United States
Environmental Protection
Agency
Environmental Research
Laboratory
Narragansett Rl 02882
Research and Development
EPA/600/S3-85/073 Mar. 1986
Project Summary
Initial Mixing Characteristics of
Municipal Ocean Discharges
W. P. Muellenhoff, A. M. Soldate, Jr., D. J. Baumgartner, M. D. Schuldt, L. R.
Davis, and W. E. Prick
The full report describes five mathe-
matical models used to examine the
behavior of plumes from submerged
wastewater discharges into waters of
greater density. Volume I contains ana-
lytical descriptions of the solutions and
computer models that provide initial
dilution and geometric characteristics
for a variety of discharge, diffuser, and
receiving water parameters. Guidance
is provided for the range of values within
which the analytical solutions provide
acceptable estimates. Model use is
recommended for conditions beyond
these ranges and for detailed analysis.
All models have the same input data
format. The user may interactively
change one or more effluent and dif-
fuser parameters without reentering
existing ambient data. Any number of
data sets may be stacked, and a sub-
routine will check that selected param-
eters are within prescribed limits. Ex-
ample calculations are provided for each
model and many of the analytical solu-
tions. Complete program listings in
FORTRAN IV—PLUS are provided in
Volume II.
Both volumes are available from the
National Technical Information Service
in hardcopy. The programs listed in
Volume II may also be obtained from
NTIS on a 9-track tape or IBM-PC
compatible diskette. The diskette pro-
grams compile using Microsoft FOR-
TRAN (Version 3.1 or higher) or IBM
Personal Computer Professional FOR-
TRAN (8087 or 80287 chip required).
This Project Summary was developed
by EPA's Environmental Research Lab-
oratory, Narragansett, Rl, to announce
key findings of the research project that
is fully documented in two separate
volumes of the same title (see Project
Report ordering information at back).
Introduction
Initial dilution is considered to be the
rapid turbulent mixing that occurs be-
tween wastewater discharged at depth
and the surrounding seawater resulting
from jet velocity at the point of release,
driven by momentum and buoyancy in the
plume relative to the ambient. The under-
standing of this mixing process may be
used to predict the initial dilution that will
occur for a set of diffuser, effluent, and
receiving water conditions. Such predic-
tions are used to optimize the design of
ocean outfalls and to determine the
potential for compliance with receiving
water quality criteria.
The trajectory of a mixing plume and
the extent of initial mixing prior to sur-
facing or subsurface spreading are de-
pendent on a number of parameters.
These include the effluent and ambient
densities, ambient current velocity, dis-
charge angle, and port flow rate, exit
speed, spacing, and configuration. Many
researchers have studied plumes under a
specific set of conditions resulting in
theoretical or empirical relationships for
dilution as a function of distance from the
injection point and trajectory to an equil-
ibrium or trapping level. However, such
relationships for the range of effluent and
receiving water conditions expected in
coastal waters are not currently available
in a single document.
The full report provides approximate
dilution and trajectory equations for sin-
gle and merging forced plumes in both
stagnant and flowing environments that
are unstratified or have a linear density
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gradient. Approaches to solving equations
for non-linear stratifications are also
cited. Complete listings are provided in
Volume II for computer use of the five
mathematical models described in the
full report. By inputting the data according
to a Universal Data Format, the user may
exercise any of the models and can vary
one or more parameters to determine the
resultant changes in dilution and trajec-
tory. The models range from very simple
and applicable to a single port and no
ambient current to relatively complex for
addressing merging plumes in the pres-
ence of currents. All models accept
arbitrary density profiles.
Procedures
General methods are presented for
determining plume initial dilutions and
approaches to defining critical minimum
initial dilution and mixing zones. Plume
modeling parameters are discussed fol-
lowed by analytical solutions for selected
discharges and receiving water condi-
tions, with example calculations. Five
numerical models and the Universal Data
file are briefly described, and numerical
model execution is explained. Required
input parameters are summarized along
with tables of output parameters and a
test run printout for each. The appendices
contain a detailed description of the
Universal Data File and the theoretical
development of average dilution and
height of rise relationships.
Results and Discussion
The characteristics of numerical mod-
els included in the full report are sum-
marized in Table 1. As shown, two models
are valid for individual plumes, two are
able to handle merged plumes as well,
and one approximates a series of closely
spaced ports as a slot discharge. This slot-
approximation model is limited to a
vertical discharge. The current speeds
allowed vary with each model, limited to
zero for UPLUME, constant with depth for
UOUTPLM, and arbitrary as a function of
depth for the remaining models. The
horizontal angle of the current relative to
the longitudinal axis of the diffuser is
limited to 90 degrees in UOUTPLM and
UMERGE, but can be between 45 degrees
and 135 degrees for UDKHDEN, and 0 to
180 degrees with ULINE.
UPLUME considers a buoyant plume
issuing at an arbitrary angle into a
stagnant, stratified environment. Plume
behavior is characterized beyondthe zone
of flow establishment by similarity pro-
files for velocity and concentration. Equa-
tions for mass, momentum, and density
disparity continuity are integrated across
the plume, reducing them to one inde-
pendent variable, arclength along the
plume axis. The model produces flux-
average dilutions and, for one output
option, also gives centerline dilutions.
The program terminates when the vertical
speed is zero, or the surface is reached.
UOUTPLM considers a series of single
plume elements which are followed as
they gain mass due to ambient fluid
entrainment. The model thereby des-
cribes a continuous plume in an ambient
with a single current speed, normal to the
diffuser axis. Density (or temperature and
salinity) are assumed to be average
properties of an element. The sum of
element and entrained mass, horizontal
momentum, and energy are conserved.
The element's radius increases based on
step changes in mass and density. Dilu-
tion is calculated by comparing the initial
and subsequent volumes of an element.
The program terminates execution when
the vertical velocity reaches zero, the
surface is reached, or either length scale
or execution step limits are reached.
UMERGE is a two-dimensional model
that also analyzes a discharge by tracing a
plume element through the course of its
trajectory and dilution. However, it ac-
counts for adjacent plume interference
and accepts arbitrary current speed var-
iations with depth. The current is as-
sumed to be normal to the diffuser axis.
Forced and aspiration entrainment are
handled in much the same way as in
UOUTPLM, except that the relative con-
tributions are adjusted depending on the
magnitude of ambient currents. The
merging equations are based on geo-
metric considerations by distributing the
overlapping mass to other portions of the
plume, calculating the element radius
changes, and adjusting entrainment
terms. After plume properties are calcu-
lated for a given time step, the iteration
process continues until vertical velocity
becomes zero, the surface is reached, or
the maximum number of specified itera-
tions is exceeded.
UDKHDEN is a three-dimensional
model that can be used for either single or
multiple port diffusers. It considers var-
iable profiles through the zone of flow
establishment and through the merging
zone of multiple plumes. Entrainment is
an explicit function dependent on the
local densimetric Froude number, plume
spacing, magnitude of the ambient veloc-
ity, and the difference in plume and
Table 1. Summary of Numerical Model Characteristics
Parameter
Port*
Discharge angle"
Density prof He
Current speed
Current angle
relative to the
diffuser*
UPLUME
single
-5° to 90°
arbitrary
no
n/a
UOUTPLM
single
-5" to 90°
arbitrary
constant with depth
assumes 90°
UMERGE
multiple
-5° to 90°
arbitrary
arbitrary
assumes 90°
UDKHDEN'
multiple
-5° to 130°
arbitrary
arbitrary
45° -135°
ULINE
slot/closely spaced
assumes 90°
arbitrary
arbitrary
0°-180°
'For a single port discharge the current angle may be in the range of 0° to 180°. For an angle greater than 90° the program converts it.to the
supplementary angle. (Note: 0° and 180° give the same results).
"A II the models except ULINE reduce the data to a single port discharge. UPLUME and UOUTPLM detect merging of adjacent plumes and alert the user.
but do not account for this in the remainder of the calculations whereas UMERGE and UDKHDEN do. ULINE converts the data to a slot discharge.
cThe discharge angle limits are those allowed by the subroutines LIMITS in each of the programs. They are not necessarily the theoretical limits
associated with these models. Caution should be exercised when using the models for angles beyond these limits.
a90° is perpendicular to the diffuser. At a discharge angle ofO° (horizontal) and a current angle of 90°, the discharge and the current are parallel and in
the same direction.
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ambient velocity. Similar profiles are
assumed for velocity, concentration, and
temperature, and are superimposed in
their merging zones. The model accepts
an arbitrary ambient velocity profile. The
program is terminated when the surface
is reached, the plume has reached its
maximum height, or error conditions are
detected.
ULINE models a vertical buoyant slot jet
discharge into a flowing ambient. The
model is based on uniform density plume
experiments and is a generalization of
published discussions of dilution achiev-
able in an arbitrarily stratified environ-
ment. The model interpolates the results
of Roberts for an arbitrary current angle.
The program numerically integrates inte-
grals used to determine the average
ambient density over the height of rise,
which is then compared to the plume
density to determine whether the plume
is trapped. Dilution is determined by
integrating the rate change in dilution as
a function of elevation, over the rise
height. The program terminates when the
trapping level is reached or when the
plume surfaces.
Conclusions and
Recommendations
The buoyant-plume phase of waste
dispersion can be described by a variety of
published methods. However, to evaluate
the water quality impacts of municipal
ocean discharges, the methods presented
in the full report are well suited and
recommended for consistency. Some may
be applicable to streams, rivers, and lakes,
although emphasis herein is on ocean
discharges. Application of these models
to these other environments may require
program modifications.
For most cases, either analytical meth-
ods or computer models can be used.
Where there is uncertainty about the
influence of simplifying assumptions, or
where more detail is required, the com-
puter models should be used. For unusual
situations or conditions, other methods
such as physical models should be con-
sidered.
W. P. Muellenhoff, A. M. Soldate, Jr., are with Tetra Tech. Inc., Corvallis, OR; the
EPA authors D. J. Baumgartner fatso the EPA Project Officer, see below), M. D.
Schuldt, L. R. Davis, and W. E. Frick are with the Hatfield Marine Science
Center, Newport, OR.
The complete report consists of two volumes with a tape and diskette, entitled
"Initial Mixing Characteristics of Municipal Ocean Discharges:"
"Volume I. Procedures and Applications," (Order No. PB 86-137 478; Cost:
$16.95)
"Volume II. Computer Programs/'fOrder No. PB 86-137 460; Cost: $16.95);
(Tape; Order No. PB 86-137 494; Cost: $685.00); (Diskette; Order No. PB
86-137 486; Cost: $75.00)
The above reports are available only from: (cost subject to change)
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Pacific Division
Hatfield Marine Science Center Si;
Newport, OR 97365 ||
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Official Business
Penalty for Private Use $300
EPA/600/S3-85/073
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
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