United States
Environmental Protection
Agency
Office of Research and
Development
Washington, DC 20460
EPA/600/3-91/073
December 1991
&EPA
CORMIX2: An Expert
System for Hydrodynamic
Mixing Zone Analysis of
Conventional and Toxic
Multiport Diffuser Discharges
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EPA/600/3-91/073
December 1991
CORMIX2: AN EXPERT SYSTEM FOR, HYDRODYNAMIC
MIXING ZONE ANALYSIS OF CONVENTIONAL AND TOXIC
MULTIPORT DIFFUSER DISCHARGES
by
Paul J. Akar and Gerhard H. Jirka
DeFrees Hydraulics Laboratory
School of Civil and Environmental Engineering
Cornell University
Ithaca, New York 14853-3501
Cooperative Agreement No. CR813093
Project Officer:
Thomas O. Barnwell, Jr.
Assessment Branch
Environmental Research Laboratory
Athens, Georgia 30613
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30613-0801
Printed on Recycled Paper
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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
spatially 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, determining
the limits of applicability, and establishing data needs, an ex-
pert 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
One of the most important tasks in the management of
water quality is the ability to achieve pollutant
concentrations within regulated standards. The Cornell
Mixing Zone Expert System (COKMIX) is a series of software
systems for the analysis, prediction, and design of aqueous
toxic or conventional pollutant discharges into
watercourses, with emphasis on the geometry and dilution
characteristics of the initial mixing zone. Subsystem
CORMIX1, reported by Doneker and Jirka (1990), deals with
submerged single port discharges. The present development,
subsystem CORMIX2 is concerned with submerged multiport
discharges into flowing water environments, such as rivers,
lakes,_estuaries, and coastal waters. It includes effects
of ambient stratification, dynamic attachment of the plume
to the bottom of the receiving water, and the limiting case
of stagnant conditions.
CORMIX2 collects the relevant data for the ambient and
discharge situation, computes the physical parameters, and
classifies the given discharge into one of many possible
hydrodynamic configurations. Then, CORMIX2 executes the
corresponding hydrodynamic simulation for the flow,
interprets the results of the simulation relative to legal
requirements including toxic discharge criteria, and
finally, suggests possible design alternatives and
improvements concerning the mixing characteristics.
CORMIX2, with its emphasis on rapid initial mixing,
assumes a conservative pollutant discharge neglecting any
physical, chemical, or biological decay processes. However,
the predictive results can be readily converted to adjust
for first-order reaction processes.
The results of the hydrodynamic simulation are in good
agreement with available field and laboratory data. In
particular, CORMIX2 correctly predicts highly complex
discharge situations involving boundary interactions,
internal layer formation, buoyant intrusions, and large-
scale induced currents in shallow environments, all features
that are beyond the predictive capabilities of other
currently available initial mixing models for multiport
diffusers.
IV
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Table of Contents
Abstract ...... iv
".Table of .Contents . . . . . . v
List of Tables x
List Of Figures . . . ix
Glossary of Symbols ' . ' . . xiv
Acknowledgements xvii
Chapter I
Introduction . . . . . . . .... ... . . • .... . • • 1
1.1 Regulatory Background 1
1.1.1 The Clean Water Act of 1977 2
1.1.2 The Cpncept of Mixing Zone 2
1.1.2.1 Mixing Zone: Regulations and Development ... 2
1.1.2.2 Special Mixing Zone Requirements for Toxic
Substances . . . . . '. . . • . . . . • • ... « 3
.1.1.3 Regulatory Practice . . ...... 4
1.1.4 The Role of Expert Systems in Mixing Zone
Analysis 4
1.2 CORMIX2: An Expert System for Mixing Zone Analysis
of Multiport Diffuser Discharges 5
1.2.1 Scope and Objective : 5
1.2.2 Summary of Present Study . . . . . . . ... • • 6
Chapter IT
Hydrodynamic Processes and Flow Classification
2.1
2.2
2.2
2.2
2.2
2 .2
2.2
2.2
2.2
2.2
2.2
2.3
2.3
2.3
2.4
Introduction
Physical Conditions
8
8
1 Ambient Conditions . . . . . . . . . . . • — ; "« • • 10
,1.1 Ambient Geometry . . . ..... . . • . • • > 10
,1.1.1 Bounded Cross-Section % ..... . . . . • • 10
,1.1.2 Unbounded Cross-Section ... . ." . . . - . 10
.1.2 Ambient Currents . . . . . . . . . . • « • • « 10
,1.3 Stratification Effects ......... ... 11
,2 Discharge Conditions .............. 13
2.1 Diffuser Geometry .............. 13
2.2 Flow Parameters ............... 17
Hydrodynamic Mixing Processes .......... 18
1 Near-Field Processes ........ ...... 18
2 Far-Field Processes .............. 20
Length Scales Definitions ............ 21
v
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2.4,
2.4,
2.4,
2.4,
2.4,
2.4,
2.5
2.5,
2.5,
2.5,
2.5,
2.5,
2.5,
2.6
2.6,
2.6,
2.6,
2.6,
2.6,
2.6,
2.6,
1 Jet to Crossflow Length Scale ....
2 Jet to Plume Length Scale ......
3 Jet/Stratification Length Scale . . .
4 Plume/Stratification Length Scale . .
5 Crossflow/Stratification Length Scale
6 Additional Comments .
Hydrodymanic Flow Classification
1.1,
1.1,
1.1.
1.1,
2.6.1.1
2.6.1
2.6.1
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
Near-Field Flow Classification
1.1 General Procedure
1.2 Flow Classes MS for Linear Ambient
Stratification .
1.3 Flow Classes MU for Buoyant Discharges into"
Uniform Ambient Layers , .
1.4 Flow Classes for MNU Negatively Buoyant
Discharges in Uniform Ambient Layers . .. . .
2 Far-Field Flow Behavior
Analysis of Individual Flow Processes ......
1 Buoyant Plane Jet Processes in Deep Water
1.1 Unstratified Ambient . .
1.1.1 Simple Plane Jet in Stagnant Environment
2 Simple Plane Plume in Stagnant Environment
3 Weakly Deflected Plane Jet in Crossflow . .
4 Strongly Deflected Plane Jet in Crossflow .
5 Weakly and Strongly Deflected Plane
Plume in Crossflow
6 Horizontal Plane Jet with Vertical
Buoyant Deflection .
1.7 Vertical Plane Plume with Horizontal
Momentum Deflection . .
2 Typical Regimes of Buoyant Plane Jets
in Linear Stratification .
1.2.1 Buoyant Plane Jet in Linear Stratification
1.2.2 Buoyant Plane Plume in Stratified
Stagnant Ambient
1.3 Surface, Bottom, and Terminal Layer :
Interaction Processes ............
2 Diffuser Induced Jet Mixing in Shallow Water
2.1 Unidirectional Diffuser . . . .
2.1.1 Stagnant Ambient . . . . . .
2.1.2 Ambient Crossflow
2.2 Staged Diffuser ........
2.2.1 Stagnant Ambient . .
2.2.2 Ambient Crossflow
2.3 Alternating Di-ffuser •...'..
2.3.1 Stagnant Ambient
2.3.2 Ambient Crossflow
2.4 Fully Mixed Fiffuser Plumes (Inter-
mediate Field) . . . . . .
3 Buoyant Spreading Processes '..'-..
1 Surface Density Current Developing Along
Diffuser Line in Parallel Alignment . .• .
3.2 Internal Density Current Developing Along
Diffuser Line in Parallel Alignment ...
.3
21
24
24
24
25
25
25
26
26
34
35
35
36
•37
.37
37
39
41
41
43
44
45
46
46
46
47
48
49
50
50
50
52
52
54
54
54
56
56
57
59
60
VI
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2.6.3.3 Upstream Intruding Density Wedges Formed
in Bounded Channels . . . . .61
2.6.3.3.1 Density Wedges with Critical Boundary
Conditions 61
2.6.3.3.2 Density Wedges with Subcritical Boundary
Conditions 63
2.6.4 Passive Diffusion Processes 64
Chapter III
CORMIX2: System Structure and Program Elements .... 66
3.1 Background on Expert Systems and Logic Programming 66
3.2 Structure of CORMIX2 . . 68
3.2.1 Data Input Element: DATIN2 71
3.2.2 Parameter Computation: PARAM2 72
3.2.3 Flow Classification Element: CLASS2 72
3.2.4 Hydrbdynamic Simulation Element: HYDRO2 .... 73
3.2.5 Summary Element: SUM2 . . . 76
Chapter IV
CORMIX2: Flow Protocols and Simulation Modules ... . 78
4.1 Flow Protocols 78
4.1.1 Flow Protocols for Buoyant Discharges into
Uniform Ambient Layers (Flow Class MU) 82
4.1.2 Flow Protocols for Negatively Buoyant
Discharges into Uniform Ambient Layers (Flow
Classes MNU) 82
4.1.3 Flow Protocols for Discharges Trapped in
Linearly Stratified Ambients (Flow Class MS) . . 82
4.2 Hydrodynamic Simulation Modules ... 92
4.2.1 Simulation Modules for Buoyant Multiport
Diffuser in Near-Field Flows 92
4.2.1.1 Introductory Comments 94
4.2.1.2 Discharge Module (MOD201) 94
4.2.1.3 Weakly Deflected Plane Jet in Crossflow
(MOD211) 94
4.2.1.4 Weakly Deflected (3-D) Wall Jet in Crossflow
(MOD212) 95
4.2.1.5 Weakly Deflected (2-D) Wall Jet in Crossflow
(MOD218) . . • 96
4.2.1.6 Near-Vertical Plane Jet in Linear Stratification
(MOD213) 96
4.2.1.7 Near-Horizontal Plane Jet in Linear
Stratification (MOD214) . . . . . 97
4.2.1.8 Strongly Deflected Plane Jet in Crossflow
(MOD216) • • . • • 97
4.2.1.9 Weakly and Strongly Deflected Plane Plume in
Crossflow (MOD221, and MOD222) ... 98
4.2.1.10 Negatively Buoyant Line Plume (MOD224) ... 99
Vll
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4.2.2 Simulation Modules for Unstable Multiport
Diffusers: Mixed Near-Field Flows .. . . . . . .
4.2.2.1 Acceleration Zone for Unidirectional
Co-Flowing Diffuser (MOD271) . . . . .
4.2.2.2 Acceleration Zone for Unidirectional
Cross-Flowing Diffuser (Tee) (MOD272) . . . .
4.2.2.3 Unidirectional Cross-Flowing Diffuser
(Tee) in Strong Current (MOD273) . ... . . . . • •
4.2.2.4 Acceleration Zone for Staged Diffuser (MOD274)
4.2.2.5 Staged Perpendicular Diffuser in Strong
Current (MOD275) •••/-,'
4.2.2.6 Alternating Perpendicular Diffuser in Unstable
Near-Field Zone (MOD277) • •
4.2.2.7 Negatively Buoyant Staged Acceleration Zone
(MOD279) ..... .........
4.2.3 Simulation Modules for Boundary Interaction
Processes for Stable Multiport Diffusers . . .
4.2-3.1 Near-Horizontal Surface/Bottom/Pycnocline
Approach (MOD235) •
4.2.3.2 Negatively Buoyant Diffuser (3-D) in Strong
Current (MOD238)
4.2.4 Simulation Modules for Unstable Multiport
Diffusers: Intermediate-Field Flows •
4.2.4.1 Diffuser Plume in Co-Flow (MOD251) . . . . . •
4.2.4.2 Diffuser Plume in Weak Cross-Flow (MOD252) . .
4.2.5 Simulation Modules for Buoyant Spreading
Processes *'""j*
4.2.5.1 Buoyant Surface/Bottom Spreading (MOD241) and
Buoyant Terminal Layer Spreading (MOD242) . .
4.2.5.2 Density Current Developing Along Parallel
Diffuser Line (MOD243) • •
4.2.5.3 Internal Density Current Developing Along
Parallel Diffuser Line (MOD244)
4.2.5.4 Diffuser Induced Bottom Density Current
(MOD245)
4.2.6 Simulation Modules for Ambient Diffusion
Processes
4.2.7 Simulation Module for Density Wedge in
Bounded Channel ......
4.2.7.1 Bottom/Surface/Internal Density Wedge1 (MOP281)
4.3 Transition Rules, Flow Criteria and Coefficient
Values •
4.3.1 Transition Rules
4.3.2 Flow Classification Criteria ....
4.3.3 Terminal Layer Expressions ....
4.3.4 Model Coefficient Values .....
99
100
100
101
101
102
102
102
103
103
105
105
106
106
106
106
107
107
107
107
107
108
108
111
111
111
Chapter V
System Validation and Application . • «
5.1 Comparison with Laboratory and Field Data . . .
5.1.1 Diffuser Discharges in Deep Receiving Water
117
117
117
Vlll
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5.1.1.1 Unstratified Ambient .
5.1.1.1.1 Stagnant Ambient ...'.'..
5.1.1.1.2 Co-Flowing Ambient ,
5.1.1.1.3 Negatively Buoyant Discharges ......
5.1.1.2 Stratified Stagnant Ambient
5.1.2 Diffuser Discharges in Shallow Receiving Water
5.1.2.1 Unidirectional Diffuser
5.1.2.2 Staged Diffuser . .
5.1.2.3 Alternating Diffuser
5.1.3 Summary and Appraisal .
5.2 Application: Case Studies
5.2.1 AAA Municipal Treatment Plant
5.2.1.1 The Problem Statement ... - • •'• • • • •
5.2.1.2 CORMIX2 Analysis .
5.2.2 PPP Electric Company
5.2.2.1 The Problem Statement
5.2.2.2 CORMIX2 Analysis . .
5.3 Additional Comments on CORMIX2
118
118
118
122
122
126
126
129
129
134
134
136
136
136
141
141
141
141
Chapter VI
Conclusions arid Recommendations . . . . . ... .
References • • •
Appendix A: Data Input Advices
Appendix B: Flow Descriptions of all Flow Classes
Appendix C: Design Recommendation Information . .
145
146
152
162
200
IX
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List of Tables
Table 2.1 Summary of Length Scales Applicable for
Multiport Diffuser ....
Table 2.2 Near-Field Flow Classification Procedure .
Table 3.1 CORMIX2 Program File Directories . . . . .
Table 4.1 Flow Description Modules of CORMIX2 . . .
Table 4.2 Flow Protocols (MU) for Buoyant Discharges
into Uniform Ambient Layers . . . . . . . .
Table 4.3 Flow Protocols (MNU) for Negatively Buoyant
Discharges into Uniform Ambient Layers . .
Table 4.4 Flow Protocols (MS) for Discharges Trapped
in Linearly Stratified Ambients ......
Table 4.5 Transition Rules ......
Table 4.6 Flow Classification Criteria . . .'.
Table 4.7 Stratified Terminal Height Expressions
Table 4.8 Module Constants
Table 4.9 Coefficients in Transition Rules ..'..,
Table 5.1 Comparison Between Laboratory Test Results
(Isaacson et al., 1983) and CORMIX2 . . .
27
28
70
79
83
86
90
109
112
113
114
116
125
x
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List of Figures
Figure 2.1 Illustrative Near-Field and Far-Field
Regions of Submerged Positively Buoyant
Discharge ..... . ........ .
Figure 2.2 Definition Diagram for Multiport Diffuser
Discharge Geometry in Ambient Channel with
Rectangular Cross-Section ........ ,12
Figure 2.3 Representative Stable Density Profiles . . 12
Figure 2.4 Submerged Multiport Diffuser ....... 14
Figure 2.5 Schematic Plan Views of Three Major
Diffuser Types ............ ... 15
Figure 2.6 Stable and Unstable Near-Field Flows
Produced by Multiport Diff users . ..... 19
Figure 2.7 Examples of Combined Effects of Momentum
Flux, Buoyancy Flux, Crossflow, and Density
Stratification on Flow Behavior ...... 22
Figure 2.8 Sub-Classification: Assessment of Ambient
Density Stratification and Different Flow
Classes for Internally Trapped Discharges . 31
Figure 2.9 Sub-Classification: Behavior of Positively
Buoyant Discharges in Uniform Ambient
Layer ......... .......... 32
Figure 2.10 Sub-Classification: Behavior of Negatively
Buoyant Discharges in Uniform Ambient
Layer .................. 33
Figure 2.11 Interference of Individual Round Jets from
Multiport Diffuser DischargesForming Two-
Dimensional (Slot) Jets or Plumes . ...
Figure 2.12 Plane Jet in Stagnant Environment ....
Figure 2.13 Plane Plume in Stagnant Environment ...
Figure 2.14 Flow Field Induced by Unidirectional
Diffuser ................ ' .
Figure 2.15 Effect of Limited Separation Distance
between Diffuser Line and Shoreline
38
40
42
53
53
Figure 2.16 Flow Induced by Staged Diffuser ..... 55
Figure 2.17 Alternating Diffuser in Stagnant Ambient . 55
xx
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Figure 2.18 Buoyant Surface Spreading . . .' . . . . . 58
Figure 2.19 Different Upstream Wedge Intrusion in
a Bounded Channel 62
Figure 2.20 Passive Diffusion Mixing Process 65
Figure 3.1 System Elements of CORMIX2 . . ...... 69
Figure 3.2 Example of Flow Description . . . ... . . 74
Figure 5.1 Horizontal Buoyant Two-Dimensional Jet in
Stagnant Ambient 119
Figure 5.2 Horizontal Multiport Buoyant Jet
Trajectory in a Co-Flowing Ambient . . . . 120
Figure 5.3 Horizontal Multiport Buoyant Jet
Trajectory in a Co-Flowing Ambient .... 121
Figure 5.4 Dilution for Buoyant Multiport Discharge
in a Co-Flowing Ambient 123
Figure 5.5 Negatively Buoyant Multiport Diffuser
Discharging Vertically Upward in a
Co-Flowing Uniform Ambient ... 124
Figure 5.6 Unidirectional Diffuser Discharging in a
Stagnant Shallow Ambient . . 127
Figure 5.7 Unidirectional Diffuser Discharging in
Shallow Ambient with Crossflow ...... 128
Figure 5.8 Staged Diffuser Discharging in a Stagnant
Shallow Ambient 130
Figure 5.9 Staged Diffuser Discharging in a
Cross-Flowing Shallow Ambient 131
Figure 5.10 Staged Diffuser Discharging in a.
Cross-Flowing Shallow Ambient ...... 132
Figure 5.11 Surface Plume from Buoyant Alternating
Diffuser 133
Figure 5.12 Buoyant Alternating Diffuser in
Perpendicular Crossflow 135
Figure 5.13 AAA Municipal Outfall: Typical Density
Profiles in Coastal Ocean . . 137
Figure 5.14 AAA Municipal Outfall: August Design Case
with Internal Flow Trapping ....... 139
XII
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Figure 5.15 AAA Municipal Outfall: March Design Case
with Surface Interaction
Figure 5.16 PPP Electric Company Outfall in Low
Ambient Current
Figure 5.17 PPP Electric Company Outfall in Strong
Ambient Current
140
142
143
Kill
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Glossary of Symbols
All symbols are defined where they first occur. Only
more common symbols are summarized here.
a0 = discharge cross-sectional area
b = plane jet/plume half-width
bh - horizontal half-width of diffuser plume
bv = vertical half-width of diffuser plume
bi'si'ti = width, dilution, and trajectory constants for flow
region i (Chapter 2)
B = equivalent slot width (section 2.2.2.2)
Bi'si'Ti = width, dilution, and trajectory constants for MOD
i (Chapter 4)
CI
D
f
= drag coefficient for density current
= discharge diameter
= ambient flow Darcy-Weisbach friction factor
F0 = nozzle/port densimetric Froude number (Eq. 5.1).
Fro = slot densimetric Froude number (Eq. 5.2).
g = gravitational acceleration
9'0 ~ discharge buoyant acceleration
h0 = height of discharge above bottom
hint = height of pycnocline (lower layer depth)
H = ambient water depth
Hs = significant layer depth (H or hj_n-t)
J0 = discharge buoyancy flux
£ = average spacing between ports and nozzles
lq = discharge (geometric) length scale
1M = slot jet/plume transition length scale
xiv
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1m7
q
LM
= slot jet/crossflow length scale
= slot jet/stratification length scale
= slot plume/stratification length scale
= crossflow/stratification length scale
= discharge (geometric) length scale
= jet/plume transition length scale
= jet/crossflow length scale
•=• plume/crossflow length scale
= jet/stratification length scale
= plume/stratification length scale
= diffuser length
= discharge momentum flux
= number of ports or nozzles
= discharge (volume flux)
== jet/crossf low ratio (Eq. 5.3).
= distance along jet/plume trajectory
= bulk dilution in plume
= centerline dilution in jet/plume
= centerline velocity in jet/plume
= ambient velocity
= discharge velocity
= width of ambient water body
x,y,z = Cartesian coordinate system
x',y',z' = Cartesian coordinate system relative to virtual
origin
y" = supplementary coordinate (section 4.2.1.1)
n
Qo
R
s
S
sc
uc
u
U
W
xv
-------
Yg = distance of discharge to nearest shore
z = vertical coordinate
Greek Symbols:
a
A/>
PO
6
= supplementary angle (Eq. 4.2)
= port (nozzle) horizontal orientation angle relative
to diffuser line
« alignment angle of diffuser line relative to ambient
current direction
= supplementary angle (Eq. 4.3)
= pycnocline density jump
= discharge density difference
= supplementary coordinate (section 4.2.1.1).
= ambient buoyancy gradient
= ambient density
= discharge density
= vertical angle of discharge
= horizontal angle of discharge relative to ambient
current
Subscripts:
c
f
i
centerline
final value within a MOD
initial value within a MOD
xv i
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Acknowledgements
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 gave encouragement for the completion
of this study on multiport diffusers in addition to the
earlier development of CORMIX1 for single port discharges.
The work was carried out using the computer facilities
of the DeFrees Hydraulics Laboratory. Dr. Robert L. Doneker
from the University of Portland, Oregon, provided valuable
assistance in the final implementation and testing of the
computer code and knowledge base software. Mr. Cameron
Willkens, Electronics Technician, generously assisted with
solutions for computer hardware and software problems. Ms.
Doreen Balwierczak did skillful wordprocessing for the final
manuscript.
This report is a revised version of the thesis submitted
by Paul J. Akar, Graduate Research Assistant, to the
Graduate School of Cornell University in partial fulfillment
of the requirements for the degree of Masters of Science.
Dr. Gerhard H. Jirka, Professor of Civil and Environmental
Engineering, was project supervisor.
xvn
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Chapter I
Introduction
One of the major environmental problems is the concern
for an adequate water quality in all bodies of water, from
streams, rivers and lakes to estuaries and coastal waters.
In order to complete this goal, all waste water discharges
in the United States are subject to Federal and/or State
regulations. A key aspect of these regulations is the
concept of a mixing zone.
The mixing zone is a legally defined spatial quantity
that allows for the initial nixing and dilution of a
discharge. Legal criteria specify the rixing zone shape and
effluent concentrations which rust be maintained outside and
at the edge of the mixing zone. .Mixing zone regulations are
a descendant of Federal water quality legislation which
started in 1948.
More recently, additional subregicns within the mixing
zone have been defined for discharges of aqueous toxic
substances. The objective of these regulations is to
require rapid mixing of toxic releases in order to limit the
exposure to toxic materials of aqueous flora and fauna.
The purpose of this report is to document the
development and implementation of an engineering tool, in
the form of a micro-computer based expert system, for the
analysis of submerged multiport diffuser discharges into
water bodies with variable and complex conditions.
Due to their great flexibility in providing a high
degree of initial mixing, submerged multiport diffusers are
increasingly being used in water quality control.
Installations range from sewage diffusers for the discharge
of treated municipal wastewater, to thermal diffusers for
heated cooling water flow from steam-electric power plants,
to industrial diffusers for process water or brine
discharges.
The goal of the expert system is to give reliable and
accurate predictions of the mixing characteristics of these
discharges along with information on any applicable legal
requirements. The development of this multiport diffuser
expert system is patterned closely after another expert
system for submerged single port discharges as reported by
Doneker and Jirka (1989).
l.l Regulatory Background
A detailed overview of the legal background governing
aqueous pollutant discharges in the United States has been
-------
given by Doneker and Jirka (1989). Some of the key aspects
are summarized here.
1.1.1 The Clean Water Act of 1977
In 1977 the Congress amended the Federal Water Pollution
Control Act of 1972, with those amendments being known as
the Clean Water Act (CWA). The Act covered general
categories of pollutants which are; i) conventional, ii)
nonconventional, iii) toxics, iv) heat, and v) dredge and
fill spoil.
Conventional pollutants are defined as pollutants that
are naturally occurring, biodegradable, oxygen demanding
materials and solids. Pollutants which are
"nonconventional" would be "those which are not toxic or
conventional" (Congressional Research Service, 1977).. A
detailed list covering the different effluent standards set
by USEPA under the 1977 amendments can be found in Doneker
and Jirka (1989).
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. On the other
hand, "best available technology economically achievable"
(BAT) effluent limitations which require a high pollutant
percentage removal and a high cost in the reduction process,
apply to nonconventional and toxic pollutants. A variance
provision for BAT standards for nonconventional pollutants
is contained in section 301 (g) of the Act. With State
approval, this provision gives authority to the USEPA to
expand effluent standards for nonconventional pollutants on
the condition that it will not interfere with water quality
standards or public health (for further details, see Doneker
and Jirka 1989).
1,1.2 The Concept of Mixing Zone
1.1.2.1 Mixing Zone; Regulations and Development
The mixing zone concept is .defined as an allocated
impact zone where water quality standards can be exceeded
as long as acutely toxic conditions are prevented. A mixing
zone is defined as a limited area or volume where the
initial dilution of a discharge occurs (Water Quality
Standards Handbook, 1982). The water quality standards have
to be met at the mixing zone boundary but not within the
mixing zone itself.
The mixing zone requirements established by USEPA state
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 ". The USEPA has published guidelines for
additional requirements (such as avoidance of settling
materials, debris, etc.) that should be met within any
mixing zone.
The proposed rules for mixing zones recognize the State
has discretion whether or not to adopt a mixing zone and to
specify its dimensions. USEPA allows the use of a mixing
zone in permit applications except where one is prohibited
in State regulations. Typically, State standards require
that water quality criteria be met at the edge of the
regulatory mixing zone in order to provide a continuous zone
of free passage that meets water quality criteria for free-
swimming and drifting organisms and to prevent impairment
of critical resource areas. Actual mixing zone definitions
are established on basis of a downstream distance, or plume
width or cross-sectional area or plume surface area or other
criteria depending on the type of water body. A summary of
mixing zone definitions is found in USEPA Technical Guidance
Manual (USEPA, 1984, see also Doneker and Jirka, 1989).
1.1.2.2 Special Mixing Zone Requirements For Toxic
Substances
When dealing with toxic discharges, the USEPA advises
careful mixing evaluation in order to prevent areas of
chronic toxicity that extend for large distances because of
poor mixing. Two regulatory criteria for toxic substances
are maintained by USEPA, these are: a criterion maximum
concentration (CMC) for protecting against acute or lethal
effects; and a criterion continuous concentration (CCC) for
protecting against chronic effects. The CCC is less
restrictive but must be met at the edge of the same
regulatory mixing zone specified for conventional and
nonconventional discharges.
The key aspect for the CMC criterion is that the CMC
must be met within a short distance from the outfall in
order to prevent lethal concentrations of toxics in the
regulatory mixing zone. One requirement for the toxic
dilution zone (TDZ) is that a minimum exit velocity of 3
meters per second (10 feet per second) must be met in order
to provide sufficiently rapid mixing which will minimize
organism exposure time to toxic material. Other geometric
'restrictions for a TDZ are required (for example, 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 spacial direction, and the CMC should be met within
50 times the discharge length scale for each multiport
-------
nozzle), and are discussed in the Technical Support Document
for Water Quality-based Toxics Control (USEPA, 1985).
1.1.3 Regulatory Practice
^ f" order to discharge any pollutant into watercourses.
the discharge must obtain a permit issued under the National
Pollution Discharge Elimination System (NPDES). The permit
is structured to insure that the discharge meets all
applicable standards.
In order to implement the mixing zone requirements, it
is necessary for the applicant to predict the discharge
initial dilution and the mixing zone characteristics. Given
the large number of possible combinations of ambient
environments, discharge conditions, and mixing zone
locations, the analyst must possess substantial skill
training, and expertise in order to pursue accurate and
reliable effluent mixing analysis.
In general, effluent mixing is induced by different
mechanisms_ along the discharge trajectory. In the "near
field' region of the discharge, jet-induced entrainment can
provide dilution, and further downstream in the "far field"
the discharge velocity decreases and ambient diffusion is
tne main mechanism for mixing.
As an alternative to mathematical models, the
determination of pollutant concentrations can be achieved
in two ways, either by physical measurement for existing
2}?? ?SrS'*°r bY *« non-P°Hutant tracer injection which
will indicate an effluent dilution. These studies require
specialized field trained personnel and require extensive
errort and time.
For these reasons and due to the complexity of the
physical mixing processes, permit writers are increasingly
relying on mathematical models to analyze the transport
behavior of pollutants (Tait, 1984). However, many of the
present models are very specialized and give precise results
only for particular cases. A few models which have been
nSmSPe™^r dialution Prediction are, PLUME, OUTPLM,
DHKPLM, MERGE, and LINE (see Mullenhoff, et. al., 1985).
1.1.4 The Role of Expert Systems in Mixing arm* Analysis
Available predictive models vary from simple analytical
equations to intricate numerical solutions to differential
equations. The USEPA (Mullenhoff, et. al., 1985) has
published advice on the use of such models, but often the
user_ has little detailed guidance for model choice and
applicability. An example of this may be seen in use of
USEPA models which may violate the assumption of an infinite
-------
receiving environment. The plume actually may become bottom
attached or may be vertically completely mixed.
Also, after running the model, the user is faced with
the problem of analyzing the results. This task can be very
challenging for the inexperienced user due to its
complexity. In summary, the user must be an "expert1' in the
interpretation of the model results, and must understand the
limitations of the models. It is expensive and costly to
train all potential users to become experts in this field,
and for this purpose the development of expert systems would
be helpful and efficient.
Expert systems mimic the logic that an expert might use
in solving a given problem. As cited in (Doneker and Jirka,
1989) , "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 base employs reasoning
procedures similar to those used by an expert when anlayzing
the problem. .
Expert systems possess great utility for solving
environmental science problems. As mentioned by Barnwell
et al. (1986), several preconditions must be satisfied
before using this technology. Those preconditions are
related to having a restricted well defined problem domain,
a logical knowledge base for solving a problem, and finally
an appropriate formalization of concepts compatible with the
shell used.
Expert systems can be a powerful tool for the analyst
if these requirements are satisfied. The analysis .and the
simulation of the effluent mixing problem satisfy these
preconc, ..tions because the mixing zone processes are
hydrodynamically well defined.
A final justification for the expert systems approach
for multiport diffuser analysis can be found in the
implemention of such a system in analyzing single port
discharges in ambient water (Doneker and Jirka, 1989). The
system has been found to be very successful in its ability
to predict mixing characteristics for complex problems,
involving a large variety of discharge/environmental
conditions. ' '
1.2 CORMIX2; An Expert System for Mixing Zone Analysis of
Multiport Diffuser Discharges
1.2.1 Scope and Objective
The purpose of this study is to create a tool for the
analysis and design of submerged multiport diffusers
discharges into ambient receiving environments, including
-------
the cases of positively or negatively buoyant discharges
issuing into stratified or non-stratified flowing , water-
courses. Furthermore, the limitations of a neutrally
buoyant discharge and of a stagnant ambient are included.
The_ expert system will be labeled CORMIX2, for Cornell
Mixing Zone Expert System, Subsystem 2. The first
subsystem, CORMIX1 (Doneker & Jirka, 1989), deals with
single port discharges into water-courses.
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, and it
should provide the analyst with detailed information and
advice regarding the initial mixing for a discharge design.
It is very difficult to create a system that applies to
every conceivable mixing zone and discharge configuration.
However, the goal of the present study is to develop an
expert system that works for better than 80% of typical
diffuser discharges, ranging from simple to fairly complex
cases. The rest of the cases may require a specialist using
either sophisticated numerical modeling or a detailed
hydraulic model study.
1.2.2 Summary of Present Study
The expert system CORMIX2 is applicable to the
prediction of mixing behavior of multiport diffusers
emphasizing discharge geometry, the characteristics of the
legal mixing zone (LMZ) , and the zone of toxic dilution
(TDZ). CORMIX2 collects all input data, conducts
hydrodynamic analyses, summarizes dilution characteristics
including any legal regions if specified, and finally
recommends design changes in order to improve dilution
characteristics.
^Since its emphasis is on initial mixing mechanisms with
their short time scales, CORMIX2 assumes a conservative
pollutant or tracer in the effluent. Thus, any physical,
chemical, biological reaction, or decay processes are
neglected. However, if first-order processes are assumed,
the predictive results can be readily converted to include
such processes (see Section 5.4). ;
Detailed explanations and descriptions of CORMIX2 are
presented in the following chapters. Chapter II presents
both the hydrodynamic flow processes occurring in effluent
mixing and the hydrodynamic flow classification. The
hydrodynamic flow processes are related to the various
stages of mixing of buoyant multiport diffuser discharges
in the ambient water. The flow classification describes
the interaction processes controlling the near-field
discharge mixing.
6
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Chapter III describes the overall system structure and
the various program elements of CORMIX2.
Chapter IV covers the detailed hydrodynamic protocols
used to simulate the model.
Chapter V is devoted to the validation of CORMIX2 with
experimental and field data. The chapter also presents some
applications through design case studies in order to
illustrate the flexibility and limitations of CORMIX2.
Chapter VI summarizes CORMIX2 capability and performance
and presents recommendations and suggestions for future,
improvements of CORMIX2.
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Chapter II
Hydrodynamic Processes and Plow Classification
2.1 Introduction
The key ingredient for a predictive expert system must
be the study and understanding of the hydrodynamic processes
occurring in the environment, including the interaction
between the discharge configuration and the ambient
environment.
The hydrodynamics of an effluent continuously discharged
into water bodies can be conceptualized as a mixing process
occurring in two separate zones (Figure 2.1). In the first
region, called the "near-field", the initial multiport
diffuser momentum flux, buoyancy flux, and outfall geometry
control the diffuser plume trajectory and its mixing
characteristics. This region covers the multiport
diffuser^s subsurface flow and any surface and bottom
interaction, or in the case of a stratified ambient, the
terminal layer interaction.
Further downstream (away from the source) , the multiport
diffuser geometry becomes less important, and hence ambient
conditions will control the mixing characteristics and
trajectory through buoyant motions and passive diffusion
due to ambient turbulence. This region is called the "far-
field" .
The mixing processes in this study are treated in two
steps:_ classification of flows based on length scale
analysis, discussed in section 2.3, and predictive models
for each flow zone covered in section 2.4.
2.2 Physical Conditions
The general ambient environment is complex arid sometimes
difficult to model due to complicated topographic
conditions. A simple configuration or schematization
representing the ambient geometry is introduced in the
expert system CORMIX2. Other difficulties are a. stratified
ambient and current effects which further complicate the
modelling process, and therefore need some simplifying
assumptions. .
Similarly, diffuser geometries may exhibit a great
degree of complexity. Therefore, restrictions to simplified
generic types have been made in CORMIX2.
-------
Plan View
Side View
c
a
u
Far Field
Illustrative Near Field and Far Field of Submerged
Buoyant Discharge
Figure 2.1
Illustrative Near-Field and Far-Field Regions
of Submerged Positively Buoyant Discharge:
An Example of Unidirectional Perpendicular
Diffuser in Unstratified Ambient Water and
Without Bottom Attachment.
-------
a.a.i 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. CORMIX2 considers two
cases of cross-sections: bounded and unbounded cross-
sections. A bounded cross-section is defined as a cross-
section having both sided bounded by banks - as rivers
streams, narrow estuaries, and other narrow watercourses!
An unbounded cross-section represents a discharge which is
located close to one boundary while the other boundary is
for practical purposes very far away (e.g. discharges into
wide lakes, estuaries, and coastal areas).
2.2,1.1 Ambient Geometry
2.2.1.1.1 Bounded Cross-Section
The methodology assumes a rectangular cross-section
(Figure 2.2) that is defined 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 to define water-courses geometrv
One way of achieving this is by the repeated use of the
program so that the user can appreciate the sensitivity of
the results .
In order to measure the roughness characteristics in
the channel, the value of the Manning "n», or alternatively
of the Darcy-Weisbach friction factor »f», must be
S^S1?3"6?; 2^eSie Param.eters influence the mixing process
only in the final far-field stage.
2.2,1.1.2 Unbounded Cross-Section
,o™i c and 9eoi*etric information is
closely related to the bounded case. CORMIX2 will conduct
its analysis by assuming an "equivalent cross-sectional
area" defined by depth, by distance from one bank to ?he
discharge position, and by ambient velocity.
2.2.1.2 ambient Currents
t Ambient currents are usually encountered in the ambient
environment. CORMIX2 will assume a uniform ambient current
and will not deal with complicated representation of current
10
-------
patterns, including shear effects and other non-
uniformities .
Data related to the ambient flow condition must be
available either as an average ambient velocity or as an
ambient discharge.
2.2.1.3 Stratification Effects
A variation of density with respect to the depth is
common in many water bodies. For example, seasonal
temperature conditions can affect the density and lead to
stratification of the ambient environment. Also often,
ambient density stratification plays an important role in
discharge design objectives. For example, in sewage
discharges the prevention of plume rise to the water surface
can be accomplished by internal trapping induced by the
density gradient.
The methodology considers four cases of density profiles
which are shown in Figure 2.3. The user must choose among
the four profiles the one that best fits the actual ambient
profile. The four profiles are:
Stratification Type A: The density varies linearly between
top and bottom.
Stratification Type B: There is an upper mixed layer with
uniform density, a sudden density jump at an intermediate
level, the so-called pycnocline (thermocline), and a lower
layer with uniform density.
Stratification Type C: There is an upper mixed layer with
a uniform density, a sudden density jump, and a lower layer
in which the density varies linearly down to the bottom
value.
Stratification Type D: There is an upper mixed layer with
uniform density. At an intermediate level, the density
begins to vary linearly down to the bottom value.
In each type, a linear buoyancy gradient e is defined as
e = - (g/pa)dpydz (2.1)
where
g : gravitational acceleration,
Pi : ambient density (reference value),
: ambient density gradient.
11
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Nearest Bank
Cross-Section
0, u0. AA,, c,
'(>• To- -0
Figure 2.2
Definition Diagram for Multiport Diffuser
Discharge Geometry in Ambient Channel with
Rectangular Cross-Section. Width W of the
Water Body may be Finite or Unlimited.
H
h
int
© Linear
Two-Layer
Figure 2.3
.Representative Stable Density Profiles (Four
?oo^lf 1Cati°n TyPes) (Ref. Doneker and Jirka,
1989).
12
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2.2.2 Discharge Conditions
Discharge conditions are related to the discharge flow
characteristics, the geometry of the discharge structure,
and the flow parameters.
2.2.2.1 Diffuser Geometry
The discharge geometry is defined by the multiport
diffuser. A multiport diffuser is a structure consisting
of many closely spaced ports or nozzles which inject a
series of high velocity turbulent jets into the receiving
water. One can distinguish among two forms of port
openings, a simple pipe with port openings (holes in the
pipe), or a pipe with attached risers leading to the actual
port or nozzle (with the possibility of multiple ports for
each riser). The diffuser installation can consist of the
diffuser pipe laid on the bottom, half buried in a trench,
or deeply buried, or a tunnel below the bottom.
A summary of all schematic ambient and discharge
characteristics is shown in Figure 2.2. The following
variables define the diffuser geometry:,
LD = diffuser length.
* N = number of diffuser openings (ports or nozzles).
a = LD/(N-1) = average port spacing.
D = port (or nozzle) diameter.
h0 = port height above bottom.
e = vertical discharge angle.
a = horizontal discharge offset angle.
7 = alignment angle.
/3 = orientation angle.
The general multiport diffuser arrangement together with
its important geometric features is shown in Figure 2.4.
Multiport diffusers can have a large amount of geometric
detail. Each geometric parameter can play an important role
in the flow behavior. For example, a variation of the
horizontal port orientation angle, ft., can induce a change
in the discharge trajectory. Three major types of multiport
diffuser geometries, each with highly different mixing
behavior, have evolved in actual engineering practice: the
unidirectional, staged. and alternating diffuser (see Figure
2.5). These diffuser types are classified mainly based on
their angle orientation relative to the diffuser axis ft.
In the unidirectional diffuser, all the ports point in the
same direction perpendicular to the diffuser axis (ft = 90°) .
In the staged diffuser, the ports all point in the same
direction parallel to the diffuser axis (ft = 0°) . In the
alternating diffuser, the ports are arranged in an
alternating fashion and point in opposite directions (ft =
± 90°) . The unidirectional and the staged diffusers possess
a net horizontal momentum input with a tendency to induce
13
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Side view
p''pe//ne
Plan view
biff user axis
Figure 2.4
Submerged Multipart Diffuser: General
Discharge Configuration (Adapted from JirkS,
1982) .
-------
EC 1
i?
<
0S 90°
Without control
a) Unidirectional diffuser, 0 ^ o°
1
Control: Fanned design
- —
Lo
/3>0°
= 0°
(3>0°
b) Staged diffuser, 00= 0°
Figure 2.5
Schematic Plan Views of Three Major Diffuser
Types, a) Unidirectional Diffuser, b) Staged
Diffuser, c) Alternating Diffuser. Any of
those diffusers may have a variable alignment
7 relative to the ambient current.
-------
•I I Hi 1 n 111- r<4
= ±90°
90°
.1 -1 . 1 . t
I 1 " t
"
loo o o o o o o o o
90 < 90°
Vertical
o
o
o
> ^
o
\ \M 1
/ //? /
\ \
Control:
Fanned design
a - ± cot'1 (± 'c
c) Alternating diffuser, da - variable
Figure 2.5 (Continued)
16
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currents within the ambient water body. The alternating
diffuser has a zero net horizontal momentum, and a lesser
tendency to generate currents and circulations.
Of course, there are variations on the basic theme for
each of the three diffuser types. A few of these
possibilities are shown on. Figure 2.5. For example, there
may be double or triple port arrangements (with a small
internal angle) for both unidirectional or staged diffusers,
and the port orientation angle ft may differ somewhat from
the nominal value, ~ 90° or =» 0°, respectively. Or in case
of the alternating diffuser, there may be multiple port
assemblies for each riser with several ports arranged in a
circular fashion. A special case of an alternating diffuser
is a diffuser with a vertical discharge, possessing zero
horizontal momentum input.
Furthermore, the designer can exercise some control over
the behavior of the discharge plume and other induced
circulations in the ambient water body. This is especially
important for diffuser discharges into shallow water that
are prone to vertical instabilities (see Section 2.3.1)
leading to concentrated high velocity diffuser plumes.
These concentrated flows can be controlled if the diffuser
nozzles have a "fanned design" with a variable orientation
angle along the diffuser
(2.2)
D
in which y* is the distance measured from the diffuser mid-
point. A variable nozzle orientation with control according
to Eq. 2.2 has been shown (Jirka and Harleman, 1973; Jirka,
1982) to improve diffuser mixing while reducing the strength
of diffuser induced velocities in the ambient water.body.
Many of those diffuser design possibilities
addressed in the input element of CORMIX2.
are
The effectiveness of each type of diffuser will further
depend on the direction of the ambient current relative to
the diffuser axis called the alignment angle 7. One can
discern two extreme cases:(1) Perpendicular alignment (7 =
90°) , (2) and Parallel alignment (7 * 0°) .
2.2.2.2 Flow Parameters
The general diffuser flow field is, of course, three-
dimensional. However, for near-field mixing analyses the
two-dimensional flow parameters are dynamically relevant.
17
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For this purpose, the details of individual discharge jets
with port diameter D and spacing SL are neglected and
T-«2
replaced by an equivalent slot width B = —|j— on the basis
of equivalency of momentum flux per unit diffuser length.
This concept has been discussed by Jirka (1982) , and by
Jirka and Akar (1991), and has been shown to be an accurate
dynamic representation. The main parameters for the two-
dimensional slot discharge are, the diffuser total flowrate
Q0, and the discharge buoyancy g'0. This leads to the
following flux parameters (per unit diffuser length), all
expressed in kinematic units
g0 = QO/LD = volume flux (flowrate) .
w<. = q0u0 = u02B = momentum flux.
Jo = q0g'0 = u0g'0B = buoyancy flux.
in which
uo = Qo/(An) = port velocity.
A« = 7rD2/4 = port cross-sectional area.
<3Ia - g(pa - Po)//>a - buoyant acceleration.
Po = discharge density.
2.3 Hydrodynamic Mixing Processes
As discussed previously in Section 2.1, the effluent
mixing process is divided into two regions (the near and far
field).
2.3.1 Near-Field Processes
The essential feature of the near-field of a diffuser
discharge is given by buoyant jet mixing. In a jet, the
high velocity of the efflux flow rapidly entrains ambient
fluid causing a high degree of dilution. The additional
effect of buoyancy can, depending on the direction of
buoyancy (acting upward or downward), further increase the
mixing intensity. Ambient currents and stratification have
a further influence on the jet mixing process.
An important aspect of the near-field dynamics of
multiport diffuser is the determination under what
combinations of discharge and ambient characteristics the
near-field will be stable or unstable (see Figure 2.6). As
explained by Jirka (1982), a near-field for buoyant
18
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0 en
§ |
I »
"** D
s pl
I i
s ^
— 73
U -
- g
5
g-
53
\
>>
y
§,
o
o
6
c
O)
T3
"5
>
O
c
u
^3 I^ •*
0) C O
O (C -
(Q
(H
O
r-l
(S
H
2 ST>5
oJ | ® 3
•H X ^ (0
I ".p W
2 " (0 fi
S ^
««8*
^ ^ 5 ""
_f^ it I
(0 -H O *
ti Q-p a
M C i-H 4->
W A Q W
ni
0)
M
•H
-------
discharges is stable when a buoyant surface layer is formed
which does not communicate with the initial buoyant jet
zone. An unstable near field is defined whenever the
layered flow structure breaks down in the discharge
vicinity, resulting in recirculating zones or mixing over
the entire water depth (see Figure 2.6).
The stability criterion for the near-field region of a
buoyant diffuser discharge in a stagnant unstratified
ambient is given by the interplay of momentum flux, buoyancy
flux, and water depth H (Jirka, 1979, 1982)
m0/(j02/3H) = C/(l + cos2*)2
(2.3a)
where all the parameters involved were defined in the
previous section and C is a constant. If an ambient
crossflow ^ exists in the environment, then another
destabilizing factor is introduced, the ambient momentum
flux per unit length, ma = u/H, where ua is the ambient
current. The additional effect of cross-flow of velocity
u, can be represented by an additional parameter ma/(j02/3 H)
which is added to the previous stabilty equation. Hence
the stability criterion for the near field of a
perpendicular diffuser discharge into a flowing water body
is given by Jirka (1982) as
m0/(j02/3H) + (m, + m0 cos* ) / (J02/3H) = C
(2.3b)
As examples, the application of those criteria (Eqs. 2.3a
and b) to municipal and industrial wastewater diffusers in
coastal waters in which the effluent possesses freshwater
density usually indicates a stable regime. On the contrary,
thermal diffusers operate with and usually in very high
flowrates, with a small density difference less deep water,
and thus an unstable regime will be present. Detailed
analysis of the stability criterion and further applications
are discussed in Jirka (1982).
Stable discharge conditions can also be referred to as
atdiffuser operating in deep water ("stable or deep water
diffuser") while unstable conditions indicate a shallow
water condition ("unstable or shallow water diffuser").
This terminology is used interchangeably in the following.
The related near-field equations for trajectory and dilution
of deep and shallow cases will be presented in Section 2.6.
2.3.2 Far-Field Processes
The far field zone begins after the flow interacts with
the water surface, pycnocline, or bottom. This zone is
composed of one or two regions, depending on the discharge
characteristics. In the1 general case, the flow possesses
enough buoyancy and thus a region of buoyant spreading will
-------
be established followed by a passive diffusion region. The
region of surface/pycnocline/bottom spreading is represented
by horizontal dynamic spreading and gradual vertical
thinning of the flow after interaction with the surface as
described by Roberts (1979) and by Koh and Brooks (1975).
In the present situation, occurrence of boundary interaction
may be possible, and hence the flow may become laterally
fully mixed in the bounded sections.
In the region of passive diffusion, the dilution is
mainly controlled by the presence of turbulent mixing in the
flowing ambient water body. Again boundary interaction may
occur, and the flow may become both laterally and vertically
fully mixed in this region. For cases of non-buoyant or
weakly buoyant flow, buoyant spreading will not be present
and only passive diffusion will take place. For the case
of stagnant ambient, the far field zone will be ignored due
to the absence of any advection.
For the case of a near-field jet flow trapped by
linearly stratified ambient, the far field is composed of
two regions: internal buoyant spreading, and passive
diffusion. The internal buoyant spreading behaves in the
same way as the surface buoyant spreading except that the
spreading occurs at the terminal layer rather than at the
water surface. The passive diffusion has the same charac-
teristics as the unstratified case with a reduced vertical
mixing due to the damping effect of ambient stratification.
2.4 Length Scales Definitions
Length scales are used to describe the relative impor-
tance of discharge momentum flux, buoyancy flux, ambient
crossflow, and density stratification in controlling flow
behavior, especially in the near-field. The equivalent slot
concept is used in the following considerations.
2.4.1 Jet to Crossflow Length Scale
When an ambient crossflow of velocity ua is present, the
plane jet with perpendicular alignment will be deflected as
shown in Figure 2.7b. The behavior of the jet in that case
is related to the momentum flux and to the crossflow. In
order to find the distance to the position where the jet
becomes affected by the crossflow, one can obtain from
dimensional analysis a jet/crossflow length scale lm
lm = m0/ua2
(2.4)
Using this length scale together with the distance along the
trajectory s, one can deduce that for s/lm « O(l) the
initial plane jet momentum flux per unit length will control
-------
Transition
Ua =
€ =0
Plume-like
a) Buoyant Plane Jet in Stagnant Uniform Environment
u,
e=0
Transition
Strongly Deflected Jet
Weakly Deflected Jet
b) Plane Jet in Uniform Cross-flow
Figure 2.7 Examples of Combined Effects of Momentum Flux,
Buoyancy Flux, Crossflux, and Density Strati-
fication on Flow Behavior.
-------
Transition
Density current
c) Plane Jet in Stagnant Stratified Ambient
Density current
•V
X
Plume-like
d) Plane Plume in Stagnant Stratified Ambient
Figure 2.7 (Continued)
-------
the flow, and for s/lm » O(l) the crossflow velocity will
have more influence on the plane jet behavior.
2.4.2 Jet to Plume Length Scale
Flows, in general, contain both momentum and buoyancy.
Initially, the momentum controls the flow until the buoyant
acceleration overcomes the momentum factor and ultimately
dominates the flow. The distance at which there is a
transition between momentum domination to buoyancy control
in a stagnant environment, is represented by a jet/plume
length scale (see Figure 2.7a) 1M
2/3
(2.5)
Thus, for s/lM « O(l) the flow behavior will be controlled
by momentum and for s/lM » o(l) the flow will be dominated
by buoyancy.
2.4.3 Jet/Stratification Length Scale
When the additional effect of ambient stratification is
introduced, other important length scales will be involved
in the analysis. In the case of a stagnant ambient, the
length scale describing the height of rise of a nonbuoyant
jet in a stratified fluid is related to the momentum flux
and the buoyancy gradient e (see Figure 2.7c). The
jet/stratification length scale is given dimensionally by
1. ... 1/3
»' = (m0/s)1/3 (2.6)
As explained by Wright (1977), the combined effect of
stratification and crossflow will introduce two limiting
possibilities in either the momentum dominated jet or
buoyancy dominated plume: either the jet is still weakly
deflected when it reaches its maximum height of rise or else
it will be significantly bent over until the stratification
causes it to stop rising. The ratio of lm'/lm « O(l)
indicates that the nonbuoyant jet will reach its maximum
height of rise in the strongly deflected stage.
2.4.4 Plume/Stratification Length Scale
In the case of a stagnant ambient, the length scale
describing the height of rise of a buoyant plume in a
stratified fluid, is related to the buoyancy flux and the
buoyancy gradient e (see Figure 2.7d). This length l'b is
defined as
V = Jc
(2.7)
24
-------
For a vertical distance of ?/!„' « O(l) the effect of
density stratification on plume behavior will be negligible.
2.4.5 Crossflow/Stratification Length Scale
When reaching the maximum elevation, a near vertical jet
will still possess some vertical momentum which causes the
jet to rise above the neutral buoyant position, but it will
face back due to its negative buoyancy. Thus, an oscilla-
tion of the flow with decreasing amplitude will occur
(Wright, 1977). The length scale la associated with this
flow behavior is characterized by an interaction of
crossflow and stratification
J/2
(2.8)
2.4.6 Additional Comments
It is interesting to note that no plume to crossflow
length scale can be defined-on dimensional ground for the
two-dimensional plume. This is in contrast to the three-
dimensional round plume (Doneker and Jirka, 1989). This
arises from the fact that the vertical velocity of a two-
dimensional plume is constant, ~ J01/3, leading in the
presence of a constant crossflow to a straight line trajec-
tory. Thus, no distinction of a plume region can be made.
However, it is possible to define a non-dimensional parame-
ter J0/ua3 whose magnitude will be a measure of the slope of
that trajectory (see Section 2.6.1.1.5). This parameter
jo/ua3 is the inverse of a Froude number defined by Roberts
(1977) .
The multiport geometry controls the flow in the initial
region after the discharge. For a strictly two-dimensional
equivalent slot diffuser a length scale lq can be defined
from its volume and momentum flux,
(2.9)
which is identical to the equivalent slot width, lq = B.
The actual multiport geometry, however, overshadows this
length scale, as the merging distance for the individual
three-dimensional jets is typically considerably larger than
2.5 Hvdrodynamic Flow Classification
In this section, 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 interac-
tions, is also discussed herein. ,
2.5.1 Near-Field Flow Classification
The objective of the hydrodynamic flow classification
is to predict for a given discharge/ambient 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 character-
izing the discharge are summarized in Table 2.1. There are
five major length scales based on the two-dimensional
properties (per unit length) of the jet: lm, 1M, im', I/,
and la. In addition, if the diffuser is seen globally (over
its entire length) then additional length scales can be
defined based on the three-dimensional bulk variables, total
momentum flux M,, = ng^ and total buoyancy flux J0 = j^.
These definitions are, on dimensional grounds, entirely
analogous to the round buoyant jet (Doneker and Jirka, 1989)
and are also included in Table 2.1. All these lengths
interact with the geometric features of the ambient water
body, its depth H and its stratification parameter e, and
with the geometry properties of the diffuser, mainly the
angles 7, and 0.
Thus, in total, a large number of length scales plus two
angles seem to influence the near field flow configuration.
Therefore, this means that there exist a wide variety of
flow configurations that may occur in environmental applica-
tions. The classification procedure presented below yields
31 generic flow configurations. The actual number of flow
classes that can be modeled with the full predictive
methodology (Chapter IV) is considerably larger (at least
twice as many) since each of the 31 generic flow classes may
apply to a layer corresponding to the full water depth or
to the region below a pycnocline.
2.5.1.1 General Procedure
The flow classification is a 12 step procedure that is
summarized in Table 2.2. This procedure is used to deter-
mine which flow class within the three major flow categories
the given discharge will exhibit. The three major flow
categories are: i) flows affected by linear stratification
26
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Table 2.1
Summary of Length Scales Applicable for
Multiport Diffuser
A) Based on Two-Dimensional Slot Parameters:
lq = goY^o = B = discharge geometric scale (Eq. 2.9).
lm = m0/ua2 - plane jet/crossflow scale (Eq. 2.4).
IM = m0/j02/3 = plane jet/plane plume scale (Eq. 2.5).
lm' = (m0/e)1/3 = plane jet/ stratification scale (Eq.
2.6).
I/ = j01/3/s1/2 = plane plume/stratification scale (Eq.
2.7) .
la = uys1/2 = crossf low/ stratification scale (Eq. 2.8)
B) Based on Global Three-Dimensional Parameters:
Lq = Qo/M02 = discharge geometric scale.
LO = J0/ua3 = plume/crossflow scale.
1^ = M^VU,, = jet/crossflow scale.
1^ = Mo^/Jo172 = jet/plume transition scale.
L'm = (Mye)174 = jet/stratification scale.
L'b = (JoA3/2)1/4 = plume/ stratification scale.
where: Q0 =
, M,, =
and J0 =
27
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Table 2.2 Near-Field Flow Classification Procedure
Step 1:
Step 2
Step 3;
Step 4;
Test for density profile stability. If the ambient
is unstratified or the given stratification is
dynamically impossible according to a flux Richard-
son number criterion, approximate ambient density
with mean value and recompute discharge parameters.
Conclude stratification is not important and go to
Step 10.
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 2.1) go to Step 4.
Ambient density profile contains step change.
Since the Stratification Type is B or C, approxi-
mate the actual lower layer stratification and the
step change with a surrogate linear stratification
(Figure 2.1). Calculate surrogate gradient s* and
surrogate stratification length scales 1
and lu.
'-mi I
Possible flow trapping in linear density stratifi-
cation. Test for internal layer formation (flow
trapping), using the scheme outlined in the upper
portion of Figure 2.8). Use height Hs (H, = H for
stratification type A, and Hs = hint for types B, C
or D) . If (Z, + h0)/Hs > 0(1), density stratifica-
tion 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 2.8 based on the actual density gradient e.
If (Z, + h0)/Hs < O(l) , conclude the flow will become
trapped in the linearly stratified layer below the
density jump, go to Step 8.
28
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Table 2.2
(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 Es = h^ 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 the 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. Eight flow classes
exist (MSI to MS8) as shown in Figure 2.8.
Step 10: Test for discharge buoyancy in uniform ambient
density layer height Hs. If discharge is negative-
ly buoyant go to Step 12.
Step 11: Perform flow classification for positively buoyant
(for neutral) jet in uniform density layer. Nine
major flow classes (MU1 to MU9) exist as shown in
Figure 2.9.
Step 12: Perform flow classification for negatively buoyant
or downward directed jet in uniform density layer.
Fourteen major flow classes exist (MNU1 to MNU14)
as shown in Figure 2.10. STOP.
29
-------
leading to internal trapping (MS classes, Figure 2.8), ii)
buoyant flows in uniform ambient layers (MU classes, Figure
2.9), and iii) negatively buoyant flows in uniform ambient
layers (MNU classes, Figure 2.10).
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 2.2 a flux Richardson criterion (see
Doneker and Jirka, 1989) is used to check for such destab-
ilization which would enforce a uniform profile.
Steps 2 through 8 in Table 2.2 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 transverse 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 2.2)
are performed. In the case of a profile with a density jump
(Stratification Types B and C in Figure 2.1) 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 2.5.1.2.
Steps 10 to 12 examine the flow behavior for those
categories for which the ambient layer can be take as
uniform (either existing or because any stratification is
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 2.5.1.3) and for negatively buoyant dis-
charges in Step 12 (see Section 2.5.1.4).
The detailed classification schemes for each flow
category (Figures 2.8 to 2.10) are discussed in the follow-
ing sections. It is stressed that all criteria presented
in this Chapter and listed on Figure 2.8 to 2.10 are "order
of magnitude" relations. The precise form of the criteria
30
-------
CO
•
CM
-------
eg
0)
M
fa
32
-------
>1 •
a) 0
£3
I j t I
« (0
O J3
•H O
-------
as well as the numerical constants are given in Chapter iV.
2.5.1.2 Flow Classes MS for Linear Ambient Stratification
Referring to Figure 2.8, the first test level of the
flow classification for a buoyant jet in a linearly strati-
fied 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 strati-
fied flows, if lm/lm' < 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, and thus the alignment angle
7 will become an important factor in classifying the flows.
But for lm/lm' > O(l) the crossflow is weak and the flow is
"stratification dominated", and hence the vertical angle 0
will become the decision variable for classifying.
For plume-like stratified flows, because of the non-
existence of the two-dimensional plume to crossflow length
scale (see Section 2.4.6), a comparison of the effect of
stratification relative to the crossflow effect uses the
length scale la. If lb'/la < O(l) the crossflow will have
strongly deflected the buoyant plume flow before the
buoyancy begins to affect the flow leading to a "crossflow
dominated" regimef (7 is the further decision parameter).
On the other hand, lb'/la > O(l) signifies a "buoyancy domi-
nated" flow (6 is the decision parameter).
The terminal heights of rise Z, equations for any of
these flows are indicated on Figure 2.8. Detailed refer-
ences for these equations are in Section 4.3.2. In general,
the height of rise depends on lm', or !„' or la with'an added
influence of lm for crossflow affected stratified flow. The
sketches at the bottom of Figure 2.7 indicate the schematic
flow configuration for each flow class. Once the terminal
height has been reached, some flows (MSI, or MS2, or MS5,
or MS6) are further deflected by the strong crossflow
leading to far-field buoyant spreading and diffusion phases.
Other flows (MS3, or MS7, or MS8) have weak crossflow and
are more nearly vertical in their approach ("impingement")
to the terminal layer with an ensuing upstream spreading
phase. Flow class MS4 with strong horizontal momentum
experiences a near-horizontal "injection" into the terminal
layer.
34
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2.5.1.3 Flow Classes MU for Buoyant Discharges into Uniform
Ambient Layers
The flow classification system for positively buoyant
discharges in uniform ambient layers appears in Figure 2.9.
In this classification, the stability criterion (expressed
here in terms of length scale), defined in Section 2.3.1
(Eq. 2.3), is used to characterize the discharge as "deep
water" or "shallow water". A deep water discharge will have
relatively weak momentum as the flow contacts the surface,
while a shallow discharge will have a strong momentum as the
flow impinges on the surface.
In the case of deep water (stable conditions) , buoyancy
tends to have a stabilizing effect on the flow as it
contacts the surface. The study distinguishes between two
kinds of flow, one with a low ambient current where
O(l) (MU1V) and one with a high ambient current where
> 0(1) (MU1H).
In the case of shallow water, the flow has a strong
vertical momentum at surface contact and tends to be
unstable. The jet is deflected downward by the surface and
an unstable recirculation zone occurs around the jet as it
re-entrains the deflected fluid flow. Therefore, the flow
is vertically completely mixed in the near-field. For these
unstable conditions, the diffuser geometry, particularly, its
total net momentum input, becomes an important factor (flow
classes MU2-MU9). As defined in Section 2.2.2.1, there are
three kinds of diffusers (unidirectional, staged, and alter-
nating) , and hence a flow configuration pattern is assigned
to each one.
For the special cases of a predominantly parallel
alignment (7 < 45°) for the unidirectional diffuser and of
a predominantly perpendicular alignment (7 > 45°) for the
staged diffuser, respectively, thus, for cross-flowing dis-
charges a test is performed to determine whether momentum
or crossflow control the fully mixed diffuser plume in the
ambient' layer depth Hs. If ijli. > O(l) the flow is con-
trolled by momentum, and crossflow has a minor role in flow
behavior (flow classes MU3 and MU5) , and in the case of l^H,
< O(l), crossflow will play the dominant role relative to
both momentum and buoyancy factors (flow classes MU4 and
MU6) . In the remainder of the flow classes the diffuser
discharge is predominantly co-flowing, or has no net-
horizontal momentum in the case of alternating diffusers.
2.5.1.4 Flow Classes for MNU Negatively Buoyant Discharges
in Uniform Ambient Layers
The classification system for negatively buoyant
discharges (Figure 2.10) bears some similarities to that for
35
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positively buoyant discharges described above. Several
negatively buoyant flow classes have a "mirror image"
analogy to the positively buoyant flows.
Again, using a similar stability criterion as before,
one can distinguish between deep and shallow cases. In the
deep water case, the first step is to determine whether
momentum or buoyancy dominates the flow with respect to the
ambient layer depth Hs. If I^E, < O(l), the flow will be
buoyancy dominated after a short distance and therefore will
not have any surface interaction. If IM/H, > O(l), the flow
will be momentum dominated in relation to the ambient layer
depth Hs. Additional testing is performed in the buoyancy
dominated branch where the momentum length scale is compared
to the ambient layer depth H.. If l^H, > O(l) , crossflow is
weak, and hence the flow will rise slightly before falling
to the bottom (MNU1) . If I^H, < O(l) , the effect of
crossflow is high, and the flow, after rising slightly,
becomes advected downstream with a gradual approach to the
bottom (MNU2). For the momentum dominated branch, the
discharge geometry becomes important. For the alternating
diffuser, the flow will behave similarly to the previous one
(MNU2). For the unidirectional diffuser, additional tests
are performed to determine whether momentum and buoyancy or
crossflow dominate the flow. The overall length scale 1^
(see Table 2.1) is used for that purpose. If IM/!^ < O(l),
the flow has a weak deflection (MNU3), otherwise, the flow
possesses a strong deflection due to crossflow (MNU4). The
same comparison is done for the staged diffuser but using
the overall length scale LM (see Table 2.1) instead of 1M.
Weak deflection is indicated for LM/LO, < O(l) (MNU5) , and
strong deflection for LM/I^ > o(l) (MNU6), respectively.
tln the fully mixed shallow water cases, the same
decision tree is used as for positively buoyant discharges
(Figure 2.9) to describe the flow configuration (MNU7-MNU14)
with the exception of bottom restratification in the far-
field.
2.5.2 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.
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 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
36
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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 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
discussed in Doneker and Jirka (1990).
2.6 Analysis of Individual Flow Processes
The dynamics of individual mixing processes and their
analysis are discussed in this Section. The first subsec-
tion deals with jet/plume dynamics in deep water including
boundary interaction processes. The second subsection
addresses the diffuser-induced fully mixed plume motions in
shallow water. Finally, specific features of buoyant
spreading and diffusion processes in the far-field are
discussed.
2.6.1 Buoyant Plane Jet Processes in Deep Water
The effluent leaving the diffuser ports behaves as a
series of round buoyant jets (see Figure 2.11, Holley and
Jirka, 1986) and hence round buoyant jet analysis can be
used for prediction. At some distance, the adjacent plumes
merge with each other, and from then^ on the flow can
essentially be considered as two-dimensional. The initial
round plume region (three-dimensional region) will not be
considered in the following analysis.
2.6.1.1 Unstratified Ambient
This section presents analytical results for plane jets
and plumes issued vertically upward from a slot of width B,
perpendicular to the crossflow. First, the simple plane jet
and plume solutions in stagnant environment are introduced.
Then the theory is expanded to include the effects of
ambient crossflow and stratification. The procedure is
based on perturbation solutions. in the sense that a simple
analytical solution is being perturbed by assuming a small
37
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SIDE VIEW
ROUND , PLANE
TOP VIEW
Jets merging in unidirectional diffuser
PIPE
SIDE VIEW
TOP VIEW A-A,
Jecs merging in alternating diffuser
Figure 2.11
Interference of Individual Round Jets from
Multiport Diffuser Discharges forming Two-
Dimensional (Slot) Jets or Plumes (Ref. Lee
and Jirka, 1991).
30
-------
effect of an additional variable (e.g. a weak crossflow) .
For the following development the simplest possible
assumptions are being made: a plane 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 influ-
ences) . Indeed, such generalizations are implemented in
the predictive elements presented in Chapter IV.
2.6.1.1.1 Simple Plane Jet in stagnant Environment
Consider a plane jet (2-D) in a stagnant ambient fluid
(Figure 2.12). In the initial stage (when flow exits from
the equivalent slot diffuser), the velocity distribution is
near uniform. After a short distance s along the jet
trajectory, the velocity profile approaches a bell-shaped
(Gaussian) distribution.
The maximum velocity uc occurs along the trajectory
centerline and a similarity profile is assumed for the
velocity distribution. Similar conditions hold for the
centerline concentration cc of pollutant or tracer mass.
The jet centerline velocity uc decreases with distance s
from the point of transition as the plane jet entrains the
stagnant ambient fluid. The momentum flux per unit length
m0 is conserved along the trajectory, and the variation and
magnitude of the plane jet centerline velocity depend
essentially upon m0 and the distance along the trajectory
s, uc « (m0,s). Using dimensional analysis, one obtains
uc = c(m0/s)
1/2
(2.10)
where c is a constant.
The width b of the plane jet can, in principle, also
depend on m0 and s, but for dimensional reason, the only
possibility is a linear spreading
b = bts
where bj is a constant.
(2-11)
The volumetric dilution S at any cross-section along the
jet is defined by S = c0/cc, where c0 is the initial concen-
tration (at the ports) . The dilution S is related to m,,,
s, and q0, and by conservation of mass, one obtains
S = Sl(m0s)1/2/q0 = Ms/I,)
where s, is a constant.
1/2
(2.12)
39
-------
Instantaneous
appearance
ENTRAINMENT
VELOCITY
(Jo. po - pa. C0
•ZONE OF
FLOW ESTABLISHMENT
CONCENTRATION
PROFILE
AMBIENT DENSITY pg
Time-averaged conditions
Figure 2.12
Plane Jet in Stagnant Environment (Reg. Holley
and Jirka, 1986).
40
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2.6.1.1.2 Simple Plane Plume in stagnant Environment
A plane plume rises vertically and experiences an
increase in vertical momentum flux per unit length with
distance z above the source (Figure 2.13). The buoyancy
flux per unit length is constant for any plume cross-section
as it rises in an unstratified ambient. By dimensional
analysis, the centerline velocity is independent of z
uc = c(j0)1/3
where c is a constant.
(2.13)
The width b of the plane plume depends on distance z
b = b3z (2.14)
where b3 is a constant.
The dilution for a plane plume can be expressed by the
buoyant acceleration g'0 (buoyancy is conserved in the plane
plume) which decreases with distance s as the plume rises
and becomes diluted by the ambient fluid. The decrease in
g'0 is directly proportional to the amount of ambient fluid
entrained in the plume, so that S = g'0/g0 . Using the
continuity equation for buoyancy flux
S = S3j0l/3s/q0 = s3s/(lqlM)
where s3 is a constant.
1/2
(2.15)
2.6.1.1.3 Weakly Deflected Plane Jet in Crossflow
For a relatively weak crossflow, the plane jet would
behave in the same manner as if it were in a stagnant
environment, except that it is slightly advected by the
ambient current (Figure 2.7b). This region is defined for
z/lm « 0(1).
Considering a plane jet issuing perpendicular to the
crossflow, after the region of flow establishment the
vertical velocity is given by Eq. (2.10). The kinematic
relationship for a plane jet moving horizontally with the
crossflow velocity ua is, in the first order
dx/ua = dz/uc
(2.16)
Substituting Eq. (2.10) into (2.16) and integrating gives
the trajectory relationship for the weakly deflected plane
jet flow expressed in terms of the jet to crossflow length
scale
z/lm =
.2/3
(2.17)
41
-------
Instantaneous appearance
ENTRAPMENT
VELOCITY
AMBIENT
DENSITY pa
CONCENTRA TION AND
BUOYANCY PROFILE
VELOCITY PROFILE
Figure 2.13
, Po.
-------
where tt is a trajectory constant.
The plane jet width is similar to the width in the
stagnant case, and is.given by Eq. (2.11).
The equation for dilution is similar to Eq. (2.12), and
expressed in terms of the length scale is
S = Sl(z/lq)1/2 (2.18)
where st is the dilution constant.
2.6.1.1.4 Stronalv Deflected Plane Jet in Crossflow
For z/lm » O(l) the ambient flow will have a more
direct effect on the flow pattern. For a strongly deflected
plane jet, the vertical velocity has decayed to less than
the value for the ambient crossflow; thus the ambient
crossflow will have significantly deflected the plane jet
as shown in Figure 2.7b.
The equations for the strongly deflected plume jet are
derived on the basis of a "plume impulse" model analogous
to the line impulse model used for the deflection of a
sifigle round jet (see Doneker and Jirka, 1989) . Using the
impulse model, the characteristic variables are the distrib-
uted momentum impulse m' (m' = myuj , the vertical rise z,
and the ambient velocity us. Applying this concept to the
plane jet, the vertical velocity of rise uc is proportional
to m0/uaz. Applying Eq. (2.16) one finds the trajectory
relation for the strongly deflected jet flow in non-dimen-
sional form
z/lm = t2(x/lm)1/2 (2.19)
where t2 is a trajectory constant.
Similar to Eq. (2.11) the jet width is proportional to
position z
b = b2z (2.20)
where b2 is a constant.
The continuity equation provides the dilution S at any
position z
S = s2z/(lmlq)1/2 (2.21)
where s2 is a dilution constant.
Little is known about the appropriate constants for such
deflected jets. Assuming that the two-dimensional plane
43
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jet is penetrated by the crossflow and broken-up into three-
dimensional elements, the coefficients t2, b2, and s2 can be
assumed to have the same values as those used for the three-
dimensional counterpart (see Doneker and Jirka, 1989).
2.6.1.1.5 Weakly and Strongly Deflected Plane Plume in
Crossflow
As remarked in Section 2.4.6, in the two-dimensional
case, a plume to crossflow length scale does not exist.
Therefore, in order to investigate the deflected plume
dynamics, one can compare the vertical plume centerline
velocity uc to the ambient velocity ua. Two cases are
possible:
a) If uc » ua, the initial buoyancy will dominate and
crossflow is of secondary importance. Therefore the flow
will behave as plume in a stagnant environment but will be
weakly advected with the crossflow. In analogy to the
weakly deflected jet flow (Section 2.6.1.1.3) , the trajecto-
ry equation for the weaklv-deflected plane plume flow ex-
pressed in terms of length scales is
z = t3X(lm/lM)^2
where t3 is the trajectory constant.
(2.22)
The plane plume width is similar to the plume issuing
in a stagnant environment and is given by Eq. (2.17).
The dilution S is similar to Eq. (2.18), and expressed
in terms of length scale is
S = s3z/(lMlq)1/2
where s3 is the dilution constant.
(2.23)
uc « ua/ the high ambient velocity will cause a
strongly deflected plane plume behavior. It is reasonable
to assume that this bent-over plume behaves as a distributed
thermal, an instantaneous release of buoyancy-driven fluid
along a line source. The characteristic variables are, the
buoyancy release, j'= J0/uj , the vertical rise z, and the
ambient velocity ua. Applying these concepts to the plane
plume, the vertical velocity uc is proportional to (J0/ua)1/2,
and the trajectory relation for the strongly-deflected plane
plume flow is
z = t
-------
b = b4z
(2.25)
where b4 is a constant for the bdh flow. Using the continu-
ity equation to find the dilution S at any position z,
S = s4z/(lmlq)1/2 (2.26)
where s4 is a dilution constant.
2.6.1.1.6 Horizontal Plane Jet with Vertical Buoyant
Deflection "
For a horizontally discharging jet with weak vertical
deflection induced by the discharge buoyancy, the centerline
velocity is given in first order by the simple plane jet
solution, Eg. (2.10), or uc = (it^/x)172 in which x is the
horizontal coordinate direction. The small vertical
deflection due to the local buoyancy-induced velocity w is
dz/dx = w/uc
(2.27)
The local buoyant vertical acceleration of a jet element is
given by
dw/dt = J0/(buc)
(2.28)
in which b = x is the plane jet width. With the Galilean
transformation dt = dx/uc, and after substitution for b and
uc, Eq. (2.27) and (2.28) can be solved to give the normal-
ized trajectory relation
z/lM = ts(x/lM)s/2
The appropriate width and dilution equations are
b = bsx
(2.29)
(2.30)
and
S = ss(x/lq)
1/2
(2.31)
where the constants bs and ss should be numerically similar
to those for the weakly deflected jet in crossflow, bs s bt/
and ss = slf 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/lM < O(l) .
45
-------
2.6.1.1.7 Vertical Plane 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.
2.5a). This will occur in the region z/lM > O(l). The
plume will have a local vertical centerline velocity given
in first order by the plane plume solution, Eq. (2.13).
The small horizontal deflection of the plume trajectory is
given by
dx/dz =
(2.32)
where uh is the induced horizontal velocity due to the
discharge momentum flux m0. Conservation of horizontal
impulse implies
bu
(2.33)
in which b = z is the plume width. The trajectory relation
is obtained after substitution and integration
x
X
t6lMln(z/zF)
(2.34)
in which XF and ZF are the ultimate value of the horizontal
and vertical deflection for the final stage (z approaches
infinity) of the vertically rising plume. The width and
dilution are given directly by Eqs. (2.14) and (2.15), or
using the appropriate length scales,
b =
and
S = s6z/(lMlq)1/2
(2.35)
(2.36)
As before, the constants b6 and s6 should be the same as
those for the weakly deflected plume, b6 & b3 and s6 & s3,
respectively.
2.6.1.2 Typical Regimes of Buoyant Plane Jets in Linear
Stratification
This section presents analytical results for plane jets
and plumes issued from a slot of width B discharging into
a stratified ambient.
2-.6.1.2.1 Plane Jet in Linear Stratification
The ratio lm'/lm « O(l) indicates that the nonbuoyant
jet will reach its maximum height of rise before it is bent
46
-------
over by the effect of crossflow. Therefore, in order to
find solutions to that region (region beginning from the
discharge point to the maximum height) where the effect of
crossflow is negligible, one has to use the differential
equations of the simple plane jet in an unstratified
stagnant ambient and extend them to include the factor of
stratification. Two extreme cases of vertical and horizon-
tal jets are addressed.
a) Vertical Jet in Linear Stratification
Using the jet differential equations (Section 2.6.2,
Holley and Jirka,1986) and adding the effect of stratifica-
tion to the buoyancy term (Section 2.7, Holley and Jirka),
one can get a solution for the zone described. The solution
details are omitted here. The equation for terminal height
of rise expressed in length scale is
z, = t6lm' (2.37)
where ts is a constant.
The width of the plane jet is similar to Eq. (2.14),
b = b6s (2.38)
where bs is a constant.
The dilution S is found to be related to the momentum
flux m0, the discharge q,,, the stratification parameter e,
and the trajectory distance s. The equation of S expressed
with appropriate length scales is
S = (s6s1/2/lq1/2) (1 - S61(s/lm')3)1/2 (2.39)
where s6 and s61 are dilution constants.
b) Horizontal Jet in Linear Stratification
Using the solution for the plane jet in an unstratified
ambient (Holley and Jirka, 1986), the equations for plane
jet width and plane jet dilution are
b = b7s
S = s7(s/lq)1/2
where b7 and s7 are respective constants.
(2.40)
(2.41)
2.6.1.2.2 Buoyant Plane Plume in Stratified Stagnant Ambient
In.contrast to the preceding solution for the pure jet
there does not exist an explicit solution for the pure plume
47
-------
in stratified stagnant ambient. However, in the region
below the terminal height, z « Zt, stratification will be
of second order and the solution can be approximated by the
line plume solution in unstratified ambient. This leads to
the dilution equation,
S = s8z/(lMlq)1/2 (2.42)
where ss is the dilution coefficient, and the width equation
b = bsz (2.43)
where b8 is a constant.
The constant related to the dilution s8 should be
similar to s from Eq. (2.15), and constant b8 similar to b3
from Eq. (2.14).
2.6.1.3 Surface, Bottom, and Terminal Layer Interaction
Processes
Ambient water bodies always have vertical boundaries:
these are the water surface and the bottom, but in addition
"internal boundaries" may exist in the form of layers of
abrupt 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 strati-
fied ambient where flow trapping may occur, other interac-
tion phenomena may take place.
In essence, these interaction processes provide a
transition between the jet mixing process in the near-field
(Section 2.6.1), and between buoyant spreading (Section
2.6.3) and passive diffusion (Section 2.6.4) in the far-
field.
Several possible interaction processes are analyzed in
detail by Doneker and Jirka (1989). These processes pertain
to single port as well as to multiport discharges. They
are: (i) near-vertical surface/bottom/pycnocline impingement
with buoyant upstream spreading, (ii) near-vertical
surface/bottom impingement with unstable recirculation,
buoyant restratification, and upstream spreading, (iii)
stratified terminal layer impingement with buoyant upstream
spreading, and (iv) stratified near-vertical surface
injection with upstream spreading.
A control volume approach is used for the following sec-
tion. 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
40
-------
"i" (initial) and "f" (final) (e.g. bi7 St) denote control
volume inflow and outflow quantities, respectively.
In the surface approach the bent over flow approaches
the water surface near horizontally at impingement angle 6i
< 45°. 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 impinge-
ment the concentration distribution for a 2-D flow changes
from the assumed Gaussian distribution to a top-hat or
uniform distribution. 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 =
cSj, where c is a constant. The width of this section is
given by the diffuser length and the alignment, 2bM =
•LoSin-y. The continuity equation for the control volume is
then
S,Q0 = uabvfLDsin7/2 (2.44)
where b^ is the final flow vertical width, and bu is the
final flow horizontal half-width.
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 Doneker and Jirka,
1990).
For the case of unstratified ambient, one more interac-
tion process exists which is the near-vertical surface
impingement with buoyant upstream spreading. A full discus-
sion on this particular flow can be found in Doneker and
Jirka (1990).
For the case of stratified ambient, two possible flow
regions can exist for terminal flow interaction; i) near-
vertical terminal layer approach with buoyancy upstream
spreading, and ii) terminal layer injection with surface
spreading (see also, Doneker and Jirka, 1990).
2.6.2 Diffuser Induced Jet Mixing in Shallow Water
As mentioned before, when the stability criterion is
exceeded in Eq. (2.3a) (stagnant case) or Eq. (2.3b) (with
ambient crossflow), then the flow becomes unstable, and
49
-------
therefore the diffuser geometry and flux parameters are the
important elements. For these cases, the unstable near-
field is typically vertically well-mixed, although the mixed
flow may re-stratify in the later far-field. Significant
currents and large-scale circulation may be introduced in
the shallow receiving water. The most frequent use of
shallow water diffuser theory is in the design of submerged
cooling water discharges.
2.6.2.1 Unidirectional Diffuser
The flow generated by a unidirectional diffuser (Figure
2.5) is generated by pressure gradients which are set up by
the momentum input (Jirka, 1982). The induced flow sepa-
rates near the diffuser ends into a contracting slipstream,
i.e. an acceleration zone (Lee and Jirka, 1980). The flow
structure is shown in Figure 2.14. The equations related
to the unidirectional diffuser are found when analyzing the
contracted slipstream. In the following the acceleration
zone solutions for the diffuser in a stagnant ambient are
presented, and then extended to include the effect of an
ambient current.
2.6..2.1.1 stagnant Ambient
The solutions for that case are given by Lee and Jirka
(1980). The bulk dilution in the acceleration zone is in
the present notation
(H/21,)1'2
(2.45)
The diffuser horizontal half-width is found to be related
to the streamline approach angle 0lr the distance x along
trajectory, and the diffuser length Lj,. For stagnant
conditions, the approach angle 0t is close to 60°, and the
transition to diffusion zone was found to occur at a
distance of about 1^/2. Due to the difficulty of mapping,
the contracting slipstream half-width bh is fit by the
following equation as an approximation to Lee and Jirka
(1980) solution ,
bh = LD/2 [a, + (1 - a,) exp(-3x'(l + X*3) ) ]
(2.46)
with x' = 2x/LD and al = contraction ratio = 1/2.
2.6.2.1.2. Ambient Crossflow
With the presence of an ambient current, it is necessary
to know the alignment of the diffuser relative to the
crossflow. Two cases are discussed here, the case of
50
-------
predominantly perpendicular (7
alignment..
90°) and parallel (7 * o°)
a) Perpendicular Alignment (-Y « 90°)
The "Cof lowing Diffuser" in which the diffuser axis is
perpendicular to the crossflow, has the same flow features
as those under stagnant conditions. The result for the bulk
dilution (Adams, 1972, and Lee and Jirka, 1980) expressed
in length scales, is
S = H/2(ll)1/2 + ((H2 + 2Hlm)/lmlq)1/2
(2.47)
Using the same procedure as for the stagnant case, with
the exception of having the approach slipstream angle as
function of dilution S, port velocity u0, and ambient
velocity ua, the horizontal diffuser half-width is
approximated by
bh = LD/2 !>! + (1 - a,) exp(-3x (1 + x3)) ]
where
x* = 2x/LD
+ 0.5)/(S(lm/lq)* + 1)
(2.48)
(2.49)
(2.50)
The performance of the unidirectional diffuser has been
found effective in a cof lowing current. But under current
reversals (e.g. in tidal conditions) the diffuser perform-
ance is poor with intense effluent concentration buildup
zones occurring whenever the nozzle direction opposes the
incoming current (counter flowing diffuser) (Adams, 1980,
Harleman and Jirka, 1971) .
b) Parallel Alignment f-v
0")
The "Tee Diffuser" in which the diffuser axis is
parallel to the ambient current, behaves in a slightly
different way than the cof lowing diffuser. Experimentally,
it has been found that the mixing performance depends on the
ambient to discharge momentum flux, v^/mof or expressed by
the ratio, H/lm. For weak currents, H/lm < 0.1, the
dilution S is similar to the previous one in Eq. (2.47);
however, for larger values of H/lm, the near-field dilution
drops. Analysis over a wide range of data (Adams and
Stolzenbach, 1977) leads to an empirical reduction factor
rs, which gives a dilution reduction relative to the perpen-
dicular case value S, Eq. (2.47)
rs =
5(H/1J]-1/2
(2.51)
51
-------
The cause of this reduction in dilution is related to the
interaction of individual jets, where the pressure distribu-
tion set up by the ambient current limits the quantity of
water which can enter from behind the diffuser (Jirka and
Lee). As for the horizontal half-width, the same equation
used for the coflowing case (Eq. 2.51) applies here.
Due to large induced flow involvement, the tee diffuser
must be located far offshore in order to provide enough
space for back entrainment flow. With a shoreline boundary
placed at a separation distance xs from and parallel to the
tee diffuser line, theoretical and experimental work (Figure
2.15) show that significant reduction of induced flows and
bulk mixing can occur if the separation distance is less
than LD/2 (Adams et al, 1982, and Lee, 1984).
2.6.2.2 Staged Diffuser
The jets in a staged diffuser (Figure 2.4b) possess a
small nozzle orientation angle /3 ~ 0° with respect to the
diffuser axis. As mentioned in Jirka (1982), experimental
observation suggests a region composed of two zones; an
acceleration zone along the whole diffuser length in which
momentum is imparted, and, beyond the diffuser, a decelera-
tion zone with lateral diffusion and bottom frictional
dissipation (Figure 2.16). The induced flow contains a
boundary layer geometry and can be modelled as a momentum
line source imparted to the ambient flow over the diffuser
length.
2,6.2.2.1 Stagnant
Using the results of Lee (1980), the dilution equation
for the acceleration zone is
(2.52)
S = s$
where ss is a dilution constant.
Using simple geometric reasoning, the horizontal
diffuser half-width, which depends on the distance along the
trajectory and the nozzle orientation relative to the
diffuser axis /3,
bh = (bs + 0.5 tan
where bs is a constant.
(2.53)
52
-------
Acceleration
zone
Diffusion zone
Figure 2.14 Flow Field Induced by Unidirectional Diffuser
(Ref. Jirka, 1982): Structure of Diffuser
Plume (half-plane with symmetry line).
sr/s
0-5
1-0
i i tn
Figure 2.15
Effect of Limited Separation Distance
between Diffuser Line and Shoreline (Sr
reduced dilution, S: original dilution) (Ref
Lee, 1984) .
53
-------
2.6.2.2.2 Ambient Crossflow
With the presence of ambient current, the mixing
performance will improve relative to the stagnant case.
The dilution S is determined by adding a term related to
crossflow to Eq. (2.52), and hence
S = ss ((1 - lm/lqH/lq)
1/2
(2.54)
For the special case of strong ambient current, the dilution
equation for the perpendicular diffuser alignment is (Jirka,
1982)
S = ssl(H/lq)1/2(l + 2.23H/1J
1/2
(2,55)
where ssl is a dilution constant.
The plume half-width is similar to the stagnant case
and is given by Eq. (2.53).
2,6.2.3 Alternating Diffuser
As described earlier, the alternating diffuser (Figure
2.5c) does not impart any net horizontal momentum, because
its jets alternately discharge in opposite directions. As
remarked earlier, the alternating diffuser category also
includes other nozzle (port) arrangements that do not impart
any net horizontal momentum e.g. vertical discharge orienta-
tion or nozzle clusters radially attached to risers.
2.6.2.3.1 Stagnant Ambient
Outside the unstable recirculation zone (Figure 2.17),
a stratified counterflow region is generated and the bulk
dilution is influenced by buoyancy effects instead of pure
momentum effects (Jirka, 1982). The transition to this
region occurs at an approximate distance of 2.5H (Jirka,
1982).
Using the two-dimensional channel analysis described by
Jirka (1982), the dilution is found (taking $c = 0.1 in
Figure 18 of Jirka, 1982), as
S = saH/(lMlq)1/2
(2.56)
where_ sa is the appropriate dilution constant. This
dilution factor characterizes the fully mixed near-field
zone extending for a width 2.5H on both sides of the
diffuser axis. A stratified counterflow system exists
outside that near-field.
54
-------
Plan view
Acceleration zone
\Vertically\
mixed
Figure 2.16 Flow Induced by Staged Diffuser (Ref. Jirka,
1982): Structure of Diffuser Plume.
Symmetry
Unstable
near field
Intermediate field
25H
Figure 2.17 Alternating Diffuser in Stagnant Ambient:
Side View: Stratified Counterflow Character-
istics in Two-Dimensional Representation
(Adapted from Jirka, 1982).
55
-------
2.6.2.3.2 Ambient Crossflow ,
The dilution in an ambient current may be estimated by
a vector addition of the stagnant water dilution and the
ambient flow dilution (Jirka, 1982). Hence adding the
ambient term, the dilution for the perpendicular alignment,
S = H[(0.251
,1/2
(2.57)
The initial half-width of the flow downstream from the
alternating diffuser is
bh = 2.5H + Lo/2
(2.58)
A reduction of 20% from the perpendicular alignment
dilution (Eg. 2.57) is typical for the parallel alignment
dilution (Jirka and Harleman, 1973).
2.6.2.4 Fully Mixed Diffuser Plumes (Intermediate Field)
Following the terminology used by Jirka (1982) the
gradually expanding diffuser plume induced outside the
acceleration zone of either the unidirectional (Figure 2.14)
or staged (Figure 2.15) diffuser is referred to as the
11 intermediate field".
The intermediate field plume is . divided into two
regions: region 1, and region 2.
Region 1 starts immediately after the acceleration zone,
and extends up to a distance where restratification occurs.
This distance is determined by the initial value of a
densimetric Froude number, Fc = u,/ (g'cHs)1/2, with g'c = g'0/S) .
As typical for intrusion processes the initial value Fc is
of order unity (Jirka, 1982). The transition distance for
region 1 is
s, = cLM4/Fc4H3 (2.59)
where c is a constant and is dominated by the length scale
LM representative for the entire diffuser.
The model for the vertically mixed two-dimensional jet
flow associated with this region has the same characteris-
tics as the regime related to the momentum dominated near
field (see Section 2.6.1.1.3) with the exception of having
a different momentum to crossflow length scale, and a
different discharge to momentum length scale respectively.
Hence, the model uses the same mixing and trajectory of
relations, Eq. (2.17) and (2.18), with a change of lm to
dm, and lq to dq, respectively, where
dm = lmLD/H
(2.60)
56
-------
and
dq =
(2.61)
In Region 2 the diffuser plume becomes stratified.
Thus, a lateral buoyant spreading motion is superimposed on
the diffusing plume. While using the same dilution and
trajectory equations as before (region 1), it is necessary
to account for the additional spreading. The buoyant
spreading rate is given by the ratio of lateral spreading
velocity to plume centerline velocity uc. Therefore, the
theory of buoyant spreading is used, where instead of using
the velocity current as a dependent variable, the jet
centerline velocity uc is used (Table 3, Holley and Jirka,
1986) in the width differential equation, and hence
(db/dx)B = (g'0h/uc2CD)
1/2
(2.62)
where h is the height (vertical thickness) of diffusing
plume and CD is the drag coefficient (of order unity) .
The horizontal width bh is
bh =
(s
7/4 -
(2.63)
where bw is the initial horizontal at transition s, and bc
is the width constant.
The vertical width is found to be
bv = S^H/Sb,
which decreases due to restratification.
(2.64)
2.6.3 Buoyant Spreading Processes
In the context of this study, buoyant spreading pro-
cesses 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
(see Figure 2.18).
The buoyant spreading phenomena 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:
5.7
-------
Front
Plan View
Condition
Cross-section A-A
Frontal Zone
H
Figure 2.18
Buoyant Surface Spreading (Ref. . Doneker and
Jirka, 1989). ;
58
-------
(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.
To a major extent the buoyant spreading processes in the
far-field of multiport diffusers are entirely similar to
those for single port discharges. The reader is referred
to Doneker and Jirka (1989) for a complete treatment of
these.
Separate buoyant spreading processes can occur for
multiport diffusers with parallel alignment when the
continuous buoyant inflow along a long diffuser line gives
a different source condition. This is discussed in the
following section for unstratified and linearly stratified
ambients, respectively.
2.6.3.1 surface Density Current Developing Along Diffuser
Line in Parallel Alignment
In contrast to Figure 2.18, a source condition of a
continuous inflow exists along the diffuser line whose
starting point is at x = Xi. The source flow for one side
of the density current is q^ = 0.53^ where Sf is the final
dilution for the near-field mixing.
The buoyancy conservation equation for the mixed flow
is adapted from Doneker and Jirka (1989) as
uad(g'bA)/dx = q.(x) + • <& (2.65)
where q^x) is the localized head entrainment at the density
current front, and bh is the lateral half-width.
Neglecting the head entrainment q«. relative to the
inflow qN, and integrating Eq. (2.65)
uag'bhbv = j0x/2 (2.66)
For constant dilution along the diffuser line, independent
of x, g' will be replaced by g'o/Sj. Benjamin (1967) has
derived an equation for the spreading velocity VB
vB2/(g'bv) = 1/CD (2.67)
where CD is a drag coefficient that depends on the relative
depth bv/H and is in the range of 1/2 to 2. Combining the
boundary condition for the streamline (VB = uadb,/dx) and Eq.
(2.67), yields
uadb,/dx = (g'0bv/CD)1/2 (2.68)
59
-------
Substituting Eq. (2.66) into (2.68), and integrating, the
flow half-width bh is
(lm/lM)3/2/(2CD) (X3'2 - X3/2))]2'3
(2.69)
where x> is the downstream distance at the beginning of the
buoyant spreading region, and b^ is the initial density
current half-width. A qualitatively similar result for the
width bh has first been obtained by Roberts (1977).
The vertical bv is given by combining Eqs. (2.69) and
(2.65), to obtain, with appropriate initial conditions at
MA
bv = St(lq lm)1/2x/2b,
- sf(l, Im)1/2xy2bh)
(2.70)
2.6.3.2 Internal Density Current Developing Along Piffuser
Line in Parallel Alignment
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 and leads to a lateral spreading while the
flow is being advected downstream.
The spreading velocity VB for the stratified case is ex-
pressed as
= V(2CD) (2.71)
where CD is the drag coefficient for the stratified case.
Proceeding in the same fashion as in Section 2.5.3.1,
one obtains the following result, for horizontal half-width
bh
hi2 + (2/CD)l/2(S,(lq Im)1/2(x2-x2)/41a .+
and for the vertical thickness bv is
bv = (Sf(lq lm)1/2(x-Xi)/2 + k)/bh
where
k - (bub,, - sf(l, lm)1/2)xi/2)
(2.72)
(2.73)
(2.74)
60
-------
2.6.3.3 Upstream Intruding Density Wedges Formed in Bounded
Channels
Multiport diffusers are frequently installed in narrow
channels (rivers or estuaries) in which the diffuser spans
a good fraction of the channel width, W, or else the
diffuser mixing capacity is controlled by the available
ambient flow. In either case, upon completion of the near-
field mixing processes, the diffuser plume will interact
with the lateral boundaries of the channel. Under certain
low ambient velocity conditios (characterized by a densime-
tric Froude number) a laterally uniform density wedge may
intrude upstream along the bottom, surface/pycnocline, or
in a terminal layer. These possibilities are indicated in
Figure 2.19. The degree of wedge intrusion is controlled
by interfacial friction along the density wedge.
Two dynamic possibilities for wedge intrusion exist: a)
wedges with a critical boundary condition, and b) wedges
with a subcritical boundary condition.
2.6.3.3.1 Density Wedges with Critical Boundary Condition
Referring to Figure 2.19a and b, assume the maximum
possible near-field dilution is controlled by the
ambient/discharge flow ratio
(2.75)
By the mass conservation principle, this dilution cannot
be exceeded in a steady-state mixing process. Thus, if this
predicted dilution within the hydrodynamic mixing zone
(near-field processes) - which do not account for a later-
ally limited ambient water body - indicates a final dilution
value Sf that is in excess of Sn, then local recirculation
processes will take place in the limited channel, resulting
in a fully mixed downstream flow with dilution equal to Sn
and a density pn = pa + Ap0/Sn.
Upstream density wedge intrusion will occur whenever the
channel densitimetric Froude number
Fch -
(2.76a)
is less than a critical value of about 0.7 (Arita and Jirka,
1987) in which g'n = (Ap^pjg and Apn = Ap0/Sn. Under these
conditions the root of the wedge (at the edge of near-field
mixing zone) will be characterized by a critical depth
hc =
(2.76b)
61
-------
a) Bottom wedge (critical)
near-field
b) Surface wedge (critical)
X/XN N X
c) Bottom wedge (subcritical)
//x.\\
XVVSNN
d) Internal wedge (subcritical)
Figure 2.19
Different Upstream Wedge Intrusion in a
Bounded Channel
-------
The wedge length L,, is given for the bottom wedge (see Arita
and Jirka, 1987) as
(2.77)
- H (
f/ ^20 Fch2
3 T? 4
TO F*
+ 3_ F V3 _ J-
4 "* 2
and for the surface wedge (Bata, 1957) as
1
H [2(1 -
- (1 -
—^—^—« " L ** \ — ~ ch
Vill
4/3 \ • f\ f yii—^\2
+ 4a( + a) (1 - Fch4/3) + 8(a(l+a)a - P.,2) (1 - F
- 8a((l+a)3 - Fch2) (log a - log(l - a - F^3) ) ]
(2.78)
in which f = Darcy-Wesbach friction factor, f, = interfacial
friction factor, and a = f/f ~ 0.5.
2.6.3.3 Density Wedaes with Subcritical Boundary Conditions
If the dif fuser plume (with predicted near-field
dilution Sf < SJ is interacting with both lateral bound-
aries, then a flow away zone is formed with a layer thicJc-
ness
v, _ Sf QQ (2.79)
1 ua W
a) For a bottom or surface layer in uniform ambient density
flow, upstream intrusion takes place if the Froude number
"hi
(2.80)
in which g'£ = (APl/Pa)g and APt = APo/S(, is less than about
unity.
Assuming the layer is sufficiently thin relative to the
water depth, so that the ambient velocity over the wedge is
constant, a simple force balance governs the flow
r, dx = |g't| h2 dh2
(2.81)
in which V = interfacial friction = (f,/8) ua2. Integration
of Eq. (2.80) gives the wedge length for subcritical
conditions, h,
-------
(2.83)
The intrusion is blocked (prevented) for FM > 1 and occurs
for F^ < 1. The governing force balance
rf dx = e h2 dh
gives, upon integration, the wedge length
T _ 8 h,
^* 3fi FM2
(2.84)
(2.85)
2,6.4 Passive 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 stratifica-
tion. In general, the passively diffusing flow is growing
in width and in thickness (see Figure 2.20). Furthermore,
it may interact with the channel bottom and/or banks. For
further details on these processes, the reader is referred
t0>Dpneker and Jirka (1989), as they are independent of
initial source conditions.
64
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Plan View
U
•Initial Conditions
, Possible Bank Interaction
r jyyysV^^
Side View
Possible Bottom Interaction
Figure 2.20
Passive Diffusion Mixing Process (Ref. Doneker
and Jirka, 1989).
65
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Chapter III
CORMIX2: System Structure and Program Elements
The Cornell Mixing Zone Expert System, Subsystem "2..,
(CORMIX2) is a series of software elements for the analysis
and design of conventional or toxic multiport submerged
buoyant, nonbuoyant, or negatively buoyant pollutant
discharges into unstratified or stratified watercourses,
with emphasis on the geometry and dilution properties of the
initial mixing zone. The cases of both stagnant and flowing
environment are included. This expert system is constructed
and designed as an analysis tool for dischargers and
regulators.
The user provides CORMIX2 with all the necessary
information concerning the ambient environment, and the
discharge characteristics. In response to this data input,
CORMIX2 supplies detailed information related to the
hydrodynamic mechanisms controlling the flow, dilution,
geometric information concerning the pollutant plume shape
in the ambient flow, and design recommendations and advice
permitting the actual user to improve the effluent mixing
characteristics. Information related to legal mixing zone
dimensions and toxic mixing zone requirements are provided
by CORMIX2 when they are requested by the user. CORMIX2
executes on a MS-DOS computer using an IBM-PC/XT along with
a printer, and a hard disk drive.
The obectives of CORMIX2 is to give the user an
understanding in the hydrodynamics of flows. Through
repeated interactive use of the software system, the user
can ultimately gain some knowledge of hydrodynamic mixing
processes.
3,1 Background on Expert Systems and Logic Programming
CORMIX2 is written in two programming languages: VP-
Expert, an expert systems "shell", and Fortran.
VP-Expert is an expert systems programming language, or
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 reason for using the two programming languages lies
in the fact that one is powerful -in knowledge representation
and the other in mathematical computations. The knowledge
base language VP-Expert is very efficient in knowledge
representation and symbolic reasoning; however it is less
powerful in numerical computational techniques. On the
66
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other hand, Fortran is effective in mathematical
computations and less efficient in symbolic reasoning.
Hence VP-Expert is used to implement the knowledge
acquisition, the length scale computation, model selection,
and, the analysis of the hydrodynamic simulation. Fortran
is used to carry out computations used in the hydrodynamic
simulation models.
.The knowledge base of an expert system contains
statements .containing facts and if-then rules about facts.
The VP-Expert knowledge base is built from the rules
supplied by the user corresponding to a problem area.
, As explained by Doneker and Jirka (1988), VP-Expert
programs are driven by a "goal" which the program tries to
validate by searching the knowledge base to construct a
"proof" by using the facts and rules in the knowledge base
needed to deduce the goal as a valid hypothesis.
All the programs in VP-Expert are constructed based on
rule statements where the rules are stated as: .if
{expression(s) or clauses called the "premise" or "head" of
the rule} - then {an expression or clause named the
"conclusion" or "tail" of the rule} statements. The
structure of a rule can consist of one or more than one
expression linked by and/or statements. An example of a
rule statement is :
IF site_description <> UNKNOWN and
ambient_conditions <> UNKNOWN and
discharge_parameters<> UNKNOWN and
mixing_zones <> UNKNOWN
THEN parameters_input = known; [1]
All the conditions have to be met in order to satisfy the
conclusion statement (parameters_input). In other words,
VP-Expert tries to satisfy all expressions in the premise
of the rule, starting in statement [1] with the first
expression "site_description <> UNKNOWN" (the <> UNKNOWN in
[1] stands for "not equal to"). If the value of the first
clause is determined, VP-Expert tries to satisfy the next
expression "ambient_conditions <> UNKNOWN". If this latter
is satisfied, then VP-Expert will try to meet the remaining
expressions in the rule structure. When all the expressions
are satisfied, the rule succeeds, and hence the conclusion
statement can be given a valuation and is added to the facts
known in the knowledge base. .
The way VP-Expert would know the expression of
"site_description" lies in the fact that there is another
rule in the knowledge base related to this subject which
is: .
6-7
-------
IF site_name <> UNKNOWN and
discharger_name <> UNKNOWN and
pollutant_name <> UNKNOWN and
design_case <>;UNKNOWN
THEN site_description = known;
[2]
The same logical pattern is followed here, but since there
is no present valuation for the expression
"site_description", VP-Expert will locate statements with
the expression "site_description" in its conclusion. If all
the expressions in [2] can be assigned valuations, then the
expression site_description is a known expression.
Within the program there is another rule placed in a form
of an "ASK statement" like
ASK site_name: " Enter a descriptive name for the
discharge location." [3]
This rule is treated as a "fact", and VP-Expert asks the
user to enter the value of "site_name" through the message
within the quotes of statement [ 3 ] . The user enters the
value for "site_name" and thus the value for this variable
is known to VP-Expert. Next, VP-Expert tries to find the
values for the remainder of statement [2] in a similar
manner. More detailed explanations on the expert systems
logic can be found in Doneker and Jirka (1989).
Thus the knowledge base is built from rules consisting
of expressions that force VP-Expert to seek valuations from
other rules. The process of seeking values for the
expressions continues in a tree-like search until all values
are determined or when the rule is exhausted without finding
a valuation. ,
When all the rules have succeeded, a listing of all the
expressions values are saved in a file to be loaded for the
next VP-Expert element.
3.2 Structure of CORMIX2
Figure 3.1 shows the overall structure of the system
elements of COPJMIX2. The program elements of CORMIX2 are
composed of DATIN2, PARAM2, CLASS2, HYDRO2, and SUM2.
During system use the elements are loaded automatically and
sequentially by the system. Table 3.1 outlines the
directory structure of CORMIX2 and contains comments about
program files.
60
-------
VP-Expert
DATIN2
User Input
Iteration
Alternatives
Corrections
VP-Expert
PARAM2
Parameter
Computation
VP-Expert
CLASS2
Flow
Classification
VP-Expert Fortrun
HYDR02
Prediction/Simulation
Program
VP-Expert
SUM 2
Summary
Evaluation
Recommendations
(Lega I /Engineering)
Figure 3.1
System Elements of CORMIX2
69
-------
Table 3.1
CORNHEX2 Program File Directories
Directory
c:\cmx2
Comments
system root directory, contains VP-Expert
system files and the knowledge base
program CORMIX2 (system driver)
c:\cmx2\advice2 contains all user-requested advice files
c:\cmx2\bat2
c:\cmx2\cache2
c:\cmx2\data2
c:\cmx2\flowdes2
c:\cmx2\kbs2
c:\cmx2\pgms2
c:\cmx2\sim2
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 fbr each
flow class
contains all knowledge base programs
'contains Fortran hydrodynamic simulation
and file manipulation programs
contains simulation results
70
-------
The system runs entirely under the VP-Expert system
shell. The hydrodynamic simulation Fortran program HYDRO2
is executed from the knowledge base program HYDRO2. All
program elements execute sequentially. For example, when
a rule in a program element DATIN2 corresponding to
statement [1] fires, the "cache" of DATIN2 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 DATIN2, the knowledge base PARAM2, and so on for
the remaining program elements.
3.2.1 Data input Element: DATIN2
DATIN2 is a VP-Expert program element for the entry of
relevant data and for the initialization of the other
program elements. DATIN2 consist of four program segments
or knowledge base sub-elements which execute sequentially.
The knowledge base sub-elements are, in execution order,
ASITE2, AMBIENT2, DISCHAR2> and ZONES2. DATIN2 is the first
program executed, and it is invoked by entering the command
"CORMIX2" at the DOS prompt.
The purpose of DATIN2 is to specify completely the
physical environment of the discharge, as well as legal or
regulatory specifications. The following data groups need
to be entered: general site and case identifier information
(knowledge base ASITE2), ambient conditions (geometry and
hydrography, knowledge base AMBIENT2), discharge conditions
(geometry and discharge fluxes, knowledge base DISCHAR2),
and information desired including legal mixing zone
definitions and toxic dilution zone criteria (knowledge base
ZONES2). DATIN2 provides consistency checks, and gives
advice for input parameter selection.
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 DATIN2 gathers was
given in Figure 2.1.
DATIN2 contains advice on how to enter data values and
rejects inappropriate or incorrect values. The advice
elements of DATIN are listed in Appendix A-, of this report.
DATIN2 will also flag unusual design cases. For example,
in the knowledge base sub-element DISCHAR2, if the users
specifies a discharge horizontal angle which is directed
against the ambient current the following message is
displayed:
71
-------
"Note that CORMIX2 will not analyse the so-called
counter-flowing discharges (with horizontal angles of
discharge between 135 to 225 degrees). In this case
the discharge momentum opposes the ambient flow
leading to complicated recirculation patterns and
concentration build-ups in the near-field. This
situation is difficult to analyzes and also
constitutes an UNDESIRABLE DESIGN. The user is
advised to re-evaluate the design or to discontinue
the analysis." [4]
At its termination DATiN2 triggers the next program
element PARAM2. ! '
3.2.2 Parameter Computation; PARAM2
PARAM2 is a VP-Expert program that computes all the
important and relevant physical parameters for the given
discharge case. This includes the momentum flux and the
buoyancy flux per unit diffuser length (m0/ and j0) , the
various length scales (lq/ lm, 1M, l'm, l'b, 1'J and other
values needed for the program evaluation. As PARAM2
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 PARAM2 triggers the next program
element, the knowledge base CLASS2.
3.2.3 Flow Classification Element; CLASS2
CLASS2 _ is a VP-Expert program that classifies the given
discharge into one of the many possible flow configurations
that have been presented in Chapter II (Figures 2.7 to 2.9) .
CLASS2 contains two program elements, the knowledge base
sub-elements CLASS2 and FLOWDES2.
The goal of CLASS2 is to find a valuation for the
expression "flow_class" in relation to the flow
classification scheme. Each of the possible flow
classification has an alphanumeric label (eg. MU1, MSI, MNU6,
etc.). CLASS2 irfputs a cache created by PARAM2 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. As an
example of the output from CLASS2, the following would
represent some of the information presented for a discharge
trapped by the pycnocline in a two layer density stratified
environment:
72
-------
"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 MU1 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
FLOWDES2. This detailed output includes a description of
the significant near field mixing processes, or the
hydrodynamic mixing zone (HMZ). For an example, the
description for flow class MU1 appears in Figure 3.2. The
flow description of all the classes are presented in
Appendix B. 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. CLASS2 also creates a cache output
file that supplies the next CORMIX2 element HYDRO2 with
instructions for running the appropriate simulation. At
its termination CLASS2 triggers the next program element
HYDR02.
3.2.4 Hvdrodvnamie Simulation Element? HYDRO2
HYDRO2 is a Fortran program which executes the
hydrodynamic simulation program for the flow classification
program specified in CLASS2. The elements of the simulation
program are based on the hydrodynamic theory discussed in
the Chapter IT and in more detail in Chapter IV.
The program HYDR02 contains control programs or
"protocols" corresponding to each hydrodynamic flow
classification (MU1, MU2, MSI, etc.) as specified in CLASS2.
73
-------
*** BEGINNING OF FLOW CLASS DESCRIPTION ***
FLOW CLASS MU1V
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 slot (2-D) jet: The flow
issuing from the equivalent slot diffuser is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.
2) Buoyancy-dominated (2-D) 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 in all directions (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 in which
strong initial mixing takes place.
*** The zones listed above constitute the HYDRODYNAMIC
MIXING ZONE ***
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
pluine 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.
Figure 3.2 Example of Flow Description
74
-------
*** Predictions will be terminated in zpne 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.
*** END OF FLOW CLASS DESCRIPTION FILE ***
Figure 3.2
(Continued)
75
-------
Each protocol executes a series of subroutines or "modules"
corresponding to the flow phenomena (e.g. weakly deflected
jet in crossflow, buoyant spreading, unidirectional diffuser
acceleration zone, surface interaction modules, buoyant
spreading, etc.) which may occur in that flow con figuration.
Hence transition rules are needed to give the spacial
expressions as to where each flow region ends. Each
subsequent flow region is given by the initial values
corresponding to the final values of the preceding flow
zone. More detailed i explanations on protocols and
transition rules are discussed in Chapter IV.
HYDR02 creates a tabular output file of the simulation
containing infprmation on;geometry (trajectory, width, etc.)
and mixing (dilution, concentration) . The user has the
option to view the tabular output file.
At its termination HYDRO2 triggers the final program
element SUM2.
3.2.5 Summary Element; SUM2
SUM2 is a VP-Expert program that summarizes the
hydrodynamic simulation results for the case under
consideration. SUM2 discusses the mixing properties,
determines the applicability of the legal mixing zone, and
suggests the possible design alternatives to improve the
mixing characteristics. Thus, SUM2 may be used as an
interactive loop to guide the user back to DATIN2 to alter
the design variables.
The output of SUM2 is divided into four parts which are:
the site description summary, the hydrodynamic simulation
summary, the analysis of the data, and finally the design
advices and recommendations. All the information related
to the site identifier, the ambient and discharge
characteristics data, and the various discharge length
scales are listed in the site description summary.
The hydrodynamic simulation summary includes the
conditions related to the hydrodynamic mixing zone, legal
mixing zone conditions, toxic dilution zone conditions,
region of interest criteria, information about upstream
intrusion, bank attachment locations, and a passive
diffusion mixing summary, depending if the preceding
properties occur. The data analysis part includes detailed
information about the toxic dilution zone criteria, the
legal mixing zone criteria, and the region of interest
criteria. The last part deals with design recommendations
where design suggestions"and advice are given for improving
the mixing properties. The design recommendation
information is listed in Appendix c.
76
-------
At the completion of SUM2, 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.
Depending on the computer configuration, J typical
CORMIX2 session for one Discharge/environment condition may
take about 5 minutes for an advanced 80386-based computer
to 20 minutes for an IBM-PC/XT, if all necessary input data
is at hand.
77
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Chapter IV
CORMIX2: Flow Protocols and Simulation Modules
This chapter covers the hydrodynamic details of the
effluent flow predictions and mixing zone analysis as
performed in program element HYDRO2 of the expert system
CORMIX2.
This chapter begins by presenting the detailed flow
protocols for each of the 32 flow classes defined in program
element CLASS2 (see Section 2.5). The actual prediction
modules for each flow zone, including near-field,
intermediate-field, and far-field processes are discussed
in Section 4.2. Finally, in Section 4.3 the appropriate
transition criteria that define spatial extent of each flow
zone (module) are presented, along with constants used in
the flow classification and simulation modules.
4.1 Flow Protocols
The prediction of effluent flow and the related mixing
zone in the program element HYDRO2 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 CLASS2.
CORMIX2 contains 32 separate flow modules that apply to
each of the diverse mixing processes that 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 4.1 summarizes the flow modules. A
detailed description of each module is given in Section 4.2.
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 II to develop the flow
classification. Detailed flow protocols for each flow class
are presented in the following sub-section with extended
explanations on their formulation.
The spatial extent of each flow module is governed by
transition rules. These determine transitions between
different near-field, and far-field mixing regions, and
distances to boundary interaction. Section 4." 3 gives a
detailed summary of the transition rules.
78
-------
Table 4.1
Flow Prediction Modules of CORMIX2
Module
(MOD)
Description
Simulation Modules for Buoyant Multiport
Diffusers; Subsurface Near-Field Flows
201
202
211
212
213
214
216
218
221
222
224
271
272
273
274
275
discharge module
discharge (staged diffuser)
weakly deflected plane jet in crossflow
weakly deflected (3-D) wall jet in crossflow
near-vertical plane jet in linear stratification
near-horizontal plane jet in linear stratification
strongly deflected plane jet in crossflow
weakly deflected (2-D) wall jet in crossflow
weakly deflected plane plume in crosssflow
strongly deflected plane plume in crossflow
negatively buoyant line plume
Simulation Modules for Unstable Multiport
Diffusers: Mixed Near-Field Flows
acceleration zone for unidirectional co-flowing
diffuser
acceleration zone for unidirectional cross-flowing
diffuser (tee)
unidirectional cross-flowing diffuser (tee) in
strong current
acceleration zone for staged diffuser
staged perpendicular diffuser in strong current
79
-------
Table 4.1
(continued)
Module
(MOD)
Description
277 alternating perpendicular diffuser in unstable
near-field zone
279 negatively buoyant staged acceleration zone
Simulation Modules for Boundary Interaction
Processes for Stable Multiport Diffusers
near-vertical surface/bottom impingement with
buoyant upstream spreading
near-vertical surface/bottom impingement, upstream
spreading, vertical mixing, and buoyant
restratification
near-horizontal surface/bottom/pycnocline approach
terminal layer stratified impingement/upstream
spreading
terminal layer injection/upstream spreading
negatively buoyant diffuser (3-D) in strong current
Simulation Modules for Unstable Multiport
Diffusers; Intermediate Field Flows
251 diffuser plume in co-flow
252 diffuser plume in weak crossflow
Simulation Modules for Buoyant Spreading Processes
241 buoyant layer spreading in uniform ambient
242 buoyant spreading in linearly stratified ambient
243 density current developing along parallel diffuser
line
244 internal density current developing along parallel
diffuser line
245 diffuser induced bottom density current
80
232
234
235
236
237
238
-------
Table 4.1
(continued)
Module
(MOD)
261
262
281
Description
Simulation Modules for Ambient Diffusion Processes
passive diffusion in uniform ambient
passive diffusion in linearly stratified
ambient
Simulation Module for Density Wedges in Bounded
Channel
Bottom/surface/internal density wedge
81
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4.1.1 Flow Protocols for Buoyant Discharges into Uniform
ambient Layers (Flow Class MU)
The classification scheme discussed in Section 2.5.1.3
with its associated criteria (see Figure 2.9) 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.
In some cases, some of the modules present in the
protocol will not be used due to special circumstances
related to discharge or ambient characteristics. For
example, for a non-buoyant discharge, the buoyant spreading
regime (MOD241) will be absent in the applicable flow
classes (MU2 to MU9), or in the case of a stagnant ambient
environment, the buoyant spreading regime (MOD241) and the
passive diffusion zone (MOD261) will be absent in the
applicable flow classes (MU1, MU2, MU3, MU5, MU7, MU8, and
MU9) . The flow protocols for the buoyant discharge cases
are listed in Table 4.2.
4.1.2 Flow Protocols for Negatively Buoyant Discharges into
Uniform Ambient Layers (Flow Classes MNU)
The flow protocols for negatively buoyant discharges
into uniform ambient layers, corresponding to the flow
classes MNU as discussed in Section 2.5.1.4 and illustrated
in Figure 2.10, are listed in Table 4.3. Some of the
unstable discharge protocols bear some resemblance to those
'for positively buoyant discharges except for bottom re-
stratification and buoyant spreading in the far-field. This
is reflected in different transition criteria.
In the cases of stable discharges, 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.
4.1.3 Flow Protocols for Discharges Trapped in Linearly
Stratified Ambients (Flow Class MS)
Table 4.4 summarizes the protocols for the eight flow
classes MS (refer to Section 2.5.1.2 and Figure 2.8) 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 .flows (see Fig. 2.'8) use special modules that
account for the ambient stratification in the initial jet
or plume phases of the flow.
82
-------
Table 4.2
Flow Class
Flow Protocols (MU) for Buoyant Discharges
into Uniform Ambient Layers
Module
Transition
MU1V
HMZ - - -
MU1H
MU2
MU3
201
211
221
232
241
261
201
211
222
235 or 243
241
261
201
271
251
241
261
201
272
252
241
261
0
1
6
0
7
0
1
6
0 or 38,
7
0
21
31
7
0
21
32
7
83
-------
Table 4.2
Flow Class
(Continued)
Module
Transition
MU4
MU5
MU6
MU7
MU8
201
273
_ _ _
241
261
202
274
252
_ _ _
241
261
202
275
_ _ _
241
261
202
274
251
_ _ '—
241
261
201
277 or 234
241
261
0
0
7
0
22
32
7
0
1
0
7
0
22
31
7
0
7
04
-------
Table 4.2
Flow Class
(Continued)
Module
Transition
MU9
201
243 or 234
•B — ^ «•» ^» •
241
261
0
38 or 0
7
05
-------
Table 4.3
Flow Protocols (MNU) for Negatively Buoyant
Discharges into Uniform Ambient Layers
Flow Class
Module
Transition
MNU1 201
224
232
HMZ - - -
241
261
MNU2 201
;
216
222
235 or 243
241
261
MNU3 201
218
245
_ _ _
241
261
MNU4 201
238
_ _ _
241
261
0
0
0
7
0
2
3
15
0 or 38
7
0
43
51
7
0
0
7
86
-------
Table 4.3
Flow Class
(Continued)
Module
Transition
MNU5 202
279
212
245
_ _ _
241
261
MNU6 202
238
- - -
241
261
MNU7 . 201
271
251
- - -
241
261
MNU8 201
272
252
_ _ _
241
261
'
0
22
45
51
7
0
0
7
0
21
31
7
0
21
32
7
O <7
O /
-------
Table 4.3
Flow Class
(Continued)
Module
Transition
MNU9
MNU10
MNU11
MNU12
MNU13
201
273
- - _
241
261
202
274
252
_ _ _
241
261
202
275
— — ! —
241
261
202
274
251
— — -
241
261
201
277 or | 234
I
241
0
0
7
0
22
32
7
0
0
7
0
22
31
7
0
0
7
261
08
-------
Table 4.3
Flow Class
(Continued)
Module
Transition
MNU14
201
243 or 234
241
261
0
38 or 0
7
89
-------
Table 4.4
Flow Protocols (MS) for Discharges Trapped in
Linearly Stratified Ambients ; ;
Flow Class
Module
Transition
MSI 201
211
216
235
HMZ - - -
242
262
MS 2 201
211
216
244
_ _ _
242
262
MS3 201
213
236
l
242
262
MS4 201
214
237
— — ' —
242
262
0
2
10
0
11
0
2
0
39
11
0
12
10
11
0
13
0
-11
90
-------
Table 4.4
Flow Class
(Continued)
Module
Transition
MS5 201
222
235
_ _ _
242
262
MS6 201
222
244
_ _ _
242
262
MS7 201
221
236
_ _ _ -
242
262
MS8 201
211
221
236
_ _ _
242
262
0
14
0
11
0
14
39
11
0
16
0
11
0
1
16
0
11
91
-------
For instance, in stratification dominated flows (classes
MS3 and MS4), the weakly deflected module (MOD211) will be
replaced by its stratified counterpart, MOD213, 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 in Section 2.5.1.2 and then continue as an
internal layer far-field flow.
4,2 Hydrodynamic Simulation Modules
This section presents all the details related for each
of the modules listed; in Table 4.1 which provide the
predictive element for !a particular mixing process. The
modules are grouped in the different flow phases (from near-
field to far-field) as indicated in Table 4.1
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.
il) The control volume type uses a control volume
approach to describe outflow values as a function of inflow
values and based on conservation principles. For either
type, the beginning values are denoted by the subscript "i"
(e.g. S; is beginning dilution) and final values are denoted
by the subscript "f" (e.g. bf is the final flow half-width).
4.2.1 Simulation Modules for Buoyant Multiport Diffusers:
Subsurface Near-Field Plows
4.2.1.1 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.
If a cross-section is made through the subsurface
multiport diffuser plume, it will exhibit an approximately
rectangular shape. The length of the rectangle is given by
the diffuser length (neglecting diffusion at both "edges"
of the plume). The width of the rectangle is measured by
twice its transverse half-width b. 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 of the jet/plume
92
-------
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 = 0.71 gives the standard deviation (61% width), and
by 21/2 = 1.41 gives the 14% width, respectively.
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 c0/cc 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 CORMIX2 a global Cartesian coordinate system (x,y,z)
is placed at the bottom of the water body with the origin
(0,0,0) at the half-way point and directly below the center
of the multiport diffuser discharge. The height of the
discharge orifices above the bottom is h0. 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 (y**)
(i.e. the discharge angle above horizontal) is 9. The
discharge-crossflow angle a is the angle between y** and the
x-axis (a = 0 for co-flowing discharges, a = 180 for
counter-flowing discharges) measured counter-clockwise from
the x-axis. The alignment angle 7 is the angle between the
diffuser axis in the x-y plane and the x-axis (7 = 0° for
parallel alignment, 7 = 90° for perpendicular alignment)
measured counter-clockwise from the x-axis. The orientation
angle of the diffuser discharge ft is the angle between the
y** and the diffuser axis (0 = 0° for a staged diffuser, ft
= 90° for a unidirectional diffuser).
A primed coordinate system, (x',y',z'), within a given
flow region is specified with respect to the virtual source
for that flow region. A virtual source is needed for each
flow region because the 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) =
(4.1)
where (x»,yv,zv) is the global position of the virtual source
for that flow region. The position of the virtual source
(K,,yv,zv) is computed by taking the known flow solution at
the transition, as given from the previous flow region, and
93
-------
back calculating the source position using the dilution
equation for the given flow region.
In general, the analysis is extended to non-vertical
three-dimensional trajectories within the ambient crossflow.
A supplementary transverse coordinate r\ is defined here in
a plane given by the z-axis and the projection of y* onto
the z-y plane. Any vertical motion of the jet flow is
controlled by the vertical component of the discharge
momentum flux per diffuser length as well as the buoyancy
flux per diffuser length (which always acts vertically).
The transverse (horizontal) motion of the jet flow is solely
controlled by the horizontal component of the discharge
momentum flux per diffuser length.
Defining a as the angle between the discharge axis y*
and the crossflow (x-axis), and the angle 5 between the
projection of y* on the vertical yz-plane (transverse
coordinate r?) and the x-axis the relationships are
a = sin~'(l - cos20cos2<7)
1/2
(4.2)
(4.3)
where e and a are the discharge angles.
4,2.1.2 Discharge Module (MOD201K
This module begins every flow sequence. In the module
the flow is converted from a uniform velocity distribution
to a Gaussian profile, with equivalent momentum flux. The
representative final flow width bt, from the discharge
module
b, = B(2A)
1/2
(4.4)
where B is the slot jet width defined earlier. No dilution
is assumed to occur, so that Sf = l.o and cf = c0, where S,
is final dilution and cf'and c0 are the final and discharge
concentrations, respectively. The final x- and y-coordinate
are 0, but zf = h0.
4.2.1.3 Weakly Deflected Plane Jet In Croaaflow (MOD21J1
The results for the mdnf presented in Section 2.6.1.1.3
are extended to include the general 3-D trajectory. For a
cross-flowing discharge (a > 45°) the trajectory is a
function of ij as the independent variable. Writing the
trajectory equations in the virtual coordinate system in
terms of the supplemental coordinate 77 gives the crossflow
induced deflection
94'
-------
X' =
+ ,?'3/2sin1/2a/ (Tu3'2lm1/2)
(4.5)
where Tn is the trajectory constant for the weakly deflected
jet. The expression for the transverse coordinate y is
simply
y' = »j'cosS
(4.6)
The vertical coordinate, however, experiences an
additional perturbation due to buoyant deflection, or
> = »?'sinS + TT11r?'5/2signJ0/(lM3/2sins/2a)
(4.7)
where TTU is a constant for the buoyancy correction, and
signJ0 is equal to +1 for a positively buoyant discharge and
is equal to -1 for a negatively buoyant discharge.
The flow width is
where Bn is a width constant. The dilution is expressed as
where Sn is the dilution constant.
If the discharge is co-flowing (« < 45°) , the simulation
should step in x as the primary independent coordinate and
the trajectory, width and dilution relationships are
(4.10)
(4.11)
(4.12)
(4.13)
z' = ,,'sinS + TTu
„' = x'tana - x'3/2sina/(Tu3/2lm1/2cos1/2a
b = Bux'/COSQ:
S = SuX'1/2/(lq1/2COS1/2a)
4.2.1.4 weakly Deflected (3-m Wall Jet in Crossflow
fMOD212l
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 ^^um
flux M,, two times the discharge momentum flux M0 to account
for the mirror image of the attached flow with the bottom
symmetry plane, so the horizontal wall momentum flux Mw -
2M0cos0. This assumption also results in Qw - 2Q0.
For a cross-flowing discharge (a > 45°), the trajectory
equations for y' in terms of x' (z = 0 for the attached
case) becomes
95 '
-------
y' = T12(2cos*)1/4Lm1/2(x' - y'cota)
.1/2
(4.14)
where T12 is a trajectory constant. The width and dilution
are given by
b = B12y'/sina
S = SI2y'(cos^/2)1/2/(Lqsina)
(4.15)
(4.16)
respectively, where B12 a width constant, S12 is a dilution
constant, and Lq is thfe three-dimensional discharge/jet
length scale (Table 2.1). A similar equation system holds
for the co-flowing wall jet (3-D) (a < 45°) in analogy to
the free jet (see Section 5.2.1.2, Doneker and Jirka, 1989).
4.2.1.5 Weakly Deflected
(MOD2181
(2-D) wall Jet in Crossflow
Similar behavior as for the 3-D jet (MOD212) is
considered here. The attached flow has a horizontal momentum
flux m,, two times the discharge momentum flux m0 to account
for the half width of the attached flow with the bottom
symmetry plane, so the horizontal wall momentum flux nu =
2m0cos5. This assumption also results in qw = 2q0.
For a cross-flowing discharge (a > 45°) , the trajectory
equation for y' in terms of x' (z = 0 for the attached case)
becomes
y' = T18(2cos0/sina)1/2lm1/3(x' - y'cota)
2/3
(4.17)
where T18 is a trajectory'constant. The width and dilution
are given by
b = Bj8y'/sina
S = S18y'1/2(2cos0/sina)1/2/lq1/2
(4.18)
(4.19)
respectively, where B18 is a width constant, and S18 is a
dilution constant. A similar equation system holds for the
co-flowing wall jet (2-D) (a < 45°) in analogy to the mdnf
(a £ 45 ) jet (see Section 4.2.1.3).
4,2.1.6 Near-Vertical Plane Jet in Linear Stratifj
(MOD213)
For jets issued near-vertically into a density
stratified environment, \a is greater than 45° so the
coordinates of the flow in the virtual coordinate system
are given in first order by a straight line trajectory
96
-------
X7 = tj'cota (4.20)
y7 = »77cosS •.. (4-21)
z' = r?'sin$ (4.22)
respectively. The width and dilution are expressed as
b - Bl3r,'/Sir\a (4.23)
. S =.Sn9'l/2;(l-S13Asin2tfi?'3/l'»3sin3a)l/2/.lq1/a ' (4.24)
respectively, where B13 is a width constant, and Su and S13A
are dilution constants. For the physical background, see
Section 2.6.1.2.1.
4^2.1.7 Near-Horizontal Plane Jet in Linear Stratification
(MOD214)
The simulation of this module (occurring in flow class
MS4) is limited to the co-flowing design, with a less than
45°. The coordinates of the flow in the virtual coordinate
system are given by
z' = rj'sinS (4.25)
y7 = r;7cos5 (4.26)
The width and dilution are given by
b = B14x7/cosa (4.27)
S = SMx7l/2/lq1/2cos1/2a (4.28)
where B14 and S14 are the width and dilution constants
respectively.
4.2.1.8 Strongly Deflected Plane Jet in Crossflow (MOD216)
In the mdff the primary variable is x7 due to the
crossflow advection. The trajectory equations are
z7 = rj'sinS (4.29)
r,' = T16lm1/2sin1/2aX7l/2 (4.30)
where T16 is the trajectory constant. The y-coordinate is
similar to that for a weakly deflected jet in a crossflow.
The width and dilution of the flow are given by
b = B16»?7 (4.31)
97
-------
S = S16>7'/(lmlq)1/2 , (4.32)
where B1S and S16 are the width and dilution constants
respectively.
4.2.1.9 Weakly and Strongly Deflected Plane Plume in
Crossflow (MOD221 and MOD2221
As mentioned in Section 2.6.1.1.5, in order to decide
if the flow has a flat or steep linear trajectory, one can
use a criterion j0/ua3 > or < C21 where C21 is a constant.
For a weakly deflected plume (MOD221, J0/ua3 > C21) the
trajectory coordinates are a generalization of the
perturbation solutions presented in Section 2.6.1.1.5. With
z' as the primary coordinate the trajectory equations are
,./ _ „ / -i l/2/m -I 1/2 ,
Jt — & -*-M / •'•21 •^•m *
(TT21AlMcos0 + TT21BlMcos01n(z'/21M)cosa (4.33)
y = T21lm1/2cos1/20sin1/2ax'1/2 +
(TT21AlMcos0 + TT21BlMcos^ln(zV21M)sina (4.34)
where T21 is a trajectory constant, TT21A and TT21B are
momentum correction coefficients. Width and dilution are
given by .;
b = B2iZ' (4.35)
S = S21z'/(lmlq)1/2 ; ; (4.36)
respectively, where B21 is a width constant and S21 is a
dilution constant. ,
The strongly deflected plume (MOD222> J0/ua3 < C21)
trajectory coordinates, written in the virtual coordinate
system as a function of z', are
x' = z'l 3/4/T 1 3/4 + •
+ TT21BlMcoS01n(z'/TT21c21M)cosa (4.37)
y' = T^l
(TT21AlMcos0 + TT21BlMcos^ln(z'/TT21c21M)sina (4.38)
where T^ is a constant.
Width is given by
90
-------
(4.39)
where B^ is a constant, and the dilution by
S = S22zV(lmlq)l/2 (4.40)
where S^ is a constant
4.2.1.10 Negatively Buoyant Line Plume (MOD2241
In this module, a control volume approach is used.
Assuming that the line plume will travel up to a distance
1M vertically, and assuming the same dilution S as in MOD221
(Eq. 2.32) with z" replaced by 1M, the final dilution is
S, - S.l^/lq172 (4-43)
Similarly the final width becomes
b, = BM1M (4.44)
where S^ differs from S21 by a recirculation factor R, S^ =
S21/R, with R « 2, and BM =» B21.
Here the final distance x- coordinate for the plume is
x, = !Mcos7/2 (4.45)
and both yf and z, are zero due to the fall-back of the plume
to the bottom.
4.2.2 Simulation Modules for Unstable Multioort Diffusers;
Mixed Near-Field Flows
The flow equations in this module group describe
vertically fully mixed (over the applicable layer depth Hs)
diffuser plumes. The horizontal trajectory position (x,y)
of the plume centerline is calculated as well as the
horizontal half-width bh, the minimum centerline
concentration cc and the corresponding centerline dilution
S. Except where noted, the local half-width is defined by
the "1/e width" of a Gaussian plume (for width conventions
see Section 4.2.1.1). The vertical thickness bv of the
plume is, of course, equal to the layer height H,. The z-
coordinate of the flow is arbitrarily placed at the top of
the layer Hs, with the exception of MOD279.
-------
4.2.2.1 Acceleration Zone for Unidirectional Co-Flowing
Diffuser (MOD271)
This region begins after MOD101 (see Section 4.2.1.2)
with an initial value of bh equal to LD/2. The flow is
analysed in the x-y plane, with y" as the independent
variable. The straight line trajectory equations in the
virtual coordinate system are
' =
ysina
= ycoscr
(4.46)
(4.47)
The dilution is constant throughout the acceleration
zone and is '
H,sin7/2(lmlq)
1/2
((H/sin27
2HslJ/lmlq)1/2
(4.48)
and the horizontal half-width bh as a function of y" is
bh = LD/2 [cr, + (1 -
where :
X* = 2X/LD
and
exp(-3x* (1 + x'3))]
(S(lm/lq)1/2sinT + 0.5)/(S(lm/lq)1/2sin7 + 1)
(4.49)
; 50)
(4.51)
Strictly speaking, the lateral flow profile gradually
evolves in the acceleration zone of the unidirectional
dif fuser from an initial: top-hat profile just downstream
from the dif fuser line to: a final Gaussian profile (see Lee
and Jirka, 1980) .
4.2.2.2 Acceleration Zone for Unidirectional Cross-Flowing
Diffuser (Tee) (MOD2721
The same procedure as the previous section is followed,
and hence the equations used in MOD271 are used here, with
an additional shoreline proximity influence (see Section
2.6.2.1.2). Thus, in case of having a discharge location
•x, less than the actual dif fuser length LD, the dilution is
reduced by an exponential; influence factor as follows
S, = S'f (1 - exp(-S72xs/LD))
(4.52)
where S^ is a constant and s'f represents the dilution value
given by Eq. (4.48).
100
-------
4.2.2.3 Unidirectional Cross-Flowing Diffuser (Tee) in
Strong Current (MOD273)
A control volume approach is used in this module. The
dilution S of Eq. (4.48) is reduced by the factor. rs (see
Eq. 2.51) to obtain S, for MOD273 ,
Sf = (Hssin7/2(lmlq)1/2 + ((Hs2sin27 + 2HslJ/lmlq)1/2J
(1 + 5Hssin2T/lJ-1/2
(4-53)
Again the same procedure as before is used for shoreline
interaction, where Eq. (4.53) is reduced by an exponential
influence factor if xs < LD.
The horizontal half -width, based on dm (see Section
2.6.2.4) , is ,
bh = dmsina/2
and the final x-, and y- coordinates are
x, = LDcosCT/2
y, = dmsina/2
(4.54)
(4.55)
(4.56)
4.2.2.4 Acceleration Zone for Staged Diffuser (MOD274)
This zone begins after a special discharge module MOD202
for the staged diffusers. The only difference to MOD201 is
that the final x- and y- coordinates are
xf = -LDcosCT/2 ,
yf = -LDsin<7/2
in order to adapt to the staged geometry.
Hence, the equations for the trajectory are
y '= ys + y"sincr
x = X; + y"cosa
The dilution S is constant in this region
S = S74 ((lm lq)1/2 - cos7)Hs/(lm lq)1/2,
and the horizontal haIf-width is
bh = (B74 + 0.5 tan /3)y"
(4.57)
(4.58)
(4.59)
(4.60)
(4.61)
(4.62)
-------
where both S74 and B?., are constants.
4.2.2.5 Staged Perpendicular Diffuser in Strong Current
(MOD275)
A control volume approach is used in this mode similar
to MOD273. The same equations are used as in MOD273 with
the exception of having the angle a replaced by 7 in Eqs.
(4.54 to 4.56). The final dilution equation is
S - S7S(Hyiq)1/2(l + 2.23HssinVlJ1/2
Shoreline proximity does; not apply in this case.
(4.63)
4.2.2.6 Alternating Perpendicular Diffuser in Unstable Near-
Field Zone (MOD277)
A control volume approach is used in this module, where
the final y- coordinate is zero, and the final x, coordinate
is as follows
xf = (Locos-/ + 5Hs)/2
The final dilution is
S - H,((0.251m + lMsin27)/lMlmlq)1/2
and the final horizontal width is
bh = (I^sin? + 5HJ/2
(4,.64)
(4.65)
(4.66)
4.2.2.7 Negatively Buoyant Staged Acceleration Zone (MOD2791
A three-dimensional diffuser plume develops along the
staged diffuser axis.
The following module equations are similar to those
developed by Lee (1980).
The dilution increases along the diffuser axis as
S = Sw(y"/lq)
the thickness as
1/2
and the horizontal width as
bh = (B* + 0.5 tan 0)v"
102
(4.67)
(4.68)
(4.6.9)
-------
The trajectory coordinates are similar to those of
MOD274.
4.2.3 Simulation Modules for Boundary Interaction Processes
for Stable Multiport Diffusers
When the flow interacts with a boundary such as the
surface, bottom, or pycnocline density jump, an appropriate
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 Doneker and Jirka, 1990).
In all of these 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 bu of the 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.
Most of the boundary interaction modules, namely the
near-vertical surface impingement with buoyant upstream
spreading (MOD232), the near-vertical surface impingement
with unstable recirculation (MOD234) , the stratified
terminal layer impingement with buoyant spreading (MOD236),
and the stratified near-vertical surface injection with
upstream spreading (MOD237) are identical to the ones
presented by Doneker and Jirka (1989 their, MOD32, MOD34,
MOD36, and MOD37 respectively). The following two modules,
however, applies to the multiport diffuser alone.
4.2.3.1 Near-Horizontal surface/Bottom/Pvcnocline Approach
(MOD235)
In this simplest approach condition, the bent over flow
approaches the interface near-horizontally with an
impingement angle 6{ < 45°.
The final x-coordinate is given by a geometric shift
due to the size of the in-flowing jet/plume
x =
(4.70)
y, is set equal to yu and z, equal to zt. The final bulk
dilution is
Sf
(4.71)
103
-------
and the vertical width is;
where SBjs is a bulk mixing conversion factor.
The final horizontal half-width is calculated (see
Section 2.6.1.3) to be
(4.72)
(4.73)
4.2.3.2 Negatively Buoyant Diffuser (3-D) in Strong Current
(MOD2381
The diffuser plume will occupy a thin layer only near
the bottom of the ambient flow.
For a parallel diffuser, the thickness is given by
bvt = B^ LM (4.74)
with a lateral width
H. -i>
cos 7 + b-
** ,
The lateral coordinate is ishifted
y, - 1^ sin a
and the downstream final position is
x, =
sin -y +
(4.75)
(4.76)
(4.77)
For a perpendicular diffuser the corresponding equations
are
1M
(4.78)
'ht = -^ COS 7 + b^
(4.79)
yf = lm sin
(4.80)
sin 7 + 1M
(4.81)
In either case, zf = 0 and the final dilution is cross-flow
controlled
104
-------
— 2
(1, 1-)
1/2
(4.82)
4.2.4 Simulation Modules for Unstable Multinort Diffusersi
intermediate-Field Flows
As mentioned in Section 2.6.2.4, the intermediate-field
plume for the unidirectional or staged diffuser is divided
into two regions. Region 1 starts immediately after the
acceleration zone, and extends up to a distance where
restratification occurs. This distance (Eq. 2.59) is
determined by a critical densimetric Froude number (Fc =
Uc/tg'cHs)1'2, g'c = g'o/S) , where Fc depends on the diffuser
type. For the unidirectional diffuser, Fc will be indicated
by F^, and for the staged by F^ (see Table 4.8).
Region 2 starts when the flow restratifies. In that
region the flow has a superimposed surface spreading
(Section 2.6.2.4).
In this module group, the conventions for horizontal
half-width bh/ the minimum centerline concentration cc, and
the corresponding dilution S are identical to those defined
in Section 4.2.2.
4.2.4.1 Diffuser Plume in Co-Flow (MOD251)
In Region 1: Because the discharge is approximately co-
flowing, the simulation steps in x' as the primary
independent coordinate. Thus,
y' = x'tana - x'3/2sina/T53/2dm1/2cos1/2a
and the dilution is
S = SaX'^/d^cos1^
and the horizontal half-width bh is
(4.83)
(4.84)
bh =
(4.85)
where T5, S5, and Bs are constants. Because the flow is
vertically completely mixed, the vertical thickness bv is
set equal to Ht.
Region 2: The same trajectory and dilution equations
are used as in the first region, but both vertical and
horizontal widths are changed, hence
bh = BB,,
(X7/4 - X',7'4)2'3 + bu
(4.86)
and
105
-------
5 (4.87)
where BBS is a constant, S, and S are the initial and local
dilution, respectively, and bw the final horizontal width
at the end of region 1. .
4,2.4.2 Diffuser Plume in Weafc Cross-Flow (MOD252Y
A procedure analogous to MOD151 is used here for both
regions. The only difference is that instead of stepping
in x7, the primary coordinate is y' because the discharge
is cross-flowing. The equations are modified accordingly.
For example, the trajectory relation is
x/ =
+ y'cota
(4.88)
4,2.5 Simulation Modules for Buoyant Spreading Processes
The flow distribution inherent in the two buoyant
spreading modules is mostly uniform (top-hat). Hence, the
same interpretations on geometric (width) and dilution (or
concentration) values apply (see introductory comments to
Section 4.2.3).
4.2.5.1 Buoyant Surface/Bottom Spreading (MODS411 and
Buoyant Terminal Laver Spreading (MOD2421
The equations for MOD241 and MOD242 are the same
equations used in Doneker and Jirka (1990), MOD41 and MOD42
respectively.
4.2.5.2 Density Current Developing Along Parallel Diffuaer
Line (MOD2431 ~~ ~~
The physical background for the cumulative density
current along the diffuser line was presented in Section
2.6.3.1. The flow equations are
bh = [(bu3'2 + (lm/lM)3'2/(2 C^) .(x3'2 - Xi3/2))]2/3 (4.89)
bv = Sf(lq lm)1/2 x/2bh + (bybyb, - Sf(lq lm)1/2x/2bh) (4.90)
where B43 is a constant and ;
khi = (LDCOS7 + 5HJ/2 (4.91)
and '
(4.92)
106
-------
The position x is defined as
x = (-Ifecosr + 5HJ/2
and the dilution is as follows
Sf = Hs(S43/lMlq + S43AsinVlmlq)V2
where S43 and S43A are both dilution constants.
(4.93)
(4.94)
4.2.5.3 Internal Density Current Developing Along Parallel
Piffuser Line (MOD244)
Referring to Section 2.6.3.2, the flow equations are
bh = [(bw2 + (2/CD)I/2(Sf(lqlJ1/2(x2-x2)/41a +
. k(x- Xi))]1'2 (4-95)
bv = (Sf(lq lJ1/2(x - Xi)/2 + k)/bh
where
k = (b^u, - st(l, lm)1/2)xi/2)
(4.96)
(4.97)
4.2.5.4 Diffuser Induced Bottom Density Current (MOD2 451
MOD245 represents a bottom density current that is
greatly affected/ however, by the momentum flux of the
diffuser thus leading to a trajectory that is similar to a
two-dimensional wall jet (MOD218) . Thus, the module
equations are similar to those for MOD218 with superimposed
spreading (MOD241) .
4.2.6 Simulation Modules for
Diffusion Processes
The physical processes underlying the two ambient
diffusion modules (MOD261 and MOD262) have ben presented in
Section 2.5.4. The equations for MOD261 and MOD262 are
identical to those used by Doneker and Jirka (1989, their
MOD61 and MOD62, respectively).
4.2.7 Simulation Module for Density Wedae in Bounded
Channel
4.2.7.1 Bottom/Surface/lnternal Density Wedae (MOD281)
Note that MOD281 does not occupy a fixed position in the
predictive protocols. However, MOD281 will .be executed at
. 107
-------
the end of the HMZ for any flow class (see Tables 4.2, 4 3
or 4.4) if two conditions hold: a) the channel is bounded
and b) examination of the HMZ final results indicates that
lateral interaction of the plume with both banks does occur
This is usually the case for strongly buoyant discharges
into a low velocity ambient environment.
The governing equations have been presented in Section
2.6.3.3. These are the limiting dilution Sn, Eq. (2.75) for
wedges with critical boundary control, the channel Froude
number, Eq. (2.76a), the icritical depth hc, Eq. (2.76b), and
the wedge lengths L, for bottom (Eq. 2.77) and surface (Eq.
2.78), respectively. I
For subcritical wedges, the corresponding equations on
oo ^ayer depth h" Eq' ; <2-79)' ^e Froude numbers, Eq.
(2.80) and (2.83), and the wedge lengths, Eq. (2.82) and
(2.85), for bottom or surface and internal wedges,
respectively.
•^ — 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 eabh 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 }ustification of all numerical coefficients is
supplied.
4.3.1 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
corresponding to the final values of the preceding flow
region. Transition rules used in the simulation appear in
Table 4.5, and the constant values for the transition rules
appear in Table 4.9. i
For example, Transitibn Rule 2 gives the final value of
a weakly deflected plane jet coordinate when it is followed
by a strongly deflected plane jet in crossflow. The
transition from one region to the other is characterized by
the plane jet/crossflow length scale lm. if the horizontal
discharge angle is a, the final supplementary coordinate
rj it and the final x-coordinate x'f, transition rule l yields
100
-------
Table 4.5
Transition Rules
Transition From To Equation
Rule MOD MOD
1
2
3
6
7
10
11
12
13
14
15
16
21
211
211
211
216
221
222
222
241
216
216
242
213
214
222
222
222
221
271
272
221 a > 45% n't = TC11M sin a
222 a < 45% X', = TC11M COS a
216 a > 45°, r)'t = Tc2lm sin a
a < 45% X'f = TC2lm COS a
O O O V ' — T1 1
£t £»£» •"•f~"~AC3J'M
232 Zf = 0.75HS + 0.25h0
235
243
261 Xf = x,+ (23/2/3)CD4l1/2(bM3/2/I^1/2)
ttt
rr/OT Vj \ / f Q -pT T "R \ 1 ' — 1 \
235 z'f = Tclolm1/4 lm'3/4 sin1/2*
244
262 X, = X; + (2CD«)1/2/(2-0) ('Lmr2btsi/'Lm/'bvi)
236 z/ = TC12 I,/ sin1/35 +
OT7 ^^ — T1 1' cfin^fl -1-
£ J / zf •'•C13-Lm Ss-L.ll C ~
rm ^l/3/l /2^ rT> 45°, y/ = TC13P lm7 Sin a
a < 45°, X,' = TC13P !„' COS a
244 Zf = Tcl4lb3/2/l,1/2
235 z, = max(0.25h0/0.25Zi)
243
236 z', = TC16V
. 251 y"( = T^LD
252
109
-------
Table 4.5 (Continued)
Transit!
Rule
22
31
32
38
39
43
45
51
.on From
MOD
274
274
279
251
252
243
244
218
212
245
To
MOD
251
252
212
241
241
241
242
245
245
241
Equation
y"f = LoCOS/5
x', = T^4/]
y't = T^V/I
| Xf = (LjjCOS?
V = i^cos-,
a > 45°, y'f
a < 45°, x'f
! o > 45°, y',
a < 45% x'f
a > 45°, y'{
a < 45°, X',
^X3
"cX3
+ 5HJ/2
/2
= Tc43lM sin a
= T^IM COS a
= TC^LM sin a
= T0)sLM COS cr
= TCSJ!^ sin a
= TCJ^ COS a
11-0
-------
«*'f = Tc2lm a > 45° (4.98)
x/f = TC2lm a < 45° (4.99)
where TC2 is a constant (Transition rule Constant 2.) .
As shown in Tables 4.2 to 4.4 the proper transition rule
depends on the sequence of current flow module to next flow
module. In general, flow transition between flow regimes
are smooth due to matching volumetric dilutions. There may
occasionally be slight discontinuities in the predicted flow
width.
4.3.2 Flow Classification Criteria
A summary of the detailed classification criteria that
have been shown in "order of magnitude" form on Figures 2 8
to 2.10 is provided in Table 4.6. The labels Cl, C2, etc
correspond to the labels used on those figures. The values
of the numerical constants are also included in the first
column of Table 4.6 with reference or comments on how they
were obtained. *
4.3.3 Terminal Laver Expressions
Table 4.7 lists the detailed terminal height equations
used in Figure 2.8 of the flow classification scheme. The
equations may differ from the usual equations available in
the literature through geometric factors that measure the
vertical or horizontal momentum strengths and throuqh
factors measuring the direction of the buoyancy force. The
first column also gives the adopted numerical values with
the appropriate reference.
4.3.4 Model Coefficient Values
Any predictive model describing turbulent flow processed
contains a number of constants that must be determined from
experimental data. The predictive flow modules and
transition rules of CORMIX2 are listed in Table 4.8 and 4.9,
respectively. A large number of constants appear as
required by the different physical processes in the various
flow zones. The reader is referred to Doneker and Jirka
(1990) regarding the procedure for adopting numerical
constants with consistency checks among different types of
constants.
Ill
-------
Table 4.6
Flow Classification Criteria
Criterion
Value
Equation Used
in CLASS2
Data Sources, and
References,
or Comments
0.75
C2 = 0.90
C3 = 2.2
C = 0.54
c* =0.1
4A
m
From List (1982),
Wright (1979,
1982) , and Roberts
(1989)
From Abdelwahed and
Chu (1982)
From Roberts (1977)
From Jirka (1973,
1982)
C4' = 0.22
C5 " 10
C- = 10
o
C? =- 0.54
C0 = 0.54
O
C9 = 0.4
C1Q = 0.17
VHs I
1m/Hs
m
VHs
LMl/Lm
From Jirka (1982)
From Jirka (1982)
From Jirka (1982)
From Jirka (1973,
1982)
From Jirka (1973,
1982)
From Abdelwahed and
Chu (1982)
From Jirka (1982) ,
Wright (1977), List
(1982) , andHolley
and Jirka (1986)
From Jirka (1982) ,
Wright (1977), List
(1982) , andHolley
and Jirka (1986)
112
-------
Table 4.7
Constant
and Value
Stratified Terminal Height Expressions
Equation Used
in CLASS2
Reference, or
Comments
'12
"T3
'T4
~T5
.= 2.4
= 2.4
= 2.3
= 2.3
"""" £t • O
CT6 - 2'5
'T7
"T8
1.7
1.7
1/41 /3/4sin1/25 From List (1982),
m and Abdelwahed
and Chu (1982)
1/41 /3/4sin1/25 From List (1982),
m m and Abdelwahed
and Chu (1982)
From List (1982)
From List (1982)
CT3Vsin
Sin
1/3,
CT5V
/I
1/2
,3/2 1/2
From Roberts (1977,
and 1989)
From Roberts (1977,
and 1989)
From Roberts (1977)
From Roberts (1977)
113
-------
Table 4.8 Module
Coefficient
rn rii
11' ^18
Sll' S13' S14' S18
Bll' B13' B14' B18
TT11
T12
S12
B12
S13A
T16
S16
B16
T21
S21
B21' B24
TT21A
TT21B
TT21C
T22
S22
B22
S24
B38A' B38B
Constants
Value
2.7
0.58
0.13
0.20
2.3
0.18
0.11
0.011
1.6
0.30
0.25
0.36
0.54
0.15
2.5
0.79
2.0
0.25
1.16
0.60
0.27
ol.is
114
Data Source,
Reference, or
From Holley
(1986)
ii
it
it
From Doneker
(1990)
ii
ii
ii
"
ii
ii
Summary
Comment
and Jirka
and Jirka
From Holley and Jirka
(1986)
"
ii
ii
ii
ii
From Davidson
(1989)
From Doneker and Jirka
(1990)
it
From Holley and Jirka
(1986)
Doneker and Jirka (1990)
-------
Table 4.8
Coefficient
(Continued)
Value
Data Source, Summary
Reference, or Comment
43
S43A
CD,
43
CD
44
•50
B
50
BB50
Fc50u
Fc50s
SNBR
70
74
B74' B79
75A
0.25
0.64
0.8
1.2
0.58
1.0
0.21
0.48
0.25
2.5
1.5
3.22
0.50
0.15
0.67
2.23
From Jirka (1982)
From Simpson (1982), and
Jirka and Arita (1987)
From Hoiley and Jirka
(1986)
From Brocard (1977),
and Stolzenbach et. al
(1976)
From Brocard (1977),
and Stolzenbach et. al
(1976)
After Lee (1984)
From Lee (1981), and
Stolzenbach Si Almquist
(1981)
From Holley and Jirka
(1986)
From Jirka (1982)
The rest of the constants for MOD232, MOD234, MOD236,
MOD237, MOD241, MOD242, MOD261, and MOD262, are identical
to MOD32, MOD34, MOD36, MOD37, MOD41, MOD42, MOD61, and
MOD62, presented by Doneker and Jirka (1990) respectively.
115
-------
Table 4.9
Coefficient
Coefficients In Transition Rules
Value Data Source, Summary
Reference, or Comment
T
•"•ci
T
1C2
T
C3
T
CIO
T
C12
TC12B
T
C13
TC13B
TC13P
T
C14
T
C16
T
C21
TC31U
TC31S
TC32u
TC32s
T
C43
T
C45
T
•"•C51
2.0
2.6
2.0
2.4
2.3
2.0
2.3
I
2.0
10.0
2.3
1.7
0.5
2.0
0.65
1.55
0.4
2.5
5.0
3.0
' 116
From Holley and Jirka
(1986)
From Wright (1977) , List
(1982), Wong (1982), and
Holley and Jirka (1986)
n . .--
ii
From Holley and Jirka
(1986)
n
From Wright (1977) , List
(1982), Wong (1982), and
Holley and Jirka (1986)
From Roberts (1989)
n
From Jirka (1982)
n
n .
it
n
From Holley and Jirka
(1986)
From Wright (1977), List
(1982), Wong (1982), and
Holley and Jirka (1986)
• ' • n
-------
Chapter V
System Validation and Application
5.1 Comparison with Laboratory and Field Data
In this section the predictions of CORMIX2 will be
compared with laboratory and field data. This section is
not meant to be an exhaustive validation of all possible
CORMIX2 flow classes and associated predictions, but rather
to test the key CORMIX2 modules that are common to many flow
protocols (flow classes) and to illustrate the flexibility
of the system in handling complex environment and discharge
conditions.
While CORMIX2 can accommodate many possible flow
configurations, actual available laboratory or field data
are quite limited. In Section 5.1.1 comparisons are made
with data for diffusers discharging in deep receiving water
in the absence of any boundary effects. Section 5.1.2
addresses flows related to diffusers discharging in shallow
receiving water in which different forms of boundary
interaction processes play a significant role.
In all of the comparisons shown below the numerical
constants and coefficient values have been consistently set
to the values summarized in Chapter IV.
To facilitate comparison with the non-dimensionalization
that is frequently used in the available literature the
following parameters are introduced:
Densimetric Froude Number based on port diameter
F0 = u0/(g'0D)l/2
Densimetric Froude Number based on slot width
Fro = u0/(g'0B)1/2 = '•« 'i ^3/4
Jet/Crossflow Ratio
R = Uo/us = (1./1,)
1/2
(5.1)
(5.2)
(5.3)
5.1.1 Diffuser Discharges in Deep Receiving Water
This sub-section presents analyses of near-field flows,
starting with buoyant raultiport diffuser in a stagnant
uniform ambient, followed by positively and negatively
buoyant multiport diffuser in uniform co-flowing currents,
and, finally, flows in stratified stagnant ambient. To
validate these buoyant jet near-field flows, CORMIX2
117
-------
predictions are compared with laboratory data from Cederwall
(1963), Davidson (1989), Isaacson et. al. (1983), and Tong
and Stolzenbach (1979).
5.1.1.1 Unstratified
5.1.1.1.1 Stagnant Amb-ienfr,
Figure 5.la and 5.lb show one case of Cederwall's (1963)
centerline dilution and trajectory data, adapted from
Davidson (1989), for a two-dimensional (slot) buoyant jet
in a stagnant uniform ambient water compared with CORMIX2
projections. The buoyant jets were discharged horizontally
(8 = 0°) into a uniform ambient density tank. For this
stagnant environment (for which lm tends to infinity)
CORMIX2 classifies the flow as MU1V (mdnf, bd-v), since the
flow is hydrodynamically stable (previously discussed in
Chapter II). Figure 5.la;shows Cederwall's two-dimensional
buoyant jet dilution data plotted against the vertical z-
coordinate (normalized by both the slot width B and the
densimetric Froude number based on slot width Fro). Figure
5.1b shows the corresponding trajectory data (both x- and
z-coordinates normalized by both the slot width B and the
densimetric Froude number based on slot width Fro) . Note
that 1M - BFro"/3 is indeed the appropriate normalization
length. The flow travels I horizontally at first, after some
distance the buoyancy force deflects the flow vertically.
For this stagnant condition the predicted dilution and
trajectory seem to be in excellent agreement with the
observed plume data. ;
5.1.1.1.2 Co-Flowing Ambient
Figure 5.2 and 5.3 show the trajectory data from an
experiment of Davidson (1989) for a multiport buoyant
discharge in a co-flowing unstratified ambient (9 = 0°, and
a - 0°) with velocity ratio R = 5 and R = 8.33 (R = u0/ua) ,
respectively. The experiment with R. = 5 (Figure 5.32)
possesses more discharge momentum (F0 = 8.3) than the one
with R = 8.33 (F0 = 5.6) (Figure 5.3). Here CORMIX2 (flow
class MU1H, mdnf, bd-h) predicts a slightly stronger
deflected plume than shown by the experimental data.
Note that this comparison is only valid for the
particular diffuser spacing to port diameter ratio (s/D =
27.3) as used in Davidson's experiment.
Furthermore, it must be stressed that in Davidson's
experiments the diffuser nozzles were well elevated above
the bottom (h0/D =- 83.33) so that the diffuser plume was
able to rise away from the bottom and ambient flow could
: 110
-------
100
10
- Data
• Cederwall, 1971 (Fro= 13.6-25.2}
- CORMIX2:
— Centerline Dilution
9 = 0°,
-------
z
^••OT*
D
80
60
40
20
Data:
o Davidson, 1989
CORMIX2: !
• Centerline Trajectory
FQ = 8.3, R = 5
0=0°, cr = q°
£ = 27.3
°°
,00
.00
00
200 400 60O 800 1000
D
Figure 5.2 Horizontal Multiport Buoyant Jet Trajectory
in a Co-Flowing Ambient (Relative Spacing s/D
=27.3)
120
-------
Data:
o Davidson, 1989
CORMIX2:
z
^M>B*
D
100
80
60
40
20
0
C
w<
_ F0=5.6,
- 0=0°,
"" — -0*7
- D " 27'
^B
HBB
00^
~~p
o 1 1
) IOO
~uieimic iiujcuiury
R = 8.33
3
oo°°
oo^0-0^'
*>
1 1 1 1 1 ^
2OO 300
X
D
Figure 5.3
Horizontal Multiport Buoyant Jet Trajectory
in a Co-Flowing Ambient (Relative Spacing s/D
= 27.3)
121
-------
pass below the plume. For lesser elevations the diffuser
plume could stay trapped to the bottom and CORMIX2 (see
criterion C,) would predict such attachment (leading to a
flow class MNU2) .
CORMIX2 assumes Gaussian distribution profiles • for
velocity and concentration; In Davidson's experiment, the
concentration profiles show considerable irregularity which
may explain some disagreement in the trajectories. Other
explanations are related to the exact method of determining
the centerline position, experimental setup, and
unsteadiness of the flow.
Figure 5.4 shows the dilution data for two different
experiments by Davidson (1989), each having a different R
and F0. Both dilution and the vertical z -coordinate are
normalized as shown in the; figure. Note that s/D is fixed
and equal to 27.3 as in the previous figures. :CORMIX2 '
somewhat underpredicts the centerline dilution.. Again, this
disagreement is related to the method of determining the
centerline position, and to the assumption , of having a
Gaussian concentration profile.
5.1.1.1.3 Negatively Buoyant Discharges
Figure 5.5 shows the centerline trajectory and plume
boundaries of an experiment by Tong and Stolzenbach (1979)
for a negatively buoyant unidirectional diffuser discharging
vertically (6 = 90°) into a co-flowing crossflow (a = 0°, and
7 = 90°) with R = 9.36. In this case CORMIX2 predicts an
JMNU2 (mdnf, mdff, bd-h, bottom approach) flow class with
numerical results that are in good agreement with the
visually observed plume boundaries (the dilution predicted
by CORMIX2 at different locations agree with the
experimental ones) , however, the flow becomes attached at
a distance greater than the observed one. This difference
is due to the initial three dimensional flow of the
individual diffuser jets near the discharge location. This
aspect can be better predicted by using CORMIX1 (using same
nozzle diameter and spacing length as channel width) .
5.1.1.. 2 Stratified Stagnant ambient:
Laboratory measurements on a multiport diffuser
discharging into a stratified ambient were performed by
Isaacson (1983). The data 'presented in Table 5.1 is for a
hydraulic model study of a sanitary wastewater diffuser
discharge into the ocean under dry weather flow conditions.
An alternating diffuser with three nozzles per riser
discharging into a stratified ..crossf lowing ambient current
(7 = 90°) was used in the model. The ocean density profiles
for the dry weather case were fitted by a type D (see Figure
122
-------
-
M
I04-
10
10'
10
O3
.dL. - py •*
o -•*•*•*
Data:
Davidson, 1989
O F0=3.2, R=5
D F0 = 33.l , R=2O
CORMIX2: Centerline Dilution
0 = 0°, cr=0°
10'
10'
10'
z
•*••>••
L;
Figure 5.4
Dilution for Buoyant Multiport Discharge in
a Co-Flowing Ambient (Relative Spacing s/D =
27.3)
123
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Table 5.1
Comparison Between Laboratory Test Results
(Isaason et. al., 1983) and CORMIX2
(cm) (m)
H
(m)
*o
Vs)
Test
#
(1)
(2) (3)
8.2 10.97 22.860.0052 DW-1 103
8.2 10.97 22.86 0.0092 DW-5 68
105 106.8
80 86.9
(1)'S = Measured minimum dilution.
x ' m
(2) S = Measured average dilution.
a
(3) S = CORMIX2 centerline dilution.
P
125
-------
2.1) profile. In both dry weather cases (DW-1 and DW-5)
CORMIX2 predicts an MS7 ;(bd-v, terminal layer impingement
with upstream spreading);flow class with numerical results
that are in good agreement (7%-14% difference) with the
average and minimum measured dilution. The comparison
between the minimum dilution predicted by CORMIX2 and the
measured average and minimum dilutions as reported by
Isaacson is given in Table 5.1. Although details (e.g.
height of terminal levels) on these model results are not
reported, the comparison:give good support to CORMIX2.
5-1.2 Diffuser Discharges in Shallow Receiving Water
This section is intended to illustrate the ability of
CORMIX2 to predict flow dynamics of different shallow
diffuser types discharging into either a stagnant or a
flowing unstratified ambient in the presence of various
boundary interaction processes. CORMIX2 predictions are
compared with experimental data from Brocard (1977), Jirka
(1973), Roberts (1977), and Stolzenbach et. al. (1976).
5.1.2.1 Unidirectional Diffuser
Figures 5.6 and 5.7 present surface isotherms for
hydraulic model results :from the experimental study of
Stolzenbach et. al. (1976) for the thermal diffuser
discharge from the Cayuga Station located at the Somerset
site. Figure 5.6 (Run :*31) shows a positively buoyant
unidirectional diffuser discharging into a stagnant ambient
(6 = p, a- = 90°, and 7 == o°), and Figure 5.7 (Run *35) a
positively buoyant unidirectional diffuser discharging into
a predominantly crossflowing ambient (0 = o°, a = 120°, and
7 - 30°) . CORMIX2 predicts an unstable (shallow water)'flow
class MU3 (tee acceleration zone, diffuser plume in cross-
flow) for Run 31. For the stagnant case (Figure 5.6) the
predicted plume shape is in good agreement with the observed
plume surface isotherms. Also the centerline concentrations
closely agree with observations. However, CORMIX2 is unable
to predict some temperature build-up ("hot spots") at the
plume periphery. This is essentially an unsteady phenomenon
(probably exaggerated by the limited laboratory basin) and
outside the capabilities of CORMIX2.
The experimental data for Run *5 show a slightly smaller
deflection than the one indicated by CORMJX2. The
centerline concentrations; (temperature rises) are in good
agreement with the experimental observations for the surface
isotherms. Note the far-field region is absent because the
ambient is stagnant (see Chapter II). The same flow class
(MU3) is obtained for Run *35 but with the additional
presence of the far-field region.
126
-------
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Once an ambient crossflow is present (Figure 5.7) the
unsteady build-up zones are prevented and CORMIX2
predictions are in good agreement with the isotherm
observations.
5.1.2.2 Staged Diffuser
Figures 5.8 and 5.9 present surface isotherms from the
laboratory model of Brocard et. al. (1977) for the thermal
diffuser discharge at the Charlestown site. Figure 5.8
(Test *5) shows a positively buoyant staged diffuser
discharging into a stagnant ambient (9 = 20°, a = 90°, and
7 = 90°), and Figure 5.9 (Test *6) a similar diffuser
discharging into a crossflow ambient (8 = 20°, a = 90°, and
•y = 90°) .
CORMIX2 predicts a shallow water flow class MU5 (staged
acceleration zone, diffuser plume in cross-flow) for Test
*5 (Figure 5.8). Again, unsteady recirculation effects are
present in the laboratory data (limited basin size) for the
stagnant case. If those effects are excluded, the near- and
intermediate field predictions of CORMIX2 give satisfactory
results. The same flow class (MU5) is obtained for Test *6,
with the additional presence of the far-field zone. As for
the staged diffuser in the presence of crossflow, a much
better agreement with predictions is obtained due to the
minimization of unsteady and/or boundary effects.
Figure 5.10 shows another staged diffuser in a shallow
crossflowing ambient (0 = 0°, a = 90°, and -y = 90°) for the
model study of Stolzenbach et al. (1976). Agreement appears
satisfactory even though some recirculation may be present
in this somewhat weak crossflow situation.
5.1.2.3 Alternating Diffuser
Figure S.lla and 5.lib show surface isotherms from the
study by Jirka and Harleman (1973) for an alternating
diffuser (6 = 45°) in a perpendicular (7 = 90°) unstratified
crossflow (Run *BC-3) and an alternating diffuser (0 = 45°)
into a parallel (7 = 0°) unstratified crossflow (Run *BC-
13). For Run *BC-3 (Figure S.lla), CORMIX2 predicts an
unstable flow class MU8 with a buoyant upstream intrusion.
The plume shape and extent of upstream intrusion is in good
agreement with the experiment. For Run *BC-13, CORMIX2
predicts an unstable flow class MU9 with upstream intrusion.
Once again, good agreement in plume shape ^ «•»—•"«•; ™
distance, and dilution values is evident.
intrusion
129
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132
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(a)
Model
Basin
Boundaries
_J 1
IOH
I.2°F
Jirka, 1973 Isotherms, Run -#BC-3
CORMIX2 Width
0=45°, y
U,
(b)
Model
Basin
Boundaries
Figure 5.11
Jirka, 1973 Isotherms, Run #BC-I3
CORMIX2 Front Prediction
0 = 45°, y=0°
Surface Plume from Buoyant Alternating
Diffuser Discharging a) Perpendicular and b)
Parallel Alignment
133
-------
Another comparison caln be made with the experimental
data of Roberts (1977) for a situation in which the flow is
hydrodynamically stable (deep water). The objective here
is to test once again the prediction of CORMIX2 for upstream
intrusion and surface spreading. Figure 5.12 shows a
photograph of a surface plume generated by an alternating
diffuser discharging into a crossflowing (F = ua3/J0 - 0.1,
-y = 90°) unstratified ambient. CORMIX2 assigned an MU1V
flow class with an upstream intrusion of 0.16 m with a half-
width of 0.42 m at surface impingement. The photograph
shows an upstream intrusion of 0.22 m and a half-width of
0.47 m at surface impingement. CORMIX2 overpredicts the
surface spreading for theisame reasons as before.
As mentioned earlier, laboratory experiments are always
conducted in model basins iof limited size and the somewhat
weaker frontal spreading :observed by Jirka and Harleman
(1973) and Roberts (1977) than that predicted by CORMIX2 is,
in part, related to boundary effects in the model studies.
5.1.3 Summary and Appraisal
Despite the limited availability of laboratory and field
data for the wide range of discharge/ambient characteristics
that is embodied in this 32 flow classes (and their
additional sub-classes) contained in CORMIX2, the preceding
comparison indicates satisfactory system performance under
quite diverse conditions. Thus CORMIX2 has been
demonstrated to have adequate flexibility and accuracy in
predicting diffuser discharging under deep water conditions,
in ambient stratification, in shallow fully mixed
environments and with negative discharge buoyancy. For
additional comments on data/system comparisons see Doneker
and Jirka (1989). j
i
i
5.2 application; Case Studies
i , -
The purpose of this section is to give an overview of
the significant features of CORMIX2 in discharge mixing zone
evaluation and design, and!to illustrate the flexibility of
CORMIX2 in highly divergent design conditions. The first
case presented represents a hypothetical example of a
discharge from a small municipal treatment plant into the
ocean illustrating the effects of density stratification,
and the second example is a discharge from a power plant
discharging heated effluent into a large lake under varying
ambient currents.
134
-------
CORMIX2 Width Prediction
u.
Visual Observations
Roberts, 1977
\
m
Figure 5.12
Buoyant Alternating Diffuser in Perpendicular
Crossflow: Plan View of Surface Fronts
135
-------
5.2.1 AAA Municipal Treatment Plant
This example will illustrate the effect of ambient
density stratification in a coastal environment on the
mixing of a buoyant effluent flow containing toxic
substances. The discharge is subject to three mixing
criteria: ^a toxic dilutiop zone, a plume width criteria on
a legal mixing zone, and !a downstream region of interest.
The analyst seeks pollutant concentrations at these
locations. The analyst will use CORMIX2 to try to study the
effect of typical winter and summer ambient density profiles
on the mixing behavior of;the discharge.
5.2.1.1 The Problem Statement
The discharge from the AAA municipal treatment plant
into coastal waters contains some toxic substances. The
mixing characteristics for topical winter and summer
profiles are to be considered (see Figure 5.13). The
discharge is to be located 3000 m from shore at a local
water depth of 24.2 m. The bathymetry is sloping
approximately linearly from the shoreline.
A 100 m long unidirectional diffuser is used with 41
ports openings. The ports are round with a diameter of 0.3
m and extend about 0.3 m above the surrounding bottom with
a vertical angle e = 30 . The diffuser is discharging in
the direction of the prevailing ambient current (co-flow)
(CT = 0°, and 7 = 90°) which has a velocity of 0.09 m/s. The
total design discharge flowrate is 3.0 m3/s and contains 100
mg/1 of a toxic substance with a CMC of 5 mg/1. The
discharge density is 994.0 kg/m3. A public beach is located
3000 m down-current from the' discharge with a legal mixing
zone (LMZ) width set at 400 m. The plume characteristics
at this distance are of interest.
5.2.1.2 CORMIX2 Analysis
The first step in the analysis would be to choose one
of the four ambient stratification types to represent the
actual density profiles as seen in Figure 5.13. An ambient
profile of Type D is chosen to represent the August data,
with surface density Ps = ;1022.7 kg/m3, bottom density Pb =
1024.9 kg/m3, and a pycnocline height h^ = 12.50 m. The
representative cross-section case places the discharge 3000
m from shore in 24.2 m o£ water. A weak linear ambient
density stratification (Type A) is chosen to represent the
March data, with surface density ps = 1025.59 kg/m3 and
bottom density pb = 1025.82 kg/m3.
136
-------
Q.
O>
Q
0
5
1.0
15
20
25
30
C
O
O
August
Conditions
1,022
1,024
P March
Conditions
6
o Observed Data
— CORMIX
Representation
p : Density (kg/m3)
Figure 5.13
AAA Municipal Outfall:
Profiles in Coastal Ocean
Typical Density
137
-------
For the August design conditions, CORMIX2 concludes the
flow will be confined to the lower stratified layer only of
the specified ambient stratification condition D, and
assigns a flow class MS8 (mdnf, bd-v, terminal layer
impingement with upstream spreading, buoyant spreading,
passive diffusion). The simulation results are shown in
Figure 5.14 indicating an upstream buoyant intrusion at the
terminal height. CORMIX2 indicates an upstream intrusion
length of about 176 m. SUM2 notifies the user that both the
hydrodynamic mixing zone (HMZ) and the legal mixing zone
(LMZ) occurs at x = 188 m downstream from-the discharge
point with plume centerline z =9.52 m, dilution value S'
= 44.6, and the plume half-width bh and thickness bv are
equal to 353 m and 2.11 m, respectively.
^ The CMC value occurs at x = 7 m from the discharge
point. SUM2 notifies the user on the criteria checked for
a TDZ; i) the discharge velocity was not equal to or greater
than, the minimum value of 3.0 m/s, ii) the downstream
distance of the TDZ (1.33 m) did not exceed the maximum
distance of 50 times the discharge length scale L, = 1.73 m,
111) the downstream distance of the TDZ was met within the
maximum distance of 5 times the water depth of 24.16 m, and
finally iv) the downstream distance of the TDZ was within
10 % of the distance to the LMZ.
t At 3000 m from the outfall, the plume dilution S = 51.1
with plume depth bv = 1.23: m and flow half-width bh = 681 m.
For the March design conditions, CORMIX2 concludes the
linear ambient density stratification is dynamically
unimportant and unstable,; and a uniform ambient density is
set_equal to the layer average of 1025.588 kg/m3. CORMIX2
assigns a flow class MU1V; for the full .water depth. The
simulation results are shown in Figure 5.15 indicating an
upstream intrusion at the; surface with an intrusion length
of about 188 m. ; .
SUM2 notifies the user that both the hydrodynamic mixing
zone (HMZ) and the legal mixing zone (LMZ) occurs at x = 266
m downstream from the discharge point with plume centerline
at the surface (z = 24.16 m) , dilution value S = 556.1, and
the plume half-width bh and thickness bv are equal to 488 m
and 19 m, respectively.
The CMC value occurs at x = 6.9 m from the. discharge
point.
At 3000 m from the outfall, the plume dilution S = 768,
the plume depth bv = 7.2 m, and the flow half-width bh =1775
m, indicating the flow does not contact the shoreline near
the public beach.
1-30
-------
.. z(m)J
".-•-.- 20
/" 10
zt=9.52m
,-s—LMZ limit
^7 . __ .
- 1
r CORMIX2
/ Cose AA*
"1 I ' U -1 ll_
f
Tr~TDZ limit
1
fl i
"
' '.
UAugust)
Buoyant
spreading
1
i I 1 -L »~
""**'**. _,nn 0 "^^ 100 200 300 4OO xlmj
a) Side View (distorted)
LMZ limit
UQ=0.09 m/s
CORMIX2
Case AAA
(August)
Figure 5.14
b) Plan View (distorted)
AAA Municipal Outfall: August Design Case
with Internal Flow Trapping
139
-------
-CORMIX2
Case AAA (March)
-LMZ limit
; 100 200
a) Side View (distorted)
300 400 xlm)
LMZ limit
ua-0,09 m/s
^-CORMIXZ
iCase AAA (March)
Figure 5.15
b) Plan View (distorted)
AAA Municipal Outfall: March Design Case with
Surface Interaction
140
-------
5.2.2 PPP Electric Power Company
This design example represents a heated discharge
effluent into a large lake from an electric power company
in relatively shallow water with various ambient currents
under a weak ambient stratification. There is no toxic
effluent in the discharge.
5.2.2.1 The Problem Statement
The lake is 8000 m wide, and the outfall is located at
a distance of 1000 m from the left side of the lake at a
local water depth of 10.0 m. Available site data indicate
a uniform ambient density profile with an average
temperature of 15 C.
A 300 m long staged diffuser is used with 31 ports
giving a spacing of 30 m. The ports issue about 0.5m above
the surrounding bottom. The ports are round with a diameter
of 0.9 m. The diffuser is discharging horizontally (0 = 0°)
and perpendicular to the direction of the prevailing ambient
current (cross-flow) (a = 90°, and -y = 90°) . The total
design discharge flowrate is 30 m3/s with a design effluent
temperature of 35 C. The discharge site is characterized
by wind-induced currents varying between 0.03 m/s and 0.15
m/s\ The diffuser is subject to a legal mixing zone (LMZ)
requirement with a local plume width of 400 m.
5.2.2.2 CORMIX2 Analysis
For the minimum ambient current speed of u. = 0.03 m/s,
and the maximum current speed, CORMIX2 assigns flow classes
MU5 and MU6, respectively. The simulation results are shown
in Figure 5.16 and 5.17 respectively.
When the current is weak, the analysis shows that the
legal mixing zone (LMZ) is reached at a distance of about
340 m downstream where the dilution S = 12 with a plume
depth bv = 1.25 m. However, with a strong ambient current,
the latter occurs within 100 m from the discharge point with
a dilution S = 17.1 and plume depth bv = 10 m.
5.3 Additional Comments on CORMIX2
As mentioned in Chapter III it is expected that CORMIX2
will be a general predictive system applicable to the
majority (better than 80%) of all multiport diffuser
discharge/environmental conditions. It is impossible,
however, to devise a system that will analyze all
conceivable submerged discharges. For this reason, CORMIX2
141
-------
ua=0.03m/s
3.3°c
bv=IOm_
AT0=ao°c
LMZ limit
CORMIX2
Case PPP (Weak Cross flow)
•-Plume restratification
Fully mixed
i
200 400 600 800 1000 x(m)
Plan View (undistorted)
Figure 5.16
PPP Electric Company Outfall in Low Ambient
Current
142
-------
y (m)
800
t
600
400
Ua=O.I5m/s 200
LMZ
limit
|O.86°C O.78°C ATC=O.73°C
/'bv = IOm
_J L_
4m
J
2.56m
2.46m
J L
'200^ 400 600 800 1000 1200 x(m)
AT0=2O°C
Plume
Restratification
CORMIX2
Case PPP (Strong Cross flow)
Plan View (undistorted)
Figure 5.17
PPP Electric Company Outfall in Strong Ambient
Current
143
-------
contains several internal criteria (limitations) designed
to avoid system misuse for such extreme conditions.
I
CORMIX2 is devised !for deeply submerged multiport
discharges in water of variable depth H. The discharge is
assumed to be located near the bottom of the water body.
CORMIX2 uses the applicability criterion for the height of
the discharge port h0
h0
0.33H
(5.4)
Eq. 5.4 is needed to assure a valid test for deep/shallow
discharge stability in the flow classification scheme.
Also the diameter D for each port or nozzle must not
exceed 20% of the water depth,
D
0.2 H
(5.5)
Finally, the height of the pycnocline (i.e. thickness
of the lower layer) h^, must be in the range between 40% to
90% of the water depth ;
0.4H < h., < 0.5H
(5.6)
It is pointed out, however, that an experienced user can
modify the data input to allow for CORMIX2 analyses that are
seemingly outside this normal range of system applicability.
Hints for those system applications can be found in Doneker
and Jirka (1989) ;
Furthermore, CORMIX2 assumes a conservative discharge
which is a reasonable assumption since its emphasis is on
initial mixing mechanisms with short time scales (for
further discussion, see Doneker and Jirka, 1989).
144
-------
Chapter VI
Conclusions and Recommendations
U.S water quality regulations contain the concept of a
mixing zone, a limited area or volume of water where initial
discharge dilution occurs. Water quality standards are
applicable at the border of, and outside, the mixing zone.
Toxic discharges are subject to additional regulatory
limitations. This water quality policy is implemented
through the National Pollution Discharge Elimination System
(NPEDS) which requires, among other factors, an estimate of
the initial mixing characteristics. There exist many
possible combinations of discharge conditions and ambient
environments, hence a considerable amount of skill and
training is required to pursue reliable mixing zone
analysis. For the purpose of facilitating this task, an
expert system methodology has been developed, the Cornell
Mixing Zone Expert System (CORMIX).
Subsystem CORMIX2 predicts trajectory and mixing
characteristics of a multiport dif fuser, discharging buoyant
(positively, negatively, or neutrally) effluents discharges
into uniform or stratified ambient environments with or
without the presence of ambient current. Knowledge gathered
from hydrodynamic expertise is used in CORMIX2 for mixing
analysis. CORMIX2 collects all input data, verifies for
data consistency, groups and executes the suitable
hydrodynamic simulation models, summarizes the simulation
results in accordance with legal requirements including
criteria for toxic substances, and finally recommends
alternatives for improving mixing characteristics. CORMIX2,
with its emphasis on rapid initial mixing, assumes a
conservative pollutant discharge neglecting any physical,
chemical, biological reaction, or decay processes. However,
the predictive results can be readily converted to adjust
for first-order reaction processes.
The results obtained for the hydrodynamic simulation are
in good agreement with laboratory and field data. CORMIX2
correctly predicts highly complex discharge situations
involving deep or shallow water environments, ambient
stratification, plume intrusions, and boundary interactions.
Many of these processes are absent in currently available
mixing models.
Further work should be accomplished in order to refine
the hydrodynamic flow protocols in the flow classification,
and to substantiate various constants in the system. This
task will require additional field and laboratory data.
Also, computer generated graphics should be developed to
plot simulation and to help the user in better understanding
the mixing processes.
145
-------
References
Abdelwahed, S. T., and Vincent H.
of Buoyant Jets in Cross Flow"r
Chu. (1978), "Bifurcation
. Technical Rept. No 78-1,
Engineering and Applied Mechanics,
Department of Civil
McGill University, Montreal, Canada.
Alam, A. M. Z., D. R. F. Harleman, and J. M Colonell (1982),
"Evaluation of Selected Initial Dilution Models". Journal
of the Environmental Engineering Division, ASCE, Vol 108,
No. EE1, February, pp 159M85.
Allan Hancock Foundation, University of Southern California
(1964), "Final Report on an Investigation on the Fate of
Organic and Inorganic Wastes Discharge into the Marine
Environment and Their Effects of Biological Productivity"
September 15.
Almquist, C. W., and Stolzenbach, K. D. (1976), "Staged
Diffusers in Shallow Wa^er"r M.I.T., Ralph M. Parsons
Laboratory for Water Resources and Hydrodynamics, Tech. Rep
No. 213. ;
Alnujuist, C. W. , and Stqlzenbach, K. D. (1980), "Staged
Multioort Diffusers", J. Hydraulics Division, Vol. 106, No.
HY2.
Anderson, J. L., Parker, F.L. and Bennedict, B.A. (1973)
"Negatively Buoyant Jets in a Crossflow", Environmental
Protection Technology Series, U.S.E.P.A., Washington, D.C.
Arita, M. and G.H. Jirka, (1987) , "Two-Layer Model of Saline
Wedcre II; Prediction of Mean Properties" r j. Hydraulic
Engineering, Vol. 113, No: 10.
Barnwell, T. O.,Brown L. C., and Marek, W. (1985),
"Development of a prototype expert advisor for the enhanced
stream water quality model QUAL2E", Internal Report,
Environmental Research Laboratory, Office of Research and
Development, U.S.E.P.A., Athens, Georgia, September, 1985.
Bata, G. L. (1957), "Recirculation of Cooling Water in
Rivers and Canals". J. Hydraulics Division, Vol. 83, No.
HY3.
i
Benjamin, T. B. (1968),\ "Gravity Currents and Related
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Briggs, G. A. (1969), Plume Rise. U.S. Atomic Energy
Commission, Division of Technical Information, Oak Ridge,
Tennessee. \
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Brocard, D. N. (1977), "Hydrothermal Studies of Staged
Diffuser Discharge in the Coastal Environment. Charlestown
Site"f Alden Research Laboratories, Tech. Report No. 136-
7/M296EF.
Cederwall, K. (1963), "The Initial Mixing of Jet Disposal
into a Recipient," Tech. Rep. 14 and 15, Div. of Hydraulics,
Chalmers Institute of Technology, Goteborg, Sweden.
Chen, J. C. (1980), "Studies on Gravitational Spreading
Currents", Rep. KH-R-40, W.M. Keck Laboratory of Hydraulics
and Water Resources, California Institute of Technology,
Pasadena, Calif.
Chu, V. H., and Jirka, G. H. (1986), "Surface Buoyant Jets
and Plumes"F Encyclopedia of Fluid Mechanics, Chapter 25,
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Clocksin, W. F. and Hellish, C. S. (1984),
Prolog, 2nd ed., Springer-Verlag.
Programming in
Congressional Research Service (1977), "Legislative History
of the Clean Water Act 1977", Congressional Research
Service, Library of Congress, October 1978, No. 95-14 p.
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Davidson, M. J. (1989), "The Behavior of Single and
Multiple. Horizontally Discharged, Buoyant Flows in a Non-
Turbulent Coflowing Ambient Fluid". Ph.D. Thesis,
Department of Civil Engineering, University of Canterbury,
Christchurch, New Zealand.
Doneker, R. L. , and G. H Jirka (1990), "CORMIXl; An Expert
System for Mixing Zone Analysis of Conventional and Toxic
Single Port Aquatic Discharges"f Tech. Rep. EPA/600/3-
90/012, Environmental Research Lab., U.S. EPA, Athens,
Georgia (also published as Tech. Rep., DeFrees Hydraulics
Laboratory, Cornell University, Ithaca, New York, 1989.
Fischer, H. B. et al. (1979), Mixing in Inland and Coastal
Waters,, Academic Press, New York.
Gaschnig, J., Reboh, and J. Reiter (1981), "Development of
a Knowledge-Based Expert System for Water Resources
Problems", Palo Alto, Calif.
Holley, E. R., and Jirka, G. H. (1986), "Mixing in Rivers".
Technical Report E-86-11, U.S. Army Corps of Engineers,
Washington, D.C.
Isaacson, M. S., Koh, R. C.Y., and Brooks, N. H. (1983),
"Plume Dilution for Diffusers with Multiport Risers", J.
Hydraulic Engineering, Vol. 109, No. 2.
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Jirka, G. H. and Harleman, D. R.F. (1973), "The Mechanics
of Submerged Multiport Diffusers for Buoyant Discharges in
Shallow Water", M.I.T., jRalph M. Parsons Laboratory for
Water Resources and Hydrodynamics, Tech. Rep No. 169.
Jirka, G. H., and Harleman, D. R.F (1979), "Stability and
Mixing of a Vertical Plane Buoyant Jet in Confined Depth",
J. Fluid Mechanics, Vol. 94, Part 2, pp.275-304,.
|
Jirka, G.' H., J. M. Jones, and F. E. Sargent (1980),
"Theoretical and Experimental intermediate Field Dynamics
of Ocean Energy Conversion Plants". Progress Report, 1978-
1979, School of Civil and Environmental Engineering, Cornell
University. ,
Jirka, G. H. (1982), "Multiport Diffuser for Heat Disposal;
a Summary"f J. of Hydraulics Division, ASCE, 108, HY12,
1982, pp. 1425-68. j
I
Jirka, G. H., Colonell/ J. M., and Jones, D. (1985),
"Outfall Mixing Design in Shallow Coastal Water Under Arctic
Ice Cover", MTS Journal, Vol. 20, No. 3.
i
Jirka, G. H., and Joseph H.-W. Lee (1991), "Waste Disposal
in the Ocean", Hydraulilc Structures Design Manual, E.
Naudascher, Ed., Vol 1Q. International Association of
Hydraulic Research, (in print).
Jirka, G.H., and P.J. Akar (1991), "Hvdrodvnamic
Classification of Submerged Multiport-Diffuser Discharges".
J. Hydraulics Div., ASCE,iVol 117, No. 9, September 1991.
i . .
Jones, J. M., G. H. Jirka, and D. A. Caughey (1985),
"Numerical Techniques for Steady Two-Dimensional
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Ithaca, New York). i
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"Modelling of Unidirectional Thermal Diffusers In Shallow
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Lee, J. H.W., and Jirka, G. H. (1979), "Heat Recirculation
Induced by Thermal Diffusers", J. Hydraulics Division, Vol.
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Lee, J. H.W., and Jirka, G. H. (1980), "Multiport Diffuser
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Lee, J. H.W. (1984), "Boundary Effects on a Submerged Jet
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Manifold in Stagnant Receiving Water of Uniform Density",
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Berkeley, California. Tech. Rept. HEL 23-1.
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in Buoyant Jets", Proc. ASCE, J. Hydraulics Division, 99,
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i
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i
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150
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Wright, S.J., Wong, D. R. , and Zimmerman, K. E. (1982),
"Outfall.Diffuser Behavior in Stratified Ambient Fluid". J.
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University of Michigan, Ann Arbor MI.
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Appendix A: Data Input Advices
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 CORMIX2 deals with buoyant submerged discharges from
MULTIPORT DIFFUSERS into blowing unstratified or stratified
water environments, such |as rivers, lake, estuaries, and
coastal waters. It included the limiting cases of non-buoyant
and negatively buoyant discharges and of stagnant ambient
conditions. t
The predictive elements j of CORMIX2 are based on the
"equivalent slot diffuser" concept. This means the details of
the individual jets emanating from the evenly spaced diffuser
ports/nozzles are neglected by assuming an equivalent slot jet
on the basis of equivalency of flux quantities per unit
diffuser length. This concept provides a dynamically accurate
representation of the actual three-dimensional diffuser if
attention lies in the region after merging. ; (In most
cases,the distance to merging is short, of the order of twice
the spacing between individual jets. If further predictive
details for the individual three-dimensional jets prior to
merging are desired, the user is advised to use CORMIXl with
the flow parameters for the individual jets).
I ; , ;
Please note that the time jfor 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'may be displayed by the
system during program execution, or may be neglected by the
user.
PROGRAM ELEMENTS:
The program elements of C0RMIX2 are listed below. During
system use the program elements are loaded sequentially and
automatically in the order igiven 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
i
! 152 ;
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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, fn.CXC,
and HYDRO2.CXE where fn is a user supplied file name.
The fn.CXD contains all necessary input data for the
hydrodynamic simulation model HYDRO2 described below.
The file fn.CXC contains all knowledge base conclusions.
The HYDR02.CXE file instructs HYDR02 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 an alphanumeric
label (Example MU1,MS4,..) and a detailed hydrodynamic
description 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 (HYDRO2) consisting
of a number, of simulations subroutines (modules) each
corresponging to a particular hydrodynamic mixing
process. For each flow configuration (Examples: MU4,
MS5) identified in CLASS, the appropriate modules are
executed sequentially according to a specific protocol.
The program prints out data on geometry (trajectory,
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width, etc.) and associated mixing (dilution,
concentration) following the path of the effluent
discharge. As mentioned above, the main predictive
elements are based on,the three-dimensional "equivalent
slot diffuser" representation of the actual multiport
diffuser.
HYDRO2 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 from HYDRO2. The fn.CXS
file is used as input;by the final program segment SUM.
I '
5) SUM |
j
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. j
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 in
arbitrary units, i.e. the user can specify these in any units
he/she desires, and all butput data must be interpreted
accordingly in these same units.
COORDINATE SYSTEM: i
All predictions in CORMIX2 are displayed using the
following three-dimensional coordinate system:
The origin is located at the half-way point of the
diffuser line. j
*** There is one exception: when the diffuser line
starts at the shore, then the origin is located
directly at the sliore. ***
The x-axis is located at the bottom of th£ water body
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 amb'ient flow direction (x-axis) .
The z-axis points vertically upward.
Note, if the ambient current direction is variable (e.g. due
to reversing tidal flows) ,; the x-axis and the y-axis will
change depending on flow^ direction. Furthermore, if a
stagnant situation is to be analysed, the x-axis may be
defined by the direction of the prevailing currents.
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*************************************************************
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 opportunitiy 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
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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 relationship is normally available from
a separate hydraulic analysis or from field measurements.
2) For the given stage-
-------
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.
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).
b) 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
157
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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
opportunitiy 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 known within +-30% the predictions
will vary by +-10% at ibhe most.
*************** ************** ********************************
ADVICE FOR SPECIFYING DISCHARGE CHARACTERISTICS: MULTIPORT
DIFFUSERS: ;
f
GENERAL INFORMATION AND DEFINITIONS:
A multiport diffuser is a linear structure consisting of many
closely spaced ports or nozzles which inject a series of
turbulent jets at high velocity into the ambient receiving
water body. These ports or nozzles may be connected to
vertical risers attached to an underground pipe or tunnel, or
may simply be openings in a pipe lying on the bottom.
The diffuser line (or axis) is a line connecting the first
port or nozzle and the last port or nozzle. Generally, the
diffuser line will coincide with the connecting pipe or
tunnel. CORMIX2 will assume;a straight diffuser line. If the
actual diffuser pipe has bends or directional changes it must
be approximated by a straight diffuser line.
The diffuser length is the distance from the first to the last
port or nozzle. The origin of the coordinate system used by
CORMIX2 is located at the center (mid-point) of the diffuser
line (there is one exception: when the diffuser line starts at
the shore, then the origin is located directley at the shore.
CORMIX2 considers the three [major diffuser types in common
engineering practice:
1) UNIDIRECTIONAL DIFFUSER: All ports (or nozzles) are
pointing to one side of the diffuser line, more or less
normally to the diffuser line, and more or less
158
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horizontally.
2) STAGED DIFFUSER: All ports are pointing in one
direction following the diffuser line (or nearly so, with
small deviations to either side of the diffuser line),
and more or less horizontally.
3) ALTERNATING DIFFUSER: The diffuser ports do not have
a preferred horizontal direction: Either they point, in
an alternating fashion and more or less horizontally, to
both sides of the diffuser line, or they all point
upward, more or less vertically.
DIFFUSER GEOMETRY SPECIFICATION:
CORMIX2 will ask for the following data on diffuser geometry.
Note, that CORMIX2 will assume uniform discharge conditions
along the diffuser line. This includes a uniform ambient
depth as specified earlier. If the depth is, in fact,
variable (e.g. due to an offshore slope) it should be
approximated by a mean depth along the diffuser line (with a
possible bias to the more shallow near-shore conditions).
Similarly, discharge parameters (e.g. port size or spacing or
discharge per port) may vary along the diffuser line; again,
they must be approximated by mean values.
1) Specify the diffuser length. Also specify the
distance from the shore for both end points of the
diffuser line.
2) Details on port or nozzle geometry and construction:
Are the ports or nozzles connected to vertical risers
from an underground pipe or tunnel? If yes, how many
risers exist, and how many ports or nozzles are attached
to each riser? If no, how many ports or nozzles are
spaced along the diffuser line? In either case, CORMIX2
will assume a uniform spacing between risers or between
nozzles or ports.
3) Specify the average diameter of the discharge ports or
npzzles. CORMIX2 assumes round ports/nozzles. Also, the
value for the jet contraction coefficient should be
specified.
4) Specify the height of the port/nozzle centers above
the ambient bottom.
5) The vertical angle of discharge (THETA) is the angle
of the port/nozzle centerline measured from the
horizontal plane. As examples, THETA is 0 deg for a
horizontal discharge, and it is +90 deg for a vertical
(upward) discharge.
159
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6) Consider a plan view of the diffuser as seen from
above. Defined for the unidirectional and staged
diffusers only, the horizontal angle of discharge (SIGMA)
is the angle between tlie port/nozzle centerline in this
plan projection and jthe ambient current direction,
measured counterclockwise from the ambient current
direction (x-axis). The possible range of SIGMA is from
0 deg to 360 deg. In case of variable orientation,
specify the average horizontal angle.
i • . .
7) The diffuser alignment angle (GAMMA) is the angle
between the diffuser !axis and the ambient current,
measured counterclockwise from the ambient current
direction (x-axis) . The possible range for the alignment
angle is from 0 deg to 180 deg. As examples, special
cases are the parallel! diffuser (GAMMA = 0 deg or 180
deg), and the perpendicular diffuser (GAMMA =90 deg).
8) The relative orientation angle (BETA) of the
port/nozzle discharge j is the nearest (clockwise or
counterclockwise) angle]between the horizontal projection
of the port/nozzle centerline and the diffuser axis. The
possible range of the BETA is between 0 deg (staged
diffuser) and 90 deg (unidirectional diffuser).
DIFFUSER FLOW VARIABLES: ; - •
1) Specify the total diffuser discharge or the discharge
velocity. Note, these two variables are related through
the total cross-sectional area of all discharge
ports/nozzles.
I
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 i^ computed after specification of
the discharge temperature.
i
i
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 CORMIX2 results for computed excess
concentrations should then be interpreted in these same
units.
i
****************************$*******************************
SPECIFICATION OF DESIRED MIXING ZONE INFORMATION:
i
The user must specify data that indicates over which spatial
160
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region information will be desired, and in what detail.
mixing zone (LMZ) requirements may exist or not.
The user has several options for this specification:
Legal
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. If the
discharge is toxic, the criterion continuous concentration
(CCC) value must be met at the boundary of the LMZ.
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
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;
in revision, 1990) 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.
161
-------
Appendix B: Flow Descriptions for all Flow Classes
*************************************************************
FLOW CLASS MSI
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. For this case, the diffuser alignment is
predominantly perpendicular to the ambient flow.
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) Weakly deflected plane jet in crossflow: The flow issuing
from the equivalent slot width is initially dominated by the
effluent momentum (jet-like) and is weakly deflected by the
ambient current.
2) Strongly deflected plane jet in crossflow: The jet has
become strongly deflected by the ambient current and is
slowly rising toward the trapping level.
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.
i
*** 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. *** i i • ••
; 162
-------
*************************************************************
FLOW CLASS MS2
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. For this case, the diffuser alignment is
predominantly parallel to the ambient flow.
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) Weakly deflected plane jet in crossflow: The flow issuing
from the equivalent slot width is initially dominated by the
effluent momentum (jet-like) and is weakly deflected by the
ambient current.
2) Strongly deflected plane jet in crossflow: The jet has
become strongly deflected by the ambient current and is
slowly rising toward the trapping level.
3) Internal density current along diffuser line: The plume
develops along the diffuser line due to continuous inflow of
mixed buoyant water. The plume spreads laterally along the
layer boundary (surface or pycnocline) which it is being
advected by the ambient current. The mixing rate is
relatively small.
*** 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 6 or 7 depending on
the definitions of the LEGAL MIXING ZONE or the REGION OF
INTEREST. *** ,
163
-------
*************************************************************
FLOW CLASS MS3 i
I
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.
i
The following flow zones exist:
1) Near-vertical plane jet iin linear stratification: The flow
issuing from the equivalent slot is initially dominated by
the effluent momentum (jetflike) 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, andjmay overshoot that level to some
extent. After impingement the flow spreads in all directions
(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. ***
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. *** I
164
-------
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 MS4
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) Near-horizontal plane jet in linear stratification: The
flow issuing from the equivalent slot width 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 /surface spreading: The weakly
bent jet/plume approaches (injects into) the terminal
layer at a near- horizontal angle. After injection the flow
spreads in all directions (more or less radiallyO at the
terminal level forming an internal layer. The residual
horizontal momentum flux 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
165
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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 bank's.
*** 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 if low (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 land 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 MS5 ;
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. For this case, the diffuser alignment is
predominantly perpendicular to the ambient flow.
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) Strongly deflected plane plume: The flow issuing from the
equivalent slot width is initially dominated by the effluent
buoyancy (plume-like) and the plume buoyancy starts to affect
the flow. The plume is strongly deflected by the current and
is slowly rising towards the terminal level.
166
-------
2) 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. ***
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. ***
*************************************************************
FLOW CLASS MS6
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. For this case, the diffuser alignment is
predominantly parallel to the ambient flow.
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) Strongly deflected planfe plume: The flow issuing from the
equivalent slot width is initially dominated by the effluent
buoyancy (plume-like) and the plume buoyancy starts to affect
the flow. The plume is strongly deflected by the current and
is slowly rising towards the terminal level.
2) 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.
167
-------
3) Internal density current along diffuser line: The plume
develops along the diffuser line due to continuous inflow of
mixed buoyant water. The;plume spreads laterally along the
layer boundary (surface or pycnocline) which it is being
advected by the ambient ! current. The mixing rate is
relatively small.
*** 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 arid/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 MS7
This flow configuration is ^profoundly affected by the linear
ambient density stratification. The predominantly plume-like
flow issues vertically, or near-vertically, and rises
vertically upward and gets trapped at some terminal
equilibrium level. The crossflow is weak in the present
situation. \
Following the trapping zohe, the discharge flow forms an
internal layer that is further influenced by buoyant spreading
and passive diffusion. i
The following flow zones ekist:
1) Weakly deflected plane plume in linear stratification: The
flow issuing from the equivalent slot width is initially
dominated by the effluent buoyancy (plume-like) and is weakly
affected by the ambient current and the density
stratification. | .
• ' i •
2) Terminal layer impingement / upstream spreading: The weakly
bent jet/plume approaches (iimpinges) the terminal layer at a
near- vertical angle, and imay overshoot that level to some
i
! 168
-------
extent. After impingement the flow spreads in all directions
(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. ***
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 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 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 MS8
This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly plume-like
flow issues horizontally, or near-horizontally, into the
density stratified layer and, after some distance, rises
vertically upward and gets trapped at some terminal
equilibrium level. The crossflow is weak in the present
situation.
169
-------
Following the trapping zone, the discharge flow forms an
internal layer that is further influenced by buoyant spreading
and passive diffusion. !
I
The following flow zones exist:
1) Weakly deflected plane ijet in crossflow: The flow issuing
from the equivalent slot diffuser is initially dominated by
the effluent momentum (jet-like) and is weakly deflected by
the ambient current. :
i
2) Weakly deflected plane plume in linear stratification:
After some distance, the flow becomes dominated by the
effluent buoyancy (plume-like) and is 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 in all directions
(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. JThis 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. •*'*.*
i
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 ishear 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
« .M.WK ,«*. / H MK«K JM .•* «1
-------
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 MU1H
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) Weakly deflected plane jet in crossflow: The flow issuing
from the equivalent slot diffuser is initially dominated by
the effluent momentum (jet-like) and is weakly deflected by
the ambient current.
2) Strongly deflected plane plume: After some distance the
discharge buoyancy becomes the dominating factor
(plume-like). The plume is deflected by the effect of the
strong ambient current.
3) Surface 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.
or
3) Density current along diffuser line: The plume develops
along the diffuser line due to continuous inflow of mixed
buoyant water. The plume spreads laterally along the layer
boundary (surface or pycnocline) which it is being advected
by the ambient current. The mixing rate is relatively small.
This zone extends from beginning to end of the diffuser line.
. *** 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
171
-------
or shoreline. |
5) Passive ambient mixing: After some distance the background
turbulence in the ambient ishear 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. *** i
**************************** 5V************************ ********
FLOW CLASS MU1V !
The discharge configuration's hydrodynamically "stable", that
is the discharge strength (measured by its momentum flux) is
weak in relation to the lajyer depth and in relation to the
stabilizing effect of the dilscharge buoyancy (measured by its
buoyancy flux) . The buoyancy effect is very strong in the
present case. 1
The following flow zones exist:
1) Weakly deflected plane jet in crossflow: The flow issuing
from the equivalent slot diffuser is initially dominated by
the effluent momentum (jet-like) and is weakly deflected by
the ambient current.
2) Weakly deflected plane! plume: After some distance the
discharge buoyancy becomes the dominating factor
(plume-like). The plume deflection by the ambient current is
still weak. '.
i
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 in all directions (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. ***
1- ' . • '
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
172
-------
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 MU2
A unidirectional multiport diffuser with perpendicular
alignment is discharging into an ambient flow. Frequently,
this is called a "co-flowing diffuser". The discharge
configuration is hydrodynamically "unstable", that is the
discharge strength (measured by its momentum flux) is very
strong in relation to the layer depth and in relation to the
stabilizing effect of the discharge buoyancy (measured by its
buoyancy flux). Rapid vertical mixing takes place over the
full layer depth.
The following flow zones exist:
1) Acceleration zone for unidirectional coflowing diffuser:
The net horizontal momentum flux provided by the diffuser jets
leads to a wholescale acceleration of the ambient water, that
flows across the diffuser line leading to rapid entrainment
and mixing in this zone. The diffuser plume is mixed over the
full layer depth, and contracts laterally in the direction of
the flow (acceleration process). The length of this zone is
about one half the diffuser length.
2) Diffuser-induced plume in co-flow: The diffuser induced
momentum flux is still controlling the flow. However, lateral
173
-------
entrainment and diffusion lead to a spreading of the diffuser
plume and additional mixing. The plume moves predominantly
in the direction of the anibient flow. At the beginning, the
plume is vertically mixed over, the full layer depth. At some
distance, stratification may take place depending on the
strength and direction of
the plume buoyancy.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
i
3) 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. '
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 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. *** i
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 hydrodyriamic mixing
zone (zones 1 and 2) and the predictions will be terminated at
this stage. !
i
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 MU3
A unidirectional multiport: diffuser with parallel alignment
(commonly called a "tee diffuser" is discharging into a weak
ambient flow. The ! discharge configuration is
hydrodynamically "unstable", that is the discharge strength
(measured by its momentum flux) is very strong in relation to
the layer depth and in relation to the stabilizing effect of
the discharge buoyancy (measured by its buoyancy flux).
174
-------
The following flow zones exist:
1) Acceleration zone for unidirectional co-flowing diffuser
(tee): The net horizontal momentum flux provided by the
diffuser jets leads to a wholescale acceleration of the
ambient water, that is diverted across the diffuser line
leading to rapid entrainment and mixing in this zone. The
diffuser plume is mixed over the full layer depth, and
contracts laterally in the direction of the flow
(acceleration process) . The length of this zone is about one
half the diffuser length. Plume deflection by the ambient
current is insignificant.
2) Diffuser-induced plume in cross-flow: The diffuser induced
momentum flux is still controlling the flow. However, lateral
entrainment and diffusion lead to a spreading of the diffuser
plume and additional mixing. Initially, the plume is
cross-flowing, but it becomes progressively deflected into
the direction of the ambient flow. At the beginning, the
plume is vertically mixed over the full layer depth. At some
distance, stratification may take place depending on the
strength and direction of the plume buoyancy.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
3) 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.
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 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.
175
-------
For practical final predictions, however, the advection and
diffusion of the ambient! flow - no matter how small in
magnitude - should be considered.
FLOW CLASS MU4
A unidirectional multiport;diffuser with parallel alignment
(commonly called a "tee diffuser" is discharging into a strong
ambient flow. The discharge configuration is
hydrodynamically "unstable11;, that is the discharge strength
(measured by its momentum flux) is very strong in relation to
the layer depth and in relation to the stabilizing effect of
the discharge buoyancy (meaisured by its buoyancy flux) . The
ambient current is very stirong in the present case.
The following flow zones exist:
1) Unidirectional cross-flowing (tee) diffuser plume in strong
current: The strong ambient crossflow rapidly deflects the
diffuser induced plume floy. The diffuser plume is advected
in the direction of the ambient flow. This plume deflection
is associated with a recirculation zone at the downstream end
(lee) of the plume. The plume is vertically mixed over the
full layer depth in this zone.
*** The zones listed above constitute 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. i
*** Predictions will be terminated in zone 2 or 3 depending on
the definitions of the LEGAL MIXING ZONE or the REGION OF
INTEREST. ***
****** *********************A*********************************
FLOW CLASS MU5 i
A staged multiport diffuser
with predominantly perpendicular
176
-------
alignment is discharging into weak ambient flow. The
discharge configuration is hydrodynamically "unstable", that
is the discharge strength (measured by its momentum flux) is
very strong 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) Acceleration zone for staged diffuser: The net horizontal
momentum flux provided by the staged diffuser jets produces
strong lateral entrainment of the ambient water and gradual
acceleration along the diffuser line. A strong concentrated
current with vertical mixing over the full layer depth is set
up. This zone extends from the beginning to the end of the
diffuser line.
2) Diffuser-induced plume in cross-flow: The diffuser induced
momentum flux is still controlling the flow. However, lateral
entrainment and diffusion lead to a spreading of the diffuser
plume and additional mixing. Initially, the plume is
cross-flowing, but it becomes progressively deflected into
the direction of the ambient flow. At the beginning, the
plume is vertically mixed over the full layer depth. At some
distance, stratification may take place depending on the
strength and direction of the plume buoyancy.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
3) 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.
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 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.
177
-------
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 MU6 j
A staged multiport diffuser with perpendicular alignment is
discharging into a strong ambient flow. The discharge
configuration is hydrodyriamically "unstable", that is the
discharge strength (measured by its momentum flux) is very
strong in relation to the flayer depth and in relation to the
stabilizing effect of the discharge buoyancy (measured by its
buoyancy flux). The ambient current is very strong in the
present case. '
The following flow zones exist:
1) Staged perpendicular plume in strong current: The strong
ambient flow rapidly deflects the diffuser induced plume.
Ambient water flows across the diffuser line, and the diffuser
plume is advected in the direction of the ambient flow. The
length of this zone is about one half of the diffuser length.
*** The zones listed above constitute 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. j
i
*** Predictions will be terminated in zone 2 or 3 depending on
the definitions of the LEGAL MIXING ZONE or the REGION OF
INTEREST. ***
FLOW CLASS MU7
178
-------
A staged multiport diffuser with predominantly parallel
alignment is discharging into an ambient flow. The discharge
configuration is hydrodynamically "unstable", that is the
discharge strength (measured by its momentum flux) is very
strong 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) Acceleration zone for staged diffuser: The net horizontal
momentum flux provided by the staged diffuser jets produces
strong lateral entrainment of the ambient water and gradual
acceleration along the diffuser line. A strong concentrated
current with vertical mixing over the full layer depth is set
up. This zone extends from the beginning to the end of the
diffuser line.
2) Diffuser-induced plume in co-flow: The diffuser induced
momentum flux is still controlling the flow. However, lateral
entrainment and diffusion lead to a spreading of the diffuser
plume and additional mixing. The plume moves predominantly
in the direction of the ambient flow. At the beginning, the
plume is vertically mixed over the full layer depth. At some
distance, stratification may take place depending on the
strength and direction of the plume buoyancy.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
3) 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.
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 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.
179
-------
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 MU8
An alternating multiport diffuser with predominantly
perpendicular alignment is |discharging into an ambient flow..
For this diffuser configuration the net horizontal momentum
flux is zero so that no significant diffuser-induced currents
are produced in the water bjody. However, the local effect of
the discharge momentum flux is strong in relation to the layer
depth and in relation to the stabilizing effect of the
discharge buoyancy, so that the discharge configuration is
hydrodynamically "unstable".
The following flow zones exist:
1) Alternating perpendicular diffuser with unstable near-field
zone: The destabilizing efffect of the discharge jets produces
an unstable near- field zone. For stagnant or weak cross-flow
conditions, a vertical recirculation zone is being produced
leading to mixing over the full layer depth: however, the flow
tends to re-stratify outside this zone that extends a few
layer depths around the diffuser line. For strong
cross-flow, additional d^stratification and mixing are
produced.
i
or, alternatively, a second possibility exists for strongly
buoyant discharges: j
I
1) Near-vertical surface impingement, upstream spreading,
vertical mixing, and buoyant restratification: The
destabilizing effect of the discharge jets produces an
unstable near-field zone. ' For stagnant or weak cross-flow
conditions, a vertical recirculation zone is being produced
leading to mixing over the full layer depth: however, the
flow tends to re-stratify outside this zone that extends a
few layer depths around the diffuser line. In particular,
upstream spreading will occur due to the strong buoyancy of
the discharge. I
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initia^ mixing takes place. ***
2) Buoyant spreading at .layer boundary: The plume spreads
laterally along the layer ^boundary (surface or pycnocline)
i
i 180
-------
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, then 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.
*************************************************************
FLOW CLASS MU9
An alternating multiport diffuser with predominantly parallel
alignment is discharging into an ambient flow. For this
diffuser configuration the net horizontal momentum flux is
zero so that no significant diffuser-induced currents are
produced in the water body. However, the local effect of the
discharge momentum flux is strong in relation to the layer
depth and in relation to the stabilizing effect of the
discharge buoyancy, so that the discharge configuration is
hydrodynamically "unstable".
The following flow zones exist:
1) Near-vertical surface impingement, upstream spreading,
vertical mixing, and buoyant restratificatipn: The
destabilizing effect of the discharge jets produces an
unstable near-field zone. For stagnant or weak cross-flow
conditions, a vertical recirculation zone is being produced
leading to mixing over the full layer depth: however, the
flow tends to re-stratify outside this zone that extends a
few layer depths around the diffuser line. In particular,
181
-------
upstream spreading will occur due to the strong buoyancy of
the discharge. '
i
or, alternatively, for calses with stronger crossflow:
1) Density current developing along parallel diffuser line:
The plume develops along tljie diffuser line due to continuous
inflow of mixed buoyant water. The plume spreads laterally
along the layer boundary (surface or pycnocline) which it is
being advected by the ambient current. The mixing rate is
relatively small. This zone extends from beginning to end of
the diffuser line. i
i
*** The zones listed above constitute 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 plumje may interact with a nearby bank
or shoreline. i
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, then 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. i
i
I
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 MNU1
A submerged negatively buoyant effluent issues the discharge
port. The discharge configuration is hydrodynamically
182
-------
"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 ambient
current is scale in this case.
The following flow zones exist:
1) Negatively buoyant line plume: The flow issuing from the
equivalent slot diffuser is dominated by the negative effluent
buoyancy. Depending on vertical discharge angle, the flow may
rise somewhat; but due to the strong buoyancy, it will quickly
descend to the bottom. The length of this region is
controlled by the jet to plume length scale.
2) 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. ***
3) 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.
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 layer surface
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
183
-------
diffusion of the ambieht flow - no matter how small in
magnitude - should be considered.
FLOW CLASS MNU2
A submerged negatively; buoyant effluent issues either
horizontally or vertically 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. |
i
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) Weakly deflected plane; jet in crossflow: The flow issuing
from the equivalent slot!diffuser is initially dominated by
the effluent momentum (jet-like) and is weakly deflected by
the ambient current. I
i
2) Strongly deflected plane jet in crossflow: The jet has
become strongly deflected by the ambient current and is
slowly rising toward the!trapping level.
I • ,
3) Strongly deflected plane plume: After some distance, the
plume buoyancy starts to affect the flow. The plume is
slightly deflected by the current and is slowly descending
towards the bottom level. ;
4) Bottom 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.
or
t
4) Density current developing along parallel diffuser line:
The plume develops along the diffuser line due to continuous
inflow of mixed buoyant water. The plume spreads laterally
along the layer boundary ([bottom) while it is being advected
by the ambient current. The mixing rate is relatively small.
This zone extends from beginning to end of the diffuser line.
.84
-------
*** 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 MNU3
A submerged negatively buoyant effluent issues from a
unidirectional diffuser that may have an arbitrary alignment
relative to the weak 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 negative discharge buoyancy
(measured by its buoyancy flux). The ambient current is
scaled in this case. As a consequence, the mixed effluent
will form a layer near the bottom of the ambient layer.
However, the total momentum flux in this case is large enough
to induce a significant current flow in this bottom layer.
The following flow zones exist:
1) Weakly deflected (2-D) wall jet: The flow issuing
horizontally from the equivalent slot diffuser adheres to the
bottom and spreads vertically through turbulent diffusion. A
gradual deflection by the ambient current takes place.
2) Diffuser-induced bottom density current: Driven by the
horizontal net momentum flux a bottom density current will
propagate forward while spreading laterally with .small
mixing. This current is further deflected by the ambient
flow into the downstream direction.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
185
-------
3) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being advected by the
ambient current. The plumei thickness may decrease during1 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 ishear 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 3 or 4 depending on
the definitions of the LEGAL MIXING ZONE or the REGION OF
INTEREST. *** i
I
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. j
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 MNU4 j :
A submerged negatively buoyant effluent issues from a
unidirectional diffuser that may have an arbitrary alignment
relative to the strong ambient current.
The discharge configuration; is hydr©dynamically "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 ambient current is
scaled in this case. As a consequence, the mixed effluent
will form a layer near the bottom of the ambient layer.
However, the total momentum flux in this case is large enough
to induce a significant current flow in this bottom layer.
The following flow zones exist:
1) Weakly deflected (2-p) wall jet: The flow issuing
horizontally from the equivalent slot diffuser adheres to the
bottom and spreads vertically through turbulent diffusion. A
186
-------
gradual deflection by the ambient current takes place.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
2) 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.
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 surface
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, then 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.
*************************************************************
FLOW CLASS MNU5
A submerged negatively buoyant effluent issues from a staged
diffuser that may have an arbitrary alignment relative to the
weak 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 negative discharge buoyancy
(measured by its buoyancy flux). The ambient current is
scaled in this case. As a consequence, the mixed effluent
will form a layer near the bottom of the ambient layer.
However, the total momentum flux in this case is large enough
to induce a significant current flow in this bottom layer.
187
-------
The following flow zones exist:
I
1) Negatively buoyant stageld acceleration zone: The negatively
buoyant flow issuing from the eguivalent slot diffuser and in
the direction of the diff user line adheres to the bottom and
spreads laterally through turbulent diffusion. The vertical
thickness of this flow zone is given by the jet to plume
length scale, and it extends over the full diffuser length.
2) Weakly deflected (3-D) wall jet: The flow issuing
horizontally from the equivalent slot diffuser adheres to the
bottom and spreads vertically through turbulent diffusion. A
gradual deflection by the ambient current takes place.
3) Diffuser-induced bottom density current: Driven by the
horizontal net momentum flux a bottom density current will
propagate forward while! spreading laterally with small
mixing. This current is further deflected by the ambient
flow into the downstream direction.
*** 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 baftk 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. j
i
*** 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 I 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.
188
-------
*************************************************************
FLOW CLASS MNU6
A submerged negatively buoyant effluent issues from a staged
diffuser that may have an arbitrary alignment relative to the
strong 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 negative discharge buoyancy
(measured by its buoyancy flux). The ambient current is
scaled in this case. As a consequence, the mixed effluent
will form a layer near the bottom of the ambient layer.
However, the total momentum flux in this case is large enough
to induce a significant current flow in this bottom layer.
The following flow zones exist:
1) Negatively buoyant staged acceleration zone: The negatively
buoyant flow issuing from the equivalent slot diffuser and in
the direction of the diffuser line adheres to the bottom and
spreads laterally through turbulent diffusion. The vertical
thickness of this flow zone is given by the jet to plume
length scale, and it extends over the full diffuser length.
2) Weakly deflected (3-D) wall jet: The flow issuing
horizontally from the equivalent slot diffuser adheres to the
bottom and spreads vertically through turbulent diffusion. A
gradual deflection by the ambient current takes place.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
3) 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.
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 layer surface
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, then advection and
189
-------
diffusion by the ambient jflow (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 MNU7 j
A ^ unidirectional multiport diffuser with perpendicular
alignment is discharging ihto an ambient flow. Frequently,
this is called a "co-flowing diffuser". The discharge
configuration is hydrodynamically "unstable", that is the
discharge strength (measure'd by its momentum flux) is very
strong in relation to the layer depth and in relation to the
stabilizing effect of the discharge buoyancy (measured by its
buoyancy flux). Rapid vertical mixing takes place over the
full layer depth. ;
i
i
The following flow zones exist:
i
1) Acceleration zone for unidirectional coflowing diffuser:
The net horizontal momentum flux provided by the diffuser jets
leads to a wholescale acceleration of the ambient water, that
flows across the diffuser line leading to rapid entrainment
and mixing in this zone. The[ dif fuser plume is mixed over the
full layer depth, and contracts laterally in the direction of
the flow (acceleration process). The length of this zone is
about one half the diffuser length.
2) Diffuser-induced plume in co-flow: The diffuser induced
momentum flux is still controlling the flow. However; lateral
entrainment and diffusion lead to a spreading of the diffuser
plume and additional mixing. The plume moves predominantly
in the direction of the ambient flow. At the beginning, the
plume is vertically mixed over the full layer depth. At some
distance, stratification may take place depending on the
strength and direction of the plume buoyancy.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
3) Buoyant spreading at layer bottom: The plume spreads
laterally along the layer boundary (bottom) while it is being
advected by the ambient current. The plume thickness may
i 190
-------
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 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 MNU8
A unidirectional multiport diffuser with parallel alignment
(commonly called a "tee diffuser" is discharging into a weak
ambient flow. The discharge configuration is
hydrodynamically "unstable", that is the discharge strength
(measured by its momentum flux) is very strong 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) Acceleration zone for unidirectional co-flowing diffuser
(tee): The net horizontal momentum flux provided by the
diffuser jets leads to a wholescale acceleration of the
ambient water, that is diverted across the diffuser line
leading to rapid entrainment and mixing in this zone. The
diffuser plume is mixed over the full layer depth, and
contracts laterally in the direction of the flow
(acceleration process). The length of this zone is about one
half the diffuser length. Plume deflection by the ambient
current is insignificant.
191
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2) Diffuser-induced plume in cross-flow: The diffuser induced
momentum flux is still controlling the flow. However, lateral
entrainment and diffusion lead to a spreading of the diffuser
plume and additional mixing. Initially, the plume is
cross-flowing, but it becomes progressively deflected into
the direction of the ambient flow. At the beginning, the
plume is vertically mixed oyer the full layer depth. At some
distance, stratification may take place depending on the
strength and direction of the plume buoyancy.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
3) Buoyant spreading at layer bottom: The plume spreads
laterally along the layer boundary (bottom) while it is being
advected by the ambient cjirrent. The plume thickness may
decrease during this phase.' The mixing rate is relatively
small. The plume may interact with a nearby bank or
shoreline. I
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 channel bottom
and/or banks.
i
*** 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. I
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.
********************* ******^t********************it ************
FLOW CLASS MNU9
A unidirectional multiport diffuser with parallel alignment
(commonly called a "tee diffuser" is discharging into a strong
ambient flow. The , discharge configuration is
hydrodynamically "unstable"; that is the discharge strength
(measured by its momentum f l|ux) is very strong in relation to
192
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the layer depth and in relation to the stabilizing effect of
the discharge buoyancy (measured by its buoyancy flux). The
ambient current is very strong in the present case.
The following flow zones exist:
1) Unidirectional cross-flowing (tee) diffuser plume in strong
current: The strong ambient crossflow rapidly deflects the
diffuser induced plume flow. The diffuser plume is advected
in the direction of the ambient flow. This plume deflection
is associated with a recirculation zone at the downstream end
(lee) of the plume. The plume is vertically mixed over the
full layer depth in this zone.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
2) Buoyant spreading at layer bottom: The plume spreads
laterally along the layer boundary (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 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. ***
*************************************************************
FLOW CLASS MNU10
A staged multiport diffuser with predominantly perpendicular
alignment is discharging into weak ambient flow. The
discharge configuration is hydrodynamically "unstable", that
is the discharge strength (measured by its momentum flux) is
very strong 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) Acceleration zone for staged diffuser: The net horizontal
momentum flux provided by the staged diffuser jets produces
strong lateral entrainment of the ambient water and gradual
acceleration along the diffuser line. A strong concentrated
153
-------
current with vertical mixing over the full layer depth is set
up. This zone extends from; the beginning to the end of the
diffuser line.
2) Diffuser-induced plume in cross-flow: The diffuser induced
momentum flux is still controlling the flow. However, lateral
entrainment and diffusion lead to a spreading of the diffuser
plume and additional mixing. Initially, the plume is
cross-flowing, but it becomes progressively deflected into
the direction of the ambie|nt flow. At the beginning, the
plume is vertically mixed over the full layer depth. At some
distance, stratification may take place depending on the
strength and direction of the plume buoyancy.
*** The zones listed above Constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
3) Buoyant spreading at layer bottom: The plume spreads
laterally along the layer boundary (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. ;
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 channel bottom
and/or banks. j
i
*** Predictions will be terminated in zone 3 or 4 depending on
the definitions of the LEGAL MIXING ZONE or the REGION OF
INTEREST. ***
f
i
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.
i ' '• •
Such stagnant water predictions may be a useful initial mixing
indicator for a given site and discharge design.
i • - - . •
For practical final predictions, however, the advection and
diffusion of the ambient flow - no matter how small in
magnitude - should be considered.
FLOW CLASS MNU11
A staged multiport diffuserj with perpendicular alignment is
i
i 194
-------
discharging into a strong ambient flow. The discharge
configuration is hydr©dynamically "unstable", that is the
discharge strength (measured by its momentum flux) is very
strong in relation to the layer depth and in relation to the
stabilizing effect of the discharge buoyancy (measured by its
buoyancy flux). The ambient current is very strong in the
present case.
The following flow zones exist:
1) Staged perpendicular plume in strong current: The strong
ambient flow rapidly deflects the diffuser induced plume.
Ambient water flows across the diffuser line, and the diffuser
plume is advected in the direction of the ambient flow. The
length of this zone is about one half of the diffuser length.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
2) Buoyant spreading at layer bottom: The plume spreads
laterally along the layer boundary (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 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. ***
*************************************************************
FLOW CLASS MNU12
A staged multiport diffuser with predominantly parallel
alignment is discharging into an ambient flow. The discharge
configuration is hydr©dynamically "unstable", that is the
discharge strength (measured by its momentum flux) is very
strong 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) Acceleration zone for staged diffuser: The net horizontal
195
-------
momentum flux provided by
the staged diffuser jets produces
strong lateral entrainment of the ambient water and gradual
acceleration along the diffuser line. A strong concentrated
current with vertical mixing over the full layer depth is set
up. This zone extends from the beginning to the end of the
diffuser line. [
2) Diffuser-induced plume in co-flow: The diffuser induced
momentum flux is still controlling the flow. However, lateral
entrainment and diffusion Ijsad to a spreading of the diffuser
plume and additional mixing. The plume moves predominantly
in the direction of the ambient flow. At the beginning, the
plume is vertically mixed over the full layer depth. At some
distance, stratification irtay take place depending on the
strength and direction of the plume buoyancy.
I
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
I
3) Buoyant spreading at layer bottom: The plume spreads
laterally along the layer boundary (bottom) while it is being
advected by the ambient durrent. 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 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. ;
i . .
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 MNU13
196
-------
An alternating multiport diffuser with predominantly
perpendicular alignment is discharging into an ambient flow.
For this diffuser configuration the net horizontal momentum
flux is zero so that no significant diffuser-induced currents
are produced in the water body. However, the local effect of
the discharge momentum flux is strong in relation to the layer
depth and in relation to the stabilizing effect of the
discharge buoyancy, so that the discharge configuration is
hydr©dynamically -"unstable".
The following flow zones exist:
1) Alternating perpendicular diffuser with unstable near-field
zone: The destabilizing effect of the discharge jets produces
an unstable near- field zone. For stagnant or weak cross-flow
conditions, a vertical recirculation zone is being produced
leading to mixing over the full layer depth: however, the flow
tends to re-stratify outside this zone that extends a few
layer depths around the diffuser line. For strong
cross-flow, additional destratification and mixing are
produced.
or, alternatively, a second possibility exists for strongly
buoyant discharges:
1) Near-vertical surface impingement, upstream spreading,
vertical mixing, and buoyant restratification: . The
destabilizing effect of the discharge jets produces an
unstable near-field zone. For stagnant or weak cross-flow
conditions, a vertical recirculation zone is being produced
leading to mixing over the full layer depth: however, the
flow tends to re-stratify outside this zone that extends a
few layer depths around the diffuser line. In particular,
upstream spreading will occur due to the strong buoyancy of
the discharge.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
2) Buoyant spreading at layer bottom: The plume spreads
laterally along the layer boundary (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 channel bottom
and/or banks.
197
-------
*** 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, then 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 advect*lon and
diffusion of the ambient flow - no matter how small in
magnitude - should be considered.
i
*************************************************************
FLOW CLASS MNU14 I , .
An alternating multiport diffuser with predominantly parallel
alignment is discharging into an ambient flow. For this
diffuser configuration the net horizontal momentum flux is
zero so that no significant diffuser-induced currents are
produced in the water body. ; However, the local effect of the
discharge momentum flux is strong in relation to the layer
depth and in relation to i the stabilizing effect of the
discharge buoyancy, so that the discharge configuration is
hydrodynamically "unstable".
The following flow zones exist:
1) Near-vertical surface impingement, upstream spreading,
vertical mixing, and buoyant restratification: The
destabilizing effect of the discharge jets produces an
unstable near-field zone. For stagnant or weak cross-flow
conditions, a vertical recirculation zone is being produced
leading to mixing over the full layer depth: however, the
flow tends to re-stratify ;outside this zone that extends a
few layer depths around the diffuser line. In particular,
upstream spreading will occur due to the strong buoyancy of
the discharge.
or, alternatively, for cases with stronger crossflow:
1) Density current developing along parallel diffuser line:
The plume develops along the diffuser line due to continuous
inflow of mixed buoyant water. The plume spreads laterally
alo'ng the layer boundary (surface or pycnocline) which it is
being advected by the ambient current. The mixing rate is
relatively small. This zone extends from beginning to end of
198
-------
the diffuser line.
*** The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***
2) Buoyant spreading at layer bottom: The plume spreads
laterally along the layer boundary (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 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, then 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.
199
-------
Appendix C: Design Recommendations :
I
*****A*********A********************************************
DESIGN RECOMMENDATIONS AND C5ENERAL ADVICE:
A reliable environmental analysis and mixing zone prediction
is possible only if each design case is evaluated through
several iterations of CORMIX. 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 CORMIX 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, iterations should be conducted in the following
order: !
A) Diffuser design changes (geometry variations),
B) Sensitivity to ambient!conditions, and
C) Discharge flow changes (process variations).
When investigating these variations the CORMIX 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) DIFFUSER DESIGN CHANGES (GEOMETRY VARIATIONS):
Most of the following recommendations are motivated by the
desire for improving conditions in the applicable mixing zones
(i.e. minimizing concentrations and/or areal extents):
1) Diffuser location: Consider moving the outfall further
offshore to a larger water depth, in order to delay flow
interaction with the bank/shore, and to improve near-field
mixing. 1 ,
2) Diffuser 'type: The diffuser type is dictated by its
nozzle/port arrangement (angles THETA and BETA with or without
fanning) and its alignment; (angle GAMMA) relative to the
200
-------
current. Many combinations are possible (see also the advice
on discharge conditions in DATIN) . No hard and fast rules can
be given on the most desirable type and arrangement. The
diffuser choice is often dictated by local bathymetry and
other conditions, e.g. clearances for navigation or fishing.
Performance features for the three major types are:
A. UNIDIRECTIONAL DIFFUSER:
This type has a directed net momentum input. It tends to
produce strong currents in the receiving water,
especially under shallow conditions, often associated
with benthic impacts. A fanned-out port/nozzle design
variable BETA) usually gives somewhat improved dilutions.
Perpendicular alignment ("co-flowing diffuser11):
This is the preferred type for non-reversing flows,
as in rivers and in some coastal conditions. Note
that in riverine situations the river flow provides
an upper limit on the achievable dilution.
Parallel alignment ("tee diffuser"): This
alignment may be acceptable for weak reversing
coastal flows to provide offshore transport for the
diffuser plume. It provides poor mixing under
strong current conditions.
B. STAGED DIFFUSER: • .
This type also provides a directed momentum input.
Hence, it can lead to strong induced currents, with
plume contact at the bottom.
Perpendicular alignment: This is a good
arrangement for shallow water conditions in the
coastal environment under weak or strong reversing
currents. Under weak currents it gives good
offshore transport, and it efficiently captures the
ambient flow under strong current conditions.
Parallel alignment: Generally not advantageous.
C. ALTERNATING DIFFUSER: _
This type has no directed net momentum input. Its
dilution efficiency is mostly dictated by its buoyancy
flux and by the ambient current. It usually has the
least benthic impact. A fanned-out (variable BETA) will
give somewhat improved dilutions especially under shallow
water conditions.
Perpendicular alignment: This is the preferred
arrangement for deep water (e.g. sewage) diffusers
in coastal environments with variable currents and
201
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stratification, tit may also be advisable for more
shallow conditions if minimal influences on the
ambient regime current are desired.
! " '
Parallel alignment: May be desirable because of
bathymetric or navigational reasons.
i -
3) Diffuser length: By and large, a longer diffuser will give
better dilutions. However*, this may not be the case for
diffusers in parallel alignment, especially with strong
ambient currents. Also keep in mind the dilution limitations
given by the total flow in riverine situations. Typically, an
alternating type will require a longer diffuser than the
unidirectional or staged type in order to achieve the same
near-field mixing.
4) Number of ports/nozzles and port/nozzle diameter (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 I 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 or tunnel.
on
5) Port/riser spacing: Given the other constraints _..
diffuser^mixing (i.e. diffuser length and discharge velocity)
the ^ spacing is a dynamically unimportant variable that has a
limited effect on overall mixing. However, the spacing plays
a role in the merging process of the individual jets/plumes,
and thus may affect the very initial mixing, e.g. as of
interest in toxic dilution zone (TDZ) predictions. As a rough
rule, merging takes place after a distance along the plume
path of about three to f;ive spacings. If the TDZ is
encountered before then,; additional single jet/plume
predictions, using CORMIX1, may be needed.
6) Port height: In most cases, this is a dynamically
unimportant parameter. however, there are " important
exceptions: For negatively buoyant discharges, the port
height may control the amount of initial mixing prior to
benthic contact. More generally, for deep water discharges
the port height to water &epth ratio has some effect on
initial mixing. Finally, in the presence of crossflow, the
port height influences the stability of the discharge, !.•&*•'
1 202
-------
the distinction between deep and shallow water discharges.
B) SENSITIVITY TO AMBIENT CONDITIONS:
Variations - of the order of 25 percent - of the following
ambient design conditions should be considered:
- ambient velocity (or ambient flowrate),
- ambient depth (or river/tidal stage), and
- ambient density structure (notably density differences).
Such variability is important for two reasons:
1) the usual uncertainty in ambient environmental data, and
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 CORMIX2 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 the 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
203
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discharge. Usually, near-field mixing is enhanced by
maximizing the total density difference (positive or negative)
between discharge flow and ambient water. in most casps,
however, this effect is minor.,
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