DRAFT: September 1990
TECHNICAL GUIDANCE MANUAL
FOR PERFORMING WASTE LOAD ALLOCATIONS
BOOK III: ESTUARIES
PART 3: Use of Mixing Zone Models in Estuarine Waste Load Allocations
Project Officer
Hiranmay Biswas, Ph.D.
Edited By
Robert B. Ambrose, Jr., P.E.1
James L Martin, Ph.D., P.E.2
Prepared by
Gerhard H. Jirka, Ph.D., P.E.3
1. Center for Exposure Assessment Modeling,
Environmental Research Laboratory, U.S. EPA, Athens, GA
2. ASCI Corporation, U.S. EPA, Athens, Georgia
3. DeFrees Hydraulics Laboratory, School of Civil and Environmental
Engineering, Cornell University, Ithaca, NY
Prepared for
U.S. Environmental Protection Agency
401 M. Street, S.W.
Washington, D.C. 20460
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841R90001
ii
Draft of 9/21/90
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Acknowledgements
1. Introduction
1.1
1.2
1.3
1.4
Table of Contents
. . . . . . . .
. . . . . . . . . .
. . . . . . . . v
. . . . .
. . . . .
. . . .
. . . . . . . . .. 1-1
. . . . . .
. . . . . .
. . . . .
. . . . . .
Initial Mixing in Estuaries and Coastal Waters. . . . . . . . . . . . . .. 1-1
Mixing Zone Requirements: Legal Background. . . . . . . . . . . . . . 1-1
Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
2. Physical Processes and Modeling Methodologies. . .
2.1
2.2
2.3
2.4
2.5
2.6
2.7
. . . .
. . . . . . . . . . . 2-1
Ambient and Discharge Conditions. . . . . . . . . . . . . . . . . . . . 2-1
Hydrodynamic Mixing Process.es ..................... 2-1
Mathematical Predictive Models. . . . . . . . . . . . . . . . . . . . . . 2-5
Buoyant Jet Integral Models. . . . . . . . . . . . . . . . . . . . . . . . 2-7
CORMIX: Expert System Methodology for Mixing Zone Analysis. . .. 2-11
Mixing Zone Predictions Under Unsteady Reversing Tidal Currents. .. 2-22
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2-25
3. Case Studies of Mixing Zone Prediction. .
3.1
3.2
3.3
3.4
3.5
3.6
. . . . . .
. . . . . . . . . . . . .
. . 3-1
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
Case AA - Single Port Discharge: Industrial Outfall in Tidal Fjord. . . . . 3-2
Case BB - Multiport Diffuser: Municipal.Sewage Discharge
into Coastal Bay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
Case CC - Single Port Discharge: Brine Discharge From
an Oil Field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8
Case DO Multiport Diffusers: Cooling Water Discharge
into Shallow Sound. . . . . . . . . . . . . . . . . . . . . . . . . .. 3-10
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3-12
iii
Draft of 9/21/90
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Acknowledgements
The author gratefully acknowledges the assistance of
Dr. Robert Doneker, Mr. Paul Akar, and Mr. Gilbert
Jones, all in the DeFrees Hydraulics Laboratory at
Cornell University, in carrying out numerous model
simulations for the case studies in Section 3.
Technical support for this project was provided by
Messrs. Hiranmay Biswas, U.S. EPA Monitoring and
Data Support Division, Robert Ambrose, U.S. EPA En-
vironmental Research Laboratory, and Anthony Donig-
ian, Aqua-Terra Consultants.
A number of useful comments and suggestions were
received from participants of workshops on Estuarine
Waste Load Allocation. Since thar are representative of
the actual user community, their input is especially
welcome and appreciated. Finally, the author wants to
thank the four technical peer reviewers for their detailed
and constructive comments.
v
Draft of 9/21/90
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1. Introduction
Initial Mixing in Estuaries and Coastal
Waters
The discharge of waste water into an estuary or coastal
water body can be considered from two vantage points
regarding its Impact on ambient water quality.
1.1
On a larger scale, or system wide context, care must
be taken that water quality conditions that protect
designated beneficial uses are achieved. This is the
realm of the general waste load allocation (WLA) pro-
cedures and models as discussed in the first two parts
of this manual. As noted, an additional benefit of a
technically sound WLA is that excessive degrees of
treatment which are neither necessary nor productive
of corresponding improvements in water quality for the
whole water body, or at least major sections thereof,
can be avoided.
On a local scale, or in the immediate discharge vicinity,
additional precautions must be taken to insure that
high initial pollutant concentrations are minimized and
constrained to small zones, areas or volumes. The
definition of these zones, commonly referred to as
"mixing zones", is embodied in United States water
quality regulations, on the Federal and/or State level.
The mixing zone is a legally defined spatial quantity -
with certain size and shape characteristics - that allows
for initial mixing of the discharge. More recent regula-
tions on discharges of toxic substances define an
additional subregion -labeled herein the "toxic dilution
zone" - within the usual mixing zone. The intent of those
regulations is to require rapid mixing of toxic releases
to limit the exposure of aqueous flora and fauna to
elevated concentrations. The detailed prediction of
pollutant concentrations and water quality constituents
in the initial mixing phase of a wastewater discharge is
the realm of mixing zone models. This is the subject of
this part of the manual. Mixing zone models are in-
tended to document for any given combination of
discharge and environmental conditions the size and
shape of legally defined "mixing zones", and for toxic
substances, of embedded ''toxic dilution zones", and
the levels of pollutant concentration within these zones
and at their edge.
There may be a great diversity in the types of initial
mixing processes for wastewater discharge. First, the
size and flow characteristics of estuaries or coastal
water can vary widely: the water body may be deep or
shallow, stagnant or flowing, and may exhibit ambient
density stratification of various degrees. Secondly, the
discharge type and configuration can be highly vari-
able: the flow may contain various pollutants ranging
from conventional to toxic substances, vary greatly In
magnitude ranging from low flowrate for a small sew-
age treatment plant to the substantial c~ing wa~er
flow for a large steam-electric power plant, Issue with
high or low velocity, be denser or lighter than the
ambient be located near shore or far offshore, and
exhibit ~arious geometric details ranging from single
port submerged discharges to multiport submerged
diffusers to surface discharges.
Given this diversity of both discharge and ambient
environmental conditions, there are a large number of
possible flow patterns which will develop as the dis-
charge waste stream mixes in the ambient water. These
flow pattems will determine the configuration, size, and
intensity of the mixing process, and any impact of the
discharge on the water body surface, bottom, shore-
line, or other areas. This, in turn, requires that engineer-
ing analyses, in the form of mixing zone models, be
robust, adaptable and reliable under a wide spectrum
of flow conditions.
1.2 Mixing ZOne Requirements: Legal
Background
1.2.1 Pollutant Types
The Clean Water Act of 1977 defines five general cate-
gories of pollutants. i) conventional, Ii) nonconven-
tional, Iii) toxics, iv) heat, and v) dredge and fill spoil.
The Act distinguishes between new and existing
sources for setting effluent standards. Table 1-1 lists
examples of the first three pollutant categories.
Pollutants designated as "conventional" would be "gen-
erally those pollutants that are naturally occurring,
biodegradable, oxygen demanding materials and sol-
ids. In addition, compounds which are not toxic and
which are similar in characteristics to naturally occur-
ring, biodegradable substances are to be designated
as conventional pollutants for the purposes of the
provision". Pollutants designated as "nonconventional"
would be ''those which are not toxic or conventional"
(Congressional Research Service, 1977).
1.2.2 Mixing Zone Definftions
The mixing zone is defined as an "allocated impact
zone" where numeric water quality criteria can be ex-
ceeded as long as acutely toxic conditions are pre-
vented. A mixing zone can be thought of as a limited
area or volume where the initial dilution of a discharge
occurs (USEP A, 19848). Water quality standards apply
at the boundary of the mixing zone, not within the
mixing zone itself. USEPA and its predecessor agen-
1-1
Draft of 9/21/90
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Table 1-1.
Examples of Conventional, Nonconventlon8J, 8IId
Toxic PolManta [USEPA 1984]
Conventional Nonconventlonal Toxic
biochemical chemical oxygen chloroform/lead
oxygen demand demand (COD)
IIBOD)
IpH flouride flourene
total suspended aluminum nickel
solids (TSS)
fecal coliform sulfide selenium
bacteria
oils and arease ammonia benzidine
cies have published numerous documents giving guid-
~nce for determining mixing zones. Guidance pub-
lished by USEPA in Water Quality Standards
Handbook (1984) supersedes these sources.
In setting requirements for mixing zones, USEPA
(1984a) requires that "the area or volume of an individ-
ual 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 com-
munity of aquatic life in the segment for which the uses
are designated," and the shape be "a simple configu-
ration that Is easy to locate In the body of water and
avoids impingement on biologically Important areas,"
and "shore hugging plumes should be avoided."
The USEPA rules for mixing zones recognize the State
has discretion whether or not to adopt a mixing zone
and to specify its dimensions. USEP A allows the use of
a mixing zone in permit applications except where one
is prohibited in State regulations. A review of individual
State mixing zone policies shows that 48 out of 50
States (the exceptions are Arizona and Pennsylvania)
make use of a mixing zone in some form (USEPA,
1984a, 1985). State regulations dealing with streams or
rivers generally limit mixing zone widths or cross-sec-
tional areas, and allow lengths to be determined on a
case-by-case basis.
I n the case of lakes, estuaries and coastal waters, some
states specify the surface area that can be affected by
the discharge. (The surface area limitation usually In-
cludes the under1ying water column and benthic area.)
If no specific mixing zone dimensions are given the
actual shape and size can be determined on a case-
by-case basis.
Special mixing zone definitions have been developed
for the discharge of municipal wastewater into the
coastal ocean, as regulated under Section 301 (h) of
the Clean Water Act (USEPA, 1982). For those dis-
charges the mixing zone was labeled as the "zone of
initial dilution" in which rapid mixing of the waste stream
(usually the rising buoyant fresh water plume within the
Draft of 9121190
ambient saline water) takes place. USEPA (1982) re-
quires that the "zone of initial dilution" be a regularly
shaped area (e.g. circular or rectangular) surrounding
the discharge structure (e.g. submerged pipe or dif-
fuser line) that encompasses the regions of high (ex-
ceeding standards) pollutant concentrations under
design conditions. In practice,limiting boundaries de-
fined by dimensions equal to the water depth mea-
sured horizontally from any point of the discharge
structure are accepted by the USEPA provided they do
not violate other mixing zone restrictions (USEPA,
1982).
Special Mbdng Zone Requirements for
Toxic Substances
USEPA maintains two water quality criteria for the
allowable concentration of toxic substances: a crite-
rion maximum concentration (CMC) to protect against
acute or lethal effects; and a criterion continuous con-
centration (CCC) to protect against chronic effects
(USEPA, 1985). The less restrictive criterion, the CCC,
must be met at the edge of the same regulatory mixing
zone specified for conventional and nonconventional
discharges.
1.2.3
I n order to prevent lethal concentrations of toxics In the
regulatory mixing zone, the restrictive CMC criterion
must be met within a short distance from the outfall or
in the pipe itself. If dilution of the toxic discharge In the
ambient environment is allowed, this requirement,
which will be defined here as a toxic dilution zone
(TOZ), is usually more restrictive than the legal mixing
zone for conventional and nonconventional pollutants.
USEP A (1985) recommends a minimum exit velocity of
3 meters per second (10 feet per second), In order to
provide sufficiently rapid mixing that will minimize or-
ganism exposure time to toxic material. I n addition, the
outfall design must also meet the following geometric
restrictions for a TDZ:
. The CMC must be met within 10% of the distance
from the edge of the outfall structure to the edge
of the regulatory mixing zone in any spatial direc-
tion.
. The CMC must be met within a distance of 50 times
the discharge length scale in any spatial direction.
The discharge length scale is defined as the
square-root of the cross-sectional area of any dis-
charge outlet. This restriction is intended to ensure
a dilution factor of at least 10 within this distance
under all possible circumstances, including situa-
tions of severe bottom interaction and surface
interaction.
. The CMC must be met within a distance of 5 times
the local water depth in any horizontal direction.
1-2
-------
The local water depth is defined as the natural
water depth (existing prior to the installation of the
discharge outlet) prevailing under mixing zone de-
sign condition (e.g. low flow for rivers). This restric-
tion will prevent locating the discharge in very
shallow environments or very close to shore, which
would result in significant surface and bottom con-
centrations. (USEPA, 1985)
1.3 Summary
The following two sections of Part III of this manual deal
with the background and the application of predictive
models for mixing zone analysis that address the vari-
ous legal requirements as outlined above.
Section 2 first gives an overview of the important phys-
ical processes that govern the hydrodynamic mixing of
aqueous discharges. Those processes are divided into
near-field processes (influenced directly by the dis-
charge geometry and dynamics and, to some extent,
controllable through appropriate design choices) and
into far-field processes (influenced primarily by the
existing environmental conditions). It is shown that
legal mixing zone requirements can encompass, in
general, processes in both near-field and far-field. Then
the mathematical background and formulations for
different mixing zone models are reviewed. For practi-
cal routine applications, these models fall into two
classes: (i) jet integral models that are applicable only
to a sub-set of near-field processes Including sub-
merged buoyant Jets without any boundary (surface or
bottom) interaction, and (ii) a mixing zone expert sys-
tem, CORMIX, that addresses both near-field and far-
field processes under a variety of discharge and
ambient conditions.
Section 3 illustrates the application of jet integral mod-
els and of the expert system CORM IX. Typical data
requirements for the implementation of these models
are discussed. Four case studies are presented in
order to demonstrate the capabilities and/or limitations
of individual models.
1.4
References
Congressional Research Service. 1977. Legislative
History of the Clean Water Act 1977. Congressional
Research Service, Library of Congress, October 1978,
No. 95-14 P. 330.
USEPA. 1982. Revised Section 301 (h) Technical Sup-
port Document. EPA 430/9-82-011, Washington, DC.
USEPA. 19848. Water Quality Standards Handbook,".
Office of Water Regulations and Standards, Washing-
ton, DC.
USEPA. 1984b. Technical Guidance Manual for the
Regulations Promulgated Pursuant to Section 301 (g)
of the Clean Water Act of 1977 (Draft)", Washington,
DC, August.
USEPA. 1985. Technical Support Document for Water
Quality-based Taxies Control. Office of Water, Wash-
ington, DC, September.
1-3
Draft of 9/21/90
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2. Physical Processes and Modeling Methodologies
2.1 Ambient and Discharge COnditions
The mixing behavior of any wastewater discharge Is
governed by the interplay of ambient conditions In the
receiving water body and by the discharge charader-
istlcs.
The ambient conditions In an estuary or coastal water
body are described by geometric parameters - such as
. plan shape of the estuary, vertical cross-sections, and
bathymetry, especially in the discharge vicinity and by
its dynamic charaderistics. The latter are given by the
velocity and density distribution in the estuary, again
primarily in the discharge vicinity.
Many estuaries are highly energetic water bodies and
their velocity field with its vertical and temporal variabil-
ity may be influenced by many factors. Usually the
most significant velocity component is controlled by
tidal influences, but freshwater inflows, wind-driven
currents and wave-induced currents may also play
important roles and, In some cases, may even domi-
nate the flow. Furthermore the mean velocity field is
often superposed by secondary currents due to topo-
graphic effeds or due to baroclinic Influences giving
rise to complicated three-dimensional flow fields.
The density distribution in estuaries is usually strongly
coupled with the velocity field. Density differences are
mostly caused by the freshwater inflow arid lighter, less
saline, water tends to overflow the more saline ocean
water. Estuaries are sometimes classified on the basis
of their density structure into well-stratified, partially-
stratified and vertically mixed estuaries (Fischer et ai.,
1979). Well stratified estuaries, usually those with weak
tidal effects, exhibit a two-layer structure with an upper
predominantly fresh water layer flowing over a lower
saline layer (the so-called salt wedge). The dominant
vertical velocity distribution in that instance is a sea-
ward flow in the upper layer and a reversed landward
flow in the lower layer. The other end of the spectrum
is given by vertically well mixed estuaries with strong
tidal energetics leading to nearly complete vertical
mixing although density gradients may still exist in the
horizontal direction (Le. along the axis of the estuary
or tidal bay).
Clearly, a majorfeature of estuarine ambient conditions
is their time variability. For tidally controlled currents
this is given by a time scale equal to the tidal period.
Other time scales, usually also of the order of several
hours, describe wind driven currents and seiche mo-
tions. However, the time scale for initial mixing pro-
cesses of effluent discharges is usually much shorter
(of the order of minutes to tens of minutes) so that it
usually suffices to analyse certain flow and density
conditions under a steady-state assumption. The con-
sideration of tidal reversals and potential pollutant ac-
cumulation is discussed further below (sedion 2.6).
The discharQe conditions relate to the geometric and
flux characteristics of the submerged outfall installa-
tion. For a single port discharge the port diameter, its
elevation above the bottom and its orientation provide
the geometry; for multi port diffuser installations the
arrangement of the individual ports along the diffuser
line, the orientation of the diffuser line and construction
details represent additional geometric features. The
fI ux characteristics are given by the discharge flow rate
from the port, by its momentum flux and by its buoy-
ancy flux. The buoyancy represents the relative density
difference between discharge and ambient that, upon
multiplication with the gravitational acceleration, is a
measure of the tendency for the effluent flow to rise (for
positive buoyancy) or to fall (for negative buoyancy).
2.2 Hydrodynamic Mixing Processes
The hydrodynamics of an effluent continuously dis-
charging into a receiving body of water can be concep-
tualized as a mixing process occurring in two separate
regions. In the first region, the initial jet characteristics
of momentum flux, buoyancy flux, and outfall geometry
influence the jet trajectory and mixing. This region will
be referred to as the "near-field", and encompasses the
buoyant jet subsurface flow and any surface or bottom
interaction, or in the case of a stratified ambient, termi-
nallayer interaction. In this region, designers of the
outfall can usually affect the initial mixing characteris-
tics through appropriate manipulation of design vari-
ables.
As the turbulent plume travels further away from the
source, the source characteristics become less import-
ant. Conditions existing in the ambient environment will
control trajectory and dilution of the turbulent plume
through buoyant spreading motions and passive diffu-
sion due to ambient turbulence. This region will be
referred to here as the "far-field".
It Is stressed at this point that the distinction between
near-field and far-field is made purely on hydrodynamic
grounds. It Is unrelated to any legal mixing zone defi-
nitions that address prescribed water quality standards
as discussed in Sedion 1.2.2. In many practical cases
the legal mixing zone may, in fad, include near-field
hydrodynamic mixing processes. But that does not
have to be so: For example, buoyant jet mixing in a
2-1
Draft 0' 9/21/90
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!.
AMBIENT DENSITY P, - CONST
z
D (ROUND JET}
B (PLANE JET}
Uo. Po
-------
~
/
--
, '-
o
i
J
~
1$
XtIX'«xx\~~~
a)
Deep water, high buoyancy.
vertIcal discharge
~
- /:,j/:~~/ ;-//~
?<}k~~
I .{( /-'1. X\X, ~. X. ~x't-.
b) Shallow watl!r, IQN bUOyancy.
vr~rt,lcal dis,=harge
/ / / -7 / / .' . , .
-,' / / / ./ / / '
, ," /, / / /-r-
/., / ' /.
J--// ,/ /, /' / , //
,.. / ~/ ...---.
/ / I . .
c) Deep water, high buoyancy,
non-wrtical discharge
-
-
d)
Shallow water, !ow buoyancy
non-vp.r'tlcal dlschargt?
Figure 2-2. Stable or Unstable Near-Field Flows Proclucec:l by Submerged Buoyant DI8Charg...
to trapping of the flow at a certain level (trapping level
or terminal level).
2.2.1.2 Boundary Interaction Processes and Near-Field
Stability
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 rapid density change (pycnoclines). Depend-
ing on the dynamic and geometric characteristics of
the discharge flow, a variety of interaction phenomena
can occur at such boundaries. Furthermore, in the
case of a continuously (e.g. linearly) stratified ambient
where flow trapping may occur, other Interaction phe-
nomena may take place.
In essence, these interaction processes provide a tran-
sition between the buoyant jet mixing process in the
near-field. and between buoyant spreading and pas-
sive diffusion in the far-field.
Interaction processes can be (I) gradual and mild or (iij
abrupt leading to vigorous transition and mixing pro-
cesses. (i) If a buoyant jet is bent-over by the cross-flow
it will gradually approach the surface, bottom or termi-
nallevel and will undergo a smooth transition with little
additional mixing.
(iij If a jet Is impinging normally, or near-normally, on a
boundary, it will rapidly spread in all directions (see
Figure 2-2). Different possibilities exist at that point: (a)
If the flow has sufficient buoyancy it will ultimately form
a stable layer at the surface (Figure 2-2a,c). In the
presence of weak ambient flow this will lead to an
upstream intrusion against the ambient current. (b) If
the buoyancy of the effluent flow is weak or its momen-
tum very high, unstable recirculation phenomena can
occur in the discharge vicinity (see Figure 2-2b,d). This
local recirculation leads to re-entrainment of already
mixed water back into the buoyant jet region. Thus,
simple buoyant jet analyses no longer suffice to predict
these phenomena.
The aspect of near-field stability. I.e. the distinction into
stable or unstable conditions. is a key feature of pollu-
tion analyses. "Stable discharge" conditions, usually
occurring lor a combination of strong buoyancy, weak
momentum and deep water, are often referred as "deep
2-3
Draft of 9/21/90
-------
u"
-
~
r
='~.
~ .
-1,
uo
I) Free Deflecl.d .I.I/Plume
in CrOSS-flow
II) Woke Attachment of
.I.t I Plum.
a) Wok. Attach""nt
a=~
~ -rp8
i) Free .let
II) Allached .1.1
b) Coon do Attachm.nt
Figure 2-3. Bottom Attachment Proc..... for Submerged
Discharge..
water" conditions. "Unstable discharge" conditions, on
the other had, may be considered synonymous to
"shallow water" conditions. Further detail on discharge
stability can be found in Jirka (1982 a,b) and Holley and
Jirka (1986).
Yet another type of interaction process concerns sub-
merged buoyant jets discharging in the vicinity of the
water bottom into a stagnant or crossflowing ambient.
Two types of dynamic interaction processes can occur
that lead to rapid attachment of the effluent plume to
the water bottom (see Figure 2-3). These may be waKa
attachment forced by the crossflow or Coanda attach-
m.en1 (due to low pressure effects) forced by the en-
trainment demand ofthe effluent jet itself. In either case
the assumption of free buoyant jets Is invalidated and
other analyses have to be pursued for these bottom-
attached flows.
2.2.1.3 Multipart Diffuser Induced Flows in Shallow
WatI!r ~ntennediate-FJeIcI)
Some multipart diffuser installations represent large
sources of momentum, while their buoyancy effects
may be relatively weak. Therefore these diffusers will
have an unstable near-field with shallow water condi-
tions. This is characteristic, for example, for cooling
water diffusers from thermal power plants. For certain
diffuser geometries (i.e. the unidirectional and the
staged diffuser types; see Section 2.3) strong motions
can be induced in the shallow water environment in the
form of vertically mixed currents that laterally entrain
ambient water and may extend over long distances
before they re-stratify or dissipate their momentum. In
Draft 0' 9/21/90
a sense, these "diffuser plumes" extend beyond the
strict near-field (of the order of the water depth) and
are sometimes referred to as the "intermediate-field"
(Jirka, 1982b).
2.2.2 Far-Field Processes
In the context of this report, far-field mixing processes
are characterized by the longitudinal advection of the
mixed effluent by the ambient current velocity.
2.2.2.1 Buoyant Spreading Processes
Buoyant spreading processes are defined as the hori-
zontally 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. If the dis-
charge Is nonbuoyant, or weakly buoyant, and the
ambient Is unstratified, there Is no buoyant spreading
region in the far-field, only a passive diffusion region.
Depending on the type of near-field flow and ambient
stratification several types of buoyant spreading may
occur: (i) spreading at the water surface, (ii) spreading
at the bottom, (iiij spreading at a sharp Internal Inter-
face (pycnocline) with a density jump, or (Iv) spreading
at the terminal level in continuously (e.g. linearly) strat-
ified ambient fluid.
As an example, the definition diagram and structure of
surface buoyant spreading processes in unstratified
crossflow is shown In Figure 2-4. The laterally spread-
Plan View
--
II
-I
-I
- I'lnitlal
CondHICIft
e,..:....,.. A-A , FA'"
---~
.E-
Buoyant Surface Spreading
FIgure 2-4. Buoyant Spreading Processes In the Far-Field
(Example: Surface Spreading).
2-4
-------
ing flow behaves like a density current and entrains
some ambient fluid in the "head region" of the current.
The mixing rate is usually relatively small. Furthermore,
the flow may interact with a nearby bank or shoreline
(not shown in the figure). The layer thickness may
decrease during this phase.
Depending on source and ambient characteristics,
buoyant spreading processes can be effective trans-
port mechanisms that can quickly spread a mixed
effluent laterally over large distances In the transverse
direction. This can be partlcular1y pronounced In cases
of strong ambient stratification In which the effluent at
the terminal level that may initially be of considerable
vertical thickness cOllapses Into a thin but very wiele
layer unless this Is prevented by lateral boundaries.
2..2.2.2 Passive Ambient Diffusion Processes
The existing turbulence In the ambient environment
becomes the dominating mixing mechanism at suffi-
ciently large distances from the discharge point. The
intensity of this passive diffusion process depends
upon the geometry of the ambient shear flow as well
as any existing stratification. In general, the passively
diffusing flow is growing In width and in thickness (see
Figure 2-5). Furthermore, it may interact with the chan-
nel bottom and/or banks.
The strength of the ambient diffusion mechanism de-
pends on a number of factors relating mainly to the
geometry of the ambient shear flow and the ambient
stratification. I n the context of classical diffusion theory
(I.e. gradient diffusion, see Fischer et ai., 1979) diffu-
sion processes In bounded flows (e.g. rivers or narrow
estuaries) can be described by constant diffusivitles In
the vertical and horizontal direction that depend on
turbulent intensity and on channel depth or width as
the length scales. On the other hand, wide "un-
Plan View
r. "-ibll "'k Inl8tOclioll
-
-
_Ua
I
I
~ Initial CandlllaM
II
Side View
~". ~ ---.
.... ~ PoI- Iottalll InltrOCtlall
Figure 2-5. P.88Ive Ambient Diffusion Pr0C88888.
bounded" channels or open coastal areas are charac-
terized by plume size dependent diffuslvities leading to
accelerating plume growth described, for example, by
the "4/3 law" of diffusion. In the presence of a stable
ambient stratification the vertical diffusive mixing is
generally strongly damped.
2.3 Mathematical Predictive Models
2.3.1 Modeling Methodology
In principle, one can conceive of two approaches to
the prediction of effluent discharges in the water envi-
ronment: complete models or zone models.
(I) Complete models: These are thre~imensional nu-
merical models that directly solve a finite difference or
finite element approximation for the full dynamic and
mass conservation equations with various assump-
tions for the turbulent shear and mass transport terms.
I n principle, with the advent of powerful computing
facilities, even on the desktop, such a complete mod-
eling approach that encompasses the entire fluid do-
main of interest with all individual mixing processes
appears feasible. However, successful applications to
date have been limited. Apparent reasons for the pres-
ent shortcomings include (1) lack of fully workable
turbulence closure techniques under the influence of
buoyancy while considering the full range of Jet-in-
duced geophysical turbulence; (2) the difficult trade-off
of modeling a large enough domain while providing
sufficient resolution in a three-dimensional model
(computer capacity and costs); and (3) the unknown
nature of the open fluid boundary conditions which
need to be specified as part of the elliptic equation
system. These boundaries may, in general, contain a
combination of stratified inflow and outflow that is
inherently difficult to specify. For these reasons, com-
plete numerical models are usually not used in routine
mixing zone analyses of effluent discharges and this is
expected to remain so for at least the next decade.
(ii) Zone Models: Instead of attempting to Integrate the
general governing equations over the whole region of
interest it Is frequently useful to divide the region into
several zones with distinct behavior (such as individual
mixing processes in the near-field and in the far-field).
WIthin these zones it Is then possible to simplify the
governing equations by dropping unimportant terms.
This gives a considerable advantage in the mathemat-
ical treatment and Improved accuracy in the solution.
However, a challenge remains because the solutions
are restricted to specific zones. Thus, criteria need to
be established for a meaningful division of the whole
region into zones, and to provide transition conditions
between zones.
2-5
Draft of 9/21/90
-------
Current practice In pollUtion analyses relies on zone
models. Such models that deal with Individual flow
~rocesses are described In the specialized research
literature as well as in sev~raI monographs (e.g. fi-
scher et al.: 1979, Holley and Jirka, 1986). However, a
problem anses because there Is limited guidance to the
model user on the limits of applicability of each model,
and on how to combine the Individual models for an
overall prediction of the entire flow process. The use of
an in~egrated expert system framework (see below)
promises to alleviate this problem.
An Important group of zone models are the so-called
buoyant Jet Integral models that are limited to the
buoyant Jet mixing process as described In Section
~.2. 1.1 withoUt attention to any problems of boundary
~nteractlon and near-field Instability. Several of such
Integral model formulations are available as compUter
programs. Whenever their applicability has been as-
certained, these models have been found through nu-
merous data-model comparisons to be reliable and
accurate. Jet integral models will be reviewed in Sec-
tion 2.4.
An integrated framework of zone models for all Import-
ant near-field and far-field mixing processes that effect
effluent mixing has recently been developed. This
framework is In the form of an expert system that
classifies each discharge/ambient condition as to
which flow processes are important and provides a
prediction through a sequence of zone models with
appropriate transition conditions. The zone modeling
expert system methodology CORMIX (Doneker and
Jirka, 1990; Akar and Jirka, 1991) is discussed In Sec-
tions 2.5 and 2.6.
2.3.2. Zone Model Schemadzations of Discharge
and Ambient Conditions
All zone models require some schematizatlon of the
complex and arbitrary ambient and discharge condi-
tions that may prevail at any discharge site. These
simplifications are needed to conform to the require-
ments of the individual models.
A schematic definition diagram for a single port dis-
charge is given in Figure 2-6. The bottom is assumed
to be flat (constant depth) while any banks (if consid-
ered In the analysis) are assumed to be vertical.
A corresponding diagram for multipart diffusers Is pro-
vided in Figure 2-7. Of particular interest for this case
is the alignment angle y between the crossflow direc-
tion and the diffuser axis, the orientation angle {3 be-
tween the individual port axes and the diffuser line, and
the vertical angle 8 between port axis and the horizontal
plane. Three major diffuser types have evolved In ac-
Draft of 9/21/90
tual design practice and can be characterized by these
angles (see Figure 2-8).
In the unidirectional diffuser, all the ports point In the
same direction perpendicular to the diffuser axis
~=90o).lnthe staged diffuser, all ports point along the
diffuser line ({3 = 0°). In the alternating diffuser, the
ports are arranged In an alternating fashion and point
In opposite directions ({3=:J: 90°). The undlrectional
and the staged diffusers possess a net horizontal mo-
mentum InpUt with a tendency to Induce 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. Some of these design
possibilities are shown in Figure 2-8. There may be
double or triple nozzle arrangements (with a small
internal angle) for both unidirectional or staged diffus-
ers, and the port orientation angle {3 may differ some-
what 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. Furthermore, alter-
nating diffusers for thermal discharges in shallow water
may have a variable port orientation along the diffuser
axis to control instabilities and horizontal circulations
(for details, see Jirka, 1982b). Another special case of
PLAN VIEW
c"oss- SECTION
~
Ua
!.
D. UO, 4,Po, Co
Pa
I
VII
N_I>cIto-
Flgur. 2-6. Schem8t1c8 of Single Port Discharg. Geometry In
Ambient Channel with Rectangular Crou
-SectIon (WIdth W May Be Finite or Unlimited).
Plan-VI..
Cro.. - S8C11on
't
H
-...
O. tI" 6,.- s
Flgur.2-7. Sch8matIc8 of Multipart DItfuMr Geometry In
Ambient Channel with Rectangular Crou -
SectIon (WIdth W May Be Finite or Unlimited).
2-6
-------
T
l.o
1
t
,
/I
,
IUter
'-'9ft'
WI_- .
c_. -- ......
!:L'
,....,..(, ... ~)
"i" 2y.
.--
lo
,..,
,
01 Unid..._1 di"-. ".d
.-
-- ---
.-0.
I'
L.
,
,-:-(~~:«~:<~:<~
1/&0"
,-.eI'
II
""'. V.'-'.'-'.'-'.-
,&d
~.o.
bJ 5'..,.. dill....,. ,.a 0"
13
ff¥R=i=##+
13 '~90.
8. < 90.
~
p'%9o"
90 < 90'
'2
g
u
).~ ~.( )~ ~.( ~.~ ~.(
p_"t9O"
8. < 90"
~
:
i
Ve,lIcal
8. " 90"
13118,":90"
I a . .
. . . .
a . . 81
13 1--1"
). ) >~ < < <
13
Control.
F- de'lQn 2Y'
(I I.'CO)
P " % cot-' ii" 109 --z;:
1--
Lo
c) Aller~atin9 d,flUHf, 8.' .a,lable
Figure 2-8. Schematic Plan Views of Three Malor DIffu.... Types. a) Unidirectional Diffuser, b) Staged Diffuser, c) Alternating
Diffuser. Any of Those Dltreruser. May Have a Variable Alignment y Relative to the Ambient Current.
an alternating diffuser is given by a vertical discharge
from all ports.
Any diffuser can be deployed with arbitrary alignment
y. However, the two major arrangements are the per-
pendicular alignment (y ::::: 90 0) and the parallel align-
ment (y ::::: 0°).
Buoyant Jet Integral Models
Basic Elements: Stagnant Unstratified
Ambient
The narrow elongated shape of the turbulent zone
within a buoyant jet (see Figure 2-1) suggests bound-
ary-layer type simplifications to the equations of fluid
motion and mass transport. The equations may be
further simplified by integrating across the local jet
cross-section thereby yielding a one-dimensional
equation set for the actual three-dimensional problem.
This is the essence of jet integral models which solve
the equation set with a simple integration scheme
marching forward along the trajectory.
2.4
2.4.1
The integral method is demonstrated in the following
for a round buoyant jet issuing into a stagnant unstrat-
ified ambient (Figure 2-1). The jet-trajectory is assumed
to lie within an x-z coordinate system. Local integration
across the buoyant jet gives the following flux (integral)
quantities:
Volume flux: Q = 21rf; U rd r = 21r It uc b2 (1)
Momentum flux (kinematic):
M = 2:Jr fO u2 r d r = 2:Jr 12 U ~ b2
o
Scalar (pollutant) mass flux:
Q c = 2:Jr fOl> U c r d r = 21r 13 Uc Cc b2
o
, Buoyancy flux:
J = 21r fOl> u g 1 r d r = 21r 13 Uc g~ b 2
o
in which u = mean velocity in the trajectory direction,
r = transverse coordinate from local jet centeriine, c
= mean concentration, and g' = mean buoyant ac-
celeration relative to the outside fluid where
(2)
(3)
(4)
, pa-p
g =-g
pa
p = local density, pa = ambient density, and g =
gravitational acceleration. In the rightmost integrated
quantities, the subscript c indicates centeriine values,
and the width b is a measure of the width of the jet (see
below). The profile constants /1. / 2, / 3, are simple
numerical values that depend on the chosen profile
shape and on the width definition (see Holley and Jirka,
1986). Frequently, a bell-shaped Gaussian profile is
chosen and the width b is conveniently defined by the
"1/e width" where the local quantities are 1 /e = 37% of
the centeriine value.
(5)
2-7
Draft of 9/21/90
-------
When the ??nservation laws are applied to these four
flux quantities using a control volume of differential
length. ds ~here s = axial direction along trajectory the
following differential equations arise:
Volume flux conservation: EQ = 21r a Uc b
ds
L~. the volume flux (discharge) increases due to en-
trainment along the jet periphery.
Axial momentum flux conservation:
dM '2
ds = 21r /4 gc b sin 8
Le., only.the sin 8 component of buoyancy produces
acceleration in the axial direction, in which 8 = local
vertical angle.
Horizontal momentum flux conservation:
d
ds (M cos 8) = 0
Le., no acceleration in the horizontal direction.
Scalar flux conservation: dQc = 0
ds
Buoyancy flux conservation: dJ = 0
ds
Le. in the uniform ambient environment both fluxes stay
constant.
(10)
I n addition, it is necessary to relate the local coordinate
system (s,8) to the fixed global one (x,z)
dx = cos 8
ds
dz . l}
ds = sm u
This system of seven ordinary differential equations is
fully specified by seven initial conditions at s = O. These
are the initial bulk fI~es Mo. Jo' 00' and 0co (alterna-
tively,given by Vo ,go = g (pa - po)/pa, Co, and D)
and the geometry xo' ZOo and 80.
(11)
(12)
Solution of this ordinary differential equation system by
any chosen numerical method yields the seven local
buoyant jet measures. These are M, J, q, and 0c (or
alternatively, the related variables uc' g c' Cc and b)
and the trajectory measures x, z, and 8.. The local bulk
(flux-averaged) dilution is then given by the ratio 0/00
and the local centerline (minimum) dilution by the ratio
colcc'
Two fundamental difficulties exist in the jet Integral
method :
Draft of 9121190
(6)
(i) The closure problem: Entrainment and mixing of
ambient fluid is a turbulent flow phenomenon. The
volume flux conservation, Equation 6, presupposes
that the mean entrainment velocity ve (see Figure 2-1)
is linearly related to the centerline velocity, Ve = a Uc.
where a = entrainment coefficient. Inspection of data
on buoyant jets that undergo a transition from initial
jet-like (momentum-dominated) to final plume-like
(buoyancy-dominated) behavior shows that a is quite
variable. In some integral models a geometric equation
is used Instead of Equation 6, namely
(7)
Jet spreading: ':: = k (6a)
I n which k = spreading coefficient with somewhat less
variability between the jet-like and plume-like stages.
The actual choice of the appropriate equation, Eqs. 6
or 6a, and the specification of the coefficient that may
be a function of local flow conditions is generally re-
ferred to as the "closure problem". The closure is made
differently in the various integral models. A more de-
tailed discussion is given by Holley and Jirka (1986).
(8)
(9)
(ii) The zone of flow establishment: The above equation
set is, strictly speaking. not valid in a short initial zone
of flow establishment in which a gradual adjustment
between the efflux profile (approximately uniform) to
the final bell-shaped profile takes place. Since this zone
is short ( == 5D to 10D, where D = diameter of the
discharge port) no major error is introduced if It Is
simply neglected. This is the case in some Integral
models. Alternately, some models include an adjust-
ment via a virtual origin or others perform a detailed,
though approximate, analysis of this zone.
The derivation of integral jet equations for the slot
buoyant jet (see the alternative source conditions indi-
cated in Figure 2-1) is quite analogous to the round jet.
It is omitted here for brevity (see Holley and Jirka,
1986). The slot buoyant jet is an important element of
the analysis of subsurface multiport diffuser plumes
that are formed after merging of the individual round
jets.
24.2 Extensions to Flowing Stratified /lmbients
The advantage of jet integral models is their ready
extension to more complex environmental conditions.
such as ambient stratification and crossflow.
If the receiving water is stratified with a stable density
gradient (dpa/dz < 0, I.e. the ambient density
= P a (z) decreases upward), then the buoyancy flux
is not conserved along an upward jet trajectory but is
constantly decreasing. Eventually the buoyant jet will
reach. and may even overshoot, its terminal level Zt at
which the local internal jet density is equal to the
2-8
-------
z
1.
~
p.
-...
u.
---
BUOYANT
JET EFFLUX
~"
II
Figure 2.9. Round Buoyant Jet In Ambient Crouflow with Drag and entrainment Forc.. (Example: Vertical Discharge).
ambient density P a (z t ). The jet will become trapped
at this level and spread horizontally in the form of a
gravitational current. The jet mechanics prior to the
terminal level are readily described with the integral
technique if two extensions are made. First, the buoy-
ancy profiles are now defined with respect to the local
reference buoyancy
g' - pa (z) -p (13)
- pa (z) g
instead of Equation 2, leading to modification of Equa-
tions 3 and 7, respectively. Second, from mass balance
requirements, the buoyancy flux is decreasing at the
same rate at which it is diluted with ambient water of
lesser density. This leads to
dJ=Q.K.dpa
d s pa d s
for the round jet, instead of Equation 10. Inherent in
these expressions is the assumption that the average
density of the entrained water is equal to the density at
the level of trajectory (centenine). This excludes cases
of very rapid local changes, such as steep pycnoclines
in estuaries.
(14)
When a round buoyant jet is discharged into an ambi-
ent crossflow of velocity ua' then it will be deflected in
the direction ofthe crossflow. This deflection is brought
about by two force mechanisms, a pressure drag force
FD and a force Fe due to the entrainment of crossflow
momentum. Referring to Figure 2-9, this situation Is
readily described in the integral analysis framework
provided that several adjustments are made. First,
neglecting the horseshoe or "kidney" shape (Fischer et
at 1979) which actually exists and assuming that the
jet may be approximated by a circular cross-section,
the velocity profile in the jet cross-section is given by
the sum of the ambient velocity component in the
?irecti~n of the trajectory, ua cosO, and the bell-shaped
Jet prof~le. This, then. affects the definition of all Jet bulk
fluxvanables, M, J, Q and Qc' The definition of the drag
force normal to the jet axis, and per unit length of the
jet axis, is (in kinematic units)
FD = ~ CD ui sin20 (2b) (15)
in whi?h CD is a drag coefficient (of order of unity), and
the width of the "jet body' is simply taken as 2b. The
entrainment force (entrainment of ambient momen-
tum) is
Fe = Ua !!£- (16)
The governing momentum equations, Equations 7 and
8 are amplified to
2-9
Draft of 9/21/90
-------
dM
ds - 27r 14g~ b 2 sine + Fe cos e
(17)
d
ds (M cos 11) = Fe + FD sin 11 (18)
Also, it is ob~erved in bent-over jets that the entrain-
ment m~hantsm Is considerably more vigorous and
the.entralnme~ velocity not simply proportional to Uc
as In the p~evlous ~se. Several analyses have sug-
gested that Jet entrainment in crossflows has a second
contrib~~on once the jet is strongly bent-over but still
slowly nSlng. This second contribution is similar to that
of a horizontal line element of fluid that is rising due to
an initial vertical impulse of momentum or due to initial
buoyancy in a stagnant ambient fluid. The rising line
element experiences turbulent growth and entrainment
that is proportional to the velocity of rise. Since the
strongly'bent-over jet is similar to this line element, this
second entrainment mechanism can be added to the
original entrainment mechanism associated with the
excess of forward jet velocity relative to the surround-
ing fluid. The result is
!!£- = 27r a Uc b + 27r a2 Ua b sin 11 cas e (19)
where a is of the same form as for a buoyant jet in
stagnant ambient (Equation 6) and a2 is the crossflow
induced entrainment coefficient.
2.4.3 Overview of Jet Integral Models Available
for Mixing Zone Analysis
A large number of jet integral models for submerged
single port or multi port discharges are reported in the
literature. However, only a few of these are available for
practical mixing zone analysis in the form of computer
programs accessible to the analyst. Several of these
are discussed below.
The validity and reliability of a jet integral model should
be promulgated on at least two considerations: First,
is its theoretical formulation sound and does it perform
accurately under limiting conditions (e.g. the pure jet
or pure plume)? Second, how do the model predictions
compare with available data, preferably field data? No
complete evaluation on these grounds of integral jet
models is attempted here, but some important model
features will be addressed in Section 3. It is stressed
again that none of the following integral jet models
include any form of boundary interaction processes; in
a sense. they all assume an unlimited receiving water
body.
The U.S. EPA has published a set of five buoyant jet
integral models (Muellenhoff et aI., 1985), aU with dif-
ferent capabilities. These models include computer
Draft of 9121190
programs written in FORTRAN for micro or minicom-
puters.
(1) The computer model UPLUME describes a buoyant
jet issuing from a single port into a stagnant environ-
ment with arbitrary stratification. UPLUME is based on
Abraham's (1963) original development using a jet
spreading equation for closure. Empirical adjustment
expressions are included for the zone of flow establish-
ment.
(2) The model UOUTPLM (based on Winiarski and
Frick, 1976) uses a somewhat different Lagrangian
description of buoyant jet mechanics instead of the
Eulerian system of equations given in Section 2.4.1.
Thus, a plume element is tracked in its time-dependent
evolution. However, the mechanisms actually included
are similar to the ones discussed above with the excep-
tion of the omission of the ambient drag force. The
model is applicable to a uniform crossflow with co-flow-
ing or cross-flowing single port orientation (excluding
counterflows) and with arbitrary density stratification.
The model is not applicable for stagnant conditions.
(3) The model UMERGE is an extension of UOUTPLM
applicable to multiport diffusers with perpendicular
alignment. Merging is assumed to occur when geomet-
ric overlap of the individual equally spaced round jets
occurs. After merging, the flow is described by the
time-dependent motion of two-dimensional plume ele-
ments.
(4) UDKHDEN is a model that computes three-dimen-
sional trajectories from either single port or multiport
discharges in crossflows with arbitrary velocity (shear
flow) and density distributions. The model is based on
the development by Hirst (1971) and later generaliza-
tions by Kannberg and Davis (1976). The initial zone of
flow establishment is computed in detail with Hirst's
model. The three-dimensional equation system is a
generalization of the type discussed in the preceding
section. An entrainment function with dependence on
a local densimetric Froude number is used for closure.
A special geometric merging routine describes the
gradual transition from individual round plumes to the
two-dimensional plume. However, the same entrain-
ment coefficient is used for round and for plane buoy-
ant jets, making it impossible to verify the model for
well-known asymptotic conditions. The diffuser align-
ment relative to the crossflow must be predominantly
perpendicular.
(5) The model ULiNE is strictly speaking not a jet
integral model but uses an analytical solution for the
two-dimensional slot plume dilution as a function of
elevation. This solution is modified on the basis of
Roberts' (1977) experimental results for the effect of
2-10
-------
alignment on a diffuser line plume in crossflow. Also a
~tepwise ~Igorithm is included to compute local mixing
In an arbitrary crossflow and stratification. The model
omits the merging process, thus assuming an initially
merged (e.g. closely spaced) diffuser discharge.
Another buoyant Jet model Is that of Jirka and Fong
(~981) to P~edict general three-dimensional traJecto-
nes for a single port discharge in a crossflow with
arb.it~ry stratification. The model uses empirical de-
scnptlons for the zone of flow establishment as pro-
posed by Schatzmann (1978). The model includes an
~ntrainment closure that meets several limiting condi-
tions and that has been extensively verified by Wong
(1984) in application to ambient stratification. An addi-
tional element of the Jirka-Fong model is the descrip-
tion of the internal vortex mechanism in crossflow that
can lead to plume bifurcation when a flow boundary or
terminal level is encountered.
2.5 CORMIX: Expert System Methodology for
Mixing ZOne Analysis
2.5.1 Introduction
The QQrnell Mixing Zone ~ert System (CORMIX) Is
a series of software elements for the analysis and
design of submerged buoyant or nonbuoyant dis-
charges containing conventional or toxic pollutants
into stratified or unstratified watercourses, with empha-
sis on the geometry and dilution characteristics of the
initial mixing zone. Subsystem CORMIX1 (Doneker and
Jirka, 1990) deals with single port discharges and
subsystem CORMIX2 (Akar and Jirka, 1991) addresses
multi port diffusers. The system Is implemented on mi-
crocomputers with the MS-DOS operating system.
The user supplies CORMIX with information about the
discharge and ambient environment. CORM IX returns
information detailing the hydrodynamic mechanisms
controlling the flow, dilution, geometric information
concerning the shape of the pollutant plume or flow in
the ambient water body, and design recommendations
allowing the user to improve the dilution characteristics
of the flow. If specified by the user, CORM IX also
presents information about legal mixing zone dimen-
sions and dilution and about toxic mixing zone require-
ments.
CORMIX contains two key elements. The first is a
rigorous flow classification scheme that classifies any
given discharge/environment situation into one of sev-
eral flow classes with distinct hydrodynamic features.
The classification scheme places major emphasis on
the near-field behavior of the discharge and uses the
length scale concept as a measure of the influence of
each potential mixing process. Flow behavior in the
far-field, mostly in the form of boundary interactions, is
also considered.
The second key element is a collection of predictive
elements (modules) that are executed according to a
protocol that pertains to each distinct flow class as
determined by the classification scheme. These pre-
dictive elements are all based on simple analytical
perturbation solutions for each flow process. Further-
more, transition rules are used to describe the spatial
extent of each flow process.
The final result is a robust composite flow and mixing
zone prediction that is applicable to a diverse variety
of discharge/ambient conditions. CORMIX1 and 2 have
been extensively validated with both laboratory and
field data.
The geometric schematizations assumed In CORMiX
have been summarized in Figures 2-6 to 2-8, respec-
tively. In addition, CORMIX assumes a uniform un-
sheared ambient velocity profiie represented by the
mean velocity ua' Furthermore, CORMIX requires that
the ambient density profile be approximated by one of
four representative stable profiles as shown in Figure
2-10. A dynamically correct approximation of the actual
distribution should keep a balance between over- and
under-estimation of the actual density data. The sim-
plest case is a linear density profile shown in Figure
2-10a (Stratification Type A). Figure 2-10b describes
two uniform density layers with a density jump
(pycnocline) between layers (Stratification Type S).
Figure 2-10c illustrates a two layer profiie in which the
upper layer is uniform, the lower layer has a linear
stratification, and a density jump occurs between lay-
ers (Stratification Type C). Finally, Figure 2-10d pres-
ents a two layer system with a uniform upper layer and
a linearty stratified bottom layer with no density jump
between layers (Stratification Type D). The uniform
upper layers in Stratification Types S, C, or Dare
representative for the well mixed upper layer that is
found in many types of ambient water bodies and
occurs due to wind induced turbulent mixing.
2.52 Length Scales
Length scales, obtained from dimensional analysis,
describe the relative importance of discharge volume
flux, momentum flux, buoyancy flux, ambient cross-
flow, and density stratification in controlling flow behav-
ior. The length scales will describe the distance over
which these dynamic quantities control the flow, in
particular within the subsurface buoyant jet regions of
the mixing process.
2.5.2. 1 Single Port Discharges
Given the important flux parameters, Qo' Mo and Jo
(see Figure 2-5), the ambient velocity ua. and the
2-11
Draft of 9/21/90
-------
z
-
6Pa
H '
\
, hint
c*'
\
,
\
Pa(Z)
@ Linear
@ Two-Layer
Figure 2-10.
-
@
@
Schematic Ambient Density Profiles for Use In Expert System CORMIX.
buoyancy gradient e = - (glpa) (d pa Id z) of a
linearly stratified ambient, the following dynamic length
scales can be derived for a single port discharge:
La = Qo1Mt2= discharge (geometric) scale
Lm = ~4 I Jt2 = jet/plume transition scale
Lm = Mt21ua = jet/crossflow scale
Lb = Jolu~ = plume/crossflow scale
L~ = (Mo Ie) V4 = jet/stratification scale
Lb = Jt4/e~8 = plume/stratification scale
The meaning of these scales is further illustrated in
Figure 2-11. For example, the jet/cros~ow lengt~ scal.e
is a measure for the distance over which a pure Jet will
intrude into a crossflow before it gets strongly deflected
(or affected). It should be noted that the length mea-
sures are only "order of magnitude"; precise coeffi-
cients have to be determined from experiments or from
more detailed flow analysis.
2.5.2.2 Multipart Diffusers
The general diffuser flow field is, of course, thr~i-
mensiona!. However, for near-field mixing analyses the
two-dimensional flow parameters are dynamically rel-
evant. For this purpose, the details of individual dis-
charge jets with port diameter D and spacing I are
neglected and replaced by an equivalent slot width 8
= (nD2)1(4/) on the basis of equivalency of momen-
tum flux per unit diffuser length. This concept has been
discussed by Jirka (1982b) among others, and has
been shown to be a dynamically accurate representa-
tion. The main parameters for the two-dimensional slot
Draft of 9/21/90
discharge are the diffuser total flowrate Qo and the
discharge buoyancy g~. This leads to the following fl~
parameters (per unit diffuser length), all expressed In
kinematic units: qo = QolLD = volume flux (flowrate),
mo, = qo Uo, = U~ B = moment~m flux, and jo =
qgo = Uogo B = buoyancy flux, In which Uo = dis-
charge velocity, and 1-0 = diffuser length.
Through interaction with the ambient parameters, the
following length scales describe a multipart diffuser
discharge:
Iq = q ~/mo = discharge geometric scale
1m = mol ~ = plane jet/crossflow scale
1M = mo/~3 = plane jet/plane plume scale
I~ = (mole)V3 = plane jet/stratification scale
Ib = it3 I e V2 = plane plume/stratification scale
la = ual e V2 = crossflow/stratification scale
It is interesting to note that no plume/crossflow length
scale can be defined on dimensional grounds for the
two-dimensional plume. This is in contrast to the three-
dimensional round plume and arises from the fact that
the vertical velocity of a two-dimensional plume is
constant, ...... i t3 , leading in the presence of a constant
crossflow to a straight-line trajectory. Thus, no distinc-
tion can be made of a plane plume in a weakly deflected
stage followed by a strongly deflected stage. However,
it is possible to define a non-dimensional parameter
i o/U ~ whose magnitude will be a measure of the
slope of the plume trajectory.
2-12
-------
2.5.3 Near-FieJd FICNI Classification
The clas~ification scheme used in CORMIX puts major
emphasIs on the near-field flow configuration. This is
because a large number of flow configurations can
occur due t.o the multiplicity of possible interadion
proces~es; In contrast the far-field flow is generally
much simpler with limited shoreline or bottom contad
possibilities.
2.5.3.1 Single Port Discharges (CORMIX1)
In the near-field the dynamic length scales LM' L,y,. 4,.
Lm I and Lb I (La has less significance) describe the
intera~tion with the geometric properties of the water
~odYI its depth H or the depth hint to the density jump
(In general, both of those are indicated by a layer depth
Hs)' Also the orientation angles 00 and Go of the
discharge are important (Figure 2-6).
~i~en.the possible ambient stratification types a clas-
sification procedure (in Doneker and Jirka, 1990) Is
u~ed to c~assify the near-field behavior of a given
discharge Into one of 35 generic flow classes that are
summa~iz&? in Figures 2-12 to 2-15. The four major flow
categories Indicated by CORMIX1 are: i) flows affected
by linear stratification leading to Internal trapping (S
classes, Figure 2-12), ii) buoyant flows in a uniform
ambient layer (yand H classes, Figure 2-13), Iii) nega-
tively buoyant flows in a uniform ambient layer (NV and
NH classes, Figure 2-14). and iv) bottom attached flows
(A classes. Figure 2-15).
Each of the flow classes is indicated on the figures by
a sketch that shows its main features in a side view or
plan view. All flow criteria shown on the figures are
given as "order of magnitude" relations; somewhat
different forms and numerical constants may be con-
tained in CORMIX1.
A wide spectrum of near-field flow configurations Is
possible: these range from flows trapped in linear strat-
ification, buoyant jets that are strongly affected by the
crossflow and gradually approach the layer boundary
(surface or pycnocline), weakly deflected buoyant jets
that Impinge on the boundary leading to upstream
spreading and/or unstable recirculation, negatively
buoyant jets that form density currents along the bot-
tom, and dynamic attachment along the bottom with
or without eventual buoyant lift-off. It is stressed also
that (i) each of these flow classes can occur in combi-
nation with an upper stratified layer (see stratification
. types S, C, or D on Figure 2-10) and (ii) the designation
"uniform ambient layer" in Figures 2-13 and 2-14 can,
in fact, also apply to a stratified layer if it has been found
that the stratification is too weak to trap the flow. Thus.
in essence, the actual number of flow configurations
that can be classified by CORMIX1 is much larger than
the 35 generic flow classes shown on these figures.
2.5.3.2 Multipart Diffusers (CORMIX2)
The classification scheme used by CORMIX2 relies on
the same methodology as for single port discharges.
The length scales of the two-dImensional slot jet, 1M
1m. lb. 1m . . and I.. are compared with the layer depth
H$ and with the diffuser variables, its length Lo and its
onentationangles, 0, y, P. G (see Figure 2-7). Theelas-
sificatlon procedure (see Akar and Jlrka, 1991, for
details) yields 31 generic flow classes that tall Into three
major categories: (i) flows affected by linear stratifica-
tion leading to Internal trapping (MS classes, Figure
2.16), Ii) buoyant flows in uniform ambient layers (MU
classes, Figure 2.17) I and Iii) negatively buoyant flows
in uniform ambient layers (MNU classes, Figure 2.18).
While there are some obvious analogies in their ap-
pearance to the flows produced by single port dis-
charges, the major difference for multiport diffusers lies
in the vertically fully mixed (over the layer depth)
plumes that can be produced by the large momentum
sources of unidirectional or staged diffusers.
2.5.4 Predictive Bements
The detailed hydrodynamic prediction of the effluent
flow and of associated mixing zones in CORMIX is
carried out by appropriate flow modules that are exe-
cuted according to a protocol that pertains to each
distinct flow configuration as determined by the classi-
fication scheme. These flow protocols have been con-
structed on the basis of the same length scale
arguments that have been used for the flow classifica-
tion. The spatial extent of each flow module is govemed
by transition rules. These determine transitions be-
tween different near-field and far-field mixing regions,
and distances to boundary interaction.
The flow modules for single port discharge predictions
(CORMIX1) are listed in Table 2-1. All modules present
basic analytical solutions for one particular flow pro-
cess with the perturbing influence of one or more other
variables superimposed. For example, the module for
the weakly deflected jet in crossflow (MOD11) is based
on a pure jet solution that experiences a gradual ad-
vection by the crossflow. The group of near-field mod-
ules (MOD01 to MOD22) represents, In total, the same
predidive ability as buoyant jet integral models (valid
in the subsurface region without'boundary interaction).
The flow modules for multiport diffuser prediction
(CORMIX2) are given in Table 2-2. Several groups of
modules, notably those for the far-field, are simiiar, or
even identical, to those of CORMIX1.
2-13
Draft of 9/21/90
-------
o
QJ
::t
g,
(0
i\)
-4
~
()
I\)
I
...
~
--
ua--
..0
--
ua
--
..0
0) Buoyant Jet in StaQnant Uniform Environment
uaaO
-
\ Transition
, ~
~(Lm) .' ..""
\ /.'
\ ~ .
\ ~ Strongl, Deflected Jet
\ .~
, Weakly Defllcted Jet
b) Pure Jet in Uniform Crossflow
Uo80
.>0
.>0
-
c) Pure Plume in Uniform Crossflow
d) Pur. Jet in StaQnant Stratified Ambient
o (Lb)
e) Pure Plume in StaQnant Stratified Ambient
fig.... 2-11. L8ngth Sc8II8 Meuurlng 1M Et18ct8 of IIoIMntur8 flux, Buoy8ncy flux, CroufIow 8nd 1tr81ltk:8tlon of 8ubIn8rged .... Behavior.
-------
N
I
....
U'I
o
~
~
co
i\)
.....
--
co
c
Zt'"
.an L:11S
~. .
>1
---
<0
---
51
~
~
TEST fOR PlUME TRAPPING
IN A LINEARLY STRATIFIED
LAYER (HEIGHT H.)
Jel-like
>1
Stratlf8oo1ion
Oomtnoted
Zt ....
L~
S2
~
>1
Zt-
lI4/L"I
II .
>1
--
S3
~
It-
~: L,:/I
>1
--.
S4
~
It-
~.
S5
~
T.rmlnal heltht
ZI
AMBIENT STRATIFICATION
~I- UNIMPORT~NT
~ Atnb6ent 0enItty
with Vtrttcol MIan Value
cO NEGAT1VELY BUOYANT JET
- Cor ~4 Or"'" Jet)
BEHAVIOR DOMINATES
FLOW CLASSES
FOR
AMBIENT STRATIFICATION
Flgur. 2-12. CORMIX1 Sub-Cla..lflcatlon: Aueument of Denatty Stratification and Flow Cia... for Int.rllllily Trapped Single Port Dlacharg...
-------
D
Ci;
~
o
-
q)
i\)
....
CO
o
I\)
I
....
0)
Deep
Lo,.
wi..
..
Mon..I"",
....
!:It
H.
1
Shallow
Loyer
..th
St~
~tum
.!i
H.
Vertical
An91t
80
80s 4~.
(Ntor) Horbontol
8H-
FLOW CLASSIFICATION
BUOYANT SUBMERGED
DISCHARGES IN
UNifORM DENSITY LAYER
1
Momentum
00mincrteI
8uoyQncy
Dominate.
-7 ; I~~~I ~
Momentum
00rNnate.
Buojoncy
Oominotta
~H2 H3
~Z:Z
SlronvtJ
~
H5-9O
-4.
Figure 2.13. CORMIXI Sub-CIa..lftC8tlon: Flow CIa.... for Poaltlvety Buoyant Single Port Dlacharg..ln Uniform Ambient Layer.
-------
o
~
~
(Q
I\)
.....
ro
<:)
NEGATIVELY BUOYANT JET
(OR DOWNWARD ORIENTED JET)
IN UNIFORM DENSITY LAYER (HEIGHT HI)
Hear - Y8rtlcal
4:1. < < 90-
N
I
....
.....
. I SIrOfttl
Bu..,
Near - HorbGfttol
.....,. > 8 > -45.
.
00trt8uoJOnc,
-------
o
ii1
::t
o
-
(C
i\)
-
CO
()
CLASSIFICATION
VI, V2, SI HI, HZ
NVI. HV2 NHI,NH2
cl
WAkE ATTACHMENT
I'\)
I
-.
Q)
Yes
Uft-Off
No
No lHt - Off
C..)AI
I
-,;
L) A2
,
-
r"'\."""~
ReclrculottGft
Recirculation
BOTTOM ATTACHMENT
Yn
Yes
With lift-Off
COANOA ATTACHMENT
No Uft - Off
PIa~
-/'iI.IfI-df
S~
Wall'" (wtth ~t)
:L-
~
(..)A5
:~
I
... ~\.,~~~
....
Wall 1-' Cnon-buoront)
figura 2.15. CORMIX1 Sub-CI...lftcatlon: A8M8sment of Dynamic Bottom Attachment Procenee and Flow Cia.... for Bottom-Attached FIowa.
Momentum
Dominat..
Buororq
DomInate.
-------
i
~
~
"
~
Perpendicular
I\)
, I'SII ,'III
~ Z _,lilt "lilt Z ..illlt "lilt
CD Z,-t~ ' Zt"".
Z,-'. z...!L z ....!L Zt-'. Terminal h.iCJhf Z,
' .. ,.. ',."1 I, III
.
AMBIENT STRATIFICATION
UNIMPORTANT
-- Approlimole Ambl."t Den.lty
with Vertical Mlon Volue
NEGATIVELY BUOYANT
JET BEHAVIOR DOMINATES
MSI MS2 M53 M54 M55 M51
~ ~ ~ ~ ~ ~ ~
~ -~
. Zt
TEST FOR PLUME TRAPPING
IN A LINEARLY STRATIFIED
LAYER (HEIGHT H,)
flgur. 2-11. CORMIX2 8ub Clu81t1c8don: Ae....ment of D8n8IIy S1r8tItIo.dIon 8IId Flow CI88M8 tor Internally Trapped MutUport DI8ch8rgee.
-------
t:J
iil
~
g,
co
i\)
-4
co
o
I\)
N
o
.
Shallow Loyer
Unslable Discharoe
MU8
=-p
Flgur. 2.17. CORMIX2 Sub-CI...lflca1Ion: Flow CI..... tor Poal1lvely Buoyant Mul1lpor1 Disch.rg.. In Uniform Ambient Layer.
'M II +cos',)' 'M-C4aho
+
H. t,"
MU2
-~
MU3 MU4
=. =.
P P
= 'p :M~
:~
p
-
p
P =P'on View
MU9
:G
P
-------
I\)
I
I\)
....
Strong
C'OIl-'Io.. >,
MNUI
o
iiJ
::t
g,
co
f\)
....
co
o
-
~S
S. Side View
NEGATIVELY BUOYANT
MUL TIPORT DIFFUSER DISCHARGE
IN UNifORM LAYER (HEIGHT H.)
< I
Deep lar"
I'MI (I+co.',)1
H.
I'MI
--;:-
>,
Stlollow larer
-
~
:*=~
p p
p. Plan View
Flow Closses MNU7 - MNUI4
(Vertically fully Miud»
(Correspond 10 flow Clollel
MU2 - MU9, Respecllvely,
wllh Ihe (acep'ion of
Bottom Reslroliflcallon
In the for Field J
Flgur. 2-18. CORMIX2 Sub-CI.../ftcetJon: FJow CIa.... for Negatively Buoyant Mu/tJpor1 DI~rg..ln Uniform Ambient Layer.
.
Dlflult,-Induced Flawl Nlar Bottom
(not full, mlud)
~
-------
Table 2-1.
Flow Prediction Modules of CORMIX1 (Single Port
Discharges)
Modules for Buoyant Jet Near-Field Flows
zone of flow establishment
weakly deflected jet in crossflow
weakly deflected wall jet In crossflow
near-vertical jet in linear stratification
near-horizontal jet in linear stratification
strongly deflected jet in crossflow
strongly deflected wall jet in crossfiow
weakly deflected plume in crossflow
strongly deflected plume in crossflow
Modules for Boundary Interaction Proc.....
near-horizontal surface/bottom/pycnocline approach
near-vertical surface/bottom/pycnocline impingement with
buoyant upstream spreading
near-vertical surface/bottom/pycnocline impingement with verti-
cal mixing
near-vertical surface/bottom/pycnocline Impingement, up-
stream spreading, vertical mixing, and buoyant restratification
terminal layer stratified impingement/upstream spreading
terminal layer injection/upstream spreading
Modules for Buoyant Spreading Proc.....
buoyant layer spreading in uniform ambient
buoyant spreading in linearly stratified ambient
Modules for Attachment/Detachment Processes
wake recirculation
lift-
-------
estuarine or coastal water bodies in a single analytical
or numerical technique. Therefore, an integration of
near-field mixing models and of predictive techniques
for the far-field effects must be employed. Far-field
processes, that include the transport by the varying
tidal flow, turbulent diffusion, and various biochemical
transformation phenomena, have been addressed In
Parts I and II of this estuarine waste load allocation
manual. The following comments provide some guid-
ance on estimating. the interaction between near-field
mixing and far-field accumulation effects. The method-
ology is adapted from that suggested by Jirka et aI.
(1976).
2.6.1 Far-Field flccumulation Effects
The two major methods for estimating the unsteady
far-field accumulation of discharged material, at vari-
able distances from the outfall and in an unsteady tidal
flow, are either numerical mcx:lels or field dispersion
~. In the following it is assumed that a dispprsion
test is being employed, but the comments apply
equally well to the results of an unsteady numerical
model.
The schematics of a field dispersion test in a reversing
tidal current system are shown in Figure 2-19. The
tracer release line may represent the location of a
submerged multlport diffuser with alternating nozzles.
The tidal system is assumed as approximately periodic
as indicated by the velocity curve. The figure also
shows the hypothetical dye concentration trace C(x,y)
measured at some point (x, y) as a function of time.
(Note that in practice, fewer discrete measurements
overtime would be available). If the field dispersion test
consists of a tracer release period, n tidal cycles long,
then the continuous monitoring would usually indicate
a period of concentration build-up. a Quasi-steady pe-
riod and a fall-off period. If an accurate simulation of
the pollutant discharge over a large-scale and for a
long-term is required, then consideration (and mea-
surement) for at least two of these periods is necessary.
Considering the maximum dye concentration during
any tidal cycle at (x, y), the following sequence is gen-
erally observable: During the first cycle Cmax is found,
in the second cycle the concentration is Cmax plus
some fraction of dye tracer returning from the previous
cycle, thusCm + rdCmax = Cmax(1 :+rd).lfthese
are continuous~repeated, then the quasI-steady max-
imum concentration Cmax is given by the geometric
series
2 3 )
l: max = C max ( 1 +r d + rd + rd +...
or, in the limit,
(20)
1
C max = C max-l
-rd
The quantity rd is labelled the dye r~tur~ r~te.of mass
discharged in the previous cycle (r d ~mphcltl~ Includes
any dye mass decay during the tidal period). The
complement quantity (1- rd) is frequently referred to as
flushing rate. The return rate will depe~d on the c~ar-
acteristlcs of the tidal flow, notably tidal excurSion,
mean velocity, diffusion, etc. rd is also dependent on
the position (x, y) with respect to the release area.
Quasi-steady conditions are typically encoun~e~ed
after about 5 to 10 tidal cycles. Build-up curves, similar
to Equation 20 correspond also to other quantities of
interest, such as the minimum or average concentra-
tions during a tidal cycle, thus
(21)
c'i(x,y,t) =Ci(X,y,t)l~rd (22)
where Ci(x,y) is a single cycle concentration quantity
of interest (Cmax' Cmin' Cave' etc.).
For the actual pollutant discharge the quasi-steady
condition is usually of primary importance. From Equa-
tion 22 it is seen that this depends on two factors: the
mixing characteristics Cj within a single tidal cycle, and
the return rate from previous cycles. To translate the
quasi-steady dye concentration conditions into pollu-
tant concentration, therefore, two adjustments are
needed:
(a) w.i1hIna tidal cycle, the pollutant concentration c is
related to the dye concentration C
Ci (x, y, t) = Ci (x, y, t) g~: e - (kc-kd) tl ( x, y ) (23)
where ti(x,y) = time interval between o~curence of
event i (maximum, minimum concentration) at (x,y)
and time of release of that tracer patch, i.e., travel time.
Qco is the pollutant mass release rate and Qdo is the
dye mass release rate. kc and kd represent the decay
constants for pollutant and dye, respectively. (for a
conservative dye, kd = 0). Determination o.f ti ~epends
on the detailed knowtedge of the velocity field; for
average concentrations the average tidal velocity is
representative. It is noted that for points far from the
release area - especially more than several tidal excur-
sions away - the exponential correction term in Equa-
tion 23 becomes significant. In the discharge vicinity,
however, it is frequently negligible, since ti is less t~an
one tidal period. This is, in fact, the usual assumption
in most mixing zone predictions.
(b) The return rate for pollutant r c is related to the dye
return rate r d
.
rc = rd e -(kc-k.J) t
(24)
2-23
Draft of 9/21/90
-------
o
iii1
:;-
o
.....
CO
i\)
-4
CD
o
N
I
N
~
Flood
E b~ \ I
'..
Instantaneous
Concentration
Oistri but ion
(Ebb Tide)
Ti d a I Velocity
Tracer
Releas. Points
~
Tracer Release Period n
C
Tracer Concentration at (x ,y)
I 2
Build -up
Period
3
4
+
Flood
.
o
e (x.y)~
.
Tidal
Period s
-I
'-1
_J
Cmax
,."
I \
C mal(
r Cmax
Tidal
Periods
Quasi - Steady
n
n+ I
n+2
Falloff
Period
Period
.r
---
Figure 2-11. Schematics of . Field Tr.e« DI8persion Teat In 8 Periodically Revemng T1daI System.
-------
*
where t = tidal period (12.4 hours). The quasi-steady
pollutant concentration ci(x,y) is therefore related to
the measured single cycle dye concentration Cj(x,y)
Ci (x ,y , t ) = q (x ,y , t ) Qeo [e - (kc-kd) tj] 1-rd
Qdo 1-re
(25)
Hence, for an accurate prediction of far-field effects
over a large area (larger than the tidal excursion length)
it is necessary to (i) measure the velocity field in some
detail so ti(x,y) can be found for the points under
consideration, and (Ii) measure not only the quasi-
steady period of tracer distribution, but also the build-
up or fall-off period so the dye return rate r d can be
evaluated as shown in Figure 2-19. In actual tracer
monitoring it is not always possible to have continuous
records. Nevertheless, a few measurements during the
build-up or fall-off period usually give some indication
of rd'
If attention is restricted to a smaller area around the
discharge and if the tracer used is relatively conserva-
tive (small kd), then both correction factors in Equation
25 are negligible and the measured concentrations can
be used directly to evaluate the pollutant accumulation
in the far-field.
2.6.2 Unkage to Initial Mixing Predictions
All initial mixing models discussed in the preceding are
steady-state models and. do not consider the far-field
return (accumulation). The following procedure pro-
vides an approximate linkage:
(a) Carry out a series of initial mixing predictions using
a steady-state near-field mixing model for different
intervals (e.g. 6 or 12, corresponding to 2 or 1-hour
intervals, respectively) within the tidal cycle. The pre-
dictions at any point of interest (e.g. at the boundary of
a Legal Mixing Zone) provide approximate time-depen-
dent predictions for pollutant concentration ci(x,y,t)
within a tidal cycle.
(b) Use the far-field pollutant return rate r c' that applies
for the region of interest (e.g. the Legal Mixing Zone),
to calculate the quasi-steady (i.e. long-term) pollutant
concentration
- 1
Ci(X,y. t) =Ci(x,y,t) _1
-re
The return rate r c that applies to the area of interest can
be estimated using the procedures outlined in the
preceding paragraph, i.e. relying on a dye dispersion
test or numeri~1 model. It .should be noted that r c' in
turn, is a function of the distance from the outfall: r c
tends to be very small in the immediate near-field,
(26)
where the pollutant concentrations are high; r c ~e-
comes larger for increasing distances, where the I~-
duced concentrations are falling off, however! This
dependence suggests - in the absence of detai~ed
measurements or predictions for r c the following
practical guidelines:
. For Toxic Dilution Zone (TDZ) predictions, the
effect of far-field return is always nagl igible (r c == 0)
due to the strong spatial restriction of the TDZ.
. For most Legal Mixing Zone predictions, the r c
factor can be expected to vary in the range of :s 0.1
to == 0.5 (highly conservative estimate). It is very
small (:s 0.1) for deep water discharges in the open
coastal zone that are often associated with internal
trapping or buoyant surface layer formation. In
those cases, the initial (buoyant jet) mixing is, in
fact, quite independent of far-field effects. It may
be reasonably high (up to 0.5) for shallow water,
vertically mixed, discharges in strongly restricted
estuaries with weak flushing. For additional flush-
ing estimates in such tidal channels, see the meth-
ods discussed in Fischer et al. (1979).
2.7 References
Abraham, G. 1963. Jet Diffusion in Stagnant Ambient
Fluid. Publ. No. 29, Delft Hydraulics Laboratory, The
Nethertands.
Akar, P. J., and G. H. Jirka. 1991. CORMIX2: An Expert
System for Hydrodynamic Mixing Zone Analysis of
Conventional and Toxic Submerged Multipart Diffuser
Discharges. Technical Report, U.S. EPA, Environmen-
tal Research Laboratory, Athens, GA, (in preparation).
Doneker, R. L., and G. H. Jirka. 1990. CORMIX1: An
Expert System for Hydrodynamic Mixing Zone Analy-
sis of Conventional and Toxic Submerged Single Port
Discharges. Technical Report EPA 600/3-90/012, U.S.
EPA, Environmental Research Laboratory, Athens, GA.
Fischer, H. B. et al. 1979. Mixing in Inland and Coastal
Waters. Academic Press, New York.
Hirst, EA 1971. Analysis of Buoyant Jets Discharged
to Rowing Stratified Ambients. Rep. ORNL-TM-4685,
U.S. Atomic Energy Commission, Oak Ridge National
Lab., Oak Ridge, Tennessee.
Holley, E. R. and G. H. Jirka. 1986). Mixing in Rivers.,
Technical Report E-86-11, U.S. Army Corps of Engi-
neers, Washington, DC.
Jirka, G. H. 1982a. Turbulent Buoyant Jets in Shallow
Auid Layers. in Turbulent Jets and Plumes, W. Rodi
(Ed.), Pergamon Press.
2-25
Draft of 9/21/90
-------
Jirka, G. H. 1982b. Multiport Diffusers for Heat Disposal
- A Summary. Journal ofthe Hydraulics Div., ASCE, V~.
108, December.
Jirka, G. H., G. Abraham, and D.R.F. Harleman. 1976.
An Assessment of Techniques for Hydrothermal Pre-
diction. Technical Report NUREG-0044, U.S. Nuclear
Regulatory Commission, Washington, DC.
Jirka, G. H. and LM. Fong. 1981. Vortex Dynamics and
Bifurcation of Buoyant Jets in Crossflow. Journal of the
Engineering Mechanics Division, American Society of
Civil Engineers, Vol. 107, No. EM3, June.
Kannberg, L D., and LR. Davis. 1976. An experimen-
tal/analytical investigation of deep submerged multiple
buoyant jets. EPA-600/3-76-101. U.S. Environmental
Protection Agency, Corvallis, OR. 266 pp.
Muellenhoff, W. P., et al. 1985. Initial Mixing Character-
istics of Municipal Ocean Discharges (Vol. 1 &2).
U.S.E.P.A., Environmental Research Laboratory, Nar-
ragansett, R.I.
Roberts, P.J.W. 1977. Dispersion of buoyant waste
discharge from outfall diffusers of finite length. Rep.
No. KH-R-35. W. M. Keck Lab. of Hydraulics and Water
Resources, California Institute of Technology, Pasa-
dena, CA, 183 pp.
Schatzmann, M. 1978. The integral equations for
round buoyant jets in stratified flows. J. Appl. Math and
Physics 29: 608-20.
USEPA. 1982. Revised Section 301 (h) Technical Sup-
port Document. EPA 430/9-82-011, Washington, DC.
Winiarski, L. D., and W.E. Frick. 1976. Cooling tower
plume model. EPA-600/3-76-100. U.S. Environmental
Protection Agency, Corvallis, OR.
Wong, D. R. 1984. Buoyant Jet Entrainment in Stratified
Fluids. Ph.D. Thesis, Civil Engineering Dept., The Uni-
versity of Michigan, Ann Arbor Mich.
Draft of 9/21/90
2-26
-------
3.' Case Studies of Mixing Zone Prediction
3.1 Introduction
3.1.1 Objectives
This case study section has several objectives: (1) To
demonstrate the typical procedures and data requIre-
ments Involved in mixing zone analysis; (2) To
demonstrate that legal mixing zone definitions may
require the analysis of both near-field and far-field
processes; and (3) To show the relative merits and
flexibility of different methodologies, including jet inte-
gral models and the expert system CORMIX.
All four case studies deal with hypothetical conditions
that may, however, exhibit some features of existing
discharges. In the first case study major emphasis is
put on various regulatory criteria. None of the case
studies is intended to document model validation. This
cannot be done since no actual field or laboratory data
exist for these hypothetical situations. For validation of
models reference should be made to the original liter-
ature on the various models as listed in Section 2.
However, a few comments on model validity are made
in the first case study in order to explain some large
differences in various model predictions.
3.1.2
Data Needs
As discussed in Section 2.1, the initial mixing of an
effluent depends on the interaction of ambient and
discharge conditions. In estuaries or coastal waters
these conditions may be highly variable. In evaluating
water quality effects and mixing zone compliance,
appropriate design conditions must be chosen. Gen-
erally, the critical design conditions relate to those
environmental and discharge factors that lead to the
lowest dilution and at times when the environment is
most sensitive. However, it is not always straightfor-
ward for the analyst to estimate exactly what combina-
tion of factors will lead to this critical condition. For this
reason, an evaluation under a variety of conditions
always seems necessary to obtain information on mix-
ing zone behavior and its sensitivity to design criteria.
Data uncertainty is also a factor of concern. The follow-
ing considerations, taken from Muellenhoff et al.
(1985), apply here:
"Predicting dilution reliably depends on the availability
of statistically val id data with which to estimate ambient
conditions. The statistical uncertainty in estimates of
absolute worst case conditions is generally great. Also
there are inherent biases to some oceanographic mea-
surements. For example, current measuring instru-
ments have finite thresholds. It therefore becomes
difficult to distinguish low values (which may be as high
as 5.0 cm/sec) from zeroes in these data sets. In
estimating environmental conditions, a more reliable
estimation can be made at the lowest 10 percentile on
a cumulative frequency distribution. Data on ambient
density structure are not routinely collected. Conse-
quently, there is not usually an existing data set for the
site under consideration. To increase the reliability of
"worst-case" estimates, data should be evaluated not
only for the discharge site but for nearby coastal areas
of similar environmental setting."
"Defining 'worst-case' conditions as a combination of
those conditions affecting initial dilution, each taken at
the worst 10 percentile on cumulative frequency distri-
butions, is recommended by USEPA. This approach
allows a reliable estimation of these conditions to be
made and prevents the unlikely occurence of more
extreme conditions from biasing the predictions. The
probability of these conditions occurring simulta-
neously is much less than 10 percent, ensuring that the
predicted dilution will be exceeded most of the time.
Application of multiple 'worst case' factors (I.e. flows.
stratification and currents) to determine a minimum
dilution must be done carefully, however, and in rec-
ognition of the criteria for which compliance is being
determined. For example, although application of an
absolute ''Worst case" dilution may be appropriate for
determining compliance with an acute toxicity limit, it
is more appropriate to identify the lowest 6-month
median dilution to determine compliance with a 6-
month median receiving water limitation."
Since the discharge conditions can also vary (e.g. its
flowrate or pollutant concentration) it is necessary to
combine the occurences of the varying pollutant load-
ing with the varying ambient parameters in order to find
the critical design conditions.
Finally, any set of ambient and discharge conditions
will require some degree of schematization in order to
meet the predictive model assumptions. This has been
discussed in Section 2.3.2 along with Figs. 2-6, 2-7 and
2-8. The literature or user's manuals for the various
models usually contain some guidance on how to
prepare the data. The expert system CORMIX, in fact,
has on-screen advice on data preparation available to
the user.
All available mixing zone models assume a conser-
vative pollutant discharge neglecting any physical,
chemical or biological decay or transformation pro-
cesses. For most, substances this is reasonable due to
the rapidity of the mixing process, especially in the
near-field, relative to the reaction time scale of most
3-1
Draft of 9/21/90
-------
z(m)
16
9
I
o
I
b.
""
o
\ / CORMIX1
\ Profile C
'0
\
\
\
\
b
,
\
\
\
b I
1,010
Po (kg/m3)
12
opprox imotion
8
4
o
1,005
I ...
Figure 3-1. Design ease AA: Vertical Ambient Density Profile
In Typical Summer Conditions.
pollutants. If first order reaction processes can be
assumed then the model results on concentration can
usually be converted with an exponential factor to
include the decay process (see Doneker and Jirka,
1990). The consideration of pollutant reactions in the
context of far-field accumulation involving a larger time
scale has also been addressed in paragraph 2.6.1.
z(m}
20
15
-
Uo
0.15 m/s 10
-
5
.l
0.5 m rrF '-v-'
Bottom
Attachment
ho=0.5m,
3.2 Case AA - Single Port Discharge:
Indus1ria1 OUtfall in Tidal Fjord.
3.2.1 Ambient and Discharge Conditions
A manufacturing plant is located near the upstream end
of a narrow tidal fjord that receives a substantial
amount of fresh water inflow. The typical cross-section
of the fjord is 600 m wide with an average depth of 16
m. The preferred discharge location Is about 90 m .from
shore where the local water depth is 17.5 m. During
typical winter conditions the characteristic ambient
(average tidal) velocity is 0.15 m/s and the vertical
ambient density distribution is quite uniform with a
value of 1,005.5 kg/m3. During summer design condi-
tions, however, the ambient velocity is lower at 0.1 0 m/s
and a significant vertical stratification exists as shown
in Figure 3.1. The density varies from a bottom value of
1,010.0 kg/m3 down to a surface value of 1,005.8
kg/m3. The plant operation is also variable. In winter
the discharge flow rate is 0.15 m3/s and has a dis-
charge temperature of 10°C. In summer the flow rate
is lower at 0.10m3/s with a temperature of 15°C. The
discharge flow is essentially freshwater but contains
1000 ppb of some organic toxic material.
Applicable state regulations limit the mixing zone to
25% of the width of the estuary. Furthermore, the
special mixing zone requirements for toxic substances
(see Section 1.2.2) apply with a CMC value of 100 ppb
for the discharged toxicant.
Smln: 164
Side View (distorted)
B =00
o
50
100
x(m)
Case AAI: Initiol Design, Unstratified Winter Conditions
Figure 3-2. ease AA1: Single Port Discharge (Initial design) Exhibiting Bottom Attachment as Predlc1ed by CORMIX1.
Draft of 9/21/90
3-2
-------
3.2.2 Case AA 1: Initial Design, Winter Conditions
An inital ?esign proposal calls for a single port dis-
charge with 0.2m port diameter and 0.5 m port height
above th~ bottom. The discharge velocity is 4.8 m/s.
!he po~ IS oriented in a co-flowing arrangement point-
Ing hOrizontally along the direction of the ambient
current.
F~gure 3-2 shows a side view of the near-field of the
discharge plume predicted by CORMIX1 (flow class
AS). The model shows strong dynamic attachment of
t~e plume to the bottom. After this a gradual buoyant
rI?e ~o the surface takes place with a minimum surface.
dilution Smin = 164. The extent of the toxic dilution
zo~e (TDZ) is about 10m, essentially comprising the
entire bottom attached zone. Thus. benthic organisms
will be exposed to toxicant concentrations above CMC
values: This initial design is considered undesirable
and rejected from further consideration.
~n view of this bottom attachment, none of the jet
Integral models, included in Section 2.4, i.e. the USEPA
models, UOUTPLM and UDKHDEN or the Jirka-Fong
~odel, would be applicable. Therefore, their predic-
tions are not shown on Figure 3-2.
3.2.3 Case AA2: Modified Design, Winter
Conditions
In order to eliminate plume bottom interference a
m~ified design is proposed with an increased Port
height of 1.0 m and a vertical discharge angle of 10°.
z(m)
5=212
This modified design, indeed, does not exhibit any
bottom attachment as shown in Figure 3-3.
The trajectory predictions of three buoyant jet integral
models (UOUTPLM, UDKHDEN and JF [Jirka-Fong])
and of CORMIX1 (flow class H2) are given in Figure 3-3.
Also shown is the width prediction for CORMIX1. All
four submerged plume trajectories are qualitatively
similar; the deviations among trajectories is contained
within the plume outline (as indicated by CORMIX1)
and well within the usual scatter of experimental data.
The TDZ is again limited (order of 10m) as predicted
by any of the four models. The jet integral models are,
of course, limited in their applicability to the submerged
jet region before surface interaction. Only CORMIX1 is
applicable to the actual interaction process and the
subsequent buoyant spreading along the water sur-
face. This process is indicated by the width boundary
in Figure 3-3.
Considerable differences exist in the predicted surface
dilution at the point of surface interaction. UOUTPLM
and UDKHDEN predict a flux-averaged dilution of 212
and 495, respectively. On the other hand, JF and
CORMIX1 predict minimum (centerline) dilutions of
220 and 146, respectively. Even if the UDKHDEN model
predictions are divided by a factor of 1.7, in order to
account for the typical ratio of flux-averaged and min-
imum dilutions a considerable difference remains rela-
tive to the lower dilution value of CORMIX1.
Smln=
146 Smin=220
S=495
-
. -S-'<:' /' /' /' ,
,,~" ~~,./. /' ~~/,/
~:~ ~~~ ,;{. d' ~~~.
(p~ ~O~~~~. ~~ .~.
.~~. ./
.~./' ~.~
.~. /' /' ..i~'4\
5 '~:~:/'Q~~\i-'
&:&/" G
~~
.L rr~ 1DZ I h~=I.O m.. 80= ~Oo
20 40
15
-.
10
-
1.0 m
Side View (distorted)
60
..
x(m)
80
100
Figure 3-3. ea.. AA2: Single Port Discharge (modified design) In Unstratified Winter Conditions; Comparison 01 Jet Int""ral
Models and CORMIX1. -.
3-3
Draft of 9121190
-------
LOLm
5-
Lb2
10~
/ /'.
UKHDEN }- I ' .
UDUTPLM S............... ",'
. I / Regression S.....,
to jot". Lee and Neville-Janes
~..,.~ 09871
Jirka and r:
Fang Sm," --'-...! I
10J n' ~ CORMIX1 Smln
III
I.:d ..
I F.li .
/c&,W
/1/
I/J./
,~..
. r-'
Id
10'
o Gosport
C Brldport
b. Hastings 119791
. Hastings 09801
100
100
10'
102
H/Lb
10J
Figure. 3.4. Comparison of Observed Minimum Surface
Dilution for Three Submerged Single Port
Outfalls (Lee and Nevllle-Jon.., 1987) with
Predictions of Jet Integral Models and CORMIX1.
y(m)
z(m)
-10
-
Ua
Left Bank
50
-----
To shed further light on this disagreement the predic-
tions of the four models Can be compared to what is
probably the most reliable and comprehensive avail-
able field data set on submerged discharges. Lee and
Neville-Jones (1987) report several hundred individual
observations of minimum surface dilution for three
single port submerged outfalls for municipal dis-
charges in the United Kingdom. All of these outfalls are
somewhat more dominated by buoyancy than design
case AA2.. (This is indicated, for example, by the fact
that CORMIX1 p~edicts a flow class H1 for these out-
falls). The predictions of all four models are compared
with the normalized field observations for minimum
surface dilution (Figure 3-4). The solid line presents the
best-fit regression line for all data points. The average
dilution given by both USEPA models is a factor of 4
(300%) larger than the observed minimum dilution.
When the dilution predictions are converted to mini-
mum dilutions (factor 1.7) the overprediction is still by
about 130%. The JF model overprediction is about
50%. CORMIX1, on the other hand, lies within about
15% with the observations. (Note that the model coef-
ficients of CORMIX1 have been chosen through exten-
sive comparison with basic laboratory data, so that this
good agreement presents indeed a model validation
and not some forced best-fit!). On the basis of this
comparison it may be concluded that the jet integral
Bank Interaction
--------
---
-r - -
I
I
I
o
--
--
Jdm)
---- 200 400 ,600
--- -___Case AA3. S
- - ~ - !:!."l.mert~o.J m/$J1
Case AA2: Wint (0 -- - --
er .15 m/s) LMZ
Winter
I
I
I
-J.-
LMZ
Summer
LMZ 5=380
I
i . -
I Case AA2: Winter LMZ.5=35
i;==~~-:=~-~=====-~===:====~~======~~~~
.~.... Case AA3: Summer I.
I
400
x(m)
a) Plan View (undistorted)
...
200
b) Side View (distorted)
600
Figure 3-5. Cases AA2 and AA3: Predicted (CORMI1) Far-Field Behaviour for Single Port Discharge (modified design) In Winter
and Summer Conditions.
Draft of 9/21/90
3-4
-------
models (notably UOUTPLM and UDKHDEN) are quite
non-conservative and tend to overestimate actual
plume dilutions, at least for unstratified ambients. The
prediction disagreement for Case AA2. (Figure 3-3) may
be considered in light of this conclusion.
The legal mixing zone LMZ (25% width) is not attained
in the hydrodynamic near-field but rather in the far-field
as shown by the CORMIX1 predictions of Figure 3-5.
In fact, the LMZ is reached at a downstream distance
of about 600 m when the surface plume is in the
buoyant spreading regime. At this point, the average
dilution has Increased to about 250 and the plume
half-width is about 75 m with a plume thickness of 1.7
m. Actual plume interaction with the bank takes place
at a further downstream distance of about 760 m. This
result illustrates the practical fact that legal mixing zone
definitions can often imply sufficiently large distances
which then include far-field mixing processes. Simple
jet integral models do not address this aspect, while
CORMIX1 has been implemented to deal with such
general ities.
Case AA3: Modified Design, Summer
Conditions
The drastic effect of ambient stratification on plume
near-field behavior is shown In Figure 3-6. With any of
the four predictive models the plume is predicted to
reach its terminal level of about 3 to 5 m above the
bottom at a distance of about 10 m downstream. The
differences among the predicted trajectories are srnall.
The TDZ is reached about 8 m downstream as indl-
3.2.4
z (m)
'\/
15
--
10
-
5
cated by CORMIX1 (flow class S3). The predicted
dilution values at the terminal level show, again, more
variability. If minimum terminal dilutions are compared,
then UOUTPLM, St = 16/1.7 = 9, CORMIX1, St = 16,
and UDKHDEN, St = 26/1.7 = 15, provide lower-end
(conservative) predictions, while JF, St = 26. Is some-
what higher.
The CORMIX1 predictions in Figure 3-6 also show the
formation of the internal stratified layer (Initial thickness
2.4 m) and its gradual collapse and widening with
additional mixing. The full development In the far-field
Is Illustrated again in Figure 3-5. The behavior under
stratified summer conditions is in marked contrast with
the unstratified winter conditions (Case AA2). The dif-
ference in dilution Is notable (related to the much
shorter buoyant jet trajectory In the near-field) as is the
much thinner internal layer. The LMZ Is reached at
about 680 m where the plume half-width is about 75 m
and the plume thickness about 0.3 m.
3.3 Case BB - Multipart Diffuser: Municipal
sewage DIscharge into Coastal Bay
3.3.1 Ambient and Discharge Conditions
A multiport diffuser is used for the discharge of treated
sewage water from a municipality located on a bay. The
proposed diffuser location is 10 km offshore with an
ambient water depth of 30 m. In a preliminary evalua-
tion two ambient design cases are to be investigated;
1) A weakly stratified ambient with a density variation
from 1,023.2 kg/m3 at the surface to 1,026.4 kg/m3 at
Side View (distorted)
UOUTPLM 5.=16
CORMIX1 Sf: 16
UDKHDEN 5f=26
JF 5.=26 5:18
Holf Width :20 m
_._COR~IX1._._. -'-'-'-.-'-'-
y~~~~~
Y'AVh-AW"A'"
.
40 x (m)
20
30
Figure 3-0. Case AA3 : Single Port Discharge (modified design) In Stratified Summer Condhlons; Comparison of Jet Integral
Models and CORMIX1.
3-5
Draft of 9/21/90
-------
z (m)
30
UDKHDEN, ULiNE
20
10
o
1.022
1.026
Po (kg/m~)
1,024
Figure 3-7. Design ea.. BB: Vertical Ambient Density Profile
for Design Conditions.
the bottom. Figure 3-7 shows the actual density varia-
tion, together with the schematizations adopted for
different models. 2) A uniform ambient with a density
of 1.026.0 kg/m3. In both cases the ambient design
velocity is 0.156 m/s for the prevailing coastal current.
The discharge flow rate is 20 m7{s (460 MGD) with a
freshwater density of 998.0 kg/m -
The preliminary design calls for a total diffuser length
of 2000 m with a perpendicular alignment relative to the
prevailing current direction. The diffuser employs 80
z(m)
30 u
.....
Uo 20
--
--
vertical risers with 8 ports attached per riser and dis-
charging in a circular fashion. The port diameter is 0.14
m, the port height is 1.5 m above bottom and the port
angle is 00 (I.e. horizontal).
The legal mixing zone (LMZ) Is prescribed by a dis-
tance of 30 m extending in any direction from the
diffuser line. No toxic substances are included in this
discharge,
3.3.2 Case 881: Stratified Imbient
When applying any model to a complex diffuser geom-
etry with riser/port assemblies, some model simplifica-
tion is needed. In case of the USEPA multipart models
(UDKHDEN,UMERGE and UUNE) the user must, in
fact, substitute a series of single ports equally spaced
along the diffuser line (thus, in this present case 80 x 8
= 640 ports). On the other hand, the input element of
CORMIX2 collects all the pertinent information about
the riser/port assemblies. the system then concludes
that the net horizontal momentum flux for this diffuser
is zero and treats the diffuser as an alternating diffuser
with a vertical equivalent slot discharge. Thus. in either
case, the local details of the eight individual buoyant
jets discharging from each assembly are neglected.
Figure 3-8 summarizes the predictions of the Jet mod-
els UDKHDEN and UUNE and of the expert system
CORMIX2 (flow class MS5). All three models Indicate
a terminal layer Zt at about 10m above the bottom
varying between 8 m and 12 m. Also all three models
show limited variability for the predicted average dilu-
tion at the terminal level, St. which is 137 for UUNE, 212
for UKHDEN, and 166 x 1.4 = 232 for CORMIX2, using
an average/minimum dilution factor of 1.4 for two-di-
mensional buoyant Jets. All these dilution values may
Side View (undistorted)
ULlNE: 2,= 12.1 rn, S,= 137
(no spatial data)
2, = 10.6 m
.-.-.-.-.-.-.-.-.-.-.-
10
40
"~A'
Y..wA~,«'
..
x(m)
80
100
60
Figure 3-8. Ca.. BB1: Multlport Diffuser Discharge under Stratified Conditions; Comparison of Jet Integral Models and
CORMIX2.
Draft of 9/21/90
3-6
-------
5-:513
(Submllged plume) h-4.1m
COSI BBI, Slrati:2ied . ----
---
Ave. dllu"an 5-292 -
Layer Ihicluleu h-!5.9m- - -
_of""
-
5-263 ,.--
h>9.5m.....,'
...:t..::
...
5>568
'" h-22.0 m
-....;;
.....,
,
'......
---
-......- ~-103
--- h-II.3
--
--
--
y(km)
4
3
2
2
4
-2
-3
-4
CORMIX2
6
10 I(kml
8
Plan View
Figure 3-9. Case BB1 and BB2: Predicted (CORMIX2) Far-Field Behavior for Multlport Diffuser Plume in Stratlfted and Uniform
Condition..
be scrutinized as to whether the mixed effluent flow per
unit diffuser length, St 0dLe, exceeds the available
ambient approach flow, UaZt, for the layer between
bottom and terminal level. Denoting the ratio
R=(StOdLe)/(uaZt) one finds R=0.7 for ULlNE,
R = 1.7 for UDKHDEN, and R = 1.4 for CORMIX2. In a
strictly two-dimensional flow (I.e. if a diffuser section or
the entire diffuser length were bounded by lateral walls)
any value R > 1 is not possible In steady-state. How-
ever for the actual three-dimensional diffuser the dif-
fuse~ entrainment demand can also be met by lateral
flow toward the diffuser line. Futhermore, additional
freedom to entrain water exists for the internally
trapped plume (zt < H where H is the water depth).
Also, note that for low ambient velocity conditions
(ua~O) the above test becomes unreliable for evaluat-
ing model performance. Thus, for the present case of
an internally trapped plume from a three-dimensional
diffuser all three model predictions appear reasonable
Note that trajectory information is provided by
UDKHDEN and CORMIX2 while UUNE does not pro-
vide any spatial data on plume behavior. The LMZ Is
predicted by CORMIX2 to have a minimum dilution of
116.
At the transition to the far-field CORMIX2lndicates an
initial internal layer thickness of about 16 m. As shown
in the far-field plan view of Figure 3-9 this internal layer
is gradually spreading, decreasing in thickness, and
experiencing a slight additional mixing in the buoyant
spreading phase. Thus, at 10 km downstream from the
diffuser line the average dilution is 313, with a half-width
of the effluent field of 4.2 km and a thickness of 4.7 m.
3.3.3 Case 882: Uniform Ambient
The corresponding model predictions for the unstrati-
fied case are given in Figure 3-10. CORMIX2 Indicates
a flow class MU8 which Includes a vertically fully mixed
near-field with an average dilution, S = 512. Although
its model printout does not specifically state so, ULINE
also predicts a vertically mixed flow with a lower dilu-
tion S = 368. In contrast, UDKHDEN does not recog-
nize the destabilizing effect of the vertically limited
environment in crossflow and predicts a plume with a
high surface dilution S = 835 and with width dimen-
sions that are of the order of the water depth (Figure
3-10)! Defining the ratios R = ($ O,.JLn)/(~aH) one
finds R = 0.8 for UUNE, R = 1.0 for COAMIX2 and R
= 1.8 for UDKHDEN. The latter result, together with the
fact that the model- while predicting plume dimensions
of the order of the water depth - does not address the
constraint of the limited ambient depth, indicates that
UDKHDEN is not applicable in this case. More gener-
ally, it appears that UDKHDEN is an unr~liable m??el
for most multi port diffuser applications In unstratified
ambients. The same reservation would hold for the
model UMERGE (not plotted here). UUNE indicates
slightly more conservative dilution values than
CORMIX2. It may be overly conservative, however,
since the UUNE model coefficients are based on a
single set of experiments by Roberts (1977) which ?id
not Include the additional mix1ng effect of the high
velocity discharge jets as is common in. act~ diffu~er
installations (this has been pointed out In a diScussion
by Jirka, 1979).
The far-field behavior of the diffuser plume is plotted in
Figure 3-9. While the plume is fully mixed in the near-
3-7
Draft of 9121/90
-------
UDKHDEN CORMIX2
5 = 835 5= 512 (fully mixed)
/ ~ '
./ /" I
,/ /' I
~~,/ ./. ,..,...-1
~"" ~~./ R~\'f..'l. .-'" I
~~/ ~ *-y"Qy' (,9,- - ~ I
.f:)" \jQ7' .~' I
~/ . ~ ....""\
~~./ ./'~'~~m(HDEN w,~h__---- I
./ /' -~. ------- II
~'--- -----
-~-,-- I I '- I I ~ ..
~r ~--AW~ 20 40 ,;.. - 60 80 . t'< ~.... 100 x (m)
Side View (undistorted) .
z(m)
30
u
-...
--
--
ULlNE: 5 =368
(fully mixed)
(no spatial data)
Figure 3-10. CUe 882: Multlport Diffuser Discharge In Uniform Ambient; Comparl8on of Jet Integra' Model. and CORMIX2.
field (about 100m downstream; see Figure 3-10) it
rest ratifies and lifts off from the bottom. At a distance
of 1.5 km downstream the vertical thickness has re-
duced to 22.0 m (compared to the initial thickness of
30.0 m equal to the water depth). At 10 km downstream
the plume has thinned to about 11.3 m while spreading
to a half-width of 4.0 km and attaining an average
dilution of 703.
3.4 Case CC - Single Port Discharge: BrIne
Discharge From an Oil Field
3.4.1 Ambient and Discharge Conditions
Brine from drilling operations in a coastal oil field is to
be discharged into coastal waters. The proposed dis-
charge site is 250 m offshore at a local water depth of
20 m. The ocean water is weakly stratified with a
pycnocline at 15 m above the bottom. However, be-
cause of the strongly negatively buoyant brine dis-
charge the density distribution above the pycnocline
appears unimportant and the ambient can, in tact, be
assumed at a constant density of 1,025.0 kg/m3 corre-
sponding to the lower layer density. Ambient design
velocities range from 0.1 m/s to 0.25 m/s. The bottom
is sandy with a Darcy-Weisbach friction factor of 0.015.
The brine flow rate is 0.03 m3/s with a density of 1,070.0
kg/m3, thus much heavier than the ocean water. The
effluent contains several toxic metals, including copper
at a concentration of 380 ppb. The extent of the LMZ
corresponds to the water depth of 20 m. The TDZ Is
governed by a CMC concentration for copper of 40
ppb.
The initial design proposes a low velocity discharge
(3.8 m/s) with a port of 0.1 m diameter at a 2.0 m height
nrRft of 9/21/90
above the bottom, angled at 600 above horizontal and
pointing laterally across the cross-flow (cross-flowing
discharge).
3.4.2 Case CC1: LON Discharge Velocity Design,
Weak Current
Even though, in principle, they ought to be applicable
for negatively buoyant discharges the U8EPA models
(UOUTPLM and UDKHDEN) do not provide any pre-
dictions for this cross-flowing upwardly angled dis-
charge with a complex three-dImensional trajectory.
Predictions are limited to CORMIX1 and the Jirka-Fong
(JF) integral model. The near-field plume configuration
for the two model predictions is shown in Figure 3-11 a
with (i) longitudinal and (Ii) transverse side views, re-
spectively. CORMIX1 predicts a flow class NV2 with
buoyant upstream intrusion along the bottom after
impingement of the falling jet. The two buoyant jet
trajectories (JF and CORMIX2) are in reasonably good
agreement prior to impingement. The predicted mini-
mum dilution is lower for CORMIX1 (8min = 22) than
for JF (56). The extent of the upstream intrusion is of
the order of 20 m from the impingement point. A thin
bottom layer of about 0.5 m thickness is formed and
spreads laterally as the bottom plume is advected
downstream. The TDZ is very short, of the order of 1 m
from the efflux point. The conditions at the LMZ (not
shown in Figure 3-11 a) indicate a thin layer of 0.35 m
thickness, 18.0 m half-width with an average dilution of
40.
3-8
-------
z(m)
D=O.IOm
uo= 3.8 m/s
LMZ (x=20m):
5=40
thickness h=0.35 m
half-width b= 18.0 m
--
( i) Side View
(undistorted)
o
Upstream
intrusion
x(m)
10
( i i) View Looking
Downstream
(undistorted)
b=IO.4m
-5
0) Case CC I: Low Velocity Design
Week Current
z (m)
5
LMZ:
5=45
h =0.60m
b = 8.0 m
-
0.25m/s
-
o
'5 t x(m)
22
10
z(m)
(ii>
y (m)
Cross- section at
impingement
-5
b) Cose CC2: Low Velocity Design
String Current
Figure 3-11. ea... CC1 and CC2: Negatively Buoyam Discharge from Single Port; Low exit Velocity Design under a) Weak and
b) Stronger Amblem Current.
3.4.3 Case CC2: LON Discharge Velocity
Design, Strong CUn-ent
When the ambient current increases from 0.1 m/s to
0.25 m/s the downstream buoyant jet deflection is
accentuated while the upstream buoyant extension is
minimized. Figure 3-11 b shows CORMIX1 (flow class
NV2) and JF predictions. The discrepancy between
predicted minimum dilutions is further increased (Smin
= 22 versus 140). Such complex three-dimensional'
trajectories represent some of the most severe tests for
model application, and in the absence of detailed ex-
perimental data for such phenomena it is difficult to
favor one model over another.
The upstream intrusion along the bottom is minimal in
the present case (order of 2 m) and the bottom density
current is thicker and less wide. At the LMZ distance
the plume half-width is only 8.0 m with a thickness of
0.60 m and an average dilution of 45.
3.4.4. Case CC3: High Discharge Velocity
Design, Strong CUrrent
In order to maximize near-field dilution a high exit
velocity design (15.2 m/s) is evaluated by halving the
port diameter to 0.05 m. The results are shown in Figure
3-12. When compared to Figure 3-11 b, this shows the
significant effect of increased jet diffusion in the near-
field. The buoyant jet shows much more rapid mixing,
and, consequently, is more liable to advection by the
ambient current. CORMIX1 (flow class NV1) no longer
predicts an upstream intrusion after the more gradual
bottom approach. There are differences in the pre-
dicted jet trajectories, as far as maximum height of rise
and bottom approach are concerned. At the LMZ these
buoyant jets are predicted to be in the water column
without any bottom contact yet. The minimum dilution
values are Smin = 247 for JF and 119 for CORMIX1,
respectively. The comparison between Figure 3-11 b
and 3-12 illustrates how LMZ constraints sometimes
are met in the hydrodynamic near-field and at other
times in the far-field, depending on the interplay of
ambient and discharge conditions.
3-9
Draft of 9/21/90
-------
Z (m)
-
0.25 m/s
-
t40
Smin=580
z(m)
( i) Side View (distorted)
60 t
Smln=570
100
x(m)
(ii) View Looking Downstream
(undistorted)
y (m)
Case CC3: High Velocity Design
Strong Current
-20
FIgure 3-12. ease CC3: NegatIvely Buoyant DIscharges from SIngle Port; HIgh ExIt Velocity DesIgn with Strong Ambient Current.
3.5 Case DD Multipart Diffusers: Cooling
Water Discharge into Shallow Sound
3.5.1 Ambient and Discharge Conditions
A once-through cooling water system for a thermal-
electric power plant discharges the heated cooling
water through a submerged multi port diffuser. At a
distance of 500 m offshore, a shallow relatively flat area
exists with an ambient water depth of 10.3 m.
The water is unstratified with an average temperature
of 200C and ocean salinity. The velocity field is tidal
ranging from slack tide (0.0 m/s) to weak velocities
(about 0.1 m/s) to a maximum velocity (0.5 m/s). The
cooling water flow rate is 67 m3/s with a discharge
temperature rise of 20.50C above ambient and the
same salinity.
A staged diffuse~ design of 260 m length is proposed
with a perpe~lcular alignment relative to the tidal
currents. The diffuser consists of 32 ports with a port
Draft of 9/21/90
height of 0.5 m, port diameter of 0.6 m and a vertical
angle of 200 above horizontal.
No LMZ is specified. Rather, the predictive results are
to be interpreted so as to make an LMZ proposal to the
state regulatory authority.
3.5.2 C2se DD1: Weak Tidal Current
None of the USEPA diffuser models are applicable for
such shallow water diffusers with strong momentum
flux and unstable near-field mixing. If they were used,
UOUTPLM and UDKHDEN would predict vertical
plume width far in excess of the available water depth.
UUNE, on the other hand, is limited to pure plume
discharges without any directed discharge momentum
flux.
Thus, reliable predictions are limited to CORMIX2 as
shown in the plan view of Figure 3-13. For this case of
a weak current, CORMIX2 (flow class MUS) indicates
an initially, vertically fully mixed diffuser plume. The
plume gets gradually deflected by the weak crossflow
3-10
-------
ylm)
1500
1000
0.1 mls
Plan View
...... Plume restratificatian
2.7.C fully mi..ed
500
..1m)
1000
CaM 001: Weak' Tidal Current 10.1 mlsl
Figure 3-13. Case DD1: Staged Muhlport Diffuser for Cooling
W8ter Discharge; CORMIX2 Predictions for
Weak Tidal Current. .
and begins to re-stratify ~ift off the bottom) after a
distance. Gradual, lateral spreading and vertical thin-
ning of the diffuser plume takes place. The induced
temperature rise is 2.70C in the near-field and drops to
1.00C at a distance of about 1500 m. (Any potential
heat loss to the atmosphere is neglected in these
conservative mixing predictions).
Figure 3-13 illustrates vividly the strong effect of the
directed momentum flux from shallow multi port diffus-
ers and the ability to induce currents over considerable
distances.
3.5.3 Case 002: Slack Tide
Stagnant ambient conditions always represent a limit-
ing case for any mixing analysis. Since there is no
ambient advective mechanism they are always associ-
ated with an unsteady flow field and mixing process,
including potential large scale recirculation effects.
The CORMIX2 (flow class MUS) predictions are given
in Figure 3-14 for unsteady conditions. The plume is
now undeflected, but has similar mixing characteristics
as the slightly deflected plume of Case 001. However,
at some distance (about 680 m) the predictions are
terminated since the induced plume velocities have
become negligibly small so that a transient recirculat-
y(m)
1000
Plan View
Distance to unsteady
recirculation
CORMIX2
Stagnant
2.7.C fully mhted
500
1000
x(m)
Case 002: Slack Tide
Figure 3-14. Case DD2: Staged Muhlport Diffuser for Cooling
Water Discharge; CORMIX2 Prediction. for
Slack Tidal Condhlon..
ylm)
1000
Plan View
500
0.5m/s
101m)
Case 003: Strong TIdal Current 10.5 mlsl
Figure 3-15. Case DD3: Staged Muhlport Diffuser for Cooling
W8ter Discharge; CORMIX2 Predictions for
Strong Tidal Current.
ingflowwould be set up. Corresponding messages are
printed out by the expert system along with the advice
to conduct predictions for stagnant ambients only as
a special limiting condition.
3.5.4 Case 0D3: Strong Tidal Current
The effect of a strong tidal current (0.5 m/s) is to
generate a strongly deflected diffuser plume (Figure
3-15) as predicted by CORMIX2 (flow class MU6). A
rapid deflection and greatly increased mixing take
place within the diffuser vicinity. The re-stratifying
3-11
Draft of 9/21/90
-------
plume is then advected by the ambient current and
grows in width and diminishes in vertical thickness, in
form of a surface buoyant spreading process.
In summary, the great variability among diffuser plume
patterns (Figure 3-13, 3-14, and 3-15) suggests that a
complete assessment of initial mixing processes
should, indeed, include the whole spectrum of ambient
conditions. It is often difficult to define a single ''typical''
design condition for mixing analysis. On the other
hand, a rapid evaluation of several ambient conditions
and of alternative designs is readily possible within the
framework of presently available models.
3.6 References
Doneker, R.L, and G.H. Jirka. 1990. CORMIX1: An
Expert System for Hydrodynamic Mixing Zone Analy-
sis of Conventional and Toxic Submerged Single Port
Discharges. Technical Report, U.S. EPA, Environmen-
tal Research Laboratory, Athens, GA.
Jirka, G.H. 1979. Discussion of "Line Plume and Ocean
Outfall Dispersion" by P.J.W. Roberts, J. ofthe Hydrau-
lics Div., ASCE, Vol. 105, HY 12.
Lee, J.H.W. and P. Neville-Jones. 1987. Initial Dilution
of Horizontal Jet in Crossflow. J. Hydraulic Engrg.,
ASCE, Vol. 113, No.5.
Muellenhoff, W.P., et al. 1985. Initial Mixing Character-
istics of Municipal Ocean Discharges (Vol. 1 &2).
U.S.E.P.A., Environmental Research Laboratory, Nar-
raganSE!tt, R.I.
Roberts, P.J.W. 1977. Dispersion of buoyant waste
discharge from outfall diffusersoffinite length. Rep. No.
KH-R-35. W.M. Keck Lab. of Hydraulics and Water
Resources, California Institute of Technology, Pasa-
dena, CA, 183 pp.
Draft of 9/21/90
3-12
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