oEPA
United States
Environmental Protection
Agency
I EPA 600/B-24/339 I December 2024 I
www.epa.gov/research
PLUMES2.0 - Dilution Model
Model Theory and User Manual
r- -t t'
Office of Research and Development
Center For Environmental Measurement and Modeling (CEMM)
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PLUMES2.0
Model Theory and User Manual
by
Khangaonkar, TP1,2
Premathilake, LT1,2
Cope, B3
Knightes, C3
Tseng, A3
1 University of Washington, Tacoma, WA
2 Pacific Northwest National Laboratory
3 US Environmental Protection Agency
US EPA Contract No. 68HERC22C0046
December 2024
Prepared for
the US Environmental Protection Agency
by the
Salish Sea Modeling Center
Center for Urban Waters, University of Washington, Tacoma
326 E D St, Tacoma, WA 98421
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Disclaimers
This report was prepared as an account of work sponsored by an agency of the United States
Government. Neither the United States Government nor any agency thereof, nor the Salish Sea
Modeling Center -University of Washington, nor Battelle Memorial Institute, nor any of their employees,
makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy,
completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents
that its use would not infringe privately owned rights. Reference herein to any specific commercial
product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily
constitute endorsement, recommendation, or favoring by the United States Government or any agency
thereof, or the Salish Sea Modeling Center - University of Washington, or the Battelle Memorial
Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of
the United States Government or any agency thereof, or the University of Washington.
This document has been reviewed by the U.S. Environmental Protection Agency,
Office of Research and Development's peer and administrative review policies and approved for
publication. Mention of trade names or commercial products does not constitute endorsement or
recommendation for use by the US EPA. Contractor's role did not include establishing Agency policy.
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Table of Contents
Disclaimers ii
List of Tables iv
List of Figures iv
Acknowledgments v
Acronyms and Abbreviations vi
1 Executive Summary 1
2 Introduction 2
2.1 Background 2
2.2 Brief History and Overview of Dilution Models 3
3 Theory and Model Formulation 6
3.1 Approach and Conceptual Framework 6
3.2 Model Architecture 7
3.3 Model Derivation 8
3.3.1 Nearfield Dilution 8
3.3.2 Farfield Dilution 11
4 PLUMES2.0 User Instructions 15
4.1 Download and Installation 15
4.2 PLUMES2.0 User Interface 15
4.2.1 Project set up 15
4.2.2 Diffuser characteristics 16
4.2.3 Effluent characteristics 19
4.2.4 Ambient characteristics 21
4.2.5 Model Run 23
4.2.6 Model Results 25
4.2.7 Independent Farfield Calculation 29
5 Summary and Discussion 32
6 References 33
Appendices 36
Appendix A: Quality Assurance 36
A.l. Quality Assurance Project Plan 36
A.2. Quality Assurance Audit 36
A.3. Data Quality Summary 36
Appendix B: PLUMES2.0 Model Validation and Testing 37
B.l Nearfield Dilution 37
B.2 Farfield Dilution 41
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List of Tables
Table 1: Variation of Width of Wastefield with Distance 13
Table 2: The analytically-derived concentrations at the center of the wastefield (Brooks, 1960) 14
List of Figures
Figure 1: Schematic representation of the conceptual model for a typical buoyant effluent discharge 6
Figure 2: Schematic representation of the model architecture 7
Figure 3: Lagrangian Control Volume representation (Premathilake and Khangaonkar, 2019) 9
Figure 4: Typical merging model for a vertically released effluent discharges 10
Figure 5: Schematic representation a typical farfield plume growth under steady conditions 13
Figure 6: Schematic representation of outfall pipe and definition of diffuser parameters 18
Figure 7: Diffuser tab populated with example diffuser configuration 19
Figure 8: Effluent tab populated with example effluent characteristics 20
Figure 9: Schematic representation of ambient cross section near an outfall diffuser 22
Figure 10: Ambient tab populated with example receiving water characteristics 23
Figure 11: Model Run tab populated with example/default settings 24
Figure 12: Example of ascii text format output from PLUMES2.0 28
Figure 13: Example of plume trajectory in Depth-x plane until the termination of initial dilution phase..29
Figure 14: Example of Farfield plume trajectory in -x direction 31
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Acknowledgments
This work was jointly initiated and led by Tarang Khangaonkar of University of Washington's
Salish Sea Modeling Center (SSMC) and Ben Cope of US EPA. Lakshitha Premathilake from SSMC was
responsible for the development and testing of PLUMES2.0 software and the Fortran version of UM3
code. Chris Knightes and Antony Tseng from US EPA provided technical oversight and project
management support. The scope of PLUMES2.0 in this first phase of development is limited to the UM3
nearfield and Brooks farfield models.
We would like thank peer reviewers - Dr. Anise Ahmed, Washington State Department of
Ecology; Chris Beegan, from California State Water Resources Control Board; Matthew Reusswig, ERG
Environmental Services; and Amy King, US EPA for conducting a hands-on review of the PLUMES2.0 user
interface and model performance. The comments provided allowed us to catch the errors and glitches
which were addressed prior to this release.
Dr. Walter Frick of US EPA (retired), the developer of Visual Plumes, kindly provided us the UM3
coded written in Pascal, which provided the foundation for developing the Fortran version of UM3
implemented in the PLUMES2.0 code.
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Acronyms and Abbreviations
AMZ Acute Mixing Zone
CORMIX A dilution model originally developed by Cornell University with EPA support
CMZ Chronic Mixing Zone
CSTR Continuously stirred tank reactor
DKHW A multiport dilution model in the VP package based on original technical
developments by Davis, Kannberg, and Hirst in the 1970s (Windows based)
FRFIELD Farfield dilution model in the VP package based on Brooks' Laws
FVCOM Finite Volume Community Ocean Model - a 3D hydrodynamic model
FVCOM-ICM Salish Sea Model biogeochemical component based on CE-QUAL-ICM
GUI Graphical User Interface
JETLAG A Lagrangian dilution model of Lee et. al., from the University of Hong Kong
LCV Lagrangian Control Volume
NPDES National Pollution Discharge Elimination System
NRFIELD Roberts, Snyder, and Baumgartner (RSB) dilution model in VP package
ORD Office of Research and Development
PDSW Prych, Davis, and Shirazi 3D plume model for Windows in VP package with the ability
to accommodate surface discharge.
PLUMES US EPA recommended package of dilution models for effluent discharges.
QA Quality assurance
QAPP Quality Assurance Project Plan
QC Quality control
RMZ Regulatory Mixing Zone
SI International System of Units
SSMC The Salish Sea Modeling Center at University of Washington
UM3 Three-dimensional version of UMERGE model which is part of the VP package
UMERGE A two-dimensional effluent dilution model with plume merging
US EPA United States Environmental Protection Agency
VP Visual Plumes
ZID Zone of Initial Dilution for a typical effluent plume
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1 Executive Summary
The ability to conduct effluent fate and transport using standalone public domain software with a
graphical user interface (GUI) is a core need of the National Pollutant Discharge Elimination System
(NPDES) program. Visual Plumes (Frick et al., 2004) was a Windows and Pascal based computer
application that provided tools for analysis of effluent fate and transport. Visual Plumes had superseded
the DOS and Fortran based PLUMES (Baumgartner, Frick, and Roberts, 1994) mixing zone modeling
system. Visual Plumes simulated single and merging submerged plumes in arbitrarily stratified ambient
flow from buoyant submerged as well as surface discharges. Among its features were multiple dilution
models, tidal pollutant build-up estimation, a sensitivity analysis capability, and a multi-stressor
pathogen decay model. Visual Plumes offered a suite of dilution models including DKHW and UM3
models that are based on the original UDKHDEN and UM models (Muellenhoff et al., 1985), the surface
discharge model PDS (Davis, 1999), the NRFIELD model based on RSB (Roberts et al., 1989 a,b,c) and the
passive farfield transport and dilution of the wastefield using Brooks' laws (Brooks, N.H., 1969). The
most widely used sub-model by default was UM3. Walter E. Frick, formerly from the US Environmental
Protection Agency (US EPA) Office of Research and Development (ORD), was the last lead on Visual
Plumes. Dr. Frick has since retired, and the Visual Plumes software became incompatible with the
current version of the Windows operating system.
As part of unrelated US EPA funded research at the Pacific Northwest National Laboratory and
Salish Sea Modeling Center (SSMC) at the University of Washington, a three-dimensional Lagrangian
approach-based plume model (FVCOM-plume) was developed (Premathilake and Khangaonkar, 2019).
The FVCOM-plume model written in Fortran includes an initial dilution module based on UM3
formulation. That imbedded initial dilution module accommodates multiport diffusers and its
performance has been confirmed against Visual Plumes (UM3).
Subsequently, the US EPA, in collaboration with SSMC scientists, initiated this effort towards
developing updated model software for simulating dilution of effluent from submerged outfalls. The
overall goal was to develop, test, and release the new version of dilution modeling software (renamed
PLUMES2.0) along with a User's Manual to US EPA and the user community for distribution. This release
and the User's Manual represent the completion of Phase 1 of the development and testing of the
software. Additional features and models may be added in subsequent phases based on user community
response and needs. In PLUMES2.0, the initial dilution of the effluent, consisting of jet and buoyancy
induced dynamic mixing of the effluent plume in the nearfield, is computed using the UM3
methodology. PLUMES2.0 then allows for analysis of plume fate following stabilization of the wastefield
at the trapping depth when it is carried away by the ambient currents and further diluted by turbulence.
This farfield transport of the wastefield and dilution is computed using Brooks laws (Brooks, N.H., 1969).
Specifically, PLUMES2.0 includes (a) UM3 - initial dilution model, (b) Brook's Farfield model, and (c) a
graphical user interface (GUI). The associated Model Theory and User Manual (this document) provides
basic theory of effluent mixing and dilution principles, concept of mixing zones, and guidance for model
use which may range from NPDES permitting to wastewater outfall diffuser design. The document
includes step-by-step instructions for setting up the input files and is suitable for new users. We expect
that experienced Plume modelers will be able to navigate the menus directly based on prior familiarity
with Visual Plumes.
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2 Introduction
2.1 Background
Wastewater from industrial and municipal facilities may contain pollutants that pose an
ecological and/or human health risk. In recognition of the fact that natural mixing causes the
concentration of pollutants to diminish in the receiving waters, regulatory agencies allow mixing zones
in evaluating water quality compliance and exposure risk. A mixing zone is defined as a small region near
the outfall where certain water-quality criteria can be exceeded as long as (a) there is no lethality to the
organisms passing through the mixing zone, (b) there are no significant risks to human health, and (c)
the designated and existing uses of the water body are not impaired (US EPA, 1991). Effluent discharges
and mixing zones are authorized through the Clean Water Act: Section 402 (40 CFR Part 122) National
Pollution Elimination System (NPDES) Permits. Water quality compliance for carcinogens and highly toxic
substances is typically evaluated at the end of pipe. But for many pollutants, compliance is evaluated at
the mixing zone boundaries after the completion of initial rapid mixing and dilution of the effluent with
the surrounding waters. The allowable dimensions of mixing zones vary from state to state based on
requirements in state water quality standards.
When two fluids carrying the same constituent but at different concentrations mix, the resultant
concentration of the mixture is simply the volume averaged concentration. For example, if a
concentrated effluent volume Ve (m3) at a concentration Ce (mg/L) is mixed with a volume Va of clean
water, the resulting concentration C/ after mixing may be simply expressed as Cf = Ce /D, where D is
the volumetric dilution factor expressed as D = (Ve + V^/Vg assuming that the ambient concentration
Ca is zero. The effluent concentration after mixing is therefore regarded as being reduced by the dilution
factor.
In realistic settings however, the ambient concentration is rarely zero. It must be accounted for
to assess compliance with regulations. To do so, the concentration of the effluent constituent of concern
is compared against the applicable water quality standard(s) Cwqs, after the completion of the dilution
process within the allocated mixing zone. The constituent concentration in the water outside the mixing
zone must remain below Cwqs. Water quality standards for protection of aquatic life are defined based
on acute and chronic effects based on duration of exposure. Aquatic organisms can endure exposure to
higher concentrations or acute exposure for a short duration of time (e.g., 1 hr). Under chronic exposure
(e.g., 96 hrs), lower concentrations can cause ecological impacts. Depending on the applicable water
quality regulations, there may be two mixing zone boundaries to consider - (a) Acute Mixing Zone (AMZ)
and (b) the Chronic Mixing Zone (CMZ), also known as the Regulatory Mixing Zone (RMZ). Dimensions of
these mixing zones vary based on site specific conditions and are explicitly defined in the NPDES permit
for the discharge. The estimation of effluent dilution over time and space is necessary for the application
of a mixing zone in permit limit derivations and/or the design of an outfall structure/location to achieve
a target dilution.
The effluent concentrations following dilution and mixing may be computed using the simple
equation below.
(1)
Where Cf = Final concentration (mg/L) of the effluent after dilution and mixing with the
ambient water,
Ce = Effluent concentration (mg/L) of the discharge or end-of-pipe concentration,
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Ca = Ambient receiving water concentration (mg/L) outside of the influence of the
effluent discharge, and
D = Volumetric dilution factor.
In a continuously stirred tank reactor (CSTR) laboratory setting with a known volume(s) the
dilution factor D may be estimated in a straightforward manner as the ratio of total volume of the mixed
fluid in the reactor to the effluent volume added. In a CSTR, the volumes are fixed and mixing of the two
fluids and diffusion process is assumed to have reached completion. In a realistic setting however,
computing the volumes of the respective fluids and extent of diffusion is complex and requires the
assistance of numerical models or physical dye studies. The process of mixing and dilution itself occurs in
the timescale order of minutes and often reaches a steady state within a short distance from the outfall.
It is dependent on multiple physical parameters controlled by effluent characteristics such as flow rate,
effluent density, outfall port/diffuser dimensions and depth, and receiving water stratification and
currents. Upon exiting the outfall, the effluent undergoes rapid mixing due to nearfield momentum (jet)
and buoyancy effects. Following this initial dilution, the plume stabilizes at the surface or at a neutrally
buoyant trapping depth. The wastefield is then carried away by ambient currents over a longer
timescale. The dilution continues to increase gradually during this farfield passive mixing phase from
natural turbulence and currents further reducing the concentration of the effluent in the plume.
Concentrations and dilution vary throughout the plume downstream of the discharge point.
Accurate determination of D at the specified mixing zone boundary (or C/ in the plume and at
the specified mixing zone location) becomes an important requirement for various regulatory needs
such as (a) Reasonable Potential Analysis - to evaluate if a constituent detected in effluent has a
reasonable potential to exceed water quality criteria, (b) Assessment of compliance with applicable
water quality standard based on discharge monitoring data, and (c) computation of Water Quality-based
Effluent Limitations (WQBELs). Similarly, the design of diffusers and siting of outfalls for existing or new
discharges requires iterative dilution ratio computations as part of feasibility and final design. These
assessments require a predictive dilution model.
2.2 Brief History and Overview of Dilution Models
Development of mathematical models to predict mixing and dilution of effluent from
wastewater outfalls dates back to early 1950s. Researchers applied principles of continuity, momentum,
and energy conservation, integrated using Gaussian principles to study the spreading of buoyant plumes
in uniform and stratified but stagnant environments (Rouse et al., 1952; Priestly and Ball, 1955).
Numerous studies improved on this early work through the addition of concepts, such as an
entrainment function based on local length scales (Morton etal., 1956), port orientation effects
(Abraham, 1963; Fan, 1967), and effects of ambient currents and cross flow (Chu, 1979; Wright, 1984).
Studies of plumes from multi-port diffusers have included line diffusers (fully merged plumes) in
stagnant ambient waters (Pearson, 1956), and experimental laboratory work on merging of plumes
(Liseth, 1970, 1976). Subsequently in the 1970s several mathematical models were proposed to simulate
buoyant plume discharges varying from single to multiport diffusers, and, mixing in uniform confined
environments to stratified flowing conditions (Koh and Fan, 1970; Cederwall, 1971; Sotil, 1971;
Kannberg and Davis, 1977; Roberts, 1977; Roberts, 1979 a,b). By the early 1980s, there were numerous
mathematical models available from various researchers, each specializing in different aspects of the
plume dilution phenomena. Although multiple literature review papers had been published by then
(Davis and Shirazi, 1978; Roberts, P.J.W., 1983, 1984, 1985), consolidation of the existing research and
models into practical tools along with clear instructions on their use in practice for outfall design or for
regulatory analysis did not exist until the mid-1980s.
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The need for such guidance became more urgent when US EPA adopted regulations
implementing Section 301(h) of the Clean Water Act (PL 97-117) (US EPA, 1982). Under these rules,
publicly owned municipal wastewater could be discharged using treatment levels less effective than
secondary treatment, after demonstrating compliance with water quality standards at the prescribed
"zone of rapid mixing" or the zone of initial dilution (ZID). The demonstrations of environmental
acceptability by the NPDES applicants and review by the permit writers required the use of plume
models. To ensure consistency in the use of available tools, and quality assurance, EPA provided
procedures for calculating the initial dilution and for describing the zone of initial dilution near a
discharge site, using five leading dilution models (Muellenhoff et al. 1985). The models were UPLUME,
UOUTPLM, UMERGE, UDKHDEN, and ULINE, based on prior work by Teeter and Baumgartner (1979) and
Roberts (1977, 1979b). These were codes written in Fortran with differences in their computational
approaches but utilized a universal input file format and structure that offered users consistency in input
parameters (effluent, diffuser, and receiving water characteristics) and results (plume characteristics
including location, size, and flux averaged plume dilution as a function of distance from the outfall).
These estimates were based on a Gaussian distribution of concentrations within a plume cross section.
The computations stopped at the completion of initial rapid mixing phase, typically after the plume
reached the surface or stabilized at a neutrally buoyant trapping depth, thereby defining the ZID.
Most plume models use simplifying assumptions in defining the discharge configuration and the
mixing processes (e.g., Gaussian distribution of plume concentration across the plume width, diffusers
with simple geometries, and domains with no bounding constraints). In realistic settings, the plume
behavior may be affected by boundary effects (bottom or bank attachment, plume stability), and
complex diffuser geometries such that simplifying assumptions in plume models may no longer be valid.
Dye studies or laboratory studies involving hydraulic scale models with precise representation of the
site-specific conditions may be needed to accurately estimate the initial dilution process. With an
emphasis on the importance of boundary interactions on the stability of the plume and mixing
processes, Cornell University with support from US EPA developed the CORMIX model. CORMIX consists
of a series of software systems for the analysis, prediction, and design of discharges with emphasis on
the role of boundary interaction to predict steady state mixing behavior and plume geometry. It
classifies momentum and buoyancy of the discharge in relation to boundary interactions to predict
mixing behavior. Boundary interactions can be surface or bottom contact or terminal layer formation in
density stratified ambient waters. CORMIX was released as a knowledge and inference based expert
system package consisting of CORMIX1 (Doneker and Jirka, 1990) for single port discharges, CORMIX2
(Akar and Jirka, 1992) for multiport diffusers, and subsequently CORMIX3 (Jones et al., 1996) for surface
discharges.
In 1991, US EPA issued technical guidance for assessing and regulating discharge of toxic
substances to the waters of the United States in NPDES permits. This Technical Support Document for
Water Quality Based Toxics Control (US EPA 1991) was comprehensive and included language about
regulatory mixing zones. The guidance was then adopted by various states to develop their own
standard procedures for conducting Mixing Zone Studies including the use of dilution models for
conducting water quality compliance evaluations. In response to a growing demand and adapting to PC
based computing platforms, US EPA released DOS Plumes (Baumgartner et al., 1994) which only
included the UM model, an updated version of UMERGE, and RSB, an updated version of ULINE based
on experimental studies on multiple T shaped port diffusers (Roberts et al. 1989 a,b,c). DOS Plumes
also incorporated the flow classification scheme of the CORMIX model (Jirka and Hinton, 1992), with
recommendations for model usage. DOS Plumes and CORMIX then became the two US EPA-supported
models for dilution modeling and mixing zone analyses.
DOS Plumes was subsequently upgraded to Visual Plumes (Frick et al., 2004), a Windows-based
application that included graphics, time-series input files, user specified units, a conservative tidal
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background-pollutant build-up capability, a sensitivity analysis capability, and a multi-stressor pathogen
decay model that predicts coliform mortality based on temperature, salinity, solar insolation, and water
column light absorption. It also included DKHW model that is based on UDKHDEN (Muellenhoff et al.,
1985), the surface discharge model PDS (Davis, 1998), the three-dimensional UM3 model based on UM,
and the NRFIELD model based on RSB. Visual Plumes was distributed by US EPA. Similarly, the DOS-
based CORMIX suite of models were upgraded to a Windows-based application, licensed and distributed
by MixZon, Inc. For nearly 15 years since their release, Visual Plumes and CORMIX were the two leading
modeling systems that were used extensively by the community for outfall design, siting studies, and
mixing zone analyses. Following the release of Windows 10, however, Visual Plumes lost its
compatibility with the PC operating system. The community has since primarily relied on CORMIX as the
only model readily available to the plume modeling community. The PLUMES2.0 project provides
renewed access to key sub-models of the Visual Plumes model suite.
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3 Theory and Model Formulation
3.1 Approach and Conceptual Framework
PLUMES2.0 directly adopts the analytical modeling framework that was used in the UM3 model.
UM3 in turn is based on the most recent and established theoretical treatment of effluent plumes
developed over several decades of research described in Section 1.2 (e.g., Akar and Jirka, 1991;
Baumgartner et al., 1994; Brooks, 1960; Fan, 1967; Fischer et al., 1979; Muellenhoff et al., 1985). The
conceptual model of a buoyant effluent plume consists of three phases or regimes of physical mixing of
two fluids, as shown in Figure 1. The plume dynamics in the immediate vicinity of the diffuser are
controlled by jet mixing where effluent is discharged to the ambient waterbody under hydraulic
pressure. The jet mixing occurs through momentum flux and turbulent shear accompanied by a drop in
pressure. This is followed by a buoyancy-induced transition phase including interaction with ambient
currents. The final phase is the farfield passive transport phase where stabilized wastefield is carried
away by ambient currents and further mixed with surrounding waters through spreading due to
combination of remnant buoyancy and natural turbulence in the receiving water.
Figure 1: Schematic representation of the conceptual model for a typical buoyant effluent discharge.
Within a short distance from the ports, the flow entrains fluid and transitions from a jet to a
plume. The buoyancy effects take over causing the plume to rise in the water column. As the plume
ascends, it further entrains ambient water, diluting it and decreasing the plume buoyancy. When the
buoyant plume is in a stratified water column, it stabilizes at a depth where its density approaches that
of the surrounding water (the neutral buoyancy depth), trapping the plume below the water surface
(also referred to as the trapping depth). In unstratified conditions, the plume often reaches the water's
surface without being trapped. This region from the diffuser port to the stabilized wastefield is referred
to as the zone of initial dilution (ZID) in secondary treatment regulations, or the region of rapid initial
mixing in the scientific literature (Baumgartner et al., 1994; Roberts, 1990). For well-designed outfalls,
the jet mixing is highly energetic near the outfall, resulting in rapid mixing and reduction in pollutant
concentrations within the plume. The completion of the initial dilution phase, including jet and
Outfall di1
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buoyancy effects, is typically constrained to a spatial scale of 10-1000 meters (m) and occurs over time
scales of 1-10 minutes. After the initial dilution is complete, the effluent is spread by ambient currents
and diffusion by natural turbulence. The farfield mixing phase is governed by advection-diffusion and
occurs over a much larger spatial scale of 100-10,000 m and time scales of 1-20 hours (Roberts, 1990).
3.2 Model Architecture
PLUMES2.0 follows the Visual Plumes approach to capture the nearfield plume characteristics
while providing the option to continue the computations to farfield transport within a common
computational framework. To facilitate this, the initial dilution component of PLUMES2.0 uses the
Lagrangian Control Volume (LCV) method, as in the UM3 model (Baumgartner et al., 1994), including the
entrainment and integrated features of plume merging. The farfield computations are conducted using
the Brooks (1968) principles.
The architecture of PLUMES2.0 is also based on the mathematical and numerical approaches
that were implemented in the UM3 model in Pascal code. In PLUMES2.0, each phase of the conceptual
model was developed independently in Fortran 90 and includes the transfer of data from one phase to
the next phase. Figure 2 shows a high-level representation of mode! design with data flow between
different phases and processes. The model requires input related to (a) discharge characteristics such as
diffuser layout, port orientation, diameter, flow rates, and (b) receiving water characteristics such as
ambient stratification (temperature and salinity) and current velocity profile data. The jet/plume phase
is numerically simulated using the LCV method. Upon the completion of nearfield computations, major
plume parameters (i.e., plume diameter and dilutions) are revised/adjusted to match the wastefield
dimensions (total width) during the transition stage prior to initiation of farfield calculations.
Figure 2: Schematic representation of the model architecture.
PLUMES2.0 was developed using Fortran 90 standards. Building and testing were conducted
using Intel Fortran compilers. For the graphical user interface (GUI) development, several options were
explored. Typical graphic libraries, application programming interfaces (APIs), and other tools are based
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on C++, Python, and Java. Using such tools for GUI development creates coupling challenges with
Fortran. To avoid the complexities and incompatibilities associated with coupling multiple programing
languages, a Fortran 90 based GUI toolset was selected for the PLUMES2.0 GUI development. The
commercially distributed third-party application - Winteracter (https://www.winteracter.com/)
provided Fortran-based GUI libraries and development toolset for this effort.
3.3 Model Derivation
3.3.1 Nearfield Dilution
The plume behavior in the nearfield is simulated using the LCV method, adopting the approach
that has been used previously in models such as UM3 and JETLAG (Baumgartner et al., 1994; Lee and
Cheung, 1990). In the LCV method, the physical properties (i.e., velocities, concentration, salinity, etc.)
of an LCV over a cross-section are assumed to be distributed uniformly using a Top-Hat profile structure.
In other words, all properties at a specific plume cross-section are uniformly distributed and drop
sharply to ambient values outside of the plume boundary. Figure 3 shows a schematic representation of
selected LCVs of the plume, and the numerical integration of all LCVs produces the expected plume
structure for the nearfield. The kinematic equations of the plume dynamics are derived by applying basic
governing equations to each LCV of the plume. The continuity equation (Equation 2) describes the
change in liquid mass in the LCV (dm) during a small-time increment (dt) is equal to the net ambient
liquid entrainment. Total ambient entrainment is computed as the summation of forced entrainment
and Taylor-induced entrainment (shear entrainment).
dm
= ~PaAp- ua + PaAjpT
In Equation 2, pa is the density of the ambient liquid Ap is the projected area vector for forced
entrainment computation while Ua is the ambient velocity vector (vector variables indicated in bold).
At is the area of the LCV in contact with ambient fluid for Taylor entrainment and wraps completely
around the element is not expressed as a vector and computed as an area of a cylindrical element
assuming an infinitesimal thickness of Lagrangian element (Baumgartner et al., 1994). /?T is the Taylor
aspiration velocity, which can be defined as pT = a\uj\ , where a is the Taylor entrainment coefficient
and Uj is the average plume velocity of the LCV. Ap lies in a vertical plane containing the velocity vector
and points upstream out of the element. Ap and Uj point in opposite directions so that their dot
product is negative. To estimate the projected area, it is necessary to express mathematically how the
length of the element changes in response to changes in other plume properties. Further details on the
mathematical estimation of Ap can be found in Frick (1984) and Frick et al. (1995).
Equation 3 represents the change of momentum in an LCV due to the momentum passed by the
entrained ambient mass and the momentum induced by the buoyancy force acting on the LCV.
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Lagrangian Control
Volume (LCV)
UJ
Figure 3: Lagrangian Control Volume representation (Premathilake and Khangaonkar, 2019).
Because the physical properties at the outer surface of the LCV are assumed to match the
properties of ambient fluid, the drag force acting on the LCV is assumed to be zero, which is consistent
with the approach of Baumgartner et al. (1994).
d(.mUj) „ dm (pa ~ Pj)
—dr = u^-m—^—9
(3)
In Equation 3, g is the gravitational vector and pj is the plume density of the LCV, which is a function of
plume temperature and salinity. The plume temperature can be determined by applying the
conservation of energy equation considering the heat exchange between the LCV and the ambient fluid.
A simplified version of the energy equation has been used to compute the plume temperature in the
dynamic phase of the plume, which is given by Equation 4,
d(m7})
dt
= T
1 n
dm
dt
(4)
where Tj and Ta denote the average plume temperature and temperature of ambient liquid,
respectively. Equation 4 was derived by assuming temporally constant specific heat at constant
pressure, which is consistent with the approach followed in UM3 model formulation. Similarly,
conservation of salinity is shown in Equation 5, in which Sj and Sa are the average salinity of the LCV and
ambient salinity, respectively.
d(mSj) dm
~dtT =Sa~dt
(5)
Both ambient and plume densities are computed from the equation of state for the sea water density
(Sigma-t function) (Fofonoff, 1985). Numerical integration of the equations from Equation 2 to 5
generates the spatial and temporal variation of the buoyant jet/plume properties.
To enhance rapid mixing and dilution of the effluent within the mixing zone, rather than
releasing the effluent through an open-ended pipe, many outfall pipes include a diffuser section. The
diffuser section of a typical ocean outfall is usually the most seaward section. The outfall pipe flow is
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blocked off with an end-flange, and the effluent is released through a series of ports. The ports may be
simple holes directly on the outfall pipe, or they may be designed with riser pipes normal to the diffuser
axis. The ports may be fitted with nozzles with a port diameter that is relatively small and oriented at
specific vertical angles, allowing the effluent to exit the outfall as a strong jet resulting in rapid
entrainment and mixing. When the effluent is released from multiple ports, the individual plumes often
merge with each other as the plumes rise in the water column, thereby affecting the individual plume
dynamics. A schematic of a typical effluent plume from a multiport diffuser with plume merging is
shown in Figure 4. Specifically, the merging processes affect the entrainment mechanism significantly as
the individual plume area is reduced. This also results in a loss of dilution efficiency.
The merging of plumes causes a reduction in the effective plume area due to overlapping plume
sections. The reduction in plume area reduces the overall entrainment causing changes to plume
dynamics. Implementation of plume merging processes requires specific factors in the computation of
the effective entrainment area. Figure 4 shows the reduction of plume areas in the overlapping plume
sections. The mathematical formulation of UM3 introduced a geometry-based correction to calculate
the entrainment area of merged plumes (Baumgartner et al., 1994). The same approach is adopted in
the mathematical model of PLUMES2.0.
The model development presented above is based on average motion of the plume element
with properties averaged over the element. The plume trajectory is traced by the center-of-mass of the
plume element. The plume element expands with time as it moves away from the source, affected by
buoyancy and entrainment of ambient water, with widely varying properties in between the element
boundaries. The concentration of the effluent mass averaged over the Lagrangian element (Cave) is
computed by the model in each step based on volume of water entrained in the element. The
assumption is that the effluent mass in the Lagrangian element at each time step remains constant. Of
importance is the calculation of difference in concentration between the plume and the ambient (Cave-
Ca), where Ca is the ambient concentration. Dilution in the plume relative to initial effluent
concentration at the end-of-the pipe Ce is given by D = (Ce — Ca)/(Cave — Ca), as in Equation 1 after
rearranging the terms. Here, Cave computed by the model in each model step replaces Cf at the end of
initial dilution process (in Equation 1).
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In the model, the concentrations are assumed to be distributed over the cross section of the
plume element following the 3/2 power profile (Kannberg and Davis, 1976), which closely matches a
Gaussian profile but is constrained to the plume geometry. The 3/2 power profile is expressed by the
following:
where, as described in Baumgartner et al. (1994), ® is an instantaneous scaling factor relating difference
between the plume and the ambient of any appropriate property, such as the concentration of some
pollutant or velocity, b is the plume radius, and r is the distance from the center of the plume to the
point within the plume at which ®\s measured. In other words, C/rJ=Cmax(Z>. This distribution ensures
that the maximum concentration is at r = 0, at the plume element centerline and approaches 0 for r = b
at the radial plume boundary.
The average concentration, Cave, provided by the model may also be expressed as flux-averaged
concentration.
f C ¦ v ¦ dA
where C and v are the instantaneous concentration and velocity in the plume element at a radial
location r distance from the centerline, A is the cross-sectional area, and dA is the corresponding
infinitesimal area. For large dilutions and currents, the velocity may be approximated to follow a top-hat
distribution and assumed constant. This simplification along with 3/2 profile for concentrations
(substituting C with Cmax(Z>) can be used to derive the relationship Cmax/Cave = 3.89 for round plumes and
2.22 for fully merged line plumes. However, as described in Baumgartner et al. (1994), the ratios can
vary. In much of the plume, the peak-to-mean ratios are considerably smaller than these limiting values,
approaching 1.0 at the source. Therefore, the centerline concentration prediction is approximate and
occasionally deviates from the expected trend when vertically varying background pollutant
concentrations are present. The dilution value D computed by the model by default is the flux-averaged
dilution, based on flux-averaged concentration Cave. The centerline dilution (an output provided by the
model) corresponds to Cmox.
The termination of the plume dynamic phase is decided by four benchmarks based on the plume
properties. The first criterion, which decides the termination of the nearfield mixing, is the stage in
which the plume density is equal to the ambient density. This also can be defined as the plume-trapping
stage, and the depth at which the plume reaches neutral buoyancy, designated as the trapping depth.
The second criterion for terminating the nearfield mixing is when the plume vertical velocity becomes
reversed, causing the plume that has overshot the trapping depth to fall back. Once the plume reaches
this stage, the plume structure collapses, and subsequent effluent transport continues as an advection-
diffusion process. Other criteria for the termination of jet/plume behavior of the effluent plume include
instances such as when the plume encounters boundaries, including the water surface, the shoreline, or
the seabed.
3.3.2 Farfield Dilution
Once the momentum-driven plume reaches the terminal criterion of nearfield dilution, the
plume structure is no longer sustainable and is dispersed as a passive effluent field by the ambient
currents. Here, the effluent (which exited with an initial end-of-pipe concentration of Ce) is already
partially mixed in the ambient environment after completion of initial dilution process (dilution ratio D)
with a resulting wastefield concentration of C0. Further mixing and dilution occurs with time as the
plume travels away from the zone of initial dilution, through natural turbulent diffusion that slowly
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reduces the wastefield concentration from C0 to C(x,y,z), asymptotically reducing towards the
background concentration. Farfield dilution factor FF may then be defined as FF=C0/C(x,y,z). Final
effluent dilution at specified farfield location is then given by D/or/fe/d = D FF. This determination of final
farfield dilution factor requires calculation of C(x,y,z). The conventional approach is to solve for C(x,y,z)
using the 3D advection-diffusion equation in the form shown below.
dC dC dC dC d ( dC\ d ( dC\ d ( dC
Tt+Ufoc + Vfy + W~d-z- dx\6xfoc)+ dy\ey^)+ dz\€zTz) W
Here, the effluent field concentration (in kg/m3) is denoted by C and u, v, and w are ambient velocities
(m/s) in x, y, and z directions, respectively. sx, sy, and sz are the corresponding eddy diffusivities (m2/s)
in x, y, and z directions. As in Visual Plumes, the PLUMES2.0 uses Brooks principles (Brooks, 1960) to
compute the farfield spreading of the wastefield and associated dilution over time and Brooks principles
are based on a simplified one-dimensional and steady-state version of the Equation 8, as shown below:
dC _ d / dC
dx dy \ ¦y dy
u HZ = 1*7. (ey^7)+ kc (9)
where k is the transformation rate of the effluent which may be growth rate or decay rate depending on
the nature of non-conservative constituent. For typical Brooks farfield applications, k value is set to zero.
The primary premise for Brooks principles, is that the wastefield grows laterally with distance (Figure 5).
The lateral growth is caused by turbulent mixing, represented by the lateral diffusion coefficient (ey).
Brooks laws were derived by solving Equation 9 analytically via length scaled relationships for ey.
A summary of Brooks principles is shown in Table 2 showing the growth of eddy diffusivity and plume
width as a function of distance. Brooks provided three case types for lateral mixing giving consideration
for environmental conditions. Case 1 represents narrow river or channel where eddy diffusivity may be
assumed constant. Case 2 represents estuarine conditions where eddy diffusivity may be expected to
grow linearly with distance from the outfall. Case 3 represents open ocean conditions where eddy
diffusivity was derived by Brooks to apply the 4/3rd power law relationship to the plume width.
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Figure 5: Schematic representation a typical farfield plume growth under steady conditions. The
inset with color contours represents a vertical cross section that shows the initial dilution
phase as well as the farfield transport. (Note: vertical spreading is assumed to be
negligible in Brooks' farfield model calculations)
Table 1: Variation of Width of Wastefield with Distance
Case 1
Constant e
e
— = 1
— = fl + 2/?—)1/2 (10)
wa \ ^ waJ
Case 2
Linear increase in e
€ W
e0 w0
— = fl + 2/3—) (11)
w0 \ W0J
Case 3
4/3-Law
£ /W\4/3
ea \w0J
— = (l +-P—Y' (12)
w0 V 3r waJ v '
wa =initial width of sewage field (w/wa = 1 at x = 0), Note, the origin or x = 0 in Brooks' calculations represents
the location of the wastefield after initial dilution is complete and is different from the origin for initial dilution
calculations at the outfall port, w = width at a distance x (x = u-t) from the start of farfield calculations, e is the
i i wwvr
eddy diffusivity at a distance x, and ea is the initial eddy diffusivity.
p — (dimensionless) (13)
uw0
The farfield dimensions of the wastefield are computed using the above rules and corresponding
dilutions at the center of wastefield (i.e., lowest dilutions or maximum concentration).
Table 2 provides the resulting equations used to calculate constituent concentration or farfield dilution
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(C0/C) in the wastefield for the three cases.
Table 2: The analytically-derived concentrations at the center of the wastefield (Brooks, 1960)
Case 1
e
— — i
C(x) = CQe fcterf
1 3
(14)
e0
J 4/3 x/wQ
Case 2
e w
C(x) = Cae~kte rf
3/2
(15)
\i
ii
1
Case 3
4/
€ / W \ '3
€0 W0/
CO) = C0e~kte rf
>
3/2
(16)
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4 PLUMES2.0 User Instructions
4.1 Download and Installation
PLUMES2.0 software is distributed in the form of a self-extracting zip file that may be
downloaded from the following locations.
US EPA's Center for Exposure Assessment Modeling via the following ink.
https://www.epa.gov/hydrowq/PLUMES2
or
from the University of Washington SSMC GitHub site
https://github.eom/ssmc-uw/PLUMES2.0
Download the zip file "PLUMES2.0-main.zip" from the US EPA site, or, from the GitHub site, download
by clicking the Code (green) button.
Copy the zip file from the download folder to your designated folder (e.g.,
C:\Users\useraccount\Desktop\) and extract the files using Windows explorer. The operating system
requirements are Windows 10 or higher. The extracted folder, also named \plumes2.0-main, contains
additional subfolders (\icons, \images, and \Example_project), multiple utility files, and the PLUMES2.0
executable. The executable is labeled plumes2.0.
Launch the application by double clicking the icon. Windows defender may require your approval to run
the application as it may not be recognized by Windows, [click "more information" prompt
©piumes2.o and select "run anyway" option. Having an organizational IT-Admin assisted install may be
required if the user does not have administrative privileges]. We recommend the option to
right click the icon and select "pin to task bar" for convenient future access.
4.2 PLUMES2.0 User Interface
The PLUMES2.0 user interface was setup to mimic many features of the Visual Plumes software
to allow seamless transition for the Visual Plumes community. Experienced users will recognize the
diffuser, effluent, and ambient tabs for entering project-specific data. The "Welcome" screen or tab
introduces PLUMES2.0, and additional information is also available under the "About' tab.
Click the "Project' tab or the ^ icon to start using PLUMES2.0.
4.2.1 Project set up
The Project tab screen provides step by step instructions on how to set up a new project
scenario. The window under the project dashboard (Project Description) allows the user to enter project
specific information and details. This could include the outfall name, project owner, project site location
and serves as a project identifier. Immediately below is the Load Existing Project button. This allows the
user to upload previously saved project configuration and data to continue prior work, or to run
additional scenarios without having to re-enter the project and case-specific information.
For a new project, click the New Project button. It opens a Windows explorer style menu.
Navigate to the directory where you would like to conduct model runs, right click in the selected
directory to create a new project folder. Double click to enter the new project folder, provide a project
file name and hit the save button. The project data and configuration that will be entered in subsequent
steps will be saved automatically under the project file name once the model run is executed. The saved
project information may be reloaded if the user wishes to close the program and return to it later,
thereby avoiding the need to re-enter the input data. Once the New Project is created, the tabs -
Diffuser, Effluent, and Ambient for entering project specific data become available along with the Model
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Run tab to run the dilution calculations (see below).
f7 >LUMES2.0
Welcome Project Djffuser Effluent Ambient Mode) Run About
Project Dashboard
Project Description
Select a working directory for the new project to save the project file
This directory holds all the input/output data files and project file wNch
records the project status
C:\UsersvD3M692\OneDrive - P N NLXDesktop\Tarang N pro^ecl
Load Existing Project
Also provided on the Project page is an added feature or option Independent Farfield Calculation
to allow stand-alone simulation of farfield transport of a wastefield using Brook's farfield transport
algorithm. This allows the user to estimate farfield plume transport independent of the nearfield
dilution process (see Section 3,2.7).
Users can perfonn an
independent far-field calculation
without the integrated near-field
computations
This far-field calculation is based on
Brooks principles and user input near-field
parameters
Independent Farfield
Calculation
4.2.2 Diffuser characteristics
Wastewater effluent is typically discharged to the surface waters through an outfall pipe. To
increase jet-induced mixing and initial dilution, the outfall design often includes a diffuser section,
located at the end of the outfall pipe. Rather than discharge directly through a pipe with a large
diameter and low velocities, the effluent is released under pressure through multiple ports with small
diameters, and therefore at higher (jet) velocities. This section of the outfall pipe with multiple ports
arranged in a row is called the diffuser section. The strong mixing provided by the diffuser also helps
trap the wastefield lower in the water column at the end of the buoyancy-induced mixing phase.
Outfall designs vary from the simplest configuration of an open-ended outfall pipe (single port)
to complex multiport diffusers with ports at the end of risers arranged uniformly or in a fan or with
alternating angles to maximize efficiency in settings with reversing tidal currents. The UM3 code is
designed for single-port or multiport diffusers with uniformly arranged ports. Diffuser configuration
consists of the following parameters.
1. Port diameter
2. Port elevation
3. Vertical angle
4. Horizontal angle
5. Number of ports
: Diameter (assuming circular opening) or equivalent diameter, m
: Distance from the seabed to port center, m
: Angle of port/discharge vector to horizontal plane,
+tive counter-clockwise from x-axis
: Angle of port/discharge vector to vertical plane,
+tive counter-clockwise from x-axis
: 1 = single port outfall, n = multiport diffuser with n ports
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6. Port spacing : Distance between ports, m (or average spacing for irregular diffusers)
7. Port depth : Distance from water surface to the port centerline
8. X and Y coordinates : Diffuser location or the starting point for the plume calculations
Figure 6 provides a schematic representation of a submerged outfall and diffuser configuration defining
the parameters for setting up a project run.
Click the Diffuser tab to see a simplified version of Figure 6 and a table where numeric values for
the diffuser parameters may be entered. The user also has an option to load a previously saved diffuser
configuration. Click the Load button to load "Diffuser_example.csv" file. This file is in the
Example_project folder. Figure 7 shows that the example diffuser has 18 ports spaced 6.1 m apart. Each
port is on a riser pipe with a port diameter of 0.076 m. Each port is angled up at 45° to the horizontal
plane. The horizontal angle of the discharge vector is at a 30° angle to the x-axis which is also the
direction of the ambient current. The diffuser location (X, Y) coordinate is specified using the centerline
of the middle port or the mid-point of the diffuser section (the user may select any arbitrary location for
the origin, and orientation of x-axis). Selecting an x-axis along the shoreline or along the current
direction simplifies data entry. The port elevation is 0.31 m and port depth at the diffuser is 11 m. Check
the case button to select this diffuser. The table may be populated with multiple diffuser designs but
only the checked diffuser configuration is used in calculations. All inputs are saved to the project file
automatically upon model run. But the user may wish to save the selected diffuser configuration for
later re-use. Additional notes on diffuser configuration:
• Port depth plus port elevation equals water depth at the diffuser location. However, water
depth away from the diffuser may be greater and may be entered via the Ambient tab. The
ambient tab allows entry of water profiles at a representative ambient location which may
be different from the diffuser site and deeper.
• The data entry by default for all parameters is in SI (metric) units, but the user may use the
drop-down arrows on the unit cell in the respective column to switch to Imperial units (foot,
pound, second). Note that all model results are provided in the SI units only.
• The Model Run tab (described later in Section 3.2.5) has two additional characteristics
related to the outfall/diffuser for user entry: diffuser contraction coefficient and distance to
nearest shoreline.
• The port elevation may be set to zero. However, initial dilution will be terminated as the
plume will immediately touch the bottom. The user will need to shut off "stop the plume at
bottom hit" criterion on the Model Run tab.
• The model cannot be applied for surface discharges. Port depth cannot be zero. Similarly,
port elevation cannot equal port depth.
• All ports must face the same direction.
• There is no limit on the number of ports, but it is assumed that the diffuser design provides
sufficient exit velocity (densimetric Froude number, Fr = U/((gD(s-l) y') > 1, to prevent
salinity intrusion. Here, U and D, are port velocity and port diameter, respectively, and's' is
the ratio of ambient and effluent densities.
Note that the entered information is not saved until the model run is executed. The diffuser
configuration may be saved using the "Save" button. Similarly, previously saved diffuser configuration
may be loaded using the "Load" button.
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Figure 6: Schematic representation of outfall pipe and definition of diffuser parameters.
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PJ • LUMES2.0 - X
Welcome Project Dtffuaef Effluent Ambient Model Run About
Water Surface
Port Depth
Diffuser Characteristics
Case
Port Diameter
Port Elevation
Vertical Angle
Horizontal Angle
No. of Ports
Port Spacing
Port Depth
X-coordinate
Y-coordinate
select v
m
m
deg
deg
a
m
m
m
m
1
D
7.60E-02
3.10E-01
4.50E-01
3.00E+01
18
6.10E+00
1.10E+01
O.OOE+OO
O.OOE+OO
2
~
3
~
4
~
5
~
6
~
7
~
8
~
9
~
Save Load Print Clear
Figure 7: Diffuser tab populated with example diffuser configuration. The dimensions may be entered in
units of meters or feet.
4.2.3 Effluent characteristics
Effluent characteristics consisting of flow rate, temperature, and salinity play an important role
in determining the behavior of the effluent plume and initial dilution at the culmination of nearfield
mixing. The wastewater effluent flow rate may vary during the year based on water use whether it is
industrial or municipal effluent. Similarly, effluent temperature may vary depending on the season,
particularly for treatment plants with settling ponds that are exposed to varying air temperatures.
Effluent salinity for municipal and industrial outfalls is typically zero. For existing outfalls, the effluent
characteristics are typically set or selected based on analysis of available monitoring data. Higher flow
rates cause stronger jet mixing, but also deliver a large volume/mass and correspondingly have less
dilution during subsequent phases. Conversely, lower flow rates provide lower jet mixing, but with a
smaller volume/mass to mix, resulting in more dilution in turbulent mixing with ambient currents. In
most situations, a combination of high effluent flow during low ambient currents results in the lowest
dilutions. Regulatory guidance varies from state to state on how to select effluent characteristics. Most
guidance documents suggest setting a combination of effluent flow rate, temperature, and salinity that
would result in lowest dilutions, representative of critical conditions.
Click the Effluent Tab to enter input data related to effluent characteristics. The user also has an
option to ioad previously saved effluent characteristics. Click the 'Load' button to load the
"Effluent_example.csv" file. Figure 8 shows loaded effluent characteristic values. Here the user also has
the option to enter pollutant concentrations for two constituents of concern for mixing zone compliance
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evaluation. The example effluent is a freshwater discharge at 8 million gallons per day (MGD) and has a
temperature of 26.3°C. Only one pollutant is entered with a concentration of 100 mg/L. PLUMES2.0 will
simulate all pollutants as conservative pollutants, meaning the pollutant concentration is only altered
upon discharge by dilution in the ambient receiving water, unless a decay rate is entered on the Ambient
tab (described in the next Section).
Also shown under the Effluent Tab is a table to enter data related to Mixing Zone dimensions.
Figure 8 also shows a schematic representation of acute and chronic mixing zone for a single port
outfall. Mixing zone requirements vary by state and are established in state water quality standards
regulations. For the example case in the PLUMES2.0 package, the selected mixing zones are chronic
mixing zone = 102 m, and acute mixing zone = 10.2 m. Mixing zone dimensions may also be loaded from
a prior saved file. Click the Load button to see to see the "Mixing_Zone_Example.csv" file.
Click the "case" buttons for the effluent characteristics and mixing zone characteristics to select
the case of interest before moving to the Ambient tab.
p| PLUMES2.0 - X
Welcome Project Diffuser Effluent Ambient Model Run />bout
Effluent Characteristics
Case
Effluent Flow Rate
Effluent Salinity
Effluent Temperature
Con. of Pollutant
select ^
MGD
psu
C
mg/L
1
o
8.00E+00
0.00E+O0
2 63E+01
1.00E+02
2
~
3
~
~
5
~
Save Load Prirt Gear
Mixing Zone Characteristics
Case
Acute Mixing Zone
Chronic Mixing Zone
select
m
m
1
D
1 .Q2E+01
1.O2E-02
2
~
3
~
4
~
5
~
6
~
7
~
Save Load Gear
Figure 8: Effluent tab populated with example effluent characteristics. The flow rate units may be
million gallons per day (MGD), cubic meters per second (cms), or cubic feet per second
(cfs). Temperature units may be °C or °F. Concentration of pollutant may be in units of
mg/L or kg/kg of effluent.
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4.2.4 Ambient characteristics
Ambient characteristics are the receiving water properties near the outfall discharge.
Specifically, PLUMES2.0 requires entry of properties that affect the mixing and dilution of the effluent
plume. They include ambient currents and stratification defined by temperature and salinity profiles.
Strong ambient currents lead to faster dilution through entrainment mixing. However, in some
situations, results may be counterintuitive. Stronger currents could also mean that the plume and the
effluent are transported rapidly to the mixing zone boundary before the dilution process is completed,
with lower initial dilution values (D) than expected. Similarly, strong stratification may result in trapping
of the plume lower in the water column, terminating the buoyancy-induced mixing. Lack of stratification
may result in rapidly surfacing plume, in which case initial dilution may be limited by water depth. To
account for such possibilities, regulatory agencies will run multiple scenarios under the range of
expected ambient conditions to address the possibility that, for stratified waterbodies, the worst-case
conditions could occur at either maximum or minimum stratification and during both low and high
current speeds.
Figure 9 provides a schematic representation of a water column cross-section with salinity,
temperature, and velocity profiles near a submerged outfall defining the ambient input data needed for
setting up a project run. The figure shows U (x-component of velocity), T (temperature, °C), and S
(salinity) plotted as a function of depth (measured positive from the water surface).
The Ambient tab (see Figure 10) includes columns to enter velocity magnitude and direction,
temperature, and salinity data as water column profiles. Note that nearfield velocity column represents
velocity profile at the diffuser site. Farfield velocity profile represents currents to be used by the model
for farfield transport and dilution calculations which may be different from currents at the diffuser
location. Often nearfield and farfield current profile are the same, but it is not uncommon see
applications where tidally averaged current velocities are entered for farfield transport when the
calculations are to be conducted over large distances and over multiple tidal cycles. As explained in the
introduction, the final concentration of the pollutant after dilution is affected by the background
concentration of the pollutant. The background concentration may be a natural condition or impacted
by pollution from upstream sources. These values may be entered under the Backg.Con column. If the
pollutant is conservative then there is no decay, but if the pollutant concentrations diminish with time,
then a decay rate may be entered in the column under Pollu.Decay. For example, if the pollutant is fecal
bacteria, then a die-off rate of ~ 1/day may be entered as a preliminary default value based on median
value from several studies (US EPA, 1985).
The last three columns on this page are data needed for conducting farfield dilution calculations
using the Brooks' method. They include the farfield velocity profiles - magnitude and direction (these
may be the same as nearfield), and a (alpha) that is used to compute initial eddy diffusivity e0 in the
Brooks farfield transport and dilution equations. Initial diffusivity is a function of initial plume width w0
and is defined by the equation below.
£,,= a(w0)4/3 (17)
where, a may vary from 0.0001 m2/3s 1 to 0.0005 m2/3s_1. A standard value of a = 0.00038 m2/3s 1 is the
recommended default, suitable for most cases (Brooks, 1960).
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Water Surface
Figure 9: Schematic representation of ambient cross section near an outfall diffuser.
Click the Ambient Tab to enter input data related to ambient characteristics. The user also has
an option to load a previously saved ambient characteristics. Click the Load button to see
"Ambient_example.csv" file. Figure 10 shows loaded effluent characteristic values. In this example, the
velocity profile shows currents varying in magnitude from 0.09 m/s at the surface to 0.05 m/s near the
bottom. The current direction is 0°, so the current is flowing parallel to the shoreline (x-direction). The
temperature profile shows warm temperatures of 14°C at the surface with a thermocline at 4 m depth,
below which the temperatures are uniform at 8°C. Ambient salinity is 32 psu, uniformly distributed with
depth. The farfield velocity field is populated with constant values of 0.05 m/s also flowing in the x-
direction, the eddy diffusivity is set at the default a of 0.0003 m2 3. Farfield calculations using Brooks'
method assume constant ambient conditions, and the model determines those conditions based on the
depth of the plume when the initial dilution ends (surface or plume trapping depth).
The user can visualize the Ambient Profile data by clicking the desired plot. Entered values may
be saved as *.csv files for future use.
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p* 1LUMES2.0
Welcome Project Diffuser Effluent Ambient Model Run ^sout
Ambient Data
Depth
Near Velocity
Near Vel. Dir.
Salinity
Temp
Backg Con.
PoBu. Decay
Far-field Velocty
Far-field VeJ. Dir.
Mph a
m
m/s
deg
psu
C
mg/L
day"-1
m/s
deg
irT(2/3)/s
1
OOOE+OO
9.00E-02
OOOE+OO
3.20E+01
140E+01
O.OOE+OO
O.OOE+OO
5.00E-02
0 00E+00
300E-04
2
2.00E+00
850E-02
0 00E+00
3.20E+01
120E+01
0.00E+00
OOOE+OO
5 00E-02
O.OOE+OO
3 OOE-04
I
3
4.00E+00
7.00E-02
O.OOE+OO
3.20E+01
8.00E+00
O.OOE+OO
OOOE+OO
5.00E-02
O.OOE+OO
3.00E-04
4
6.00E-00
6.50E-02
O.OOE+OO
3.20E+01
8.00E+00
O.OOE+OO
O.OOE+OO
5.00E-02
O.OOE+OO
3.00E-04
5
8.00E+00
6.00E-02
O.OOE+OO
3.20E+01
8.00E+00
O.OOE+OO
O.OOE+OO
5.00E-02
OOOE+OO
3.Q0E-O4
Save
Pnnt
Gear
Note: Eddy Diffusvity Eo = (alpha)"(width)A{4/3). Standard value of alpha is
0.00038 m"(2/3)/s which is suitable for many user cases
Ambient Profiles
v Currents
U-vek)dty (x-direction)
V-velocity (y-direction)
Velocity Magnitude
> Stratification
Velocity Along Depth
~ -2-
o .4 _
•3
g- -6-
Q
£ -8"
£ -10-
-12-
.045 .050 .055
060
.065 .070 .075 .080
Velocity in x-direction (m s)
.085
.090 .095
Figure 10: Ambient tab populated with example receiving water characteristics. Depth and velocity
data may be entered in units of m and m/s or ft and ft/s.
4.2.5 Model Run
Once the diffuser, effluent, and ambient data entry are completed, the final model run settings
may be selected and a dilution run initiated. Click the Model Run tab to enter the nearfield and farfield
settings. For convenience, many of the menu items are pre-selected or pre-filled with default values.
Under the Nearfield Setting tab, the following three entries are pre-filled with default values
(same values as Visual Plumes defaults for UM3; see insert below or Figure 11).
• Aspiration coefficient: The aspiration coefficient specifies the rate at which ambient fluid is
entrained into the plume. The default value of 0.1 is an average value that has been commonly
used. A different value causes increases or decreases in plume spreading and affects other
characteristics, like plume rise.
Diffuser contraction coefficient: Users may specify a
contraction coefficient (reduction in area of the jet relative to
the port area) based on the type of discharge ports on the
diffuser. The discharge coefficient of sharp-edged ports
(cylindrical hole in the diffuser pipe wall) is about 0.61. For
Nearfield Settings
Aspiration Coefficient 1.00E-01
Diffuser Contraction Coefficient 1 00E+OQ
Light /^sorption Coefficient 1 60E-01
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I December 2024 I EPA/600/B-24/339 I
bell-shaped ports (flaring inward into the direction of flow), a value of 1.0 is usually used. The
default value is 1.0.
• Light absorption coefficient jnot used in current version of PLUMES2.0): This coefficient is
provided as an option for future development. It is for specifying the light absorption coefficient
for the Mancini bacteria model. This is the coefficient ke found in Mancini, 1978, that describes
water clarity. The default value is 0.16.
PI PLUMES2.0
Welcome Project Diffuser Effluent Ambient Model Run About
NearfiekJ Settings
Aspiration Coefficient
Diffuser Contraction Coefficient
Light /^sorption Coefficient
1.00E-01
1.00E+00
1.G0E-01
0 Stop the plume at bottom hit
0 Stop the plume at the surface hit
0 Sop the plume at the shoreline hi
No. of Maximum Plume Rise or Fall
2:
0 : hrubal Trap Level, 1 : Max. Rise or Fall
2 : 2hd Trap Level. 3 : 2nd Max Rise or Fall
Output Formats
0 Text Formats (ASCII - *lxt)
0 Graphics Outputs
Near-field Output Intervals
fin steps)
Rename for Text Outputs
Model Results_TxtOutputs
Select Variables for
Outputs
RuxAvg-Dilution
Plume-Diameter
Position-Xdr
Position-Ydir
Plume-Depth
Reset Default List
Outfall Location
Shoreline
Shoreline Vector (distance
.angle)
m v
deg v
OOOE+OQ
0.00E+00
Farfield Settings
0 PLUMES Integrated Farfield Calculations
PLUMES2.Q's far-field is based on Brook's principles
Please select the type of eddy diffusivity to be used for
far-field calculations
O Constant Eddy Diffusivity
0 Linearly Varying Eddy Diffusivity
0 4/3 Power Law based Eddy Diffusivity
Maximum Dilution Limit for the Far-field Calculations
(default is 5000)
5.00E+03
Output Formats
0 Text Formats (ASCII - *.txt)
0 Graphics Outputs
Far-field Output Interval (in meters)
10
Distance (m) to Stop the Far-field
Plume Calculations (default is chronic
mixing zone boundary)
1.02E+Q2
Select Variables for Outputs
Run the model with the current
settings
Run PLUMES2.0 »
Model Results »>
Reset Default List
Figure 11: Model Run tab populated with example/default settings.
Here the user should also select the options that define termination of the initial dilution stage
of calculations, based on impingement with boundaries including the bottom, free surface, shoreline,
and/or trapping depth, by checking the suitable box(es). As shown in Figure 11, the boxes "Stop the
plume at bottom hit" and the "Stop the plume at the surface hit" are checked as default. If these values
are used, the initial dilution calculations will be terminated automatically if the plume surfaces or
encounters the bottom. If the shoreline hit box is selected, then the model asks for the vector
corresponding to the shortest distance to the shoreline from the diffuser. For atypical settings such as
diffusers on a slope with downward facing ports, bottom impingement can occur immediately. The user
must ensure that ambient water depth in such settings is significantly greater than the port depth.
Selection of "No of Maximum Plume Rise or Fall" (0, 1, 2, or 3) provides additional options to
24
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I December 2024 I EPA/600/B-24/339 I
instruct the program when to terminate initial dilution and begin far-field calculations. In some
situations, the plume may stabilize in the middle of the water column, or the user may wish to allow the
calculations to continue beyond surface interaction (boil). When "0" is selected, initial dilution is
terminated during the initial plume rise when the neutral buoyancy depth (initial trapping depth) is
reached. When "1" is selected, the plume momentum is allowed to carry it beyond the initial trapping
depth to its maximum rise in the water column. When the default value of "2" is selected, gravity allows
the plume to settle back to a new neutral buoyancy depth (2nd trapping depth). When "3" is selected,
the downward momentum allows the plume to sink deeper beyond the 2nd trapping depth to its
maximum fall. For discharges with negative vertical angle of the discharge, the rise and fall sequence is
reversed. As described in in Frick et al. (2003), under ideal conditions a plume will oscillate about a
varying trapping level at the so-called Brunt-Vaisala frequency as a wave form.
A schematic is shown on the top right panel of the tab with cells for entering distance and
direction to the shoreline. The convention for the angle is +tive counter-clockwise from the x-axis. Under
"Output Formats", the user may enter the selections for type of model output (ascii text or graphical).
The "Select Variables for Outputs", with a dropdown menu, allows the user to add more variables to be
included in addition those indicated in the default list. Model results are written to output files at a user-
defined number of intervals (steps). This allows the user to add or reduce the output resolution. For the
nearfield, the setting is based on internal model steps and the highest resolution is setting the interval =
1 (model step). The default value in the model is set at 5.
Under the farfield settings section, the user may select linked computation of nearfield and
farfield dilution by checking the box next to PLUMES Integrated farfield calculations (already checked as
default). By doing so, the model transitions automatically from the nearfield phase to the farfield phase,
using the projected area calculations to determine the initial wastefield width, and initiates the Brooks
method for farfield dilution calculations. Depending on the nature of the ambient waterbody, the user
may select (a) Constant Eddy Diffusivity (for rivers and narrow channels), (b) Linearly Varying Eddy
Diffusivity (for estuarine condition), or (c) Eddy Diffusivity Variation based on Brooks 4/3rd law (for open
ocean conditions, checked as default) (Table 2).
This tab also provides an option to limit Maximum Dilution (a high value such as 5000:1, default)
or distance values (such as chronic mixing zone length or user-defined distance beyond the study area of
interest) to terminate the farfield calculations. As in the nearfield menu, the user may select variables to
be printed in addition to those listed as default and select text or graphical output formats (or both).
For the farfield model, the output interval is in meters and the default is set at 10 m. A larger
number for the interval (steps for the nearfield and meters for farfield) results in lower spatial resolution
but a shorter printout. The user may also enter the file name for the model results output file to be
saved in the project directory.
Once the model inputs are completed, click the Model Run button to initiate the model run. If
the inputs are complete and the model runs without errors, a message "Model run was completed
successfully!" is displayed.
4.2.6 Model Results
The results are saved in the filename provided in the box under "Filename for Text Outputs" on
the Model Run page. In this example the filename provided was "ModelResults_TxtOutputs". After the
model runs, click OK to close the dialogue box indicating message "Model run was completed
successfully!". At the lower right corner of the Model Run tab, a new Model Results tab becomes
available following the completion of model run. Click the Model Results to see Graphic Outputs. Slide
the Graphic Outputs window and move it to a side to see the Text Output window hidden behind.
The text output organization was deliberately designed to be identical to the output file that
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I December 2024 I EPA/600/B-24/339 I
users are familiar with from the Visual Plumes interface (see Figure 12). The Ambient Table and Diffuser
Table summarize user-provided inputs for the scenario. Simulation Results are provided immediately
below. The results are written in rows at the indicated model steps. The default output columns include
(1) Flux-averaged Dilution, (2) Plume Diameter, (3) and (4) x- and y- coordinates of the plume centerline,
(5) Plume depth relative to water surface. Optional user-specified output parameters included in the
example in Figure 12 were (6) Plume salinity, and (7) Pollutant concentration. Note that the results are
only presented in metric system of units.
In this example, the buoyant plume rises in the water column and is also carried away in the x-
direction by the ambient currents. The plume dilution increases with each step as the plume rises all the
way to the water surface. In this example, the upward momentum of the plume carries it past the
trapping depth to the surface and the calculations are terminated when the plume outer boundary
touches the water surface (see Figure 13(a)). A shown in the text output in Figure 12, this occurs when
the plume upward momentum has carried it beyond the initial trapping depth of 3.0 m to a (plume
centerline) depth of 2.5 m below the surface when the outer boundary of the plume touches the water
surface. The volumetric dilution of the plume at this stage is 169.8:1.
If the user had unchecked the "Stop the plume at the surface hit", the upward momentum
would have carried the plume to the boil-over stage to a maximum centerline elevation, a depth of 1.9
m. This distance is less than the plume diameter (-7.8 m in this case) indicating the formation of a plume
boil, and with a higher initial dilution of 185:1. With the "No. of Maximum Plume Rise of Fall" switch set
at the default value of 2, the plume calculations continue. The plume reverses direction and falls back to
the second trapping depth of 3.4 m. The plume at this stage is further away from the diffuser and at a
higher initial dilution of 217:1. Note that caution is advised when using the model beyond the boundary
interaction point (surface hit), because the model over-simplifies the complex mixing in a plume boil.
Back to the Figure 12 example, having checked PLUMES Integrated Farfield Calculations and
Brooks 4/3rd Power Law for Eddy Diffusivity, the computations transition automatically to the farfield
phase. The farfield calculations begin with two key, internally calculated wastefield characteristics: (1)
starting dilution of the wastefield after initial dilution, 169:8, and (2) the width of the wastefield in the
direction of the current (note that this will represent the width of merged plumes from a multiport
diffuser). This internally computed value is based on final multiple merged plumes at the termination of
initial dilution dimensions, affected by current direction and diffuser configuration (109 m in this
example).
Results shown in Figure 12 indicate that, at a distance 100 m, just before the specified 102 m
mixing zone boundary, flux averaged dilution of the plume is 176.7:1 and the wastefield is 143.1 m wide.
To see the result at the exact 102 m distance, the user must set the farfield output interval to 1 m
instead of the 5 m interval used in the example. .
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I December 2024 I EPA/600/B-24/339 I
!n the Graphic Outputs window (see insert), the user can
choose to explore numerous visualization options that are
available. Two examples are provided below.
Figure 13 shows plots of the plume trajectory in x-y or
Depth-X plane. Figure 13(a) corresponds to the case when the
plume calculations were terminated at surface impact (consistent
with the example project). Figure 13(b) corresponds to the case
described above when plume calculations were allowed to go past
the surface impact and shows the plume boiling over.
As shown in the insert to the right or in Figure 13, there
are many plotting options available to the user for examining
various plume properties such as Plume (flux averaged) Dilution,
Plume Diameter, Plume (centerline dilution), Temperature,
Salinity, and Density. Double-click each option to see the desired
plot.
| Graphic Outputs
V
' Near Field
v Plume Trajectory
Depth-X Plane
Depth-Y Plane
! XY Plane
v FluxAvg Dilution
;¦¦¦ Vs. Distance
Vs. Depth
' Plume Diameter
j- Vs. Distance
Vs. Depth
v Centerline Dilution
j- Vs. Distance
^ Vs. Depth
\
' Plume Temperature
j- Vs. Distance
Vs. Depth
v Plume Salinity
] Vs. Distance
'• Vs. Depth
v Plume Density
; Vs. Distance
¦ Vs. Depth
v FarReld
\
' Dilution
'•Vs. Distance
v Plume Width
Vs. Distance
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I December 2024 I EPA/600/B-24/339 I
Ambient Table:
Depth
Amb-cur
Amb-dir
Amb-sal
Amb-tem
Amb-pol
Decay
Far-spd
Far-dir
Disprsn
m
m/s
deg
psu
C
kg/kg
s-1
m/s
deg
mO.67/s2
0.000
0.090
0.000
32.000
14.000
0.000
0.000
0.050
0.000
0.00030
2.000
0.085
0.000
32.000
12.000
0.000
0.000
0.050
0. 000
0.00030
4.000
0.070
0.000
32.000
8.000
0.000
0.000
0.050
0.000
0.00030
6.000
0.065
0. 000
32.000
8.000
0.000
0.000
0.050
0.000
0.00030
8.000
0.060
0.000
32.000
8.000
0.000
0.000
0.050
0.000
0.00030
10.000
0.055
0.000
32.000
8.000
0.000
0.000
0.050
0.000
0.00030
12.000
0.050
0.000
32.000
8.000
0.000
0.000
0.050
0.000
0.00030
Diffuser Table:
P-dia
p-elev
v-angle
H-angle
Ports
spacing
AcuteMZ
chrncMZ
P-depth
Ttl-flo
Cm)
Cm)
Cdeg)
Cdeg)
C)
Cm?
Cm)
Cm)
Cm)
Cm3/s)
0.08
0. 31
45.00
30.00
18.00
6.10
10. 20
102.00
11.00
0.35
Eff-sal
(psu)
0.00
Temp Polutnt
CO (kg/kg)
2.63 100.00
simulation Results:
Avg-Di1
step
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
180
185
190
195
200
205
210
215
220
225
230
235
240
245
250
p-dia x-posn y-posn
Cm) Cm) Cm)
0.083 0.011 0.007
0.091 0.024 0.014
0.101 0.038 0.022
0.111 0.054 0.031
0.122 0.071 0.040
0.135 0.089 0.051
0.149 0.110 0.063
0.164 0.133 0.076
0.181 0.158 0.090
0.199 0.185 0.105
0.220 0.216 0.122
0.242 0.249 0.141
0.266 0.286 0.161
0.293 0.326 0.183
0.323 0.370 0.207
0.355 0.419 0.233
0.391 0.472 0.261
0.430 0.530 0.292
0.472 0.594 0.325
0.518 0.663 0.360
0.569 0.738 0.399
0.624 0.820 0.440
0.683 0.910 0.484
0.747 1.007 0.531
0.817 1.111 0.581
0.892 1.225 0.633
0.972 1.346 0.689
1.059 1.476 0.747
1.151 1.614 0.806
1.250 1.758 0.867
1.355 1.910 0.929
1.467 2.069 0.992
1.586 2.235 1.055
1.713 2.407 1.118
1.847 2.586 1.181
1.988 2.771 1.244
2.139 2.963 1.306
2.298 3.162 1.367
2.466 3.369 1.427
2.644 3.583 1.486
2.832 3.805 1.544
3.031 4.035 1.600
3.241 4.275 1.655
3.463 4.525 1.708
3.698 4.785 1.760
3.947 5.057 1.811
4.209 5.341 1.860
4.486 5.639 1.907
4.784 5.949 1.952
5.144 6.256 1.994
Plume traps
255 147.499 5.462 6.466 2.020 -3.029
merging happened
260 155.017 5.722 6.621 2.038
265 161.123 5.987 6.763 2.055
270 165.961 6.243 6.894 2.069
plume surfaces
275 169.754 6.481 7.017 2.082
starting Farrieia calculations --
Farfield dispersion based on wastefield width of :
4/3 Power Law based Eddy Diffusivity is used:
Dilution width Distance
C) Cm) Cm)
169.754 109.610 7.320
169.754 110. 556 10.000
169.754 114.075 20.000
169.756 117.598 30.000
169.795 121.149 40.000
169.999 124.732 50.000
170.519 128.345 60.000
171.445 131.988 70.000
172.796 135.662 80.000
174.549 139.365 90.000
176.666 143.099 100.000
Reached Chronic Mixing 2
177.706 144.760 104.421
C)
1.101
1. 213
1. 337
1.474
1.624
1.791
1.975
2.178
2.402
2.650
2.923
3.225
3. 558
3. 926
4. 332
4.780
5. 275
5. 822
6.425
7.092
7.827
8. 640
9. 536
10.527
11.620
12.827
14.159
15.631
17.255
19.049
21.029
23.215
25.629
28.294
31.236
34.485
38.072
42.032
46.404
51.232
56.562
62.446
68.943
76.117
84.036
92.781
102.435
113.094
124.863
137.648
Depth
Cm)
-10.987
-10.972
-10.956
-10.938
-10.919
-10.898
-10.874
-10.848
-10.820
-10.789
-10.754
-10.717
-10.676
-10.631
-10.582
-10.528
-10.469
-10.405
-10.335
-10.259
-10.176
-10.085
-9.987
-9.879
-9.763
-9.636
-9.499
-9.351
-9.192
-9.024
-8.844
-8.654
-8.453
-8.241
-8.017
-7.782
-7.536
-7.278
-7.008
-6.726
-6.432
-6.126
-5.807
-5.475
-5.132
-4.775
-4.406
-4.024
-3.632
-3.263
-2.869
-2.732
-2.614
___-2._512 _
109.59 Cm)
Figure 12: Example of ascii text format output from PLUMES2.0. initial dilution was terminated when
the plume boundary encountered the water surface, when the plume centerline was at a
depth of 2.5 m below the water surface at an initial dilution of 169.8:1. The farfield
calculations began at this point with a merged wastefield width of 109 m. The farfield
calculations were terminated at the Chronic Mixing Zone boundary (102 m). The dilution
of the plume at this distance was approximately 177:1 with interpolation.
28
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I December 2024 I EPA/600/B-24/339 I
f Graphic Outputs
v Near Field
v Rune Trajectory
Depth-X Plane
Depth-Y Plane
XY Plane
v RuxAvg Dilution
Vs. Distance
Vs. Depth
> Plume Diameter
> Centerline Dilution
> Rume Temperature
> Rume Salinity
> Rune Density
> Farfield
(b)
p^l Graphic Outputs
v Near Field
v Rume Trajectory
Depth-X Plane
Depth-Y Rane
| i XY Rane
v RuxAvg Dilution
Vs. Distance
Vs. Depth
> Rume Diameter
> Centertine Dilubon
> Rume Temperature
> Rume Salinity
> Rume Density
> FarField
Hume Trajectory'
-6
-7
-8
-9
-10
-11
-12
1 1
1 ' 1
: / :
! ! !
: / :
j
; i :
/: :
/ : :
"'7 "1 "
/ I • S
1 _ ;
• « /
: ;
X- . . .
i : /
: :/
y/l ¦
; /
I y \ S
: — v—
v : :
/ 1/ -"J"'
s jS. '•
> '
2 3 4 5 6 7
X-Distance from the Outfall (m)
Rume Trajectory
~ -6-
4 6 8 10
X-Distance from the Outfall (m)
12 14
Figure 13: Example of plume trajectory in Depth-x plane until the termination of initial dilution
phase, (a) initial dilution is terminated at surface hit; (b) initial dilution is allowed to
continue past surface hit to completion of the boil.
4,2.7 Independent Farfield Calculation
There are many instances where effluent transport and mixing in the surface waters occurs
without the benefit of nearfield mixing provided by an outfall diffuser. A wastefield may form because of
discharges from multiple sources, irregularly distributed in a localized area. The wastefield may then be
carried away by ambient currents being diluted by farfield mixing processes. Conventional use of a
29
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I December 2024 I EPA/600/B-24/339 I
(D
Users can perform an
independent farfield calculation
without the integrated nearfield
computations
dilution mode! such as PLUMES2.0 is riot feasible in such instances. However, transport and dilution of
the wastefield may be estimated through independent application of Brooks' laws.
To facilitate use of the model for such situations, we have included the Independent Farfield
Calculation option. This can be accessed from the Project
page. The only inputs required are (a) Initial wastefield
dilution (existing dilution ratio at the start of farfield
transport), (b) Initial wastefield width, (c) Initial wastefield
location (distance from the outfall), (d) Mixing zone location
(distance from the outfall), and (e) Ambient current velocity.
If Initial wastefield dilution is known, then the Brooks'
calculations provide the combined Farfield dilution as a
function of distance travelled. If the initial dilution is
unknown, the users may enter 1 (a conservative approach
assuming no dilution of the effluent in the wastefield at the
start of farfield calculations). The Brooks' calculations then
provide a relative farfield dilution factor.
Click the independent Farfield Calculation button.
This opens a new dialogue box. It is not possible to save the
settings of the Independent farfield calculations, so the user must input values each time.
in this example, Initial
This farfield calculation is based on Brooks
principles and user input nearfield
parameters
Independent Farfield
Calculation
Independent Farfield Calculation
Dilution factor of the plume after initial dilution
Plume width after initial cSlution (m)
Plume travel distance after initial dilution (m)
Distance from the outfal to mixing zone boundaiy (m)
Unidirectional ambient current speed (m/s)
Estimated Diffusivity Parameter (alpha).
Eo = (alpha Xwidth)A(4/3)
Farfield calculation is based on Brook's principles Please select the type of eddy
diffusivity to be used for farfield calculation.
0 Constant Eddy Diffusivity
0 Linearly Varying Eddy Diffusivity
Q 4/3 Power Law based Eddy Diffusivity
1.00E+02
S.QQE-01
1 00E-03
2.QQE*02
5 00E-Q2
3.00E-W
wastefield dilution was set at 100:1.
Initial wastefield width was set at 50 m.
The Initial wastefield location was set to
0.001 m. (note this value can be as
small as 0.001m but not zero). The
mixing zone boundary was set at 200 m
from the outfall. The unidirectional
ambient current speed (same as
Farfield velocity) was set at 0.05 m/s.
The value of a that is used to estimate
initial Eddy Diffusivity of the wastefield
is set at 0.0003 as a default. Results for
this example are shown in Figure 14
below.
The user has the option to
O.OOE+OO select the variation of Eddy Diffusivity
O.OQE+OQ based on the environment. Typically,
Constant Eddy diffusivity is selected for
rivers and bounded channels, Linearly
Varying Eddy diffusivity is
recommended for estuarine settings,
and Brooks' 4/3rd power law variation is recommended for open ocean conditions. The user has the
option to specify the Initial Concentration of the Pollutant in the wastefield, and a decay rate if
applicable. Click the Run Farfield Calculations button to initiate the Independent Farfield Simulation. The
text output results open in a new window and must be saved by clicking the File and Save as options.
Pollutant concentration after Initial dilution lg/m"3)
Pollution decay rate (1/day)
Run Farfield Calculations »>
30
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I December 2024 I EPA/600/B-24/339 I
| Text Outputs for Independent Farfield Calculation
File Edit Search
« q.1 b p a
Farfield dispersion based on wastefield width of^ 50.00 (m)
4/3 Power Law based Eddy Diffusivity is used:
The alpha value used for dispersion calculation: 0.0003
The ambient current in the farfield (m/s): 0.0500
simulation Results:
cone
Dilution
Wi dth
Di stance
Ti me
(kg/mA3)
()
(m)
(m)
(hrs.)
0.000
100.000
52.137
8.001
0.044
0.000
100.004
54.303
16.001
0.089
0. 000
100.100
56.499
24.001
0.133
0.000
100.495
58.724
32.001
0.178
0.000
101.326
60.977
40.001
0.222
0. 000
102.609
63.258
48.001
0.267
0. 000
104.294
65.567
56.001
0. 311
0.000
106.319
67.903
64.001
0. 356
0. 000
108.625
70.266
72.001
0.400
0. 000
111.163
72.657
80. 001
0.444
0. 000
113.894
75.073
88.001
0.489
0.000
116.786
77.516
96.001
0. 533
0.000
119.816
79.985
104.000
0. 578
0.000
122.965
82.480
112.000
0.622
0. 000
126.216
85.000
120.000
0. 667
0. 000
129.559
87.545
128.000
0,711
0. 000
132.984
90.115
136.000
0.756
0.000
136.483
92.709
144.000
0.800
0. 000
140.049
95.329
152.000
0. 844
0. 000
143.678
97.972
160.000
0. 889
0.000
147.365
100.639
168.000
0.933
0.000
151.106
103.330
176.000
0.978
0. 000
154.899
106. 045
184.000
1.022
0. 000
158.740
108.783
192.000
1.067
0.000
162.627
111.544
200.000
1.111
0.000
166.559
114.328
208.000
1.156
0. 000
170.534
117.135
216.000
1.200
0. 000
174.550
119.965
224.000
1.244
Figure 14: Example of Farfield plume trajectory in -x direction. Initial wastefield width was set to 50
m and ambient current carrying the wastefield or plume away from the source was 0.05
m/s.
In its present state of development, the user does not have control over the output interval in
the independent farfield calculator. The calculator divides the user-defined distance to the mixing zone
boundary into 25 steps, and 3 additional steps beyond the mixing zone boundary are included in the
output. In the example above, the distance to the mixing zone boundary (200 m) is divided by the fixed
number of output steps (25) and the model outputs the dilution in 8 m intervals. Three additional steps
past the mixing zone boundary result in the final model output at 224 m.
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I December 2024 I EPA/600/B-24/339 I
5 Summary and Discussion
The Visual Plumes (UM3) model has been a workhorse for public domain mixing zone modeling
for many years. The original Visual Plumes was a Windows-based computer application that superseded
the DOS based PLUMES mixing zone modeling system. However, its availability and usability waned in
recent years due to compatibility issues with the latest versions of mandatory Windows upgrades. As a
result, many users were inconvenienced. SSMC scientists had developed a Fortran version of UM3 as
part of the Salish Sea Model. The objective of this work was to take advantage of the preliminary
development efforts by the SSMC scientists and develop, test, and release a new version of PLUMES
(PLUMES2.0) along with a User's Manual. This goal has been accomplished with potential for future
improvements such as addition of carbonate chemistry modules for pH and total alkalinity (TA) and
simplified dissolved oxygen kinetics. Since then, the model development team has become aware of
another (web based) public domain version of Visual Plumes UM3 offered by the San Francisco Estuary
Institute and the Aquatic Science Center (SFEI 2024). The user community is therefore now well
supported by two independent sources of public domain software based on the Visual Plumes suite of
tools.
The simplicity and ease of use allows PLUMES2.0 application to many complex problems. For
example, simulation of dissolved oxygen (DO) or pH can be supported by PLUMES2.0 estimates of
nearfield dilution to estimate concentrations prior to further biogeochemical or carbonate chemistry
analyses. However, caution must be exercised as many settings will likely fall outside of the ideal
combinations of diffuser geometries and receiving water conditions that were assumed in the
development of the model formulations and numerical solutions. For example, the model assumes
steady state and laterally uniform receiving water conditions with a cross flow. In stagnant
environments or in tidally reversing currents, re-entrainment can occur. The actual dilutions of the
effluent may be different from those provided by the model due to unsteady conditions and cumulative
effects on ambient concentrations. Limitations of the model relating to boundary interaction was
discussed previously. While the model provides options for the plume calculations to be terminated
upon boundary impingement, experienced users may use the model beyond this limit with proper
selections of eddy diffusivity and other parameters. Validation of model predictions using dye-dilution
field studies is recommended while using PLUMES2.0 in complex and non-ideal settings. Similarly,
although the model is designed to accommodate only regular geometry (e.g., linear diffuser with all
ports in the same direction), experienced users can simulate irregular settings by breaking up the
complex discharges into simpler geometries and using the principle of superposition. It is also important
to note that the model was designed for simulating buoyant discharges. Discharge of brine or sediment
loaded fluids heavier than ambient through PLUMES2.0 is possible by adjusting the density through T
and S, but the model will terminate soon after the initial jet phase as the plume with water heavier than
ambient begins to reverse before the initial dilution process is completed. Also, as discussed in Section
2.3.1, the model provides an estimate of centerline dilution, which is the minimum dilution for circular
plumes with the understanding that dilution can vary significantly from near the port to the termination
of initial dilution.
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I December 2024 I EPA/600/B-24/339 I
6 References
Abraham, G. 1963. Jet Diffusion in Stagnant Ambient Fluid. Publ. No. 23 Delft Hydraulics Laboratory July 1963.
Akar, P.J., Jirka, G.H., 1991. CORMIX2: An Expert System for Hydrodynamic Mixing Zone Analysis of Coventional
and Toxic Multiport Diffuser Discharges. DeFrees Hydraulic Laboratory, School of Civil and Environmental
Engineering, Cornell University, New York. EPA/600/3-91/073.
Baumgartner, D.J., Frick, W.E., Roberts, P.J.W., 1994. Dilution Models for Effluent Discharges. Office of Research
and Development, US Environmental Protection Agency, Washington, D.C.
Brooks, N.H., 1960. Diffusion of sewage effluentin an ocean current, in: Pearson (Ed.), Proceedings of the First
Conference on Waste Disposal in the Marine Environment. Pergamon Press, New York, USA, pp. 246-
267.
Cederwall, K. 1971. Buoyant slot jets into stagnant or flowing envirorment. Rep. No. KH-R-25. W. M. Keck Lab. of
Hydraul. and Water Resources, California Institute of Technology, Pasadena, CA. 86 pp.
Chu, V. H. (1979). "L. N. Fan's data on buoyant jets in a crossflow." J. Hydr. Div., ASCE, 105, 612-617
Davis, L.R., and M.A. Shirazi. 1978. A review of thermal plume modeling. Keynote address, pp. 109-126. In:
Proceedings of the Sixth International Heat Transfer Conf., Amer. Soc. Mech. Eng., August 7-11,1978,
Toronto, Canada.
Davis, L.R. 1998. Fundamentals of Environmental Discharge Modeling. 1st Edition E-book.
https://doi.org/10.1201/978020375531Q
Doneker, R. L, and G. H. Jirka (1990), "Expert System for Hydrodynamic Mixing Zone Analysisof Conventional and
Toxic Submerged Single Port Discharges (CORMIX1)," Report No. 109 EPA/600/3-90/012, US
Environmental Protection Agency, Env. Research Laboratory, Athens, Georgia.
Ecology 2018. Appendices: Permit Writers Mannual. Water Quality Program. Washington State Department of
Ecology. WAC
Fan, L. N. (1967). 'Turbulent buoyant jets into stratified or flowing ambient fluids."Rep. No. KH-R-15, Calif. Inst, of
Technol., Pasadena, California.
Fischer, E. J. List, R. C. Y. Koh, J. Imberoer and N. H. Brooks. 1979 Mixing in Inland and Coastal Waters. Academic
Press, 1979. 483 pp.
Fofonoff, N.P., 1985. Physical properties ofseawater: a new salinity scale and equation of state for seawater. J.
Geophys. Res. 90, 3332. https://doi.org/10.1029/JC090iC02pQ3332
Frick, W.E., 1984. Non-empirical closure of the plume equations. Atmos. Environ. 18, 653-662.
https://doi.org/10.1016/0004-698K84) 90252. https://doi.org/10.1016/0004-6981(84)90252-X
Frick, W.E., Baumgartner, D.J., Fox, C.G., 1995. Improved prediction of bending plumes. J. Hydraul. Res. 32, 935-
950. https://doi.org/10.1080/002216894Q9498699
Frick, W.E. 2004. Visual Plumes mixing zone modeling software. Environmental Modelling & Software 19 (2004)
645-654.
33
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I December 2024 I EPA/600/B-24/339 I
Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, J., Brooks, N.H., 1979. Mixing in inland and coastal waters. Academic
Press, New York, USA
Fofonoff, N.P., 2008. Physical properties of seawater: a new salinity scale and equation ofstate for seawater. J.
Geophys. Res. 90, 3332. https://doi.org/10.1029/ic090ic02pQ3332.
Jirka, G.H., and P. J. Akar (1990), "CORMIX2: Expert System for Multiport Diffuser Discharges," Proc. Nat'l.
Conference on Hyd. Eng., ASCE, San Diego, California
Jirka, G. and S.W. Hinton, 1992. User's guide for the Cornell mixing zone expert system (CORMIX). National
Council of the Paper Industry for Air and Stream Improvement, Inc.. Technical Bulletin No. 624. February,
1992.
Jones G.R., Nash J.D., Jirka G.H. 1996. CORMIX3: an expert system for mixing zone analysis and prediction of
buoyant surface discharges, DeFrees Hydraulics Laboratory, Cornell University (1996)
Kannberg, L.D., and L.R. Davis. 1976. AA experimental/analytical investigation of deep submerged multiple buoyant
jets. EPA-600/3-76-101. US Environmental Protection Agency, Corvallis, OR. 266 pp.
Koh, R.C.Y., and L.N. Fan. 1970. Mathematical models for the prediction of temperature distributions resulting
from the discharge of heated water in large bodies of water. Water Pollution Control Research Series
Rep. 16130DW0101/70. US Environmental Protection Agency, Corvallis, OR. 219 pp.
Lee, J.H.W., Cheung, V., 1991. Generalized Lagrangian model for buoyant jets in current. J. Hydraul. Eng. 116,
1085-1106.
Liseth, P. 1976. Wastewater Disposal by Sub merged Manifolds. Jour. Hydraul Div.,. Proc. Amer. Soc. Civil Engr.,
102,1.
Liseth, P., 1970. Mixing of merging buoyant jets in stagnant receiving water of uniform density. Ph.D. Thesis,
University of California, Berkeley.
Mancini, J., 1978. Numerical estimates of coliform mortality rates under various conditions. Journal of Water
Pollution Control Federation. November 1978.
Morton, B. R., Taylor, G., Turner, J. S. 1956. Turbulent Gravitational Convection from Maintained and
Instantaneous Sources. Proceedings of the Royal Society of London. Series A, Mathematical and Physical
Sciences, Volume 234, Issue 1196, pp. 1-23
Muellenhoff, W.P., A.M. Soldate, Jr., D.J. Baumgartner, M.D. Schuldt, L.R. Davis, and W.E. Frick. 1985. INITIAL
MIXING CHARACTERISTICS OF MUNICIPAL OCEAN DISCHARGES VOLUME I - PROCEDURES AND
APPLICATIONS
Pearson, E.A. 1956. An Investigation of the. Efficacy of Submarine Outfall Disposal of. Sewage and Sludge. Pub No.
14. State Water Pollution Control Board, Sacramento, CA. 258 pp.
Premathilake L, T Khangaonkar. 2019. FVCOM-plume - A three-dimensional Lagrangian outfall plume dilution and
transport model for dynamic tidal environments: Model development. Marine Pollution Bulletin, 149:
110554. https://doi.Org/10.1016/j.marpolbul.2019.110554
Priestly, C.H.B, and F.K. Ball. 1955. Continuous convection from an isolated source of heat. 81 (1955), pp. 144-157.
Roberts, P.J.W. 1977. Dispersion of buoyant waste discharge from outfalldiffusers of finite length. Rep. No. KH-R-
34
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I December 2024 I EPA/600/B-24/339 I
35. W. M. Keck Lab. of Hydraul. and Water Resources, California Institute of Technology, Pasadena, CA.
183 pp.
Roberts, P.J.W. 1979a. Line plume and ocean outfall dispersion. J. Hydraulic. Div., Am. Soc. Civ. Eng. 105:313-331.
Roberts, P.J.W. 1979b. A mathematical model of initial dilution for deepwater ocean outfalls. Proceedings of a
specialty conference on conservation and utilization of water and energy resources. San Francisco, CA.
Aug. 8-11. Am. Soc. Civ. Eng. pp. 218-225.
Roberts, P.J.W. 1983. Mixing and transport. J. Water Pollut. Control Fed. Literature Review Issue 55:752-57.
Roberts, P.J.W. 1984. Mixing and transport. J. Water Pollut. Control Fed. Literature Review Issue 56:692-697.
Roberts, P.J.W. 1985. Mixing and transport. J. Water Pollut. Control Fed. Literature Review Issue 57:634-638.
Roberts, P.J.W., W.H. Snyder, and D.J. Baumgartner, 1989 a. Ocean outfalls I: submerged wastefield formation.
ASCE Journal of Hydraulic Engineering. 115. No. 1. pp 1-25.
Roberts, P.J.W., W.H. Snyder, and D.J. Baumgartner, 1989 b. Ocean outfalls II: spatial evolution of submerged
wastefield. ASCE Journal of Hydraulic Engineering. 115. No. 1. pp 26-48.
Roberts, P.J.W., W.H. Snyder, and D.J. Baumgartner, 1989 c. Ocean outfalls III: effect of diffuser design on
submerged wastefield. ASCE Journal of the Hydraulic Engineering. 115. No. 1. pp 49-70.
Roberts, P.J.W., 1990. Outfall design considerations. In: Le Mehaute, B., Hanes, D.M. (Eds.), The Sea, Ocean
Enginereing Sciences. John Wiley & Sons, Ltd, New York, USA, pp. 661-689.
Rouse, H., C.S. Yih, H.W. Humphreys. Gravitational convection from a boundary source. Tellus, 4 (1952), p. 201
Sotil, C. A. 1971. Computer program for slot buoyant jets into stratified ambient environments. Tech. Memo 71-2.
W. M. Keck lab. of Hydraul. and Water Resources, California Institute of Technology, Pasadena, CA. 21
pp.
US EPA. 1982. Modifications of secondary treatment requirements for discharges into marine waters. Federal
Register, November 26,1982. 47(228):53666-53685. Washington, DC.
US EPA, 1985. Rates Constants and Kinetics Formulations in Surface Water Quality Modeling. EPA Environmental
Research Laboratory, Athens, GA. EPA/600/3-85/040
US EPA. 1991. Technical Support Document for Water Quality Based Toxics Control. EPA/505/2-90-001.
Wright, S.J. Mean Behavior of Buoyant Jets in a Crossflow. J. Hydraul. Div. 1977,103,12944
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I December 2024 I EPA/600/B-24/339 I
Appendices
Appendix A: Quality Assurance
A.l. Quality Assurance Project Plan
The information generated in this report was performed under CEMM Quality Assurance Project Plan
(QAPP) "Quality Assurance Project Plan for - Development of Visual Plumes Model Update (PLUMES
2.0)" J-ACESD-0033631-QP-l-l, approval date: June 27, 2023.
A.2. Quality Assurance Audit
An audit, J-IO-Audit-1537, was conducted on this project and findings were identified. Corrective
actions were implemented and completed prior to the closing of the audit. The audit was closed prior to
this STICS clearance.
The findings from the audit were as follows.
Finding 01: Deviation documented, approved, and closed: The information required from the contractor
was received in a different format as described in the QAPP. The deviation of format was determined to
be acceptable by the EPA Project Lead.
Finding 02: Deviation documented, approved, and closed: The comment-line documentation was
determined insufficient during the audit of J-IO-Audit-1537 from the contractor and whether it has been
corrected to the satisfaction of the technical lead of the project. Contractor corrected and the code was
reviewed to be satisfactory by the EPA Project Lead.
Finding 03: Documented and closed. GUI testing and verification needed to state what was done for
testing, whether it was documented at the time of testing, and attach any supporting information
identifying the testing was done. This includes internal Technical Reviews or summary of test results (All
Pass or Satisfactory or not), and whether the type/amount of testing that has been done is satisfactory
to still meet the Data Quality Objectives identified in the QAPP and pose any limitations on the quality of
the system.
Finding 04: Deviation documented, approved, and closed Records were missing from the contractor on
for code versioning, and the difference in tools used. Documentation includes potential impacts this may
or may not pose once code is transferred to the EPA. No further corrective action can be performed for
not having proper versioning. EPA will perform proper versioning once the application is transferred to
the EPA moving forward.
The corrective actions for each deviation that resulted in a finding for the audit J-IO-Audit-1537, were
deemed acceptable at addressing the root cause of the finding. Objective evidence supplied
demonstrated corrective actions were put in place; therefore, this audit was closed prior to clearance of
this product.
A.3. Data Quality Summary
This effort included comparing model results from testing (see Appendix B : PLUMES2.0 Model
Validation and Testing) to previously reported Visual Plumes model runs and resulting output.
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I December 2024 I EPA/600/B-24/339 I
Appendix B: PLUMES2.0 Model Validation and Testing
Verification and testing were conducted for the three main stages of the PLUMES2.0
development process. The objective was to ensure that the Fortran based PLUMES2.0 reproduced the
Visual Plumes (VP) UM3 model outputs for both nearfield and farfield calculations. The first stage of
testing and verification was conducted after the completion of nearfield development. A comprehensive
set of scenario cases were simulated with PLUMES2.0 covering a wide range of ambient currents,
stratifications (temperature and salinity), discharge flowrates, and several diffuser configurations (i.e.,
single port/multiport/different port orientation angles/staggered/non-staggered). The results were then
compared with the corresponding outputs produced by UM3. In the second stage of testing, similar
comprehensive scenarios were examined for the farfield plume parameters computed with Brooks
principles implemented in PLUMES2.0. The model results were compared against the Brooks farfield
parameters produced by Visual Plumes. Third stage testing and verification was conducted to ensure the
proper operation of the GUI.
B.l Nearfield Dilution
The model testing and validation were conducted for three major plume parameters: (1) Plume
diameter; (2) Plume height; and (3) Plume dilution at termination of nearfield mixing. Figures A.l, A.2,
and A.3 compare PLUMES2.0 model performance against UM3 results. As shown in the figures, the
PLUMES2.0 produces almost identical results to those from UM3 for all the cases. Although we expect
the results to be identical, the differences are caused by differences in precision levels in language
specific intrinsic mathematical functions. Table A.l shows the model skill metric (Average absolute
relative error percentage) for each plume parameter which is less than 0.5%. This demonstrates that the
PLUMES2.0 can robustly reproduce the UM3 model performance for the nearfield plume parameters
together with the fate of the plume (trapping, surfacing, merging, and bottom contact).
85 i
80-
co
75-
2
70-
3
i
65-
If
60-
l
0
55-
0
E
50-
ra
b
45-
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I December 2024 I EPA/600/B-24/339 I
co
3
i
c
o
*¦+-'
Q
0)
E
Q.
1000 n
800-
600-
400-
200-
200 400 600 800
Plume Dilution - PLUMES 2.0
1000
Figure B.2: The Comparisons of PLUME 2.0 results and UM3 model results; Plume Dilution.
CO
2
Z>
CT)
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I December 2024 I EPA/600/B-24/339 I
Table B.2: Comparison of
PLUMES2.0 output and VP (UM3)
Output for Nearfield Plume Dilution
Nearfield Plume Dilution
PLUMES2.0
VP (UM3)
132.714803
133.00
362.409223
362.40
122.412558
122.00
114.73999
116.10
128.264756
130.20
527.947369
527.90
325.749201
328.20
376.840461
373.90
369.656583
369.70
384.58932
384.60
410.996562
408.10
362.409203
362.40
362.409206
362.40
362.409211
362.40
167.45121
167.50
145.845113
145.80
778.153221
784.50
255.734072
256.20
259.15555
255.60
259.356519
256.00
259.649461
257.40
256.902562
256.20
257.164794
255.30
93.0727418
93.69
139.245838
138.80
100.646919
101.10
64.7438084
64.74
56.3660052
56.37
70.0746303
70.07
70.073837
70.07
49.0750747
49.08
900.00
800.00
700.00
600.00
500.00
400.00
300.00
200.00
y= 1.0026x-0.7751 9
R2 = 0.9999
100.00 §
/
0.00
200
400 600
PLUMES2.0
800 1000
Figure B.4: Nearfield Plume Dilution Comparison of PLUMES2.0 results
and UM3 model
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I December 2024 I EPA/600/B-24/339 I
Table B.3. Comparison of PLUMES2.0
output and VP (UM3) Output for
Nearfield Plume Diameter
Nearfield Plume Diameter
PLUMES2.0
VP (UM3)
65.9576239
65.79
46.8691099
46.87
31.6317789
31.48
30.8299141
31.06
33.5800443
33.90
57.3057271
57.31
44.3267589
44.51
47.8163873
47.61
47.1856959
47.19
48.0446643
48.04
49.6646848
49.47
46.8681112
46.87
46.8682562
46.87
46.8684768
46.87
31.9081993
31.91
29.811709
29.81
49.147933
49.36
69.5674545
69.68
70.6634704
69.40
70.6760233
69.47
70.7648909
69.90
69.976245
69.70
70.2115447
69.50
64.2614455
64.39
78.8906576
78.59
76.0334049
75.89
41.5216712
41.52
27.6311397
27.63
26.3766259
26.38
25.8573627
25.86
29.0015315
29.00
Nearfield Plume Diameter
90.00
80.00
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
a r\ n
+ 0.4998 9
>996 ?
y = 0.9872x
R2 = 0.5
/
f
/
0
0
0
/
/
20 40 60
PLUMES2.0
80
100
Figure B.5: Nearfield Plume Diameter Comparison of PLUMES2.0
results and UM3 model
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I December 2024 I EPA/600/B-24/339 I
B.2 Farfield Dilution
Since the Brooks farfield model is comprised of a set of explicit analytical equations, no specific
numerical modeling technique is required to calculate the associated farfield parameters. PLUMES2.0's
farfield results were compared against the Visual Plumes model results for various farfield ambient
conditions as part of quality assurance and quality control validation. The model comparisons shown in
Figure A.4 is for 12 cases of different ambient conditions with both constant eddy diffusivity and 4/3
power law-based eddy diffusivity (option 1 and 3). The relative error percentages for dilution of plume
width predictions of PLUMES2.0 in comparison with Visual Plumes for 12 farfield cases are listed in Table
A.2. For each test, R2 = 1.0000, which meets the evaluation criteria of R2 = 1.0.
Table B.4. Comparison of
PLUMES2.0 Output and VP
(UM3) Output for Farfield
Plume Dilution
Farfield Plume Dilution
PLUMES2.0
VP (UM3)
109.182
109.2
116.41
116.4
127.797
127.7
139.479
139.4
150.703
150.6
161.35
161.2
171.445
171.3
181.04
180.9
190.191
190
198.947
198.7
Farfield Plume Dilution
y = 0.9976x+0.2585 „
R2:
4
= 1.0
0 50 100 150 200 250
PLUMES2.0
Figure B.6: Nearfield Plume Diameter Comparison of PLUMES2.0 results
and UM3 model
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I December 2024 I EPA/600/B-24/339 I
Table B.4. Comparison of
PLUMES2.0 Output and VP
(UM3) Output for Farfield
Plume Dilution
Farfield Plume Width
PLUMES2.0
VP (UM3)
65.217
65.19
77.715
77.66
88.464
88.39
98.042
97.95
106.764
106.7
114.825
114.7
122.356
122.2
129.45
129.3
136.175
136
142.583
142.4
Farfield Plume Width
160
140
120
g 100
5 80
£ 60
40
20
0
0 20 40 60 80 100 120 140 160
PLUMES2.0
y =
0.998x +
¦0.1111.
g.M*
0
R2 = 1
Figure B.7: Farfield Plume Width Comparison of PLUMES2.0 results and
UM3 model.
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I December 2024 I EPA/600/B-24/339 I
600-,
w
<1)
E
Gi-
ro
to
500-
> 400-|
i
c
o
Q
33
Q)
"£
ro
300-
200-
—i—
200
600-,
w
a;
^ 500-
ro
3
C/5
> 400-
300-
^ 200-
_D
CL
110^
t
03
300 400 500
Farfield Dilution - PLUMES 2.0
—i
600
100 200 300 400 500
Farfield Plume Width (m) - PLUMES 2.0
600
Table B.4. Comparison of PLUMES2.0 Output arid VP (UM3) Output for
Farfield Plume Dilution
43
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I December 2024 I EPA/600/B-24/339 I
Table B.6: PLUMES2.0 Model Skill Relative to Visual Plumes for Farfield Plume Parameters
for the 12 test cases
Dilution Ratio
Relative Error (%)
Plume Width
Relative Error (%)
0.12
0.13
0.25
0.26
0.06
0.09
0.13
0.15
0.06
0.07
0.09
0.10
0.54
0.07
0.07
0.62
0.03
0.06
0.06
0.08
0.12
0.13
0.25
0.26
44
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