/3z5/3)/(I^L^) (2.25)
where s3 is the dilution constant for the bdnf flow.
2.1.4.4 Strongly Deflected Plume in Crossflow
For z/I^ » 0(1) the ambient flow will have a pronounced
effect on the flow pattern. When strongly deflected, the
plume vertical velocity has decayed to less than the value
for the ambient crossflow; the ambient crossflow will have
significantly deflected the plume as shown in Figure 2.4c.
The deflected plume should behave as a rising thermal,
i.e. an instantaneous release of a buoyant cylindrical fluid
mass along a line source. The important variables are J',
the buoyant weight per unit length, vertical rise z, and
time t. Dimensional reasoning implies for the thermal
J't2/z3 = constant (2.26)
Substituting x/ua for t and replacing J' by J0/ua yields the
trajectory relationship for the strongly deflected plume
flow (i.e. "buoyancy-dominated far-field", bdff) expressed
in terms of length scales
37
-------
= t^x/Lj,)2'3 (2.27)
where t4 is a trajectory constant.
Plume width b is analogous to Eq. (2.21), or
b = b4z (2.28)
where b4 is a spreading constant.
The mass conservation equation is used to determine the
dilution at any position z, c0Q0 & cb2ua, leading to
S= s4z2/(LgIJ (2.29)
in analogy to Eq. (2.22), where s4 is a dilution constant
for the bdff flow.
2.1.4.5 Horizontal Jet with Vertical Buoyant Deflection
For a horizontally discharging jet with weak vertical
deflection induced by the buoyancy the centerline velocity
is given in first order by the pure jet solution, Eq. (2.3) ,
or uc ss M01/2x"1 in which x is the horizontal coordinate
direction. The small vertical deflection due to the local
buoyancy-induced velocity w is given by
dz/dx = w/uc (2.30)
The local buoyant vertical acceleration of a jet element is
given by
dw/dt * J,/(auc) (2.31)
in which a = b2 is the local jet cross-sectional area and b
= x is the jet width. With the Galilean transformation dt
= dx/uc, and after substitution for b and uc, Eqs. (2.30) and
(2.31) can be solved to give the normalized trajectory
relation
z/I* = ts(x/V3 (2.32)
The appropriate width and dilution equations are
b = bsx (2.33)
and
S = SX/L) (2.34)
38
-------
where the constants b. and ss should be numerically similar
to those for the weakly deflected jet in crossflow, b. « bv
and s5 * s^t respectively. In either case the perturbation
effects are small and the equations must be identical if no
perturbation is present . The above solutions are valid in
the region x/I^ « 0(1).
2.1.4.6 Vertical Plume with Horizontal Momentum Deflection
The final phase of a horizontal buoyant jet will be a
vertically rising plume which is weakly deflected by the
effect of the horizontal discharge momentum (see Fig.
(2.4a). This will occur in the region z/I^, » 0(1). The
plume will have a local vertical centerline velocity given
in first order by the pure solution, Eq. (2.6). The small
horizontal deflection of the plume trajectory is given by
dx/dz - uh/uc (2.35)
where uh is the induced horizontal velocity due to the
discharge momentum flux M0. Conservation of horizontal
impulse implies
auh » M(/uc (2.36)
in which a a b2 is the local plume cross-sectional area and
b * z is the plume width. The trajectory relation is
obtained after substitution and integration
x/Ly, = XF - t^z/I^r1'3 (2.37)
in which XF is the ultimate value of the horizontal
deflection for the final stage (as z approaches infinity)
of the vertically rising plume. The width and dilution are
given directly by Eqs. (2.7) and (2.8), or using the
appropriate length scales,
b - b6z (2.38)
and
S - s6z5/3/(I*2/3I*) (2.39)
As before, the constants b6 and s6 should be the same as
those for the weakly deflected plume, b6 * b3 and s6 * s3,
respectively.
The buoyant trajectory equations for the horizontal
buoyant jet in a stagnant environment, Eqs. (2.32) and
(2.37), are similar to those first derived by Abraham
(1963), albeit with a different methodology.
39
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2.2.4.7 Vertical Jet in Linear Stratification
A vertically discharging jet in a linear ambient density
environment will , in its initial stage, behave purely jet-
like. In the final stage, however, as it approaches the
terminal level, it will be increasingly modified by the
ambient density gradient. In particular the local jet
momentum flux, M at uc2b2, and local buoyancy flux, J &
ucgc'b2, where gc' is the local centerline buoyancy (gc' =
g(pa(z)-pc)/pa(z) , where pc is the centerline density and
pa(z) is the local ambient density), will change.
The conservation equations are
dM/dz at gc'b2 a bJ/M1/2 (2.40)
for momentum and
dJ/dz » -Qe at -M1/2be (2.41)
for buoyancy, in which Q = ucb2 is the local jet discharge
(volume flux) and e is the linear buoyancy gradient. In
addition, a linear jet spreading equation applies in first
order
db/dz at k (2.42)
where k is the spreading coefficient. Integration of these
three equations with the boundary conditions b = 0 (point
source), M = M0, and J = 0 (pure jet discharge) at z = 0
leads to the solution
M/M0 = 1 - m7(z/V)4 (2.43)
where m7 is an appropriate constant. Eq. (2.43) indicates
that for Z/LH/ « 0(1) the jet momentum is essentially
conserved, M = M0 (pure jet), while the terminal level is
approached at a height, Z^/I^' = (l/m7)1/4, at which point the
local jet momentum vanishes, M = 0. Other aspects of the
solution are the linear spread
b = b7z (2.44)
and the dilution
S = s7((l-m7(z/Lm')4))1/22/LQ (2.45)
where the constants b7 and s7 should be similar to those of
the pure jet, b7 = b,, and s7 * s1.
40
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No similar closed-form solutions seem possible for cases
with a discharge buoyancy (non-zero J0) including the
limiting case of a pure plume.
2.2 Buoyant Spreading Processes
In the context of this study, buoyant spreading
processes are defined as the horizontally transverse
spreading of the mixed effluent flow while it is being
advected downstream by the ambient current. Such spreading
processes arise due to the buoyant forces caused by the
density difference of the mixed flow relative to the ambient
density.
The buoyant spreading phenomenon is a far-field mixing
process. Usually it is preceded by buoyant jet mixing in
the near-field and is followed by passive diffusion, another
far-field mixing process. If the discharge is nonbuoyant,
or weakly buoyant, and the ambient is unstratified, there
is no buoyant spreading region in the far-field, only a
passive diffusion region.
Depending on the type of near-field flow and ambient
stratification several types of buoyant spreading may occur:
(i) spreading at the water surface, (ii) spreading at the
bottom, (iii) spreading at a sharp internal interface
(pycnocline) with a density jump, or (iv) spreading at the
terminal level in continuously (e.g. linearly) stratified
ambient.
2.2.1 Buoyant Surface Spreading
The definition diagram and structure of a surface
buoyant spreading process in unstratified crossflow is shown
in Figure 2.5. The laterally spreading flow behaves like
a density current and entrains some ambient fluid in the
"head region" of the current. The mixing rate is usually
relatively small. Furthermore, the flow may interact with
a nearby bank or shoreline (not shown in Figure 2.5). The
flow depth may decrease during this phase. The analysis of
this region is based on arguments presented for surface
buoyant spreading by Jones et al. (1985).
The continuity equation for the density current is
uaabv/3x + 3(vbv)/3y = we (2.46)
where we is the net velocity across the interface, ua is the
ambient current, v(x,y) is the local transverse velocity,
bv is the vertical density current thickness, x is the
41
-------
Front
Plan View
u,
Initial
Condition
Cross-section A-A
Frontal Zone
I Pa
H
Buoyant Surface Spreading
Figure 2.5 Buoyant Surface Spreading Process
42
-------
downstream distance, and y is the distance lateral to the
crossflow. Benjamin (1967) has derived an equation for the
spreading velocity VB
v.2/(g'bv) = 1/CD (2.47)
where C0 is a drag coefficient that depends on the relative
depth bv/H and is in the range of 1/2 to 2. Combining Eqs.
(2.46) and (2.47) and integrating laterally over the density
current width gives
uad (*>,£) /dx = q.(x) (2.48)
where q^x) is the localized head entrainment representative
of the dominant mixing mechanism, and bh is the lateral
half -width.
The localized head entrainment of the density current
is parameterized as qe(x) = 0vBbv where ft is a constant with
a range of 0.15 to 0.25 (Simpson and Bitter, 1979; Jirka and
Arita, 1987) .
The flow half -width bh is obtained for any downstream
distance x by using the boundary condition for the
streamline (VB * uadbh/dx) and integrating Eq. (2.46)
bh " Cbhi3/2 + 3/2(V2CD)V2(x - X,-)]2/3 (2.49)
where x{ is the downstream distance at the beginning of the
buoyant spreading region, and bhi is the initial density
current half -width. This 2/3 power law of flow spreading
is in agreement with the previous work of Larsen and
Sorensen (1968) .
The vertical flow width bv is given by integrating Eq.
(2.48) to obtain
bv - bviOVbhi)^"1 (2-5°)
Due to mixing the local concentration c and local
buoyancy g' gradually change with distance x. The bulk
dilution S, given by CQ/C, is equivalent to the ratio g0'/g'
of buoyancy which is a conservative tracer in this case.
Buoyancy conservation in the density current can be
expressed as u^'b^ = constant. The initial conditions and
appropriate substitutions provide the expression for
dilution S
S= S,.(bh/bhy (2.51)
where S, is the initial dilution.
43
-------
2.2.2 Buoyant Bottom Spreading
This spreading process is analogous to the surface
spreading (Figure 2.5) except that the mixed flow density
is pa + Ap, i.e. heavier than the ambient. If bottom
friction is neglected in the spreading process, then the
same equation system as derived above will apply.
2.2.3 Buoyant Spreading at Pycnocline
Referring to Figure 2.6a, a sharp density change may
exist separating an ambient lower layer with density pL and
an upper layer with density p^. A mixed zone may exist as
a result of a near-field mixing process. The mixed zone
density is pL - Lp, so that a difference Lp exists relative
to the lower layer. If the local (at any x) thickness of
the density current is bv, then this region extends for
hydrostatic reasons partially over the upper layer, so the
expression for hy is
hjj = bvAp/(pL-pu) (2.52)
and partially over the lower layer, so that hL = by-hy.
Other than this hydrostatic adjustment mechanism the buoyant
spreading process at the pycnocline has the same flow
equations, i.e. Eqs. (2.49, 2.50, 2.51), as the buoyant
surface current.
2.2.4 Buoyant Spreading at Terminal Level
In an ambient stratification with a linear density
gradient, a near-field mixing process may lead to a layer
formation at a terminal level Zt/ i.e. a mixed current is
produced whose density is equal to the ambient density at
the terminal level. The mixed zone perturbs the ambient
stratification as shown in Figure 2.6b and leads to a
lateral spreading while the flow is being advected
downstream, qualitatively similar to Figure 2.5.
The spreading velocity VB for the stratified case is
expressed as
VB2/(ebv2) = 1/(2CD) (2.53)
where CD is. the drag coefficient for the stratified case.
Proceeding in the same fashion as in Section 2.21 gives
the following results, for horizontal half-width bh
44
-------
Pycnocline
Level
Density current
h
A/5
PL
u
a) Spreading at Pycnocline
Ambient
Density current
b) Spreading at Terminal Level of
Linear Stratification
Figure 2.6
Density Perturbation of Ambient Stratification
Leading to Buoyant Spreading Processes
45
-------
bh - [+ (2-54)
while the expression for the vertical thickness bv is
)- (2.55)
Dilution is given by continuity as
S= S,.(Vbhi)^ (2-56)
2.3 Passive Ambient Diffusion Processes
The existing turbulence in the ambient environment
becomes the dominating mixing mechanism at sufficiently
large distances from the discharge point. The intensity of
this passive diffusion process depends upon the geometry of
the ambient shear flow as well as any existing
stratification. In general, the passively diffusing flow
is growing in width and in thickness (see Figure 2.7).
Furthermore, it 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
a of a diffusing plume in crossflow can be written in terms
of the transverse turbulent diffusivity E
a2 - 2Ex/U8 (2.57)
in which x is the distance following the ambient flow with
the point release located at x = 0. The coefficient of eddy
diffusivity depends on the turbulence conditions in the
environment and may be a function of distance x (or plume
size a) .
2.3.1 Diffusion in Unbounded Channel Flow
In open channel flow the eddy diffusivity can be related
to the friction velocity u, and the channel depth H
Ez = 0.2U.H (2.58)
for vertical diffusivity, and
Ey = 0.6u«H (2.59)
for horizontal diffusivity. The friction velocity is given
46
-------
Plan View
i Initial Conditions
X:
Possible Bank Interaction
Side View
i
Possible Bottom Interaction
Passive Diffusion Process
Figure 2.7 Passive Ambient Diffusion Process
47
-------
by u* = (f/8)1/2ua where f is the Darcy-Weisbach friction
factor. Due to some anisoptropy in a typical channel flow,
the diffusivity in the horizontal transverse direction is
usually larger than the diffusivity in the vertical
direction. The coefficients included in Eqs. (2.58) and
(2.59) are average values for reasonably uniform channels.
The coefficients may be considerably larger (up to a factor
of 2) for highly non-uniform cross-sections and/or strongly
curved channels (see also Holley and Jirka, 1986).
Solution of Eq. (2.57) with these diffusivities and with
initial flow width conditions specified at x{ (see Figure
2.7) gives the vertical thickness bv and half-width bh/
respectively
bv = [7rEz(x-x()/ua) + bvi2]1/2 (2.60)
bh = OE^x-x^/uJ + bhi2]1/2 (2.61)
where x,., bvj, and bh). are the distance, half-width, and depth
of the plume, respectively, at the beginning of the passive
diffusion region. The above lengths are related to the
standard deviations, bv = (*/2)1/2ff2 and bh = (7r/2)1/2ay, and
assume an equivalent top-hat plume with same centerline
concentration and pollutant mass flux.
The continuity equation applied to the plume in
crossflow 2uabvbh a SQ0 yields the dilution
S = 2bvbh/(I^|LQ) (2.62)
Beyond the distance when the flow becomes fully mixed
(bv = H), the dilution expression is
S « 2Hbh/(L^) (2.63)
2.3.2 Horizontal Diffusion in Unbounded Channel Flow
Many environmental flows without any significant
limitation on the transverse dimension (coastal water, large
lakes, etc.) exhibit an accelerating turbulent diffusive
growth pattern. The horizontal diffusivity is often
specified by the so called "4/3 law" (see Fischer et al.,
1979)
Ey = a(3ay)4/3 (2.64)
in which a is a coefficient equal to 0.01 cm2/3/s
(appropriate for small plume sizes) and E is in units of
[cm /s] and a in [cm] . Integration of the applicable
diffusion equation with this variable Ey yields a solution
48
-------
for plume growth (Brooks, I960, see also Fischer et al.,
1979)
bh = bhi[l + (7r/3)Eyi(x-x-)/(uabhi2)]3/2 (2.65)
in the present notation and width convention. E is the
initial value of diffusivity, so from Eq. (2.64) at position
xi
Eyj = 0.0015bhl-4/3 (2.66)
with units of [m2/s] for Eyi and [m] for the initial width
bhj. The dilution expressions are the same as before, given
by Eqs. (2.63) and (2.62).
2.3.3 Vertical Diffusion in stratified Shear Flow
In the presence of a stable ambient stratification the
vertical diffusive mixing is generally inhibited. An
expression proposed by Munk and Anderson (1948) can be used
to specify the reduced vertical diffusivity
Ez = E0(l +3.33RJ)"1'5 (2.67)
in which E0 is the vertical diffusivity under neutral shear
flow conditions (given by Eq. (2.59)) and Rf is the gradient
Richardson number. For linearly stratified shear flow with
a layer depth Hs, a simple expression for the gradient
Richardson number is
Rj = EK2HS2/U.2 (2.68)
where e is the buoyancy gradient, K is the von Karman
constant (= 0.4), and u, is the shear velocity.
2.4 Interaction Processes: Surface or Bottom Boundaries, and
Internal Layer Formation
Ambient water bodies always have vertical boundaries:
the water surface and the bottom, but in addition "internal
boundaries" may exist in the form of layers of rapid density
changes (pycnoclines). Depending on the dynamic and
geometric characteristics of the discharge flow, a large
number of interaction phenomena can occur at such
boundaries. Furthermore, in the case of a linearly
stratified ambient where flow trapping may occur, other
interaction phenomena may take place.
In essence, these interaction processes provide a
transition between the jet mixing process in the near-field
49
-------
(Section 2.1), and between buoyant spreading (Section 2.2)
and passive diffusion (Section 2.3) in the far-field.
The analysis of several interaction processes is
presented in the following sections. Many other situations
are possible depending upon discharge configuration,
direction of buoyancy and other factors; however all of
these are related to the generic cases and they will be
briefly summarized (without analysis) in Chapter V.
A control volume approach is used for the following
sections. When the flow contacts the boundary, bv and bh are
defined as the vertical depth and horizontal half-width of
the subsequent flow, respectively. The variable subscripts
"i" (initial) and "f" (final) (e.g. bf, Sf) denote control
volume inflow and outflow quantities, respectively.
2.4.1 Near-Horizontal Surface Approach
In the surface approach the bent over flow approaches
the water surface near horizontally at impingement angle 0{
< 45« (Figure 2.8a). The flow is advected with the ambient
velocity field at a rate equal to ua. This situation occurs
for crossflow dominated jet-like and plume-like cases that
are relatively weakly buoyant, hence the flow will be
strongly deflected when it contacts the surface.
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 2.8a). 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 = cS{, where c is of the order of 1.5 to
2.0. An equivalent cross-section aspect ratio for the
outflow section of 2:1 is assumed. The continuity equation
for the control volume in Figure 2.8a is then
SfQ0 - ua2bhf*bvf (2.69)
where b, is the initial half-width (radius), bvf is the final
flow vertical width, and bhf is the final flow horizontal
half-width. This is evaluated as bvf - bhf = (S^L^/2)1/2.
A dynamically analogous situation exists for the bottom
approach of a downward oriented jet or negatively buoyant
flow. Also the approach process to any internal pycnoclines
is quite similar, even though the layer configuration will
adjust itself hydrostatically along the pycnocline depending
on the density jump conditions (see Section 2.2.3 and Figure
50
-------
Cross-section
'f (rectangular)
i (round) widtn bh
width b
a) Surface Approach (Near-Horizontal)
Figure 2.8 Flow Interaction Process with Water Surface
(i indicates inflow values in control volume
and f outflow values)
bl
-------
Side View
Plan View
Stagnation
Point
Inclined Front
b) Surface Impingement with Buoyant Upstream Spreading
Figure 2.8 (continued)
52
-------
Side View
c) Surface Impingement with Full Vertical Mixing
Side View
u,
d) Surface Impingement with Buoyant Upstream Spreading,
Full Vertical Mixing, and Buoyant Restratification
Figure 2.8 (continued)
-------
2.6a). Finally the near-horizontal approaches towards the
terminal layer in continuously stratified flow will be
analyzed with a similar approach.
2.4.2 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 0,. (Figure
2.8b), where 0f > 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 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 Ls, dilution s, horizontal width b^, 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 methodology to predict the upstream spreading
of a buoyant radial discharge in crossflow.
A length scale 1^ representing the turbulent mixing
action of the horizontal momentum flux versus stability
effect of buoyancy force is given by
1^ = (defected horizontal momentum f lux)3/4/J01/2 (2.70)
For the weakly deflected plume, Holley and Jirka, (1986)
give an expression for the vertical momentum of a plume
M * 0.85J02/V/3 (2.71)
where, z (= H) is the vertical distance along the flow
trajectory. Substituting appropriate values into Eq.
(2.70), the length scale for a weakly deflected plume at
impingement becomes
L,, * 0.367H(l-cos0j) (2.72)
where the factor (1-cos^) accounts for the deflected
horizontal momentum flux, in analogy to the vane equation
in classical fluid mechanics.
54
-------
Jones et al. define an intrusion length scale L: , by
the interaction of buoyancy force with the crossflow force
L, = J0/(2ffC0u.3) (2.73)
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. (2.72) and
(2.73)
Lj/Ly, = 0.54(VH) (l/(l-cos0,.)) (2.74)
which describes the relative importance of buoyancy to
momentum forces at surface impingement.
Jones et al. provide a numerical solution for the
upstream intrusion length (their Figure 5-14) which can be
summarized as follows
LS/L, = 4.2(LI/LN)'2/3 for LJ/LH 3.3 (2.76)
Noting that Lt = Lj/5 with CD = 1 and since the flow is a
weakly deflected plume at surface approach, the upstream
intrusion length Ls in Eq. (2.75) can be expressed in the
present notation as
Ls = 1.26Lb((l-COs5i)/(VH)) (2.77)
Ls = 1.91^ (2.78)
for the conditions L^H < 6. 11 (1-cos^-) and Lj/H > 6.11(1-
COS0,.) in Eqs. (2.75) and (2.76), respectively.
Jones et al. (their Figure 7-8) also give the dilution
for a radial surface discharge
S/FS = 1.6(L,/LN)1/3 (2.79)
where Fg is a radial surface spreading Froude number. This
Froude number is defined as
Fs = ur/(g'L0)1/2 (2.80)
where ur is the discharge velocity of the radial jet and L0
is a characteristic length scale defined by
L0 = (2wr,h,) (2.81)
with TJ and h, are the radius and depth of the buoyant radial
surface spreading flow, respectively.
55
-------
The results of Lee and Jirka can be used to evaluate the
surface spreading Froude number F , so the dilution S from
Eg. (2.79) 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 Jirka define the Froude number at surface
impingement
F, « ur/(g'h,)1/2 (2.82)
where ur is the radial surface spreading velocity and h, is
the depth after impingement. For large values of H/D, the
value F, * 4.62 and the value h,/H a 0.0775. The radius of
the flow TJ is r, a «H, where e a 0.11. By substituting
these asymptotic values into Eg. (2.81), the characteristic
length scale L0 becomes
L0 * 0.23H (2.83)
which when combined with asymptotic values for Eq. (2.82)
gives
Fs = F,(h,/L0)1/2 a 2.65 (2.84)
indicating that the flow in this region is jet-like.
Finally, note that the radial surface spreading Froude
number Fs can be expressed in terms of the discharge flux
variables as QJ01/2/M0 .
This result can be then used to determine a bulk
dilution at the end of the region Sf. From Eqs. (2.79) and
(2.84) the expression for final dilution in the surface
impingement region is
Sf - a^gS^V*1)1-008*,-)" (2.85)
The geometry of the surface flow as computed by Jones
et al. will be used to determine the width and depth within
the region. From Jones et al. (their Figure 7.1), the
width, bhf, at impingement is about 2.6 times larger that L8,
or
bhf - 2.6LS (2.86)
The typical depth of the flow in the upstream intrusion
region hs, is found using the vertical length scale from
Jones et al. where
56
-------
(2.87)
s
where Sf
2
with CD = 0.8. With the definition g'= g0'/S
the total bulk dilution, and using the identity u Q,j/J0 =
ua QoMo / ( ^Wo ) * VW the stagnation flow thickness hs
hs =
(2.88)
The final depth bvf (at x=0) is found using again the
continuity equation, bvf (x=0) = Q0Sf/ (2bhfua) , leading to
) (2.89)
2.4.3 Near-Vertical Surface Impingement with Full Vertical
Mixing
In this surface approach region, the weakly bent flow
impinges on the water surface at a near-vertical angle
(Figure 2.8c). Given a shallow ambient water depth and a
weak buoyancy of the discharge, the flow may become unstable
after impingement, and may recirculate.
The recirculation region causes the flow to entrain
ambient fluid from the flow itself causing dilution within
the flow to decrease. Because of unstable recirculating
flow, the centerplane dilution increases to Sf = RSf , where
R is a mixing factor. Experimental data indicate R ranges
from l.o to 4.0. The final flow width, bhf, is found from
the continuity equation
bhf =
and final outflow location xf is approximated as
+ H
(2.90)
(2.91)
where xf is the flow position at the beginning of the
region. The additional distance H accounts for the typical
length of a recirculating zone.
For more buoyant yet unstable discharges, the full
vertical mixing in the near-field can occur in combination
with upstream spreading as discussed in Section 2.4.2. This
is illustrated in Figure 2.8d.
2.4.4 Bottom Interaction Processes
A submerged buoyant jet discharging in the vicinity of
the water bottom into a stagnant or cross-flowing ambient
can experience two types of dynamic interaction processes
57
-------
that lead to rapid attachment of the effluent plume to the
water bottom (see Figure 2.9). These may be wake attachment
forced by the crossflow or Coanda attachment forced by the
entrainment demand of the effluent jet itself. A physical
description of these processes is given below. Appropriate
criteria for the occurrence of such attachment processes are
discussed in Chapter III.
2.4.4.1 Wake Attachment
In wake attachment (Figure 2.9a), the presence of the
discharge outfall structure and the jet efflux interrupts
the ambient velocity field and causes a recirculation region
in the wake downstream from the discharge.
The appropriate length scale measuring the outfall
structure/jet efflux combination is given by Lg = (hgLg) 1/2
where h0 is the port height or by Lg = L,, for a flush
discharge (zero port height) . The downstream extent XR of
the recirculation region is a few multiples of Lg,
XR = CLg (2.92)
where C = 5.0. Furthermore, in many such recirculation
processes the dilution is limited to low values, SR & 2 . 0 to
4.0 (see Jirka et al., 1975). Thus by continuity the width
of the attached (semi-circular) cross-section at the end of
the recirculation zone is given by
bR = [(2A)SRLJ^] (2.93)
with virtual source conditions assumed for the discharge.
A wall jet, with initial width bR/ is formed downstream
from the recirculation region. If boundary friction in that
wall jet is neglected - a reasonable assumption as indicated
by the data summarized in Rajaratnam, 1976 - then the
dynamics of the attached wall jet are similar to those of
the free jet as discussed earlier. Further details of such
jet models are presented in Chapter V.
Depending on discharge buoyancy, the wall jet may adhere
to the bottom for long distances (weak, zero or negative
buoyancy) or it may lift-off form the bottom at some
distance (strong positive buoyancy) . Such possibilities are
considered in the classification scheme in Chapter III.
58
-------
UQ
U,
i) Free Deflected Jet/Plume ii) Wake Attachment of
in Cross-flow Jet/Plume
a) Wake Attachment
i) Free Jet ii) Attached Jet
b) Coanda Attachment
Figure 2.9 Near-Field Attachment Processes
59
-------
2.4.4.2 Coanda Attachment
When a jet discharges parallel (or near-parallel) to a
boundary that is located nearby, rapid dynamic attachment
can occur. This process is often referred to as a "Coanda
effect". It occurs because of the entrainment demand of the
jet flow at its periphery. If a boundary limits the
approach flow of ambient water then low pressure effects
cause the jet to be deflected towards that boundary thereby
forming a wall jet. Thus the mixing process of Coanda
attached flow is governed by wall jet dynamics. Criteria
for the occurrence of Coanda attachment under the added
influences of buoyancy or weak crossflow are discussed in
the following chapter.
60
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Chapter III
Hydrodynamic Flow Classification
The previous chapter has presented a summary of the
multitude of distinct flow and mixing processes that can
occur with effluent discharges into the water environment.
Obviously, depending on the interplay of these mixing
processes, the size and appearance of any discharge flow
field and its associated mixing zone may vary greatly from
case to case.
In this chapter, a rigorous flow classification scheme
is developed that classifies any given discharge/environment
situation into one of several flow classes with distinct
hydrodynamic features. The classification scheme places
major emphasis on the near-field behavior of the discharge
and uses the length scale concept as a measure of the
influence of each potential mixing process. Flow behavior
in the far-field, mostly in the form of boundary
interactions, is also discussed herein.
3.1 Ambient and Discharge Data: Geometry and Flow Variables
Given the diversity of possible ambient environments
(e.g. highly varying water depth, curved channels, unsteady
flow conditions, etc.) some form of engineering
simplification, or schematization, is necessary to perform
predictions of effluent flow conditions and mixing zone
analyses.
3.1.1 Ambient Geometry and Flow Conditions
Ambient conditions are defined by the hydrographic and
geometric conditions in the vicinity of the discharge. For
this purpose, typical cross-sections normal to the ambient
flow direction at the discharge site and further downstream
need to be considered. The cross-section can be defined
as: i) bounded cross-section: If the cross-section is
bounded on both sides by banks - as in rivers, streams,
narrow estuaries, and other narrow watercourses -, then the
cross-section is considered "bounded", and ii) unbounded
cross-section: In some cases the discharge is located close
to one boundary while the other boundary is for practical
purposes very far away. This would include discharges into
61
-------
wide lakes, estuaries and coastal areas. These situations
are defined as "unbounded".
The following flow classification and subsequent
predictive models assume a rectangular cross-section that
is given by a width and a depth which are constant in the
downstream direction following the ambient flow. Thus if
the actual ambient is curved or meandering, it is assumed
that the schematic rectangular cross-section represents a
straight "stretched-out" counterpart. The discharge and
ambient schematization for a typical single-port discharge
appear in Figure 3.1.
This schematization may be quite evident for
well-channeled and regular rivers or artificial channels.
For highly irregular cross-sections or unbounded sections,
it may require more judgement and experience, perhaps
combined with an iterative use of the classification scheme,
to get a better feeling on the sensitivity of the results
to different schematizations.
The hydrodynamic classification assumes steady state
ambient flow conditions. Thus for time varying ambient
flows, as in tidal currents, a quasi-steady analysis must
be conducted choosing certain design flow conditions.
Generally this is acceptable because the time scale for
variation in ambient currents (e.g. the tidal period) is
usually much larger than the time scale for near-field
mixing processes (in the order of minutes to tens of
minutes). Furthermore, any shear effects in the ambient
flow are neglected and a uniform velocity equal to the
depth-averaged value is assumed.
3.1.2 Ambient Density Stratification
Ambient density stratification occurs frequently in
aqueous environments. A stable density profile occurs when
density increases vertically with increasing depth from the
water surface to the bottom. If the density decreases with
depth, the water column is unstable, and subsequent overturn
mixing will eventually yield a stable or uniform profile.
In the unstable density profile, water of lesser density
located below water of greater density would rise towards
the surface, and water of greater density would sink towards
the bottom. Density stratification may be associated with
variations of salinity or temperature within the vertical
water profile.
Stable density variations in ambient environments can
arise in many possible profiles. Four simple representative
62
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PLAN VIEW
CROSS-SECTION
w
f T>/ / t , ;m s\ | i/ f s
/
/
/
/
/
/
C0
Flux quantities: Oo - discharge
Mo= U00O = momentum flux
J0 = ( A/o0//)Q) q 00 = buoyancy flux
Figure 3.1
Definition Diagram for Single Port Discharge
Geometry in Ambient Channel with rectangular
Cross-Section. Width W of the water body may
be finite or unlimited.
63
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density profiles are illustrated in Figure 3.2. Any
existing ambient stratification is approximated by the
schematic profile that most closely resembles it. A
dynamically correct approximation of the actual distribution
should keep a balance between over- and under-estimation of
the actual density data.
The simplest case is a linear density profile shown in
Figure 3.2a (Stratification Type A). Figure 3.2b describes
two uniform density layers with a density jump between
layers (Stratification Type B). This density jump is often
referred to as a pycnocline or thermocline. Figure 3.2c
illustrates a two layer profile in which the upper layer is
uniform, the lower layer has a linear stratification, and
a density jump occurs between layers (Stratification Type
C). Finally, Figure 3.2d presents a two layer system with
a uniform upper layer and a linearly stratified bottom layer
with no density jump between layers (Stratification Type D) .
The uniform upper layers in Stratification Types B, C, or
D is representative for the well mixed upper layer (often
referred to as the epilimnion) that is found in many types
of ambient water bodies and occurs due to wind induced
turbulent mixing.
3.1.3 Discharge Parameters
The salient discharge conditions are shown in Figure
3.1. The discharge geometry is given by the diameter D of
the port or nozzle, its height h0 above the bottom, and its
orientation angles 00 and OQ.
The vertical angle of discharge 00 is the angle of the
port centerline measured from the horizontal plane. For
practical applications, this angle may range between -45°
and 90°. As examples, the vertical angle is 90° for a
discharge pointing vertically upward, and it is 0° for a
horizontal discharge. The horizontal angle of discharge CTO
is the angle measured counterclockwise from the ambient
current direction (x-axis) to the plan projection of the
port centerline. This angle may range between 0° and 360°.
As examples, the horizontal angle is 0° if the port points
downstream with the ambient flow (co-flowing discharge), it
is 90° or 270° if it points across the ambient flow (cross-
flowing discharge) , and it is 180° if it points upstream
opposing the ambient flow (counter-flowing discharge).
The important dynamic variables of the discharge are its
momentum flux M0, its buoyancy flux J0/ and to a lesser
degree, the discharge flow (volume flux) QQ. These bulk
parameters, first derived in Chapter II, are listed on
Figure 3.1. Note that in case of stratified ambients, the
64
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Figure 3.2 Representative Stable Density Profiles (Four
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65
-------
discharge buoyancy g0' refers to the ambient density
conditions at the level of the discharge, h0/ i.e. g0' =
3.2 Near-field Flow Classification
The purpose of the hydrodynamic flow classification is
to predict for a given discharge/environment situation the
type of flow configuration that will occur. Once a reliable
classification has been established, it becomes much easier
to provide actual predictions for flow properties including
pollutant concentration distributions within the distinct
hydrodynamic zones pertaining to each flow class.
The present flow classification procedure uses the
length scale concept. The dynamic length scales
characterizing the discharge are summarized in Table 3.1.
There are six major scales: Lg, 1^,, 1^, 1^' , and 1^' .
It should be noted that there are functional
interdependences, e.g. 1^ = L^//I and 1^' = I^'/!* / and
it can be readily shown that there are only four independent
length scales. These length scales interact with the
geometric properties of the ambient water body, its layer
depth Hs, stratification e, and orientation angles 8Q and a0.
Thus in total at least seven independent length
parameters plus two angles seem to influence the near field
flow configuration, even within the relatively simple
rectangular channel schematization discussed in Section 3.1.
Assuming two values (high and low) for each of these
lengths, two values of 0 or 90° for 8Q, and three values of
0°, 90° (or 270°) , or 180° for CTO, it appears that there exist
at least 27"1 x 2 x 3 = 384 possible different flow
configurations! Indeed such a simple calculation gives an
indication of the potential variety of flow patterns that
can occur in environmental conditions.
In fact, many of these potential configurations are not
possible on theoretical grounds, and many will not occur for
practical reasons. The classification procedure presented
below yields 35 generic flow configurations. The actual
number of flow classes that can be modeled with the full
predictive methodology (Chapter V) is considerably larger
(about 100 flow classes) since: i) each of the 35 generic
flow classes may apply to a layer corresponding to the full
water depth or to the region below a pycnocline, and ii)
certain sub-processes may be present or absent in a
particular flow classes (a typical example is the absence
of a weakly deflected jet region close to the discharge port
if the ambient velocity is very large) .
66
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Table 3.1 Flow Classification Variables and Length
Scales
Ambient and Discharge Variables:
H = ambient depth at discharge
h0 = discharge port height above bottom
hint = ambient internal density jump height
H8 = stratified layer height (equal to H or hjnt)
ua = ambient velocity
f = Darcy-Weisbach friction factor for ambient shear flow
9Q = discharge vertical angle
a0 = discharge horizontal angle relative to current
Length Scales:
LQ = Qo/M01/2 = discharge (geometric) scale (Eg. 2. 9)
LH = M03/4/J0V2 - jet/plume transition scale (Eq.2.12)
1^, = M01/2/ua = jet/crossflow scale (Eg. 2. 10)
LH, = Jo/ua3 = plume/crossflow scale (Eg. 2. 11)
L/- (Mo/e)174 - jet/stratification scale (Eg. 2. 13)
1/A/e3/8 - plume/stratification scale (Eg. 2. 14)
67
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3,2.1 General Procedure
The flow classification is a 13 step procedure that is
summarized in Table 3.2. This procedure is used to
determine which of four major flow categories the given
discharge will exhibit. The four major flow categories are:
i) flows affected by linear stratification leading to
internal trapping (S classes, Figure 3.3), ii) buoyant flows
in a uniform ambient layer (V and H classes, Figure 3.4),
iii) negatively buoyant flows in a uniform ambient layer
(NV and NH classes, Figure 3.5), and iv) bottom attached
flows (A classes, Figure 3.6).
Even though a stable ambient density profile may be
specified for a given situation, that profile may be weak
or even dynamically impossible in the presence of the
destabilizing effect of an ambient flow with mean velocity
ua. In Step 1 of Table 3.2 a flux Richardson criterion (see
Appendix A) is used to check for such destabilization which
would enforce a uniform profile.
Steps 2 through 8 in Table 3.2 determine the effect of
ambient density stratification (if present) on the flow.
In general, if the predicted terminal height of rise Zt for
near-field flows is greater than the actual layer height Hs/
then the effect of the linear stratification will be
unimportant and the buoyant jet will traverse this layer as
if it were in fact of uniform density.
If the terminal height of rise Zt is less than the layer
height Hs additional tests (Steps 3 through 7, Table 3.2)
are performed. In the case of a profile with a density jump
(Stratification Types B and C in Figure 3.2) these tests
determine if the flow will be trapped by the pycnocline, or
in the case of Stratification Type C, trapped within the
lower density layer. If the flow is trapped by the
pycnocline, the details of stratification below the
pycnocline are unimportant and the region below the
pycnocline will be represented by a uniform density layer
in all cases.
Step 9 is the detailed flow classification for those
flow classes whose dynamics are directly affected by linear
ambient stratification. The linearly stratified layer may
extend over the full water depth or be confined to the
region below the pycnocline. Further details on this
classification are given in Section 3.2.2.
Steps 10 to 12 examine the flow behavior for those
categories in which the ambient layer can be taken as
uniform (either existing or because any stratification is
68
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72
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Table 3.2 Near-Field Flow Classification Procedure
Step 1: Test for density profile stability. If the ambient
is unstratified or the given stratification is
dynamically impossible according to a flux
Richardson number criterion, approximate ambient
density with mean value and recompute discharge
parameters. Conclude stratification is not
important and go to Step 10.
Step 2: Ambient has stable density stratification. Check
for density step change. If the ambient does not
contain a density step change (Types A or D in
Figure 3.2) go to Step 4.
Step 3: Ambient density profile contains step change. Since
the Stratification Type is B or C, approximate the
actual lower layer stratification and the step
change with a surrogate linear stratification
(Figure 3.2). Calculate surrogate gradient e* and
surrogate stratification length scales 1^' and 1^'.
Step 4: Possible flow trapping in linear density
stratification. Test for internal layer formation
(flow trapping), using the scheme outlined in the
upper portion of Figure 3.3. Use height Hs (Hs = H
for Stratification Type A, and Hs = hint for Types
B, C or D) . If (Zt+h0)/Hs > 0(1), density
stratification will not trap flow. Therefore
conclude ambient density stratification is not
dynamically important. Approximate ambient density
with mean value, recompute discharge parameters,
and go to step 10.
Step 5: Stratification is important and flow trapping may
occur. If there is no density jump in the profile
(Types A or D) go to Step 8.
Step 6: Test for trapping at density jump or in linearly
stratified layer. If Stratification Type is C,
perform a second test for internal layer formation
using the scheme outlined in the upper portion of
Figure 3.3 based on the actual density gradient e.
If (Zt+h0)/Hs < 0(1), conclude the flow will become
trapped in the linearly stratified layer below the
density jump, go to Step 8.
73
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Table 3.2 (continued)
Step 7: Trapping at the density jump (pycnocline) . The
linear stratification below the density jump is
dynamically unimportant. The effluent flow will
be confined to the lower layer of Stratification
Types B or C due to the strong density jump. For
Type C, approximate linear ambient density profile
of lower layer with mean, and recompute discharge
parameters. Set Hs = hjnt and go to Step 10.
Step 8: Check for flow interaction with bottom for flows
influenced by linear density stratification. Flow
may interact with bottom if its buoyancy is
negative or jet is directed downward. If Zt + h0 <
0, flow will interact with the bottom. Proceed to
Step 12.
Step 9: Complete flow classification for buoyant jet in
linearly stratified layer. Five flow classes exist
(SI to S5) as shown in Figure 3.3. Go to Step 13
for final check on near-field bottom attachment.
Step 10: Test for discharge buoyancy in uniform ambient
density layer height Hs. If discharge is
negatively buoyant go to Step 12.
Step 11: Perform flow classification for positively buoyant
(or neutral) jet in uniform density layer. Fifteen
major flow classes (VI to V6, HI to H5) exist as
shown in Figure 3.4. Go to Step 13 for final check
on near-field bottom attachment.
Step 12: Perform flow classification for negatively buoyant
or downward directed jet in uniform density layer.
Ten major flow classes exist (NV1 to NV5, NH1 to
NH5) as shown in Figure 3.5. STOP.
Step 13: Perform flow classification for bottom attached
effluent flows. Five major attached flow classes
exist (Al to A5) in the form of wake and Coanda
effects as shown in Figure 3.6. STOP.
74
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weak and dynamically unimportant compared to the discharge
fluxes). The detailed classification for positively buoyant
(or neutral) discharges in such a layer is contained in Step
11 (see Section 3.2.3) and for negatively buoyant discharges
is given in Step 12 (see Section 3.2.4).
The final Step 13 performs an additional test and
classification for dynamic bottom attachment (see Section
3.2.5). Most (but not all) of the flow classes that may
have been concluded in Step 8, 11, or 12 may experience such
attachment effects which then radically alter the near-field
flow configuration leading to a new category of attached
flows.
The detailed classification schemes for each flow
category (Figures 3.3 to 3.6) are discussed in the following
sections. It is stressed that all criteria presented in
this chapter and listed on Figure 3.3 to 3.6 are "order of
magnitude" relations. The precise form of the criteria as
well as the numerical constants are given in Chapter V.
3.2.2 Flow Classes B for Linear Ambient Stratification
Referring to Figure 3.3, the first test level of the
flow classification for a buoyant jet in a linearly
stratified layer is to determine whether the flow is mostly
jet-like or mostly plume-like as it rises in the stratified
layer. This is achieved through the comparison of the
stratification length scales, Lm*
The next determination is the relative importance of
crossflow on these stratified flows. For jet-like
stratified flows, if ^\' < 0(1), the crossflow will have
strongly deflected the buoyant jet flow by the time the
stratification starts to influence the flow leading to a
"crossflow dominated" regime. But for l^/l^' > 0(1) the
crossflow is weak and the flow is "stratification
dominated. "
For plume-like stratified flows, if Lj/1^' < 0(1) the
crossflow will have strongly deflected the buoyant plume
flow before the stratification begins to affect the flow
leading to a "crossflow dominated" regime. On the other
hand, L^LI,' > 0(1) signifies a "stratification dominated"
flow.
The terminal height of rise Zt predicted for any of
these flows is indicated on Figure 3.3. Detailed discussion
and references for these equations are in Section 5.3. In
general, the height of rise depends on L,/ or 1^' with an
added influence of L,,, or l^ for crossflow affected stratified
flow. The sketches at the bottom of Figure 3.3 indicate the
75
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schematic flow configuration for each flow class. Once the
terminal height has been reached, some flows (SI or S4) are
further deflected by the strong crossflow leading to far
field buoyant spreading and diffusion phases. Other flows
(S2 or S5) have weak crossflow and are more nearly vertical
in approach ("impingement") to the terminal layer with an
ensuing upstream spreading phase. Flow class S3 with strong
horizontal momentum experiences a (near-) horizontal
"injection" into the terminal layer.
3.2.3 Flow Classes V or H for Buoyant Discharges into
Uniform Ambient Layers
The flow classification system for positively buoyant
discharges in uniform ambient layers appears in Figure 3.4.
Two major branches occur within this classification
depending on the vertical angle of the discharge 00 as shown
in Figure 3.4. The vertical discharge angle 80 is used to
define the sub groups of (near-) vertical (V classes) and
(near-) horizontal discharges (H classes). This distinction
is necessary because V classes may have surface contact with
strong vertical momentum, while for the H classes the
momentum is directed in the horizontal plane.
The flow classification system then uses the ratio of
IV/HS 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 discharge will have strong momentum as the
flow is influenced by, or impinges on, the surface.
The next level of the classification assesses the role
of buoyancy with respect to the ambient layer height H8.
For LI/HS > 0(1) the flow will have a strong buoyancy effect
when contact with the surface or upper layer occurs, while
for Lfc/Hg < 0(1) the buoyancy influence will be minor.
An additional determination needs to be made in those
cases where both momentum and buoyancy effects have found
to be weak, or both to be strong, respectively. A criterion
LH/HJ is used to determine which one of the two effects
predominates.
As a result, discharges can be classified as "stable"
or "unstable" . Flows with strong momentum and weak buoyancy
occurring in shallow water layer tend to be unstable (V4,
V6, and H5) . In this case the jet is affected by the
shallowness and an unstable recirculation zone occurs around
the jet as it re-entrains the fluid already mixed. In a
stable discharge, buoyancy tends to have a stabilizing
76
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effect on the flow as it contacts the surface, causing the
flow to form a stratified layer on the surface.
Discharges into deep water layer have stable flow
classes (VI, V2, V3, HI, H2, and H3) , with strong similarity
among the V and H classes in this case, as well as the
shallow water cases V5 and H4 that have extremely strong
buoyancy as a stabilizing factor in an otherwise shallow
layer. Some of these stable flow classes with strong
buoyancy (V3, V5, H3, and H4) experience upstream spreading
once surface contact has occurred.
An important aspect of such a classification scheme is
its robustness under extreme conditions. Two such
conditions are of interest; i) zero discharge buoyancy (g0'
= 0 and thus J0 = 0) , and ii) stagnant ambient (ua = 0) . In
the first case, the length scales are L^ = 0, and 1^ goes
to infinity. In the second case 1^ goes to infinity. In
the combined case (zero buoyancy flux and ambient velocity)
1^ is indeterminate.
Case i) Non-buoyant discharges into a flowing ambient
lead to flow classes V2 or H2. A special sub class of
this flow is a rapidly deflected small "passive source"
(well below the layer surface) with a rapid transition
to far-field ambient diffusion.
Case ii) Stagnant ambient conditions lead to flow
classes V5, V6, H4, or H5, respectively. In particular,
if the discharge is weakly buoyant (or, in the extreme,
nonbuoyant) flow classes V6 or H5 will occur.
Obviously, far-field mixing process are absent for these
situations, which rarely occur anyway in actual
environmental conditions.
The flow classes H4 and H5 contain a sub-classificatieon
depending on whether the discharge is coflowing (a0 a 0°) ,
cross-flowing (a0 as 90°) , or counter-flowing (a0 » 180°) .
This is necessary since the strong horizontally oriented
momentum flux in these shallow environments leads to a
drastically different flow configuration as a function of
discharge direction relative to the crossflow. In fact some
of these configurations (e.g. the counter-flowing ones) lead
to complicated recirculation zones that may be difficult to
analyze and undesirable in actual design practice.
3.2.4 Flow Classes NV or NH for Negatively Buoyant
Discharges in Uniform Ambient Layers
The classification system for negatively buoyant
discharges (Figure 3.5) bears some similarities to that for
positively buoyant discharges described above. Several
77
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negatively buoyant flow classes have a "mirror image"
analogy to positively buoyant flows which appear in Figure
3.4.
Again, the flow classification system has two main
branches; for discharge angles 90 > 45° the flows are
classified as near-vertical (NV-classes), while for -45° <
9Q < 45° the flows are classified as near-horizontal (NH-
classes).
The first level is to determine if momentum or buoyancy
dominates with respect to the ambient layer depth H . If
I^/Hg < 0(1) the flow will be buoyancy dominated after a
short distance and therefore will not have any surface
interaction. If it is discharged upward, it will quickly
fall back towards the bottom. If 1^/H8 > 0(1) the flow will
be momentum dominated in relation to the ambient layer depth
Hs. For near-vertical jets, surface interaction will occur.
For near-horizontal discharges, the potential for surface
interaction will depend on the horizontal angle of discharge
CTo-
Additional tests for flow behavior are based on the
crossflow scales Lra and 1^. The negatively buoyant flow
classes are separated into those without layer or surface
interaction (NV1, NV2, NH1, NH2, NH3, and NH4) and those
with interaction (NV3, NV4, and NV5). The extremely strong
negative buoyancy causes upstream spreading in flow classes
NV2 or NH2. Unstable discharge configurations with vertical
mixing and recirculation zones exist in flow classes NV4,
NV5, and NH5. Finally, it should be noted that this
classification also applies for a downward oriented jet (00
< 0°, regardless of buoyancy) that is trapped by linear
ambient stratification near the bottom of the water layer
(see Step 8 of Table 3.2). In this instance, flow
configurations NH1 to NH3 may result.
3.2.5 Flow Classes (..)A for Bottom Attached Flows
Two types of flow attachment appear in Figure 3.6: wake
attachment and Coanda attachment. The physical processes
for these have been described in the previous chapter.
Several flow classes appear to be prone to some kind of
1Strictly speaking 1^ and 1^ are negative quantities
for negatively buoyant discharges since g0' < 0, and thus
J0 < 0 . In this clas
quantities are used.
J0 < 0 . In this classification the absolute values of these
78
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attachment while others are not as shown in Figure 3.6.
For example, a vertical discharge cannot experience Coanda
attachment.
Wake attachment will not occur if the effluent intrudes
sufficiently far away from the boundary. An estimate of the
intrusion distance is given by the sum of port height h0 and
the crossflow length scale 1^, for jet-like or L^ for plume-
like flows, respectively. If these intrusion distances are
small relative to the source dimension, (1^, + h0) < Lg, and
(1^ + h0) < Lg, then wake attachment to the bottom will
occur. A supplementary criterion based on a local
Richardson number condition tests for potential buoyant
lift-off (flow class Al) following the recirculation zone
in the wake of the discharge (see Figure 3.6) . For weak (or
negative) buoyancy no such lift-off will occur (flow class
A2) .
Jet-induced Coanda attachment depends primarily on the
vertical angle 8Q of the (near-)horizontal discharge and on
the initial jet separation given by the total spreading
angle (with a tangent of 0.2 for a jet flow). A simple
criterion for attachment is indicated by tan0Q < (0.2 -
h0/L) where L is the distance of the jet region. For weak
crossflow (stagnant) conditions, L is given by the jet/plume
scale LH leading to flow classes A3 or A4, depending on the
strength of buoyancy. In a strong crossflow, L is given by
the jet/crossflow length scale L^, leading to flow class
A5.
As has been noted earlier, the flow class is checked for
wake and Coanda attachment after the primary classification
(S, V, NV, or NH) has been completed. In the actual expert
system implementation of this scheme, if the flow is
attached, it is given the appropriate attachment suffix
(e.g. A2) to the already determined flow class (e.g. V1A2).
This is done for practical reasons as a guidance to the
analyst: simple modification of the discharge geometry (e.g.
a larger angle 9Q) can often lead to avoidance of attachment
in which case the primary flow class (e.g. VI) will describe
the flow.
3.3 Far-Field Flow Behavior
After the effluent flow has interacted with the water
surface, bottom, pycnocline, or terminal layer and has thus
completed its near-field phase, the -far field mixing begins.
This region consists of one or two mixing processes,
depending on discharge characteristics. In the general
case, the discharge flow contains sufficient buoyancy and
there will be a buoyant spreading region followed by a
passive diffusion region. The buoyant spreading region is
79
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characterized by dynamic horizontal spreading and gradual
vertical thinning of the mixed effluent flow while being
advected by the ambient current. Vertical boundary
interaction may occur, and the flow may contact one or both
lateral boundaries (shorelines). 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 within the layer height
Hs in this region. If the flow is non-buoyant or weakly
buoyant there is no buoyant surface spreading region, only
a passive diffusion region.
In contrast to the near-field flow there is no need for
an advance classification scheme to determine the behavior
of the far-field flow for a given discharge/environment
situation. Since the effluent flow in the far-field is
always advected in the direction of the ambient flow, the
various interaction processes are simply calculated as part
of the downstream modeling process of the applicable far-
field solutions. This applies also to the transition
between buoyant spreading and passive ambient diffusion
(based on a flux Richardson number criterion). These
aspects are directly implemented in the predictive elements
for the detailed effluent flow and mixing zone predictions
as summarized in Chapter V.
80
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Chapter IV
Expert System CORMIX1: General Framework
The Cornell Mixing Zone Expert System, Subsystem I
(CORMIX1) contains a series of software elements for the
analysis and design of conventional or toxic single port
submerged buoyant or nonbuoyant pollutant discharges into
stratified or unstratified watercourses, with emphasis on
the geometry and dilution characteristics of the initial
mixing zone. It is intended as an analysis tool for
environmental regulators, discharge designers, and more
generally, students of hydraulics. The system is designed
for use under the MS-DOS operating system on an IBM-PC/XT
with a hard disk and a math co-processor as the minimum
hardware configuration.
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 purpose of CORMIX1 is to obviate for the novice
analyst the need for detailed understanding and experience
in hydrodynamic mixing processes. A general environmental
science or engineering background at the BS level appears
to be the 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 appear to be required for a first time user to
gain initial facility with system requirements, limitations,
and interpretation of results.
Depending on the computer configuration, a typical
CORMIX1 session for one discharge/environment condition may
take about 5 minutes for an advanced 80386-based micro-
computer to 20 minutes for an IBM-PC/XT, if all necessary
input data is at hand.
81
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4.1 Background on Expert Systems and Logic Programming
CORMIX1 is implemented in two programming languages: VP-
Expert (Paperback Software, Inc.)/ and Fortran . VP-Expert
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
facilities for both forward and backward reasoning,
debugging aids, consistency checking, input and output
menus, and explanation facilities. The two programming
languages are used to exploit their respective strengths
while avoiding their respective weaknesses. VP-Expert, 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 VP-Expert is employed to implement the
knowledge acquisition, simple length scale and dynamic
variable calculation, model selection, and analysis of the
hydrodynamic simulation portions of the expert system.
Fortran is used for the hydrodynamic flow simulation, which
is called from a VP-Expert program element.
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 VP-Expert 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
language. In essence the selection of VP-Expert as the
language for the symbolic reasoning tasks gives the
programmer significant leverage. A VP-Expert knowledge base
is very similar in structure to a PROLOG (PROgramming LOGic)
program. PROLOG was developed in Europe and is designed to
manipulate logical expressions (Clocksin and Hellish, 1984).
A VP-Expert program is built from statements containing
facts and if-then rules about facts. This is called the
knowledge base. The knowledge base is constructed with an
expert in the problem domain, in this case hydrodynamic
mixing processes.
Logic programs, such as VP-Expert, are driven by a
"goal" which the program tries to validate by searching the
knowledge base to construct a "proof". The proof is
constructed by using the facts and rules in the knowledge
base to deduce the goal as a valid hypothesis. The
following paragraphs give a more detailed explanation of how
this is accomplished, using the CORMIX1 knowledge base
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AMBIENT as an illustrative example. AMBIENT is a knowledge
base designed to gather information on ambient conditions
at the discharge site.
The execution of each knowledge base program is driven
by attempting to satisfy a goal. In the AMBIENT knowledge
base this is written in VP-Expert as:
FIND = ambient_conditions [1]
Here the goal is to satisfy or find a valuation for the
expression "ambient_conditions".
All rules in VP-Expert 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 rule} statements. The premise of a rule in
VP-Expert can contain more than one expression connected by
and/or statements. VP-Expert will try to satisfy the goal
(here the expression "ambient_conditions") by searching for
a rule in the knowledge base whose conclusion contains the
expression "ambient_conditions = (valuation)".
A rule in AMBIENT that has "ambient_conditions = known"
in its conclusion is:
if ambient_advice <> UNKNOWN and
bounded_section = yes and
channel_width <> UNKNOWN and
depths <> UNKNOWN and
nearest_bank <> UNKNOWN and
ambient_velocity_field <> UNKNOWN and
friction_factor <> UNKNOWN and
ambient_density_field <> UNKNOWN
then ambient_conditions = known [2]
Here, in the conclusion of the rule the expression
"ambient_conditions" is assigned the valuation "known".
First, an explanation is given on how VP-Expert uses
information contained within if - then rules to assign
valuations to expressions. VP-Expert always tries to
satisfy a valuation in the conclusion of the rule by proving
its premise. Thus, VP-Expert tries to satisfy all
expressions in the premise of the rule, beginning in
statement [2] with the first expression "ambient_advice <>
UNKNOWN" (the "<>" in [2] stands for "not equal to"). If
the valuation of the variable in the first clause is
satisfied, i.e. the expression site_description does indeed
have a valuation other than "UNKNOWN", then VP-Expert tries
to satisfy the second expression, "bounded_section = yes".
If this valuation is satisfied, VP-Expert will try to
satisfy the remaining expressions in the premise of the
83
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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 of the
rule can be given a valuation and this information is added
to the facts known in the knowledge base.
So how does VP-Expert know the expression
"ambient_advice" has a valuation other than "UNKNOWN"?
Because there is another rule in the knowledge base which
is:
if ambient_query = yes
then ambient_advice = yes [3]
This statement is invoked by statement [2] when it tries to
find a valuation for the first expression "ambient_advice".
Since there is no present valuation for the expression
"ambient_advice", VP-Expert locates statement [3] with the
expression "ambient_advice" in its conclusion. If the
expression "ambient_query" in the premise of statement [3]
can be assigned a valuation equal to "yes", then the
expression ambient_advice is assigned the valuation "yes"
(which is not equal to "UNKNOWN"). VP-Expert will now try
to find a valuation for ambient_query, the first and only
expression in the premise of statement [3]. Within AMBIENT
there is another rule:
ASK ambient_query: "Do you want a detailed
description of the ambient environmental data needed?" [4]
This rule is a treated as a "fact", and VP-Expert prompts
the user for a valuation of "ambient_query" with the message
within the quotes of statement [4]. The user enters a value
(yes or no) which is bound to "ambient_query". VP-Expert
continues to find valuations for the remainder of the
expressions in statement [2] in a similar manner. When all
expressions in the premise of statement [2] are assigned a
valuation, the conclusion "ambient_conditions = found" is
added as a fact to the knowledge base.
Thus, as was shown with the previous example, the
knowledge base AMBIENT is built from rules which contain
expressions that force VP-Expert to seek valuations from
other rules. The process of seeking valuations of
expressions continues until either all the valuations are
found or the rule base is exhausted without finding a
valuation. VP-Expert will never assign a valuation which
is in contradiction within a rule, so one is assured
whatever valuations are concluded are taken from a rule
within the knowledge base. Care must be taken in program
structure however, since the search strategy of VP-Expert
may not consider all rules needed to find a valuation for
a given expression. In general, the rule base should be
84
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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 to agree with the valuation given for that
clause within the rule, e.g. the expression "depths" in
statement [2] is found to have the valuation "UNKNOWN", then
the rule fails, no valuation can be assigned to the
expression "ambient_conditions" from that rule. VP-Expert
will stop trying to satisfy the remaining expressions in the
premise of that rule. VP-Expert will continue to try to
satisfy the expression "ambient_conditions" by looking for
another rule in the knowledge base with "ambient_conditions"
in the conclusion of the rule.
Rules in AMBIENT contain 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.
4.2 Structure of CORMIX1
Figure 4.1 shows the overall structure of the system
elements of CORMIX1. The program elements of CORMIX1 are
DATIN, PARAM, CLASS, HYDRO, and SUM. During system use the
elements are loaded automatically and sequentially by the
system. Table 4.1 outlines the directory structure of
CORMIX1 and contains comments about program files.
The system runs entirely under the VP-Expert program
shell. The hydrodynamic simulation Fortran program HYDRO
is executed from the knowledge base program HYDRO. All
program elements execute sequentially. For example, when
a rule in a program element 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 a
program element that have been assigned a valuation. This
cache file is read by the next sequential element in DATIN,
the knowledge base PARAM, and so on for the remaining
program elements.
4.2.1 Data Input Element: DATIN
DATIN is a VP-Expert program for the entry of relevant
data and for the initialization of the other program
elements. DATIN consists of four program segments or
85
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VP-Expert
DAT IN
User Input
Iteration
Alternatives
Corrections
VP-Expert
PARAM
Parameter
Computation
VP-Expert
CLASS
Flow
Classification
VP-Expert Fortran
HYDRO
Prediction/Simulation
Program
VP-Expert
SUM
Summary
Evaluation
Recommendations
(Legal/Engineering)
Figure 4.1 System Elements of CORMIX1
86
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Table 4.1
Directory
CORMIX1 Program File Directories
Comments
C:\crnx
system root directory, contains VP-Expert
system files and the knowledge base
program CORMIX1 (system driver)
c:\cmx\advice
c:\cmx\bat
c:\cmx\cache
c:\cmx\data
c:\cmx\desc
c:\cmx\kbs
c:\cmx\pgms
c:\cmx\sim
contains all user-requested advice files
contains batch files for program
execution, data file manipulation, and
program control
contains cache "fact" files exported from
knowledge base programs
contains constants used in flow
classification and other knowledge base
programs
contains flow descriptions for each flow
class
contains all knowledge base programs
contains Fortran hydrodynamic simulation
and file manipulation programs
contains simulation results
87
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knowledge base sub-elements which execute sequentially. The
knowledge base sub-elements are, in execution order, ASITE,
AMBIENT, DISCHARG, and ZONES. The user executes DATIN by
invoking the CORMIX1 expert system by entering the command
"CORMIX1" at the DOS prompt . DATIN program elements
automatically prompt the user for needed information.
The purpose of DATIN is to specify completely the
physical environment of the discharge, as well as legal or
regulatory requirements on the discharge. The following
data groups need to be entered: general site and case
identifier information (knowledge base ASITE), ambient
conditions (geometry and hydrography, knowledge base
AMBIENT), discharge conditions (geometry and discharge
fluxes, knowledge base DISCHARG), and information desired
including legal mixing zone definitions and toxic dilution
zone criteria (knowledge base ZONES). DATIN provides
consistency checks and gives advice for input parameter
selection.
CORMIX1 assumes a deeply submerged single port discharge
into the 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, was given in Figure 3.1.
DATIN contains advice on how to enter data values and
rejects inappropriate or incorrect values. A listing of the
input advice available on-line to the user of CORMIX1 is
given in Appendix B. DATIN will also flag unusual design
cases. For example, in the knowledge base sub-element
DISCHARG, if the user specifies a discharge horizontal angle
which directs the effluent towards the nearest bank, the
following message is displayed:
"The discharge port or nozzle points towards the nearest
bank. Since this is an unusual design, make sure you
have specified the discharge horizontal angle correctly.
CORMIX1 will continue with cne analysis with the
horizontal angle as specified, but be aware that CORMIX1
may predict a hydrodynamically unstable discharge
because of the interaction of the discharge near field
with the bank."
At its termination DATIN triggers the next program
element PARAM.
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4.2.2 Parameter Computation Element: PARAM
PARAM is a VP-Expert knowledge base that computes
relevant physical parameters for the given discharge
situation. This includes various fluxes; Q0, M0, and J0/
length scales Lg, 1^, 1^,, 1^, l^', L^', as well as other
values needed by the remaining CORMIX1 elements. As PARAM
executes, the user is notified about important
characteristics of the flow. For example:
"The effluent density (1003.2 kg/m**3) is greater than
the surrounding ambient water density at the discharge
level ( 997.3 kg/m**3). Therefore, the effluent is
negatively buoyant and will tend to sink towards the
bottom."
At its termination PARAM triggers the next program
element, the knowledge base CLASS.
4.2.3 Flow Classification Element: CLASS
CLASS is an VP-Expert program that classifies the given
discharge into one of the many possible flow configurations
that have been presented in Chapter III (Figures 3.3 to
3.6). CLASS contains two program elements, the knowledge
base sub-elements CLASS and FLOWDES.
The goal of CLASS is to find a valuation for the
expression "flow_class" in relation to the flow
classification scheme. Each of the possible flow
classifications has an alphanumeric label(e.g. VI, SI, H1A1,
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. CLASS
first tries to satisfy the goal of "flow_class" by initially
seeking a value for "flow_type". For example a rule
corresponding to flow case V2 would appear in simplified
form for illustration purposes as:
if flow_type = UNKNOWN and
uniform_layer_flow = yes and
flow_direction = upward and
THETA > 45.0 and
THETA <= 90.0 and
C4 > (Lm /(0.8*(HS-HO))) and
C6 > (Lb /(0.8*(HS-HO))) and
C9 <= (LMM /(0.8*(HS-HO)))
then flow_type = V2
coanda_attachment = no
find wake_attachment [5]
89
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in which C4, C6, and C9 are constants. If all of the
conditions in the premise of [5] are true, then "flow_type"
is assigned a value of V2. The possibility of coanda
attachment does not exist for this case, but wake attachment
can occur. The system then looks for rules in which to
satisfy a valuation for Mwake_attachment". If wake
attachment does not occur, other rules within the knowledge
base will fire and a value "flow_type" (i.e. V2) will be
assigned to "flow_class". If the knowledge base rules fire
that conclude wake attachment with buoyant lift-off from the
bottom, V2A1 will be assigned to "flow_type".
As an example of the output from CLASS, the following
would represent some of the information presented for a
discharge trapped by the pycnocline in a two-layer density
stratified environment:
"The near field flow configuration will have the
following features:
The specified two layer ambient density stratification
is dynamically important. The discharge near field flow
will be confined to the lower layer by the ambient
density stratification. Furthermore, it is trapped in
the lower layer by the ambient density jump at the
pycnocline.
The following conclusion on the flow configuration
applies to the lower layer only of the specified ambient
stratification condition B.
Note that the lower layer will be overlaid by the
surface layer of the ambient density stratification.
The surface layer will remain undisturbed by the near
field discharge flow (with the exception of some
possible intrusion along the pycnocline).
The flow class is V2 for the design case represented by
the DOS file name EXAMPLE."
A detailed hydrodynamic description of the flow is
available to the user in the knowledge base sub-element
FLOWDES. This detailed output includes a description of the
significant near field mixing processes, or the hydrodynamic
mixing zone (HMZ) . The complete listing of the flow
descriptions for all major flow classes is contained in
Appendix C. Typically, the HMZ is the region of strong
initial mixing where the particular design of the outfall
can have an 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.
90
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CLASS also creates a cache output file that supplies the
next CORMIX1 element HYDRO with instructions for running the
appropriate simulation. At its termination CLASS triggers
the next program element HYDRO.
4.2.4 Hydrodynamic Simulation Element: HYDRO
HYDRO is a knowledge base that runs the hvdrodynamic
simulation program for the flow classification program
specified in CLASS. The actual simulation program HYDRO is
written in Fortran. The simulation program is based on the
analytical description of the physical mixing processes
presented in Chapter II and discussed in more detail in
Chapter V.
HYDRO consists of control programs or "protocols" for
each hydrodynamic flow classification (e.g. VI, S2, H3,
etc.) as specified by CLASS. Each protocol executes a
series of subroutines or "modules" corresponding to the flow
phenomena (e.g weakly deflected jet in crossflow (mdnf),
surface spreading, etc.) which may occur in that flow
classification. Thus HYDRO assembles the appropriate
simulation sequence by picking the correct flow modules.
HYDRO creates a tabular output file of the simulation
containing information on geometry (trajectory, width, etc.)
and mixing (dilution, concentration) . The user has the
option to view the tabular output file. An example of such
an output file is given in Appendix D.
At its termination HYDRO triggers the final program
element SUM.
4.2.5 Hydrodynamic Simulation Summary Element: SUM
SUM is a VP-Expert program that summarizes the
hydrodynamic simulation results for the case under
consideration. SUM describes 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 hvdrodynamic
simulation summary lists conditions at the end of the
hydrodynamic mixing zone, legal mixing zone conditions,
toxic dilution zone conditions, region of interest criteria,
91
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upstream intrusion information, and bank attachment
locations, if applicable. 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 suggestions for
sensitivity studies and design changes for improving initial
dilution. An example of a case summary and design
recommendations appear in Appendix E.
At the completion of SUM, the user is given the option
to exit to DOS, start a new design example, or modify the
discharge and mixing zone data for the design case under
consideration using the same general ambient data base.
92
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Chapter V
CORMIX1: Flow Protocols and simulation Modules
This chapter provides the hydrodynamic details of the
effluent flow predictions and mixing zone analysis as
performed in program element HYDRO of the expert system
CORMIX1.
First, detailed flow protocols for each of the 35 flow
classes defined in program element CLASS (see Section 3.2)
are give*h. The full hydrodynamic description of these flow
classes (which is available on-line to the system user)
appears in Appendix C. In Section 5.2 the actual prediction
modules for each flow zone, including near-field and far-
field processes, are discussed. Finally, in Section 5.3 the
appropriate transition criteria that define the spatial
extent of each flow zone (module) are presented, along with
all constants used in the flow classification and simulation
modules.
5.1 Plow Protocols
The hydrodynamic prediction of the effluent flow and of
associated mixing zones in program element HYDRO is carried
out by appropriate flow modules that are executed according
to a protocol that pertains to each distinct flow
configuration as determined by the classification scheme
CLASS.
CORMIX1 contains 22 separate flow modules that apply to
each of the diverse mixing processes that can occur in the
near- and far-field of an effluent discharge. The physical
background of these mixing processes has been discussed in
Chapter II. Table 5.1 summarizes the flow modules. A
detailed description of each module is given in Section 5.2.
The sequence of module execution is governed by a flow
protocol for each flow class. These flow protocols have
been constructed on the basis of the same arguments that
have been presented in Chapter III to develop the flow
classification. Detailed flow protocols for each flow class
are presented in the following sub-sections with extended
explanations on their formulation.
The spatial extent of each flow module is governed by
transition rules. These determine transitions between
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Table 5.1 Flow Prediction Modules of CORMIX1
Module
(MOD) Description
Modules for Buoyant Jet Near-Field Flows
01 zone of flow establishment (zofe)
11 weakly deflected jet in crossflow (mdnf)
12 weakly deflected wall jet in crossflow (mdnf-wj)
13 near-vertical jet in linear stratification
(mdls-v)
14 near-horizontal jet in linear stratification
(mdls-h)
16 strongly deflected jet in crossflow (mdff)
17 strongly deflected wall jet in crossflow (mdff-wj)
21 weakly deflected plume in crossflow (bdnf)
22 strongly deflected plume in crossflow (bdff)
Modules for Boundary Interaction Processes
31 near-horizontal surface/bottom/pycnocline approach
32 near-vertical surface/bottom/pycnocline impingement
with buoyant upstream spreading
33 near-vertical surface/bottom/pycnocline impingement
with vertical mixing
34 near-vertical surface/bottom/pycnocline
impingement, upstream spreading, vertical mixing,
and buoyant restratification
36 terminal layer stratified impingement/upstream
spreading
37 terminal layer injection/upstream spreading
94
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Table 5.1 (Continued)
Module
(MOD) Description
Modules for Buoyant Spreading Processes
41 buoyant layer spreading in uniform ambient
42 buoyant spreading in linearly stratified ambient
Modules for Attachment/Detachment Processes
51 wake recirculation
52 lift-off/fall-down
Modules for Ambient Diffusion Processes
61 passive diffusion in uniform ambient
62 passive diffusion in linearly stratified ambient
95
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different near-field and far field mixing regions, and
distances to boundary interaction. Section 5.3 gives a
detailed summary of the transition rules.
5.1.1 Flow Protocols for Buoyant Discharges into Uniform
Ambient Layers (Flow Classes V and H)
The classification scheme discussed in Section 3.2.3
with its associated criteria (see Figure 3.5) already gives
an indication of which flow processes will occur for each
of the flow classes, and hence which sequence of flow
modules is necessary for simulation. The length scales are
the basis for the sequence determination in the near-field.
As an example, consider flow class VI. In the submerged
phase of that flow there are four possible flow zones (i.e.
mdnf, mdff, bdnf, or bdff) that might be involved. The
question is, which will occur and in what sequence?
Provided that L,,, and 1^ are both substantially larger than
Lg two possible transitions can occur (see Figure 5.1):
i) For Lfo/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. This is the initial sequence for the subsurface
flow modules in flow class VI.
ii) If L^/^j < bdnf -> bdff. This is an
alternate initial sequence (labeled VI') which has not
been illustrated in Figure 3.4.
In each of the preceding cases boundary interaction
interrupts the sequence of flow regions. When boundary
interaction occurs, the sequence will change to include the
appropriate boundary interaction effect and then continue
as a surface far-field flow. The listing of the flow
protocols for the flow categories V and H is given in Table
5.2.
No protocols are given for flow classes H4-180, H5-
90, and H5-180. These discharge types lead to a complicated,
irregular, and perhaps time-dependent (pulsating) flow
behavior for which no reliable predictive methodology exists
and which also seem undesirable in engineering practice.
Additional criteria are also imbedded into the actual
flow modules which may lead to by-pass of certain flow
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Transition]
Transition
N
N
z=0
a) Lm»Lb ; Momentum Dominates
Z=0-L-
b) Lm«Lb; Buoyancy Dominates
General Behavior for Buoyant Jets in Unconfined
Crossf low (Assuming Near-Vertical Discharge)
Figure 5.1
General Behavior for Buoyant Jet in Unconfined
and Unstratified Crossflow
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Table 5.2 Flow Protocols for Buoyant Discharges into
Uniform Ambient Layers
Flow
Class
VI, HI
vi SHI'
V2,H2
Flow
Zone
discharge
mdnf
bdnf
bdff
surface approach
surface buoyant spreading
passive diffusion
discharge
mdnf
mdff
bdff
surface approach
surface buoyant spreading
passive diffusion
discharge
mdnf
mdff
surface approach
surface buoyant spreading
passive diffusion
MOD
01
11
21
22
31
41
61
01
11
16
22
31
41
61
01
11
16
31
41
61
TR
0
1
3
5
10
17
0
2
4
5
0
7
0
2
5
0
7
MOD = module, TR = transition rule
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Table 5.2 (continued)
Flow Flow MOD TR
Class Zone
V3,H3 discharge 01 0
mdnf 11 1
bdnf 21 6
surface impingement with buoyant
upstream spreading 32 0
surface buoyant spreading 41 7
passive diffusion 61
V4 discharge 01 0
mdnf 11 5
surface impingement with full
vertical mixing 33 0
surface buoyant spreading 41 7
passive diffusion 61
V5, H4-0 discharge 01 0
H4-90 mdnf 11 1
bdnf 21 6
surface impingement with
buoyant upstream spreading 32 0
surface buoyant spreading 41 7
passive diffusion 61
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Table 5.2 (continued)
Flow
Class
H5-0
Flow
Zone
discharge
mdnf-wj
surface impingement with
full vertical mixing
surface buoyant spreading
passive diffusion
MOD
01
12
33
41
61
TR
0
9
0
7
V6 discharge 01 0
surface impingement with
unstable recirculation, full
vertical mixing, buoyant
upstream spreading, and
buoyant restratification 34 0
surface buoyant spreading 41 7
passive diffusion 61
100
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modules. For example, if the source dimension is large and
the crossflow is strong, i.e. L^ » Ly, then the weakly
deflected jet (MOD11) may be omitted in some flow classes,
and a strongly deflected jet or plume may follow the initial
discharge. For a non-buoyant discharge, the buoyant
spreading regime (MOD41) will be absent in the applicable
flow classes (V2 or H2) . Given all these possible sub-
classes the actual variety of flow configurations that will
be modeled is much larger than indicated by the primary
classes (see also Section 3.2)
5.1.2 Flow Protocols for Negatively Buoyant Discharges into
Uniform Ambient Layers (Flow Classes NV and NH)
The flow protocols for negatively buoyant discharges
into uniform ambient layers, corresponding to the flow
classes NV and NH as discussed in Section 3.2.4 and
illustrated in Figure 3.6, are listed in Table 5.3. Some
of the unstable discharge protocols bear some resemblance
to those for positively buoyant discharges except for
restratification and buoyant spreading in the far-field.
This is reflected in different transition criteria.
Also some protocols for stable discharges classes (e.g.
NV1, NH1) appear similar to their positively buoyant
counterpart (e.g. VI, HI) . However, some differences in
transition criteria as well as the downward acting buoyancy
force act to produce entirely different flow configurations
(see sketches in Figures 3.5 and 3.6 , respectively).
5.1.3 Flow Protocols for Discharges Trapped in Linearly
Stratified Ambients (Flow Class S)
Table 5.4 summarizes the protocols for the five flow
classes S (refer to Section 3.22 and Figure 3.4) in which
the ambient stratification causes an internal trapping of
the effluent flow leading to a terminal layer formation and
subsequent far-field processes. All stratification
dominated flow (see Fig. 3.4) use special modules that
account for the ambient stratification in the initial jet
or plume phases of the flow.
For instance, in the jet-like stratification dominated
flows (classes S2, and S3) the mdnf will be replaced by its
stratified counterpart, the mdls, before terminal layer
interaction.
When terminal layer interaction occurs the normal
sequence of flow regions is interrupted, and the sequence
will change to include the appropriate terminal layer
interaction (see Section 3.2.2) and then continue as an
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Table 5.3 Flow Protocols for Negatively Buoyant
Discharges into Uniform Ambient Layers
Flow
Class
NV1
NH1
NV2 , NH2
Flow
Zone
discharge
mdnf
mdff
bdff
bottom approach
bottom buoyant spreading
passive diffusion
discharge
mdnf
bdff
bottom approach
bottom buoyant spreading
passive diffusion
discharge
mdnf
bdnf
bottom impingement with
buoyant upstream spreading
bottom buoyant spreading
passive diffusion
MOD
01
11
16
22
31
41
61
01
11
22
31
41
61
01
11
21
32
41
61
TR
0
2
16
17
0
7
0
16
17
0
7
0
16
17
0
7
MOD = module, TR = transition rule
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Table 5.3 (continued)
Flow Flow MOD TR
Class Zone
NV3 discharge
mdnf
mdff
surface approach
fall down
bdff
bottom approach
bottom buoyant spreading
passive diffusion
01
11
16
31
52
22
31
41
61
0
1
5
0
0
17
0
7
NH3 discharge 01 0
mdnf 11 2
bdnf 21 17
bottom approach 31 0
mdnf-wj 12 18
flow turning 31 0
bottom buoyant spreading 41 7
passive diffusion 61
NV4 discharge 01 0
mdnf 11 5
surface impingement with
full vertical mixing 33 0
surface buoyant spreading 41 7
passive diffusion 61
103
-------
Table 5.3 (continued)
Flow Flow MOD TR
Class Zone
NH4 discharge
mdnf
mdff
bdff
bottom approach
bottom buoyant spreading
passive diffusion
01
11
16
22
31
41
61
0
2
16
17
0
7
NV5 discharge 01 0
bottom impingement with
unstable recirculation, full
vertical mixing, buoyant
upstream spreading, and
buoyant restratification 34 0
bottom buoyant spreading 41 7
passive diffusion 61
NH5 discharge 01 0
mdnf 11 5
bottom impingement with
full vertical mixing 33 0
surface buoyant spreading 41 7
passive diffusion 61
104
-------
Table 5.4 Flow Protocols for Discharges Trapped in
Linearly Stratified Ambients
Flow Flow MOD TR
Class Zone
SI discharge 01 0
mdnf 11 2
mdff 16 10
terminal layer approach 31 0
internal buoyant spreading 42 11
passive stratified layer
diffusion 62
S2 discharge 01 0
mdls-v 13 12
terminal layer impingement with
upstream spreading 36 0
internal buoyant spreading 42 11
passive stratified layer
diffusion 62
S3 discharge 01 0
mdls-h 14 13
terminal layer injection with
buoyant upstream spreading 37 0
internal buoyant spreading 42 11
passive stratified layer
diffusion 62
MOD = module, TR = transition rule
105
-------
Table 5.4 (Continued)
Flow Flow MOD TR
Class Zone
S4 discharge
mdnf
bdnf
bdff
terminal layer approach
internal buoyant
spreading
01
11
21
22
31
42
0
1
3
14
0
11
passive stratified layer
diffusion
62
S5 discharge 01 0
mdnf 11 1
bdnf 21 15
terminal layer impingement with
buoyant upstream spreading 36 0
internal buoyant spreading 42 11
passive stratified layer
diffusion 62
106
-------
internal layer far-field flow.
5.1.4 Flow Protocols for Bottom Attached Flows (Flow Classes
The flow protocols corresponding to Section 3.2.5 and
Figure 3.7 are listed in Table 5.5. The first flow module
following the discharge refers to either wake recirculation
for wake attachment classes (Al and A2) ; or to wall jet flow
for Coanda attachment classes (A3 to A5) . Flow class A3 has
a sub-class A3' (determined by using an internal criterion)
depending on whether a weakly deflected jet flow (MOD17)
exists. Whenever a lift-off occurs due to positive buoyancy
the remaining flow regimes after lift-off are similar to
the parent flow class given by the prefix (..).
For wake attached jets, the near-field flow regimes are
replaced by a wake-recirculation module as described in
Section 5.3.3.8. In the (..)A1 class, buoyancy is
sufficient to cause lift off, so the wake recirculation is
followed by a bdff. For negatively buoyant flow classes
with no lift off ((..)A2 class), the wake recirculation can
be followed by a buoyant bottom spreading module.
In the Coanda attached jet, the usual mdnf and mdff are
replaced by their attached counterparts, the mdnf -wall jet
and the mdff -wall jet, respectively. If sufficient buoyancy
is present, as in attachment classes A3, A3', and A4 , lift-
off will occur.
5.2 Hydrodynamic Simulation Modules
This section provides the salient details for each of
the modules listed in Table 5.1 which provide the predictive
element for a particular mixing process. The modules are
grouped into the different flow phases (from near-field to
far-field) as indicated in Table 5.1
There are two types of flow modules:
i) The continuous types describe the evolution of a flow
process along a trajectory. Depending on user input,
a small or large step interval can be used to obtain
flow and mixing information along that trajectory.
ii) The control volume type uses a control volume
approach to describe outflow values as a function of
inflow values based on conservation principles.
For either type, the beginning values are denoted by the
subscript "i" (e.g. S,- is beginning dilution) and final
107
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Table 5.5 Flow Protocols for Bottom Attached Flows
Flow Flow MOD TR
Class Zone
discharge 01 0
wake recirculation 51 0
lift-off 52 0
bdff 22 5
surface approach 31 0
surface buoyant spreading 41 7
passive diffusion 61
(..)A2 discharge 01 0
wake recirculation 51 0
bottom buoyant spreading
(NV and NH only) 41 7
passive diffusion 61
discharge 01 0
mdnf-wj 12 18
lift-off 52 0
bdff 22 5
surface approach 31 0
surface buoyant spreading 41 7
passive diffusion 61
MOD = module, TR = transition rule
108
-------
Table 5.5 (continued)
Flow Flow MOD TR
Class Zone
( . . ) A4 discharge
mdnf-wj
lift-off/fall down
bdnf
surface impingement with
buoyant upstream spreading
surface buoyant spreading
passive diffusion
01
12
52
21
32
41
61
0
8
0
6
0
7
(,.)A5 discharge 01 0
mdnf-wj 12 2
mdff-wj 17 19
surface approach 31 0
surface buoyant spreading 41 7
passive diffusion 61
109
-------
values are denoted by the subscript "f" (e.g. bf is the
final flow half-width).
5.2.1 Simulation Modules for Buoyant Jet Near-Field Flows
5.2.1.1 Introductory Comments
The flow equations in this module group describe the
trajectory (x,y,z) of the jet/plume centerline and provide
values along that trajectory for the flow half-width b, the
local concentration c, and the local dilution S.
The half-width b is defined here as the "1/e width" as
a typical convention for Gaussian jet-like profiles (see for
example Holley and Jirka, 1986). Thus, b is the half-width
(radius) of the jet/plume flow where the local concentration
is 1/e, or 37%, of the centerline concentration. Since
alternate width definitions are sometimes used in pollution
analysis, the width definition when multiplied by 0.83 gives
the 50% width, by 1/21/2 gives the standard deviation (61%
width), and by 2 /2 gives the 14% width, respectively. In
the case of atmospheric plumes the later definition is often
taken as the "visual width" of the plume.
The local concentration in this group of modules refers
to the maximum centerline concentration cc at the jet/plume
centerline. Thus, the corresponding dilution refers to the
minimum dilution CO/GC in which c0 is the initial discharge
concentration. It is important to keep in mind these flow
definitions since they differ, in general, from those found
in modules for subsequent flow zones. These differences are
unavoidable due to different profile shapes for the effluent
flow distribution governed by the various mixing processes.
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) located directly below the center of the discharge
orifice. The height of the discharge orifice above the
bottom is hQ. 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 8Q. The discharge-crossflow angle aQ is the
angle between the projection of y* on the x-y plane and the
x-axis (a0 = 0° for co-flowing discharges, afl = 180° for
counter-flowing discharges).
A primed coordinate system, (x',y',z'), within a given
buoyant jet flow region is specified with respect to the
virtual source for that flow region. A virtual source is
110
-------
needed for each flow region because the perturbation
analyses used in each module assume a point discharge
source, which is physically unrealistic. The primed
coordinate system is related to the global coordinate by
(x,y,z) = (x',y',z') + (xv,yv/zv) (5.1)
where (xv/yv,zv) is the global position of the virtual source
for that flow region. The position of the virtual source
(xv/yv,zv) is computed by taking the known flow solution at
the transition, as given from the previous flow region, and
then back calculating the source position using the dilution
equation for the given flow region. This procedure assures
continuity of the dilution and concentration predictions
from one module to another. However, ocassionally slight
discontinuities in the predicted half-widths can occur.
In general, the simple analytical results of Chapter II
are extended to non-vertical three dimensional trajectories
within the ambient crossflow. A supplementary transverse
coordinate >j is defined here inw a plane given by the z-axis
and rj is the projection of y* into the z-y plane. Any
vertical motion of the jet flow is controlled by the
vertical component of the discharge momentum flux as well
as the buoyancy flux (which always acts vertically) . The
transverse (horizontal) motion of the jet flow is solely
controlled by the horizontal component of the discharge
momentum flux.
Defining 7* as the angle between the discharge axis y
and the crossfl^ow (x-axis) , and the angle 60 between the
projection of y* on the yz-plane (transverse coordinate ^)
and the y-axis the relationships for the discharge angles
8Q and CTO are
70 = sin'1(l - cos200cos2<70)1/2 (5.2)
60 = tan"1 (tan^o/sinCTg) (5.3)
5.2.1.1 Discharge Module (MODOl)
This module begins every flow sequence. In the module
the flow is converted from a uniform velocity distribution
to a Gaussian profile, with equivalent volume flux (note
that momentum flux conservation is assured due to the bulk
flow parameters used in the analysis) . The representative
final flow width bf for the discharge module is
bf = (a,/*)* (5.4)
where a0 is the port cross sectional area. No dilution is
assumed to occur, so that Sf = 1.0 and cf = CQ, where Sf is
111
-------
final dilution and cf and c0 are the final and discharge
concentrations, respectively. The final x- and y-coordinate
are 0, but zf = h0.
5.2.1.2 Weakly Deflected Jet In Crossflow (MODll, mdnf)
The results for the mdnf presented in Section 2.1.4.1
are extended to include the general 3-D trajectory. For a
cross-flowing discharge (70 > 45°) the trajectory is a
function of ij as the independent variable. Writing the
trajectory equations in the virtual coordinate system for
the mdnf in terms of the supplemental coordinate ^ gives the
crossflow induced deflection
(5-5)
where T^ is the trajectory constant for the mdnf. The
expression for the transverse coordinate y is simply
y' = rj'cosSg (5.6)
The vertical coordinate, however, experiences an
additional perturbation due to buoyant deflection, or
z' = r,'sin*0 + T^^signJo/d^sin^) (5.7)
where T11B is a constant for the buoyancy correction in the
mdnf, and signJp is equal to +1 for a positively buoyant
discharge and is equal to -1 for a negatively buoyant
discharge.
The flow width (radius) is
b - Bu'/siivy, (5.8)
where Bn is a width constant for the mdnf. The dilution is
expressed as
S = S11f?//(Vin7o) (5.9)
where sn is the dilution constant.
If the discharge is co-flowing (70 < 45°) , the simulation
should step in x as the primary independent coordinate and
the trajectory, width, and dilution relationships are
z' = r,'sin6Q + T11Bx/3signJ0/(I^2cos370) (5.10)
»' = x'tan7o - x'2tanV(Tn2LJ (5.11)
b = B1tX'/COS70 (5.12)
112
-------
S = S11X//(LQCOS7o) (5.13)
5.2.1.3 Weakly Deflected Wall Jet in Crossflow (MOD12, mdnf-
wj)
In this flow region unequal entrainment and spreading
will be neglected in directions parallel and normal to the
boundary wall. The attached flow has a horizontal momentum
flux Mw two times the discharge momentum flux MQ to account
for the mirror image of the attached flow with the bottom
symmetry plane, so the horizontal wall momentum flux MH =
This assumption also results in Qw = 2Q0.
For a cross-flowing discharge (a0 > 45°) , the trajectory
equation for y' in terms of x' (z = 0 for the attached case)
becomes
y' = T12(2cos00)1/V/2(*' - y'cota0)1/2 (5.14)
where T12 is a trajectory constant for the mdnf-wj . The
width and dilution are given by
b = B12y'/sina0 (5.15)
S = s12y'(cosV2)1/2/(LQsina0) (5.16)
respectively, where B12 a width constant, and S12 is a
dilution constant for the mdnf-wj . A similar equation
system holds for the co-flowing wall jet (a0 < 45°) in
analogy to the free jet (previous sub-section) .
5.2.1.4 Near-Vertical Jet in Linear Stratification (MOD13,
mdls-v)
For jets issued (near-) vertically into a density
stratified environment, 70 is greater than 45° so the xyz-
coordinates of the flow in the virtual coordinate system
are given in first order by a straight line trajectory
(5.17)
y' = r,'cosS0 (5.18)
z' = T)'sin6Q (5.19)
respectively. The width and dilution are expressed as
b = B^'/sin^ (5.20)
S = S13C(l-S13Asin^0r7'4/(sinS0LIn'4)]f?'/(I^sin50) (5.21)
113
-------
respectively, where B13 is a width constant, and S13 and S13A
are dilution constants for the mdls-v. For the physical
background see Section 2.2.4.7.
5.2.1.5 Near-Horizontal Jet in Linear Stratification (MOD14,
mdls-h)
The simulation of this module (occurring in flow classes
S3^ is limited to the co-flowing design, with 70 less than
45 . The trajectory in the virtual coordinate system is
given by
z' = x'tan7osin$0 + [T14BvV (VcosV4*0) ]3 (5.21)
y' = x'cos
-------
5.2.1.8 Strongly Deflected Wall Jet in Crossflow (MOD 17,
mdff-wj)
The assumption for jet attached momentum flux MH is the
same as in previous section for the mdnf-wj . Expressing
the trajectory equations for y' in terms of x' (z = 0 for
the attached case) gives in analogy to the free jet
y' - T17(2cos*0)2/\2/3(sina0)1/3x'V3 (5.29)
The dilution is
S - S14y'2/ (21^) (5.30)
where Su is a dilution constant.
5.2.1.4 Weakly Deflected Flume in Crossflow (MOD21, bdnf)
The bdnf trajectory coordinates are a generalization of
the perturbation solutions presented in Section 2.1.4.6.
With z' as the primary coordinate the trajectory equations
are
x' = (zV(T21Lb1/4))4/3+ (5.31)
2/31/1/3'1/3
y' = T21I^cossina0x' + (5.32)
where T21 is a trajectory constant for the bdnf, and T21M1 and
T21M2 are momentum correction coefficients. Width and
dilution are given by
b = B21z' (5.33)
S = S^L^'V5'3/^!*) (5.34)
respectively, where B21 is a width constant and S21 is a
dilution constant for the bdnf.
5.2.1.9 Strongly Deflected Flume in Crossflow (MOD22/bdff)
The bdff trajectory coordinates, written in the virtual
coordinate system as a function of x' are
z/ = TsignJo (5.35)
y' = T16Lln2/3cos1/3?0sin1/3a0x'1/3 (5.36)
115
-------
where T22 is a constant for the bdff, and T-6 is a constant
for the mdff since the transverse deflection is momentum
induced.
Width and dilution are given by
b = B22z' (5.37)
S = S22z'2/(W (5.38)
respectively.
5.2.2 simulation Modules for Boundary Interaction Processes
When the flow interacts with any boundary such as the
surface, bottom, or pycnocline density jump, a similar
interaction module will be used to describe the process.
The only difference is the centerline height of the flow as
well as any hydrostatic adjustment process for pycnocline
flows (see Section 2.23).
In all of the following modules a control volume
approach is used. Generally, a bell-shaped jet/plume inflow
is transformed to a more uniform (top-hat) outflow zone that
follows the boundary (surface, bottom, pycnocline) or flows
in the stratified terminal layer. Thus, after
transformation the final geometric values are the trajectory
(xf, yf, zf) , the total vertical thickness b,, and the
horizontal half-width bhf of the top-hat profile. Also
concentration and dilution values refer to average values
which, within the top hat profile, tend to be close to
extreme (maximum or minimum, respectively) values.
5.2.2.1 Near-Horizontal Surface/Bottom/Pycnocline Approach
(MOD31)
In this simplest approach condition, the bent over flow
approaches the interface near-horizontally at impingement
angle 9{ < 45° (Figure 2.8a and Section 2.4.1).
The final x-coordinate is given by a geometric shift due
to the size of the in-flowing jet/plume
xf = x,. + 2b,. (5.39)
yf is set equal to ys, and zf equal to z-. The final bulk
dilution is
Sf = 883,8, (5.40)
116
-------
where SB31 is a bulk mixing conversion factor.
5.2.2.2 Near-Vertical Surface/Bottom/Pycnocline Impingement
with Buoyant Upstream Spreading (MOD32)
In this surface approach condition, the weakly bent flow
impinges on the surface at a near-vertical angle &. , where
0j > 45°. The physical process has been summarized in
Section 2.42 with reference to Figure 2.8.b. 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 dilution is expressed as (see Eq. 2.85)
sf = SiSSB32[V(Hs(l-cos^iCOSai))]1/3 (5.41)
where SSB32 is a dilution constant. The upstream intrusion
length Ls is given by
Ls = A^I^l-COSfljCOSajtVHs) (5.42)
for (Lb/Hs) < 165(1- COSfljCOSaj)
and
Ls = AL^Lfe (5.43)
for (Ifc/HJ > 165(1- cos0jCos<7j)
where AL^ and ALj28 are constants. The typical vertical
thickness within the upstream stagnation region is
hs - CD^S^V^ (5-44)
where CD32 is a constant. The dimensions of the effluent
flow are
bhf = BH32LS (5.45)
bvf = SfLfcV(2bhf> (5-46)
The final flow coordinates are xf = x1 +0.5bvf, yf = y( , and
xf = X,- .
117
-------
5.2.2.3 Near-Vertical Surface/Bottom/Pycnocline Impingement
with Pull Vertical Mixing (MOD33)
In this surface approach region, the weakly bent flow
impinges on the water surface at a near-vertical angle
(Figure 2.8c). Because of the unstable recirculating flow,
the centerplane dilution increases
Sf = SR33S,. (5.47)
where SR33 is a recirculation factor. The final flow width,
bhf/ is found from the continuity equation
bhf = SfI^V(2H8) (5.58)
and final outflow location xf is approximated as
xf = x, + Hs (5.49)
where x,- is the plume position at the beginning of the
region, and yf = yf and zf = z-.
5.2.2.4 Near-Vertical Surface/Bottom/Pycnocline Impingement
with Unstable Recirculation, Buoyant Restratification, and
Upstream Spreading (M0034)
In this surface approach region, the flow rises near-
vertically and impinges on the water surface (Figure 2.8d) .
After impingement the mixed flow recirculates over the
limited water depth and becomes partially re-entrained into
the flow. The final dilution Sf is given by
sf * S34H,5/3/(I*2/3lM) (5.50)
where S34 is a dilution constant. The upstream intrusion
length Ls is given by
LS = AL^ (5.5i)
The upstream intrusion thickness hs is
hs - C^SfW^, (5.52)
The final half-width bhf and thickness bvf and coordinates
are analogous to those for MOD32.
5.2.2.5 Stratified Terminal Layer Impingement with Buoyant
Upstream Spreading (MOD36)
In this condition, the flow becomes trapped in a
stratified terminal layer before surface contact. This
118
-------
terminal layer approach is defined for near-vertical,
strongly buoyant stratified flows that do not interact with
the surface or pycnocline density jump. The detailed
equations are similar to the previously presented
unstratified case (MOD32) and are not presented here.
5.2.2.6 Stratified Near-Vertical Surface Injection with
Upstream Spreading (MOD37)
This module simulates a terminal layer approach for
near-horizontal, strongly stratified jet-like flows that do
not interact with the surface or pycnocline density jump.
With the exception of an added effect on the horizontal
discharge momentum, the development is similar to MOD36 and
is omitted for brevity.
5.2.3 Simulation Modules for Buoyant Spreading Processes
The flow distribution inherent in the two buoyant
spreading modules is again mostly uniform (top-hat). Hence,
the same interpretations on geometric (width) and dilution
(or concentration) values apply (see introductory comments
to Section 5.2.2) .
5.2.3.1 Buoyant Surface/Bottom Spreading (MOD41)
The physical background for buoyant spreading process
at the boundary of an flowing abient was discussed in
Section 2.2.1. Thus the flow equations are
bh = tbhiV2 + l.5(V(2CD41))1/2(x - x,.)]2/3 (5.53)
bv = bvi (Vbhi~ (5.54)
S = S,(b/bvi)^ (5.55)
The trajectory is a straight line following the ambient
flow and located at the appropriate vertical boundary.
Also, if the plume contacts a lateral boundary (shoreline)
the trajectory centerline shifts over to that boundary and
the further spreading process is limited to one frontal
zone. These coordinate switching functions are included in
MOD41.
119
-------
5.2.3.2 Buoyant Terminal Layer Spreading (MOD42)
Referring to Section 2.8.4, the flow equations are
bh = [bhi2"^+ (5.56)
bv " bvi(Vbhi~ (5.57)
S = Sjb^/tb^b,,,.) (5.68)
MOD42 also contains boundary interaction features.
5.2.4 Simulation Modules for Attachment/Detachment Processes
The variable definitions in the following section are
similar to those for jet/plume processes (Section 5.2.1).
5.2.4.1 Wake Recirculation (MOD51)
This module describes the recirculation process for wake
attached flows (see Section 2.4.4.1). The flow equations
are for minimum dilution
Sf = »/2bvf/(V*) (5.69)
the flow half -width
bhf = BV51xf (5-70)
with bvf = bhf, and the longitudinal extent
(5.71)
5.2.4.1 Lift-Off/Fall-Down (MOD52)
This is the reverse of MOD31 and performs a conversion
form a uniform (top-hat) profile to a final Gaussian profile
as a buoyant plume separates form a. boundary.
5.2.5 Simulation Modules for Ambient Diffusion Processes
The physical processes underlying the two ambient
diffusion modules have ben presented in Section 2.3. The
following flow definitions apply here: The passive plumes
have a Gaussian profile, the vertical thickness bv and
horizontal half-width represent the 46% width value (i.e.
(7r/2)1/2 times the standard deviation of the Gaussian passive
120
-------
diffusion profile). This width convention is equal to the
width of a top-hat profile that has the same centerline
concentration. This difference relative to the jet/plume
regimes arises due to the different mass flux conservation
equations for passive versus active (discharge induced)
effluent flows. The representative concentration is the
maximum centerline concentration, and the dilution is the
corresponding minimum.
5.2.5.1 Passive Diffusion in uniform Ambient (MOD61)
The passive plume trajectory is straight following the
abient flow. The geometric expressions are
bv = [*Ez(x-x,.)/ua + bvi2]1/2 (5.72)
bh = [*Ey(x-x,.)/ua + bhl.2]1/2 (7.73)
with the appropriate diffusion coefficients Ez and Ey
discussed in Section 2.31 for bounded channel flow. In
unbounded channel flow, the "4/3 diffusion law" coefficient
(Section 2.3.3) is used, and Eq. (2.65) is the expression
for the half-width bh. Changes in centerline trajectories
occur when the plume interacts with vertical or lateral
boundaries.
5.3.5.4 Passive Diffusion in stratified Ambient (MOD62)
The flow expression for this module are analogous to
MOD61 with the substitutions of a Richardson number
dependence for the vertical diffusivity (Section 2.3.3).
Also there are more complex interaction possibilities with
vertical boundaries.
5.3 Transition Rules/ Flow Criteria and Coefficient Values
This section provides the detailed equations for the
transition rules listed in the flow protocols that control
the spatial extent of each flow module. It also provides
the complete functional form for the criteria, including
terminal height evaluations that have been used in the flow
classification presented in Chapter III. Furthermore, a
listing and justification of all numerical coefficients is
supplied.
121
-------
5.3.1 Transition Rules
Transition rules are needed to give the spatial
expressions as to where each flow region ends. Each
subsequent flow region is assigned initial values that
correspond to the final values of the preceding flow region.
Transition rules used in the simulation appear in Table 5.6,
and the associated constant values appear in Table 5.7.
For example, Transition Rule I gives the final value of
a weakly deflected jet coordinate when it is followed by a
weakly deflected plume. The transition from one region to
the other is characterized by the jet/plume length scale L,,,.
If the discharge angle relative to the x-axis is -y0, the
final supplementary coordinate r?f', and the final x-
coordinate xf' are given by Transition Rule 1 as
r,f' = CTIVI'LH 7o > 45 (5.74)
Xf' = CT1V2-I^ 7o < 45° (5.75)
where CT1V1 and CT1V2 are constants (Constant for Transition
rule I, first Value and second Value, respectively) .
Note that some transition rules apply within the primed
coordinate system (limiting xf', yf', zf', or r?f') while
others apply to the global coordinate system (limiting xf/
Yf/ zf/ or r/f) .
As shown in Table 5.6 the proper transition rule depends
on the sequence of current flow module to next flow module.
In general, flow transitions between flow regimes are smooth
due to matching volumetric dilutions. There may
occasionally be slight discontinuities in the predicted flow
width.
5.3.2 Flow Classification Criteria
A summary of the detailed classification criteria that
have been shown in "order of magnitude" form on Figures 3.4
to 3.7 is provided in Table 5.8. The labels Cl, C2, etc.
correspond to the labels used on those figures. The
detailed criteria often contain factors (e.g. 0.8 that
describes the thickness of a buoyant layer formation at a
boundary after impingement) that effectively reduce the
existence of certain flow zones which are being tested for.
The values of the numerical constants are also included in
the first column of Table 5.7 with reference or comments on
how they were obtained.
122
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Table 5.6 Transition Rules
TR CMOD NMOD Equation
1 11 21 70 > 45 ijf' =
70 < 45° xf' = CT1V2-LM
V2_
2 11 16 7o ^ 45 r,f' = CT2Vl.Lmsin'/S0
12 17 7Q < 45° Xf' = CT2Vl-LmCOS1/270
3 21 22 zf' =
4 16 22 xf' = CT4Vl'L)l((Ll/I^)1/6
5 22 31 zf = Hs
16 31
11 33
6 21 32 zf = 0.8HS 4- 0.2hQ
7 41 61 Xf = X,- + (23/2/3) -CD411/2
,h 3/2/T 1/2* , r ,R
(°hi /-hs M I (8
8 17 52 aQ ^ 45 yf' =
12 52 a0 < 45° xf' = CT8V2-L>,
TR = Transition Rule, CMOD = Current module,
NMOD = next module
123
-------
Table 5.6 (continued)
TR CMOD NMOD Equation
9 12 33 <70 > 45° yf' - (H./B,,) sinaQ
* < 45° ' = (
10 16 31 zf = h0 + CTlOVl«I^,1/3Lill/2/3sin«01/3signtf0
11 42 62 Xf = x, + (2CD42)1/2/(2-/3)(V2bhi/Vbvi)
12 13 36 zf = h0
13 14 37 7o > 45° »?/ - CTISVI'L/
70 < 45° Xf' = CT13V2-Lm/
14 22 31 Zf - h0 + CT14Vl-LbV9Lb'8/9signJ
15 21 36 zf = h0 +
16 11 22 70 > 45° ijff = CT16V1-L,,
7 < 45° X' =
17 22 31 Zf - 0
21 31
18 12 31 a0 > 45° yf' = CT18V1-L,,,
19 17 31 Xf' = CT19V1'L^(COS00)V2
124
-------
Table 5.7
Coefficient
Coefficients Used In Transition Rules
Value Data Source, References,
or Comment
CT1V1, CT1V2
CT2V1, CT2V2
CT3V1
CT4V1
CT8V1,CT8V2
CT10V1
CT12V1
CT13V1,CT13V2
CT13V3
CT14V1
CT15V1
CT16V1
CT16V2
CT18V1
CT19V1
RfC
2.5
2.0
1.0
2.7
1.5
2.1
2.1
3.0
2.0
2.6
2.5
1.75
2.5
1.5
30.0
1.0
A) From trajectory and
terminal height equations
given by Wright (1977),
List (1982), Wong (1984),
and Hoi ley and Jirka
(1986) .
See A
See A
See A
Sharp (1977), Sobey et
al. (1988)
B) From terminal
equations given
(1982) and Wong
(See Table 5.8)
See B
See B
See B
See B
See B
See A
See A
See A
See A
height
in List
(1984)
Critical flux Richardson
number
125
-------
Table 5.8
Criterion
and Value
Flow Classification Criteria
Equation Used Data Sources, References, or
in CLASS Comments
Cl - 1.0
A) From trajectory and
terminal height equations
given by Wright (1977), List
(1982), Wong (1984), and
Holley and Jirka (1986) .
C2 - 1.8
C3 = 3.0
C4 - 0.65
C5 - 0.65
CIO = 2.0
Lm/Lm'*C2
SC4
See A
See A
] See A
j-hg) ] See A
5C5
C6,C7,C8 Lb/[0.8(Hs-hQ) ] See A
- 1.0 S(C6,C7,C8)
C9,C11 Lb/[0.8(Hs-h0) ] See A
= 0.4 *(C9,C11)
B) Lee and Jirka (1981)
SC10
C12,C13
- 0.65 *C(12,13)
See A
C14,C15,C16 LM/H8 Sobey et al. (1988)
= 4.3 *(C14,C15,C16)
C17 = 0.55 V[0.8(H,-h0)] See A
SC17
126
-------
Table 5.8 (continued)
Criterion Equation Used Data Sources, References, or
and Value in CLASS Comments
C18 = 0.4 L/CO.S^-ho) ] See A
SC18
C19,C22
= 0.6
See A
5(C19,C22)
C25 = 2.5
C20 = 1.0
C21 = 0.65 Ln/Hs^C21
See B
See A
C23 = 0.65 Lm/[0.8(Hs-h0) ] See B
SC23
C24 = 0.65 L|]/HS*C24
SC25
SC25
See B
Derived on basis of data
comparison for wake attached
jets/plumes
C26 = 1.0 I^/fS-LgL^ Richardson number
(f/8) ]*C26 criterion for buoyant lift-off
C27,C28
= 0.20
Knudsen and Wood (1990)
S(C27,C28 Sharp (1977)
C29 = 1.0
See B
127
-------
5.3.3 Terminal Layer Expressions
Table 5.9 lists the detailed terminal height equations
used in Figure 3.4 of the flow classification scheme. The
equations differ from the usual equations available in the
literature through geometric factors that measure the
vertical or horizontal momentum strengths and through
factors measuring the direction of the buoyancy force. The
first column also gives the adopted numerical values.
5.3.4 Model Coefficient Values
Any predictive model describing turbulent flow processes
contains a number of constants that must be determined from
experimental data. The coefficient values for flow modules,
transition rules, and classification criteria of CORMIX1 are
listed in Tables 5.10, 5.7, and 5.8, respectively. A large
number of constants appear as required by the different
physical processes in the various flow zones.
The consistent procedure used in evaluating the
numerical values of the coefficients was to refer to basic
experiments reported (or summarized) in the literature that
deal with specific flow processes. The majority of the
coefficients values have been chosen in this fashion without
any adjustment. If conflicting data were reported in the
literature, a mean value was adopted or seemingly dubious
data were rejected. In several instances (notably for
recirculation zone estimates for full vertical mixing) no
reliable data, or no data at all, has been reported in the
literature. Often these processes are difficult to measure
and some judicious estimation was made. Subsequent system
evaluation and validation (see next chapter) led to some
adjustment of coefficients in that category. Ultimately,
it is expected as more detailed experiments are conducted
in the future that those system coefficients that currently
have a limited data base can be confirmed or modified.
Furthermore, it should be noted that there is a
considerable overlap among flow constants for various
modules (Table 5.10), the transition rules (Table 5.7), the
flow criteria (Table 5.8), and the terminal height
expressions (Table 5.9). Care has been taken in setting
values so that there is consistency between the various
coefficient types.
Of course, the ultimate validation of the present
predictive methodology together with the relevant
coefficient values must come from the ability to simulate
complex flow and mixing phenomena in agreement with
available data. This is addressed in the following Chapter.
128
-------
Table 5.9
Stratified Terminal Height Expressions
Constant
Value
CT1 =2.1
Equation Used
in CLASS
Zt = (CTl-Lj^L /2/3sin001/3)sini90
+ (CT4-Lb1/9Lb'8/9)cos00
References or
Comments
Coef
f i c i ent
values adapted
CT2 =2.1
CT3 =2.0
CT4 =2.6
CT5 =2.9
Zt = CT2-Lm'sin001/4
Zt = CTS-Lj/VfV30083'4^)
Zt = CT4'Lb1/9Lb/8/9
Z^ = CT5-L '
from
List
and
Wong
(1982)
(1984)
129
-------
Table 5.10
Module Constants
Coefficient Value
Data Source, Summary Reference, or
Comment
Tii,T12
S11'S12
Bn,B12
T11B
S13
S13A
B13
Su
Bu
T14B
?16'T17
S16'S17
B16'B17
B21
T16B
T21
T21M1
T21M2
T22
S22
B22
2.3
0.18
0.11
0.07
0.18
0.0058
0.11
0.18
0.11
2.0
1.6
0.30
0.3
0.11
0.5
1.5
5.6
7.5
1.0
0.35
0.3
A) Adapted from Wright (1977),
Fischer et al. (1979), List (1982),
Holley and Jirka (1986) , Lee et al.
(1987) .
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
130
-------
Table 5.10 (Continued)
Coefficient Value Data Source, Summary Reference, or
Comment
SB31'SB33
SB32
ALj2A
AL32B
CD32
TJtJ "DU
BH32 , BH34
SR33
SB34
AL,,
CD34
SB36,SB37
HSS36
CD36,CD37
css36
AL36'AL37B
BH36 , BH37
HSS37
AL37A
CD,,
1.7
1.4
11.4
0.38
1.0
2.6
2.0
1.3
0.1
2.0
1.4
0.5
1.2
0.65
0.26
2.0
1.7
0.69
2.0
Center line/bulk dilution
conversion, Holley and
Jirka, (1986), Leeetal.
B) Upstream intrusion in crossflow,
Jones et al. (1982), Chu and Jirka
(1986)
See B
See B
See B
See B
See B
See B
See B
See B
Wong (1984)
See B
See B
See B
See B
See B
See B
See B
C) Density current . spreading,
Simpson (1982) , Jirka and Arita
(1987)
0.25 See C
131
-------
Table 5.10 (Continued)
Coefficient Value
Data Source, Summary Reference, or
Comment
CD42
E«2
BV51
XR51
EZ61/EZ62
EY61 , EY62
E061/E062
2.0
0.25
0.3
5.0
0.2
0.5
0.0015
See C
See C
D) Based on data comparison
recirculation
See D
E) Fischer et al. (1979)
and Jirka (1986)
See E
See E
for wake
, Holley
132
-------
Chapter VI
System Evaluation and Verification
In this chapter the predictions of CORMIX1 will be
compared with laboratory and field data. This chapter is
not meant to be an exhaustive validation of all possible
CORMIX1 flow classes and associated predictions, but rather
a test of key CORMIX1 modules which are common to many flow
protocols (flow classes) and an illustration of the
flexibility of the system in handling complex environment
and discharge conditions.
While CORMIX1 can accommodate many possible flow
configurations, actual available laboratory or field data
are quite limited. In Section 6.1 comparisons are made with
data for the initial subsurface regimes (buoyant jets) of
mixing processes in the absence of any boundary effects.
This validation for the initial flow modules (MODs 11
through 23) is important in view of the strong initial
mixing common in most (but not all) environmental discharge
situations and in view of the larger body of literature
concerning the behavior of unconfined buoyant jets. Section
6.2 addresses more complex flows where different forms of
boundary interaction processes play a significant role.
In all of the comparisons shown below the numerical
constants and coefficients values have be consistently set
to the values summarized in Chapter V.
To facilitate comparison with the non-dimensionalization
that is frequently used in the available literature the
following parameters are introduced:
Densimetric Froude Number
F0 = u0/(g0'D)V2 = (x/4)1/4VLQ (6-D
Jet/Crossflow Ratio
R = uo/ua = VLQ (6-2)
Stratification Parameter
T = APo/[D(-dPa/dz)] = VV(I*V> (6'3)
133
-------
6.1 Buoyant Jets in Unconfined Ambient
6.1.1 Comparison With Experimental Data
The following sections will present analyses of near-
field flows, starting with buoyant jets in a stagnant
uniform ambient, followed by neutrally, positively, and
negatively buoyant jets in uniform crossflows, and finally
flows in a stratified stagnant ambient. To validate these
buoyant jet near-field flows, CORMIX1 predictions are
compared with laboratory data from Anwar (1972), Cederwall
(1963) Fan (1967), Jordinson (1956), Wright (1977), Margason
(1968), and Anderson et al. (1973).
6.1.1.1 Stagnant Ambient
Figure 6.1 shows two cases of Fan's (1967) trajectory
data for a buoyant jet in a stagnant uniform ambient
compared with CORMIX1 projections. Fan released a dyed
buoyant jet horizontally (0Q = 0°) into a uniform ambient
density tank. Photographs recorded visual plume outlines.
For this stagnant environment (for which both 1^ and 1^ tend
to infinity) CORMIX1 classifies the flow as H4-0 (see
section 5.1.1), since for finite depth H (equal to the
laboratory tank depth) some boundary interaction will
inevitably occur. However, Fan does not report any detail
on these interaction processes.
Figure 6. la shows Fan's buoyant jet with relatively
strong horizontal momentum flux (F0 = 66) . The flow travels
horizontally at first, after some distance the buoyancy
force deflects the flow vertically. For this stagnant
condition the predicted trajectory is in excellent agreement
with the observed plume outline. As noted in Section
5.2.1.1, CORMIX1 predicts a plume half-width b that
corresponds to a local concentration of 1/e = 37% of the
centerline concentration. Assuming a 10% width for the
photographically recorded plume boundary (as traced by Fan)
these values may be expected to be wider by a factor of
about 1.5. This interpretation appears in good qualitative
agreement with the predictions.
In contrast, Figure 6.1b shows a horizontal buoyant jet
with relatively weaker momentum (F0 = 10) . In this case the
horizontal intrusion of the jet is small, and the flow
exhibits a strong vertical deflection, which appears to be
slightly under-predicted by CORMIX1.
CORMIX1 results for horizontal buoyant jets in stagnant
ambients with a wide range of Froude numbers appear in
Figure 6.2 in comparison with three different experimental
data sources. This figure seems to illustrate two facts:
134
-------
120
Data:
Fan (1967), Visual Boundary
CORMIX1
Centerline
Z/D
(a)
2/D
I20
100
80
60
40
20
0
200
Data:
Fan (I967) Visual Boundary
F0»IO, V°°
CORMIXI :
Centerline
Width b
0 20 40 60 80 IOO
x/D
(b)
Figure 6.1 Horizontal Buoyant Jet Trajectory in Stagnant
Ambient, a) Weak jet, b) strong jet.
135
-------
220
200
180
160
140
120
r R
z/D
o
4
8
I I
14
20
33
42
A
A
O
Experiments
Anwar (1972)
Anwar (1972)
Anwar (1972)
Fan (1967)
Cederwall (1963)
Fan (1967)
Fan (1967)
Horizontal Round
Buoyant Jet
CORMIX1 Centerline
20
40
60
X
/D
80
IOO
I20
I40
Figure 6.2
Horizontal Buoyant Jet Trajectories in
Stagnant Ambient Over a Range of Froude
Numbers
136
-------
i) the agreement of CORMIX1 with the observed trajectories
is good, within ± 20% for the horizontal penetration, and
ii) the disagreement among different experimental data
source is at least as large. This can be seen indirectly
using CORMIX1 as the standard since in some cases an over-
prediction and in others an under-prediction is apparent.
Such discrepancies, or levels of accuracy, are typical in
predictions and/or experiments with turbulent flows, and may
be related to the experimental setup, some unsteadiness, the
exact method of determining centerline position, and other
factors. In summary, Figure 6.2 shows that overall CORMIX1
predictions are quite good, and well within the normal
scatter evident from the experimental results.
It should be noted that all the buoyant jet trajectories
displayed in Figure 6.2 could have been collapsed into a
single curve (at least for sufficiently large FQ) if the
appropriated length scale 1^ was used in normalization
instead of D. This was avoided in order to better display
the jet behavior and data scatter. The appropriate
normalization has been used in Figure 6.3 in which
centerline dilution data form three experimental sources
covering a wide range of F0 is displayed in a compact
fashion (Note that DFp= [ (4/*) 1ALM]) . The agreement is
satisfactory in the entire jet/plume transition range.
6.1.1.2 Flowing Unstratified Ambient
6.1.1.2.1 Pure Jets In Crossflow
Figure 6.4 shows the centerline trajectory from an
experiment of Jordinson (1956) for a pure jet (F0 = «)
discharging vertically in a crossflow with velocity ratio
R = 6.2 (R = Ug/uJ . Here, the CpRMIXl predictions (flow
class V2) show slightly more jet deflection than the
experimental data near the orifice, and slightly less after
the flow becomes strongly deflected.
Again, such disagreement has to be interpreted in the
light of the experimental methods employed. The centerline
used by Jordinson was defined as the maximum velocity point
which for a cross-flow deflected jet (especially in the
weakly deflected stage) is always considerably upstream of
the point half-way between the upstream and the downstream
jet boundary. This factor, related to the horse-shoe like
concentration distribution in the cross-section of such
jets, is also addressed by Fan (1967), Rajaratnam (1976),
and Jirka and Fong (1981).
Two other examples of jet trajectories in a crossflow
are given in Figure 6.5 in comparison to Margason's (1968)
data. Figure 6.5a illustrates a slightly co-flowing
discharge (8Q = 60°, a0 = 0°) for two crossflow ratios (R
137
-------
100
10
S/F,
O.I
i i i i T r
,rj , r T T in,|
Data:
Liseth (1970)
A Hansen and Schroder (1968)
a Cederwall (1968)
CORMIX1
Centerline Dilution
O.I
10
z/OR,
too
Figure 6.3 Horizontal Buoyant Jet Dilution in Stagnant
Ambient
138
-------
12
Jordinson, 1956, data
F0=oo, R = 6.2
CORMIX Centerline
Z/D
.
O1-^
J I I I
8
/D
J I
16
Figure 6.4
Non-buoyant Jet Trajectory
Crossflow
in Uniform
139
-------
a)
10
z/0
Data:
O Margoson (1966)
CORMIX1
Centerlines
R»IO
10
x/D
b)
20
z/D
10
OatO:
P_IQ O Morqoson (1968)
.*** CORMIX1
Centerlines
^- Width b
I '
."O
R=5
-5
5
x/D
10
Figure 6.5 Non-Buoyant Jets at Various Discharge Angles
in Uniform Crossflow
140
-------
= 5 and R = 10) . Excellent agreement can be seen. The
more severe test oof a slightly counter-flowing discharge (00
= 60°, CTO = 180°) is shown in Figure 6.5b for the same
crossflow ratios. For the strong crossflow case, R = 5,
the predicted jet trajectory is somewhat more deflected than
the observed one.
6.1.1.2.2 Buoyant Jets in Crossflow
The effect of adding buoyancy to the jet flow will now
be considered. Figures 6.6 and 6.7 present Fan's
trajectory, dilution, and width data for a vertically
discharging buoyant jet, 00 = 90°, in crossflow. Figure 6.6
shows Fan's experiment with F0 = 20 and R = 12. CORMIX1
(flow class VI, mdnf, mdff, bdff) predictions are in good
agreement with trajectory, dilution, and width data. Figure
6.7 shows a jet with similar buoyancy (F0 = 20) but with a
considerably stronger cross-flow (R = 4), causing the flow
to deflect more strongly. Excellent agreement is apparent.
Figure 6.8 shows a CORMIX1 trajectory prediction (flow
class VI mdnf, mdff, bdff) for a laboratory experiment by
Wright (1977). Figure 6.8 employs a logarithmic scale (as
used by Wright) to show the trajectory data for a vertical
buoyant jet (R = 37 and F0 = 67) into a crossflow. The
logarithmic scale display exhibits the different
trajectories laws (slopes in Figure 6.8, equivalent to the
exponents of the power laws) that are used in CORMIX1. As
opposed to Fan's data, CORMIX1 shows for this case a slight
over-prediction (factor of 1.5) in the predicted vertical
rise of the flow.
6.1.1.2.3 Negatively Buoyant Jets in Crossflow
Figure 6.9 shows the results of an experiment by
Anderson et al. (1973) for a negatively buoyant jet into a
slightly co-flowing crossflow (00 = 60 , aQ = o°, F0 = 11.0,
and R = 5.5) . In this case CORMIX1 predicts an NV1 flow
class (mdnf, mdff, bdff) with numerical results that are in
good agreement with trajectory, dilution, and width data.
In particular, note that CORMIX1 predicts the flow
trajectory decreasing in elevation in the bdff as is typical
for negatively buoyant flows.
6.1.1.2.4 Buoyant Jets with Three-Dimensional Trajectories
Figure 6.10 presents Ayoub's (1971) buoyant jet
experiment with a transverse horizontal discharge in a weak
crossflow (F0 = 15, R = 15, 9Q = 0°, a - 90°) . The
141
-------
a)
z/D
100
x/D
b)
Fan (1967), Visual Boundary
O Dilution
D Width b
CORMIX1
Centerline
Width b
0.5
100
10
D
O''
'0.5
10
100 200
S/D
Figure 6.6
Buoyant Jet Discharging Vertically into Weak
Crossflow. a) Trajectory, b) width and
dilution.
142
-------
a)
40
z/D
20
0 50
x/D
- ' Fan (1967), Visual Boundary
O Dilution
D Width b
CORMIX1
--- Centerline
--- Width b
IOO
05
b)
60
D
1 ' '
X
S po
o*
g
/
/'
10
100 200
s/D
Figure 6.7 Buoyant Jet Discharging Vertically into Strong
Crossflow. a) Trajectory, b) width and
dilution.
143
-------
10
z(m)
10
' ' rl r
O Wright 1977 data
- - CORMIX1 Centerline
F0>67 R=37
Lm« 0.0664m
Lb'O.OI85m
LQ*0. 0018m
10
-2
10
-I
x (m)
Figure 6.8
Buoyant Jet Discharged Vertically into Weak
Crossflow (Logarithmic presentation)
144
-------
a)
5r
10
z/D
Did
0
10
20 30 40 50
x/D
b) 100
10
b/D
R»O.I8
o /'
o ./
S~" A *
b/D A^
. i . . . ,i
0
s/D
Data:
O A Anderson et al.
(1973)
CORMIX1:
Prediction
IOO
000
Figure 6.9
Negatively Buoyant Jet Discharging Obliquely
Upward in Uniform Crossflow. a) Trajectory,
b) dilution and width.
145
-------
0)
z/D
10
Data.-
o Ayoub (1971)
Centerline Predictions
CORMIX1
UDKHDEN
20 40 60
x/D
80
IOO
b)
80r
60
y/D
= 30,
Figure 6.10
Three-Dimensional Trajectory of Transverse
Horizontal Buoyant Jet in Weak Crossflow.
a) Side view, b) plan view.
146
-------
experimental trajectory results are compared to CORMIX1
predictions as well as to the jet integral model UDKHDEN
(see Muellenhoff, et al. 1985). CORMIX1 predicts an HI
flow class (mdnf, mdff, bdff) for this discharge. The
observed transverse penetration (Figure 6.10b) is reasonably
well predicted by both models. The vertical rise, solely
due to buoyancy effects, however, is under-predicted by both
models (Figure 6.10a). Unfortunately no detailed data or
photographs are available for Ayoub's data, but it is
suspected that this flow may be influenced by flume boundary
(shallowness) effects.
Much better agreement, with both predictive models, is
obtained for a case of stronger crossflow (or alternately,
for the same crossflow, a weaker buoyant jet so that the
shallowness will have less influence) . This is shown in
Figure 6.11 for the conditions F0 = 15 and R = 5.
6.1.1.3 Buoyant Jet in Stratified Stagnant Ambient
The effect of ambient density stratification on buoyant
jets is illustrated in Figure 6.12. Figure 6.12a shows the
plume boundary for Fan's buoyant jet experiment for a
linearly stratified stagnant ambient. This plot represents
a horizontal discharge (00 = 0°, <70 = 0°) with a Froude
number F0 = 26 and stratification parameter T = 1200.
CORMIX1 predicts a plume-like flow class S5 (mdnf, bdnf).
Trajectory data, including the terminal level, zt/D = 76,
agree well with Fan's visual results.
In the absence of any specified ambient crossflow
CORMIX1 does not predict any properties of the buoyant
spreading regime except the thickness of the terminal layer
of bv/D = 38 which is in good agreement with the visual
data. As discussed in Section 2.2 this process is strongly
influenced by the crossflow strength and for stagnant
conditions no steady-state solution is possible. Hence, the
layer thickness (shown on the left and right margins of
Figure 6.12a) are not comparable to any steady-state model
predictions. CORMIX1 however provides some results of the
near-field "boil" produced by the vertically rising plume,
such as the maximum "boil" elevation of z^/D = 116 (see Fig.
6.12a) which is slightly greater than the visual plume
outline.
The effect of ambient density stratification (T = 1200)
on a stronger jet (F0 = 51) discharging near-vertically (8Q
= 45°, a« = 0°) is shown in Figure 6.12b. CORMIX1 predicts
a jet-like flow class S3 (mdnf, mdls-v) and its trajectory
data agree well with Fan's results. The predicted terminal
level, zt/D & 43, the maximum elevation of rise z^D = 43,
and the width b/D = 44 at the terminal level are all in
147
-------
a)
z/D
80
60
40
20
Data:
o Ayoub (1971)
Centerline Predictions
CORMIX1
UDKHDEN
IOO
b)
y/D
80
60
40
F0 - 15 , R = 5
V0°.
-------
a) '20
z/D
100
Fan, 1967, Visual Boundary
CORMIX1 Centerline
Width b
x/D
200
b)
80
z/D
40
, T = 2IO
0=45°
IOO
j I
x/D
200
Figure 6.12
Buoyant Jet Trajectory in Stratified Stagnant
Ambient, a) Horizontal discharge, b) oblique
discharge.
149
-------
agreement with Fan's visual results.
6.1.2 Comparison of Predictions with Jet Integral Models
Because experimental data on buoyant jets is limited,
this section presents CORMIX1 predictions in comparison with
some common jet integral models. Several such model
formulations exist and have been extensively tested against
various data sources (Muellenhoff et al. 1985, Wong, 1984).
Of course, such integral models are limited to buoyant jet
flows in unconfined ambients and cannot address any boundary
interaction.
6.1.2.1 Buoyant Jet in Uniform Crossflow
Figure 6.13 presents a comparison of CORMIX1 with the
integral jet models by Jirka and Fong (1981) and UDKHDEN
(Muellenhoff, 1985). Model predictions for trajectory
(Figure 6.13a) and dilution (Figure 6.13b) are given for ao
buoyant jet (F0 - 10) in a crossflow (R = 10) with 00 = 90°
and 0Q = 0°. The trajectory relationships for the three
models appear to be in general agreement, with CORMIX1 and
UDKHDEN predicting a stronger bending by the crossflow than
the model of Jirka and Fong. CORMIX1 predicts the most
conservative dilution values of the three models as shown
in Figure 6.13b. It should be noted that the bulk dilution
values from UDKHDEN were adjusted by dividing by 1.7 to
represent centerline dilution as shown for the other two
models.
Another comparison with the jet model UDKHDEN already
has been included in Figures 6.10 and 6.11 as discussed
earlier.
6.1.2.2 Buoyant Jet in Stratified Crossflow
Figure 6.14 illustrates the effect of a stratified
crossflow on buoyant jet behavior for the three previously
discussed models. No fully documented experiments are
reported in the literature for this flow configuration.
Figure 6.14 represents the effect of a strong crossflow (R
= 3.0) with a mild density stratification (T = 1000) on a
weakly buoyant jet (F0 = 40) . CORMIX1 predicts a crossflow
dominated flow class SI (mdnf, mdff) with a terminal height
of zt/D =30 which is obtained at a downstream distance x/D
= 1210 as seen in Figure 6.14a. In this case, the
trajectory and stratified terminal height of CORMIX1 are in
good agreement with the integral models, with CORMIX1
predicting the highest terminal level and the model of Jirka
150
-------
a)
z/D
10
CORMIX1
Jirka 8 Fonq,l98l
UDKHOEN
20 30
X/D
40 50 60
b) ioo
80
60
40
20
20 40 60 80 100
x/D
120
Figure 6.13
Comparison of CORMIX1 Predictions with
Integral Buoyant Jet Models in Uniform
Crossflow
151
-------
a)
z/D
Terminal
levels
10-
CORMIX1
Jirko S Fong, I98I
UDKHOEN
FQ = 40
IOOO
500
1000
x/D
b) 200 -
500
IOOO
x/D
Figure 6.14 comparison of CORMIX1 Predictions with
Integral Buoyant Jet Models in Stratified
Crossflow
152
-------
and Fong the lowest, zt/D = 26 at x/D - 1350. Figure 6.14b
shows again that CORMIX1 predicts the most conservative
centerline dilutions, with a difference of about 50% among
the three models.
6.2 Complex Flows With Boundary Interaction
This section is intended to illustrate the ability of
CORMIX1 to correctly classify and predict flow dynamics in
the presence of various boundary interaction processes.
6.2.1 Jet Flows in Shallow Receiving Waters
Figure 6.15 presents the laboratory data of Abdelwahed
and Chu (1978) for vertical discharges into shallow uniform
crossflow. Figure 6.15a and 6.15b show a pure jet (F0 = «)
in weak crossflow (R = 12, Test 2001) and strong crossflow
(R = 6, Test 2004), respectively. CORMIX1 predicts a flow
class V2 (mdnf, mdff, surface approach, passive mixing) for
both cases where the subsurface regions are limited and the
surface passive mixing occurs shortly downstream of the
discharge. Passive surface plume dimensions are in good
agreement with visual plume outlines for both of these
nonbuoyant cases. Figure 6.15c illustrates the additional
influence of buoyant surface spreading for a buoyant
discharge in strong crossflow (F0 = 12, R = 6). CORMIX1
predicts a flow class V2 but with a buoyant spreading region
before passive mixing occurs. Again the plume prediction
agrees well with the visual surface plume boundary. This
documents the importance of including both far-field
processes, namely buoyant spreading and passive diffusion,
in a predictive methodology.
6.2.2 Strongly Buoyant Jets in Shallow Receiving Waters
Fischer et al. (1979) present 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
5.5 m below the surface in 9.6 m deep water off the
California coast. The temperature difference between the
ambient current and the discharge is 11.1°C giving rise to
a buoyant acceleration of g'0 = 0.032 m2/s. CORMIX1 predicts
a flow class of V5, which represents an stable discharge
with buoyant upstream intrusion and subsequent buoyant
surface spreading as the plume travels downstream.
Figure 6.16a shows the CORMIX1 results compared with
actual field results obtained from a tracing of an infrared
picture of the actual plume. Two different crossflow
velocities were used to account for possible variation in
153
-------
a)
-20H
= 7.62cm
100 x(cm)
R = I2
b)
y (cm)
20
Visual boundary
Abdelwohed and Chu (1978)
CORMIX1, width b
Lm = 2.l6 cm
Lb = 0cm
= 2.l6 cm
Lb=0.48 cm
Figure 6.15
Vertical Jet Discharge into Shallow Crossflow,
Plan view of plumes at water surface.
154
-------
CORMIX1 width b
ua=0.2 m/s
un = 0.25m/s
z(m)4
IO--
!!
L^
5
L-
Cl^"*
I -^Discharge
D = 4.3m
50=25.2
00""""* 0 1 00
"S~n J^^ ' "" ' TTn* * **"
m3/s
i i i
200 300 400
i -
x (m)
Figure 6.16
Cooling Water Outfall from San Onofre Nuclear
Power Plant (Unit 1) . a) Comparison of CORMIX1
prediction for surface plume, b) predicted
subsurface flow pattern (side view).
155
-------
the ambient data and to illustrate the sensitivity of the
model. For a crossflow velocity of 0.2 m/s CORMIX1 predicts
a buoyant upstream intrusion of 42 m with a flow half-width
of 110 m at surface impingement. Using the slightly higher
crossflow velocity of 0.25 m/s, as reported by Fischer et.
al., CORMIX1 predicts a smaller buoyant upstream intrusion
of 22 m with a flow half-width of 56 m at surface
impingement. The field data indicate an upstream intrusion
and half-width at surface impingement of about 30 m and 85
m, respectively. Overall CORMIX1 agrees well with the
photographic surface data.
No field data are available for the sub-surface flow
region as well as for the induced temperature field. Figure
6.16b illustrates model predictions from CORMIX1 for the
discharge cross-section for the two ambient velocities. The
upstream intrusion and gradual thinning in the downstream
direction due to buoyant spreading is demonstrated and is
consistent with the information from the plan view
photograph.
6.2.3 Flows with Wake Interaction
A discharge operating in a strong crossflow can cause
wake attachment. CORMIX1 was applied to data for cooling
tower experiments from Viollet (1979); as reported by EPRI
(1981) and illustrated in Figure 6.17. Dilution data are
also included in Figure 6.17, as indicated by concentration
isolines. Figure 6.17a represents an unattached flow with
a strong buoyancy (F0 = 0.8) and weak crossflow (R = 2.0).
CORMIX1 predicts an unattached flow class VI. The
experimental data show slightly stronger deflection than is
indicated by the CORMIX1 prediction. The concentration
decay CC/CQ along the centerline of the CORMIX1 predictions
(indicated by arrows) is in excellent agreement with the
experimental contour values C/CQ.
The effect of a much stronger crossflow is illustrated
in Figure 6.17b with F0 = 0.8 and R = 0.33. Here CORMIX1
predicts an attached flow class V1A1 (wake recirculation).
This is in agreement to the attachment of the experimental
cooling tower plume indicated in Figure 6.17b. CORMIX1 also
predicts the plume will contain enough buoyancy to
subsequently lift-off from the ground at x/D =6.4. However
experimental data further downwind are not available to
fully verify this aspect. The concentration predictions of
CORMIX1 are in satisfactory agreement with the contour
values for this complicated flow process.
156
-------
a)
z/D
10
Viollet, 1977 Centerline
Isoconcentration c/c0
CORMIX1 Centerline
Width b
20 x/D
b)
z/D
F0=0.8 R = 0.33
0.045
-0.03
-^ V 10
Wake XLift-off
recircuiation
20 x/D
Figure 6.17
Strongly Buoyant Plume in Crossflow, a) Weak
crossflow without attachment, b) strong
crossflow with wake attachment.
157
-------
6.2.4 Negatively Buoyant Flows With Upstream Spreading Along
Bottom
The CORMIX1 prediction for the bottom interaction of
negatively buoyant flows is shown in Figure 6.18 in
comparison with the laboratory data of Tong and Stolzenbach
(1979). This implies a flow class NV2, and CORMIX1 predicts
bottom contact at x = 0.45 m, an upstream intrusion of 0.02
m and an intrusion thickness of 0.10 m, which is less than
the visual data indicate. The predicted trajectory
prediction tends to deflect somewhat less in the direction
of the crossflow than the visual data indicate. The
experiments conducted in a laboratory flume of limited width
may exaggerate the extent of the bottom upstream intrusion
for two reasons: First, due to the sidewalls there is less
freedom for lateral spreading and therefore more upstream
intrusion. Secondly, due to the viscous boundary layer in
the ambient approach-flow there is less resistance
(stagnation pressure) to the intrusion flow. For the
analysis the ambient velocity was adjusted upward to 0.08
m/s from the reported mean velocity of 0.07 m/s to account
for the contraction of the ambient flow caused by the
presence of the density current in the laboratory channel.
The important conclusion is that CORMIX1 recognizes this
complicated interaction process with a negatively buoyant
plume and upstream bottom buoyant spreading.
6.3 Summary and Appraisal
Seen as a whole, the preceding data/model comparisons
indicate that CORMIX1 is a satisfactory modeling system for
the mixing prediction of aqueous single port discharges in
diverse conditions. CORMIX1 appears to be i) reliable and
ii) accurate.
i) The system's reliability seems rooted in its robust
classification scheme that determines which flow
configuration (class) will occur for a given discharge/
environmental situation before the appropriate simulation
model is executed.
ii) The overall accuracy of the system is of the order
of ±50% for the spatial definition of the flow zones (e.g.
trajectories, width, etc.) and for tracer (pollutant)
concentration. Given the broad range of flow conditions
this accuracy level for a comprehensive, non-specialized
model appears fully acceptable from an engineering
standpoint. As usual, any lack of accuracy in such
comparisons has to viewed in the perspective of turbulent
mixing processes with their intrinsic fluctuations and
unsteadiness. Variations can also be caused by disturbing
influences in experiments or field conditions; e.g. a shear
158
-------
z (cm)'
60
40
20
0
U0-6.93 cm/sec
F0=I77
R = 144
CORMIX1 Centerline
Width b
long S Stolzenbach, 1979
Visual Boundary
20 40
x (cm)
60
Figure 6.18 Interaction of Negatively Buoyant Jet with
Bottom Boundary
159
-------
flow instead of a uniform mean flow, and by different data
interpretation and analysis techniques employed by
researchers.
Emphasis has been placed in the data/model comparison
on the near-field mixing characteristics of the effluent
discharge, with comparatively less attention to the passive
far-field mixing. This emphasis is of course motivated by
the intended primary use of CORMIX1 as a predictive tool for
mixing zone analysis. Another reason, however, is the fact
that far-field mixing processes are reasonably well
understood. The CORMIX1 far-field modules rely on standard
plume models of the passive ambient diffusions processes (as
discussed in Section 2.3) and the numerical values are well
established (see Fischer, et al., 1979, Holley and Jirka
1986).
For many of the flow classes that can be predicted by
CORMIX1, actual field or laboratory data are quite limited.
One of the continuing goals of CORMIX1 is to update,
enhance, and validate the knowledge base and predictive
capability of the system as more information becomes
available.
160
-------
Chapter VII
Applications of CORMIX1
The purpose of this chapter is twofold: i) to give an
overview of the typical steps of CORMIX1 application,
including data input, in discharge design and mixing zone
evaluation, and ii) to illustrate the flexibility of CORMIX1
using three hypothetical examples of highly divergent design
or environmental conditions. The first case study
represents a small toxic industrial discharge into a river
(Section 7.1), the second is a toxic discharge into coastal
waters illustrating the effects of density stratification
(Section 7.2), and the third is a cooling water discharge
into the ocean under different ambient currents (Section
7.3) .
7.1 AB Chemical Company
This example illustrates a buoyant discharge in a
bounded riverine section. The discharge flow represents a
complex three-dimensional trajectory subject to three legal
mixing criteria; a toxic dilution zone, a plume width
criterion on a legal mixing zone defined by existing channel
width, and a downstream region of interest. The analyst
seeks pollutant concentrations at these locations. The
analyst will use CORMIX1 to potentially improve dilution
characteristics of the discharge by altering the discharge
angles of the outfall design.
7.1.1 The Problem Statement
AB Chemical Company discharges a heated industrial
effluent into the Ohio River through a submerged pipe
outfall. The discharge flow is 0.053 m3/s and contains 500
Mg/1 of a toxic substance. The material has a criterion
maximum concentration (CMC) value of 25 M
-------
The outfall is located 55 m from the berm line near the
left bank. The right bank is under the jurisdiction of the
State of Ohio. The initial design proposed for this
discharge is as follows: The port is pointing directly
offshore (normal to the ambient flow) and is directed
horizontally along the bottom (00 = 0°) . The round port has
a diameter of 15 cm and its center lies 0.4 m above the
river bottom (see Figure 7.1).
The mixing zone limitations of the State of West
Virginia have to be considered. For this case the mixing
zone will be assumed to have a maximum width value equal to
10% of the river width, and the dilution values 3000 m
downstream from the discharge point are of interest because
of an intake to a public water supply on the Ohio shore.
This will be labeled design case No. 1.
7.1.2 CORMIXl Analysis
Design Case No. 1:
The first step in the analysis is to schematize the
bounded cross-section as shown in Figure 7.1. Stream cross-
sections are usually highly irregular; the trapezoidal
cross-section represents an initial approximation of the
actual stream cross-section. CORMIXl assumes an equivalent
rectangular cross-section as shown in Figure 7.1, which the
analyst would approximate. Using DATIN, the site parameters
are specified.
An 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 schematized 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 that the distance to the
nearest bank (West Virginia) was 225.25 m, i.e. the
complement value, 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). [1]
and the user is given another chance to enter the correct
value of 37.5 m.
After completing DATIN, the system executes PARAM,
followed by CLASS. In CLASS the analyst is advised of the
intermediate conclusions reached; i.e. the discharge is
positively buoyant. CORMIXl assigns a flow class H1A3 to
162
-------
Cross-section View
55m
W.Vo.
Ohio
230m
Plan View
262.
37.5m
t
ua=0
t t t
75m
.3m/s
t f
1
0=0.15
0.4m
Detail of Discharge
Schematization of Cross-section
Figure 7.1
AB Chemical Company: Schematization of Cross-
Section at the Discharge site
163
-------
the discharge indicating a Coanda attached jet with buoyant
lift-off (attached wall jet, lift-off, strongly deflected
plume (bdff), surface approach, buoyant surface spreading,
passive diffusion).
After the program element HYDRO executes, the program
element SUM summarizes the hydrodynamic simulation output
for the design case. The results are shown in Figure 7.2.
Figure 7.2a gives a longitudinal side view of the near-field
and surface interaction. Figure 7.2b gives the detail of
the near-field attachment looking downstream in the z-y
plane. The buoyancy of the discharge causes lift-off at x
= 2.5 m downstream. SUM notifies the user that surface
interaction and thus the limit of the hydrodynamic mixing
zone (HMZ), a region of strong initial discharge induced
mixing (but of no legal significance), occur at x = 117 m
downstream from the discharge point where the dilution value
is S = 620 and the plume half-width bh and vertical
thickness b%, are both = 7.4 m.
V
The toxic dilution zone (TDZ), where the tracer
concentration falls below the CMC value, occurs at x & 13
m in the submerged plume region (bdff). SUM concludes that
the criterion maximum concentration (CMC) value for the
toxic discharge does not meet all legal restrictions. SUM
notifies the user on the criteria checked for a TDZ; i) the
discharge velocity was equal to or greater than the minimum
value of 3.0 m/s, ii) the downstream distance of the TDZ (13
m) exceeded the maximum distance of 50 times the discharge
length scale 1^ = 0.13 m, i.e. 6.5 m, iii) the downstream
distance of the TDZ was less than the maximum distance of
5 times the water depth of 12 m, and finally iv) the
downstream distance of the TDZ was less than the maximum of
10% of the distance to the LMZ. Thus SUM notifies the user
that the discharge did not meet criterion (ii) for the toxic
dilution zone. For this reason an alternative design case
No. 2 will be evaluated.
Design Case No. 2:
Using the expert advice given by SUM an attempt is made
to avoid the Coanda attachment of the discharge by
increasing the vertical angle of the discharge. If
attachment is averted, improvements in dilution within the
near-field - and thus the TDZ - may be possible. These
design changes will also illustrate the sensitivity of the
model and flow classification wheno the vertical discharge
angle is changed from 9Q = 0° to 30° (aQ = 270°) .
Using the new discharge orientation CORMIX1 indeed
assigns an unattached flow class HI to the discharge (mdnf,
mdff, bdff, surface approach, buoyant surface spreading,
passive mixing) indicating the increase in vertical
164
-------
z(m)
HMZ.
Limit
Surface approach |
Begining of
buoyant
spreading
"Lift-off
50
00
x(m)
a) Longitudinal Side View (distorted scale)
z(m)
\ (-»-TDZ Limit
x
b) Vertical View Looking Downstream (undistorted)
Figure 7.2 AB Chemical Co. Design Case No. 1: Predictions
(bottom attached jet)
165
-------
discharge angle to 30° avoids Coanda attachment. A close-
up of the near field of the discharge appears in Figure 7.3.
This should be compared to the attached case as shown in
Figure 7.2b.
SUM indicates the hydrodynamic mixing zone (HMZ) is
limited to the surface contact at x a 108 m downstream from
the discharge point with dilution value S a 594. The plume
half-width bh and thickness b are both a 7.2 m,
demonstrating that altering the discharge angles did not
significantly improve mixing characteristics in the HMZ.
In this case, only a small decrease in HMZ size and dilution
is apparent.
The TDZ, however, shows a marked improvement of the
unattached case. The CMC value of 25 ^g/l is met at a
downstream distance x = 6.1 m from the discharge point in
the mdff region. Thus a shorter downstream distance than
for the previous attached case is required to achieve the
CMC value. Because of this, SUM concludes that the
criterion maximum concentration (CMC) value for the toxic
discharge now does meet all legal restrictions.
The overall plume shape, extending into the far-field,
for this design case is shown in Figure 7.4. The transition
from buoyant surface spreading plume to passive mixing
occurs at x a 835 m. The plume contacts the left bank in
the passive mixing region at x a 1211 m downstream from the
discharge point, where the plume also becomes vertically
fully mixed over the water depth (bv = 12 m) m.
At the position of the public water supply located on
the Ohio shore 3000 m downstream from the discharge point,
the dilution value in the surface buoyant spreading region
is S a 6763, and the plume half-width is bh = 97 m (bank
attached to left shoreline). The plume is vertically fully
mixed (bv = 12 m) . Therefore, the plume does not influence
the water supply intake.
The plume meets the legal mixing zone (LMZ) criteria of
10% of the stream width at x = 199 m downstream of the
discharge in the buoyant surface spreading region, where S
= 582. At this point the plume thickness is bv = 4.5m and
the plume half-width is bh = 14 m.
In summary, this example illustrates that the effect of
altering discharge angles on mixing is often limited to the
immediate near-field of the discharge. Plume attachments
to the bottom should be avoided to insure rapid mixing in
the near-field of the discharge. This is especially
important for toxic dilution zones. However, altering
discharge angles may have a limited effect on overall plume
166
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00=30° cr0=270°
-10 y(m)
mdnf mdff \
region region \-TDZ limit
Figure 7.3 AB Chemical Co. Design Case No. 2: Close-up
View of Unattached Buoyant Jet Near Discharge
167
-------
0
IGOOV 2000 3000
Bottom Attachment
a) Longitudinal Side View (distorted)
.(m)
y (m) /
100
*»
Ja 0
-100
-200
'LMZ Limit1
Bonk Attachment
/ W Va.
-I Region
Ohio
b) Plan View (distorted)
X ww'"
Water Supply
Intake
Figure 7.4 AB Chemical Co. Design Case No. 2: Overall
Appearance of Discharge Plume
168
-------
mixing behavior, especially in the far-field at large
downstream distances from the source.
7.2 MM Municipal Treatment Plant
In this hypothetical example a mid-size municipality
(about 100,000 inhabitants) is discharging its treated
effluent into adjacent costal waters. A local metal
processing plant is proposing to dispose its brine waste
water containing toxic materials combined with the municipal
effluent. This buoyant discharge is subject to three mixing
criteria: a toxic dilution zone, a plume width criterion on
the legal mixing zone, and a downstream region of interest.
The analyst will use CORMIX1 to study the effect of typical
winter and summer ambient density profiles on the mixing
behavior of the discharge.
7.2.1 The Problem Statement
Typical winter and summer profiles have been measured
in the discharge area and are shown in Figure 7.5a. The
discharge is to be located 2000 m from shore at a local
water depth of 24.4 m. The bathymetry is sloping
approximately linearly from the shoreline.
The discharge port is round with a diameter of 0.5 m
and extends about 0.5 m above the surrounding bottom with
the vertical angle 6Q = 30° in the direction of the
prevailing ambient current (co-flow, a0 = 0°) which is of the
order of 0.25 m/s. The design discharge flowrate is 0.6
m3/s and contains 100 ^9/1 of a toxic metallic substance
with a CMC of 10 ^g/1- The discharge density for the
mixture of municipal effluent and industrial brine is 1015
kg/m3. A public beach is located 2000 m down-current from
the discharge point, so that plume characteristics at this
distance are of interest.
7.2.2 CORMIX1 Analysis
The first step in the analysis would be to choose one
of the four ambient stratification types as seen in Figure
5.3 to represent the actual density profiles . An ambient
profile of (Stratification Type C, Figure 7.5b) is chosen
to represent the August data, with surface density ps =
1022.6 kg/m5, bottom density pb = 1024.4 kg/m3, and ambient
density jump Ap =0.83 kg/m at the stratified layer height
Hs = 12.61 m. The schematized cross-section in this case of
a linearly sloping bottom would assume would place the
discharge 1000 m from "shore" in 24.4 m of water. A weak
linear ambient density stratification (Stratification Type
169
-------
^^^
£
IM
j£
"5.
\
b
V
\
o
\_
^
i i i
o
1
i
0
i
i
H
o
I
i
o
i
i
0
I
i
O
i
n
Figure 7.5
1,022 1,024 1,026
Density (kg/m3)
b) CORMIX1 Representation
MN Treatment Plant: Typical Density Profiles
for Summer and Winter Conditions
170
-------
A, Figure 7.5b) is chosen to represent the March data, with
surface density ps = 1025.6 kg/m , bottom density pb = 1025.7
kg/m3, and the stratified layer height Hs equal to the full
discharge depth of 24.4 m.
Summer Design Case;
For the August design conditions, CORMIX1 concludes the
flow will be confined to the lower density layer by the
ambient density jump at the pycnocline and assigns a flow
class H2 (mdnf, mdff, surface approach, buoyant spreading,
passive diffusion). The simulation results are shown in
Figures 7.6 and 7.7. SUM notifies the user that the
hydrodynamic mixing zone (HMZ) occurs at x a 54 m downstream
from the discharge point with plume centerline height z a
12.6m (indicating a submerged plume trapped by the
pycnocline density jump), the dilution value is S s 39, and
the plume half-width bh and thickness bv are both % 5.8 m.
The CMC (Figure 7.6) value occurs at x s 16.4 m from the
discharge point in the mdff. SUM notifies the user that all
criteria checked for the TDZ are satisfied.
The far-field behavior of the internally trapped plume
is shown in Figure 7.7. The plume is still in the internal
buoyant spreading regime. A very thin, but wide, layer of
mixed effluent flow arises.
The legal mixing zone (LMZ, Figure 7.7) width of 200 m
occurs in the subsurface buoyant spreading region at x a 784
m from the discharge point with a dilution S = 76. At the
LMZ the flow is at the pycnocline height z = 12.6 m and not
bank attached, with plume half-width bh = 100 m and plume
depth bv « 0.9 m.
At 2000 m from the outfall, the plume dilution is S ^
910, and the flow half-width bh and thickness bv are a 196
m and 0.55 m, respectively. This indicates the subsurface
buoyant spreading region still does not contact the
shoreline near the public beach.
Winter Design Case:
For the March design conditions, CORMIX1 concludes the
linear ambient density stratification is too weak to trap
the flow, and a uniform ambient density is set equal to the
depth average value of 1025.6 kg/m3. CLASS assigns a flow
class HI (mdnf, mdff, bdff, surface approach, buoyant
spreading, passive diffusion) for the full water depth. It
should be noted that the flow is classified as HI (instead
of H2 as in the previous example) because within the deeper
layer the flow will develop a bdff region before surface
contact. The simulation results for the near field are
171
-------
z(m)
ix
JDZ Limit , HMZ Limit
Pycnocline Interaction
Buoyant Spreodingj
a) Side View (distorted)
y(m)
ua=0.25m/s
-20-
b) Plan View (undistorted)
Figure 7.6 MN Treatment Plant Summer Design Case:
Internal Flow Trapping Caused by Pycnocline
Density Jump
172
-------
z(m>4 ^xHMZ Limit
LMZ Limit
20r[* Buoyant Ambient Spreading
'
500 ' ~^ 1000 1500
a) Side View (distorted)
0
2000 x(m)
1000
0
-1000
Buoyant Ambient Spreading
b) Plan View (distorted)
Public Beach
2000 x(m)
Figure 7.7 MN Treatment Plant Summer Design Case: Far-
Field Behavior of Internally Trapped Flow
173
-------
shown in Figure 7.8.
The hydrodynamic mixing zone (HMZ) occurs at surface
contact at x * 81 m downstream from the discharge point with
plume centerline height z = 24.4 m, dilution S as 149, and
plume half-width bh and thickness by both a 13.3 m,
indicating slightly greater HMZ dimensions and associated
dilutions than the strongly stratified August design.
For the March design the legal mixing zone (LMZ) width
of 200 m occurs in the surface buoyant spreading region at
x a 753 m from the discharge point with a larger dilution
S = 248. At the LMZ the surface flow does not contact the
shoreline, with plume half-width bh & 102 m and plume depth
bv = 2.9 m.
The CMC value occurs at x = 16 m from the discharge
point, again indicating that all criteria for the TDZ are
met for this discharge design condition.
In summary, this example illustrates the flexibility of
CORMIX1 in predicting flow behavior in density stratified
environments, where plume trapping by the pycnocline may
inhibit dilution.
7.3 PQ Power Company
This design example represents an ocean cooling water
outfall from a small steam-electric power plant in
relatively shallow water and varying ambient tidal currents
with weak ambient density stratification. There is no legal
mixing zone under consideration for this discharge. But
because the cooling water intake structure for the power
plant is located on the shoreline 1000 m from the discharge
point, the behavior of the heated effluent over this region
is sought.
7.3.1 The Problem Statement
The outfall is located 300 m offshore at a local water
depth of 5.0 m. The bathymetry is given by a an
approximately flat shelf region. Available site data
indicate a linear ambient density profile with a osurface
temperature of 18° C and a bottom temperature of 15° C.
The outfall port is round with a diameter of 1.0 m which
extends about 0.5 m above the surrounding bottom. The
cooling water is discharged vertically at a flowrate of 3.0
m3/s. The design discharge temperature is 30° C. The
discharge site is characterized by varying tidal currents
between 0.2 m/s and 0.8 m/s.
174
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z(m)
Surface Interaction Region
_2 . _*_
Buoyant Sui face Spreading
y(m)1
20
0
-20
a) Side View (distorted)
-TDZ Limit
Surface Plume
I I
b) Plan View (undistorted)
Figure 7.8
MN Treatment Plant Winter Design Case: Plume
Surface Interaction
175
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7.3.2 CORHIXl Analysis
Low Current Case:
For the minimum ambient current speed of ua = 0.2 m/s,
CORMIX1 concludes linear ambient density stratification
resulting from the difference in surface and bottom
temperatures is weak and dynamically unimportant. CLASS
assigns a flow class V5 (mdnf, bdnf, surface impingement
with upstream spreading, buoyant surface spreading, and
passive mixing). The simulation results are shown in Figure
7.9.
CORMIX1 indicates an upstream intrusion length of x =
66 m with the intrusion layer maximum thickness of 4.34 m
at the leading front (stagnation point). The buoyant
intrusion rapidly collapses into a wide and shallow density
current. At the edge of the HMZ the density current has a
half-width bh of 173 m and a thickness bv of only 0.15 m.
Farther downstream in the far-field, the dilution is
still limited to S = 3.5 at x a lOOO m (not shown in Figure
7.9) from the outfall where the buoyant surface spreading
plume half-width bh and thickness by = 189 m and 0.14 m,
respectively, indicating very little mixing under a low
ambient crossflow. The plume would not influence the
cooling water intake under these conditions.
Note that CORMIX1 does not include any decay processes
in the effluent. In practice, the heated effluent in this
design case would undergo surface heat exchange processes
which would be reasonably strong due the small degree of
mixing. A discussion of the adaptation of CORMIX1 to
include such decay is given in Section 7.4.4.
High Current Case;
For the maximum ambient current speed of ua = 0.8 m/s,
CORMIX1 concludes that the weak linear ambient density
stratification is again unimportant. CLASS assigns a flow
class V4 (mdnf, boundary impingement with full vertical
mixing; buoyant surface spreading, and passive mixing). The
simulation results are shown for the near-field in Figure
7.10, indicating that the stronger ambient current prevents
buoyant upstream intrusion, and an unstable mixing zone
occurs around the discharge. The plume makes a transition
from buoyant surface spreading to passive mixing at x = 703
m from the outfall (not shown in Figure 7.10). However, the
stratified passively mixing plume only slowly approaches the
shoreline. At 1000 m downstream from the outfall, the
dilution is still limited to S = 34 and the plume half-width
bh a 40.5 m and the thickness bv * 1.5 m. Thus, one can
176
-------
50
0
a) Side View (distorted)
y (m),
200-
100
Buoyant Upstream
Spreading \
x
'Stagnation
Point
-200
b) Plan View (distorted)
Figure 7.9 PQ Cooling Water Outfall in Low Current Design
Case: Near-Field Plume Behavior
177
-------
Unstable Recirculation
Zone
150 x(m)
a) Side View (distorted)
b) Plan View (undistorted)
Figure 7.10 PQ Cooling Water Outfall High Current Design
Case: Near-Field Plume Behavior
178
-------
conclude the cooling water intake would not experience a
temperature rise due to heated discharge re-entrainment.
In conclusion, this example illustrates that ambient
current can have a significant effect on discharge mixing
and plume behavior, especially on discharges with strong
buoyancy dominated boundary interaction and subsequent
buoyant spreading. Because of the normal variation in
natural systems, the analyst should study plume
characteristics under a range of ambient environmental
conditions.
In all three of the previous examples, the buoyant
spreading region extends to large distances downstream from
the outfall. Discharge buoyancy tends to stabilize the
plume in the far-field and prevents the transition to
passive ambient mixing, which in general, is a more
efficient mixing mechanism. Toxic dilution zone criteria
may be most restrictive and occur in the near-field in the
vicinity of the discharge. The legal mixing zone commonly
occurs in the far-field in either the buoyant spreading or
passive mixing region.
7.4 Comments on the Application of CORMIX1
As mentioned in Chapter IV it is expected that CORMIX1
will be a general predictive system applicable to the
majority (better than 95%) of submerged single port
discharge/environmental conditions. It is impossible,
however, to devise a system that will analyze all
conceivable submerged discharges. For this reason, CORMIX1
intentionally contains several internal criteria
(limitations) designed to avoid system misuse for such
extreme conditions. These limitations are summarized in
Section 7.4.1. However, an experienced user can modify the
data input to allow for CORMIX1 analysis for conditions
(e.g. near-surface discharges) that are seemingly outside
the normal range of system applicability. Hints for such
system application are given in Section 7.4.2
7.4.1 Limitations of CORMIX1
CORMIX1 is devised for submerged single port discharges
in water of variable depth H (see Figure 7.11). Thus the
discharge is assumed to be located near the bottom of the
water body. CORMIX1 uses the applicability criterion for
the height of the discharge port hQ
h0 < 0.33H (7.1)
Eg. (7.1) is needed to assure a valid test for deep/shallow
discharge stability in the flow classification scheme.
179
-------
z=h. -
mt
H
inl
Density profile
example
------ hint=0.4H
h0=0.33H
Range
mt
Range
of h0
00 > 45° D ^ H
90 < 45° D< H/3
Range
of D
Figure 7.11 Parameter Range of CORMIX1 Applicability
180
-------
Also the discharge port diameter D must not exceed
practically unrealistic (yet theoretically conceivable)
values of the order of the water depth, thus for near-
vertical discharges
D < H (7.2)
and for near-horizontal discharges
D < 0.5H (7.3)
Finally, the height of the pycnocline (i.e. thickness
of the lower layer) h1nt must be more that 40% but less than
90% of the water depth
0.9H > h,nt > 0.4H (7.4)
7.4.2 Hints for CORMIX1 Use in Extreme Conditions
7.4.2.1 (Near-)Surface Discharges
As an example, assume that a positively buoyant
discharge is located at a small submergence - perhaps at 10%
of the depth - below the free surface of an unstratified
water body. Clearly, the condition of Eq. 7.1 is violated
so CORMIX1 cannot be used with such input data (in fact the
system will reject this input, and ask the user to check
the data!).
Yet a valid application of CORMIX1 for buoyant
discharges is still possible if the reverse situation - i.e.
a "mirror image" - of the ambient/discharge configuration
is considered using the water surface as the plane of
symmetry. In this situation the discharge jet - now with
reversed "negative" buoyancy - is located near the "bottom".
After appropriate data input, CORMIX1 would conclude a
negatively buoyant flow class (NH) and all system
predictions have to be interpreted in the coordinate system
of the mirror image.
Even more complicated ambient stratification conditions,
can be handled in this mirror image interpretation as long
as careful attention is paid to the specification of the
reverse stable profile.
However, CORMIX1 is not applicable to (near-)surface
discharge conditions that i) experience strong shoreline
interaction, or ii) have a highly non-uniform cross-section
(aspect ratio) as in a channel inflow.
i) The near-field processes considered in CORMIX1 are
valid only for offshore conditions and do not include any
shoreline (bank) interaction (Such interaction is allowed
only in the far-field in CORMIX1). Shoreline interaction
181
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processes may sometimes dominate surface discharge dynamics
as discussed in detail by Chu and Jirka (1986).
ii) Surface discharges may often have a large cross-
sectional aspect ratio (e.g. width/depth ratio of a channel
inflow). Since CORMIX1 neglects the geometric details of
the zone of flow establishment it is valid only for round
or near-square cross-sections with maximum aspect ratio
values of about 3:1.
7.4.2.2 Elevated Discharges
If a discharge is still well submerged but elevated
above one third of the water depth as specified by Eq. 7.1,
then CORMIX1 can still be used in the following iterative
fashion:
Case i) : For a strongly buoyant jet that tends to
quickly rise to the surface, assume the water bottom lies
higher so that the port elevation relative to the reduced
depth is within the 33% limit expressed in Eq. 7.1. The
CORMIX1 predictions will be valid if they indicate a stable
flow class for this reduced depth condition without any
unstable recirculation.
Case ii) : For a strongly negatively buoyant jet that
would rapidly sink towards the bottom, assume the water
surface is sufficiently higher so that Eq. 7.1 is met.
Evaluate the CORMIX1 predictions to check for stable
discharge configurations that wouJd not interact with the
actual water surface.
Case iii): If unstable discharge conditions are expected
(this would be indicated if the above assumptions are
violated) then the actual port elevation is frequently of
secondary importance, while the water depth is the primary
parameter. In this case, a reduced port elevation - within
the limits of Eq. 7.1 - can be specified.
Clearly the experienced user will proceed with a careful
iterative evaluation of such complex, and perhaps unusual,
cases that fall outside the normal CORMIX1 problem domain
of deeply submerged single port discharges.
7.4.3 Applications to Non-Dimensional Coordinate systems
Available data on buoyant jet mixing processes are
usually presented in non-dimensional form. Often the port
diameter D is used for length normalization and the non-
dimensional parameters F0/ R, and T (Eqs. 6.1, 6.2, and 6.3,
182
-------
respectively) are given. Also the coordinate system is
frequently put at the discharge orifice.
Since COKMIX1 uses the SI System of units (e.g. length
expressed in meters) a simple numerical comparison is
achieved by preparing the buoyant jet input data as follows:
D = 1 m, pa ~ 1000 kg/m3, pQ = 990 kg/m3, UQ = 0.3132F0, ua =
Ug/R, h0 = 0 m, and H^ = 1000 m (unless the actual normalized
water depth H/D = H* is known in the experiment, in which
case H = H* m) . Furthermore, for linearly stratified cases,
the ambient density pa(H) at the water surface is specified
t>Y P^(H) = 1000(1 - 10/T) kg/m3, where T is the
stratification parameter given by Eq. (6.3), and the ambient
bottom density pb = 1000 kg/m3. If this convention is made,
all lengths (m) predictions by provided by CORMIX1 can be
conveniently interpreted as predictions normalized by the
diameter D, i.e. they are numerically the same.
Since the port height h0 is zero for these simulations,
CORMIX1 assumes a bottom at z = 0, and hence for many cases
an attachment process is indicated. However, in program
element CLASS the user can override this attachment and
CORMIX1 will provide predictions for the unconfined and
unattached flow.
7.4.4 Adaptation to First-Order Reaction Processes
CORMIX1 assumes a conservative pollutant or tracer in
the effluent. This assumption is reasonable since the
emphasis of CORMIX1 is on initial mixing mechanisms that
have very short time scales (order of minutes) much less
than the typical reaction times for growth or decay of most,
though not all, discharged substances.
If the physical, chemical, and/or biological reaction
mechanism can be represented as a first-order process with
reaction time constant Kr [s~1], then the user can convert
the conservative pollutant concentration c predicted by
CORMIX1 in the far-field, i.e. the buoyant spreading and
ambient diffusion regimes. The conversion to reacting
substances yields a non-conservative concentration cn
cn = c exp (-Krx/ua) (7.5)
in which x/ua represents the travel time in the far-field.
This simple adaptation is acceptable if the reaction time
scale, l/Kr, is sufficiently larger than the travel time to
the end of the near-field (i.e. the hydrodynamic mixing
zone) , *HMZ/ua. For substances with faster reactions more
detailed analyses which consider the actual travel time
within the near-field have to be performed.
183
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Chapter VIII
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 analyses. 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. Against this background, a micro-computer based
expert system, the Cornell Mixing Zone Expert System
(CORMIX), was developed as a tool for effluent flow
prediction and mixing zone analysis.
Subsystem CORMIX1 predicts the dilution and trajectory
of a single port buoyant (positively, negatively, or
neutrally) discharge into a uniform or stratified density
environment with or without crossflow. CORMIX1 uses
knowledge and inference rules obtained from hydrodynamic
expertise to classify and predict mixing processes. 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.
CORMIX1, with its emphasis on rapid initial mixing,
assumes a conservative pollutant discharge neglecting any
physical, chemical, or biological reaction or decay process.
However, the predictive results can oe readily converted to
adjust for first-order reaction processes.
The results of the hydrodynamic simulation are in good
to excellent agreement with field and laboratory data and
other available simulation models. In particular, CORMIX1
correctly predicts a wide range of highly complex discharge
situations involving boundary interactions, stratified
terminal layers, buoyant intrusions, and bottom attachments,
all features which are not predicted by other currently
184
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available initial mixing models. Overall CORMIX1 appears
to be an excellent first cut tool for the analyst.
As more data become available and experience with using
the expert system is obtained, the hydrodynamic flow
protocols in the flow classification system should be
further analyzed along with verification of the constants
used within the model. For some possible flow
configurations, the existing data base is limited for
conducting rigorous validation studies indicating a need for
additional field and laboratory data. Also the
implementation of computer graphics should be pursued in
order to display the results of CORMIX1 predictions.
185
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Book), Guidelines for State and Area Wide Water Quality
Management Program, Washington, D.C. (Chapter 5).
64. USEPA (1984), Water Quality Standards Handbook. Office
of Water Regulations and Standards, Washington, D.C.
65. USEPA (1984), "Technical Guidance Manual for the
Regulations Promulgated Pursuant to Section 301 (g) of the
Clean Water Act of 1977 (Draft) ", Washington D.C., August.
66. USEPA (1985), "Technical Support Document for Water
Quality-based Toxics Control". Office of Water, Washington,
D.C., September.
67. Viollet, P.-L. (1977) "Study of Jets in Transverse
Currents in Stratified Environments". Doctoral Dissertation,
Curie University, Paris, France, February, 1977. (in French)
68. Wright, S. J. (1977), "Effects of Ambient Crossflovs
and Density Stratification on the Characteristic Behavior
of Round Turbulent Buoyant Jets". Rep. KH-R-36, W.M. Keck
Laboratory of Hydraulics and Water Resources, California
Institute of Technology, Pasadena, Calif.
69. Wong, D. R. (1984), "Buoyant Jet Entrainment in
Stratified Fluids". Ph.D. Thesis, Civil Engineering Dept.,
The University of Michigan, Ann Arbor Mich.
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Appendix A
Stability of Stratified Ambient Shear Plows
Within the context of this study there are several
possibilities for stratification effects superimposed on the
ambient shear flow. The stratification may be present due
to existing environmental conditions, or it may be induced
by the buoyancy of the effluent discharge (i.e. within the
buoyant spreading phase). In either case, a determination
can be made as to whether such stratification (i.e. density
gradient) can in fact be maintained or whether it will be
rapidly eroded by the ambient turbulence.
The flux Richardson number, Rfc, is defined as the ratio
of the buoyant energy flux to the shear energy production
(Tennekes and Lumley, 1972). In terms of the eddy
diffusivitiy convention (Turner, 1973) this can be written
as
Rf= -gkH(dp/dz)/(PkM(du/dz)2) (A.I)
in which k,,, kH = eddy diffusivity for momentum and for a
scalar (heat) , respectively, p = local density, and u is the
local velocity. A critical value of Rfc = 0.10 to 0.20 has
been suggested (Monin and Yaglom, 1971 and Turner, 1973) .
Above this value, turbulence is damped and a stable
stratified profile can be maintained; below this value,
turbulence erodes the density profile and the ambient
environment will become fully mixed.
Jirka (1980) has proposed an adaptation of Eq. (A.I) for
the present shear flow conditions. In the limit of
marginally stable conditions, the eddy diffusivities are of
the same order, k^ ^ ^ (Reynolds analogy). Hence if s is
the existing or the imposed buoyancy gradient, and the
velocity gradient is given by the logarithmic law argument,
(du/dz) = U»/(KHS) in which u* = shear velocity, « = 0.4 =
von Karman constant, and Hs = layer height of the ambient
flow. This leads to
Rf = e/c2Hs2/U«2 (A. 2)
With the Darcy-Weisbach friction law, u* = (f/8)1/2ua, where
f = friction factor, the critical value of the buoyancy
gradient is derived as
ec = cf(ua/Hs)2 (A. 3)
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where c = Rfc/(8«;)2 a o.02. If the actual e < ee then the
stratified shear flow will be unstable and will tend to
rapid mixing.
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APPENDIX B
CORMIX1 SYSTEM ADVICE
B.I Introductory Advice
CORNELL MIXING ZONE EXPERT SYSTEM: GENERAL INFORMATION
The Cornell Mixing Zone Expert System (CORMIX) is a series
of software subsystems for the analysis, prediction and
design of aqueous discharges into watercourses, with
emphasis on the geometry and dilution characteristics of the
initial mixing zone. Subsystem CORMIX1 deals with buoyant
submerged single port discharges into flowing unstratified
or stratified water environments, such as rivers, lake,
estuaries, and coastal waters. It includes the limiting
cases of non-buoyant and negatively buoyant discharges and
of stagnant ambient conditions. Please note that the time
for loading of individual program elements will depend on
the speed of your computer and the size of the program
element. The time for these file operations may range from
a few seconds (IBM PS/2 Model 70, 80386-based) to more than
a minute (IBM PC/XT, 8088-based). Also DOS file
manipulation information is displayed by the system during
program execution and may be neglected by the user.
PROGRAM ELEMENTS: The program elements of CORMIX1 are
listed below. During system use the program elements are
loaded sequentially and automatically in the order given
below.
1) DATIN This is a knowledge base program for the entry
of relevant data about the discharge situation and for
the initialization of the other program elements. DATIN
consist of four subprograms that execute automatically;
each subprogram assembles a data group. You are
presently using DATIN. The four data groups DATIN seeks
are: general identifier information, ambient conditions
(geometry and hydrography), discharge conditions
(geometry and fluxes), and output information desired
including legal mixing zone definitions. After each
subprogam executes, the values for data entered or
concluded are displayed. DATIN is a detailed program
with complete explanations on data preparations,
assumptions and schematizations. DATIN along with the
programs PARAM and CLASS (described below) automatically
creates the files fn.CXD, and HYDRO.CXE where fn is a
user supplied file name. The fn.CXD contains all
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necessary input data for the hydrodynamic simulation
model HYDRO described below. The HYDRO.CXE file
instructs HYDRO which fn.CXD file to load as input for
the current session.
2) PARAM This is a knowledge base program that computes
the relevant physical parameters for the given discharge
situation. Output from PARAM is included in the fn.CXD
file.
3) CLASS This is a knowledge base program that
classifies the given discharge into one of many possible
hydrodynamic configurations, e.g. a boundary attached
discharge, an unstable vertically mixed case, or mixing
controlled by the ambient crossflow. Each separate flow
configuration has a unique alphanumeric label (Example
VI,S5,..). A detailed hydrodynamic description for each
flow configuration is available. Output from CLASS is
contained in the fn.CXD file.
4) HYDRO This is a knowledge base program that executes
the external FORTRAN hydrodynamic program consisting of
a number of simulations subroutines (modules) each
corresponding to a particular hydrodynamic mixing
process. For each flow configuration (Examples: VI,
S5)identified in CLASS, the appropriate modules are
executed sequentially according to a specific protocol.
The program outputs data on geometry (trajectory ,
width, etc.) and associated mixing (dilution,
concentration) following the path of the effluent
discharge. CLASS automatically creates the files fn.CXO
and fn.CXS where fn is the user supplied file name. The
fn.CXO contains the output file data for the HYDRO. The
fn.CXS file is used as input by the final program
segment SUM.
5) SUM This is a knowledge base program that summarizes
the given situation, comments on the mixing
characteristics, evaluates how applicable legal
requirements are satisfied, and suggests possible
design alternatives and improvements.
UNITS OF MEASUREMENT: CORMIX uses the SI system of
measurement, specifically: length in m, mass in kg, time in
s, and temperature in deg C. Furthermore, all pollutant
concentrations are considered without units, i.e. the user
can specify these in any units he/she desires and all output
data must be interpreted accordingly in these same units.
COORDINATE SYSTEM: All predictions in CORMIX1 are displayed
using the following three-dimensional coordinate system:
-The origin is located at the bottom of the water body
vertically below the center of the discharge port.
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-The x-axis is located at the bottom and directed in
the downstream direction following the ambient flow.
-The y-axis is located at the bottom and points to the
left normal to the ambient flow direction (x-axis).
-The z-axis points vertically upward.
B.2 Ambient advice
DATA REQUIREMENTS FOR AMBIENT CONDITIONS: Ambient
conditions are defined by the hydrographic and the geometric
conditions in the vicinity of the discharge. For this
purpose typical cross-sections normal to the ambient flow
direction at the discharge site and further downstream need
to be considered:
A) Bounded cross-section: If the cross-section is bounded
on both sides by banks - as in rivers, streams, narrow
estuaries, and other narrow watercourses -, then the
cross-section is considered "bounded".
B) Unbounded cross-section: In some cases the discharge is
located close to one boundary while the other boundary is
for practical purposes very far away. This would include
discharges into wide lakes, estuaries and coastal areas.
These situations are defined as "unbounded".
A) BOUNDED CROSS-SECTION: Hydrographic information: Data
on the design ambient flow condition - such as average river
discharge or low flow discharge - needs to be available. The
user has the option of entering such data directly as the
discharge or as an average velocity. The ambient density
profile (i.e. the vertical distribution of the ambient water
density) must be approximated. It may be specified as either
uniform (within given limits) or approximated as one of four
simplified profiles. An opportunity for obtaining more
detailed information on these profiles is given later. The
ambient density can be specified directly, or -in case of
freshwater- is computed after specification of the ambient
temperature. Geometric information: CORMIX will conduct
its analysis assuming a rectangular cross-section that is
given by a width and a depth both of which are constant in
the downstream direction following the ambient flow. This
schematization may be quite evident for well-channeled and
regular rivers or artificial channels. For highly irregular
cross-sections, it may require more judgement and experience
- perhaps combined with a repeated use of CORMIX to get a
better feeling on the sensitivity of the results. In any
case, the user is advised to consider the following steps:
1) Be aware that a particular flow condition (such as a
river discharge) is usually associated with a certain water
surface elevation ("stage"). Data for a stage-discharge
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relationship is normally available from a separate hydraulic
analysis or from field measurements.
2) For the given stage-discharge combination display the
cross-section at the discharge location and several
downstream cross-sections. Look over these. Determine an
"equivalent rectangular cross-sectional area". Very shallow
bank areas or shallow floodways may be neglected. Also more
weight should be given to the cross-sections at, arid close
to, the discharge location.
3) Determine the surface width and depth of the equivalent
rectangular area. In case that ambient discharge and ambient
velocity data are available, note that the continuity
relation specifies that discharge = (velocity *
cross-sectional area). The width and depth values thus
chosen need to be specified to CORMIX which will check for
any inconsistencies. Note On Stagnant Conditions: If zero
(or a very small value) for ambient velocity is entered,
CORMIX will label the discharge environment as stagnant. In
this case CORMIX will predict only the near field of the
discharge. Although stagnant conditions represent an extreme
limiting case for dilution prediction, a more realistic
assumption for natural water bodies would be to consider a
finite ambient crossflow, no matter how small. It is
therefore recommended to conduct subsequent analysis with
a small crossflow.
4) As a measure of geometric non-uniformity also specify the
actual maximum depth of the cross-sections (again with more
weight given to the near-discharge cross-sections).
5) As a measure of the roughness characteristics in the
channel the value of the Manning "n", or alternatively of
the Darcy-Weisbach friction factor "f", must be specified.
These parameters influence the mixing process only in the
final stage considered by CORMIX and are not very sensitive
to the predictions. Generally, if these values are assumed
known within +-30% the predictions will vary by +-10% at the
most.
B)UNBOUNDED CROSS-SECTIONS: Both hydrographic and geometric
information are closely linked in this case:
1) Determine the water elevation (given by lake or reservoir
elevation or tidal stage etc.) for which the analysis should
be conducted.
2) Assemble cross-sectional profiles that plot water depth
as a function of distance from the shore for the discharge
location and for several positions downstream following the
ambient current direction.
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3) a) If detailed hydrographic data (from field surveys or
from some hydraulic numerical model calculations) are
available, determine the cumulative ambient discharge from
the shore to the discharge location for the discharge
cross-section. For each of the subsequent downstream
cross-sections determine the distance from the shore at
which the same cumulative ambient discharge has been
attained.Mark this position on all cross-sectional profiles.
Now consider the velocity (vertically averaged) and the
depth at these positions. Specify to CORMIX a typical
ambient velocity and a typical depth from these data by
giving most weight to the conditions at, and close to, the
discharge location. Specify a typical distance from the
shore by dividing the cumulative ambient discharge by
(ambient velocity * depth).
3b) If detailed hydrographic data is not available - but at
least data, or estimates, on the vertically averaged
velocity at the discharge location must be available! -
then determine the cumulative cross- sectional area from
the shore to the discharge location for the discharge
cross-section.For each of the subsequent downstream
cross-sections, mark the position where the cumulative
cross-sectional area has the same value as at the discharge
cross-section. Determine the typical ambient velocity and
the typical ambient depth at these positions with most
weight given to conditions at, or close to, the discharge
location. Specify the typical distance from the shore by
dividing the cumulative cross-sectional area by the ambient
depth.
4) In summary, CORMIX will conduct its analysis for the
unbounded case by assuming an "equivalent rectangular
cross-sectional area" defined by depth, by distance from
one bank to the discharge position, and by ambient
velocity. Note the similarities to the bounded case
discussed above. As for the bounded cross-section, the
ambient density profile (i.e. the vertical distribution of
the ambient water density) must be approximated. It may be
specified as either uniform (within given limits) or
approximated as one of four simplified profiles. An
opportunity for obtaining more detailed information on these
profiles is given later.The ambient density can be
specified directly, or -in case of a freshwater ambient -
is computed by specification of the ambient temperature.
5) As a measure of the roughness characteristics of the flow
area the value of the Manning "n", or alternatively of the
Darcy-Weisbach friction factor "f", must be specified.
These parameters influence the mixing process only in the
final stage considered by CORMIX and are not very sensitive
to the predictions. Generally, if these values are assumed
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known within +-30% the predictions will vary by +-10% at the
most.
B.3 Density Profile Advice
SPECIFICATION OF AMBIENT DENSITY STRATIFICATION:
Since the ambient density is not uniform over the water
column, the actual vertical density distribution - as
determined by field data - must be approximated by one of
the schematic stratification types. These are:
Type A: Linear Density Profile
Type B: Two-Layer System With Constant Densities and Density
Jump
Type C: Constant Density Surface Layer with Linear Density
Profile in Bottom Layer Separated by a Density Jump
Type D: Constant Density Surface Layer With Linear Density
Profile in Bottom Layer Without a Density Jump
Brief sketches for these four stratification types follow
below. Note that a dynamically correct approximation of the
actual distribution should keep a balance between over - and
under - estimation of the actual data similar to a best-fit
in regression analysis. It is desirable to test through
repeated use of CORMIX different approximations (i.e. with
different stratification types and/or parameter values) in
order to evaluate the sensitivity of the resulting model
predictions.
B.4 Discharge Advice
ADVICE FOR SPECIFYING DISCHARGE CHARACTERISTICS
SINGLE PORT DISCHARGE DISCHARGE GEOMETRY:
1) In most cases, the port or nozzle geometry will be round
so that the radius or diameter must be specified. If not,
then the cross-sectional area must be specified.
2) Specify the height of the port center above the bottom.
3) The vertical angle of discharge is the angle between the
port centerline and a horizontal plane, in CORMIX1 this
angle may range between -45 deg and 90.0 deg. As examples,
the vertical angle is 90 deg for a discharge pointing
vertically upward, and it is 0 deg for a horizontal
discharge.
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4) Consider a plan view of the discharge situation as seen
from above. The horizontal angle of discharge is the angle
measured counterclockwise from the ambient current direction
(x-axis) to the plan projection of the port centerline. In
CORMIX1 this angle may range between 0 deg and 360 deg. As
examples, the horizontal angle is 0 deg if the port points
downstream with the ambient flow, it is 90 deg if it points
to the left of the ambient flow, it is 180 deg if it points
upstream opposing the ambient flow, and it is 270 deg if it
points to the right of the ambient flow, respectively.
DISCHARGE FLOW VARIABLES:
1) The discharge flow rate or the discharge velocity should
be specified. Note that these two variables are related
through the port diameter or cross-sectional area.
2) The discharge density can be specified directly, or -in
case of an essentially freshwater discharge in which the
addition of any pollutant or tracer has negligible effect
on density - it is computed after specification of the
discharge temperature.
3) The discharge concentration of the material of interest
(pollutant, tracer, or temperature) is defined as the excess
concentration above any ambient concentration. The user can
specify this quantity in any units and the CORMIX1 results
for computed excess concentrations should then be
interpreted in these same units.
B.5 Mixing Zone Advice
SPECIFICATION OF DESIRED MIXING ZONE INFORMATION:
The user must specify data that indicates over which spatial
region information will be desired, and in what detail.
Legal mixing zone (LMZ) requirements may exist or not. The
user has several options for this specification:
1) LEGAL MIXING ZONE (LMZ): Options exist for specifying the
legal mixing zone as a maximum distance from the discharge
location, or as a maximum cross-sectional area occupied by
the plume, or as the maximum width of the effluent plume.
2) REGION OF INTEREST (ROI): When legal mixing zone
restrictions do not exist or when the user is interested in
information over a larger area, then a region of interest
must be specified as the maximum distance in the direction
of mixed effluent flow.
3) HYDRODYNAMIC MIXING ZONE (HMZ) : In all cases, CORMIX will
label a usually smaller initial region in which
discharge-induced mixing takes place as the "hydrodynamic
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mixing zone". The dilution conditions in the HMZ may be a
useful measure for the outfall designer when attempting to
optimally design the discharge conditions.
4) TOXIC DILUTION ZONE (TDZ): For all discharges that have
been designated as toxic by USEPA standards (Technical
Support Document for Water Quality- Based Toxics Control,
USEPA, 1985) CORMIX will automatically define the
concentration values at the edge of the toxic dilution zone
as defined in that document. CORMIX will indicate if the
criterion maximum concentration (CMC) standard has been met.
After all applicable data have been specified on these
zones, CORMIX also needs information on the level of detail
for the output data within these zones and, simultaneously,
within all the hydrodynamic elements (modules) that may
occupy these zones.
B.6 Design Advice
A reliable environmental analysis and mixing zone prediction
is possible only if each design case is evaluated through
several iterations of CORMIX1. Small changes in ambient or
discharge design conditions can sometimes cause drastic
shifts in the applicable flow configuration (flow class) and
the size or appearance of mixing zones. Iterative use of
CORMIX1 will give information on the sensitivity of
predicted results on design and ambient conditions.Each
predictive case should be carefully assessed as to: - size
and shape of LMZ - conditions in the TDZ (if present)-
bottom impact of the discharge flow - water surface
exposure- bank attachment, and other factors. In general,
iteration should be conducted in the following order:
A) Discharge design changes (geometry variations)
B) Sensitivity to ambient conditions
C) Discharge flow changes (process variations)
When investigating these variations the CORMIX1 user will
quickly appreciate the fact that mixing conditions at short
distances (near-field) are usually quite sensitive and
controllable. In contrast, mixing conditions at large
distances (far-field) often show little sensitivity unless
the ambient conditions change substantially or drastic
process variations are introduced.
A) DISCHARGE DESIGN CHANGES (GEOMETRY VARIATIONS): Most of
the following recommendations are motivated by the desire
of improving conditions in the applicable mixing zones (i.e.
minimizing concentrations and/or areal extent).
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1) Outfall location: Consider moving the discharge
farther offshore to a larger water depth in order to
delay flow interaction with the bank and/or surface, and
to improve near-field mixing.
2) Height of discharge port: For positively buoyant or
neutral discharges it is usually desirable to minimize
the port height in order to provide a low submerged
jet/plume trajectory. However, if the port height is
too small undesirable flow bottom attachment may result.
A typical range for port heights is from two to ten
diameters. For negatively buoyant discharges, on the
other hand, it may be desirable to maximize the port
height. Navigational requirements may put further limits
on large port heights.
3) Vertical angle of discharge: Near-field dilution for
positively or neutrally buoyant discharges is often
improved by providing a near-horizontal discharge. In
order to prevent bottom interference a slight upward
orientation (in the range of +15 to +30 degrees) may be
advisable. In contrast, a vertical or near-vertical
angle may be favorable for negatively buoyant
discharges.
4) Horizontal angle of discharge: This angle provides
the discharge orientation relative to the ambient
current. A co-flow design (angle of about 0 degrees)
or a cross-flow design (about 90 or 270 degrees,
respectively) are preferable. A counter-flow design
(about 180 degrees) is undesirable from the viewpoint
of mixing zone predictability and bottom impacts.
Cross-flow designs may be particularly effective in
optimizing near-field mixing, and if they are chosen,
the port should point in the offshore direction.
5) Port diameter/area (discharge velocity): Remember
that for a given discharge flow rate the port area and
discharge velocity are inversely related: a small
discharge port implies a high discharge velocity, and
a consequently high discharge momentum flux. Typically,
a high velocity discharge will maximize near-field
mixing. Note, however, that high velocity discharges
a) may lead to unstable near-field flow configurations
perhaps involving undesirable mixing patterns, and b)
usually have little, if any, effect on dilutions over
the far-field where a LMZ may apply.Discharge velocities
in typical engineering designs may range from 3 m/s to
8 m/s. Very high velocities may lead to excessive
pumping energy requirements. Very low velocities (less
than 0.5 m/s) may lead to undesirable sediment
accumulation within the discharge pipe.
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B) SENSITIVITY TO AMBIENT CONDITIONS:Variations - of the
order of 10 percent - of the following ambient design
conditions should be considered:- ambient velocity (or
ambient flowrate) - ambient depth (or river/tidal stage)
ambient density structure (notably density
differences)Such variability is important for two reasons:
1) the usual uncertainty in ambient environmental data,
2) the schematization employed by CORMIX1 Please refer
to the detailed advice on the specification of
environmental data, including the density structure,
that is available in program element DATIN. In
particular, note the advisory comments on stagnant
ambient conditions.
C) DISCHARGE FLOW CHANGES (PROCESS VARIATIONS): Actual
process changes can result in variations of one or more of
three parameters associated with the discharge: flowrate,
density, or pollutant concentration. In some cases, such
process changes may be difficult to achieve or too costly.
Note, that "off-design" conditions in which a discharge
operates below its full capacity also fall into this
category.
1) Pollutant mass flux: The total pollutant mass flux
is the product of discharge flow (m**3/s) times the
discharge pollutant concentration (in arbitrary units).
Thus, decreasing the pollutant mass flux will, in
general, decrease the resulting pollutant concentration
in the near-field and far-field. This occurs, of
course, during off-design conditions.
2) Discharge flow: For a given pollutant mass flux, an
increase in discharge flow implies an increase in
discharge pollutant concentration,and vice versa. For
the variety of flow classes contained in CORMIX1 there
is no universal rule whether high or low volume
discharges are preferable for optimizing near-field
mixing. Mostly, the sensitivity is small, and even more
so for far-field effects. Note that a change in
discharge flow will influence in turn the discharge
velocity and hence momentum flux.
3) Discharge density: The actual density of the
discharge flow controls the buoyancy effects relative
to the ambient water. Occasionally, the discharge
density is controllable through the amount of process
heating or cooling occurring prior to discharge.
Usually, near-field mixing is enhanced by maximizing
the total density difference (positive or negative)
between discharge flow and ambient water. In most cases,
however, this effect is minor.
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APPENDIX C
Flow Classification Descriptions
C.I V-Flow Classes
FLOW CLASS VI
A submerged buoyant effluent issues vertically or
near-vertically from the discharge port.
The discharge configuration is hydrodynamically "stable",
that is the discharge strength (measured by its momentum
flux) is weak in relation to the layer depth and in relation
to the stabilizing effect of the discharge buoyancy
(measured by its buoyancy flux).
The following flow zones exist:
I) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Buoyancy-dominated near-field plume: After some distance
the discharge buoyancy becomes the dominating factor
(plume-like). The plume deflection by the ambient current
is still weak.
Alternate possibility: Depending on the ratio of the jet to
crossflow length scale to the plume to crossflow length
scale the above zone may be replaced by a momentum-dominated
far-field jet:
2) Momentum-dominated far-field jet: The jet has become
strongly deflected by the ambient current.
3) Buoyancy-dominated far-field plume: The plume has been
strongly deflected by the current and is slowly rising
toward the surface.
4) Layer boundary approach: The bent-over submerged
jet/plume approaches the layer boundary (water surface or
pycnocline) . Within a short distance the concentration
distribution becomes relatively uniform across the plume
width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
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5) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The
plume thickness may decrease during this phase. The mixing
rate is relatively small. The plume may interact with a
nearby bank or shoreline.
6) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 5 or 6 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
FLOW CLASS V2
A submerged buoyant effluent issues vertically or
near-vertically from the discharge port. The discharge
configuration is hydrodynamically "stable", that is the
discharge strength (measured by its momentum flux) is weak
in relation to the layer depth. The discharge buoyancy
plays a minor role in this case. The following flow zones
exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Momentum-dominated far-field jet: The jet has become
strongly deflected by the ambient current and is slowly
rising toward the surface.
3) Layer boundary approach: The bent-over submerged
jet/plume approaches the layer boundary (water surface or
pycnocline). Within a short distance the concentration
distribution becomes relatively uniform across the plume
width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase. The mixing rate
is relatively small. The plume may interact with a nearby
bank or shoreline.
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5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST.***
SPECIAL CASE: If discharge is non-buoyant, then the layer
boundary buoyant spreading regime (zone 4) is absent.
PLOW CLASS V3
A submerged buoyant effluent issues vertically or
near-vertically from the discharge port. The discharge
configuration is hydrodynamically "stable", that is the
discharge strength (measured by its momentum flux) is weak
in relation to the layer depth and in relation to the
stabilizing effect of the discharge buoyancy (measured by
its buoyancy flux). The buoyancy effect is very strong in
the present case. The following flow zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Buoyancy-dominated near-field plume: After some distance
the discharge buoyancy becomes the dominating factor
(plume-like). The plume deflection by the ambient current
is still weak.
3) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary (water surface
or pycnocline) at a near-vertical angle. After impingement
the flow spreads more or less radially along the layer
boundary. 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 zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place. ***
4) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase. The mixing rate
is relatively small. The plume may interact with a nearby
bank or shoreline.
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5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
PLOW CLASS V4
A submerged buoyant effluent issues vertically or
near-vertically from the discharge opening. The discharge
configuration is hydrodynamically "unstable", that is the
discharge strength (measured by its momentum flux) dominates
the flow in relation to the limited layer depth. The role
of buoyancy is secondary. The following flow zones exist:
1) Momentum-dominated near-field jet: The flow is dominated
by the effluent momentum (jet-like) and is weakly deflected
by the ambient current.
2) Layer boundary impingement/full vertical mixing: The
weakly bent jet impinges on the layer boundary (water
surface or pycnocline) at a near-vertical angle. Given the
shallow layer depth and the weak buoyancy of the discharge,
the flow becomes unstable after impingement. This results
in a recirculating region immediately downstream that
extends over the full layer depth.
3) Passive ambient mixing: The vertically fully mixed plume
is further advected by the ambient flow and spreads
laterally through ambient diffusion. The plume may interact
with a nearby bank or shoreline.
***The ambient flow plays an important role in this flow
configuration. Hence, all the zones listed above constitute
the HYDRODYNAMIC MIXING ZONE with strong initial mixing.
Predictions will be terminated in zone 3 depending on the
definitions of the LEGAL MIXING ZONE or the REGION OF
INTEREST. ***
FLOW CLASS V5
A submerged buoyant effluent issues vertically or
near-vertically from the discharge port. The discharge
configuration is hydrodynamically "stable", that is the
discharge strength (measured by its momentum flux) is weak
in relation to the layer depth and in relation to the
stabilizing effect of the discharge buoyancy (measured by
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its buoyancy flux). The buoyancy effect is very strong in
the present case. The following flow zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Buoyancy-dominated near-field plume: After some distance
the discharge buoyancy becomes the dominating factor
(plume-like). The plume deflection by the ambient current
is still weak.
3) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary (water surface
or pycnocline) at a near-vertical angle. After impingement
the flow spreads more or less radially along the layer
boundary. 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 zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase. The mixing rate
is relatively small. The plume may interact with a nearby
bank or shoreline.
5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST.***
SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion by the ambient flow (zones 4 and 5) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a given site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
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FLOW CLASS V6
A submerged buoyant effluent issues vertically or
near-vertically from the discharge port. The discharge
configuration is hydrodynamically "unstable", that is the
discharge strength (measured by its momentum flux) dominates
the flow in relation to the limited layer depth and in
relation to the weak stabilizing effect of the discharge
buoyancy (measured by its buoyancy flux). However, the
buoyancy is generally strong enough to affect the flow at
larger distances downstream from the unstable initial
region. The following flow zones exist:
1) Unstable recirculation/buoyant restratification/upstream
spreading: The buoyant jet rises near-vertically and
impinges on the layer boundary (water surface or
pycnocline). After impingement the mixed flow recirculates
over the limited layer depth and becomes partially
re-entrained into the discharge jet. The degree of
recirculation - and hence the overall mixing in this region
- is controlled by restratification of the flow at the edge
of this recirculating region. The restratified flow spreads
along the layer boundary. In particular, the flow spreads
some distance upstream against the ambient current, and
laterally across the ambient flow.
*** The region described above constitutes the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
2) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase. The mixing rate
is relatively small. The plume may interact with a nearby
bank or shoreline.
3) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 2 or 3 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST.***
SPECIAL CASE: If the ambient is stagnant, so that advection
and diffusion by the ambient flow (zones 2 and 3) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zone 1) and the predictions will be terminated at this
stage. Such stagnant water predictions may be a useful
initial mixing indicator for a given site and discharge
design. For practical final predictions, however, the
209
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advection and diffusion of the ambient flow - no matter how
small in magnitude - should be considered.
SPECIAL SPECIAL CASE: If, in addition, the discharge is non-
buoyant, then no steady-state behavior is possible in this
case. The repeated recirculation in the near-field will lead
to an unsteady concentration build-up. This would be an
UNDESIRABLE discharge design, and no reliable predictive
techniques exist for this situation.
CORMIX1 WILL NOT PROVIDE A DETAILED PREDICTION FOR THIS
CASE.
C.2 H-Flow Classes
FLOW CLASS HI
A submerged buoyant effluent issues horizontally or near-
horizontally from the discharge port. The discharge
configuration is hydrodynamically "stable", that is the
discharge strength (measured by its momentum flux) is weak
in relation to the layer depth and in relation to the
stabilizing effect of the discharge buoyancy (measured by
its buoyancy flux). The following flow zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Buoyancy-dominated near-field plume: After some distance
the discharge buoyancy becomes the dominating factor
(plume-like). The plume deflection by the ambient current
is still weak. Alternate possibility: Depending on the ratio
of the jet to crossflow length scale to the plume to
crossflow length scale the above zone may be replaced by
a momentum-dominated far-field jet:
2) Momentum-dominated far-field jet: The jet has become
strongly deflected by the ambient current.
3) Buoyancy-dominated far-field plume: The plume has been
strongly deflected by the current and is slowly rising.
4) Layer boundary approach: The bent-over submerged
jet/plume approaches the layer boundary (water surface or
pycnocline). Within a short distance the concentration
distribution becomes relatively uniform across the plume
width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
210
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5) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase. The mixing rate
is relatively small. The plume may interact with a nearby
bank or shoreline.
6) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 5 or 6 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
FLOW CLASS H2
A submerged buoyant effluent issues horizontally or near-
horizontally from the discharge point. The discharge
configuration is hydrodynamically "stable", that is the
discharge strength (measured by its momentum flux) is weak
in relation to the layer depth. The discharge buoyancy
plays a minor role in this case. The following flow zones
exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Momentum-dominated far-field jet: The jet has become
strongly deflected by the ambient current and is slowly
rising.
3) Layer boundary approach: The bent-over submerged
jet/plume approaches the layer boundary (water surface or
pycnocline). Within a short distance the concentration
distribution becomes relatively uniform across the plume
width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place. ***
4) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase. The mixing rate
is relatively small. The plume may interact with a nearby
bank or shoreline.
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5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
SPECIAL CASE: If discharge is non-buoyant, then the layer
boundary buoyant spreading regime (zone 4) is absent.
FLOW CLASS H3
A submerged buoyant effluent issues horizontally or near-
horizontally from the discharge port. The discharge
configuration is hydrodynamically "stable", that is the
discharge strength (measured by its momentum flux) is weak
in relation to the layer depth and in relation to the
stabilizing effect of the discharge buoyancy (measured by
its buoyancy flux). The buoyancy effect is very strong in
the present case. The following flow zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Buoyancy-dominated near-field plume: After some distance
the discharge buoyancy becomes the dominating factor
(plume-like). The plume deflection by the ambient current
is still weak.
3) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary (water surface
or pycnocline) at a near-vertical angle. After impingement
the flow spreads more or less radially along the layer
boundary. 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 zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase. The mixing rate
is relatively small. The plume may interact with a nearby
bank or shoreline.
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5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
FLOW CLASS H4-0
A submerged buoyant effluent issues horizontally or near-
horizontally from the discharge port. The discharge is
co-flowing or nearly co-flowing with the ambient current.
The discharge configuration is hydrodynamically "stable",
that is the discharge strength (measured by its momentum
flux) is weak in relation to the layer depth and in
relation to the stabilizing effect of the discharge
buoyancy (measured by its buoyancy flux). The buoyancy
effect is very strong in the present case. This discharge
configuration is very susceptible to attachment of the
jet/plume to the bottom of the receiving water. The
following flow zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
advected by the ambient current.
2) Buoyancy-dominated near-field plume: After a short
distance the discharge buoyancy becomes the dominating
factor (plume-like). The plume rises upward while the
advection by the ambient current is still weak.
3) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary (water surface
or pycnocline) at a near-vertical angle. After impingement
the flow spreads more or less radially along the layer
boundary. 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 zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The
plume thickness may decrease during this phase. The mixing
rate is relatively small. The plume may interact with a
nearby bank or shoreline.
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5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion by the ambient flow (zones 4 and 5) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a given site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
FLOW CLASS H4-90
A submerged buoyant effluent issues horizontally or near-
horizontally from the discharge port. The discharge is at,
or approximately at, a right angle with the ambient current.
The discharge configuration is hydrodynamically "stable",
that is the discharge strength (measured by its momentum
flux) is weak in relation to the layer depth and in relation
to the stabilizing effect of the discharge buoyancy
(measured by its buoyancy flux). The buoyancy effect is very
strong in the present case. This discharge configuration is
very susceptible to attachment of the jet/plume to the
bottom of the receiving water. The following flow zones
exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
advected by the ambient current.
2) Buoyancy-dominated near-field plume: After a short
distance the discharge buoyancy becomes the dominating
factor (plume-like). The plume rises upward while the
advection by the ambient current is still weak.
3) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary (water surface
or pycnocline) at a near-vertical angle. After impingement
the flow spreads more or less radially along the layer
boundary. In particular, the flow spreads some distance
upstream against the ambient flow, and laterally across the
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ambient flow. This spreading is dominated by the strong
buoyancy of the discharge.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase. The mixing rate
is relatively small. The plume may interact with a nearby
bank or shoreline.
5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion by the ambient flow (zones 4 and 5) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a given site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
FLOW CLASS H4-180
A submerged buoyant effluent issues horizontally or near-
horizontally from the discharge port. The discharge is
directly opposed (or approximately so) to the direction of
the ambient current. This is a highly complicated and
UNDESIRABLE discharge configuration. Generally, the
upstream issuing jet may exhibit an unsteady pulsating
pattern with potential attachment to the bottom. There is
no reliable prediction methodology for this flow.
CORMIX1 WILL NOT PROVIDE A DETAILED PREDICTION FOR THIS
CASE.
FLOW CLASS H5-0
A submerged buoyant effluent issues horizontally or near-
horizontally from the discharge port. The discharge is
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co-flowing, or nearly co-flowing, with the ambient flow.
The discharge configuration is hydrodynamically "unstable",
that is the discharge strength (measured by its momentum
flux) dominates the flow in relation to the limited layer
depth. The effect of buoyancy is negligible and the initial
discharge is usually attached to the bottom. The following
flow zones exist:
1) Momentum-dominated near-field jet (bottom-attached): The
flow is dominated by the effluent momentum (jet-like). The
jet attaches to the bottom and is weakly advected by the
ambient flow.
2) Layer boundary contact/full vertical mixing: After some
distance the jet has grown vertically over the full layer
depth. From now on the flow is vertically mixed and
generally ceases to be jet-like.
3) Passive ambient mixing: The vertically fully mixed plume
is further advected by the ambient flow and spreads
laterally through turbulent diffusion. The plume may
interact laterally with any nearby bank or shoreline.
*** The ambient flow plays an important role in this flow
configuration. Hence, all the zones listed above constitute
the HYDRODYNAMIC MIXING ZONE with strong initial mixing.
Predictions will be terminated in zone 3 depending on the
definitions of the LEGAL MIXING ZONE or the REGION OF
INTEREST. ***
SPECIAL CASE: If the ambient is stagnant, so that advection
and diffusion by the ambient flow (zone 3) cannot be
considered. The mixing is limited to the discharge-induced
mixing zones (zones 1 and 2) and the predictions will be
terminated at this stage. Such predictions will present a
conservative lower bound on the mixing capacity as they
neglect any further mixing beyond the stage where the jet
has grown to the full layer depth. Such stagnant water
predictions may be a useful initial mixing indicator for a
given site and discharge design. For practical final
predictions, however, the advection and diffusion of the
ambient flow - no matter how small in magnitude - should be
considered.
FLOW CLASS H5-90
A submerged buoyant effluent issues horizontally or near-
horizontally from the discharge port. The discharge is at,
or approximately at, a right angle with the ambient current.
The discharge configuration is hydrodynamically "unstable",
that is the discharge strength (measured by its momentum
flux) dominates the flow in relation to the limited layer
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depth. The effect of buoyancy is negligible and the initial
discharge is usually attached to the bottom. This is a
highly complicated and UNDESIRABLE discharge configuration.
The laterally discharging jet the tends to full vertical
mixing and will block the ambient flow. This will cause a
recirculating eddy region downstream of the discharge. There
is no reliable prediction methodology for this flow.
CORMIX1 WILL NOT PROVIDE A DETAILED PREDICTION FOR THIS
CASE.
FLOW CLASS H5-1SO
A submerged buoyant effluent issues horizontally or near-
horizontally from the discharge port. The discharge is
directly opposed, or nearly opposed, to the direction of
the ambient current. The discharge configuration is
hydrodynamically "unstable", that is the discharge strength
(measured by its momentum flux) dominates the flow in
relation to the limited layer depth. The effect of buoyancy
is negligible and the initial discharge is usually attached
to the bottom. This is a highly complicated and UNDESIRABLE
discharge configuration. Generally, the upstream issuing
jet may exhibit an unsteady pulsating pattern and blocking
of the ambient flow over the full water depth. There is no
reliable prediction methodology for this flow.
CORMIX1 WILL NOT PROVIDE A DETAILED PREDICTION FOR THIS
CASE.
C.3 S-Flow Classes
FLOW CLASS SI
This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly jet-like
flow gets trapped at some terminal (equilibrium) level. The
trapping is also affected by the reasonably strong ambient
crossflow. Following the trapping zone, the discharge flow
forms an internal layer that is further influenced by
buoyant spreading and passive diffusion. The following flow
zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Momentum-dominated far-field jet: The jet has become
strongly deflected by the ambient current and is slowly
rising toward the trapping level.
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3) Terminal layer approach: The bent-over submerged
jet/plume approaches the terminal level. Within a short
distance the concentration distribution becomes relatively
uniform across the plume width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading in internal layer: The discharge flow
within the internal layer spreads laterally while it is
being advected by the ambient current. The plume thickness
may decrease during this phase. The mixing rate is
relatively small. The plume may interact with a nearby bank
or shoreline.
5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the upper
layer boundary, channel bottom and/or banks.
*** Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
FLOW CLASS 82
This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly jet-like
flow issues vertically, or near-vertically, upward and gets
trapped at some terminal (equilibrium) level. The crossflow
is weak in the present situation. Following the trapping
zone, the discharge flow forms an internal layer that is
further influenced by buoyant spreading and passive
diffusion. The following flow zones exist:
1) Momentum-dominated near-field jet in linear
stratification: The flow is initially dominated by the
effluent momentum (jet-like) and is weakly deflected by the
ambient current and the density stratification.
2) Terminal layer impingement/upstream spreading: The weakly
bent jet/plume approaches (impinges) the terminal layer at
a near- vertical angle, and may overshoot that level to some
extent. After impingement the flow spreads more or less
radially at the terminal level forming an internal layer.
In particular, the flow spreads some distance upstream
against the ambient flow, and laterally across the ambient
flow. This spreading is dominated by the buoyant collapse
of the internal layer within the linear ambient
stratification.
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*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
3) Buoyant spreading in internal layer: The discharge flow
within the internal layer spreads laterally while it is
being advected by the ambient current. The plume thickness
may decrease during this phase. The mixing rate is
relatively small. The plume may interact with a nearby bank
or shoreline.
4) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the upper
layer boundary, channel bottom and/or banks.
*** Predictions will be terminated in zone 3 or 4 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST.***
SPECIAL CASE: If the ambient is stagnant, then advection
and diffusion by the ambient flow (zones 3 and 4) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 and 2) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a given site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
FLOW CLASS S3
This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly jet-like
flow issues horizontally, or near-horizontally, into the
density stratified layer and gets trapped at some terminal
(equilibrium) level. The crossflow is weak in the present
situation. Following the trapping zone, the discharge flow
forms an internal layer that is further influenced by
buoyant spreading and passive diffusion. The following
flow zones exist:
1) Momentum-dominated near-field jet in linear
stratification: The flow is initially dominated by the
effluent momentum (jet-like) and is weakly deflected by the
ambient current and the density stratification.
2) Terminal layer injection/upstream spreading: The weakly
bent jet/plume approaches (injects into) the terminal layer
at a near- horizontal angle. After injection the flow
spreads more or less radially at the terminal level forming
an internal layer. The residual horizontal momentum flux
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within the jet affects that spreading process. In
particular, the flow spreads some distance upstream against
the ambient flow, and laterally across the ambient flow.
This spreading is dominated by the buoyant collapse of the
internal layer within the linear ambient stratification.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
3) Buoyant spreading in internal layer: The discharge flow
within the internal layer spreads laterally while it is
being advected by the ambient current. The plume thickness
may decrease during this phase. The mixing rate is
relatively small. The plume may interact with a nearby bank
or shoreline.
4) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the upper
layer boundary, channel bottom and/or banks.
*** Predictions will be terminated in zone 3 or 4 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
SPECIAL CASE: If the ambient is stagnant, then advection
and diffusion by the ambient flow (zones 3 and 4) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 and 2) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a given site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
FLOW CLASS S4
This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly plume-like
flow gets trapped at some terminal (equilibrium) level. The
trapping is also affected by the reasonably strong ambient
crossflow. Following the trapping zone, the discharge flow
forms an internal layer that is further influenced by
buoyant spreading and passive diffusion. The following flow
zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
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2) Momentum-dominated far-field jet: The jet has become
strongly deflected by the ambient current.
3) Buoyancy-dominated far-field plume: After some distance,
the plume buoyancy starts to affect the flow. The plume is
strongly deflected by the current and is slowly rising
toward the terminal level.
4) Terminal layer approach: The bent-over submerged
jet/plume approaches the terminal level. Within a short
distance the concentration distribution becomes relatively
uniform across the plume width and thickness.
***The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
5) Buoyant spreading in internal layer: The discharge flow
within the internal layer spreads laterally while it is
being advected by the ambient current. The plume thickness
may decrease during this phase. The mixing rate is
relatively small. The plume may interact with a nearby bank
or shoreline.
6) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the upper
layer boundary, channel bottom and/or banks.
*** Predictions will be terminated in zone 5 or 6 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
PLOW CLASS S5
This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly plume-like
flow rises vertically upward and gets trapped at some
terminal equilibrium level. The crossflow is weak in the
present situation. Following the trapping zone, the
discharge flow forms an internal layer that is further
influenced by buoyant spreading and passive diffusion. The
following flow zones exist:
1) Momentum-dominated near-field jet in linear
stratification: The flow is initially dominated by the
effluent momentum (jet-like) and is weakly deflected by the
ambient current and the density stratification.
2) Buoyancy-dominated near-field plume in linear
stratification: After some distance, the flow becomes
dominated by the effluent buoyancy (plume-like) and is
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weakly affected by the ambient current and the density
stratification.
3) Terminal layer impingement/upstream spreading: The weakly
bent jet/plume approaches (impinges) the terminal layer at
a near- vertical angle, and may overshoot that level to some
extent. After impingement the flow spreads more or less
radially at the terminal level forming an internal layer.
In particular, the flow spreads some distance upstream
against the ambient flow, and laterally across the ambient
flow. This spreading is dominated by the buoyant collapse
of the internal layer within the linear ambient
stratification.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading in internal layer: The discharge flow
within the internal layer spreads laterally while it is
being advected by the ambient current. The plume thickness
may decrease during this phase. The mixing rate is
relatively small. The plume may interact with a nearby bank
or shoreline.
5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the upper
layer boundary, channel bottom and/or banks.
*** Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion by the ambient flow (zones 4 and 5) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a given site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
C.4 NV-Plow Classes
FLOW CLASS NV1
A submerged negatively buoyant effluent issues vertically
or near- vertically from the discharge port. The effect of
ambient velocity is relatively strong. The discharge
configuration is hydrodynamically "stable", that is the
discharge strength (measured by its momentum flux) is weak
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in relation to the layer depth and in relation to the
stabilizing effect of the negative discharge buoyancy
(measured by its buoyancy flux). The following flow zones
exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the upward effluent momentum (jet-like) and is
weakly deflected by the ambient current.
2) Momentum-dominated far-field jet: The jet becomes
strongly deflected by the ambient current. It rises to a
maximum height, less than the layer depth, which is
controlled by the opposing action of the negative buoyancy.
3) Buoyancy-dominated far-field plume: After the maximum
height of rise, the negative discharge buoyancy becomes the
dominating factor giving plume-like flow. The strongly
deflected plume is slowly descending toward the bottom.
4) Bottom approach: The bent-over submerged plume approaches
the bottom boundary. Within a short distance the
concentration distribution becomes relatively uniform
across the plume width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
5) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being advected by the
ambient current. The plume thickness may decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline.
6) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the layer
surface and/or banks.
*** Predictions will be terminated in zone 5 or 6 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
FLOW CLASS NV2
A submerged negatively buoyant effluent issues vertically
or near- vertically from the discharge port. The effect of
ambient velocity is weak. The discharge configuration is
hydrodynamically "stable", that is the discharge strength
(measured by its momentum flux) is weak in relation to the
layer depth and in relation to the stabilizing effect of the
223
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negative discharge buoyancy (measured by its buoyancy flux) .
The following flow zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the upward effluent momentum (jet-like) and is
weakly deflected by the ambient current. It rises to a
maximum height, less than the layer depth, which is
controlled by the opposing action of the negative buoyancy.
2) Buoyancy-dominated near-field plume: After the maximum
height of rise, the negative discharge buoyancy becomes the
dominating factor (plume-like flow). The strongly deflected
plume is rapidly falling toward the bottom.
3) Bottom boundary impingement/upstream spreading: The
weakly bent jet/plume impinges on the bottom boundary at a
near-vertical angle. After impingement the flow spreads more
or less radially along the bottom. 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 zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being advected by the
ambient current. The plume thickness may decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline.
5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the layer
surface and/or banks.
*** Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion by the ambient flow (zones 4 and 5) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a giv^n site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
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FLOW CLASS NV3
A submerged negatively buoyant effluent issues vertically
or near- vertically from the discharge port. The effect of
ambient velocity is relatively strong. The discharge
configuration is hydrodynamically "stable", that is the
discharge strength (measured by its momentum flux) is weak
in relation to the layer depth and in relation to the
stabilizing effect of the negative discharge buoyancy
(measured by its buoyancy flux). The following flow zones
exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the upward effluent momentum (jet-like) and is
weakly deflected by the ambient current.
2) Momentum-dominated far-field jet: The jet becomes
strongly deflected by the ambient current.
3) Layer boundary approach: The bent-over submerged
jet/plume approaches the layer boundary (water surface or
pycnocline). Within a short distance the concentration
distribution becomes relatively uniform across the plume
width and thickness.
4) Fall down: Because of the negative buoyancy the plume
detaches from the layer boundary and starts to descend
toward the bottom.
5) Buoyancy-dominated far-field plume: After the maximum
height of rise, the negative discharge buoyancy becomes the
dominating factor giving plume-like flow. The strongly
deflected plume is slowly descending toward the bottom.
6) Bottom approach: The bent-over submerged plume approaches
the bottom boundary. Within a short distance the
concentration distribution becomes relatively uniform across
the plume width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
7) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being advected by the
ambient current. The plume thickness may decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline.
8) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
225
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in depth and in width. The plume may interact with the layer
surface and/or banks.
*** Predictions will be terminated in zone 7 or 8 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
FLOW CLASS NV4
A submerged negatively buoyant effluent issues vertically
or near-vertically from the discharge port. The layer depth
is limited. The discharge configuration is hydrodynamically
"unstable", that is the discharge strength (measured by its
momentum flux) dominates the flow in relation to the
limited layer depth. The role of the negative buoyancy is
secondary. The following flow zones exist:
1) Momentum-dominated near-field jet: The flow is dominated
by the effluent momentum (jet-like) and is weakly deflected
by the ambient current.
2) Layer boundary impingement/full vertical mixing: The
weakly bent jet impinges on the layer boundary (water
surface or pycnocline) at a near-vertical angle. Given the
shallow layer depth and the weak buoyancy of the discharge,
the flow becomes unstable after impingement. This results
in a recirculating region immediately downstream that
extends over the full layer depth.
3) Passive ambient mixing: The vertically fully mixed plume
is further advected by the ambient flow and spreads
laterally through ambient diffusion. The plume may interact
with a nearby bank or shoreline.
*** The ambient flow plays an important role in this flow
configuration. Hence, all the zones listed above constitute
the HYDRODYNAMIC MIXING ZONE with strong initial mixing.
Predictions will be terminated in zone 3 depending on the
definitions of the LEGAL MIXING ZONE or the REGION OF
INTEREST. ***
PLOW CLASS NV5
A submerged negatively buoyant effluent issues vertically
or near-vertically from the discharge port, the layer depth
is limited. The discharge configuration is hydrodynamically
"unstable", that is the discharge strength (measured by its
momentum flux) dominates the flow in relation to the limited
layer depth and in relation to the weak stabilizing effect
of the discharge buoyancy (measured by its buoyancy flux).
However, the negative buoyancy is generally strong enough
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to affect the flow at larger distances downstream from the
unstable initial region. The following flow zones exist:
1) Unstable recirculation/buoyant restratif ication/upstream
spreading: The buoyant jet rises near-vertically and
impinges on the layer boundary (water surface or
pycnocline). After impingement the mixed flow recirculates
over the limited layer depth and becomes partially
re-entrained into the discharge jet. The degree of
recirculation - and hence the overall mixing in this region
- is controlled by restratification of the flow at the edge
of this recirculating region. The restratified flow spreads
along the layer bottom. In particular, the flow spreads some
distance upstream against the ambient current, and laterally
across the ambient flow.
*** The region described above constitutes the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
2) Buoyant spreading at layer bottom: The plume spreads
laterally along the bottom while it is being advected by the
ambient current. The plume thickness may decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline.
3) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the layer
upper boundary and/or banks.
*** Predictions will be terminated in zone 2 or 3 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST.***
SPECIAL CASE: If the ambient is stagnant, so that advection
and diffusion by the ambient flow (zones 2 and 3) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zone
1) and the predictions will be terminated at this stage.
Such stagnant water predictions may be a useful initial
mixing indicator for a given site and discharge design. For
practical final predictions, however, the advection and
diffusion of the ambient flow - no matter how small in
magnitude - should be considered.
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c.5 NH-Flow Classes
FLOW CLASS NH1
A submerged negatively buoyant effluent issues horizontally
or near-horizontally from the discharge port. The effect of
ambient velocity is relatively strong. Alternatively, this
flow may arise - even though the discharge may be
positively buoyant - when the discharge is oriented downward
and is arrested near the bottom by some ambient
stratification. The discharge configuration is
hydrodynamically "stable", that is the discharge strength
(measured by its momentum flux) is weak in relation to the
layer depth and in relation to the stabilizing effect of the
negative discharge buoyancy (measured by its buoyancy flux).
The following flow zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current. It rises to a maximum
height (less than the layer depth) which is controlled by
the negative buoyancy.
2) Buoyancy-dominated far-field plume: After the maximum
height of rise, the negative discharge buoyancy becomes the
dominating factor (plume -like flow). The strongly deflected
plume is slowly descending toward the bottom.
3) Bottom approach: The bent-over submerged plume approaches
the bottom boundary. Within a short distance the
concentration distribution becomes relatively uniform
across the plume width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being advected by the
ambient current. The plume thickness may decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline.
5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
layer surface and/or banks.
*** Predictions will be terminated in zone 5 or 6 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
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FLOW CLASS NH2
A submerged negatively buoyant effluent issues horizontally
or near-horizontally from the discharge port. The effect of
ambient velocity is weak. Alternatively, this flow may
arise - even though the discharge may be positively buoyant
- when the discharge is oriented downward and is arrested
near the bottom by some ambient stratification. The
discharge configuration is hydrodynamically "stable", that
is the discharge strength (measured by its momentum flux)
is weak in relation to the layer depth and in relation to
the stabilizing effect of the negative discharge buoyancy
(measured by its buoyancy flux). The following flow zones
exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current. It rises to a maximum
height (less than the layer depth) which is controlled by
the negative buoyancy.
2) Buoyancy-dominated near-field plume: After the maximum
height of rise, the negative discharge buoyancy becomes the
dominating factor (plume-like flow). The strongly deflected
plume is rapidly falling toward the bottom.
3) Bottom boundary impingement/upstream spreading: The
weakly bent jet/plume impinges on the bottom boundary at a
near-vertical angle. After impingement the flow spreads more
or less radially along the bottom. 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 zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being advected by the
ambient current. The plume thickness may decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline.
5) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
layer surface and/or banks.
*** predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
229
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SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion by the ambient flow (zones 4 and 5) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a given site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
FLOW CLASS NH3
A submerged negatively buoyant effluent issues horizontally
or near-horizontally from the discharge port. The discharge
is cross- flowing or counterflowing with respect to the
ambient flow, and the ambient velocity is weak.
Alternatively, this flow may arise - even though the
discharge may be positively buoyant - when the discharge is
oriented downward and is arrested near the bottom by some
ambient stratification. The discharge configuration is
hydrodynamically "stable", that is the discharge strength
(measured by its momentum flux) is weak in relation to the
layer depth and in relation to the stabilizing effect of the
negative discharge buoyancy (measured by its buoyancy flux).
The following flow zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Buoyancy-dominated near-field plume: After some distance,
the negative discharge buoyancy becomes the dominating
factor (plume- like flow). The strongly deflected plume is
descending toward the bottom.
3) Bottom approach: The bent-over submerged plume approaches
the bottom boundary. Within a short distance the
concentration distribution becomes relatively uniform across
the plume width and thickness.
4) Wall jet: The bottom attached flow forms a wall jet that
propagates across or against the ambient flow.
5) Flow turning: At some distance the wall jet becomes
turned into the ambient flow direction. Also, the
concentration distribution becomes relatively uniform across
the plume width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
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6) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being advected by the
ambient current. The plume thickness may decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline. 7) Passive
ambient mixing: After some distance the background
turbulence in the ambient shear flow becomes the dominating
mixing mechanism. The passive plume is growing in depth and
in width. The plume may interact with the layer surface
and/or banks.
*** Predictions will be terminated in zone 6 or 7 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST.***
COUNTERFLOW DISCHARGE: If the discharge is opposing the
ambient flow then the flow pattern tends to become
complicated and irregular with potential unsteady
pulsations. This is an UNDESIRABLE discharge configuration.
CORMIX1 WILL NOT PROVIDE A DETAILED PREDICTION FOR A
COUNTERFLOW DISCHARGE GEOMETRY.
SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion by the ambient flow (zones 4 to 7) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a given site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
FLOW CLASS NH4
A submerged negatively buoyant effluent issues horizontally
or near-horizontally from the discharge port. The effect of
ambient velocity is relatively strong. Alternatively, this
flow may arise - even though the discharge may be positively
buoyant - when the discharge is oriented downward and is
arrested near the bottom by some ambient stratification. The
following flow zones exist:
1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Momentum-dominated far-field jet: The jet becomes
strongly deflected by the ambient current. It rises to a
maximum height, less than the layer depth, which is
controlled by the opposing action of the negative buoyancy.
231
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3) Buoyancy-dominated far-field plume: After the maximum
height of rise, the negative discharge buoyancy becomes the
dominating factor in plume-like flow. The strongly deflected
plume is slowly descending toward the bottom.
4) Bottom approach: The bent-over submerged plume approaches
the bottom boundary. Within a short distance the
concentration distribution becomes relatively uniform across
the plume width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
5) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being advected by the
ambient current. The plume thickness may decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline.
6) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the layer
surface and/or banks.
*** Predictions will be terminated in zone 5 or 6 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST.***
FLOW CLASS NH5
A submerged negatively buoyant effluent issues horizontally
or near-horizontally from the discharge port. The discharge
is cross- flowing or counterflowing with respect to the
ambient current. The discharge configuration is
hydrodynamically "unstable", that is the discharge strength
(measured by its momentum flux) dominates the flow in
relation to the limited layer depth. The effect of buoyancy
is negligible and the initial discharge is usually attached
to the bottom. This is a highly complicated and UNDESIRABLE
discharge configuration. The discharging jet tends to full
vertical mixing and will block the ambient flow. This will
cause a recirculating eddy region downstream of the
discharge. There is no reliable prediction methodology for
this flow.
CORMIX1 WILL NOT PROVIDE A DETAILED PREDICTION FOR THIS
CASE.
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C.6 Attached Flow Classes
FLOW CLASS (..)A1
Irrespective of the buoyancy or direction of the discharge,
the near-field of this flow configuration is dominated by
wake attachment. The ambient crossflow effect is strong
and/or the height of the discharge port above the bottom is
too small. This leads to rapid attachment of the discharge
flow to the bottom with a recirculation wake in the lee of
the discharge structure. Following the recirculation the
discharge flow will lift off from the bottom due to its
strong buoyancy.
FLOW CLASS (..)A2
Irrespective of the buoyancy or direction of the discharge,
the near-field of this flow configuration is dominated by
wake attachment. The ambient crossflow effect is strong
and/or the height of the discharge port above the bottom is
too small. This leads to rapid attachment of the discharge
flow to the bottom with a recirculation wake in the lee of
the discharge structure. Following the recirculation the
discharge flow will remain attached to the bottom due to its
weaker negative buoyancy. In the absence of wake attachment
the dominant flow class would be given by the prefix (..).
You may request detailed information on that flow class
further below. Additional advice on how to prevent bottom
attachment (e.g. by increasing the height of the discharge
port) will be provided in the summary program element SUM.
The following flow zones exist:
1) Recirculation zone: The discharge flow becomes quickly
deflected by the ambient flow and attaches to the bottom.
A recirculation eddy exists in the lee of the discharge
structure.
2) Buoyant spreading at bottom: In case of negative
discharge buoyancy only, the plume spreads laterally along
the bottom while it is being advected by the ambient
current. The plume thickness may decrease during this phase.
The mixing rate is relatively small. The plume may interact
with a nearby bank or shoreline.
3) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in thickness and in width. The plume may interact with the
layer upper boundary and/or banks.
***The ambient flow plays an important role in this flow
configuration. Hence, all the zones listed above constitute
233
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the HYDRODYNAMIC MIXING ZONE with strong initial mixing.
Predictions will be terminated in zones 2 or 3 depending on
the definitions of the LEGAL MIXING ZONE or the REGION OF
INTEREST.***
FLOW CLASS (..)A3
Controlled primarily by the geometry of the discharge, the
near-field of this flow configuration is dominated by Coanda
attachment. The port orientation is more or less horizontal
and/or the height of the discharge port above the bottom is
too small. This leads to rapid dynamic attachment (Coanda
attachment) of the discharge flow to the bottom and the
formation of a wall jet. At some distance the discharge flow
will lift off from the bottom due to its strong buoyancy.
In the absence of Coanda attachment the dominant flow class
would be given by the prefix (..). You may request detailed
information on that flow class further below. Additional
advice on how to prevent bottom attachment (e.g. by
increasing the vertical angle of the discharge port) will
be provided in the summary program element SUM. The
following flow zones exist:
I) Momentum-dominated near-field wall jet: The rapidly
attaching discharge flow (wall jet) is initially dominated
by the effluent momentum and weakly deflected by the ambient
current.
2) Momentum-dominated far-field wall jet: The wall jet has
become strongly deflected by the ambient current. Depending
on the ratio of the jet to plume transition length scale to
the jet to crossflow length scale this flow zone may be
absent.
3) Lift-off: Because of the positive buoyancy the plume
detaches from the bottom and starts to rise upward.
4) Buoyancy-dominated far-field plume: The plume has been
strongly deflected by the current and is slowly rising
toward the surface.
5) Layer boundary approach: The bent-over submerged
jet/plume approaches the layer boundary (water surface or
pycnocline). Within a short distance the concentration
distribution becomes relatively uniform across the plume
width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
6) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
234
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while it is being advected by the ambient current. The plume
thickness may decrease during this phase. The mixing rate
is relatively small. The plume may interact with a nearby
bank or shoreline.
7) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 6 or 7 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST.***
FLOW CLASS (..)A4
Controlled primarily by the geometry of the discharge, the
near-field of this flow configuration is dominated by Coanda
attachment. The port orientation is more or less horizontal
and/or the height of the discharge port above the bottom is
too small. This leads to rapid dynamic attachment (Coanda
attachment) of the discharge flow to the bottom and the
formation of a wall jet. At some distance the discharge flow
will lift off from the bottom due to its strong buoyancy.
In the absence of Coanda attachment the dominant flow class
would be given by the prefix (..) . You may request detailed
information on that flow class further below. Additional
advice on how to prevent bottom attachment (e.g. by
increasing the vertical angle of the discharge port) will
be provided in the summary program element SUM. The
following flow zones exist:
1) Momentum-dominated near-field wall jet: The rapidly
attaching discharge flow (wall jet) is initially dominated
by the effluent momentum and weakly deflected by the ambient
current.
2) Lift-off: Because of the positive buoyancy the plume
detaches from the bottom and starts to rise upward.
3) Buoyancy-dominated near-field plume: The plume is quickly
rising and weakly deflected by the ambient current.
4) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary (water surface
or pycnocline) at a near-vertical angle. After impingement
the flow spreads more or less radially along the layer
boundary. 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.
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*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
5) Buoyant spreading at layer boundary: The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase. The mixing rate
is relatively small. The plume may interact with a nearby
bank or shoreline.
6) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
*** Predictions will be terminated in zone 5 or 6 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST.***
SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion by the ambient flow (zones 5 and 6) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 4) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a given site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
FLOW CLASS (..)A5
Controlled primarily by the geometry of the discharge, the
near- field of this flow configuration is dominated by
Coanda attachment. The port orientation is more or less
horizontal and/or the height of the discharge port above the
bottom is too small. This leads to rapid dynamic attachment
(Coanda attachment) of the discharge flow to the bottom and
the formation of a wall jet. The discharge flow will remain
attached to the bottom due to its weak or negative buoyancy.
In the absence of Coanda attachment the dominant flow class
would be given by the prefix (..). You may request detailed
information on that flow class further below. Additional
advice on how to prevent bottom attachment (e.g. by
increasing the vertical angle of the discharge port) will
be provided in the summary program element SUM. The
following flow zones exist:
1) Momentum-dominated near-field wall jet: The rapidly
attaching discharge flow (wall jet) is initially dominated
236
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by the effluent momentum and weakly deflected by the ambient
current.
2) Momentum-dominated far-field wall jet: The wall jet has
become strongly deflected by the ambient current.
3) Flow turning: At some distance the wall jet becomes
turned into the ambient flow direction. Also, the
concentration distribution becomes relatively uniform across
the plume width and thickness.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***
4) Buoyant spreading at bottom: The plume spreads laterally
along the bottom while it is being advected by the ambient
current. The plume thickness may decrease during this phase.
The mixing rate is relatively small. The plume may interact
with a nearby bank or shoreline.
6) Passive ambient mixing: After some distance the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the
channel bottom and/or banks.
***Predictions will be terminated in zone 4 or 5 depending
on the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion by the ambient flow (zones 4 and 5) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this stage. Such stagnant water predictions may be a
useful initial mixing indicator for a given site and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
237
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Appendix D
HYDRO output File Example
This Fortran output file corresponds to the AB Chemical
Company Design Case No.2 in Section 7.1.2.
SIMULATION / CASE DESCRIPTION
SITE NAME: AB-L
DISCHARGER NAME: NEW
POLLUTANT NAME: ANGLES-HO
DESIGN CASE: TEST
DOS FILE NAME: AB-1
DATE AND TIME OF FORTRAN SIMULATION: 06-08-1989_15:09:37
ENVIRONMENT PARAMETERS (METRIC UNITS)
BOUNDED SECTION
BS - 262.75 AS - 3153.00
BANK - left YB - 37.50
HA - 12.00 HD - 12.00
UA .30 F - .0198
UNIFORM DENSITY ENVIRONMENT
RHOA - 998.39
DISCHARGE PARAMETERS (METRIC UNITS)
DO -.15000E+00 AO -.17671E-01 HO - .40
THETAO - 30.00 SIGMAO -270.00
UO -.30000E+01 QO -.53014E-01
RHOO - 987.80 DRHOO - 10.5840 GPO - .1040E+00
CO -.50000E+03
FLUX PARAMETERS (METRIC UNITS)
QO -.53014E-01 MO -.15904E+00 JO - .5511E-02 SIGNJO - 1.0
FLOW CLASSIFICATION
FLOW CLASS: HI
FLOW DIRECTION: upward
238
-------
ATTACHMENT TYPE: NONE
HS - 12.00
NON-DIMENSIONAL PARAMETERS
FRO - 24.02 R - 10.00
LENGTH SCALES (METRIC UNITS)
LQ - .1329 LM - 3.3924 Lm - 1.3293 Lb -
.2041
MIXING ZONE / TOXIC DILUTION / AREA OF INTEREST PARAMETERS
CO -.50000E+03
NTOX - 1 CMC - .25E+02
XINT - .30E+04
LEGMZ - 1 LEGSPC - 2 LEGVAL - 26.27
XLEG - .OOE+00 WLEG - .26E+02 ALEG - .OOE+00
XMAX - .30E+04
NSTEP = 6
SUBSURFACE FLOW: MDNF -> MDFF -> BDFF
BEGIN MOD01: DISCHARGE MODULE
PREDICTION
X Y Z S C B
.00 .00 .40 1.00 .500E+03 .08
END OF MOD01: DISCHARGE MODULE
BEGIN MOD11 MDNF: MOMENTUM DOMINATED NEAR-FIELD
COORDINATES
GAMMA - 90.00 DELTA - 150.00
45 < GAMMA < 135 DEGREES
JET INTO CROSSFLOW
STARTING VALUES
239
-------
ETAI -
ETAIP -
.4000 XI -
.7385 XIP -
.0000 YI
.0775 YIP
.0000 ZI
-.6396 ZIP
.4000
.3714
VIRTUAL ORIGIN LOCATION
ETAV - -.3385 XV - -.0775 YV - .6396 ZV
FINAL VALUES
.0286
ETAF - 2 .
ETAFP - 2.
PREDICTION
X
.00
.08
.19
.33
.50
.70
.93
END OF MOD11
3201
6586
Y
.00
-.28
-.55
-.83
1.11
1.39
1.66
MDNF
XF -
XFP - 1
Z
.40
.56
.73
.90
1.08
1.27
1.46
: MOMENTUM
.9275
.0050
S
1.00
1.43
1.87
2.30
2.73
3.17
3.60
YF - -
YFP - -
C
. 500E+03
.349E+03
.268E+03
.217E+03
.183E+03
.158E+03
.139E+03
1.6629 ZF -
2.3025 ZFP -
B
.08
.12
.15
.19
.22
.26
.29
1.4569
1.4283
DOMINATED NEAR- FIELD
BEGIN MOD16
MDFF:
MOMENTUM
DOMINATED FAR
FIELD
STARTING VALUES
ETAI - 2 .
ETAIP - 1.
2108
4562
XI -
XIP -
.9275
.4266
YI - -
YIP - -
1.6629 ZI -
1.2611 ZIP -
1.4569
.7280
VIRTUAL ORIGIN LOCATION
ETAV - .7546 XV -
FINAL VALUES
ETAF - 4.4015 XF -
ETAFP - 3.6469 XFP -
PREDICTION
X Y Z
.5008 YV - -.4018 ZV -
7.2018 YF
6.7009 YFP
-3.5601 ZF
-3.1583 ZFP
.7289
2.0958
1.3669
240
-------
.93
1.97
3.02
4.06
5.11
-1.66
-2.31
-2.68
-2.96
-3.19
1.46
1.75
1.88
1.97
2.03
3.60
8.22
11.76
14.82
17.59
.139E+03
.608E+02
.425E+02
.337E+02
.284E+02
.44
.66
.79
.89
.97
THE POLLUTANT CONCENTRATION IN THE PLUME FALLS BELOW THE
CMC VALUE OF .25E+02 IN THE CURRENT PREDICTION INTERVAL.
THIS IS THE EXTENT OF THE TOXIC DILUTION ZONE.
6.16 -3.39 2.07 20.16 .248E+02 1.03
7.20 -3.56 2.10 22.57 .221E+02 1.09
END OF MOD16 MDFF: MOMENTUM DOMINATED FAR FIELD
BEGIN MOD22 BDFF: BUOYANCY DOMINATED FAR-FIELD
STARTING VALUES
XI - 7.2018
XIP - 13.7306
YI - -3.5601 ZI
YIP - -4.4148 ZIP
2.0958
3.3763
.8548 ZV
-1.2805
VIRTUAL ORIGIN LOCATION
XV - -6.5288 YV =
FINAL VALUES
XF - 100.:
XFP - 107.J
PREDICTION
X
7.20
22.77
38.33
53.89
69.46
85.02
100.58
END OF MOD22 BDFF: BUOYANCY DOMINATED FAR-FIELD
84
13
-3
-4
-5
-6
-6
-7
-7
2
0
Y
.56
.83
.70
.38
.95
.45
.90
YF
YFP
Z
2.
4.
6.
7.
9.
10.
12.
-
M
10
31
15
78
28
68
00
-7.
-8.
22
61
109
162
220
283
349
9005
7553
S
.57
.99
.40
.73
.89
.18
.11
ZF - 12
ZFP = 13
C
.222E+02
.807E+01
.457E+01
.307E+01
.226E+01
.177E+01
.143E+01
.0000
.2805
1
1
2
2
3
3
3
B
.01
.68
.23
.72
.17
.59
.98
241
-------
BEGIN MOD31: LAYER/BOUNDARY/TERMINAL LAYER APPROACH
CONTROL VOLUME
PREDICTION
X Y Z S C B
100.58 -7.90 12.00 349.3 .143E+01 3.98
X Y Z S C BV BH ZU ZL
108.55 -7.90 12.00 593.9 .842E+00 7.24 7.24 12.00 4.76
END OF MOD31: LAYER/BOUNDARY/TERMINAL LAYER APPROACH
*** END HYDRODYNAMIC MIXING ZONE (HMZ) ***
BEGIN MOD41: BUOYANT AMBIENT SPREADING
PREDICTION STAGE 1 NOT BANK ATTACHED
X Y Z S C BV BH ZU ZL
108.55 -7.90 12.00 593.9 .842E+00 7.24 7.24 12.00 4.76
** LEGAL MIXING ZONE BOUNDARY **
IN THIS PREDICTION INTERVAL THE PLUME WIDTH MEETS OR EXCEEDS
THE LEGAL VALUE - 26.27 M. THIS IS THE EXTENT OF THE LEGAL MIXING
ZONE.
X Y Z S C BV BH ZU ZL
229.67 -7.90 12.00 717.3 .697E+00 4.11 15.42 12.00 7.89
350.78 -7.90 12.00 781.9 .639E+00 3.17 21.77 12.00 8.83
471.89 -7.90 12.00 827.4 .604E+00 2.68 27.30 12.00 9.32
593.01 -7.90 12.00 863.0 .579E+00 2.36 32.31 12.00 9.64
714.12 -7.90 12.00 892.5 .560E+00 2.13 36.96 12.00 9.87
835.23 -7.90 12.00 917.9 .545E+00 1.96 41.33 12.00 10.04
END MOD41: BUOYANT AMBIENT SPREADING
242
-------
BOTTOM COORDINATE FOR FAR-FIELD IS DETERMINED BY AVERAGE DEPTH,
ZFB - 0.0
BEGIN MOD61: PASSIVE AMBIENT MIXING IN UNIFORM AMBIENT
VERTICAL DIFFUSIVITY OF AMBIENT FLOW: EDIFFV - .0358(M**2/S)
HORIZONTAL DIFFUSIVITY OF AMBIENT FLOW: EDIFFH - .0894(M**2/S)
PREDICTION STAGE 1 NOT BANK ATTACHED
X
835
898
960
1023
1086
1149
.23
.00
.77
.53
.30
.06
Y
-7.90
-7.90
-7.90
-7.90
-7.90
-7.90
Z
12.00
12.00
12.00
12.00
12.00
12.00
S
917
2489
3449
4238
4937
5581
.9
.0
.9
.3
.4
.0
C
.545E+00
.201E+00
.145E+00
.118E+00
.101E+00
.896E-01
BV
1.96
5.23
7.13
8.63
9.90
11.02
BH
41.33
42.04
42.73
43.41
44.09
44.75
12
12
12
12
12
12
ZU
.00
.00
.00
.00
.00
.00
ZL
10.04
6.77
4.87
3.37
2.10
.98
PLUME INTERACTS WITH BOTTOM
THE PASSIVE DIFFUSION PLUME BECOMES VERTICALLY FULLY MIXED WITHIN THIS
PREDICTION INTERVAL.
1211.83 -7.90 12.00 6166.1 .811E-01 12.00 45.40 12.00
.00
SIMULATION LIMIT BASED ON MAXIMUM SPECIFIED DISTANCE - 3000.00(M).
THIS IS THE REGION OF INTEREST LIMITATION.
PREDICTION STAGE 2 BANK ATTACHED
X
1211.83
1509.86
1807.89
2105.91
2403.94
2701.97
3000.00
37
37
37
37
37
37
37
Y
.50
.50
.50
.50
.50
.50
.50
Z
12.00
12.00
12.00
12.00
12.00
12.00
12.00
S
6166.1
6269.6
6371.5
6471.7
6570.4
6667.7
6763.5
C
.811E-01
.797E-01
.785E-01
.773E-01
.761E-01
.750E-01
.739E-01
BV
12.00
12.00
12.00
12.00
12.00
12.00
12.00
BH
90.
92.
93
95.
96.
98
99.
80
33
.83
30
75
.19
60
ZU
12.
12.
12
12.
12.
12
12.
00
00
.00
00
00
.00
00
ZL
.00
.00
.00
.00
.00
.00
.00
END MOD61: PASSIVE AMBIENT MIXING IN UNIFORM LAYER
243
-------
Appendix E
SUM Case Summary and Design Recommendations Example
The following represents the SUM knowledge base output
file from the winter design case for the MN municipal
treatment plant in section 7.2.2.
************************** CASE SUMMARY ******************************
SIMULATION / CASE DESCRIPTION
Site name: MN-2
Discharger name: WEAK
Pollutant name: STRATIFICATION
Design case: TEST
Dos file name: MN-2
Date and time of FORTRAN simulation: 08-09-1989 08:47:46
DISCHARGE/ENVIRONMENT DATA:
ENVIRONMENT PARAMETERS (METRIC UNITS)
Bounded section - no
Bounded section width - 88888.8 (m)
Nearest bank - left (m)
Location of discharge from bank - 1000. (m)
Average depth = 24.35 (m)
Depth at discharge - 24.35 (m)
Ambient velocity - .25 (m/s)
Darcy F .02
Stratification Type - A
Surface density - 1025.60 (kg/m**3)
Pycnocline density - 0.0 (kg/m**3)
Bottom density - 1025.76 (kg/m**3)
Layer height - 24.35 (m)
DISCHARGE PARAMETERS (METRIC UNITS)
Port diameter - .5 (m)
Port area - .19635 (m**2)
Discharge port height - 0.5 (m)
Vertical angle of discharge - 30 (deg)
Horizontal angle of discharge - (deg)
Discharge velocity - 3. (m/s)
Discharge density - 1015.00 (kg/m**3)
Density difference - 10.679932 (kg/m**3)
Buoyant acceleration - .10 (m**2/s)
244
-------
Discharge concentration - 100.000000
FLUX PARAMETERS (METRIC UNITS)
Discharge flow rate - 0.589032 m**3/s
Momentum flux - 1.76 m**4/s**2
Buoyancy flux - 0.060147 m**4/s**3
NON-DIMENSIONAL PARAMETERS
Froude Number - 13.276936
Velocity Ratio - 12
DISCHARGE/ENVIRONMENT LENGTH SCALES (m):
LQ - .44 Lm - 5.31 Lb - 3.84
LM - 6.24 Lm' - 99999.90 Lb' - 99999.90
(These refer to the final discharge/environment length scales as
concluded in CLASS)
MIXING ZONE / TOXIC DILUTION ZONE / AREA OF INTEREST PARAMETERS
Toxic discharge - yes
CMC concentration - 10.000000
Legal mixing zone - yes
Legal mixing zone specification - width
Legal mixing zone value - 200. (m, or m**2)
Region of interest - yes
Region of interest distance - 2000. m
*** SUMMARY OF HYDRODYNAMIC SIMULATION AND MIXING ZONE PREDICTION ***
Flow Class - HI
Attachment type - NONE
This flow configuration applies to a layer corresponding to the full
water depth at the discharge site. The ambient density stratification
at the discharge site is relatively weak and unimportant so the
discharge flow penetrates to the surface and/or breaks down the
existing stratification through vigorous mixing.
HYDRODYNAMIC MIXING ZONE (HMZ) CONDITIONS :
Note: The HMZ is the zone of strong initial mixing. It has no legal
implication. However, this information may be useful for the discharge
designer because the mixing in the HMZ is usually sensitive to the
discharge design conditions.
245
-------
Pollutant concentration at edge of HMZ - .67
Dilution at edge of HMZ - 149.19
HMZ Location (centerline coordinates) (m):
x - 81.79 y - .00 z - 24.35
HMZ Plume Dimensions (ra):
plume half-width - 13.25 plume thickness - 13.25
REGION OF INTEREST (ROI) CONDITIONS :
Minimum pollutant concentration at edge of ROI - .339
Corresponding dilution at edge of ROI - 294.8
ROI Location (centerline coordinates) (m):
x - 2000.00 y - .00 z - 24.35
ROI Plume Dimensions (m):
plume half-width - 202. plume thickness - 1.72
******************* MIXING ZONE PREDICTION SUMMARY ********************
LEGAL MIXING ZONE (LMZ) CONDITIONS :
Predicted minimum pollutant concentration at edge of LMZ - .402060
Corresponding dilution at edge of LMZ - 248.719300
LMZ Location (centerline coordinates) (m):
x - 753.166900 y - .000000 z - 24.350000
LMZ Plume Dimensions (m):
plume half-width - 102.400900 plume thickness - 2.861374
At this position, the flow is still unattached to any bank.
****************** XOXIC DILUTION ZONE SUMMARY ********************
TOXIC DILUTION ZONE (TDZ) ANALYSIS:
Criterion maximum concentration (CMC) - 10.000000
Toxic dilution zone downstream distance - 16.28 (m) .
The exit velocity of the discharge from the port is equal
to 3. m/s and is greater than the minimum of 3.0 m/s.
* The discharge velocity test for TDZ has been satisfied. *
The downstream distance equal to 16.28 (m) at which to flow equals the
criterion maximum concentration (CMC) is less than or equal to 50 times
the discharge length scale of LQ = .44 (m).
* The discharge length scale test for TDZ has been satisfied. * The
criterion maximum concentration (CMC) has been met at a distance
downstream equal to 16.28 (m) which is less than or equal to 5 times
the ambient water depth HD - 24.35 (m) .
246
-------
* The ambient depth test for TDZ has been satisfied.*
The criterion maximum concentration (CMC) of CMC has been met
at 16.28 (m) downstream which is less than or equal to one tenth the
distance of the of the legal mixing zone of 753.166900 (m)
downstream.
* The legal mixing zone test for TDZ has been satisfied. *
**** An criteria for TDZ are satisfied for this configuration. ****
TOXIC DILUTION ZONE (TDZ) CONDITIONS :
Note: The TDZ corresponds to the criteria issued in the USEPA Technical
Support Document "Technical Support Document for Water Quality-based
Toxics Control". Office of Water, Washington, D.C., September, 1985.
Maximum pollutant concentration at edge of TDZ - 9.83
Corresponding dilution at edge of TDZ - 10.165760
TDZ Location (centerline coordinates) (m):
x - 16.28 y - .00 z - 8.25
TDZ Plume Dimensions (m):
plume half-width - 2.68 plume thickness - .00
***************************** NOTICE *********************************
If you desire detailed printed information on the present discharge case
you can obtain this by issuing the following DOS command after you have
returned to DOS:
print c:\cmx\sim\MN-2.cxo
This gives a detailed listing of the results of the hydrodynamic
simulation program element HYDRO. This information may be useful if
you want to construct graphical displays of the flow configuration or
if you want to compare results with available field or laboratory data.
print c:\cmx\desc\Hldes
The detailed description of the flow configuration for the unattached
flow class HI will be printed.
A reliable environmental analysis and mixing zone prediction is possible
only if each design case is evaluated through several iterations of
CORMIX1. Small changes in ambient or discharge design conditions can
sometimes cause drastic shifts in the applicable flow configuration
247
-------
(flow class) and the size or appearance of mixing zones. Iterative use
of CORMIX1 will give information on the sensitivity of predicted results
on design and ambient conditions.Each predictive case should be
carefully assessed as to: - size and shape of LMZ - conditions in the
TDZ (if present)- bottom impact of the discharge flow - water surface
exposure- bank attachment, and other factors. In general, iteration
should be conducted in the following order:
A) Discharge design changes (geometry variations)
B) Sensitivity to ambient conditions
C) Discharge flow changes (process variations)
When investigating these variations the CORMIX1 user will quickly
appreciate the fact that mixing conditions at short distances
(near-field) are usually quite sensitive and controllable. In contrast,
mixing conditions at large distances (far-field) often show little
sensitivity unless the ambient conditions change substantially or
drastic process variations are introduced.
A) DISCHARGE DESIGN CHANGES (GEOMETRY VARIATIONS): Most of the
following recommendations are motivated by the desire of improving
conditions in the applicable mixing zones (i.e. minimizing
concentrations and/or areal extent).
1) Outfall location: Consider moving the discharge farther offshore
to a larger water depth in order to delay flow interaction with the
bank and/or surface, and to improve near-field mixing.
2) Height of discharge port: For positively buoyant or neutral
discharges it is usually desirable to minimize the port height in
order to provide a low submerged jet/plume trajectory. However,
if the port height is too small undesirable flow bottom attachment
may result. A typical range for port heights is from two to ten
diameters. For negatively buoyant discharges, on the other hand,
it may be desirable to maximize the port height. Navigational
requirements may put further limits on large port heights.
3) Vertical angle of discharge: Near-field dilution for positively
or neutrally buoyant discharges is often improved by providing a
near-horizontal discharge. In order co prevent bottom interference
a slight upward orientation (in the range of +15 to +30 degrees)
may be advisable. In contrast, a vertical or near-vertical angle
may be favorable for negatively buoyant discharges.
4) Horizontal angle of discharge: This angle provides the discharge
orientation relative to the ambient current. A co-flow design
(angle of about 0 degrees) or a cross-flow design (about 90 or 270
degrees, respectively) are preferable. A counter-flow design (about
248
-------
180 degrees) is undesirable from the viewpoint of mixing zone
predictability and bottom impacts. Cross-flow designs may be
particularly effective in optimizing near-field mixing, and if they
are chosen, the port should point in the offshore direction.
5) Port diameter/area (discharge velocity): Remember that for a
given discharge flow rate the port area and discharge velocity are
inversely related: a small discharge port implies a high discharge
velocity, and a consequently high discharge momentum flux.
Typically, a high velocity discharge will maximize near-field
mixing. Note, however, that high velocity discharges a) may lead
to unstable near-field flow configurations perhaps involving
undesirable mixing patterns, and b) usually have little, if any,
effect on dilutions over the far-field where a LMZ may
apply .Discharge velocities in typical engineering designs may range
from 3 m/s to 8 m/s. Very high velocities may lead to excessive
pumping energy requirements. Very low velocities (less than 0.5
m/s) may lead to undesirable sediment accumulation within the
discharge pipe.
B) SENSITIVITY TO AMBIENT CONDITIONS:Variations - of the order of 10
percent - of the following ambient design conditions should be
considered:- ambient velocity (or ambient flowrate) - ambient depth (or
river/tidal stage) - ambient density structure (notably density
differences)Such variability is important for two reasons:
1) the usual uncertainty in ambient environmental data,
2) the schematization employed by CORMIX1 Please refer to the
detailed advice on the specification of environmental data,
including the density structure, that is available in program
element DATIN. In particular, note the advisory comments on
stagnant ambient conditions.
C) DISCHARGE FLOW CHANGES (PROCESS VARIATIONS): Actual process changes
can result in variations of one or more of three parameters associated
with the discharge: flowrate, density, or pollutant concentration. In
some cases, such process changes may be difficult to achieve or too
costly. Note, that "off-design" conditions in which a discharge operates
below its full capacity also fall into this category.
1) Pollutant mass flux: The total pollutant mass flux is the
product of discharge flow (m**3/s) times the discharge pollutant
concentration (in arbitrary units). Thus, decreasing the pollutant
mass flux will, in general, decrease the resulting pollutant
concentration in the near-field and far-field. This occurs, of
course, during off-design conditions.
2) Discharge flow: For a given pollutant mass flux, an increase in
discharge flow implies an increase in discharge pollutant
concentration,and vice versa. For the variety of flow classes
contained in CORMIX1 there is no universal rule whether high or low
249
-------
volume discharges are preferable for optimizing near-field mixing.
Mostly, the sensitivity is small, and even more so for far-field
effects. Note that a change in discharge flow will influence in
turn the discharge velocity and hence momentum flux.
3) Discharge density: The actual density of the discharge flow
controls the buoyancy effects relative to the ambient water.
Occasionally, the discharge density is controllable through the
amount of process heating or cooling occurring prior to discharge.
Usually, near-field mixing is enhanced by maximizing the total
density difference (positive or negative) between discharge flow
and ambient water. In most cases, however, this effect is minor.
You have now completed the analysis of the design case MN-2. At this
time you have three options:
1) Quit this session of CORMIX1.
2) Perform another iteration of CORMIX1 for this general design
(You will only change the discharge and mixing zone data bases).
3) Perform another iteration of COPxMIXl for this general design
(You will only change the mixing zone data base).
4) Start another design case (You will enter a complete new data
base).
When the next screen appears, choose '8)Quit' option to return to
DOS.
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250
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