September 1996

USER'S MANUAL FOR CORMIX:

A HYDRODYNAMIC MIXING ZONE MODEL

AND DECISION SUPPORT SYSTEM

 FOR POLLUTANT DISCHARGES INTO SURFACE WATERS

 

by

Gerhard H. Jirka , Robert L. Doneker , and Steven W. Hinton 12 3

DeFrees Hydraulics Laboratory

School of Civil and Environmental Engineering

Cornell University

Ithaca, New York 14853-3501

now at: Institute for Hydromechanics, University of Karlsruhe 1

Karlsruhe, D-76131, Germany

now at: Oregon Graduate Institute, PO Box 91000, Portland, OR 97291-1000 2

 National Registry of Capacity Rights, West Peabody, MA 01960 3

Cooperative Agreement No. CX824847-01-0

Project Officer:

Dr. Hiranmay Biswas

OFFICE OF SCIENCE AND TECHNOLOGY

U.S. ENVIRONMENTAL PROTECTION AGENCY

WASHINGTON, DC 20460
ii

Abstract

The Cornell Mixing Zone Expert System highly unsteady environments, such as tidal

(CORMIX, Version 3.0 or higher) is a software reversal conditions, in which transient

system for the analysis, prediction, and design of recirculation and pollutant build-up effects can

aqueous toxic or conventional pollutant occur.

discharges into diverse water bodies. The major

emphasis is on the geometry and dilution In addition, two post-processing models

characteristics of the initial mixing zone -- are linked to the CORMIX system, but can also be

including compliance with regulatory constraints--, used independently. These are CORJET (the

but the system also predicts the behavior of the Cornell Buoyant Jet Integral Model) for the

discharge plume at larger distances. The highly detailed analysis of the near-field behavior of

user-interactive CORMIX system is implemented buoyant jets, and FFLOCATR (the Far-Field

on microcomputers (IBM-PC, or compatible), and Plume Locator) for the far-field delineation of

consists of three integrated subsystems: discharge plumes in non-uniform river or estuary

---CORMIX1 for submerged single port

discharges, This user's manual gives a comprehensive

---CORMIX2 for submerged multiport diffuser description of the CORMIX system; it provides

discharges, guidance for assembly and preparation of

---CORMIX3 for buoyant surface discharges. required input data for the three subsystems; it

While CORMIX was originally developed guidance for interpretation and graphical display

under the assumption of steady ambient of system output; and it illustrates practical

conditions, Version 3.0 also allows application to system application through several case studies.

environments.

delineates ranges of applicability; it provides
iii

Acknowledgments

An earlier version of this user's manual with the United States Environmental Protection

covering the three separate CORMIX subsystems Agency. The authors would like to extend their

(Version 1.0) before they were integrated into a appreciation to Dr. Hiranmay Biswas, Project

comprehensive single system was developed Officer, for his guidance of the project. 

under support form the National Council of the

Paper Industry for Air and Stream Improvement Additional support for the development,

Inc. (NCASI) and was published as Technical testing and evaluation of CORMIX system

Bulletin No. 624 of NCASI (Jirka and Hinton, elements was provided by the State of Delaware

1992). With the permission of NCASI, that user's Department of Natural Resources (Mr. Rick

guide has up until recently also been distributed Greene, Project Officer) during 1991, by the

by the USEPA-Center for Environmental Austrian Verbundgesellschaft (Dr. Gerhard

Assessment Modeling (CEAM), Athens, GA, as Schiller, Project Officer) during 1991/92, and by

part of the modeling support for CORMIX. the State of Maryland Department of Natural

With the completion of CORMIX Version 1992 to 1995.

3.0 and its many new program features, the

present revision and update of the user's manual Cameron Wilkens, Electronics Technician,

has become necessary. This work was in the DeFrees Hydraulics Laboratory, generously

conducted at the DeFrees Hydraulics Laboratory, assisted with solutions for computer hardware

Cornell University, as a Cooperative Agreement and software problems. 

Resources (Dr. Paul Miller, Project Officer) during
iv

Table of Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Metric Conversion Factors 

for Dimensions Used in CORMIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

I Introduction ................................................................. 1

II Background:

Mixing Processes and Mixing Zone Regulations ............................... 3

2.1 Hydrodynamic Mixing Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Near-Field Processes ........................................... 3

2.1.2 Far-Field Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Mixing Zone Regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 Legal Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2 Mixing Zone Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.3 Special Mixing Zone Requirements for Toxic Substances . . . . . . . . . . . . . . 13

2.2.4 Current Permitting Practice on Mixing Zones . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.5 Relationship Between Actual Hydrodynamic Processes and Mixing Zone

Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

III General Features of the CORMIX System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Capabilities and Major Assumptions of the Three Subsystems and the Post-Processor

Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2.1 CORMIX Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2.2 Post-Processor Models CORJET and FFLOCATR . . . . . . . . . . . . . . . . . . . . 18

3.3 System Processing Sequence and Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.4 CORMIX Data Input Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.5 Logic Elements of CORMIX: Flow Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.6 Simulation Elements of CORMIX: Flow Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.7 CORMIX Output Features: Design Summary and Iterations . . . . . . . . . . . . . . . . . . . . 21

3.7.1 CORMIX Session Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.7.2 CORMIX1, 2 or 3 Prediction File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.7.3 CMXGRAPH Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.8 Post-Processor Models CORJET and FFLOCATR: Input and Output Features . . . . 23

3.9 Equipment Requirements, System Installation and Run Times . . . . . . . . . . . . . . . . . . 23

IV CORMIX Data Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1 General Aspects of Interactive Data Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Site/Case Identifier Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.3 Ambient Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3.1 Bounded Cross-Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
v

4.3.2 Unbounded Cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3.3 Tidal Reversing Ambient Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.3.4 Ambient Density Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.5 Wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.4. Discharge Data: CORMIX1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.4.1 Discharge Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.4.2 Port Discharge Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.5 Discharge Data: CORMIX2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.5.1 Diffuser Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.5.2 Diffuser Discharge Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.6 Discharge Data: CORMIX3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.6.1 Discharge Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.6.2 Discharge Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.7 Pollutant Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.8 Mixing Zone Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.9 Units of Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

V CORMIX Output Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.1 Qualitative Output: Flow Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.1.1 Descriptive Messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.1.2 Length Scale Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.1.3 Description of Flow Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.2 Quantitative Output: Numerical Flow Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.2.1 Summary Output in SUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.2.2 Detailed Prediction Output Filefn'.CXn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.3 Graphical Output: Display and Plotting of Plume Features Using CMXGRAPH . . . . 57

5.3.1 Access to CMXGRAPH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.3.2 Use of CMXGRAPH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

VI Post-Processor Models CORJET and FFLOCATR:

Input and Output Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.1 CORJET: The Cornell Buoyant Jet Integral Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.1.1 General Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.1.2 Access to CORJET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.1.3 CORJET Input Data File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.1.4 CORJET Output Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.2 FFLOCATR: The Far-Field Plume Locator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.2.1 General Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.2.2 Access to FFLOCATR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.2.3 FFLOCATR Cumulative Discharge Input Data File . . . . . . . . . . . . . . . . . . . . 76

6.2.4 FFLOCATR Output Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

VII Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

7.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

7.2 System and Documentation Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

7.3 User Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Literature References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Appendix A

Flow Classification Diagrams for the Three CORMIX Subsystems . . . . . . . . . . . . . . . 83
vi

Appendix B

CORMIX1: Submerged Single Port Discharge in a Deep Reservoir . . . . . . . . . . . . . . . 93

Appendix C

CORMIX1 and 2: Submerged Single Port Discharge

and Multiport Diffuser in a Shallow River . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Appendix D

CORMIX3: Buoyant Surface Discharge In An Estuary . . . . . . . . . . . . . . . . . . . . . . . . . 125

Appendix E

Two Applications of CORJET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
vii

Glossary

Actual Water Depth (HD) - the actual water depth at the submerged discharge location. It is also called

local water depth. For surface discharges it is the water depth at the channel entry location.

Alignment Angle (GAMMA) - the angle measured counterclockwise from the ambient current direction

to the diffuser axis. 

Allocated Impact Zone - see mixing zone.

Alternating Diffuser - a multi-port diffuser where the ports do not point in a nearly single horizontal

direction.

Ambient Conditions - the geometric and dynamic characteristics of a receiving water body that impact

mixing zone processes. These include plan shape, vertical cross sections, bathymetry, ambient

velocity, and density distribution.

Ambient Currents - A velocity field within the receiving water which tends to deflect a buoyant jet into

the current direction.

Ambient Discharge (QA) - the volumetric flow rate of the receiving water body.

Average Diameter (D0) - the average diameter of the discharge ports or nozzles for a multi-port diffuser.

Average Depth (HA) - the average depth of the receiving water body determined from the equivalent

cross sectional area during schematization.

Bottom Slope (SLOPE) - the slope of the bottom that extends from a surface discharge into the

receiving water body.

Buoyant Jet - a discharge where turbulent mixing is caused by a combination of initial momentum flux

and buoyancy flux. It is also called a forced plume.

Buoyant Spreading Processes - far-field mixing processes which arise due to the buoyant forces caused

by the density difference between the mixed flow and the ambient receiving water.

Buoyant Surface Discharge - the release of a positively or neutrally buoyant effluent into a receiving

water through a canal, channel, or near-surface pipe.

Coanda Attachment - a dynamic interaction between the effluent plume and the water bottom that

results from the entrainment demand of the effluent jet itself and is due to low pressure effects.

Cumulative Discharge - refers to the volumetric flow rate which occurs between the bank/shoreline and

a given position within the water body.

Cumulative Discharge Method - an approach for representing transverse plume mixing in river or

estuary flow by describing the plume centerline as being fixed on a line of constant cumulative discharge

and by relating the plume width in terms of a cumulative discharge increment

Darcy-Weisbach Friction Factor - a measure of the roughness characteristics in a channel.

Deep Conditions - see near-field stability.
viii

Density Stratification - the presence of a vertical density profile within the receiving water.

Diffuser Length (LD) - The distance between the first and last port of a multi-port diffuser line. See

diffuser line.

Diffuser Line - a hypothetical line between the first and last ports of a multi-port diffuser. 

Discharge Velocity (U0) - the average velocity of the effluent being discharged from the outfall structure.

Discharge from Shore (DISTB) - the average distance between the outfall location (or diffuser midpoint) and the shoreline. It is also specified as a cumulative ambient discharge divided by the product

UA times HA.

Distance from Shore (YB1, YB2) - the distance from the shore line to the first and last ports of a multiport diffuser.

Discharge Flow Rate (Q0) - the volumetric flow rate from the discharge structure.

Discharge Channel Width (B0) - the average width of a surface discharging channel. 

Discharge Channel Depth (H0) - the average depth of a surface discharging channel.

Discharge Conditions - the geometric and flux characteristics of an outfall installation that effect mixing

processes. These include port area, elevation above the bottom and orientation, effluent discharge flow

rate, momentum flux, and buoyancy flux.

Far-field - the region of the receiving water where buoyant spreading motions and passive diffusion

control the trajectory and dilution of the effluent discharge plume.

Far-field Processes - physical mixing mechanisms that are dominated by the ambient receiving water

conditions, particularly ambient current velocity and density differences between the mixed flow and the

ambient receiving water.

FAST-CORMIX - a version of CORMIX data entry with short questions and without help sections; can

be chosen in main menu; for advanced users.

Flow Classification - the process of identifying the most appropriate generic qualitative description of

the discharge flow undergoing analysis. This is accomplished by examining known relationships

between flow patterns and certain calculated physical parameters.

Flux Characteristics - the properties of effluent discharge flow rate, momentum flux and buoyancy flux

for the effluent discharge.

Forced Plume - see buoyant jet.

Generic Flow Class - a qualitative description of a discharge flow situation that is based on known

relationships between flow patterns and certain physical parameters.

Height of Port (H0) - the average distance between the bottom and the average nozzle centerline.

High Water Slack (HWS) - the time of tidal reversal nearest to MHW

Horizontal Angle (SIGMA) - the angle measured counterclockwise from the ambient current direction
ix

to the plane projection of the port center line.

Hydrodynamic Mixing Processes - the physical processes that determine the fate and distribution of

effluent once it is discharged.

Input Data Sequence - a group of questions from one of four topical areas.

Intermediate-field Affects - induced flows in shallow waters which extend beyond the strictly near-field

region of a multi-port diffuser.

Iteration Menu - the last menu (red panel) the user can choose after completion of a design case; allows

iteration with different ambient/discharge/regulatory conditions.

Jet - see pure jet.

Laterally Bounded - refers to a water body which is constrained on both sides by banks such as rivers,

streams, estuaries and other narrow water courses.

Laterally Unbounded - a water body which for practical purposes is constrained on at most one side.

This would include discharges into wide lakes, wide estuaries and coastal areas.

Legal Mixing Zone (LMZ) - see regulatory mixing zone.

Length Scale - a dynamic measure of the relative influence of certain hydrodynamic processes on

effluent mixing.

Length Scale Analysis - an approach which uses calculated measures of the relative influence of certain

hydrodynamic processes to identify key aspects of a discharge flow so that a generic flow class can be

identified.

Local Water Depth (HD) - see actual water depth.

Low Water Slack (LWS) - the time of tidal reversal nearest to MLW

Main Menu - the first menu (red panel) the user can choose from when entering CORMIX.

Manning's n - a measure of the roughness characteristics in a channel. 

Maximum Tidal Velocity (Uamax) - the maximum velocity occurring within the tidal cycle

Mean Ambient Velocity (UA) - the average velocity of the receiving water body's flow.

Mean High Water (MLW) - the highest water level (averaged over many tidal cycles) in estuarine or

coastal flows.

Mean Low Water (MLW) - the lowest water level (averaged over many tidal cycles) in estuarine or

coastal flows.

Merging - the physical interaction of the discharge plumes from adjacent ports of a multi-port diffuser.

Mixing Zone - an administrative construct which defines a limited area or volume of the receiving water

where the initial dilution of a discharge is allowed to occur. In practice, it may occur within the near-field

or far-field of a hydrodynamic mixing process and therefore depends on source, ambient, and regulatory
x

constraints.

Mixing Zone Regulations - The administrative construct that intends to prevent any harmful impact of

a discharged effluent on the aquatic environment and its designated uses.

Momentum Jet - see pure jet.

Multi-port Diffuser - a structure with many closely spaced ports or nozzles that inject more than one

buoyant jet into the ambient receiving water body.

Near-field - the region of a receiving water where the initial jet characteristic of momentum flux,

buoyancy flux and outfall geometry influence the jet trajectory and mixing of an effluent discharge.

Near-Field Region (NFR) - a term used in the CORMIX printout for describing the zone of strong initial

mixing where the so called near-field processes occur. It is the region of the receiving water where

outfall design conditions are most likely to have an impact on in-stream concentrations.

Near-field Stability - the amount of local recirculation and re-entrainment of already mixed water back

into the buoyant jet region. Stable discharge conditions are associated with weak momentum and deep

water and are also sometimes called deep water conditions. Unstable discharge conditions have

localized recirculation patterns and are also called shallow water conditions.

Negative Buoyancy - the measure of the tendency of an effluent discharge to sink in a receiving water.

Non-buoyant Jet - see pure jet.

Open Format - data input which does not require precise placement of numerical values in fixed fields

and which allows character strings to be entered in either upper or lower case letters.

Passive Ambient Diffusion Processes - far-field mixing processes which arise due to existing turbulence

in the ambient receiving water flow.

Plume - see buoyant jet.

Positive Buoyancy - the measure of the tendency of an effluent discharge to rise in the receiving water.

Post-Processor - several options available within CORMIX (main menu or iteration menu) for additional

computation or data display, including a graphics package, a near-field buoyant jet model, and a far-field

plume delineator.

Pure Jet - a discharge where only the initial momentum flux in the form of a high velocity injection

causes turbulent mixing. It is also called momentum jet or non-buoyant jet.

Pure Plume - a discharge where only the initial buoyancy flux leads to local vertical accelerations which

then lead to turbulent mixing. 

Pycnocline - a horizontal layer in the receiving water where a rapid density change occurs.

Pycnocline Height (HINT) - the average distance between the bottom and a horizontal layer in the

receiving water body where a rapid density change occurs.

Region Of Interest (ROI) - a user defined region of the receiving water body where mixing conditions

are to be analyzed.
xi

Regulatory Mixing Zone (RMZ) - the region of the receiving water where mixing zone regulations are

applied. It is sometimes referred to as the legal mixing zone.

Relative Orientation Angle (BETA) - the angle measured either clockwise or counterclockwise from the

average plan projection of the port centerline to the nearest diffuser axis.

Schematization - the process of describing a receiving water body's actual geometry with a rectangular

cross section.

Shallow Water Conditions - see near-field stability.

Stable Discharge - see near-field stability.

Staged Diffuser - a multi-port diffuser where all ports point in one direction, generally following the

diffuser line. 

Stagnant Conditions - the absence of ambient receiving water flow. A condition which rarely occurs in

actual receiving water bodies.

Submerged Multi-port Diffuser - an effluent discharge structure with more than one efflux opening that

is located substantially below the receiving water surface.

Submerged Single Port Discharge - an effluent discharge structure with a single efflux opening that is

located substantially below the receiving water surface.

Surface Buoyant Jets - positively or neutrally buoyant effluent discharges occurring horizontally at the

water surface from a latterly entering channel or pipe.

Surface Width (BS) - the equivalent average surface width of the receiving water body determined from

the equivalent rectangular cross sectional area during schematization.

Tidal cycle - the variation of ambient water depth and velocity as a function of time occurring due to tidal

(lunar and solar) influences.

Tidal period (PERIOD) - the duration of the tidal cycle (on average 12.4 hours).

Tidal reversal - the two instances in the tidal cycle when the ambient velocity reverses its direction.

Toxic Dilution Zone (TDZ) - the region of the receiving water where the concentration of a toxic chemical

may exceed the acute effects concentration.

Unidirectional Diffuser - a multi-port diffuser with all ports pointing to one side of the diffuser line and

all ports oriented more or less normally to the diffuser line. 

Unstable Discharge - see near-field stability.

Vertical Angle (THETA) - the angle between the port centerline and the horizontal plane.

Wake Attachment - a dynamic interaction of the effluent plume with the bottom that is forced by the

receiving water crossflow.

Zone of Initial Dilution - a term sometimes used to describe the mixing zone for the discharge of

municipal wastewater into the coastal ocean, limited to the extent of near-field mixing processes.
xii

Metric Conversion Factors

for Dimensions Used in CORMIX

Length: 1 m = 3.281 ft

= 39.37 in

= 0.0006214 mile

Velocity: 1 m/s = 3.281 ft/s (fps) 

= 2.237 miles/hr (mph) 

= 1.943 knots

Discharge: 1 m /s = 35.31 ft /s (cfs) 3 3

= 22.82 million-gal/day (mgd)

Density: 1000 kg/m = 62.43 lb/ft 3 3

Temperature: C = ( F - 32.0) * 0.5556 o o
1

I Introduction

The Cornell Mixing Zone Expert System Several factors provided the original

(CORMIX) is a software system for the analysis, impetus for system development including: (a) the

prediction, and design of aqueous toxic or considerable complexity of mixing processes in

conventional pollutant discharges into diverse the aquatic environment, resulting from the great

water bodies. It was developed under several diversity of discharge and site conditions and

cooperative funding agreements between U.S. requiring advanced knowledge in a specialized

EPA and Cornell University during the period field of hydrodynamics; (b) the failure of

1985-1995. It is a recommended analysis tool in previously existing models (e.g. the U.S. EPA

key guidance documents (1,2,3) on the permitting plume models (4) originally developed for

of industrial, municipal, thermal, and other point municipal discharges in deep coastal waters) to

source discharges to receiving waters. Although adequately predict often routine discharge

the system's major emphasis is on predicting the situations, especially for more shallow inland

geometry and dilution characteristics of the initial sites; (c) the issuance in 1985 by the U.S. EPA of

mixing zone so that compliance with water quality additional guidelines (1) for the permitting of toxic

regulatory constraints may be judged, the system aqueous discharges, placing yet another burden

also predicts the behavior of the discharge plume on both applicants and regulators in delineating

at larger distances. special zones for the initial mixing of these

The highly user-interactive CORMIX computer methods, so-called expert systems, for

system is implemented on IBM-DOS compatible making accessible to the user, within a simple

microcomputers, utilizes a rule-based systems personal computing environment, the expert's

approach to data input and processing, and knowledge and experience in dealing with

consists of three subsystems. These are: (a) complex engineering problems.

CORMIX1 for the analysis of submerged single

port discharges, (b) CORMIX2 for the analysis of Four separate publications (5,6,7,8)

submerged multiport diffuser discharges and (c) describe the scientific basis for the CORMIX

CORMIX3 for the analysis of buoyant surface system and demonstrate comparison and

discharges. Without specialized training in validation with field and laboratory data. The

hydrodynamics, users can make detailed results of these works are summarized in the

predictions of mixing zone conditions, check peer-reviewed literature (9,10,11,12,13,14,15,

compliance with regulations and readily 16,17). The CORMIX systems approach and its

investigate the performance of alternative outfall performance relative to the earlier U.S. EPA

designs. The basic CORMIX methodology relies plume models in the context of estuarine

on the assumption of steady ambient conditions. applications is also described in EPA's technical

However, recent versions also contain special guidance manual for performing waste load

routines for the application to highly unsteady allocations in estuaries (3).

environments, such as tidal reversal conditions, in

which transient recirculation and pollutant build-up EPA's established policy is to make the

effects can occur. CORMIX system freely available to all potential

In addition, several post-processing facility at the U.S. EPA Center for Environmental

options are available. These are CORJET (the Assessment Modeling (CEAM) in Athens,

Cornell Buoyant Jet Integral Model) for the Georgia. Some of the CORMIX subsystems have

detailed analysis of the near-field behavior of been available to the industrial and regulatory

buoyant jets, FFLOCATR (the Far-Field Plume user communities since December 1989 when

Locator) for the far-field delineation of discharge distribution of CORMIX1 was commenced by

plumes in non-uniform river or estuary Cornell University for the purpose of identifying

environments, and CMXGRAPH, a graphics subtle programming errors through application to

package for plume plotting. actual mixing zone analysis problems by a

substances; and (d) the availability of new

users through its modeling software distribution
2

controlled users group. After this testing was management positions desiring an overview of

deemed complete, CEAM commenced the the CORMIX systems capabilities, and 2)

distribution of CORMIX1 in November 1990. A technical staff needing assistance in actual

similar approach was used to introduce CORMIX2 applications. Chapter II provides a summary of

which began CEAM distribution in October 1991. the physical processes of effluent mixing, as well

In 1992, CORMIX1, CORMIX2, and CORMIX3 as an overview of the regulatory background and

were integrated a single program and distributed practice on mixing zone applications. The

by USEPA-CEAM as CORMIX Version 2.1 as of general features of the CORMIX system are

1993. explained in Chapter III including summaries of:

Additional development of the post- overall system structure and method of

processor modules, including plume graphics, the processing information, (c) user interaction, and

jet-integral model, and the far-field locator, were (d) individual computational elements. Detailed

added to the system and distributed as CORMIX guidance on the preparation and entry of input

Version 3.0 as of 1994. data, as required by the three CORMIX

This manual describes the operation of a provides a description of system output,

revised version, including a special routine for containing descriptive, quantitative, and graphical

unsteady tidal applications, denoted as CORMIX information on the predicted effluent flow.

Version 3.1 that has been distributed by Cornell Chapter VI describes the background, input and

as of June 1995. A slightly updated Version 3.2 output features of the CORJET jet integral model

will be distributed by USEPA-CEAM as of and the far-field plume locator program

September 1996. FFLOCATR. The closing remarks in Chapter VII

The objectives of this user's guide are as user support, and on possible future

follows: (a) to provide a comprehensive developments and enhancements.

description of the CORMIX system; (b) to provide

guidance for assembly and preparation of Appendices to this guide present four

required input data for all three subsystems as case studies on the application of all three

well as the post-processor models; (c) to CORMIX subsystems and its post-processor

delineate ranges of applicability of the models. These are adapted from actual

subsystems; (d) to provide guidance for the situations and illustrate the complete input

interpretation and graphical display of system requirements and output capabilities of the

output; and (e) to illustrate practical system system. In addition, some of the assumptions on

application through several case studies. data schematization, problem simplification, and

This manual is organized to meet the displays are discussed in a context typical of

informational needs of two distinctly different many mixing zone model applications. 

groups of readers: 1) personnel in environmental

(a) predictive capabilities and limitations, (b)

subsystems, is given in Chapter IV. Chapter V

contain information on system availability and

output interpretation, and construction graphical
3

II Background:

Mixing Processes and Mixing Zone Regulations

When performing design work and and construction details represent additional

predictive studies on effluent discharge problems, geometric features; and for surface discharges

it is important to clearly distinguish between the the cross-section and orientation of the flow

physical aspects of hydrodynamic mixing

processes that determine the effluent fate and

distribution, and the administrative construct of

mixing zone regulations that intend to prevent

any harmful impact of the effluent on the aquatic

environment and associated uses.

2.1 Hydrodynamic Mixing Processes

The mixing behavior of any wastewater

discharge is governed by the interplay of ambient

conditions in the receiving water body and by the

discharge characteristics.

The ambient conditions in the receiving

water body, be it stream, river, lake, reservoir,

estuary or coastal waters, are described by the

water body's geometric and dynamic

characteristics. Important geometric parameters

include plan shape, vertical cross-sections, and

bathymetry, especially in the discharge vicinity.

Dynamic characteristics are given by the velocity

and density distribution in the water body, again

primarily in the discharge vicinity. In many cases,

these conditions can be taken as steady-state

with little variation because the time scale for the

mixing processes is usually of the order of

minutes up to perhaps one hour. In some cases,

notably tidally influenced flows, the ambient

conditions can be highly transient and the

assumption of steady-state conditions may be

inappropriate. In this case, the effective dilution

of the discharge plume may be reduced relative to

that under steady state conditions.

The discharge conditions relate to the

geometric and flux characteristics of the

submerged outfall installation. For a single port

discharge the port diameter, its elevation above

the bottom and its orientation provide the

geometry; for multiport diffuser installations the

arrangement of the individual ports along the

diffuser line, the orientation of the diffuser line,

entering the ambient watercourse are important.

The flux characteristics are given by the effluent

discharge flow rate, by its momentum flux and by

its buoyancy flux. The buoyancy flux represents

the effect of the relative density difference

between the effluent discharge and ambient

conditions in combination with the gravitational

acceleration. It is a measure of the tendency for

the effluent flow to rise (i.e. positive buoyancy)

or to fall (i.e. negative buoyancy).

The hydrodynamics of an effluent

continuously discharging into a receiving water

body can be conceptualized as a mixing process

occurring in two separate regions. In the first

region, the initial jet characteristics of momentum

flux, buoyancy flux, and outfall geometry influence

the jet trajectory and mixing. This region will be

referred to as the "near-field", and encompasses

the buoyant jet flow and any surface, bottom or

terminal layer interaction. In this near-field region,

outfall designers can usually affect the initial

mixing characteristics through appropriate

manipulation of design variables.

As the turbulent plume travels further

away from the source, the source characteristics

become less important. Conditions existing in the

ambient environment will control trajectory and

dilution of the turbulent plume through buoyant

spreading motions and passive diffusion due to

ambient turbulence. This region will be referred

to here as the "far-field". It is stressed at this

point that the distinction between near-field and

far-field is made purely on hydrodynamic grounds.

It is unrelated to any regulatory mixing zone

definitions.

2.1.1 Near-Field Processes

Three important types of near-field

processes are submerged buoyant jet mixing,

boundary interactions and surface buoyant jet

mixing as described in the following paragraphs.
4

Submerged Buoyant Jet Mixing: The effluent ports. After merging, a two-dimensional buoyant

flow from a submerged discharge port provides a jet plane is formed as illustrated in Figure 2.1d.

velocity discontinuity between the discharged fluid Such plane buoyant jets resulting from a multiport

and the ambient fluid causing an intense shearing diffuser discharge in deep water can be further

action. The shearing flow breaks rapidly down affected by ambient currents and by density

into a turbulent motion. The width of the zone of stratification as discussed in the preceding

high turbulence intensity increases in the direction paragraph. 

of the flow by incorporating ("entraining") more of

the outside, less turbulent fluid into this zone. In

this manner, any internal concentrations (e.g. fluid

momentum or pollutants) of the discharge flow

become diluted by the entrainment of ambient

water. Inversely, one can speak of the fact that

both fluid momentum and pollutants become

gradually diffused into the ambient field.

The initial velocity discontinuity may arise

in different fashions. In a "pure jet" (also called

"momentum jet" or "non-buoyant jet"), the initial

momentum flux in the form of a high-velocity

injection causes the turbulent mixing. In a "pure

plume," the initial buoyancy flux leads to local processes provide a transition between the

vertical accelerations which then lead to turbulent buoyant jet mixing process in the near-field, and

mixing. In the general case of a "buoyant jet"

(also called a "forced plume"), a combination of

initial momentum flux and buoyancy flux is

responsible for turbulent mixing.

Thus, buoyant jets are characterized by a

narrow turbulent fluid zone in which vigorous The assessment of near-field stability,

mixing takes place. Furthermore, depending on i.e. the distinction of stable or unstable conditions,

discharge orientation and direction of buoyant is a key aspect of effluent dilution analyses. It is

acceleration, curved trajectories are generally especially important for understanding the

established in a stagnant uniform-density behavior of the two-dimensional plumes resulting

environment as illustrated in Figure 2.1a. from multiport diffusers, as shown by some

Buoyant jet mixing is further affected by

ambient currents and density stratification. The

role of ambient currents is to gradually deflect

the buoyant jet into the current direction as

illustrated in Figure 2.1b and thereby induce

additional mixing. The role of ambient density

stratification is to counteract the vertical

acceleration within the buoyant jet leading

ultimately to trapping of the flow at a certain level.

Figure 2.1c shows a typical buoyant jet shape at

the trapping or terminal level.

Finally, in case of multiport diffusers, the

individual round buoyant jets behave

independently until they interact, or merge, with

each other at a certain distance from the efflux

Boundary Interaction Processes and NearField Stability: Ambient water bodies always

have vertical boundaries. These include the

water surface and the bottom, but in addition,

"internal boundaries" may exist at pycnoclines.

Pycnoclines are layers of rapid density change.

Depending on the dynamic and geometric

characteristics of the discharge flow, a variety of

interaction phenomena can occur at such

boundaries, particularly where flow trapping may

occur. 

In essence, boundary interaction

between buoyant spreading and passive diffusion

in the far-field. They can be gradual and mild, or

abrupt leading to vigorous transition and mixing

processes. They also can significantly influence

the stability of the effluent discharge conditions. 

examples in Figure 2.2. "Stable discharge"

conditions, usually occurring for a combination of

strong buoyancy, weak momentum and deep

water, are often referred to as "deep water"

conditions (Figures 2.2a,c). "Unstable

discharge" conditions, on the other hand, may be

considered synonymous to "shallow water"

conditions (Figure 2.2b,d). Technical discussions

on discharge stability are presented elsewhere

(18,19).

A few important examples of boundary

interaction for a single round buoyant jet are

illustrated in Figure 2.3. If a buoyant jet is bentover by a cross-flow, it will gradually approach the

surface, bottom or terminal level and will undergo

a smooth transition with little additional mixing
impingement point can take on one of the

following forms: (a) If the flow has sufficient

buoyancy it will ultimately form a stable layer at

the surface (Figure 2.3b). In the presence of

weak ambient flow this will lead to an upstream

intrusion against the ambient current. (b) If the

buoyancy of the effluent flow is weak or its

momentum very high, unstable recirculation

phenomena can occur in the discharge vicinity

(Figure 2.3~). This local recirculation leads to reentrainment of already mixed water back into the

buoyant jet region. (c) In the intermediate case, a

combination of localized vertical mixing and

upstream spreading may result (Figure 2.3d).

holly

lurne-like

O) Buoyant Jet in Stagnant

Uniform Ambient

Ambient

Slronqly deflected

Neokly

deflected

b) Euoyont Jet in Uniform

Ambient Cross-Current

Another type of interaction process

concerns submerged buoyant jets discharging in

the vicinity of the water bottom into a stagnant or

flowing ambient. Two types of dynamic interaction

processes can occur that lead to rapid attachment

of the effluent plume to the water bottom as

illustrated in Figure 2.4. These are wake

attachment forced by the receiving water’s

crossflow or Coanda attachment forced by the

entrainment demand of the effluent jet itself. The

latter is due to low pressure effects as the jet

pertphely is close to the water bottom.

Terminal

C) Buoyant Jet in Stagnant

Stratified Ambient

Round_, Plane

p jets I jet

d)

Side View Tap View

Jet Merging for Unidirectional

Multipart Diffuser Forming Plane

Buoyant Jet

Figure 2.1: Typical buoyant jet mixing flow patterns under different ambient conditions

5

-
6

Figure 2.2: Examples of near-field stability and instability conditions for submerged discharges in

limited water depth
7

Figure 2.3: Examples of boundary interactions for submerged jets in finite depth
8

Figure 2.4: Examples of wake (crossflow induced) attachment and Coanda attachment conditions for

jets discharging near boundaries
9

Surface Buoyant Jet Mixing: Positively

buoyant jets discharged horizontally along the

water surface from a laterally entering channel or

pipe (Figure 2.5) bear some similarities to the

more classical submerged buoyant jet. For a

relatively short initial distance, the effluent

behaves like a momentum jet spreading both

laterally and vertically due to turbulent mixing. 

After this stage, vertical entrainment becomes

inhibited due to buoyant damping of the turbulent

motions, and the jet experiences strong lateral

spreading. During stagnant ambient conditions,

ultimately a reasonably thin layer may be formed

at the surface of the receiving water; that layer

can undergo the transient buoyant spreading

motions depicted in Figure2.5a.

2.5: Typical buoyant surface jet mixing flow patterns under stagnant or flowing ambient conditions
10

In the presence of ambient crossflow, Far-field mixing processes are

buoyant surface jets may exhibit any one of characterized by the longitudinal advection of the

following three types of flow features: They may mixed effluent by the ambient current velocity.

form a weakly deflected jet that does not interact

with the shoreline (Figure 2.5b). When the

crossflow is strong, they may attach to the

downstream boundary forming a shore-hugging

plume (Figure 2.5c). When a high discharge

buoyancy flux combines with a weak crossflow,

the buoyant spreading effects can be so strong

that an upstream intruding plume is formed that

also stays close to the shoreline (Figure 2.5d).

Intermediate-Field Effects for Multiport large distances in the transverse direction,

Diffuser Discharges: Some multiport diffuser

installations induce flows in shallow water which

extend beyond the strict near-field region. The

resulting plumes are sometimes referred to as the

"intermediate-field" (18) because they interact

with the receiving water at distances that are

substantially greater than the water depth; the

order of magnitude of the water depth is typically

used to define the dimensions of the near-field

region. Intermediate fields may occur when a

multiport diffuser represents a large source of

momentum with a relatively weak buoyancy effect.

Such a diffuser will have an unstable near-field

with shallow water conditions. For certain diffuser

geometries (e.g. unidirectional & staged diffuser

types; see Section V) strong motions can be

induced in the shallow water environment in the

form of vertically mixed currents that laterally

entrain ambient water and may extend over long

distances before they re-stratify or dissipate their

momentum. 

Another type of interaction process

concerns submerged buoyant jets discharging in

the vicinity of the water bottom into a stagnant or

flowing ambient. Two types of dynamic

interaction processes can occur that lead to rapid

attachment of the effluent plume to the water

bottom as illustrated in Figure 2.4. These are

wake attachment forced by the receiving water's

crossflow or Coanda attachment forced by the

entrainment demand of the effluent jet itself. The

latter is due to low pressure effects as the jet

periphery is close to the water bottom.

2.1.2 Far-Field Processes 

Buoyant Spreading Processes: These are

defined as the horizontally transverse spreading

of the mixed effluent flow while it is being

advected downstream by the ambient current.

Such spreading processes arise due to the

buoyant forces caused by the density difference

of the mixed flow relative to the ambient density.

They can be effective transport mechanisms that

can quickly spread a mixed effluent laterally over

particularly in cases of strong ambient

stratification. In this situation, effluent of

considerable vertical thickness at the terminal

level can collapse into a thin but very wide layer

unless this is prevented by lateral boundaries. If

the discharge is non-buoyant, or weakly buoyant,

and the ambient is unstratified, there is no

buoyant spreading region in the far-field, only a

passive diffusion region.

Depending on the type of near-field flow

and ambient stratification, several types of

buoyant spreading may occur. These include: (a)

spreading at the water surface, (b) spreading at

the bottom, (c) spreading at a sharp internal

interface (pycnocline) with a density jump, or (d)

spreading at the terminal level in continuously

stratified ambient fluid. As an example, the

definition diagram and structure of surface

buoyant spreading processes somewhat

downstream of the discharge in unstratified

crossflow is shown in Figure 2.6.

The laterally spreading flow behaves like

a density current and entrains some ambient fluid

in the "head region" of the current. During this

phase, the mixing rate is usually relatively small,

the layer thickness may decrease, and a

subsequent interaction with a shoreline or bank

can impact the spreading and mixing processes.

Passive Ambient Diffusion Processes: The

existing turbulence in the ambient environment

becomes the dominating mixing mechanism at

sufficiently large distances from the discharge

point. In general, the passively diffusing flow

grows in width and in thickness until it interacts
11

The strength of the ambient diffusion

mechanism depends on a number of factors

relating mainly to the geometry of the ambient

shear flow and the amount of ambient

stratification. In the context of classical diffusion

theory (20), gradient diffusion processes in the

bounded flows of rivers or narrow estuaries can

be described by constant diffusivities in the

vertical and horizontal direction that depend on

turbulent intensity and on channel depth or width

as the length scales. In contrast, wide

"unbounded" channels or open coastal areas are

characterized by plume size dependent

diffusivities leading to accelerating plume growth

described, for example, by the "4/3 law" of

diffusion. In the presence of a stable ambient

stratification, the vertical diffusive mixing is

generally strongly damped. 

Figure 2.6: Buoyant spreading processes downstream of the near-field region (example of spreading

along the water surface)
12

Figure 2.7: Passive ambient diffusion process with advection in the far-field

2.2 Mixing Zone Regulations

The discharge of waste water into a

water body can be considered from two vantage

points regarding its impact on ambient water

quality. On a larger scale, seen over the entire

receiving water body, care must be taken that

water quality conditions that protect designated

beneficial uses are achieved. This is the realm

of the general waste load allocation (WLA)

procedures and models.

On a local scale, or in the immediate

discharge vicinity, additional precautions must be

taken to insure that high initial pollutant

concentrations are minimized and constrained to

small zones, areas, or volumes. The generic

definition of these zones, commonly referred to

as "mixing zones", is embodied in federal water

quality regulations and often cited in the

regulations of permit granting authorities. As

stated previously, mixing zones are

administrative constructs that are independent of

hydrodynamic mixing processes.

2.2.1 Legal Background

The Clean Water Act of 1977 defines five

general categories of pollutants. These are: (a)

conventional, (b) nonconventional, (c) toxics, (d)

heat, and (e) dredge and fill spoil. The Act

distinguishes between new and existing sources
13

for setting effluent standards. Pollutants to adopt a mixing zone and to specify its

designated as "conventional" would be "generally dimensions. The U.S. EPA allows the use of a

those pollutants that are naturally occurring, mixing zone in permit applications except where

biodegradable, oxygen demanding materials and one is prohibited in State regulations. A previous

solids. In addition, compounds which are not review (5) of individual State mixing zone policies

toxic and which are similar in characteristics to (1,22) found that 48 out of 50 States make use of

naturally occurring, biodegradable substances are a mixing zone in some form; the exceptions are

to be designated as conventional pollutants for Arizona and Pennsylvania. State regulations

the purposes of the provision." Examples of dealing with streams or rivers generally limit

conventional pollutants are: biochemical oxygen mixing zone widths or cross-sectional areas, and

demand (BOD), total suspended solids, and fecal allow lengths to be determined on a case by case

coliform bacteria. Pollutants designated as basis.

"nonconventional" would be "those which are not

toxic or conventional", and some examples are: In the case of lakes, estuaries and coastal

chemical oxygen demand (COD), fluoride, and waters, some states specify the surface area that

ammonia. "Toxic" pollutants are those that cause can be affected by the discharge. The surface

harmful effects, either acute or chronic, at very area limitation usually applies to the underlying

low concentrations; examples of some designated water column and benthic area. In the absence of

toxic substances are: nickel, chloroform, or specific mixing zone dimensions, the actual shape

benzidine. and size is determined on a case-by-case basis.

2.2.2 Mixing Zone Definitions Special mixing zone definitions have been

The mixing zone is defined as an wastewater into the coastal ocean, as regulated

"allocated impact zone" where numeric water

quality criteria can be exceeded as long as

acutely toxic conditions are prevented. A mixing

zone can be thought of as a limited area or

volume where the initial dilution of a discharge

occurs (21). Water quality standards apply at the zone was labeled as the "zone of initial dilution"

boundary of the mixing zone, not within the mixing in which rapid mixing of the waste stream (usually

zone itself. The U.S. EPA and its predecessor the rising buoyant fresh water plume within the

agencies have published numerous documents ambient saline water) takes place. EPA requires

giving guidance for determining mixing zones. that the "zone of initial dilution" be a regularly

Guidance published by U.S. EPA in the 1984 shaped area (e.g. circular or rectangular)

Water Quality Standards Handbook (21) surrounding the discharge structure (e.g.

supersedes these sources. submerged pipe or diffuser line) that

In setting requirements for mixing zones, standards) pollutant concentrations under design

U.S. EPA (22) requires that "the area or volume of conditions (23). In practice, limiting boundaries

an individual zone or group of zones be limited to defined by dimensions equal to the water depth

an area or volume as small as practicable that will measured horizontally from any point of the

not interfere with the designated uses or with the discharge structure are accepted by the EPA

established community of aquatic life in the provided they do not violate other mixing zone

segment for which the uses are designated," and restrictions (23).

the shape be "a simple configuration that is easy

to locate in the body of water and avoids 2.2.3 Special Mixing Zone Requirements for

impingement on biologically important areas," and Toxic Substances

"shore hugging plumes should be avoided."

The U.S. EPA rules for mixing zones criteria for the allowable concentration of toxic

recognize the State has discretion whether or not substances: a criterion maximum concentration

developed for the discharge of municipal

under Section 301(h) of the Clean Water Act (23).

Frequently, these same definitions are used also

for industrial and other discharges into coastal

waters or large lakes, resulting in a plurality of

terminology. For those discharges, the mixing

encompasses the regions of high (exceeding

The U.S. EPA maintains two water quality
14

(CMC) to protect against acute or lethal effects; situations of severe bottom interaction

and a criterion continuous concentration (CCC) to and surface interaction.

protect against chronic effects (1). The CMC

value is greater than or equal to the CCC value --- The CMC must be met within a distance

and is usually more restrictive. The CCC must be of 5 times the local water depth in any

met at the edge of the same regulatory mixing horizontal direction. The local water depth

zone specified for conventional and noncon- is defined as the natural water depth

ventional discharges. (existing prior to the installation of the

Lethality to passing organisms within the zone design condition (e.g. low flow for

mixing zone can be prevented in one of four rivers). This restriction will prevent

ways: locating the discharge in very shallow

The first alternative is to meet the CMC which would result in significant surface

criterion within the pipe itself. and bottom concentrations (1).

 The second alternative is to meet the A fourth alternative is to show that a

CMC within a short distance from the outfall. If drifting organism would not be exposed more than

dilution of the toxic discharge in the ambient 1-hour to average concentrations exceeding the

environment is allowed, a toxic dilution zone

(TDZ), which is usually more restrictive than the

legal mixing zone for conventional and

nonconventional pollutants, may be used. The

revised 1991 Toxics TSD document (1)

recommends for new discharges a minimum exit

velocity of 3 meters per second (10 feet per

second) in order to provide sufficiently rapid

mixing that would minimize organism exposure

time to toxic material. The TSD does not set a

requirement in this regard, recognizing that the

restrictions listed in the following paragraph can in

many instances also be met by other designs,

especially if the ambient velocity is large.

As the third alternative, the outfall design

must meet the most restrictive of the following

geometric restrictions for a TDZ:

--- The CMC must be met within 10% of the

distance from the edge of the outfall

structure to the edge of the regulatory

mixing zone in any spatial direction.

--- The CMC must be met within a distance

of 50 times the discharge length scale in

any spatial direction. The discharge

length scale is defined as the square-root

of the cross-sectional area of any

discharge outlet. This restriction is

intended to ensure a dilution factor of at

least 10 within this distance under all

possible circumstances, including

discharge outlet) prevailing under mixing

environments or very close to shore,

CMC. 

2.2.4 Current Permitting Practice on Mixing

Zones

It is difficult to generalize the actual

practice in implementing the mixing zone

regulations, given the large number and diverse

types of jurisdictions and permit-granting

authorities involved. By and large, however,

current procedure falls into one of the following

approaches, or may involve a combination

thereof.

(i) The mixing zone is defined by some

numerical dimension, as discussed above. The

applicant must then demonstrate that the existing

or proposed discharge meets all applicable

standards for conventional pollutants or for the

CCC of toxic pollutants at the edge of the

specified mixing zone.

(ii) No numerical definition for a mixing

zone may apply. In this case a mixing zone

dimension may be proposed by the applicant. To

do so the applicant generally uses actual

concentration measurements for existing

discharges, dye dispersion tests or model

predictions to show at what plume distance, width,

or region, the applicable standard will be met.

The applicant may then use further ecological or

water use-oriented arguments to demonstrate that
15

the size of that predicted region provides

reasonable protection. The permitting authority 2.2.5 Relationship Between Actual Hydrodynamic

may evaluate that proposal, or sometimes pursue Processes and Mixing Zone Dimensions

its own independent proposal for a mixing zone.

This approach resembles a negotiating process actual hydrodynamic processes of mixing. With

with the objective of providing optimal protection few exceptions, the toxic dilution criteria apply to

of the aquatic environment consistent with other the near-field of most discharges since the TDZ

uses. criteria (2) are spatially highly restrictive. The

As regards the acute, or CMC, criterion for located in the near-field or the far-field of the

toxic pollutants, the spatial restrictions embodied actual effluent discharge flow since they are

in the Toxics TSD document (1) call for very administratively determined by the permit-granting

specific demonstrations of how the CMC criterion authority. Thus, the analyst must have tools at his

is met at the edge of the "toxic dilution zone". disposal with the capability to address both the

Again, field tests for existing discharges or

predictive models may be used.

The spatial requirements in mixing zone

regulations are not always correlated with the

regular mixing zone boundaries, however, may be

near and far-field situations.
16
17

III General Features of the CORMIX System

This section provides a general are prone to locally recirculating flows. Other

description of common features of CORMIX. non-applicable cases may arise to complicated

CORMIX Version 3.1 has three different discharge geometries in which case CORMIX

subsystem modules for diverse discharge advises the user not to proceed with the analysis.

conditions. The subsystems are CORMIX1, Whenever the model is applicable extensive

CORMIX2, and CORMIX3 for the analysis of comparison with available field and laboratory

submerged single port, submerged multiport, and data has shown that the CORMIX predictions on

buoyant surface outfall configurations, dilutions and concentrations, with associated

respectively. Furthermore, two post-processor plume geometries, are accurate to within ± 50 %

models CORJET, a near-field jet integral model, (standard deviation).

and FFLOCATR, a far-field plume locator in nonuniform channels, are included. The following two The methodology provides answers to

sections give a detailed guidance for developing questions that typically arise during the

the required input data and for understanding application of mixing zone regulations for both

program output. Reference is made throughout conventional and toxic discharges. More

this document to CORMIX Version 3.1 dated June importantly, this is accomplished by utilizing the

1995 or Version 3.2 dated September 1996; other customary approaches often used in evaluating

versions may differ somewhat. and implementing mixing zones, thereby providing

3.1 Overview

The CORMIX system represents a robust

and versatile computerized methodology for

predicting both the qualitative features (e.g. flow

classification) and the quantitative aspects (e.g.

dilution ratio, plume trajectory) of the

hydrodynamic mixing processes resulting from

different discharge configurations and in all types

of ambient water bodies, including small streams,

large rivers, lakes, reservoirs, estuaries, and

coastal waters. The methodology: (a) has been

extensively verified by the developers through

comparison of simulation results to available field

and laboratory data on mixing processes

(5,6,7,8), (b) has undergone independent peer

review in journal proceedings (9,10,11,12,13,

14,15,16,17) and (c) is equally applicable to a

wide range of problems from a simple single

submerged pipe discharge into a small stream

with rapid cross-sectional mixing to a complicated

multiport diffuser installation in a deeply stratified

coastal water. 

System experience suggests that

CORMIX1 applies to better than 95% of

submerged single-port designs, CORMIX2 to

better than 80% of multiport diffusers, and

CORMIX3 to better than 90% of surface

discharges. Lack of applicability is usually given

by highly non-uniform ambient flow conditions that

a common framework for both applicants and

regulatory personnel to arrive at a consensus

view of the available dilution and plume trajectory

for the site and effluent discharge characteristics.

The methodology also provides a way for

personnel with little or no training in

hydrodynamics to investigate improved design

solutions for aquatic discharge structures. To

limit misuse, the system contains limits of

applicability that prevent the simulation of

situations for which no safe predictive methodology exists, or for discharge geometries that are

undesirable from a hydrodynamic viewpoint.

Furthermore, warning labels, data screening

mechanisms, and alternative design

recommendations are furnished by the system.

The system is not fool proof, however, and final

results should always be examined for

reasonableness.

Finally, CORMIX is an educational tool

that intends to make the user more

knowledgeable and appreciative about effluent

discharge and mixing processes. The system is

not simply a black box that produces a final

numerical or graphical output, but contains an

interactive menu of user guidance, help options,

and explanatory material of the relevant physical

processes. These assist users in understanding

model predictions and exploring the sensitivity of

model predictions to assumptions. 
18

3.2 Capabilities and Major Assumptions of the

Three Subsystems and the Post-Processor

Models

3.2.1 CORMIX Subsystems

CORMIX1 predicts the geometry and

dilution characteristics of the effluent flow

resulting from a submerged single port diffuser

discharge, of arbitrary density (positively,

neutrally, or negatively buoyant) and arbitrary

location and geometry, into an ambient receiving

water body that may be stagnant or flowing and

have ambient density stratification of different

types.

CORMIX2 applies to three commonly

used types of submerged multiport diffuser

discharges under the same general effluent and

ambient conditions as CORMIX1. It analyzes

unidirectional, staged, and alternating designs of

multiport diffusers and allows for arbitrary

alignment of the diffuser structure within the

ambient water body, and for arbitrary

arrangement and orientation of the individual

ports. For complex hydrodynamic cases,

CORMIX2 uses the "equivalent slot diffuser"

concept and thus neglects the details of the

individual jets issuing from each diffuser port and

their merging process, but rather assumes that

the flow arises from a long slot discharge with

equivalent dynamic characteristics. Hence, if

details of the effluent flow behavior in the

immediate diffuser vicinity are needed, an

additional CORMIX1 simulation for an equivalent

partial effluent flow may be recommended.

CORMIX3 analyzes buoyant surface

discharges that result when an effluent enters a

larger water body laterally, through a canal,

channel, or near-surface pipe. In contrast to

CORMIX1 and 2, it is limited to positively or

neutrally buoyant effluents. Different discharge

geometries and orientations can be analyzed

including flush or protruding channel mouths, and

orientations normal, oblique, or parallel to the

bank.

Additional major assumptions include the

following:

--- All subsystems require that the actual

cross-section of the water body be

described as a rectangular straight

uniform channel that may be bounded

laterally or unbounded. The ambient

velocity is assumed to be uniform within

that cross-section. 

--- In addition to a uniform ambient density

possibility, CORMIX allows for three

generic types of ambient stratification

profiles to be used for the approximation

of the actual vertical density distribution

(see Section 4.3).

--- All CORMIX subsystems are in principle

steady-state models, however recent

developments (beginning with Version

3.1) allow the analysis of unsteady

mixing in tidal environments. 

--- All CORMIX systems can predict mixing

for both conservative and first-order decay

processes, and can simulate heat transfer

from thermal plumes. 

3.2.2 Post-Processor Models CORJET and

FFLOCATR

CORJET, the Cornell Buoyant Jet Integral

Model, is a buoyant jet integral model that

predicts the jet trajectory and dilution

characteristics of a single round jet or of a series

of merging jets from a multiport diffuser with

arbitrary discharge direction and positive, neutral

or negative buoyancy in a general ambient

environment. The ambient conditions can be

highly non-uniform with both ambient current

magnitude, current direction, and density a

function of vertical distance. In general, CORJET

can be used as an enhancement to the near-field

predictions provided by CORMIX1 or 2 in order to

investigate local details that have been simplified

within the CORMIX representation. The major

limitation of CORJET lies in the assumption of an

infinite receiving water body, similar to all other

available jet integral type models. Thus, CORJET

should only be used after an initial CORMIX

classification has shown that the single or multiple

port discharge is indeed of the deep water type,

i.e. hydrodynamically stable, without boundary

interactions.

FFLOCATR, the Far-Field Plume Locator,

uses the cumulative discharge method to

delineate the CORMIX predicted far-field plume
19

within the actual irregular (meandering or winding) possible generic flow configurations. HYDRO

river or estuary channel geometry with uneven performs the actual detailed numerical prediction

distribution of the ambient flow. of the effluent plume characteristics. Finally, SUM

3.3 System Processing Sequence and

Structure

The general CORMIX layout appears in

Figure 3.1, which shows the overall structure and

the execution sequence of the program elements.

The system has overall common data input

features for the three different discharge

elements. During program execution, the

elements are loaded automatically and

sequentially by the system. Each element

provides user interaction and prompting in

response to displayed information. This may

somewhat extend the total time required for a

single CORMIX session, but has offsetting benefit

of allowing the user to gain process knowledge

and insight on design sensitivity. 

The user has numerous options with the

Main Menu at start-up. Option 1 is to start a new

CORMIX session. Option 2 is to re-run and

modify a former case. Option 3 is to simply redisplay (without new computation) results of a

former design case. Option 4 is to use the PostProcessor, which includes the CORJET near-field

jet integral model, the FFLOCATR far-field

locator, and the plume display graphics which will

be discussed in Section V of this document.

Option 5 is the file manager which lists all files

from previous simulations. Option 6 is to

set/change CORMIX system speed. Here the

user can select REGULAR CORMIX, complete

with detailed queries and user help, or FASTCORMIX, which has terse questions and limited

user help. Option 7 contains system information

and reference material. Option 7 is to quit the

CORMIX system and return to DOS. 

The common program elements of

CORMIX are composed of DATIN, PARAM,

CLASS, HYDRO, and SUM (Figure 3.1). DATIN

is the program element for the entry of data and

initialization of other program elements. PARAM

uses the input data to compute a number of

important physical parameters and length scales,

as precursor to CLASS which performs the

hydrodynamic classification of the given

discharge/ambient situation into one of many

summarizes the results from the classification and

prediction, interprets them as regards mixing zone

regulations, suggests design alternatives, and

allows sensitivity analysis to be conveniently

conducted using the current input data. At this

point the iteration menu allows the user to

perform an iteration with different

ambient/discharge/regulatory conditions, or start

a new design case, or make use of the postprocessor options.

Due to its diverse programming

requirements, CORMIX is written in two

programming languages: VP-Expert, an "expert

systems shell", and Fortran. The former is

powerful in knowledge representation and logical

reasoning, while the latter is adept at

mathematical computations. Program elements

DATIN, PARAM, CLASS, and SUM are written

exclusively in VP-Expert. HYDRO is written in

VP-Expert, but uses three Fortran executables

HYDRO1, 2 and 3 for the actual detailed

computation of plume characteristics. Finally,

C++ is used in the specially developed graphics

package CMXGRAPH.

3.4 CORMIX Data Input Features

All data is entered interactively in

response to the CORMIX system prompts

generated by the data input program element

DATIN. DATIN queries the user for a complete

specification of the physical environment of the

discharge, as well as the applicable regulatory

considerations for the situation undergoing

analysis. A CORMIX session commences with

questions on four topics which are asked

sequentially in this order: site/case descriptions,

ambient conditions, discharge characteristics, and

regulatory mixing zone definitions. Data entry is

entirely guided by the system and the available

advice menu options provide expanded

descriptions of the questions, if clarification is

needed. 

Chapter IV provides complete details on

input specification for the three CORMIX

discharge subsystems. Chapter VI deals with the

input features of the post-processor models

CORJET and FFLOCATR.

21

3.5 Logic Elements of CORMIX: Flow

Classification

To make predictions of an effluent

discharge's dilution and plume trajectory,

CORMIX typically combines the solutions of

several simple flow patterns to provide a complete

analysis from the efflux location all the way into

the far-field. 

The logic processing elements of

CORMIX identify which solutions should be

combined to provide the complete analysis. This

process, called flow classification, develops a

generic qualitative description of the discharge

flow and is based on known relationships

between flow patterns and certain calculated

physical parameters. 

PARAM is the program element that

computes relevant physical parameters including:

the various length scales, fluxes, and other values

needed for the execution of other program elements. Length scales are calculated measures of

the length of dynamic influence of various

physical processes (see Chapters IV and V).

 At the heart of CORMIX is a flow

classification system contained in the program

element CLASS. It provides a rigorous and

robust expert knowledge base that carefully

distinguishes among the many hydrodynamic flow

patterns that a discharge may exhibit. As

examples, these possibilities include discharge

plumes attaching to the bottom, plumes vertically

mixing due to instabilities in shallow water,

plumes becoming trapped internally due to

density stratification, and plumes intruding

upstream against the ambient current due to

buoyancy, and many others. Theoretically based

hydrodynamic criteria using length scale analysis

and empirical knowledge from laboratory and field

experimentation, are applied in a systematic

fashion to identify the most appropriate flow

classification for a particular analysis situation.

For all three subsystems, a total of about 80

generic flow configurations or classes can be

distinguished. 

The classification procedure of CORMIX

is based on technical principles and has been

verified by the developers through repeated

testing and data comparison. It has also

undergone independent peer review and the four

documentation manuals (5,6,7,8) give the detailed

scientific background for the classification

scheme, in form of a number of criteria. The

actual criteria constants are listed in the technical

reports with comments on their sources and

degree of reliability. Experienced users,

especially those involved in research applications,

may want to inspect these data values contained

in the source code and occasionally vary some

constant values within certain limits in order to

examine improved prediction fits with available

high-quality data. Extreme caution must be

exercised when doing that as some values are

interdependent; furthermore, if changes are

made, they should be carefully documented. 

When CLASS has executed, a description

of the particular flow class is available to the user

in the form of on-screen or hardcopy computer

output; these description are also contained in the

documentation reports (5,6,7). It is recommended

that the novice or intermediate user review these

to gain an appreciation of the involved

hydrodynamic mixing processes.

3.6 Simulation Elements of CORMIX: Flow

Prediction

Once a flow has been classified, CORMIX

assembles and executes a sequence of

appropriate hydrodynamic simulation modules in

the program element HYDRO1, 2 or 3. HYDRO

consists of: (a) control programs or "protocols" for

each hydrodynamic flow classification and (b) a

large number of subroutines or "simulation

modules" corresponding to the particular flow

processes, and their associated spatial regions,

that occur within a given flow classification. The

simulation modules are based on buoyant jet

similarity theory, buoyant jet integral models,

ambient diffusion theory, and stratified flow

theory, and on simple dimensional analysis, as

described elsewhere (5,6,7,8). The basic tenet of

the simulation methodology is to arrange a

sequence of relatively simple simulation modules

which, when executed together, predict the

trajectory and dilution characteristics of a complex

flow. Each of the simulation models uses the final

values of the previous module as "initial

conditions".
22

3.7 CORMIX Output Features: Design

Summary and Iterations

In addition to the narrative feedback

during user input, the CORMIX system provides

three types of output on-screen or in print: a)

CORMIX Session Report that is a narrative

summary, mostly for regulatory evaluation, of all

discharge input data and global plume features,

including compliance with mixing zone

regulations, b) CORMIX1, 2 or 3 Prediction File

that is a detailed listing of all plume properties as

predicted by the Fortran program, and c)

CMXGRAPH Plots representing plan, side, and

trajectory views and concentration distribution of

the predicted plume.

3.7.1 CORMIX Session Report

Region of Interest (ROI): The ROI is a

SUM is the final program element that user defined region of the receiving water

summarizes the hydrodynamic simulation results body where mixing conditions are to be

for the case under consideration. The output in analyzed. It is specified as the maximum

the CORMIX Session Report is arranged in four analysis distance in the direction of mixed

groups: effluent flow and is particularly important

(1) Site summary gives the site identifier exist or when information over a larger

information, discharge and ambient environment area is of interest.

data, and discharge length scales.

(2) Hydrodynamic simulation and mixing zone on toxic dilution zone criteria, regulatory mixing

summary lists conditions at the end of the near- zone criteria, stagnant ambient environment

field region (NFR), regulatory mixing zone (RMZ) information, and region of interest criteria.

conditions, toxic dilution zone (TDZ) conditions,

region of interest (ROI) conditions, upstream (4) Design recommendations section contains

intrusion information, bank attachment locations, design suggestions in three general areas for

and a passive diffusion mixing summary. Users improving initial dilution. These include: (a)

should be cognizant of the four major zone geometry variations in discharge port design, (b)

definitions, and associated acronyms, introduced sensitivity to ambient conditions, and (c) process

above and defined as follows: variations in discharge flow characteristics. The

 user is given guidance on the potential changes

Near-Field Region (NFR): The NFR is

simply the zone of strong initial mixing,

corresponding to the "near-field"

processes discussed in Chapter II. It has

no regulatory implication whatsoever.

However, the information on size and

mixing conditions at the edge of the NFR Different options for iteration exist on the iteration

is given as a useful guide to the discharge

designer because mixing in the NFR is

usually sensitive to design conditions, and

therefore somewhat controllable. A

notable exception is the effluent discharge

into very shallow flow-limited streams

where the actual discharge port design

detail may have little bearing on instream

concentrations.

Regulatory Mixing Zone (RMZ): The

RMZ corresponds to either: (1) the

applicable mixing zone regulation with

specified size dimensions, or (2) a

preliminary proposal for a mixing zone

(see Section 2.2.4 (ii) ). 

Toxic Dilution Zone (TDZ): The TDZ

corresponds to the EPA's definition of

where toxic chemical concentrations may

exceed the CMC value (see Section

2.2.3).

when legal mixing zone restrictions do not

(3) Data analysis section presents further details

in mixing conditions from varying parameter

values within these groups.

Finally, SUM is also used as an interactive

loop to guide the user back to DATIN to alter

design variables and perform sensitivity studies.

menu depending on what input data changes are

to be made. The importance of performing an

ample number of CORMIX iterations cannot be

sufficiently stressed. To obtain a design that
23

adequately meets water quality and engineering

construction objectives, it is necessary to get a

feel for the physical situation and its sensitivity to

design changes through repeated system use.

3.7.2 CORMIX1, 2 or 3 Prediction File

The CORMIX1, 2 or 3 Prediction File is a

detailed listing of all simulation input data as well

as the predicted plume properties (plume shapes

and concentration distributions) arranged by the

individual flow modules that form part of the

simulation. Additional information, such as

encounter of local mixing zone regulations, plume

contact with bottom or shoreline, etc., are listed in

the output. Detailed output features are

discussed in Chapter V.

3.7.3 CMXGRAPH Plots

The post-processing graphics package

CMXGRAPH can be exercised flexibly by the user

at different stages: directly after a CORMIX case

prediction for an initial evaluation of the design

case, or later to inspect or prepare plots for an

earlier design case, or outside the CORMIX

system to plot any plume predicted by CORMIX or

CORJET. The user can view different views of

the plume, with scaling and zooming possibilities.

Finally, hardcopy printouts can be prepared

through a direct print-screen option or by writing

to a Postscript file. Details of the graphics feature

are discussed in Chapter V.

3.8 Post-Processor Models CORJET and

FFLOCATR: Input and Output Features to restore normal operations. A bootable floppy

The near-field jet integral model CORJET command FORMAT a:/S. 

and the far-field plume locator model FFLOCATR

can be exercised both within the CORMIX The CORMIX must be installed on a hard

system, with guided input data assembly, or disk drive. The directory structure of CORMIX

separately, with a simple Fortran input file. In (Table 3.1) is fixed; it gets set up during the

both cases, only limited data are needed. installation process; and it consists of a

Chapter VI provides a detailed discussion of the subsystem root directory, called "CORMIX", and

data requirements. six sub-directories. Complete installation

The output from these models is displayed distribution diskette.

on-screen or as a printed file. Furthermore,

CORJET output can also be plotted with the Depending on computer configuration, a

CMXGRAPH program (see Section 5.3). typical CORMIX session for one

3.9 Equipment Requirements, System

Installation and Run Times

The minimum recommended hardware

configuration required for CORMIX is an IBMDOS compatible microcomputer with: (a) a

minimum of 550Kb of available RAM memory, (b)

approximately 3Mb of hard disk space, (c) DOS

3.3 or higher operating system, and (d) a

minimum 80386 with math co-processor to

provide acceptable performance, especially with

plume graphics display. The system will run on

systems with less advanced processors, however

simulation times can be long.

The RAM memory requirement of

CORMIX may present an obstacle to many users

because the configuration requirements of many

commercial applications packages and the

installation of memory resident software, or

running DOS from windows, frequently reduce

available RAM memory to less than 550Kb. The

amount of available RAM memory can be

determined with the DOS command CHKDSK.

Although there are numerous approaches for

increasing the size of a computer's available RAM

memory, the simplest way is "boot" the computer

from a floppy "system" disk that contains no

AUTOEXEC.BAT or CONFIG.SYS files which

consume additional memory. This should be done

just prior to beginning an analysis session since

it will temporary disable programs that consume

RAM memory. The CONFIG.SYS file should

allow the number of open files to be set to at least

20 by including the line statement "files=20". At

the completion of the analysis session, the

computer should be "booted" from the hard drive

system disk can be created with the DOS

instructions are available with the CORMIX

discharge/ambient condition may take less than 5
24

minutes for an Pentium-based computer to about the numerical simulation routines in HYDROn

20 minutes for an 80286-based computer if all may take up to 10 minutes to converge on

necessary input data is at hand. In some unusual Pentium-based systems.

cases (such as attached flow classes, e.g. H1A5)

Table 3.1

Directory Structure 

CORMIX

Version 3.1 June 1995, Version 3.2 September 1996

Directory Name Comments

 

CORMIX system root directory; contains VP-Expert system files, the

CORMIX\DATA contains cache "fact" files exported from knowledge base

CORMIX\EXE contains Fortran hydrodynamic simulation programs

CORMIX\KBS contains all knowledge base programs (*.kmp or *.kbs)

CORMIX\POST contains three post-processor programs CORJET,

CORMIX\POST\CJ contains CORJET numerical prediction files (fn.CJT) and

CORMIX\POST\FF contains FFLOCATR cumulative discharge input data files

(*.FFI) and prediction files (fn.FFX)

CORMIX\SIM contains simulation results (Fortran files "fn.CXn", where n =

CORMIX\SIM\CXn contains simulation data files for each subsystem n (cache

files "fn.CXC" and record keeping file "summary")

CORMIX\TEXT contains all user-requested advice files and flow descriptions

knowledge base program CORMIX.kmp or kbs (system

driver), and the start-up batch file CMX.bat, and several other

batch files to be used for starting up CORJET, CMXGRAPH,

and FFLOCATR when used independently

programs

HYDROn and file manipulation programs (*.exe)

CMXGRAPH, and FFLOCATR

graphical postscript files (fn.Pvn, where v = view type, and n

= 0 to 9)

1,2,3, and fn = user designated filenames) and graphical

postscript files (fn.Pvn, where v = view type, and n = 0 to 9)

(*.txt)
25

 IV CORMIX Data Input

4.1 General Aspects of Interactive Data Input Regular CORMIX versus FAST-CORMIX:

All CORMIX data input occurs interactively speed is set to "Regular CORMIX". In this mode

in response to system prompts and is entirely the user will see detailed input questions with

guided by the system. The user is automatically ample explanations for each variable. Also there

prompted for a complete specification of: will be opportunities to consult advice sections. It

site/case descriptions, ambient conditions, is recommended that the novice user employ this

discharge characteristics, and regulatory defini- mode for about a dozen or so CORMIX sessions

tions. The data for each of these four topical until he/she has become thoroughly familiar with

areas are called input data sequences herein.

Questions are asked in plain English. Advice

menu options within the program are available to

provide help on how to prepare and enter data

values when clarification of the system prompts is

needed. The contents of these are also available

in the documentation reports (5,6,7). 

Upon in its initial installation the CORMIX system

the system. The advanced user can switch to the

"FAST-CORMIX" mode in which only short

questions are asked, thereby greatly accelerating

data input and compacting it on screen. Certain

advice section are not available. The differences

are illustrated in the following:

Examples of three questions asked in Regular CORMIX:

1) Do you want detailed ADVICE on how to specify the ambient density 

stratification?

[no] [yes]

2) Can the ambient density be considered 'UNIFORM' throughout the water column,

or

is there a 'NON-UNIFORM' vertical density stratification?

As practical guideline, uniformity can be assumed if the vertical density 

variation between top and bottom is limited to 0.1 kg/m^3 or the temperature

variation to 1 degC.

[uniform] [non-uniform]

3) What is the WIDTH of the channel in the vicinity of the discharge (m)?

Corresponding questions in FAST-CORMIX:

1) <Question not asked>

2) AMBIENT DENSITY?

[uniform] [non-uniform]

3) Channel WIDTH (m)?

Data can be entered in an open format

without concern for letter case or decimal

placement. The only constraint is that the

following characters may not be entered in

response to any question:

+ = { } , < > ' " / \ ;

The system checks data entries for

consistency with question type (e.g. an alphabetic

character for water depth), obvious physical errors

(e.g. a negative length), possible inconsistencies

with previous entries (e.g. an angular value

implying that a port points directly back to the
26

shoreline) and situations outside the ranges of analysis to verify that all necessary data are

model applicability. Inconsistency with question available.

type and obvious physical errors require

immediate re-entry while possible inconsistencies

with previous entries lead to a warning label and

the opportunity for later correction. Entries

specifying situations outside the ranges of model

applicability usually require the re-entry of the

entire data segment. 

 Warning: No attempt should be made to

alter input data by manipulating any of the data

files that are used by the HYDROn Fortran

programs and execute these programs separately

without using the VP-Expert segments DATIN,

PARAM, and CLASS. Because of the inherent

error and compatibility checking of input data

within these program segments, unreliable

prediction may result if they are by-passed! 

As discussed in Chapter III, data input

occurs in three or four program segments that

load automatically. At the end of each data

sequence (usually of the order of 5 to 20 items

long) the entire sequence is displayed and the

user is requested to accept or not accept the

sequence. If it is not accepted, i.e. an error has

been made, the user has another opportunity for

entering the sequence. If an error is detected

earlier there is no way of correcting immediately,

it is best then to give a short answer (e.g. the

value of 1) to all remaining questions and thus

quickly move to the end of the sequence for the

re-start opportunity.

Due to the similarity of data entry, a

common description is given for all input data

sequences, except discharge data to which a

separate subsection for each CORMIXn

subsystem is devoted below. Further guidance

on data specification can be obtained from

examining the case studies in the Appendices

and from the documentation manuals (5,6,7).

Following the discussion of input data sequences,

units of measure conversion factors and

checklists for input preparation are presented.

All the data input requirements of

CORMIX are included in the Checklist for Data

Preparation (see following page) that can be

photocopied by the reader for future multiple use.

The checklist aids in the assembly and

preparation of this data prior to beginning an

4.2 Site/Case Identifier Data

The first input data sequence determines

basic information needed for the program to

operate. These include: a two-part identifier for

labeling output and a computer file name. 

It is necessary to specify three site/case

labels that facilitate the rapid identification of

printed output and aid in good record-keeping.

The system provides for one label called SITE

NAME (e.g. Blue River), another called DESIGN

CASE (e.g. 7Q10-low-flow, or High-velocity-port).

The user needs to supply a DOScompatible FILE NAME, up to eight characters

long, and without extension (e.g. sdif7q10).

CORMIX will use that user-specified file name fn,

and create, transfer, or store intermediate or final

data files with that same file name, but with

different extensions. The most important of these

are the two output data files, SIM\fn.CXn and

SIM\CXn\fn.CXC, where n = 1, 2 or 3, which are

discussed further in Chapter V.

4.3 Ambient Data

Ambient conditions are defined by the

geometric and hydrographic conditions in the

vicinity of the discharge. Due to the significant

effect of boundary interactions on mixing

processes, the ambient data requirements for the

laterally bounded and unbounded analysis

situations are presented separately in the

discussions below. CORMIX analyses, as all

mixing zone evaluations, are usually carried out

under the assumption of steady-state ambient

conditions. Even though the actual water

environment is never in a true steady-state, this

assumption is usually adequate since mixing

processes are quite rapid relative to the time

scale of hydrographic variations. In highly

unsteady tidal reversing flows the assumption

is no longer valid and significant concentration

build-up can occur. CORMIX will assess this

situation and compute some re-entrainment

effects on plume behavior. The data requirements

for that purpose are discussed in the Section

4.3.3. Following are discussions on ambient

HA2 
 HA1

QA2

QA1

3

5

28

 

density specification and on wind effects. cross-sections, it may require more judgment and

CORMIX requires that the actual cross- better feel on the sensitivity of the results to the

section of the ambient water body be described assumed cross-sectional shape. 

by a rectangular channel that may be bounded

laterally or unbounded. Furthermore, that In any case, the user is advised to

channel is assumed to be uniform in the consider the following comments:

downstream direction, following the mean flow of

the actual water body that may be non-uniform or a) Be aware that a particular flow condition

meandering. The process of describing a such as a river discharge is usually associated

receiving water body's geometry with a with a certain water surface elevation or "stage."

rectangular cross-section is herein called Data for a stage-discharge relationship is norschematization. 

Additional aids exist for the CORMIX user

for interpreting plume behavior in the far-field of

actual non-uniform (winding or meandering) flows

in rivers or estuaries (see Section 6.2 for the postprocessor option FFLOCATR).

The first step towards specifying the

ambient conditions is to determine whether a

receiving water body should be considered

"bounded" or "unbounded." To do this, as well

as answer other questions on the ambient

geometry, it is usually necessary to have access

to cross-sectional diagrams of the water body.

These should show the area normal to the

ambient flow direction at the discharge site and at

locations further downstream. If the water body is

constrained on both sides by banks such as in

rivers, streams, narrow estuaries, and other

narrow watercourses, then it should be

considered "bounded." However, in some cases

the discharge is located close to one bank or

shore while the other bank is for practical

purposes very far away. When interaction of the

effluent plume with that other bank or shore is

impossible or unlikely, then the situation should

be considered "unbounded." This would include

discharges into wide lakes, wide estuaries, and

coastal areas. 

4.3.1 Bounded Cross-Section

Both geometric (bathymetric) and hydrographic

(ambient discharge) data should be used for

defining the appropriate rectangular crosssection. This schematization may be quite

evident for well-channeled and regular rivers or

artificial channels. For highly irregular

perhaps several iterations of the analysis to get a

mally available from a USGS office; otherwise it

can be obtained from a separate hydraulic

analysis or from field measurements. 

In the simplest case of a river flow, if river

depth is known for a certain flow condition

(subscript 1 in the following) corresponding

perhaps to the situation at the time of a field

study, then the depth for a given design (e.g. low)

flow (subscript 2) can be predicted from

Manning's equation

in which QA is the ambient river flow and HA the

mean ambient depth. This approach assumes

that the both the ambient width and frictional

characteristics of the channel (i.e. Manning's n)

remain approximately the same during such a

stage change.

b) For the given stage/river discharge

combination to be analyzed, assemble plots

showing the cross-sections at the discharge and

several downstream locations. Examine these to

determine an "equivalent rectangular

cross-sectional area." Very shallow bank areas or

shallow floodways may be neglected as

unimportant for effluent transport. Also, more

weight should be given to the cross-sections at,

and close to, the discharge location since these

will likely have the greatest effect on near-field

processes. Figure 4.1a provides an example of

the schematization process for a river or estuary

cross-section.
29

Figure 4.1: Examples of the schematization process for preparing CORMIX input data on ambient

cross-sectional conditions
f 
 8 g

n2

HA1/3

30

c) The input data values for surface width The simulation of stagnant conditions

(BS) and (average) depth (HA) should be

determined from the equivalent rectangular crosssectional area. When ambient discharge and

ambient velocity data are available, the

reasonableness of the schematization should be

checked with the continuity relation. It specifies

that ambient discharge equals velocity times

cross-sectional area, where the area is given by

the product of average width and depth.

The discussion of the cumulative

discharge method (see Section 6.2 and Figure 6.2

for an illustration) will provide further perspective

on the choice of these variables.

d) CORMIX also requires specification of

the actual water depth (HD) in the general

discharge location to describe local bathymetric Darcy-Weisbach friction factor f, must be

features. A check is built in allowing the local specified. Friction values are useful for

depth HD not to differ from the schematized applications in laboratory studies. If Manning's n

average depth HA by more than +/- 30%. This is given, as is preferable for field cases, CORMIX

restriction is included to prevent CORMIX misuse internally converts it to an f friction value using the

in several discharge/ambient combinations following equation

involving strongly non-uniform channels.

Alternative schematizations can be explored by

the user to work around the restriction. The

choice for these alternatives may be influenced

somewhat by the expected plume pattern. As an

example, Figure 4.1b illustrates a small buoyant

discharge that is located on the side slope of a

deep reservoir and that is rising upward. In this

situation, the correct representation of the deeper

mean reservoir depth is irrelevant for plume

predictions. Although the illustration is for an

unbounded example, the comments on choice of

HA apply here, too.

When schematizing HA and HD in highly

non-uniform conditions, HD is the variable that

usually influences near-field mixing, while HA is

important for far-field transport and never

influences the near-field.

e) The ambient discharge (QA) or mean

ambient velocity (UA) may be used to specify

the ambient flow condition. Depending which is

specified, the program will calculate and display

the other. The displayed value should be

checked to see whether it is consistent with

schematizations and continuity principles

discussed above.

should usually be avoided. If zero or a very small

value for ambient velocity or discharge is entered,

CORMIX will label the ambient environment as

stagnant. In this case, CORMIX will predict only

the near-field of the discharge, since steady-state

far-field processes require a mean transport

velocity. Although stagnant conditions often, but

not necessarily always, represent the extreme

limiting case for a dilution prediction, a real water

body never is truly stagnant. Therefore, a more

realistic assumption for natural water bodies

would be to consider a small, but finite ambient

crossflow. 

f) As a measure of the roughness

characteristics in the channel the value of

Manning's n, or alternatively of the

in which g = 9.81 m/s .2

The friction parameters influence the

mixing process only in the final far-field diffusion

stage, and do not have a large impact on the

predictions. Generally, if these values can be

estimated within +/-30%, the far-field predictions

will vary by +/-10% at the most. The following list

is a brief guide for specification of Manning's n

values; additional details are available in

hydraulics textbooks (e.g. 24).

g) The channel appearance can have an

effect on the far field mixing by increasing

turbulent diffusivity for the passive mixing

process, but will not significantly affect near-field

mixing. Three channel appearance types are

allowed in CORMIX. Type 1 are fairly straight and

uniform channels. Type 2 have moderate

downstream meander with a non-uniform

channel. Type 3 are strongly winding and have

highly irregular downstream cross-sections.
31

Channel type Manning's n

Smooth earth channel, no weeds 0.020

Earth channel, some stones and weeds 0.025

Clean and straight natural rivers 0.025 - 0.030

Winding channel, with pools and shoals 0.033 - 0.040

Very weedy streams, winding, overgrown 0.050 - 0.150

Clean straight alluvial channels 0.031 d1/6

(d = 75% sediment grain size in feet)

unavailable, data or estimates of the vertically

4.3.2 Unbounded Cross-section determine the cumulative cross-sectional area

Both hydrographic and geometric discharge cross-section. For each of the

information are closely linked in this case. The subsequent downstream cross-sections, mark the

following comments apply: position where the cumulative cross-sectional

a) From lake or reservoir elevation or tidal cross-section. Then proceed as discussed in the

stage data, determine the water depth(s) for the preceding paragraph. 

receiving water condition to be analyzed. 

b) For the given receiving water condition

to be analyzed, assemble plots showing water

depth as a function of distance from the shore for

the discharge location and for several positions

downstream along the ambient current direction.

c) If detailed hydrographic data from field

surveys or from hydraulic numerical model

calculations are available, determine the

"cumulative ambient discharge" from the shore

to the discharge location for the discharge

cross-section. For each of the subsequent

downstream cross-sections, determine the

distance from the shore at which the same

cumulative ambient discharge has been attained.

Mark this position on all cross-sectional profiles.

Examine the vertically averaged velocity and the

depth at these positions to determine typical

values for the ambient depth (HA) and ambient

velocity (UA) input specifications. The conditions offshore from the discharge exit. It does not

at, and close to, the discharge location should be describe the conditions immediately in front of the

given the most weight. The distance from the

shore (DISTB) for the outfall location is typically

specified as the cumulative ambient discharge

divided by the product UA times HA.

When detailed hydrographic data are the ambient roughness characteristics as

averaged velocity at the discharge location can be

used to specify HA, UA, and DISTB. First,

from the shore to the discharge location for the

area has the same value as at the discharge

d) The specification of the actual water

depth at the submerged discharge location

(HD) in CORMIX1 and 2 is governed by

considerations that are similar to those discussed

earlier for bounded flow situations discussed

above. Figure 4.1b shows an illustration of the

schematization for a small buoyant discharge

located on the side slope of a deep reservoir.

The plume is expected to rise upward and stay

close to one shore, with bottom contact and

vertical mixing not expected. In this situation, no

emphasis on replicating the mean reservoir depth

and the actual width is necessary. However, care

must still be taken to specify an ambient mean

velocity that is: (a) characteristic of the actual

reservoir and (b) not determined using the

reduced depth assumption.

The specification of HD for CORMIX3 is

dictated by the depth condition some distance

discharge channel exit. When in doubt, set HD

simply equal to HA in the CORMIX3 case.

e) Either Manning's n or the DarcyWeisbach friction factor f can be specified for
32

described previously for the bounded case (see

above). If the unbounded case represents a large

lake or coastal area, it is often preferable to use

the friction factor f. Typical f values for such open

water bodies range from 0.020 to 0.030, with

larger values for rougher conditions.

4.3.3 Tidal Reversing Ambient Conditions

When predictions are desired in an

unsteady ambient flow field, information on the

tidal cycle must be supplied. In general, estuaries

or coastal waters can exhibit considerable

complexity with variations in both velocity

magnitude, direction and water depth. As an

example, Figure 4.2 shows the time history of tidal

velocities and tidal height for a mean tidal cycle at

some site in Long Island Sound. The tidal height

varies between mean Low Water (MLW) and

Mean High water (MHW).

The tidal velocity changes its direction

twice during the tidal cycle at times called slack

tide. One of these times occurs near, but is not

necessarily coincident with, the time MLW and is

referred to as Low Water Slack (LWS). The slack

period near MHW is referred to as High Water

Slack (HWS). The rate reversal (time gradient of

the tidal velocity) near these slack tides is of

considerable importance for the concentration

build-up in the transient discharge plume, as tidal

reversals will reduce the effective dilution of a

discharge by re-entraining the discharge plume

remaining from the previous tidal cycle (8). 

Hence, CORMIX needs some information on the

ambient design conditions relative to any of the

two slack tides.

Figure 4.2: Example of tidal cycle, showing stage and velocity as a function of time after Mean

High Water (MHW)
33

The tidal period (PERIOD) must be

supplied; in most cases it is 12.4 hours, but in considered as uniform or as non-uniform within

some locations it may vary slightly. The the water body, and in particular within the

maximum tidal velocity (UAmax) for the location

must be specified; this can usually be taken as

the average of the absolute values of the two

actual maxima, independent of their direction. A neglected. For uniform conditions, the average

CORMIX design case consists then of an

instantaneous ambient condition, before, at or

after one of the two slack tides. Hence, the

analyst must specify the time (in hours) before, When conditions are non-uniform,

at, or after slack that defines the design

condition, followed by the actual tidal ambient

velocity (UA) at that time. The ambient depth

conditions are then those corresponding to that

time.

In general, tidal simulations should be

repeated for several time intervals (usually hourly

or two-hourly intervals will suffice) before and

after slack time to determine plume

characteristics in unsteady ambient conditions. 

Strongly unsteady conditions can also

occur in other environments, such as in windinduced current reversals in shallow lakes or

coastal areas. In this case, any typical reversal

period can be analyzed following an approach

similar to the above.

4.3.4 Ambient Density Specification

Information about the density distribution

in the ambient water body is very important for the

correct prediction of effluent discharge plume

behavior. CORMIX first inquires whether the

ambient water is fresh water or non-fresh (i.e.

brackish or saline). If the ambient water is fresh

and above 4 C, the system provides the option of o

entering ambient temperature data so that the

ambient density values can be internally

computed from an equation of state. This is the

recommended option for specifying the density of

fresh water, even though ambient temperature

per se is not needed for the analysis of mixing

conditions. In the case of salt water conditions,

Figure 4.3 is included as a practical guide for

specifying the density if "salinity values" in partsper-thousand (ppt) are available for the water

body. Typical open ocean salinities are in the

range 33 - 35 ppt.

The user then specifies whether the

ambient density (or temperature) can be

expected plume regions. As a practical guide,

vertical variation in density of less than 0.1 kg/m3

or in temperature of less than 1 C can be o

ambient density or average temperature must

be specified. 

CORMIX requires that the actual measured

vertical density distribution be approximated by

one of three schematic stratification profile types

illustrated in Figure 4.4. These are: Type A, linear

density profile; Type B, two-layer system with

constant densities and density jump; Type C,

constant density surface layer with linear density

profile in bottom layer separated by a density

jump. Corresponding profile types exist for

approximating a temperature distribution when it

is used for specifying the density distribution. 

Note: When in doubt about the

specification of the ambient density values it is

reasonable to first simplify as much as possible.

The sensitivity of a given assumption can be

explored in subsequent CORMIX simulations.

Furthermore, if CORMIX indicates indeed a flow

configuration (flow class) with near-field stability,

additional studies with the post-processor option

CORJET (see Section 6.1) can be performed to

investigate any arbitrary density distribution.

After selecting the stratification

approximation to be used, the user then enters all

appropriate density (or temperature) values and

pycnocline heights (HINT) to fully specify the

profiles. The pycnocline is defined as zone or

level of strong density change that separates the

upper and lower layers of the water column. The

program checks the density specification to insure

that stable ambient stratification exists (i.e. the

density at higher elevations must not exceed that

at lower elevations).

Note that a dynamically correct

approximation of the actua ldensity distribution

should keep a balance between over-and

under-estimationof the actual data similar to a

best-fit in regression analysis. If simulation

results indicate internal plume trapping, then it is
34

Figure 4.3: Diagram for density of seawater as a function of temperature and salinity

Figure 4.4: Different approximations for representing the ambient density stratification
35

desirable to test --through repeated use of for non-circular shaped ports) (Note: The

CORMIX-- different approximations (i.e. with specification of the port dimension should account

different stratification types and/or parameter for any contraction effects that the effluent jet may

values) in order to evaluate the sensitivity of the experience upon leaving the port/nozzle!) , (d)

resulting model predictions.

4.3.5 Wind speed

When specifying the wind speed (UW) at

design conditions, it should be kept in mind that

the wind is unimportant for near-field mixing, but

may critically affect plume behavior in the far-field.

This is especially important for heated discharges

in the buoyant spreading regions. Wind speed

data from adjacent meteorological stations is

usually sufficient for that purpose.

The following guidelines are useful when

actual measured data are not available. The

typical wind speed categories measured at the 10

m level are:

 --- breeze (0-3 m/s)

--- light wind (3-15 m/s)

--- strong wind (15-30 m/s)

If field data are not available, consider using the

recommended value of 2 m/s to represent

conservative design conditions. An extreme low

value of 0 m/s is usually unrealistic for field

conditions, but useful when comparing to

laboratory data. A wind speed of 15 m/s is the

maximum value allowed in CORMIX.

 4.4. Discharge Data: CORMIX1

Figure 4.5a is a definition sketch giving the

geometry and flow characteristics for a

submerged single port discharge within the

schematized cross-section.

4.4.1 Discharge Geometry

To allow the establishment of a reference

coordinate system and orient the discharge to that

reference, CORMIX1 requires the specification of

6 data entries. These specifications are illustrated

in Figure 4.5a and include: (a) location of the

nearest bank (i.e. left or right) as seen by an above restrictions, Section 7.4 of Doneker and

observer looking downstream in the direction of Jirka (5) contains a number of hints on how to

the flow, (b) distance to the nearest bank

(DISTB), (c) port radius (or cross-sectional area

height of the port (H0) center above the bottom,

(e) vertical angle of discharge (THETA)

between the port centerline and a horizontal

plane, and (f) horizontal angle of discharge

(SIGMA) measured counterclockwise from the

ambient current direction (x-axis) to the plan

projection of the port centerline. Angle THETA

may range between -45 and 90 . As examples, o o

the vertical angle is 90 for a discharge pointing o

vertically upward, and it is 0 for a horizontal o

discharge. Angle SIGMA may range between 0o

and 360 . As examples, the horizontal angle is o

0 (or 360 ) when the port points downstream in o o

the ambient flow direction, and it is 90 , when the o

port points to the left of the ambient flow direction.

In order to prevent an inappropriate

system application, CORMIX1 checks the

specified geometry for compliance with the three

criteria illustrated in Figure 4.5b. These are: (a)

the port height (H0) value must not exceed onethird of the local water depth (HD) value, (b) the

port diameter value must not exceed HD's value

for near-vertical designs, and one-third of HD's

value for near-horizontal designs, and (c) the

pycnocline value must be within the 40 to 90

percent range of HD's value. The port height

restriction results from the fact that CORMIX1

only applies to submerged discharge applications.

 In ordinary design practice, submerged

implies a discharge close to the bottom, and not

anywhere within the main water column or near

the water surface. The port diameter restriction

excludes very large discharge diameters relative

to the actual water depth since these are

unrealistic and/or undesirable. The distance

separating the upper and lower layers of the

ambient density profile type B or C is restricted in

order to prevent: (a) discharges into the upper

layer or (b) an unrealistically thick plume relative

to a thin upper layer. For those few extreme

situations that would normally be limited by the

conduct these difficult analyses; only advanced

users should attempt these techniques. 
36

Figure 4.5: CORMIX1 discharge geometry and restrictions
37

4.4.2 Port Discharge Flow located at the center (mid-point) of the diffuser

For discharge characteristics, CORMIX1 starts at the shore; then the origin is located

requires the specification of 3 data entries. These directly at the shore.

specifications include: (a) the discharge flow

rate (Q0) or discharge velocity (U0), (b) the

discharge density or discharge temperature for

an essentially freshwater discharge, and (c) the

discharge concentration of the material of

interest. The Q0 and U0 variables are related

through the port cross-sectional area and the

program computes and displays the alternate

value allowing for user inspection and verification.

For a freshwater discharge, discharge density can

be directly related to temperature via an equation

of state since the addition of any pollutant or

tracer has negligible effect on density. horizontally; and (c) the alternating diffuser

The specification of the pollutant in the horizontal direction. In the latter case, the ports

effluent is described in Section 4.7 below. may point more or less horizontally in an

4.5 Discharge Data: CORMIX2

A generalized definition sketch showing

the geometry and flow characteristics for a typical

multiport diffuser installation is provided in

Figure 4.6a. Due to the great number of

complexities which may rise in describing an

existing or proposed diffuser design, a few

definitions are introduced prior to discussing

actual data requirements of CORMIX2.

A multiport diffuser is a linear structure

consisting of many more or less closely spaced

ports or nozzles which inject a series of turbulent

jets at high velocity into the ambient receiving

water body. These ports or nozzles may be

connected to vertical risers attached to an

underground pipe or tunnel or they may simply be

openings in a pipe lying on the bottom.

The diffuser line (or axis) is a line

connecting the first port or nozzle and the last port

or nozzle. Generally, the diffuser line will coincide

with the connecting pipe or tunnel. CORMIX2 will

assume a straight diffuser line. If the actual

diffuser pipe has bends or directional changes it bank (DISTB), (c) average diameter (D0) of the

must be approximated by a straight diffuser line.

The diffuser length is the distance from from 1 for well rounded ports --usual value-- down

the first to the last port or nozzle. The origin of to 0.6 for sharp-edged orifices), (e) average

the coordinate system used by CORMIX2 is

line. The only exception is when the diffuser line

CORMIX2 can analyze discharges from

the three major diffuser types used in common

engineering practice. These are illustrated in

Figure 4.7 and include: (a) the unidirectional

diffuser where all ports (or nozzles) point to one

side of the diffuser line and are oriented more or

less normally to the diffuser line and more or less

horizontally; (b) the staged diffuser where all

ports point in one direction generally following the

diffuser line with small deviations to either side of

the diffuser line and are oriented more or less

where the ports do not point in a nearly single

alternating fashion to both sides of the diffuser

line or they may point upward, more or less

vertically.

4.5.1 Diffuser Geometry

CORMIX2 assumes uniform discharge

conditions along the diffuser line. This includes

the local ambient receiving water depth (HD) and

discharge parameters such as port size, port

spacing and discharge per port, etc. If the actual

receiving water depth is variable (e.g. due to an

offshore slope), it should be approximated by the

mean depth along the diffuser line with a possible

bias to the more shallow near-shore conditions.

Similarly, mean values should be used to specify

variable diffuser geometry when it occurs. 

To allow the establishment of a reference

coordinate system and orient the discharge to that

reference, CORMIX2 requires the specification of

13 data entries. These specifications are

illustrated in Figure 4.6a and include: (a) location

of the nearest bank (i.e. left or right) as seen by

an observer looking downstream in the direction

of the flow, (b) average distance to the nearest

discharge ports or nozzles, (d) contraction ratio

for the port/nozzle is required (This can range
38

Figure 4.6: CORMIX2 discharge geometry and restrictions

40

height of the port centers (H0) above the

bottom, (f) average vertical angle of discharge

(THETA) between the port centerlines and a

horizontal plane (-45 and 90 ), (g)for the o

unidirectional and staged diffusers only, the

average horizontal angle of discharge (SIGMA)

measured counterclockwise from the ambient

current direction (x-axis) to the plan projection of

the port centerlines (0 to 360 ), (h) approximate o

straight-line diffuser length (LD) between the

first and last ports or risers, (I) distance from the

shore to the first and last ports or risers (YB1,

YB2) of the diffuser line, (j) number of ports or

risers and the number of ports per riser if risers

are present, (k) average alignment angle

(GAMMA) measured counterclockwise from the

ambient current direction (x-axis) to the diffuser

axis (0 to 180 ), and (l) for the unidirectional and o

staged diffusers only, relative orientation angle

(BETA) measured either clockwise or

counterclockwise from the average plan

projection of the port centerlines to the nearest

diffuser axis (0 to 90 ). Note that CORMIX2 o

always assumes a uniform spacing between

risers or between ports, and a round port crosssectional shape.

As examples of angle specifications,

THETA is 0 degrees for a horizontal discharge

and it is +90 degrees for a vertically upward

discharge, SIGMA is 0 degrees (or 360 ) when o

the ports point downstream in the ambient flow

direction and it is 90 degrees when the ports point

to the left of the ambient flow direction, GAMMA

is 0 degrees (or 180 ) for a parallel diffuser and it o

is 90 degrees for a perpendicular diffuser, and

BETA is 0 degrees for a staged diffuser and it is

90 degrees for a unidirectional diffuser.

CORMIX2 performs a number of

consistency checks to ensure the user does not

make arithmetical errors when preparing and

entering the above data and it also checks the

specified geometry for compliance with three

criteria to prevent an inappropriate system

application. Figure 4.6b shows the imposed limits

of system application for CORMIX2 which are: (a)

the port height (H0) value must not exceed onethird of the local water depth (HD) value, (b) the the channel entry (HD0) and (e) bottom slope

port diameter value must not exceed one-fifth of

HD's value, and (c) the pycnocline value must be

within the 40 to 90 percent range of HD's value. 

The restrictions are similar to those shown in

Figure 4.5b for CORMIX1 with the exception of

the diameter limit for each port. 

4.5.2 Diffuser Discharge Flow

For discharge characteristics, CORMIX2

requires the specification of 3 data entries. These

specifications include: (a) the total discharge

flow rate (Q0) or discharge velocity (U0), (b) the

discharge density or discharge temperature for

an essentially freshwater discharge, and (c) the

discharge concentration of the material of

interest. The Q0 and U0 variables are related

through the total cross-sectional area of all

diffuser ports and the program computes and

displays the alternate value allowing for user

inspection and verification.

The specification of the pollutant in the

diffuser effluent is described in Section 4.7 below.

4.6 Discharge Data: CORMIX3

A definition sketch for the discharge

geometry and flow characteristics for a buoyant

surface discharge is provided in Figure 4.8. In

general, CORMIX3 allows for different types of

inflow structures, ranging from simple rectangular

channels to horizontal round pipes that may be

located at or near the water surface. In addition,

three different configurations relative to the bank

are allowed as illustrated in Figure 4.9. Discharge

structures can be: (a) flush with the bank/shore,

(b) protruding from the bank or (c) co-flowing

along the bank.

4.6.1 Discharge Geometry

To allow the establishment of a reference

coordinate system and orient the discharge to that

reference, CORMIX3 requires the specification of

up to 7 data entries. These specifications are

illustrated in Figure 4.8 and include: (a) location of

the nearest bank (i.e. left or right) as seen by an

observer looking downstream in the direction of

the flow, (b) discharge channel width (B0) of the

rectangular channel, (c)discharge channel

depth (H0), (d) actual receiving water depth at

(SLOPE) in the receiving water body in the vicinity

of the discharge channel, and (f)horizontal angle

of discharge (SIGMA) measured counterclockwise from the ambient current direction (x-axis) to
41

Figure 4.8: CORMIX3 discharge channel geometry
42

Figure 4.9: Possible CORMIX3 discharge configurations of discharge channel relative to

bank/shoreline
43

the plan projection of the port centerline. In the The discharge concentration of the

case of a circular discharge pipe, the (b) pipe

diameter and (c) depth of bottom invert below

the water surface (water surface to bottom edge

of pipe) must be specified, respectively. In all

cases, CORMIX3 assumes the discharge is being

issued horizontally.

CORMIX3 uses the variable HD0 for the

actual water depth just in front of the channel exit

and requires an additional specification for the

receiving water bottom slope, again in front of the

exit, extending into the receiving water body.

These details are important for identifying cases

where plume attachment to the bottom can occur.

In the case of a circular pipe discharge

CORMIX3 assumes the outlet is flowing full and

that it is not submerged under the water surface

by more than 1⁄2 of the outlet diameter. If the

discharge outlet has an odd cross-sectional

shape (e.g. a pipe flowing partially full) then it

should be represented schematically as a

rectangular outlet of the same cross-sectional coefficient of decay (positive number) or

area and similar channel depth.

For open channel discharges,

considerable care should be exercised when

specifying discharge channel depth since this

parameter is directly linked to the ambient

receiving water depth (stage). This is especially

important for tidal situations.

 To prevent an inappropriate system

application, CORMIX3 only allows for a discharge

channel depth-to-width aspect ratio of 0.05 to 5.

This prohibits the use of extremely oblong

discharge geometry.

4.6.2 Discharge Flow

For discharge characteristics, CORMIX3

requires the specification of 3 data entries. These

specifications include: (a) the total discharge

flow rate (Q0) or discharge velocity (U0), (b) the

discharge density or discharge temperature for

an essentially freshwater discharge, and (c) the

discharge concentration of the material of

interest. The Q0 and U0 variables are related

through the channel cross-sectional area; the

program computes and displays the alternate

value allowing for user inspection and verification.

material of interest (pollutant, tracer, or

temperature) is defined as the excess

concentration above any ambient concentration of

that same material. The user can specify this

quantity in any units. CORMIX1 predictions

should be interpreted as computed excess

concentrations in these same units. If no specific

pollutant is under consideration, simply specify a

discharge concentration of 100%.

4.7 Pollutant Data

CORMIX allows three types of pollutant

discharges:

(a) Conservative Pollutant:

The pollutant does not undergo any decay/growth

processes.

(b) Non-conservative Pollutant:

The pollutant undergoes a first order decay or

growth process. One needs to specify the

growth (negative number) in units: /day (per day).

(c) Heated Discharge: 

The discharge will experience heat loss to the

atmosphere in cases where the plume contacts

the water surface. It is necessary to specify the

discharge condition in terms of excess

temperature ("delta T") above ambient in units

degC, and the surface heat exchange

coefficient in units W/m ,degC. Values of the 2

heat exchange coefficient depend on ambient

water temperature and wind speed. The following

listing provides a guideline for the selection.

Typically, the near-field behavior is quite

insensitive to the choice of these values, but it

may affect the prediction results at greater

distances in the far-field.

The discharge concentration (C0) of the

material of interest (pollutant, tracer, or

temperature) is defined as the excess

concentration above any ambient background

concentration of that same material. The user

can specify this quantity in any units of

concentration (e.g. mg/l, ppm, %, C). CORMIX o

predictions should be interpreted as computed

excess concentrations in these same units.
44

 SURFACE HEAT EXCHANGE COEFFICIENT (W/m , C) 2 o

 Values for a lightly heated, natural water surface 

 (local excess temperatures 0 to 3 C) o

Ambient Water Wind Speed (m/s)

Temp. ( C) 0 1 2 4 6 8 o

 5 5 10 14 24 33 42

10 5 11 16 27 38 49

15 5 12 18 31 44 59

20 5 14 21 38 52 68

25 6 16 25 45 63 82

30 6 19 30 54 76 100

Ref: "Heat Disposal in the Water Environment", E.E. Adams, D.R.F. Harleman, G.H. Jirka, and

K.D. Stolzenbach, Course Notes, R.M. Parsons Laboratory, Mass. Inst. of Techn., 1981.

 

If no pollutant data at all is available, it is occur at correct regulatory concentrations

most convenient to specify C0 = 100 %. because they are interpreted as excess

In case of an ambient background

concentration it is important to treat all pollutant

related data items in a consistent fashion. This 4.8 Mixing Zone Data

includes the specification of any regulatory values

as discussed in Section 4.8 below. The user must indicate: (a) whether EPA's

Example: suppose the actual discharge whether an ambient water quality standard exists,

concentration for a particular pollutant is (c) whether a regulatory mixing zone (RMZ)

100 mg/l, and values of CMC and CCC for definition exists, (d) the spatial region of interest

the pollutant are 20 mg/l and 10 mg/l, (ROI) over which information is desired, and (e)

respectively. If the background ambient number of locations (i.e. "grid intervals") in the

concentration for the same pollutant is 4 ROI to display output details. Depending on the

mg/l, the data entry to CORMIX would be responses to the above, several additional data

for the discharge concentration = 96 mg/l, entries may be necessary as described in the

for CMC = 16 mg/l, and for CCC = 6 mg/l, following paragraphs. 

respectively. All concentration values

listed in the diverse CORMIX output (see When TDZ definitions apply, the user

Chapter V) must then be interpreted must also indicate the criterion maximum

accordingly, and the actual concentration concentration (CMC) and criterion continuous

values are computed by adding the concentration (CCC) which are intended to

background concentration value. E.g. if protect aquatic life from acute and chronic effects,

the CORMIX predicted value for one respectively. CORMIX will check for compliance

particular point happens to be 13.6 mg/l, with: (a) the CMC standard at the edge of the

then the total concentration value at that TDZ and (b) the CMC standard at the edge of the

point would be 17.6 mg/l. Also, all RMZ, proving a RMZ was defined. See

program mixing zone messages would Subsection 2.2.2 for additional discussion.

plume concentrations above ambient. 

toxic dilution zone (TDZ) definitions apply, (b)
45

 When a RMZ definition exists, it can be

specified by: (a) a distance from the discharge

location, (b) the cross-sectional area occupied by

the plume, or (c) the width of the effluent plume.

The ROI, which is a user defined region

where mixing conditions are to be analyzed, is

specified as the maximum analysis distance in the

direction of mixed effluent flow. The level of detail

for the output data within the ROI and thus, for the

entire hydraulic simulation, is established by

specifying the number of grid intervals that will be

displayed in the output files. This parameter's

allowable range is 3 to 50 and the chosen value

does not affect the accuracy of the CORMIX

prediction, only the amount of output detail. A low

value should be specified for initial calculations to

minimize printout lengths while a large value

might be desirable for final predictions to give

enough resolution for plotting of plume

dimensions.

4.9 Units of Measure

CORMIX uses the metric system of

measurement. When data values are provided to

the user in English units, these must be converted

to equivalent metric measures. The list at the

beginning of this manual gives the five metric

dimensions used by CORMIX in the left column,

and on the right, their equivalents in some

common English units.

Pollutant concentrations can be entered in

any conventional measure such as mg/L, ppb,

bacteria-count, etc.

Considering the potential accuracy of

CORMIX predictions, 3 to 4 significant digits are

sufficiently accurate for most input data values as

suggested in the above conversion list. The only

exceptions are the ambient and effluent density

values. These may require 5 significant digits,

especially when simulating the discharge to an

ambient density-stratified receiving water body.
46
47

V CORMIX Output Features

CORMIX is a highly interactive system and computation results and (c) flow class

conveys information to the user through descriptions. The paragraphs within this Section

qualitative descriptions and detailed quantitative aid in the interpretation of that information.

numerical predictions. This output can be viewed

on-screen in text mode or graphics mode, can be The program elements PARAM and

directed to a printer, and is stored in subdirectory CLASS, in particular, provide essential

CORMIX\SIM and CORMIX\SIM\CXn files. In information on the expected dynamic behavior of

this chapter the label n = 1, 2 or 3 designates the the discharge. By actively participating in the

appropriate CORMIX subsystem. interactive process, the novice and intermediate

5.1 Qualitative Output: Flow Descriptions

After completion of the input data entry

sequences, the system proceeds through the

program elements following the flow chart

displayed in Figure 3.1. In addition to the routine

operational messages provided during program

execution, important qualitative information is

displayed on-screen about the ongoing analysis

of the given ambient/discharge case. The three

general types of descriptive information provided

are: (a) descriptive messages, (b) length scale

user can derive a substantial educational benefit

and a technical appreciation of the physical

aspects of initial mixing processes. Although

advanced users may find some of the presented

material somewhat repetitive, they should still

consult the length scale computation results. 

5.1.1 Descriptive Messages

These messages provide both physical

information and insight into the logic reasoning

employed by CORMIX. Three example

descriptive messages are:

"The effluent density (1004.5 kg/m^3) is greater than the surrounding

water density at the discharge level (997.2 kg/m^3).

Therefore, the effluent is negatively buoyant and will tend to sink

towards the bottom."

"STRONG BANK INTERACTION will occur for this perpendicular diffuser

type due to its proximity to the bank (shoreline). The shoreline will

act as a symmetry line for the diffuser flow field.

The diffuser length and total flow variables are doubled (or

approximately doubled, depending on the vicinity to the shoreline).

All of the following length scales are computed on that basis."

"The specified two layer ambient density stratification is dynamically

important. The discharge near field flow will be confined to the lower

layer by the ambient density stratification.

Furthermore, it may be trapped below the ambient density jump at the

pycnocline."

The preceding example output highlights analysis conditions. In some instances, the

several features of CORMIX's descriptive provided information may be obvious to the user,

messages. These include: (a) conveying basic while in others it may not, particularly for

information about the involved mixing processes, situations involving linear ambient stratification.

(b) using a careful terminology (e.g. "..tend to The use of a careful terminology is necessary

sink.."), (c) describing key calculation because messages are presented as the analysis

assumptions, and (d) alerting the user to sensitive proceeds and subsequent tests may alter, or
48

amplify, initial results. For example, near-field local water depth (HD), this is an immediate

instabilities, which are tested for late in the indication to the user that the crossflow is very

analysis, can prevent an otherwise sinking plume. strong, leading to complete bending of the

5.1.2 Length Scale Computations buoyant jet. If the reverse holds true, the

The program element PARAM computes is negligible, and the buoyant jet will strongly

so-called "length scales" which represent

important dynamic measures about the relative

influence of certain hydrodynamic processes on

effluent mixing. These calculated values are

subsequently used in program element CLASS to

identify the generic flow class upon which the

hydraulic simulations will be based. This flow

classification is accomplished through formal

dynamic length scale analysis, which is a key

aspect of the theoretical underpinnings for the

CORMIX approach. The CORMIX documentation

manuals (5,6,7) and related journal publications

provide the theoretical background on length

scale definitions and significance, their derivation

from principles of dimensional analysis, and their

use in the CORMIX flow classification approach.

Although flow classification is a formal

process using criteria derived from theoretical

studies and/or experimental data, a great deal

can be deduced about the flow dynamics by

comparing the calculated length scales to the

actual physical measures of the

ambient/discharge situation. Of greatest

importance are comparison to such geometric

measures as: the available water depth (HD), a

pycnocline height (HINT) and the distance to the

nearest bank (DISTB). The following discussion

provides a brief explanation of the more important

length scales and examples on how to make

appropriate comparisons in a given application.

Users are encouraged to make these

comparisons.

a) Single port discharges: Some

important length scales relating to submerged

round buoyant jets (CORMIX1) are described in

Table 5.1. All of these scales are defined from

an interplay of the momentum and buoyancy flux

quantities of the discharge with each other or with

the current velocity and stratification gradient

variables.

As an example, consider a vertically

discharging buoyant jet into an unstratified

ambient receiving water. When both calculated

L and L values are substantially less than the m b

crossflow may be so weak that its deflecting effect

interact (impinge) with the water surface. In the

first instance, a situation as depicted in Figures

2.1b combined with Figure 2.1a will result, while

in the second instance, a flow resembling Figures

2.2c or 2.2d may arise, depending on the relation

of the two scales with each other. 

As another example, consider a buoyant

jet discharging into a linearly stratified ambient. If

both L ' and L ’ both larger than the pycnocline m b

height (HINT) and even the water depth (HA), this

would be an indication that the existing stratification is so weak that it will not lead to any

trapping of the effluent plume within the available

vertical space.

By making such comparisons, users will

gradually get a good feel for the behavior of the

buoyant jet, and other mixing processes within the

space constraints of the ambient environment.

Those interested in design can quickly gain an

appreciation of the length scale measures and

their sensitivity to design choices. However, there

are limitations to these simplistic comparisons

because the "length scales" are by no means

precise measurements for the influence of the

different processes. As their name implies they

should be taken only as "scale" estimates. The

actual CORMIX classification scheme uses formal

criteria when comparing the length scale

measures with the geometric constraints or each

other.

b) Multiport diffusers: Some important

length scales for multiport diffusers (CORMIX2)

are described in Table 5.2.

To a large extent, these scales have a

similar meaning for the behavior of the plane

buoyant jet as the earlier ones discussed for the

round buoyant jet (Table 5.1). However, they are

calculated differently because the CORMIX2

system uses the "equivalent slot diffuser" concept

to model the overall dynamics of the submerged

multiport diffuser (Section 3.1). Except for the

immediate close-up zone before the individual jets

merge (Figure 2.1d) this concept is a dynamically

valid and accurate representation of multiport

diffuser flows (6). 
49

Table 5.1

Length Scales for Single Port Submerged Discharges 

(Used in CORMIX1 and CORMIX2)

Jet/plume transition length scale L = M / J Mo o

3/4 1/2

interpretation: For combined buoyant jet flow, the distance at which the transition from

jet to plume behavior takes place in a stagnant uniform ambient.

Jet/crossflow length scale L = M / u mo a

1/2

interpretation: In the presence of a crossflow, the distance of the transverse (i.e. across

ambient flow) jet penetration beyond which the jet is strongly deflected (advected) by the

cross flow. For a strictly co-flowing discharge ( = 0, ) = 0), the length of the region

beyond which the flow is simply advected.

Plume/crossflow length scale L = J / u b oa

3

interpretation: The vertically upward or downward flotation distance beyond which a

plume becomes strongly advected by crossflow.

Jet/stratification length scale L ' = M / m o  1/4 1/4

interpretation: In a stagnant linearly stratified ambient, the distance at which a jet

becomes strongly affected by the stratification, leading to terminal layer formation with

horizontally spreading flows.

Plume/stratification length scale L ' = J / b o  1/4 3/8

interpretation: In a stagnant linearly stratified ambient, the distance at which a plume

becomes strongly affected by the stratification, leading to terminal layer formation with

horizontally spreading flows.

_______________

Notes: M = U Q , kinematic momentum flux o oo

J = g' Q , kinematic buoyancy flux o oo

Q = U a , source discharge volume flux o oo

a = port area o

u = ambient velocity a

U = port discharge velocity o

 = ambient buoyancy gradient

.

g' = discharge buoyancy = g( o a oa ' - ' )/'

However, there are some exceptions and notable example is circulating motions induced in

additional complexities to interpreting the two- shallow receiving waters due to intermediate-field

dimensional slot length scales measures effects (Section 2.1.1). The immediate close-up

described in Table 5.2. In addition to the zone before the individual jets merge is also not

predominately two-dimensional flow behavior, addressed by the two-dimensional length scales.

some of the large scale dynamics of multiport Additional discussion of these and other

diffusers may also be influenced by other scales peculiarities can be found elsewhere (6,18).

depending on the overall diffuser flow pattern. A
50

Table 5.2

Dynamic Length Scales for Multiport Diffuser (CORMIX2) in the

Two-Dimensional "Slot" Discharge Representation 

Slot jet/plume transition length scale 5M oo = m / j 2/3

interpretation: For combined buoyant jet flow, the distance at which the transition from

jet to plume behavior takes place in a stagnant uniform ambient.

Slot jet/crossflow length scale 5m oa = m / u 2

interpretation: In the presence of a crossflow, the distance of the transverse (i.e. across

ambient flow) jet penetration beyond which the jet is strongly deflected (advected) by the

cross flow. For a strictly co-flowing discharge ( = 0, ) = 0), the length of the region

beyond which the flow is simply advected.

Slot jet/stratification length scale 5m o ' = m /  1/3 1/3

interpretation: In a stagnant linearly stratified ambient, the distance at which a jet

becomes strongly affected by the stratification, leading to terminal layer formation with

horizontally spreading flows.

Slot plume/stratification length scale 5b o ' = j /  1/3 1/2

interpretation: In a stagnant linearly stratified ambient, the distance at which a plume

becomes strongly affected by the stratification, leading to terminal layer formation with

horizontally spreading flows.

Crossflow/stratification length scale 5a a = u / 1/2

interpretation: The vertically upward or downward floatation distance beyond which a

plume becomes strongly advected by crossflow.

_______________

Notes: m = U q , kinematic momentum flux per unit length o oo

j = g' q , kinematic buoyancy flux per unit length o oo

q = U na /L , source discharge volume flux o o oD

a = port area o

u = ambient velocity a

U = port discharge velocity o

 = ambient buoyancy gradient

.

g' = discharge buoyancy = g( o a oa ' - ' )/'

 n = total number of nozzles

L = overall diffuser length D

c) Buoyant surface jets: Some

important length scales that describe the nearfield dynamics of buoyant surface jets discharging

into unstratified receiving waters (CORMIX3) are

listed in Table 5.3. These scales are defined in a

similar manner to the submerged discharged

cases but due to the discharge location at the

surface, they have different interpretations. For

example, L is compared to the channel width m

(BS) instead of the local water depth as it was in

submerged case examples; if it exceeds BS, the

discharge will quickly interact with the opposing

bank. 
51

Table 5.3

Dynamic Length Scales for Buoyant Surface Jets (CORMIX3)

Discharging into Unstratified Receiving Water

Jet/plume transition length scale L = M / J Mo o

3/4 1/2

interpretation: For stagnant ambient conditions, the extent of the initial jet region before

mixing changes over into an unsteady surface spreading motion.

Jet/crossflow length scale L = M / u mo a

1/2

interpretation: The distance over which a discharging jet intrudes into the ambient crossflow before it gets strongly deflected.

Plume/crossflow length scale L = J / u b oa

3

interpretation: A measure of the tendency for upstream intrusion for a strongly buoyant

discharge.

_______________

Notes: M = U Q , kinematic momentum flux o oo

J = g' U , kinematic buoyancy flux o oo

Q = U a , source discharge volume flux o oo

 a = channel cross-sectional area o

u = ambient velocity a

U = channel discharge velocity o

g' = discharge buoyancy = g( o a oa ' - ' )/'

 

d) Tidal reversing flows: Additional

length and time scales can be defined for

unsteady flows in which the scale of influence of

oscillating plume depends on the rate of velocity

reversal change at slack tide (8,17). CORMIX will

take the actual steady-state predictions and

adjust their concentration values according to the

time after reversal relative to the time scale T and u

also limit their areal applicability relative to L .u

5.1.3 Description of Flow Classes

Program element CLASS, performs a

rigorous classification of the given

discharge/ambient situation into one of many

generic flow classes with distinct hydrodynamic

features. In a way, this amounts to identifying a

general pictorial description of the expected flow

configuration.

Table 5.5 lists and describes the broad

categories of flow classes available in CORMIX.

CORMIX1, 2 and 3, consider 35, 31 and 11

distinct flow classifications, respectively. Each

flow class identification consists of an

alphanumeric label corresponding to the flow

category and a number (e.g. MU2). Text

descriptions of the flow classes are available onscreen during the analysis and can printed from

the files stored within sub-directory

CORMIX\TEXT (Table 3.1). Pictorial illustrations

of the flow classes can be found in Appendix A.

As an example, Figure 5.1 shows the pictorial

illustration and text description for flow class S1,

a case of an effluent that becomes trapped in

ambient stratification. It is strongly recommended

that novice or intermediate users scrutinize these

materials to gain a qualitative understanding of

the effluent flow's behavior. 
Lu 
 Mo


dua /dt 


1/3

Tu 
 Mo


dua /dt 
1/4

1/6

52

Table 5.4

Dynamic Length and Time Scales for 

Discharges into Unsteady Tidal Reversing Flows

Jet-to unsteady-crossflow length scale 

interpretation: A measure of the distance of the forward propagation into the ambient

flow of a discharge during the reversal episode.

Jet-to unsteady-crossflow time scale 

interpretation: a measure of the duration over which an effluent may be considered as

discharging into stagnant water while the velocity field is reversing.

_______________

Notes: M = U Q , kinematic momentum flux o oo


du /dt
 = time rate of reversal of ambient velocity (absolute value) a

Table 5.5

Flow Class Categories and Descriptions

CORMIX1: 35 flow classes

Classes S: Flows trapped in a layer within linear stratification.

Classes V,H: Positively buoyant flows in a uniform density layer.

Classes NV,NH: Negatively buoyant flows in uniform density layer.

Classes A: Flows affected by dynamic bottom attachment.

 CORMIX2 : 31 flow classes

Classes MS: Flows trapped in a layer within linear ambient stratification.

Classes MU: Positively buoyant flows in a uniform density layer.

Classes MNU: Negatively buoyant flows in uniform density layer.

CORMIX3 9 flow classes

Classes FJ: Free jet flows without near-field shoreline interaction.

Classes SA: Shoreline-attached discharges in crossflow.
53

Classes WJ: Wall jets/plumes from discharges parallel to shoreline.

Classes PL: Upstream intruding plumes.

FLOW CLASS S1 

This flow configuration is profoundly affected by the linear

ambient density stratification. The predominantly jet-like flow

gets trapped at some terminal (equilibrium) level. The trapping

is also affected by the reasonably strong ambient crossflow.

Following the trapping zone, the discharge flow forms an internal

layer that is further influenced by buoyant spreading and passive

diffusion. 

The following flow zones exist: 

1) Weakly deflected jet in crossflow: The flow is initially

dominated by the effluent momentum (jet-like) and is weakly

deflected by the ambient current. 

2) Strongly deflected jet in crossflow: The jet has become strongly

deflected by the ambient current and is slowly rising toward the

trapping level. 

3) Terminal layer approach: The bent-over submerged jet/plume

approaches the terminal level. Within a short distance the

concentration distribution becomes relatively uniform across the

plume width and thickness. 

*** The zones listed above constitute the NEAR-FIELD REGION

 in which strong initial mixing takes place. ***

4) Buoyant spreading in internal layer: The discharge flow within

the internal layer spreads laterally while it is being advected by

the ambient current. The plume thickness may decrease during this

phase. The mixing rate is relatively small. The plume may interact

with a nearby bank or shoreline.

5) Passive ambient mixing: After some distance the background

turbulence in the ambient shear flow becomes the dominating mixing

mechanism. The passive plume is growing in depth and in width. The

plume may interact with the upper layer boundary, channel bottom

and/or banks. 

*** Predictions will be terminated in zone 4 or 5 depending on

 the definitions of the REGULATORY MIXING ZONE or the REGION OF

 INTEREST. *** 

Figure 5.1: Example of a Flow Class Description
54

5.2 Quantitative Output: Numerical Flow

Predictions

After execution of the detailed flow

prediction in program element HYDROn, the

system provides two types of detailed numerical

output on effluent plume trajectory and mixing and

on compliance with regulations. A concise

summary is available on-screen in the final

system element SUM and a detailed numerical

output file is also generated for inspecting and

plotting the plume's behavior after the analysis.

5.2.1 Summary Output in SUM

The self-explanatory summary output

which can be displayed on-screen includes: (a)

the date and time of the analysis section, (b) a

complete echo of the input data, (c) the calculated

flux, length scale and non-dimensional parameter

values, (d) the flow classification used for

predicting plume trajectory and mixing, (e) the

coordinate system used in the analysis, (f) a

summary of the near-field region (NFR)

conditions, (g) the far-field locations where the

plume becomes essentially fully mixed (i.e.

uniform concentration) in the horizontal and

vertical directions, (h) a summary of the toxic

dilution zone (TDZ) conditions, and (I) a summary

of the regulatory mixing zone (RMZ) conditions.

Although the raw data used to construct this

summary output is permanently stored in file

'fn'.CXC within the output sub-directory

CORMIX\SIM\CXn, a hard-copy printout should

be requested during the analysis session because

the raw data file is unformatted and does not

contain the explanatory text that is available

during program execution; 'fn' is the filename

specified by the user during input data entry. 

The coordinate system conventions

pertain to the origin location and axis direction. In

CORMIX1 analyses, the origin is located at the

bottom of the receiving water just below the

discharge port center and thus, at a depth HD

below the water surface. In CORMIX2 analyses,

the origin is located at the bottom of the receiving

water, at the midpoint of the diffuser line and thus,

at a depth HD below the water surface. In

CORMIX3 analyses, the origin is located at the

water surface where the discharge channel

centerline and receiving water shoreline intersect.

The x-axis lies in the horizontal plane and points

downstream in the direction following the ambient

flow; the y-axis lies in the horizontal plane and

points to the left as seen by an observer looking

downstream along the x-axis; and the z-axis

points vertically upward. Note that when the

ambient current direction varies (e.g. due to

reversing tidal flows), the interpretation of

simulation results becomes more involved since

the x-axis and the y-axis will change depending

on flow direction. 

In addition to the numerical predictions of

the plume size, location and chemical

concentration, the summary of the near-field

region (NFR) conditions describes other relevant

plume features such as bottom attachment, bank

interaction and the degree of upstream intrusion.

This information is useful for both engineering

design and for determining whether important

resource areas may be exposed to undesirable

chemical concentrations.

In case of a toxic discharge, the summary

toxic dilution zone (TDZ) conditions will indicate

the location along the plume where the local

concentration begins to fall below the specified

CMC. CORMIX automatically checks compliance

with the three geometric restrictions listed for

mixing zones associated with toxics discharges

under alternative 3 (see Subsection 2.3.3) and the

results of these comparisons are displayed. The

user can evaluate the fourth alternative by

referring to travel times given at the end of each

simulation module in the related output files.

When regulatory mixing zone (RMZ)

criteria have been specified during input data

entry, the geometric, dilution and concentration

conditions at the edge of the specified or

proposed RMZ are compared to these criteria

and/or to the applicable CCC concentration

following the practices discussed in Subsection

2.2.4. The results of these comparisons are

displayed.

5.2.2 Detailed Prediction Output Filefn'.CXn

The file 'fn'.CXn stored within sub-directory

CORMIX\SIM contains the same kinds of

information available in the summary output plus

the detailed numerical predictions on plume

geometry and mixing produced during the

hydraulic simulation. Data in that file forms the
55

basis for further analysis, inspection, evaluation, 'fn".CXn output reflects that sequence and is a

and plotting of the plume shape and trajectory. arranged in output blocks for each module.

The graphics package also uses the same data to

plot on-screen, and print if desired, the plume Each simulation module has a "MODnxx"

properties as explained in Section 5.2.3. label where "n" is 1, 2, or 3 corresponding to

During program execution, the user has number. The two general types of modules are

several opportunities to display on-screen or print continuous flow and control volume.

out this file. It can also be printed at a later date

by using the DOS PRINT command or any word

processor. CORMIX will not erase any of the files

with .CXn (or .CXC) extension that get stored in

the CORMIX\SIM sub-directory. Consequently,

periodic directory maintenance is recommended

to remove old and superfluous files. This is best

accomplished with a built-in file manager (see

Main Menu) that deletes the specified files from

the hard disk, but also erases their entry from the

record keeping file CORMIX\SIM\CXn\summary.

The 'fn'.CXn file is a FORTRAN output file

generated by the HYDROn prediction program.

As is typical of many FORTRAN outputs, its

display features are terse with tight format control

and data items labeled in symbolic form only (e.g.

"Q0" for discharge flow rate). Complete output file

examples can be inspected in Appendices B, C

and D.

All three CORMIXn subsystems produce

a 'fn'.CXn output file with common appearance

and features as described in the following

paragraphs.

a) Lead-in information: The output starts (and

ends) with a "111...111", "222...222", or

"333...333" banner line to accentuate which

subsystem has been used. The date and time of

the analysis session and all important input data

are the next items in the file. These are

subsequently followed by the calculated length

scale values, non-dimensional numbers of

interest to the specialist, the flow class

identification, and the coordinate system is

displayed.

b) Prediction results for each flow "module":

As was mentioned previously in Subsection 3.6,

the CORMIX prediction methodology utilizes a

number of simulation modules that are executed jet or plume regions, the ratio of flux-average to

sequentially and that correspond to the different minimum centerline dilution S /S = 1.7 and 1.3,

flow processes and associated spatial regions for single-port round and multiport plane

which occur within a given flow class. The discharges, respectively.

CORMIXn, and "xx" is a two-digit identification

The continuous flow module type

describes the continuous evolution of a flow

region along a trajectory. Depending on the

number of grid intervals specified by the user,

information on plume geometry, flow, and mixing

information along the plume trajectory may be

available for a few or many water body locations.

Figure 5.2 provides examples of typical

output from continuous flow modules. The

annotations along the right margin illustrate

important features of the output format.

Figure 5.2a was taken from a CORMIX1

simulation output file and shows an example of a

submerged jet region module (MOD110,

equivalent to CORJET). The output contains

labeling information on the module, and

explanatory notes on profile definitions. It also

gives a numerical list on the predictions, first

repeating the final values from the preceding flow

module and then one line for each user-specified

grid interval. This information gives the x-y-z

position of the jet/plume centerline, the dilution (S)

and concentration (C) at the centerline, and the

jet width (B). 

Dilution (S) is defined as the ratio of the

initial concentration (at the discharge port) to the

concentration at a given location, irrespective of

any decay or growth effects if specified for a nonconservative pollutant. However, concentration

(C) will include any first-order effects for nonconservative pollutants. Dilution (S) given by

CORMIX for submerged jet or plume regions is

the minimum centerline dilution for the jet/plume.

The control volume and buoyant spreading

modules give bulk dilutions, which are equivalent

to flux-averaged dilutions for these regions. If a

flux-averaged dilution S is desired for submerged f

 f
56

-----------------------------------------------------------------------------

BEGIN CORJET (MOD110): JET/PLUME NEAR-FIELD MIXING REGION

 Jet/plume transition motion in weak crossflow.

 Zone of flow establishment: THETAE= 0.00 SIGMAE= 277.06

 LE = 3.39 XE = 0.21 YE = -3.38 ZE = 1.00

 Profile definitions:

 B = Gaussian 1/e (37%) half-width, normal to trajectory

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 X Y Z S C B

 0.00 0.00 1.00 1.0 0.100E+03 0.76

 0.21 -3.38 1.00 1.0 0.100E+03 0.76

 0.90 -7.41 4.11 1.8 0.562E+02 1.13

 1.55 -9.36 9.07 3.3 0.300E+02 1.59

 2.23 -10.55 14.27 5.4 0.186E+02 2.10

 2.95 -11.39 19.56 7.9 0.127E+02 2.63

 3.72 -12.02 24.85 10.8 0.928E+01 3.16

 Cumulative travel time = 18. sec

END OF CORJET (MOD110): JET/PLUME NEAR-FIELD MIXING REGION

-----------------------------------------------------------------------------

a) Submerged buoyant jet module

----------------------------------------------------------------------------- BEGIN MOD341:

BUOYANT AMBIENT SPREADING Profile definitions:

 BV = top-hat thickness, measured vertically

 BH = top-hat half-width, measured horizontally from bank/shoreline

 S = hydrodynamic average (bulk) dilution

 C = average (bulk) concentration (includes reaction effects, if any)

 Plume Stage 1 (not bank attached):

 X Y Z S C BV BH

 1.93 -.82 0.00 8.4 .884E+00 .03 .58

 2.07 -.82 0.00 8.5 .869E+00 .03 .62

 2.20 -.82 0.00 8.6 .856E+00 .03 .65

 ** WATER QUALITY STANDARD OR CCC HAS BEEN FOUND **

 The pollutant concentration in the plume falls below water quality standard

 or CCC value of .850E+00 in the current prediction interval.

 This is the spatial extent of concentrations exceeding the water quality 

 standard or CCC value.

 2.34 -.82 0.00 8.8 .844E+00 .03 .68

 2.48 -.82 0.00 8.9 .833E+00 .03 .71

 2.62 -.82 0.00 9.0 .822E+00 .03 .74

 2.76 -.82 0.00 9.1 .811E+00 .03 .77

 2.89 -.82 0.00 9.2 .801E+00 .03 .80

 2.96 -.82 0.00 9.3 .796E+00 .03 .82

 Cumulative travel time = 95. sec

----------------------------------------------------------------------------- Plume is ATTACHED

to LEFT bank/shore.

 Plume width is now determined from LEFT bank/shore.

 Plume Stage 2 (bank attached):

 X Y Z S C BV BH

 2.96 .00 0.00 9.3 .796E+00 .03 .82

 16.05 .00 0.00 31.3 .237E+00 .03 2.59

 29.13 .00 0.00 96.8 .764E-01 .06 3.77

 42.22 .00 0.00 220.7 .335E-01 .10 4.76

 55.31 .00 0.00 411.4 .180E-01 .16 5.64

 68.39 .00 0.00 675.3 .110E-01 .23 6.45

 81.48 .00 0.00 1017.8 .727E-02 .31 7.20

 94.56 .00 0.00 1443.5 .513E-02 .40 7.91

 101.11 .00 0.00 1688.9 .438E-02 .45 8.26

 Cumulative travel time = 3367. sec

 END OF MOD341: BUOYANT AMBIENT SPREADING 

----------------------------------------------------------------------------- 

b) Far-field flow module (example of buoyant spreading with bank contact)

Figure 5.2: Examples of continuous flow modules within CORMIX
57

The cumulative travel time (T) is given at

the end of each simulation module. The travel

time can be used to assess the applicability of the c) Numerous other supplementary messages

steady-state predictions given by CORMIX to time on plume behavior (e.g. bottom attachment, bank

scales appropriate for the particular application. contact, etc.) and on possible model restrictions

Another example of a continuous flow restricted river) are contained in the output as

module output is shown in Figure 5.2b. It was warranted; Figures 5.2 and 5.3 provide but a few

abstracted from a CORMIX simulation output file examples of these user aids. 

and shows predictions for the far-field process of

buoyant ambient spreading (Figure 2.6).

Although it is terse, the output file values and

commentary generally provide a complete picture

of flow conditions. In this example output (Figure

5.2b), evidence of this completeness includes: (a)

the prediction output is separated in two stages

corresponding to before and after bank

interaction, respectively; due to the typical oblong

cross-section of the plume in this stage, width

dimensions for the vertical and lateral extent are

given and defined; the coordinates for the upper

and lower boundaries of the plume are listed as a

convenience for plotting; and the system

searches for criteria that apply to mixing zone

regulations and when a criterion is satisfied, a

remark gets inserted in the output list at the

appropriate spatial position. (Note: The length

dimensions in Figure 5.2b are small as they relate

to a laboratory simulation.)

Some mixing flow processes are so

complicated that no mechanistically-based

mathematical description of them is presently

available in state-of-the-art science. Those

processes are best analyzed with control

volume modules as shown in Figure 5.3. inspection and evaluation of results.

In the control volume modeling approach, the prediction after the file has been stored,

outflow values for a region are computed as a by entering the Post-Processor option in

function of the inflow values and are based on the Iteration Menu.

conservation principles. (1c) It can be accessed on earlier existing

An output example for control volumes Processor option in the Main Menu.

modules is illustrated in Figure 5.3. It is taken

from a CORMIX1 simulation output file and gives (2) Use outside CORMIX:

predictions for a flow case corresponding to an The graphics system can be invoked

unstable near-field (Figure 2.2c). Note that a directly by typing:

separate listing of inflow variables and outflow

variables is given with appropriate explanations. cmxgraph (or simply: cg) filename

The tabular listing of plume shape is based on an where filename (including path and

interpolation routine using a generic plume shape extension) is any prediction file generated

for these upstream intruding motions, rather than by CORMIX or by CORJET. 

a detailed computation.

(e.g. ambient dilution limitations in a flow5.3 Graphical Output: Display and Plotting of

Plume Features Using CMXGRAPH

5.3.1 Access to CMXGRAPH

CMXGRAPH is a specially developed

graphics package, written in C++, for the display

and plotting of CORMIX (and also CORJET, see

Section 6.2) predicted effluent plumes. It uses

the prediction files 'fn'.CXn that are stored in the

directory CORMIX\SIM, and plots plume features

based on the numerical and narrative information

contained in these files.

The graphics system can be accessed in

different ways:

(1) Use within CORMIX: Different access modes

exist here. 

(1a) The user can display the plume

graphics immediately after the actual

prediction and before the file information

is stored. This is useful for an initial

(1b) It can be accessed at an end of the

files by directly choosing the Post-
58

-----------------------------------------------------------------------------

BEGIN MOD132: LAYER BOUNDARY IMPINGEMENT/UPSTREAM SPREADING

 Vertical angle of layer/boundary impingement = 79.65 deg

 Horizontal angle of layer/boundary impingement = 324.93 deg

 UPSTREAM INTRUSION PROPERTIES:

 Upstream intrusion length = 328.95 m

 X-position of upstream stagnation point = -325.23 m

 Thickness in intrusion region = 0.55 m

 Half-width at downstream end = 470.97 m

 Thickness at downstream end = 0.70 m

 In this case, the upstream INTRUSION IS VERY LARGE, exceeding 10 times

 the local water depth.

 This may be caused by a very small ambient velocity, perhaps in

 combination with large discharge buoyancy.

 Control volume inflow:

 X Y Z S C B

 3.72 -12.02 24.85 10.8 0.928E+01 3.16

 Profile definitions:

 BV = top-hat thickness, measured vertically

 BH = top-hat half-width, measured horizontally in Y-direction

 ZU = upper plume boundary (Z-coordinate)

 ZL = lower plume boundary (Z-coordinate)

 S = hydrodynamic average (bulk) dilution

 C = average (bulk) concentration (includes reaction effects, if any)

 X Y Z S C BV BH ZU ZL

 -325.23 -12.02 28.00 9999.9 0.000E+00 0.00 0.00 28.00 28.00

 -313.94 -12.02 28.00 46.5 0.215E+01 0.13 66.61 28.00 27.87

 -258.63 -12.02 28.00 19.3 0.519E+01 0.31 161.78 28.00 27.69

 -203.31 -12.02 28.00 14.5 0.688E+01 0.40 218.89 28.00 27.60

 -148.00 -12.02 28.00 12.5 0.802E+01 0.47 263.91 28.00 27.53

 -92.68 -12.02 28.00 11.4 0.878E+01 0.52 302.30 28.00 27.48

 -37.37 -12.02 28.00 10.9 0.919E+01 0.54 336.34 28.00 27.46

 17.95 -12.02 28.00 11.0 0.913E+01 0.55 367.24 28.00 27.45

 73.26 -12.02 28.00 14.4 0.694E+01 0.59 395.73 28.00 27.41

 128.58 -12.02 28.00 19.1 0.522E+01 0.65 422.30 28.00 27.35

 183.89 -12.02 28.00 22.0 0.455E+01 0.68 447.30 28.00 27.32

 239.21 -12.02 28.00 23.2 0.431E+01 0.70 470.97 28.00 27.30

 Cumulative travel time = 3037. sec

END OF MOD132: LAYER BOUNDARY IMPINGEMENT/UPSTREAM SPREADING

-----------------------------------------------------------------------------

Figure 5.3: Example of control volume flow module
59

As mentioned, numerous flow features (as

evidenced by the different flow classes) can 5.3.2 Use of CMXGRAPH

occur. It is difficult to develop a robust graphics

package that operates safely for all of these The graphics system has a selfpossibilities. The CMXGRAPH system has been explanatory screen interface as shown in Figure

widely tested, but occasional crashes can occur

for rare flow module combinations and then only

for certain plot types. Should a crash occur and

the direct access mode (1a), listed above, has

been used then the current file information will be

lost. In those cases, it is safer to first save the

current session file data and then exercise the

graphics system.

5.4. The menu is controlled by the keyboard

alone by typing the letters that appear in capital

on the menu buttons, or by user the four cursor

keys when in zoom mode.

The GRAPHICS MENU COMMANDS are as follows:

Help an advice section is available listing the same information as given here

Quit exits the graphics system

There exist FIVE PLOT TYPES:

Plan generates a plan view of plume (x-y), as seen from above (entry option)

Side generates a side view of plume (x-z), as seen by an observer looking from the

bank/shore

Traj generates a side view along trajectory of plume. The view is stretched out along the

actually curving centerline trajectory.

c-X generates a plot of concentration on the plume centerline plotted against downstream

distance x

c-D generates a plot of concentration on the plume centerline plotted against distance along

the plume trajectory

The user can CONTROL the plume VIEW:

Near displays the near-field region only ; useful for close-up details (entry option)

Full displays the complete near- and far-field regions (i.e. the entire prediction results)

SHOW/HIDE FEATURES can be exercised to display additional information:

Labels puts identifier labels (site/case information) on top of plot (entry option)

Wqual displays information on regulatory mixing regulations (TDZ, RMZ, ...) on the plot; this is
60

displayed by dotted lines where particular regulations are encountered.

Module shows boundaries of prediction modules 

ZOOM/SCALE CONTROL allows control of plot details:

Zoom allows the user to enlarge any RECTANGULAR SECTION of the current plot; this is

accomplished by:

-- Use CURSOR Control keys to move cursor (up,down,left,right)

-- Cursor SPEED can be modified by typing any number: 1(slowest),2,.. to 0(fastest)

-- Press RETURN when first corner of desired rectangle has been reached

-- Move cursor to find opposite corner and press RETURN to fix opposite corner

sKale allows the user to FIX SCALE distortion of current plot. The current scale is displayed

in a window on the menu bottom (see Figure 5.4).

-- Type in desired distortion at the prompt: All subsequent versions of the plot (including

zooms will be fixed at this scale distortion.

 -- Use the sKale button again, to release the scale distortion.

Bkup back-up to earlier zoomed/scaled versions of current plot

Esc exit from zoom/scale mode (also Quit or repeated Bkup can be used to exit)

Several PRINT OPTIONS are available:

pfIle writes the current plot to a POSTSCRIPT FILE for later printing. The file can be edited

and/or printed later using any compatible software (including public domain software,

such as Ghostscript).

-- Each print file is stored as \"filename.Pvn\" where: 

filename = CORMIX or CORJET assigned filename,

Pvn = file extension indicating a Postscript file,

v = P, S, T, X or D, for one of the five view types,

n = 0 to 9, increasing file number.

-- If the total file number for a particular view type exceeds the maximum of ten (10), the

first file in the series will be erased and replaced by the new file.

psCrn allows a PRINT SCREEN action of the current plot 

 -- The plot is first recreated without the menu interface and plot border.

 -- Then use the Shift-PrintScreen buttons, to print the plot on-line.

Important: The PRINTER must have been initialized for GRAPHICS MODE with the

DOS command: \"graphics [type] /r\" where: [type] = type of printer (e.g.: color4,

laserjetii).
61

Figure 5.4 CMXGRAPH interface with menu options including example plot
c(n) 
 cc

e

	( n

b

)

2

62

The case study materials in the

Appendices show some of the possibilities that

can be exercised in the graphics display the

plume features described in the fn.CXn output

files. As shown above, the plume is characterized

by its centerline trajectory, dilution, and width

values. For understanding added detail in the

plume cross-section, it is important to keep in

mind the different concentration distributions and

meanings of "plume width". These are explained

in the supplemental statements at the beginning

of each flow module (see Figures 5.2 and 5.3).

Also, Figure 5.5 may be useful for further

illustration. It gives the cross-sectional distribution

of concentration for many of the commonly

occurring plume cross-sections in the various

regions predicted by the CORMIXn subsystems.

In some instances, users may desire to

plot concentration isolines for the predicted plume

shapes. The information contained in the

HYDROn output file for each module and the

definitions shown in Figure 5.5 are sufficient to

construct such plots. In particular, in submerged

plume or passive mixing regions having a

Gaussian distribution, the following formula can

be used

where c(n) is the lateral concentration, n is the

coordinate position measured tranversely away

from the centerline, cc is the centerline

concentration, e is the natural logarithm base, and

b is the local plume half-width. However, this

equation can not be used to plot concentration

isolines in the control volume or buoyant

spreading regions because they are defined with

a top-hat or uniform concentration profile and not

a Gaussian distribution.

By and large, all CORMIXn predictions are

continuous from module to module satisfying the

conservation of mass, momentum and energy

principles. Occasionally, some mismatches in

plume width can occur as a consequence of

enforcing these principles. Most of these will be

barely noticeable with the usual plotting resolution

and they can usually be safely ignored. Some of

the mismatches or discontinuities can be kept to

a minimum by specifying a large number for the

grid intervals (see Section 4.9) to increase the

resolution of the CORMIX prediction. This is

especially useful for the final simulations on a

particular design case.

In addition, when bottom attachment or

bank interaction occurs, the plume trajectory is

assumed to (and simulation predictions do) shift

suddenly to the boundary. In actuality, that shift

would be much more gradual and this should be

considered when interpreting the results of the

CMXGRAPH plots or, alternatively, when plotting

plume features by hand. 
63

Figure 5.5: Cross-sectional distributions of CORMIX predicted jet/plume sections
64
65

VI Post-Processor Models CORJET and FFLOCATR:

Input and Output Features

The CORMIX system contains three post- recent CORMIX system enhancements. CORJET

processor options which be accessed directly is a type of a jet integral model whose original

from within the system or independently outside of development in a two-dimensional framework and

CORMIX. In either case, the post-processor for a round jet only was first reported in the peeroptions provide additional enhancements to reviewed literature by Jirka and Fong (25).

CORMIX in terms of plume display, and more Detailed verification studies with various

detailed computation of near- and far-field plume experimental data sources have been reported

features. (8,26).

The first of the options, the graphics In jet integral models the hydrodynamic

package CMXGRAPH, has already been equations governing the conservation of mass

described in Section 5.3. The second option is and momentum, and of other quantities as

CORJET, the Cornell Buoyant Jet Integral Model, pollutant mass, density deficit, temperature and/or

for the detailed analysis of the near-field behavior salinity, are solved step-wise along the general

of buoyant jets. FFLOCATR, the Far-Field curved jet trajectory. The solution yields values of

Plume Locator, for the far-field delineation of the trajectory position itself and of the centerline

discharge plumes in non-uniform river or estuary concentrations of these quantities, while the

environments is the third option. The latter two actual cross-sectional distribution is fixed a priori

are described in this chapter. (mostly as a Gaussian distribution) in these

6.1 CORJET: The Cornell Buoyant Jet Integral

Model

6.1.1 General Features

CORJET is a Fortran model that solves

the three-dimensional jet integral equations for

submerged buoyant jets --either a single round

jet or interacting multiple jets in a multiport

diffuser-- in a highly arbitrary ambient

environment. The ambient/discharge conditions

include an arbitrary discharge direction, positive,

neutral or negative discharge buoyancy, an

arbitrary stable density distribution, and a nonuniform ambient velocity distribution with

magnitude and direction as a function of vertical

position. 

Figure 6.1 displays these general

characteristics for the case of a single port. In

case of the multiport diffuser all the discharge

port/nozzles point in the same direction

(unidirectional or staged design) and the diffuser

line can have an arbitrary alignment angle relative

to the ambient current (for definitions see Section

4.5.1).

The detailed theoretical basis for CORJET

can be found in the documentation report (8) on

models. Literally several dozen such model

developments have been reported in the literature

over the last thirty years or so of research on

these mixing phenomena. Most of these

developments differ (I) in the degree of simplifying

assumptions on the ambient/discharge

characteristics (e.g. two-dimensional trajectories

or uniform ambient conditions only), and (ii) in the

type of closure that is made to specify the

turbulent growth and entrainment behavior in

these jets under a variety of forcing conditions.

Thus, some of these models can be

demonstrated to be unduly limited for practical

applications, and others to be clearly invalid in

certain limiting regimes of plume behavior.

Whenever a jet integral model is

reasonably general in its formulation and has

been validated through experimental data

comparison under a number of conditions it can

be considered a useful prediction tool for nearfield plume analysis. For practical purposes, all

the models that meet the above conditions, in

fact, differ little in their prediction results. The

deviation among model results is usually less

than the scatter in experimental data that is used

for their verification. This holds true also for

CORJET as well as another jet integral model, 
66

Figure 6.1: General three-dimensional trajectory of submerged buoyant jet in ambient flow with

arbitrary density and velocity distribution: Case of a single round jet

(27), that has current USEPA support and

distribution. 

Both CORJET and PLUMES, although

they differ in their internal formulation and

closure assumptions, have a wide generality in

discharge/ambient conditions and a reasonable

verification base for a variety of conditions. They

can deal with three-dimensional trajectories, with

positive, neutral or negative discharge buoyancy,

with conditions of reversible buoyancy (so-called

nascent conditions in freshwater systems due to

the density maximum at 4o

C, requiring use of the

full non-linear equation of state), with first-order

pollutant decay, with variable stable ambient

density, and with sheared non-uniform ambient

currents, and with the merging of multiple port

diffuser plumes. Three specialized features that

the PLUMES model cannot deal with are a

variable current direction at different levels,

arbitrary diffuser alignments (with the extreme of

a fully parallel alignment, γ = 0o

 in Figure 4.6),

and applications to atmospheric plumes (using

the concept of potential temperature and

density).

 Jet integral models, such as CORJET and
67

PLUMES, appear as useful and efficient tools for by entering the Post-Processor option in

the rapid analysis of the near-field mixing of the Iteration Menu.

aqueous discharges. They require fairly little (1b) It can be accessed on earlier

input data and are numerically efficient. However, existing files by directly choosing the Posttheir inherent limitations must be kept in mind. Processor option in the Main Menu.

All jet integral models, including

CORJET, assume an infinite receiving water

body, without any boundary effects due to limiting

dimensions vertically (surface, bottom, or

pycnocline) or laterally (banks or shore). Thus,

they do not deal with such hydrodynamic effects

as jet attachment and near-field instabilities that

are so prevalent in many aqueous discharge

plumes as emphasized in Section 2.1.1.

Furthermore, they are near-field models only

and do not give predictions on what happens to

the entire mixing zone that may often cover larger

distances (see Section 2.2.5).

In summary, jet integral models if used

alone and by an inexperienced analyst are not a

safe methodology for mixing zone analysis.

They become safe only when used in conjunction

with a more comprehensive analysis using the full

CORMIX system. Therefore, in case of

engineering design applications, CORJET should

be employed after prior use of the expert

system CORMIX has indicated that the

buoyant jet will not experience any

instabilities due to shallow water or due to

attachment to boundaries.

In fact, the CORMIX system has built in

several safeguards and warning statements to the

user as explained below. When used in that

context CORJET becomes a highly useful

addition to the CORMIX system that can provide

considerable additional detail and sensitivity

analysis in the immediate near-field of the

discharge plume.

6.1.2 Access to CORJET

CORJET, like the other post-processor

options such as the graphics system (Section

5.3.1), can be accessed in different ways:

(1) Use within CORMIX:

(1a) It can be accessed at an end of the

prediction after the file has been stored,

In either case, once the CORJET

option is chosen the user must first

specify whether a CORMIX1 or 2

simulation should be analyzed for the

near-field with CORJET. Then the

CORMIX1 or 2 filename in the

CORMIX\SIM directory must be specified.

CORJET will run automatically using the

input data of the given CORMIX data file.

(2) Use outside CORMIX:

CORJET can be invoked directly by

typing:

corjet (or simply: cj) filename

where filename (including path and

extension) is any specially prepared input

data file (see following section). 

Alternatively if one types:

corjet (or simply: cj)

the model will prompt the user for the

input data filename.

6.1.3 CORJET Input Data File

This section for data preparation applies

only if CORJET is run independently from the

CORMIX system as discussed above. The

checklist given on the following page is useful

for data assembly prior to input data entry.

In this case, the Fortran model CORJET

reads input data file with filename that is userspecified with arbitrary name, extension and

directory. For user convenience it is

recommended that all such files be kept in the

special directory CORMIX\POST\CJ.

The input data file is a Fortran-readable

file that is read in open format, that is all pertinent

data values are arranged on a line and separated

by one or more open spaces. The file consists of

five data blocks, each of which must be lead in by

two dummy lines that are not read. Table 6.1

gives an example of a data file in which the

dummy lines are indicated by the # sign.
68

Table 6.1

Example of an input data file for CORJET

#CORJET INPUT FILE

#Title line (50 characters max.):

Case2: SINGLE PORT, STRATIFIED, VARIABLE CURRENT

#Fluid (1=water,2=air), Density option (1=calculate,2=specify directly):

#Fluid (1⁄2): Density option (1⁄2): Ambient levels (1-10): 

1 1 3

#Ambient conditions (if d.o.=1, fill in TA+SA; if 2, fill in RHOA):

#Level ZA TA SA RHOA UA TAUA

1 0. 12. 30. 0.5 0.

2 5. 15. 29.5 0.8 0.

3 15. 20. 28. 1.2 0.

#Discharge conditions (T0+S0, or RHO0 as above; if NOPEN=1: set LD=0,ALIGN=0):

#NOPEN D0 H0 U0 THETA0 SIGMA0 C0 KD T0 S0 RHO0 LD ALIGN

1 0.5 0. 3.0 45. 45. 100. 0. 30. 0. 0. 0.

#Program control:

#ZMAX ZMIN DISMAX NPRINT

30. 0. 200. 10

The required input data values (all in SI

units) are discussed in the following. The

definition of these values is entirely consistent

with those for CORMIX (in particular, see Section

4.4 and 4.5 for discharge conditions).

Block 1: Identifier

LABEL: Any descriptive label/text (should not exceed 50 characters, so that it does not get truncated on

the graphics plots)

Block 2: Fluid and density specification

IFLUID: 1 (water) or 2 (air, for atmospheric applications)

IDENOP: 1: in case of water: Density will be calculated from specified temperature and/or salinity

In case of air: Potential density will be calculated from potential temperature assuming

dry adiabatic conditions

2: Density values will be specified directly 

LEVAMB: Number of levels for which ambient conditions are given (1 to 10)

Block 3: Ambient Conditions (specify LEVAMB lines)

LEV: Level number (increasing from 1 to LEVAMB)

ZA: Specify vertical level (z-coordinate) (m)

TA : if IFLUID=1(water): Temperature at ZA (degC) (omit if IDENOP=2)

if IFLUID=2(air): Potential temperature at ZA (degC) (omit if IDENOP=2)

SALA: Salinity at ZA (ppt) (omit if IDENOP=2 or if IFLUID=2) 

RHOA: if IFLUID=1: Density at ZA (kg/m ) (omit if IDENOP=1) 3

if IFLUID=2: Potential density at ZA (kg/m ) (omit if IDENOP=1) 3

UA: Ambient velocity (speed) at ZA (m/s)

TAUA: Angle of ambient velocity vector measured CCW from x-axis (deg) (set = 0. unless velocity

distribution in vertical is skewed, i.e. spiral-type)

Block 4: Discharge Conditions

NOPEN: 1: if SINGLE PORT DISCHARGE (i.e. 1 opening)

>= 3: number of openings (ports) for MULTIPORT DIFFUSER

D0: Port diameter (m) (should include contraction effects if any)

H0: Port center height above x-y plane (m)

U0: Jet exit velocity (m/s)

THETA0: Vertical angle of discharge (deg)

70

SIGMA0: Horizontal angle of discharge axis measured CCW from x-axis (deg)

Examples: 0. = co-flow, 90. or 270. = cross-flow, 180. = counterflow

C0: Discharge concentration (any units that need not be specified)

KD: Coefficient of substance decay [negative value if growth] (/s)

T0: Discharge temperature (degC) (omit if IDENOP=2)

S0: Discharge salinity (ppt) (omit if IDENOP=2 OR IF IFLUID=2)

RHO0: Discharge density (kg/m ) (omit if IDENOP=1) 3

LD: Diffuser length (m) (set = 0. [non-blank] if NOPEN=1)

ALIGN: Diffuser alignment angle (deg) measured CCW from x-axis (set = 0. if NOPEN=1)

Examples: 0. = parallel diffuser, 90. = perpendicular diffuser

Block 4: Program Control

ZMAX: Maximum vertical coordinate of interest (m)

ZMIN: Minimum vertical coordinate of interest (m)

ZMAX and ZMIN are cutoffs for + and - buoyancy, respectively!

DISMAX: Maximum distance of interest along trajectory (m)

NPRINT: Print intervals (any positive number less than 100; recommended value 5 to 10; does not affect

accuracy of computation!)

Note on density specification: It is at the level of origin.

important to note the mutual exclusivity for the

indirect or direct density specification as listed The CORMIX system contains upon its

above. Omit the values (i.e. leave blank spaces)

depending on the value of the IDENOP

parameter. This can be seen in the preceding

example data file. Up to 10 ambient levels can be

specified for density and velocity distribution. This

is sufficient to replicate complicated observed

ambient profiles. CORJET performs internal

consistency checks to test whether the specified

density distribution is statically stable. Regardless of the access mode (within or

The coordinate system in CORJET can,

in principle be taken as consistent with the

CORMIX1 and 2 conventions (Section 5.2.1), i.e.

the origin at the bottom of the receiving water (a) CORJET Output File: 

body. (In fact, this convention is exercised

whenever CORJET is run from within CORMIX.) (a.1) Use within CORMIX:

However, since CORJET does not recognize the

dynamic effect of the presence of the actual The output file gets stored as

bottom boundary it is often convenient to set the CORMIX\POST\CJ\fn.CJX where fn is the

origin at the center of the discharge port. In that CORMIX1 or 2 filename that has been specified

case the port height H0 must be entered as 0.0. during the data entry. This file can be viewed onx points horizontally in the downstream direction, screen or printed within CORMIX.

y laterally across in the horizontal plane, and z

vertically upward. In the rare case when the A typical CORJET output file generated in

ambient velocity distribution is skewed in the this access mode is shown in Table 6.2 below

vertical, the definition of the x direction is best corresponding to the input example presented

made by the direction of the ambient velocity at

the level of origin (then TAUA is 0.0 at that level!),

but any other convention is possible, too, and can

be implemented by the choice of the TAUA value

installation several CORJET case studies (see

also Appendix E) that are installed as

CORMIX\POST\CJ\case*.inp. It is recommended

to copy one or more of these files and use the

copy for constructing any future input data file. 

6.1.4 CORJET Output Features

outside of CORMIX) CORJET has two output

mechanisms, a numerical output file and a

graphical display by means of CMXGRAPH.

above. The header information starts with the

banner ‘JJJ’ and then echoes all the pertinent

data that had been supplied to CORMIX and had

been picked up for the CORJET simulation. The
71

underlying CORMIX1 or 2 flow class is listed. If

one of the unstable or bottom-attaching flow

classes is encountered in this access mode, then

CORJET will not provide any predictions since

a pure jet integral model would not be applicable.

The tabular listing (see Table 6.2 ) gives

the plume values along the trajectory. CORJET

will cut off at a vertical level ZMAX that is equal to

the water depth at discharge or ZMIN = 0.0 (for

negatively buoyant cases) equal to the water body

bottom. In neither case does it compute the

actual boundary approach or impingement

processes (as does the more complete CORMIX

model in which some CORJET elements are, in

fact, integrated, starting with Version 3.0). The

interpretation of data values in this tabular listing

is consistent with that for CORMIX1 or 2 (see

Section 5.2.2).

Table 6.2

Example of CORJET output file when accessed within CORMIX

 CORJET PREDICTION FILE:

 JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ

 CORJET: CORNELL BUOYANT JET INTEGRAL MODEL Version 4.0, March 1995

 ----------------------------------------------------------------------------

 FILE NAME: cormix\post\cj\SAMPLE1.CJX 

 Label/identifier: A-PLANT^SUMMER^STRATIFICATION 

 Time of CORJET run: 4/12/96--18:40:19

 NEAR-FIELD DATA values for earlier CORMIX1 prediction (metric):

 Site name/label: DEEP^RESERVOIR 

 Design case: A-PLANT^SUMMER^STRATIFICATION 

 FILE NAME: cormix\sim\SAMPLE1 .CX1

 Time of CORMIX run: 06/24/95--22:29:54 

 HD = 30.50 UA = .01 CUNITS= PPM 

 STRCND= C density stratified environment 

 RHOAS = 996.21 RHOAB = 999.61 HINT = 15.50 DRHOJ = 2.181

 FLOCLS= S3 

 Corresponding CORJET ambient conditions:

 LEV ZA RHOA UA TAUA

 1 .00 999.61 .01 .00

 2 14.75 998.39 .01 .00

 3 16.25 996.21 .01 .00

 4 30.50 996.21 .01 .00

 Pycnocline thickness has been set to 1/10 of upper layer thickness.

 Discharge conditions (metric): SINGLE PORT

 D0 H0 U0 THETA0 SIGMA0 C0 KD RHO0

 .254 .60 3.02 10.00 90.00 .35E+04 .00E+00 998.21

 Program control:

 ZMAX ZMIN DISMAX NPRINT

 30.50 .00 1525.00 10

 Flux variables (based on ambient at discharge level):

 Q0 = .153E+00 M0 = .462E+00 J0 = .203E-02 GP0 = .133E-01

 Length scales (m) and parameters: 

 LQ = .23 LM = 12.44 Lm = 45.31 Lb = 601.53

 Lmp = 4.88 Lbp = 3.06

 FR0 = 52.01 R = 201.31

 ----------------------------------------------------------------------------

 CORJET PREDICTION: Stepsize = .2251 Printout every 10 steps

 Single jet/plume:

 X Y Z Sc Cc B | DIST Save Gpc Flc

 .00 .00 .60 1.0 .350E+04 .13| .00 1.0 .13E-01 52.01

 .01 1.23 .82 1.0 .350E+04 .13| 1.25 1.4 .16E-01 95.03

 .04 3.45 1.22 2.5 .142E+04 .37| 3.50 4.2 .50E-02 33.42

 .11 5.65 1.65 4.1 .852E+03 .62| 5.75 7.0 .25E-02 21.98

 .22 7.85 2.13 5.8 .607E+03 .87| 8.00 9.8 .12E-02 19.01

 .35 10.04 2.65 7.4 .471E+03 1.12| 10.25 12.6 .32E-03 25.46

 .44 11.13 2.92 8.3 .423E+03 1.25| 11.38 14.0 -.59E-04 50.81

 Level of buoyancy reversal in stratified ambient.

 .53 12.22 3.19 9.1 .384E+03 1.37| 12.50 15.4 -.40E-03 16.80

 .74 14.40 3.68 10.8 .325E+03 1.63| 14.76 18.2 -.97E-03 8.35

 .99 16.61 4.06 12.4 .282E+03 1.88| 17.01 21.0 -.13E-02 5.70

 1.28 18.83 4.20 14.1 .248E+03 2.14| 19.26 23.8 -.13E-02 4.61

 1.31 19.05 4.20 14.3 .245E+03 2.17| 19.48 24.1 -.13E-02 4.56

 Maximum jet height has been reached.

 1.62 21.05 4.05 15.9 .220E+03 2.40| 21.51 26.8 -.99E-03 4.54

 1.99 23.23 3.63 17.8 .196E+03 2.66| 23.76 30.0 -.34E-03 6.68

 2.19 24.31 3.37 18.8 .187E+03 2.80| 24.89 31.6 .27E-04 22.15

 Terminal level in stratified ambient has been reached. PROGRAM STOPS!

 ----------------------------------------------------------------------------

 END OF CORJET PREDICTION: Total number of integration steps = 106

 JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ
72

The main usefulness of CORJET when 6.1.2(2) ). This file can be viewed on-screen or

run in this mode lies in the short and separate printed using any text processor.

display of the near-field buoyant jet only. In some

cases, the pertinent regulatory constraints may be The CORJET output file corresponding to

limited to that region. the input data file of Table 6.1 is listed in Table

(a.2) Use outside of CORMIX: data and then lists the calculated length scale and

The output file gets stored as non-dimensional numbers controlling the mixing

filename.OUT in the same directory for which the process.

user had specified the input file (see Section

6.3. The lead-in data provide an echo of the input

Table 6.3

Example of CORJET output file

 CORJET PREDICTION FILE:

 JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ

 CORJET: CORNELL BUOYANT JET INTEGRAL MODEL Version 4.0, March 1995

 ----------------------------------------------------------------------------

 FILE NAME: post\cj\case2.OUT 

 Label/identifier: Case2: SINGLE PORT, STRATIFIED, VARIABLE CURRENT 

 Time of CORJET run: 4/10/96--19:28: 6

 Ambient conditions: No. of levels: 3 Fluid: Water Density option: 1

 LEV ZA TA SA RHOA UA TAUA

 1 .00 12.00 30.00 1022.71 .50 .00

 2 5.00 15.00 29.50 1021.74 .80 .00

 3 15.00 20.00 28.00 1019.43 1.20 .00

 Discharge conditions (metric): SINGLE PORT

 D0 H0 U0 THETA0 SIGMA0 C0 KD T0 S0 RHO0

 .500 .00 3.00 45.00 45.00 .10E+03 .00E+0 30.0 .0 995.65

 Program control:

 ZMAX ZMIN DISMAX NPRINT

 30.00 .00 200.00 10

 Flux variables (based on ambient at discharge level):

 Q0 = .589E+00 M0 = .177E+01 J0 = .153E+00 GP0 = .259E+00

 QT0 = .106E+02 QS0 = -.177E+02

 Length scales (m) and parameters: 

 LQ = .44 LM = 3.92 Lm = 2.66 Lb = 1.22

 Lmp = 5.61 Lbp = 6.71

 FR0 = 8.33 R = 6.00

 Zone of flow establishment (m): 

 LE = 1.30 XE = .75 YE = .62 ZE = .86

 THETAE= 38.34 SIGMAE= 34.00 GAMMAE= 49.43

----------------------------------------------------------------------------

 CORJET PREDICTION: Stepsize = .2659 Printout every 10 steps

 Single jet/plume:

 X Y Z Sc Cc B | DIST Save Gpc dTc dSALc

 .00 .00 .00 1.0 .100E+03 .25| .00 1.0 .26E+00 18.0-30.0

 .75 .62 .86 1.0 .100E+03 .25| 1.30 1.4 .27E+00 20.8-34.7

 2.81 1.50 2.27 3.0 .334E+02 .64| 3.96 4.6 .83E-01 5.2 -9.9

 5.22 1.96 3.28 5.7 .176E+02 .94| 6.62 8.3 .42E-01 2.1 -5.1

 7.74 2.22 4.07 8.4 .118E+02 1.16| 9.27 12.1 .26E-01 .8 -3.3

 10.31 2.40 4.74 11.2 .890E+01 1.34| 11.93 15.8 .18E-01 .1 -2.4

 12.90 2.52 5.32 14.0 .716E+01 1.49| 14.59 19.5 .13E-01 -.3 -1.9

 15.51 2.61 5.84 16.6 .601E+01 1.62| 17.25 23.2 .96E-02 -.6 -1.5

 18.12 2.68 6.31 19.2 .520E+01 1.74| 19.91 26.7 .70E-02 -.8 -1.2

 20.75 2.73 6.74 21.7 .460E+01 1.84| 22.57 30.0 .50E-02 -1.0 -1.0

 23.38 2.78 7.13 24.1 .414E+01 1.93| 25.23 33.3 .34E-02 -1.1 -.8

 26.01 2.82 7.48 26.4 .379E+01 2.01| 27.89 36.3 .21E-02 -1.3 -.6

 28.65 2.85 7.80 28.5 .351E+01 2.08| 30.54 39.1 .10E-02 -1.4 -.5

 31.29 2.88 8.09 30.4 .329E+01 2.14| 33.20 41.6 .15E-03 -1.5 -.4

 31.82 2.89 8.14 30.8 .325E+01 2.15| 33.73 42.1 -.13E-04 -1.5 -.4

 Terminal level in stratified ambient has been reached. PROGRAM STOPS!

 ----------------------------------------------------------------------------

 END OF CORJET PREDICTION: Total number of integration steps = 123

 JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ
73

The actual tabular listing of the numerical accomplished.

output is divided in two halves by a vertical line.

The left half lists data exactly in the same fashion

as a CORMIX1 or 2 prediction file (see Section

5.2.2). The right half gives additional detailed

information on the following variables:

 DIST: distance (m) along the jet

trajectory

 Save: average (bulk) dilution, defined on

the basis of total volume flux

within the jet relative to the initial

volume flux (discharge)

 Gpc: centerline buoyant acceleration

(m/s )2

 dTc: centerline temperature difference

relative to local ambient

temperature ( C) (if IDENOP = 1) o

 dSALc: centerline salinity difference

relative to local ambient salinity

(ppt) (if IDENOP = 1)

 Flc: local densimetric Froude number

(if IDENOP = 2)

In this mode CORJET becomes an

important engineering tool for design sensitivity

analysis --and also for research purposes-- to

evaluate the behavior of the near-field processes

to some of the ambient/discharge details, some of

which had to be simplified (schematized) within

the CORMIX approach. The user can learn to

understand through repeated use of CORJET that

plume mixing can indeed often be represented by

simple linear, or even uniform, approximations to

the ambient density structure.

Again, it is emphasized that CORJET

when used alone is not a safe prediction

methodology because of the limiting assumption

of infinite receiving water. For that reason an alert

is printed at the end of each CORJET output file:

Note: CORJET has been used outside the

CORMIX system, assuming unlimited

receiving water.

Carefully examine all results for

possible boundary effects due to

surface, bottom, or lateral

boundaries.

Previous application of CORMIX assures a

careful examination of the interaction of the

discharge with boundaries has been

(b) Graphics display and plotting of CORJET

results:

The graphical display and plotting of the

CORJET prediction results by means of

CMXGRAPH is similar to that of CORMIX results

as described in Section 5.3. 

The graphics package can be invoked in

either access mode (within or outside of

CORMIX) immediately after the computation or

independently on any existing CORJET output file

that has been computed earlier. Thus,

CMXGRAPH has been configured to deal with

both CORMIX prediction files and CORJET

output files.

6.2 FFLOCATR: The Far-Field Plume Locator

6.2.1 General Features

Although the main emphasis of CORMIX

is on the near-field mixing behavior of discharges

it can also be used for providing plume

predictions at larger distances in the far-field

provided the flow is not highly irregular with

pronounced recirculating zones and eddies in the

ambient flow. 

The CORMIX predicted far-field always

applies to a rectangular schematized crosssection with a straight uniform channel (see

Sections 4.3.1 and 4.3.2). The FFLOCATR is a

simple method for interpreting the schematized

CORMIX far-field plumes within the actual flow

patterns in natural rivers and estuaries. This

procedure, based on the cumulative discharge

method, is illustrated in Figure 6.2.

The cumulative discharge method, first

proposed by Yotsukura and Sayre (28; see also

19,20), is a convenient approach of dealing with

lateral mixing in natural irregular (but not highly

irregular with recirculating zones!) channels. In

such channel geometry the passive far-field

plume that is vertically mixed, or approaches

vertical mixing, will be positioned around the

“streamline”, or more precisely the “cumulative

discharge line”, that passes through the plume
____________________________________________________________________________________

74

Figure 6.2: Illustration of the cumulative discharge method for translating the CORMIX predicted far field

plume to the actual flow characteristics in winding irregular rivers or estuaries
q(y

) 
 P

y

0

ua(y) H(y) dy

ua

75

center when it enters the far-field. Lateral Further technical details on the

spreading around this line occurs by lateral FFLOCATR model can be found in the report on

turbulent diffusion and can be enhanced CORMIX enhancements (8).

buoyancy induced processes.

Looking downstream at a particular cross- 6.2.2 Access to FFLOCATR

section (see Figure 6.2a) the cumulative

discharge q(y) is defined as FFLOCATR can also be accessed in

in which y1 is the lateral coordinate pointing from by entering the Post-Processor option in

the right bank to the left across the flow (y1 differs the Iteration Menu.

from y as defined in CORMIX whose origin is at

the discharge location), H is the local depth, and (1b) It can be accessed on earlier

is the depth-averaged local velocity. When the existing files by directly choosing the Postabove equation is integrated across the full Processor option in the Main Menu.

channel width B then the total discharge will s

result Q = q(B ) a s . Hence, if the local values q(y1) In either case, once the

are divided by Q the results can be presented in FFLOCATR option is chosen the user a

normalized form as the cumulative discharge lines must first specify whether a CORMIX1, 2

ranging from 0% at the right bank to 100% at the or 3 simulation should be interpreted for

left bank. The full distribution of such cumulative the far-field with FFLOCATR. Then the

discharge lines in a river or estuary gives an CORMIX filename in the CORMIX\SIM

appearance of the overall flow pattern that is directory must be specified. Finally, the

important for pollutant transport. Closely spaced user must specify the name of the

discharge lines are mostly indicative of areas of cumulative discharge input data file, or if

large depth and higher velocities as they occur in that does not yet exist, the user can first

the outside portion of river bends or meanders (as create such file by entering data on the

sketched in Figure 6.2a). cumulative discharge distribution at

In the CORMIX schematization of ambient

flow characteristics and channel cross-section it (2) Use outside CORMIX:

is, in fact, useful to keep in mind the cumulative

transport aspects of the ambient flow as remarked FFLOCATR can be invoked directly by

in Section 4.3.1 and 4.3.2. Thus, the uniform typing the command line with three

CORMIX flow field with the constant depth arguments:

laterally is indeed conforming to a cumulative

discharge distribution with equally spaced fflocatr CORMIXn fn POST\FF\cumdata.FFI

discharge lines, as indicated in Figure 6.2b. It is

then conceptually straightforward to translate the (alternatively, ffl can be typed instead of

CORMIX plume prediction back to the actual flow fflocatr) where CORMIXn, n = 1, 2 or 3,

distribution by calculating and plotting the plume specifies which earlier CORMIX

boundaries within the given cumulative discharge simulation should be analyzed for the farlines as shown in Figure 6.3c. The actual plume field, fn (without path and extension) is

pattern may then show some surprising features the name of the CORMIX prediction file in

such as strong “shifting back and forth” between the CORMIX\SIM directory, and cumdata

opposing banks and an apparent “thinning’ of the (with directory designation POST\FF and

plume width. These realistic plume features are fixed extension FFI) is the cumulative

simply dictated by the non-uniform flow field. discharge input data file (see following

different ways:

(1) Use within CORMIX:

(1a) It can be accessed at an end of the

prediction after the file has been stored,

several cross-sections.
76

section) existing in directory In general, it is more convenient to

CORMIX\POST\FF. construct the cumdata.FFI file outside of CORMIX

and store it in the CORMIX\POST\FF directory.

Alternatively if one types: This option is described first.

fflocatr (or simply: ffl)

without the three arguments, the model will

prompt the user for the file information.

6.2.3 FFLOCATR Cumulative Discharge Input

Data File

(a) Input Data File Prepared Outside of

CORMIX:

FFLOCATR is a Fortran program and

reads the cumdata.FFI file in open format. An

example is shown in Table 6.4 (corresponding to

the test case discussed in Appendix B).

Table 6.4

Example of a cumulative discharge input data file for FFLOCATR

SHALLOW RIVER CUMULATIVE DISCHARGE (applies to Sample2)

Number of Cross-sections (XS):

3

XS 'Label-' Dist. 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

<> <------> <----> <---> <---> <---> <---> <---> <---> <---> <---> <---> <--->

1 'STA1' 30.5 6.1 12.2 15.9 20.7 27.5 33.6 58.0 76.3 82.4 88.5

2 'STA2' 152.5 9.2 16.8 21.4 24.4 27.5 33.6 36.6 39.7 54.9 79.3 

3 'STA3' 305. 18.3 33.6 39.3 45.8 48.8 51.9 54.0 56.4 61.0 67.1

The required input data values (SI units) are:

 Line 1: Any descriptive label.

 Line 2: <dummy line; not read>

 Line 3: NUMXS = Number of cross-sections (1 to 10) for which discharge data values will be

entered

 Line 4: <dummy line useful for formatting subsequent data; not read>

 Line 5: <dummy line useful for formatting subsequent data; not read>

 Lines 6ff: NUMXS lines must be entered, each containing the following data:

XS = number of cross-section, numbered sequentially beginning with 1

STALAB = arbitrary label for cross-section, bracketed by apostrophes ‘ with

maximum total length of 10 characters (e.g. ‘RM595' standing for river

mile 595)

YCD = 10 values, representing the position of the cumulative discharge line (m)

measured from the right bank, beginning with the 10% line, incrementing

by 10%, and ending with the 100% line. The 100% line is also equal to

the channel width at that cross-section.

Consistency checks are performed on

each data file to make sure that the entered

values YCD are monotonically increasing.

Essentially two methods can be used for

obtaining the values for the cumulative discharge

positions YCD in specific cases:

1) On the basis of detailed stream-gaging

surveys, for example using the standard methods

employed by the U.S. Geological Survey. This is

the preferable approach for small to medium

streams or rivers.
77

2) Using the results of detailed numerical

models for the flow distribution in open channel

flow. This is preferable for larger rivers or

estuaries. 

The primary application for FFLOCATR is

for bounded channels such as streams, rivers or

estuaries. The model will not execute when it

encounters a CORMIX file for a design case

involving an unbounded ambient flow.

Nevertheless, it may sometimes be useful

to provide a detailed far-field plume delineation

also for unbounded flow situations, such as

coastal areas or lakes. This can be done when

detailed hydrographic data or numerical model

predictions describing the flow distribution in the

near-shore where the plume may be located are

available. A CORMIX simulation can then be rerun specifying a “bounded channel” with a width

equal to some arbitrary bounding offshore

streamline. The YCD data can then be specified

relative to the value of that chosen streamline.

FFLOCATR will thus predict the far-field plume

location in the irregular coastal zone (assuming

recirculating eddies do not exist in the flow).

(b) Input Data File Prepared Within CORMIX:

The user can generate the data file with

exactly the same data structure as discussed

above also within CORMIX. The system will

prompt the user for the individual data items (up

to 10 cross-sections can be entered) and then for

a cumdata filename. The file will then be stored

automatically in directory CORMIX\POST\FF with

extension FFI.

6.2.4 FFLOCATR Output Features

FFLOCATR generates an output file

CORMIX\POST\FF\fn.FFX indicating that the farfield plume prediction for the CORMIX design

case fn has been interpreted under the actual farfield flow distribution. This file can be inspected

on-screen when in CORMIX or externally with any

text processor, and can be printed out. No

graphics plotting option exists for this file.

As an example, Table 6.5 on the next

page shows the output file that combines the

cumulative discharge input data of Table 6.4 with

the CORMIX2 plume predictions that are part of

Appendix B. The output file preceded by the

banner ‘FFF’ consists of three parts. The first part

lists some of the underlying CORMIX data

including file information. The second part

echoes the complete cumulative discharge input

data file.

The actual results of the FFLOCATR

translation routine are given in the third part. For

each of the specified cross-sections (stations) the

output file lists the station label, the downstream

distance, and the position of plume center, left

edge and right edge, respectively, each measured

from the right bank, and the local centerline

dilution and concentration. Data of this kind can

then readily be used to prepare plots of far-field

plumes superimposed on maps of the actual flow

field. This last step has been illustrated in Figure

6.2c. 

It should be understood that the plume

centerline in the far-field does not necessarily

coincide with the cumulative discharge line that

passes through the offshore discharge location

(as has been illustrated in Figure 6.2 where a coflowing discharge had been assumed). The

plume centerline can shift because of near-field

processes, as in case of a cross-flowing

discharge, or if bank interaction occurs in the farfield, causing the centerline to shift to one

bank/shore.
78

Table 6.5

Example of FFLOCATR output file

 FFLOCATR RESULTS FILE:

 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

 FFLOCATR: FAR-FIELD PLUME LOCATOR Version 1.0, March 1994

 ----------------------------------------------------------------------------

 Output FILE NAME: POST\FF\SAMPLE2.FFX 

 Time of FFLOCATR run: 1995/ 6/ 2-- 8:54:38

 ----------------------------------------------------------------------------

 FAR-FIELD DATA values from earlier CORMIX2 prediction:

 FILE NAME: SIM\SAMPLE2.cx2 

 Site name/label: B-PLANT^SHALLOW-RIVER 

 Design case: LOW-FLOW^7Q10 

 Time of CORMIX2 run: 09/20/94--15:24:11 

 

 Channel characteristics (metric):

 BS = 50.00 HA = .30 UA = .54

 BANK = right DISTB = 20.00

 STRCND= U uniform density environment

 

 Pollutant data:

 C0 = 100.00 CUNITS= PERCENT 

 

 ----------------------------------------------------------------------------

 CUMULATIVE DISCHARGE DATA (m):

 FILE NAME: POST\FF\SH-RIVER.ffi 

 Data label: SHALLOW RIVER CUMULATIVE DISCHARGE 

 Number of XS: 3

 XS'Label-' Dist. 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

 1 'STA1 ' 30.5 6.10 12.20 15.90 20.70 27.50 33.60 58.00 76.30 82.40 88.00

 2 'STA2 ' 152.5 9.20 16.80 21.40 24.40 27.50 33.60 36.60 39.70 54.90 79.00

 3 'STA3 ' 305.0 18.30 33.60 39.30 45.80 48.80 51.90 54.00 56.40 61.00 67.00

 

 ----------------------------------------------------------------------------

 FAR-FIELD PLUME PROPERTIES (m):

 XS 'Label-' Distance Left Plume Right Dilution Conc.

 # downstream edge centerline edge

 1 'STA1 ' 30.50 27.50 20.70 13.28 30.1 .332E+01

 2 'STA2 ' 152.50 27.50 24.40 17.80 31.4 .318E+01

 3 'STA3 ' 305.00 48.80 45.80 34.32 33.0 .303E+01

 ----------------------------------------------------------------------------

 END OF FFLOCATR: FAR-FIELD PLUME LOCATOR

 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
79

VII Closure

7.1 Synopsis

The Cornell Mixing Zone Expert System

(CORMIX) is a series of software subsystems for The CORMIX system programs can be

the analysis, prediction, and design of aqueous obtained from:

toxic or conventional pollutant discharges into

diverse water bodies. The major emphasis is on U.S. EPA - Center for Environmental

the geometry and dilution characteristics of the Assessment Modeling (CEAM)

initial mixing zone including compliance with Environmental Research Laboratory

regulatory constraints. The system also predicts 960 College Station Road

the behavior of the discharge plume at larger Athens, GA 30605-2700 USA

distances in the far-field. Tel. 706-546-3549 (or FTS 250-3590)

The highly user-interactive CORMIX E-mail: ceam@athens.ath.epa.gov

system is implemented on IBM-PC compatible

microcomputers and consists of three As of the release of this manual (late 1996) the

subsystems. These are: CORMIX1 for following versions of CORMIX are available:

submerged single port discharges, CORMIX2 for CORMIX Version2.1 (1993, without graphics and

submerged multiport diffuser discharges and post-processor features) and Version3.1 (August

CORMIX3 for buoyant surface discharges. The 1996, as described in this report). The models

basic CORMIX methodology relies on the can be obtained by mail or over the electronic

assumption of steady ambient conditions. bulletin board operated by CEAM. Information on

However, recent versions also contain special program installation and computer configuration

routines for the application to highly unsteady are also provided by CEAM. The ftp address is:

environments, such as tidal reversal conditions, in

which transient recirculation and pollutant build-up

effects can occur.

In addition, two post-processing models

are linked to the CORMIX system, but can also be

used independently. These are CORJET (the

Cornell Buoyant Jet Integral Model) for the

detailed analysis of the near-field behavior of

buoyant jets, and FFLOCATR (the Far-Field

Plume Locator) for the far-field delineation of

discharge plumes in non-uniform river or estuary

environments.

This user's manual gives a comprehensive

and uniform description of all three CORMIX

subsystems; it provides advice for assembly and

preparation of required input data; it delineates

ranges of applicability of the three subsystems; it

provides instruction for the interpretation and

graphical display of system output; and it

illustrates practical system application through

several case studies.

7.2 System and Documentation Availability

 Fax:706-546-3402

 ftp://ftp.epa.gov/epa_ceam/wwwhtml/ceamhome.htm

The distribution versions of CORMIX

contain only the executable code of the

FORTRAN programs HYDROn; they do not

include the source code. The source code can be

requested separately by writing to CEAM at U.S.

EPA-ERL and giving the reason for code

inspection and possible manipulation. The full

code, while made up of simple individual

modules, is complex with multiple

interdependencies; only experienced research

personnel should attempt this work when

engaged in comparison of model predictions to

new field or laboratory data.

The technical documentation

reports(5,6,7,8) are available as U.S. EPA and

NITS publications, and have also been issued as

technical reports of the DeFrees Hydraulics

Laboratory. 
80

7.3 User Support

Technical and scientific support for

CORMIX under contract from the USEPA is

provided by:

 Dr. Robert L. Doneker

 Department of Environmental Science and 

 Engineering

 Oregon Graduate Institute

 PO Box 91000

 Portland, OR 97291-1000

 Tel. 503-690-4053, Fax. 503-690-1273

 email: doneker@ese.ogi.edu

This includes assistance on problems of system

installation and execution, and advice on the

specification of input data as well as interpretation

of CORMIX output.

Any high-quality field or laboratory data on

effluent mixing processes is a valuable asset for

any future development or updates on CORMIX.

Transmittal of such data to the following address

will be greatly appreciated:

 Prof. Gerhard H. Jirka

 Institute for Hydromechanics

 University of Karlsruhe

 PO Box 6380

 D-76128 Karlsruhe, GERMANY 

 Tel. (49) 721/608-2200, Fax. (49) 721/66-16-86
81

Literature References

(1) "Technical Support Document for Water (8) Jirka, G.H., P.J. Akar and J.D. Nash,

Quality-based Toxics Control," U.S. EPA, “Enhancements to the CORMIX Mixing

Office of Water, Washington, DC, Zone Expert System: Technical

September, 1991. Background”, Tech. Rep., DeFrees

(2) "Assessment and Control of Environmental Engineering, Cornell

Bioconcentratable Contaminants in University, 1996, (also to be published by

Surface Waters," U.S. EPA, Office of U.S. Environmental Protection Agency,

Water, Washington, DC, March, 1991. Tech. Rep., Environmental Research Lab,

(3) Jirka, G. H., "Use of Mixing Zone Models 

in Estuarine Waste Load Allocation," Part (9) Doneker, R.L. and G.H. Jirka, "Expert

III of Technical Guidance Manual for Systems for Design and Mixing Zone

Performing Waste Load Allocations, Book Analysis of Aqueous Pollutant

III: Estuaries, Ed. by R. A. Ambrose and J. Discharges", J. Water Resources

L. Martin, U.S. EPA, Washington, D.C., Planning and Management, ASCE, Vol.

EPA-823-R-92-004, 1992. 117, No.6, 679-697, 1991.

(4) Muellenhoff, W. P., et al.,"Initial Mixing (10) Jirka G. H. and R. L. Doneker,

Characteristics of Municipal Ocean "Hydrodynamic Classification of

Discharges (Vol I & II)," USEPA, Submerged Single Port Discharges", J.

Environmental Research Laboratory, Hydraulic Engineering, ASCE, Vol.117,

Narragansett, RI, 1985. 1095-1112, 1991.

(5) Doneker, R. L., and G. H. Jirka, (11) Jirka G. H. and P. J. Akar, "Hydrodynamic

"CORMIX1: An Expert System for Mixing Classification of Submerged Multiport

Zone Analysis of Conventional and Toxic Diffuser Discharges," J. Hydraulic

Single Port Aquatic Discharges", U.S. Engineering, ASCE, (117), 1113-1128,

EPA, Environmental Research HY9, 1991.

Laboratory, Athens, GA, EPA-600/600/3-

90/012, 1990. (12) Akar, P.J. and G.H. Jirka, "Buoyant

(6) Akar, P. J. and G. H. Jirka, "CORMIX2: An Transport and Mixing. Part I: Lateral

Expert System for Hydrodynamic Mixing Spreading in Strong Ambient Current", J.

Zone Analysis of Conventional and Toxic Hydraulic Research, Vol. 32, 815-831,

Submerged Multiport Discharges," U.S. 1994.

EPA, Environmental Research Laboratory

Athens, GA, EPA/600/3-91/073, 1991. (13) Akar, P.J.and G.H. Jirka, "Buoyant

(7) Jones, G.R., J.D. Nash and G.H. Jirka, Transport and Mixing. Part II: Upstream

"CORMIX3: An Expert System for Mixing Spreading in Weak Ambient Current", J.

Zone Analysis and Prediction of Buoyant Hydraulic Research, Vol. 33, 87-100,

Surface Discharges", Tech. Rep., 1995.

DeFrees Hydraulics Laboratory, School of

Civil and Environmental Engineering, (14) Mendéz Díaz, M.M. and G.H. Jirka,

Cornell University, 1996, (also to be "Trajectory of Multiport Diffuser

published by U.S. Environmental Discharges in Deep Co-Flow", J.

Protection Agency, Environmental Hydraulic Engineering, ASCE, Vol.122,

Research Lab, Athens, GA). HY6, 1996 (in press).

Hydraulics Laboratory, School of Civil and

Athens, GA).

Spreading Processes in Pollutant

Spreading Processes in Pollutant
82

(15) Jones, G.R., J.D. Nash and G.H. Jirka, (22) "Technical Guidance Manual for the

"Buoyant Surface Discharges into Water Regulations Promulgated Pursuant to

Bodies, Part 1: Classification," J. Section 301 (g) of the Clean Water Act of

Hydraulic Engineering, ASCE, (submitted 1977 (Draft)," U.S. EPA, Washington, DC,

1996). August, 1984.

(16) Jones, G.R. and G.H. Jirka, "Buoyant (23) "Revised Section 301 (h) Technical

Surface Discharges into Water Bodies, Support Document," EPA 430/9-82-011,

Part 2: Prediction," J. Hydraulic U.S. EPA, Washington, DC, 1982.

Engineering, ASCE, (submitted 1996).

(17) J.D. Nash and G.H. Jirka, "Buoyant McGraw-Hill, New York, 1959.

Surface Discharges into Unsteady

Ambient Flows", Dynamics of (25) Jirka, G.H. and Fong, H.L.M., "Vortex

Atmospheres and Oceans, 24, 75-84, Dynamics and Bifurcation of Buoyant Jets

1996. in Crossflow", J. Engineering Mechanics

(18) Jirka G. H., "Multiport Diffusers for Heat 1981.

Disposal: A Summary," J. Hydraulics

Division, ASCE, (108), HY12, pp. 1423- (26) Jirka, G.H., "Single and Multiple Buoyant

68, 1982. Jets in Crossflow", J. Hydraulic Research,

(19) Holley, E. R. and G. H. Jirka, "Mixing in

Rivers," Technical Report E-86-11, U.S. (27) Baumgartner, D.J., W.E. Frick and P.J.W.

Army Corps of Engineers, Washington, Robert, “Dilution Models for Effluent

DC, 1986. Discharges (Third Edition)”, U.S. EPA,

(20) Fischer, H. B. et al., Mixing in Inland and OR, EPA/600/R-94/086, 1994.

Coastal Waters, Academic Press, New

York, 1979. (28) Yotsukura, N. and W.W. Sayre,

(21) "Water Quality Standards Handbook," Water Resources Research, Vol.12, 695-

U.S. EPA, Office of Water Regulations 704, 1976.

and Standards, Washington, DC, 1984.

(24) Chow, V. T., Open Channel Hydraulics,

Division, ASCE, Vol.107, pp. 479-499,

(submitted 1996).

Pacific Ocean Systems Branch, Newport,

“Transverse mixing in natural channels”,
83

Appendix A

Flow Classification Diagrams for the Three CORMIX Subsystems

CORMIX1: Submerged Single Port Discharges ........................................................84

CORMIX2: Submerged Multiport Diffuser Discharges ...............................................88

CORMIX3: Buoyant Surface Discharges ...................................................................91








92
93

Appendix B

CORMIX1: Submerged Single Port Discharge in a Deep Reservoir

This case study illustrates the application The stratification can be expected to be

of CORMIX1 to the prediction of the effluent from horizontally uniform and therefore similar

a small manufacturing plant into a large and deep conditions will hold at the discharge site. Also,

stratified reservoir. the river inflow is colder than the surface layer of

B.1 Problem Statement

A manufacturing plant (A-Plant) is

discharging its effluent into an adjacent deep

reservoir. The plant design flowrate is 3.5 mgd (

0.15 m /s). The effluent contains heavy metal at 3

a concentration of 3500 ppb, and is released at a

temperature of 68 F (= 20 C). The density of the o o

effluent at this low concentration can be

considered equivalent to freshwater.

The existing reservoir has been formed by

flooding a river valley. The reservoir length is

about 60 miles. The water level in the reservoir is

fluctuating depending on the release operation at

the downstream dam with its hydropower

installation. During summer conditions, the

reservoir level is typically at an elevation of 710 ft

above sea level. This results in a reservoir width

of about 4000 ft ( 1200 m) and a maximum

depth of 310 ft ( 95 m) at the discharge location.

The mean river flow into the reservoir during the

summer low-flow conditions is about 18,540 cfs (

525 m /s). The typical temperature of the 3

inflowing river water is 55 F ( 13 C). o o

Figure B.1 shows the local bathymetry (as

obtained from a USGS map) in the vicinity of the

proposed discharge. Since the discharge is very

small relative to the reservoir size and the

ambient flowrate, it is expected that mostly local

conditions will be important, and not overall

reservoir dimensions. (Note: Any such

conjecture has to be verified against the final B.2 Problem Schematization and Data

simulation results, and adjustments have to be

made if needed.)

Temperature data as a function of depth

obtained from field measurements in the center of

the reservoir show a significant temperature

stratification (see Figure B.2), as is typical for

such deep reservoirs during summer conditions.

the stratified reservoir. The reservoir has a

selective withdrawal structure at the dam,

therefore it can be expected that the river water

will flow predominantly in a vertically limited layer,

that may extend from a depth of about 35 m to the

surface. The velocity of that flow is estimated at

about 1.5 cm/s ( 0.015 m/s), given the 35 m thick

layer and an about 1000 m width at that elevation.

(Note: More detailed hydrodynamic

investigations, using available models for

stratified reservoir dynamics, can be used to

obtain more precise estimates of the velocity field.

Generally, however, it cannot be assumed that

the velocity in stratified reservoirs is given by the

simple average of the flowrate divided by the

cross-sectional area.)

The proposed discharge location on the

side slope of the cross-section is also shown in

Figure B.1: a submerged single port discharge at

an elevation of 610 ft above sea level, i.e. at a

local depth of 100 ft ( 30.5 m) below the surface,

is proposed in the initial design phase. The port

diameter is 10 in ( 0.254 m) and is located 2 ft (

0.6 m) above the local bottom. The discharge is

pointing offshore and is angled upward at 10 .o

The discharge is subject to State mixing

zone regulations whereby the mixing zone width

is less than 10% of the width of the water body.

Furthermore, the heavy metal in the effluent is

considered toxic with CMC and CCC limits of

1200 and 600 ppb, respectively.

Preparation

Figure B.3 is the data checklist that

summarizes the CORMIX1 input for the present

problem. The ambient water body has been

characterized as unbounded in line with the

expectation that the discharge plume will be small
94

Figure B.1: Local details of Deep Reservoir cross-section and CORMIX1 schematization

Figure B.2: Temperature field data as a function of depth and CORMIX1 representation of

Type C temperature profile

96

in size relative to the reservoir width. here). The detailed plume properties are

Furthermore, since (1) the discharge elevation is computed in program element HYDRO, and are

well above the lowest point of the reservoir and displayed in the Fortran CORMIX1 prediction file

(2) the plume is expected to rise toward the (see Table B.2, discussed in more detail further

surface, the ambient water depth is taken as 150 below). 

ft (35.0 m) only.

The depth at the discharge corresponds to prediction are summarized in program element

the local depth at the discharge location. SUM of the session record (see Table B.1).

Because of the sloping bank from the discharge Notably, all aspects pertaining to mixing zone

to the near shoreline, the distance to bank (46 m) regulations are contained in that summary. For

corresponds to one-half of the actual distance example, it can be seen quickly from that

from the outlet to the shoreline at the water summary that the present discharge configuration

surface. The ambient velocity corresponds to the meets all three toxic dilution zone (TDZ) criteria

estimate made above for the stratified water body. and also the regulatory mixing zone (RMZ)

A Manning's n of 0.02 describes the smooth limitation. Obviously, other ambient conditions

bottom. and discharge variations should be considered in

Density data is simply entered via the this should be deemed fully satisfactory.

temperature values of the fresh water body. A

Stratification Type C is chosen to describe the

actual temperature profile.

The discharge data values summarize the

discharge situation as described above. Finally,

the mixing zone specifications include a width

value of 120 m, corresponding to 10 % of the

actual width of 1200 m. Information is desired

over about one mile ( 1600 m) which represents

the region of interest (ROI) limitation.

B.3 CORMIX1 Session and Results

If desired by the user, CORMIX1 provides

a summary of the data as they are entered, and

then a full record of the simulation sequence and

final results. This session summary report is

shown in Table B.1. Of particular interest to the

user are the evaluations in program element

PARAM and CLASS. Note, that the computed

length scales L ' m b and L ' are quite small,

indicating that the jet or plume will be trapped

quickly by the ambient stratification; thus, this is

the first numerical indication that the near-field

jet/plume will indeed be small relative to the

reservoir. The ambient flow related scales L and m

L are quite large, indicating that the ambient b

velocity is very weak. The resulting flow class S3

is dominated by the ambient stratification; the

plume will be limited to the lower layer of the

stratification. The user should also consult the

description of flow class S3 that is available

during the CORMIX1 session (not reproduced

Many important features of the plume

additional simulations before a design such as

B.4 Graphical Displays of Detailed Plume

Predictions

As for most engineering studies it is

desirable to produce graphical displays for

visualization of the predicted results. The data

contained in the CORMIX1 prediction file (Table

B.2) form the basis for such plots. Unfortunately,

it is often difficult to display all plume features in

one single plot because the plume may contain a

lot of near-field details while extending over large

distances into the far-field. A short examination of

Table B.2 proves that point: The plume gets

quickly trapped within a very limited near-field but

with considerable mixing (see MOD110 =

CORJET of the CORMIX1 prediction). Yet after

that the plume extends over large distances into

the far-field forming a wide thin layer within the

stratified reservoir (see MOD142).

Using the graphics package CMXGRAPH,

two plots have been prepared to display the

jet/plume side view in the near-field, using

distorted and undistorted 1:1 scales, respectively,

(Figure B.4) and the plan view in the near-field

and larger scale far-field (Figure B.5) of the

effluent plume. Figure B.4 shows the initial

trajectory of the slightly upward curved jet that

rises to maximum level of 4.29 m and then gets

trapped at an elevation of 3.44 m above the local

bottom. In the trapping stage the jet undergoes a

complicated transition (MOD137) to the

horizontally spreading layer. CORMIX1 predicts


99

Table B.2

CORMIX1 Prediction File for A-Plant discharge into Deep Reservoir with summer

stratification

CORMIX1 PREDICTION FILE:

11111111111111111111111111111111111111111111111111111111111111111111111111111

 CORNELL MIXING ZONE EXPERT SYSTEM

Subsystem CORMIX1: Subsystem version:

 Submerged Single Port Discharges CORMIX_v.3.1__________June_1995

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

CASE DESCRIPTION

 Site name/label: DEEP^RESERVOIR 

 Design case: A-PLANT^SUMMER^STRATIFICATION 

 FILE NAME: cormix\sim\SAMPLE1 .cx1

 Time of Fortran run: 06/24/95--22:29:54 

ENVIRONMENT PARAMETERS (metric units)

 Unbounded section

 HA = 35.00 HD = 30.50

 UA = .015 F = .010 USTAR = .5200E-03

 UW = 2.000 UWSTAR= .2198E-02

 Density stratified environment

 STRCND= C RHOAM = 997.6240

 RHOAS = 996.2053 RHOAB = 999.6072 RHOAH0= 999.5599 E = .7730E-03

 DRHOJ = 2.1813 HINT = 15.50 ES = .2153E-02

DISCHARGE PARAMETERS (metric units)

 BANK = RIGHT DISTB = 46.00

 D0 = .254 A0 = .051 H0 = .60

 THETA = 10.00 SIGMA = 90.00

 U0 = 3.020 Q0 = .153 = .1530E+00

 RHO0 = 998.2051 DRHO0 = .1355E+01 GP0 = .1329E-01

 C0 = .3500E+04 CUNITS= PPB 

 IPOLL = 1 KS = .0000E+00 KD = .0000E+00

FLUX VARIABLES (metric units)

 Q0 = .1530E+00 M0 = .4620E+00 J0 = .2034E-02 SIGNJ0= 1.0

 Associated length scales (meters)

 LQ = .23 LM = 12.43 Lm = 45.31 Lb = 602.57

 Lmp = 4.94 Lbp = 3.12

NON-DIMENSIONAL PARAMETERS

 FR0 = 51.96 R = 201.30

FLOW CLASSIFICATION

 111111111111111111111111111111111111111111

 1 Flow class (CORMIX1) = S3 1 

 1 Applicable layer depth HS = 15.50 1

 111111111111111111111111111111111111111111

MIXING ZONE / TOXIC DILUTION / REGION OF INTEREST PARAMETERS

 C0 = .3500E+04 CUNITS= PPM 

 NTOX = 1 CMC = .1200E+04 CCC = CSTD

 NSTD = 1 CSTD = .6000E+03

 REGMZ = 1

 REGSPC= 2 XREG = .00 WREG = 120.00 AREG = .00

 XINT = 3500.00 XMAX = 3500.00

X-Y-Z COORDINATE SYSTEM:

 ORIGIN is located at the bottom and below the center of the port:

 46.00 m from the RIGHT bank/shore.

 X-axis points downstream, Y-axis points to left, Z-axis points upward.

NSTEP = 20 display intervals per module

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD101: DISCHARGE MODULE 

 X Y Z S C B

 .00 .00 .60 1.0 .350E+04 .13

END OF MOD101: DISCHARGE MODULE 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN CORJET (MOD110): JET/PLUME NEAR-FIELD MIXING REGION 
100

 Jet-like motion in linear stratification with weak crossflow.

 

 Zone of flow establishment: THETAE= 10.00 SIGMAE= 89.45

 LE = 1.25 XE = .01 YE = 1.23 ZE = .82

 

 Profile definitions:

 B = Gaussian 1/e (37%) half-width, normal to trajectory

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 X Y Z S C B

 .00 .00 .60 1.0 .350E+04 .13

 .01 1.23 .82 1.0 .350E+04 .14

 .02 2.30 1.01 1.7 .205E+04 .26

 .04 3.48 1.23 2.6 .136E+04 .39

** CMC HAS BEEN FOUND **

 The pollutant concentration in the plume falls below CMC value of .120E+04

 in the current prediction interval.

 This is the extent of the TOXIC DILUTION ZONE.

 .08 4.67 1.45 3.5 .101E+04 .53

 .13 5.97 1.72 4.4 .790E+03 .67

 .18 7.14 1.97 5.3 .658E+03 .80

** WATER QUALITY STANDARD OR CCC HAS BEEN FOUND **

 The pollutant concentration in the plume falls below water quality standard

 or CCC value of .600E+03 in the current prediction interval.

 This is the spatial extent of concentrations exceeding the water quality 

 standard or CCC value.

 .24 8.32 2.24 6.2 .564E+03 .94

 .32 9.49 2.52 7.1 .493E+03 1.07

 .40 10.65 2.81 8.0 .437E+03 1.21

 .49 11.82 3.10 8.9 .393E+03 1.34

 .60 12.99 3.39 9.8 .357E+03 1.48

 .71 14.15 3.66 10.7 .328E+03 1.61

 .84 15.33 3.90 11.6 .303E+03 1.75

 .98 16.51 4.09 12.4 .281E+03 1.89

 1.13 17.70 4.23 13.3 .262E+03 2.03

 1.27 18.77 4.29 14.2 .247E+03 2.15

 Maximum jet height has been reached.

 1.45 19.96 4.27 15.1 .232E+03 2.29

 1.63 21.15 4.16 16.1 .218E+03 2.43

 1.83 22.32 3.97 17.1 .205E+03 2.57

 2.04 23.48 3.72 18.1 .193E+03 2.71

 2.26 24.63 3.44 19.1 .183E+03 2.85

 Terminal level in stratified ambient has been reached.

 Cumulative travel time = 63. sec

END OF CORJET (MOD110): JET/PLUME NEAR-FIELD MIXING REGION 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD137: TERMINAL LAYER INJECTION/UPSTREAM SPREADING 

 UPSTREAM INTRUSION PROPERTIES:

 Maximum elevation of jet/plume rise = 7.64 m

 Layer thickness in impingement region = 1.29 m

 Upstream intrusion length = 90.24 m

 X-position of upstream stagnation point = -87.99 m

 Thickness in intrusion region = 1.29 m

 Half-width at downstream end = 191.87 m

 Thickness at downstream end = .95 m

 Control volume inflow:

 X Y Z S C B

 2.26 24.63 3.44 19.1 .183E+03 2.85

 Profile definitions:

 BV = top-hat thickness, measured vertically

 BH = top-hat half-width, measured horizontally in Y-direction

 ZU = upper plume boundary (Z-coordinate)

 ZL = lower plume boundary (Z-coordinate)

 S = hydrodynamic average (bulk) dilution

 C = average (bulk) concentration (includes reaction effects, if any)

 X Y Z S C BV BH ZU ZL

 -87.99 24.63 3.44 9999.9 .000E+00 .00 .00 3.44 3.44

 -84.26 24.63 3.44 75.2 .465E+02 .33 27.13 3.60 3.27

 -66.02 24.63 3.44 31.3 .112E+03 .79 65.91 3.83 3.04
101

 -47.77 24.63 3.44 23.8 .147E+03 1.04 89.17 3.96 2.92

 -29.53 24.63 3.44 20.8 .169E+03 1.19 107.51 4.03 2.84

 -11.28 24.63 3.44 19.4 .180E+03 1.28 123.15 4.07 2.80

 6.96 24.63 3.44 19.3 .181E+03 1.29 137.02 4.08 2.79

 25.21 24.63 3.44 22.5 .155E+03 1.22 149.61 4.05 2.82

 43.45 24.63 3.44 27.7 .126E+03 1.11 161.21 3.99 2.88

 61.70 24.63 3.44 32.1 .109E+03 1.02 172.04 3.95 2.93

 79.95 24.63 3.44 34.4 .102E+03 .97 182.22 3.92 2.95

 98.19 24.63 3.44 35.6 .982E+02 .95 191.87 3.91 2.96

 Cumulative travel time = 6459. sec

END OF MOD137: TERMINAL LAYER INJECTION/UPSTREAM SPREADING 

----------------------------------------------------------------------------- 

** End of NEAR-FIELD REGION (NFR) **

 In this design case, the discharge is located CLOSE TO BANK/SHORE.

 Some boundary interaction occurs at end of near-field.

 This may be related to a design case with a very LOW AMBIENT VELOCITY.

 The dilution values in one or more of the preceding zones may be too high. 

 Carefully evaluate results in near-field and check degree of interaction.

 Consider locating outfall further away from bank or shore.

 In the next prediction module, the plume centerline will be set

 to follow the bank/shore.

 ** REGULATORY MIXING ZONE BOUNDARY is within the Near-Field Region (NFR) **

----------------------------------------------------------------------------- 

BEGIN MOD142: BUOYANT TERMINAL LAYER SPREADING 

 Plume is ATTACHED to RIGHT bank/shore.

 Plume width is now determined from RIGHT bank/shore.

 Profile definitions:

 BV = top-hat thickness, measured vertically

 BH = top-hat half-width, measured horizontally in Y-direction

 ZU = upper plume boundary (Z-coordinate)

 ZL = lower plume boundary (Z-coordinate)

 S = hydrodynamic average (bulk) dilution

 C = average (bulk) concentration (includes reaction effects, if any)

 Plume Stage 2 (bank attached):

 X Y Z S C BV BH ZU ZL

 98.19 -46.00 3.44 35.6 .982E+02 1.38 262.50 4.13 2.74

 268.28 -46.00 3.44 42.7 .820E+02 .93 468.27 3.90 2.97

 438.37 -46.00 3.44 48.4 .722E+02 .81 609.62 3.84 3.03

 608.46 -46.00 3.44 54.7 .640E+02 .77 728.17 3.82 3.05

 778.55 -46.00 3.44 61.7 .568E+02 .75 836.14 3.81 3.06

 948.64 -46.00 3.44 69.2 .505E+02 .75 938.66 3.81 3.06

 1118.73 -46.00 3.44 77.3 .453E+02 .76 1038.24 3.82 3.06

 1288.82 -46.00 3.44 85.9 .408E+02 .77 1136.20 3.82 3.05

 1458.91 -46.00 3.44 94.8 .369E+02 .78 1233.26 3.83 3.04

 1629.00 -46.00 3.44 104.0 .336E+02 .80 1329.86 3.84 3.04

 1799.10 -46.00 3.44 113.6 .308E+02 .81 1426.23 3.84 3.03

 1969.19 -46.00 3.44 123.4 .284E+02 .83 1522.53 3.85 3.02

 2139.28 -46.00 3.44 133.5 .262E+02 .84 1618.85 3.86 3.02

 2309.37 -46.00 3.44 143.8 .243E+02 .86 1715.24 3.86 3.01

 2479.46 -46.00 3.44 154.4 .227E+02 .87 1811.74 3.87 3.00

 2649.55 -46.00 3.44 165.2 .212E+02 .88 1908.37 3.88 2.99

 2819.64 -46.00 3.44 176.2 .199E+02 .90 2005.12 3.88 2.99

 2989.73 -46.00 3.44 187.4 .187E+02 .91 2102.02 3.89 2.98

 3159.82 -46.00 3.44 198.7 .176E+02 .92 2199.06 3.90 2.98

 3329.91 -46.00 3.44 210.3 .166E+02 .93 2296.24 3.90 2.97

 3500.00 -46.00 3.44 222.1 .158E+02 .95 2393.56 3.91 2.96

 Cumulative travel time = 233246. sec

 Simulation limit based on maximum specified distance = 3500.00 m.

 This is the REGION OF INTEREST limitation.

END OF MOD142: BUOYANT TERMINAL LAYER SPREADING 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

CORMIX1: Submerged Single Port Discharges End of Prediction File

11111111111111111111111111111111111111111111111111111111111111111111111111111
102

Figure B.4: Different side views of near-field jet/plume discharge in stratified reservoir. a) distorted unscaled view, b) view with fixed undistorted scale, and c) undistorted view along trajectory (in the x-y

plane).
103

Figure B.5: Plan view of diffuser plume in a) complete field (near- and far), and b) near-field only.

(Note: since in this simulation the discharge was schematized as an unbounded cross-section, the

resulting plume would actually contact far shoreline when the plume width exceeds the actual crosssection width of 1000 m. This occurs when BH ≅ 1000 m at x ≅ 1000 m downstream as shown in view a).

Thus, if plume concentration data were required after far shoreline contact, a bounded cross-section

would need to be specified (BS = 1000) in a new simulation.
____________________________________________________________________________________

104

Figure B.6: Concentration distribution as a function of distance along plume centerline

a few parameters such as the upstream intrusion

length, downstream width, and shape of the

intrusion. As indicated in Figure B.5, reasonable

transition boundaries can be assumed to provide

smooth transitions to the far-field processes.

The side and plan views show the wide

and thin layer that forms as the plume collapses

laterally within the ambient stratification while it is

advected by the weak ambient flow.

Some discontinuity in the predicted

plume dimensions occurs in the transition from

the control volume (MOD137) describing

upstream spreading to the continuous prediction

for ambient buoyant spreading (MOD142). The

cause for this discontinuity is the simultaneous

interaction of the plume with the channel

boundary that occurs within MOD137. 

CORMIX1 detects such complicated

simultaneous processes and warns the user who

then can compensate by providing reasonable,

mass-conserving transitions.

It is also possible to include

concentration values, e.g. along the centerline, in

plots of this type. This has not been done in

these figures in order not to overload them. 

Alternatively, the concentration distribution

following the centerline of the plume is plotted in

Figure B.6. The rapid drop-off within the initial

buoyant jet region is evident. Also, the

thresholds for all water quality parameters and

module boundaries have been exercised in the

plot. Hence, the locations where the CMC (i.e.

TDZ) and CCC values are met have been

indicated.

B.5 Details of Buoyant Jet Near-field Mixing

The CORJET model option can be

employed if further details within the very initial

buoyant jet motion are desired. This option can

be exercised internally at the conclusion of the

CORMIX design case by choosing the postprocessor. The CORJET output corresponding

to this has already been shown as an example in
105

Section 6.1, namely as Table 6.2. That output approximations to the ambient density profile

agrees well with that listed in Table B.2. and/or velocity distribution. The reader is

More importantly, CORJET could also be the procedures explained in Section 6.1 and

used separately to examine different illustrated in Appendix E.

encouraged to explore this approach, following
106
107

Appendix C

CORMIX1 and 2: Submerged Single Port Discharge

and Multiport Diffuser in a Shallow River

The design modification of an existing the discharge reach. River cross-sections were

(hypothetical situation) discharge from a plant into determined by depth measurements at several

a shallow river is considered in this case study. stations as indicated. For example, Figure C.2

This affords an opportunity to demonstrate the gives the cross-section at the discharge location.

joint use of CORMIX and of a dye field study in All cross-sections exhibit quite some nonorder to analyze an existing effluent plume from a uniformity as is typical for a gently meandering

single port discharge and to suggest a design alluvial (gravel) river. The indicated water level

conversion to a multiport diffuser with improved corresponds to the river discharge of 840 cfs (

mixing characteristics. 23.7 m /s) that was measured during the field

C.1 Problem Statement

An industrial plant (B-Plant) is currently

discharging its effluent into an adjacent shallow

river. The design flowrate is quite small at 2.1

mgd ( 0.092 m /s). The river is about 200 to 300 3

ft wide at the discharge location and the following

downstream reach. Water depth is, of course,

dependent on the river discharge that is

seasonally variable. An examination of available

streamflow records (USGS data) suggests a

7Q10 low flow discharge of 285 cfs ( 8.06 m /s). 3

Recent water quality studies in the

discharge reach performed during low flow

summer conditions have shown occasional

coloration problems in the discharge plume that

seem to be related to inadequate mixing

characteristics of the present submerged single

port discharge. For that reason the plant operator

is considering an improvement of the discharge

structure.

C.2 Existing Single Port Discharge: Dye Field

Study and CORMIX1 Comparison

An initial field study was conducted in

order (1) to measure the geometric and hydraulic

characteristics of the discharge reach with special

emphasis on the first 1000 ft downstream, and (2)

to determine plume concentrations by means of a

dye injection into the plant effluent.

Figure C.1 shows the plan geometry of

3

survey using the usual USGS stream-gaging

methods. The ambient temperature at this

flowrate was 20 C. The discharge pipe (diameter o

= 8 in  0.2 m) is located about 95 ft from the right

bank, and is pointing in the downstream direction.

In order to obtain a detailed description of

the flow field in the river, reach discharge

measurements were conducted at several more

downstream stations (200, 400, 750, and 1000 ft,

respectively). Figure C.1 includes the cumulative

discharge isolines, expressed in % of the total

discharge as measured from the right bank, for

the reach. These lines provide a useful indication

of the mean flow pattern in such a winding river

for subsequent interpretation of observed plume

features (see also comments on cumulative

discharge method in Section 6.2).

A dye test was carried out by continuously

discharging a fluorescein dye solution into the

plant effluent. The dye concentration exiting the

discharge pipe was 560 ppb with a temperature of

22 C. Dye concentration were measured at the o

transects indicated in Figure C.1, and have been

plotted in Figure C.3 as a function of distance

from the right bank. The observed concentration

profiles show decreasing peak (maximum) values

with increasing downstream distances.

Observations indicated a vertically mixed plume at

all locations. In the display of Figure C.3 the

plume centerline position is clearly shifting relative

to the right bank, and the plume width

occasionally appears to slightlycontract in width.

An initial CORMIX1 evaluation was carried

out to ascertain its applicability in this somewhat
108

Figure C.1: Plan view of downstream reach of Shallow River with cumulative discharge measurement

stations and distribution

Figure C.2: River cross-section at discharge location
109

Figure C.3: Measured dye concentration plotted as a function of distance from right bank

irregular flow environment. For this purpose, the

cross-section was schematized as a rectangular

cross-section putting emphasis on the depth

conditions around the discharge location. The

average and local depths at this flow rate are both

1.9 ft or (» 0.6 m).

Information from the cumulative discharge

data was used. Note that the cumulative

discharge data shows the discharge located at the

60 % line, i.e. it is hydraulically closer to the left

bank, while it appears geographically closer to the

right! This is reflected in the schematization: 

Within the 165 ft (» 50 m) wide rectangular

channel, the discharge is located 20 m from the

left bank. The roughness of the slightly winding,

but otherwise clean natural channel has been

specified by a Manning's n value of 0.03.

Figure C.4 is the data checklist prepared

for the CORMIX1 session, while Table C.1

represents the detailed CORMIX1 Prediction File

(the session report is not given here). CORMIX1

predicts that the plume gets rapidly mixed over the

shallow depth, and is primarily influenced by farfield mixing processes, a feature that is quite

consistent with observations. The dye

concentration distribution predicted by CORMIX1

in the schematic rectangular channel are plotted in

Figure C.5 and show a much more regular mixing

pattern than the earlier Figure C.3. However,

matters can be readily reconciled when both field

data and CORMIX1 predictions are interpreted as

a function of cumulative discharge (for example

by means of the far-field post-processor

FFLOCATR, although the details of the

FFLOCATR application are not shown herein).

This has been done in Figure C.6 where

both distributions are directly superposed on the

cumulative discharge pattern. The agreement is

excellent. This entire procedure points out the

need for high-quality field data if detailed

interpretations and predictions of discharge

plumes are desired.

C.3 Proposed Multiport Diffuser Discharge

Under 7Q10 flow Conditions: CORMIX2

Predictions

The following strategy is pursued in order

111

Table C.1

CORMIX1 Prediction File for dye test in Shallow River

CORMIX1 PREDICTION FILE:

11111111111111111111111111111111111111111111111111111111111111111111111111111

 CORNELL MIXING ZONE EXPERT SYSTEM

Subsystem CORMIX1: Subsystem version:

 Submerged Single Port Discharges CORMIX_v.3.10__________June_1995

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

CASE DESCRIPTION

 Site name/label: Shallow^River 

 Design case: Dye^Test 

 FILE NAME: cormix\sim\dye1 .cx1

 Time of Fortran run: 04/14/96--11:03:24 

ENVIRONMENT PARAMETERS (metric units)

 Bounded section

 BS = 50.00 AS = 30.00 QA = 23.70 ICHREG= 2

 HA = .60 HD = .60

 UA = .790 F = .084 USTAR = .8081E-01

 UW = 2.000 UWSTAR= .2198E-02

 Uniform density environment

 STRCND= U RHOAM = 998.2051

DISCHARGE PARAMETERS (metric units)

 BANK = LEFT DISTB = 20.00

 D0 = .200 A0 = .031 H0 = .15

 THETA = .00 SIGMA = .00

 U0 = 2.929 Q0 = .092 = .9200E-01

 RHO0 = 997.7714 DRHO0 = .4337E+00 GP0 = .4260E-02

 C0 = .5600E+03 CUNITS= ppb 

 IPOLL = 1 KS = .0000E+00 KD = .0000E+00

FLUX VARIABLES (metric units)

 Q0 = .9200E-01 M0 = .2694E+00 J0 = .3920E-03 SIGNJ0= 1.0

 Associated length scales (meters)

 LQ = .18 LM = 18.89 Lm = .66 Lb = .00

 Lmp = 99999.00 Lbp = 99999.00

NON-DIMENSIONAL PARAMETERS

 FR0 = 100.31 R = 3.70

FLOW CLASSIFICATION

 111111111111111111111111111111111111111111

 1 Flow class (CORMIX1) = H5-0 1 

 1 Applicable layer depth HS = .60 1

 111111111111111111111111111111111111111111

MIXING ZONE / TOXIC DILUTION / REGION OF INTEREST PARAMETERS

 C0 = .5600E+03 CUNITS= ppb 

 NTOX = 0

 NSTD = 0

 REGMZ = 0

 XINT = 1000.00 XMAX = 1000.00

X-Y-Z COORDINATE SYSTEM:

 ORIGIN is located at the bottom and below the center of the port:

 20.00 m from the LEFT bank/shore.

 X-axis points downstream, Y-axis points to left, Z-axis points upward.

NSTEP = 20 display intervals per module

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD101: DISCHARGE MODULE 

 COANDA ATTACHMENT immediately following the discharge.

 X Y Z S C B

 .00 .00 .00 1.0 .560E+03 .14

END OF MOD101: DISCHARGE MODULE 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN CORJET (MOD110): JET/PLUME NEAR-FIELD MIXING REGION 

 Bottom-attached jet motion.
112

 

 Profile definitions:

 B = Gaussian 1/e (37%) half-width, normal to trajectory

 Half wall jet, attached to bottom.

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 X Y Z S C B

 .00 .00 .00 1.0 .560E+03 .10

 1.05 .00 .00 1.2 .483E+03 .16

 2.10 .00 .00 1.7 .337E+03 .21

 3.15 .00 .00 2.1 .263E+03 .26

 4.21 .00 .00 2.6 .216E+03 .29

 5.26 .00 .00 3.0 .185E+03 .32

 6.31 .00 .00 3.4 .163E+03 .35

 7.36 .00 .00 3.8 .146E+03 .38

 8.41 .00 .00 4.2 .132E+03 .40

 9.46 .00 .00 4.6 .121E+03 .42

 10.51 .00 .00 5.0 .112E+03 .44

 11.56 .00 .00 5.3 .105E+03 .46

 12.62 .00 .00 5.7 .983E+02 .48

 13.67 .00 .00 6.0 .927E+02 .50

 14.72 .00 .00 6.4 .878E+02 .51

 15.77 .00 .00 6.7 .834E+02 .53

 16.82 .00 .00 7.0 .795E+02 .55

 17.87 .00 .00 7.4 .761E+02 .56

 18.92 .00 .00 7.7 .729E+02 .57

 19.97 .00 .00 8.0 .701E+02 .59

 21.03 .00 .00 8.3 .675E+02 .60

 Cumulative travel time = 14. sec

END OF CORJET (MOD110): JET/PLUME NEAR-FIELD MIXING REGION 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD133: LAYER BOUNDARY IMPINGEMENT/FULL VERTICAL MIXING 

 Control volume inflow:

 X Y Z S C B

 21.03 .00 .00 8.3 .675E+02 .60

 Profile definitions:

 BV = layer depth (vertically mixed)

 BH = top-hat half-width, in horizontal plane normal to trajectory

 ZU = upper plume boundary (Z-coordinate)

 ZL = lower plume boundary (Z-coordinate)

 S = hydrodynamic average (bulk) dilution

 C = average (bulk) concentration (includes reaction effects, if any)

 X Y Z S C BV BH ZU ZL

 20.43 .00 .60 8.3 .675E+02 .00 .00 .60 .60

 20.55 .00 .60 8.3 .675E+02 .60 .11 .60 .00

 20.67 .00 .60 8.3 .675E+02 .60 .15 .60 .00

 20.79 .00 .60 8.3 .675E+02 .60 .19 .60 .00

 20.91 .00 .60 8.3 .675E+02 .60 .22 .60 .00

 21.03 .00 .60 8.3 .675E+02 .60 .24 .60 .00

 21.15 .00 .60 8.8 .637E+02 .60 .27 .60 .00

 21.27 .00 .60 9.9 .568E+02 .60 .29 .60 .00

 21.39 .00 .60 10.8 .517E+02 .60 .31 .60 .00

 21.51 .00 .60 11.4 .493E+02 .60 .33 .60 .00

 21.63 .00 .60 11.6 .482E+02 .60 .35 .60 .00

 Cumulative travel time = 15. sec

END OF MOD133: LAYER BOUNDARY IMPINGEMENT/FULL VERTICAL MIXING 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD153: VERTICALLY MIXED PLUME IN CO-FLOW 

 Phase 1: Vertically mixed, Phase 2: Re-stratified

 Phase 1: The plume is VERTICALLY FULLY MIXED over the entire layer depth.

 This flow region is INSIGNIFICANT in spatial extent and will be by-passed.

----------------------------------------------------------------------------- 

 Phase 2: The flow has RESTRATIFIED at the beginning of this zone.

 This flow region is INSIGNIFICANT in spatial extent and will be by-passed.
113

END OF MOD153: VERTICALLY MIXED PLUME IN CO-FLOW 

----------------------------------------------------------------------------- 

** End of NEAR-FIELD REGION (NFR) **

 

 The initial plume WIDTH values in the next far-field module will be 

 CORRECTED by a factor 3.25 to conserve the mass flux in the far-field!

 The correction factor is quite large because of the small ambient velocity

 relative to the strong mixing characteristics of the discharge!

 This indicates localized RECIRCULATION REGIONS and internal hydraulic JUMPS.

 Flow appears highly UNSTEADY and prediction results are UNRELIABLE!

----------------------------------------------------------------------------- 

BEGIN MOD141: BUOYANT AMBIENT SPREADING 

 Discharge is non-buoyant or weakly buoyant.

 Therefore BUOYANT SPREADING REGIME is ABSENT.

END OF MOD141: BUOYANT AMBIENT SPREADING 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD161: PASSIVE AMBIENT MIXING IN UNIFORM AMBIENT 

 Vertical diffusivity (initial value) = .970E-02 m^2/s

 Horizontal diffusivity (initial value) = .242E-01 m^2/s

 The passive diffusion plume is VERTICALLY FULLY MIXED at beginning of region.

 Profile definitions:

 BV = Gaussian s.d.*sqrt(pi/2) (46%) thickness, measured vertically

 = or equal to layer depth, if fully mixed

 BH = Gaussian s.d.*sqrt(pi/2) (46%) half-width,

 measured horizontally in Y-direction

 ZU = upper plume boundary (Z-coordinate)

 ZL = lower plume boundary (Z-coordinate)

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 Plume Stage 1 (not bank attached):

 X Y Z S C BV BH ZU ZL

 21.63 .00 .60 11.6 .482E+02 .60 1.12 .60 .00

 70.55 .00 .60 25.3 .222E+02 .60 2.44 .60 .00

 119.47 .00 .60 33.8 .166E+02 .60 3.26 .60 .00

 168.39 .00 .60 40.5 .138E+02 .60 3.92 .60 .00

 217.30 .00 .60 46.3 .121E+02 .60 4.48 .60 .00

 266.22 .00 .60 51.5 .109E+02 .60 4.98 .60 .00

 315.14 .00 .60 56.1 .998E+01 .60 5.43 .60 .00

 364.06 .00 .60 60.5 .926E+01 .60 5.84 .60 .00

 412.98 .00 .60 64.5 .869E+01 .60 6.23 .60 .00

 461.90 .00 .60 68.3 .820E+01 .60 6.60 .60 .00

 510.81 .00 .60 71.9 .779E+01 .60 6.95 .60 .00

 559.73 .00 .60 75.3 .744E+01 .60 7.28 .60 .00

 608.65 .00 .60 78.5 .713E+01 .60 7.59 .60 .00

 657.57 .00 .60 81.7 .686E+01 .60 7.90 .60 .00

 706.49 .00 .60 84.7 .661E+01 .60 8.19 .60 .00

 755.41 .00 .60 87.6 .639E+01 .60 8.47 .60 .00

 804.33 .00 .60 90.4 .619E+01 .60 8.74 .60 .00

 853.24 .00 .60 93.2 .601E+01 .60 9.01 .60 .00

 902.16 .00 .60 95.8 .584E+01 .60 9.27 .60 .00

 951.08 .00 .60 98.4 .569E+01 .60 9.52 .60 .00

 1000.00 .00 .60 101.0 .555E+01 .60 9.76 .60 .00

 Cumulative travel time = 1249. sec

 Simulation limit based on maximum specified distance = 1000.00 m.

 This is the REGION OF INTEREST limitation.

END OF MOD161: PASSIVE AMBIENT MIXING IN UNIFORM AMBIENT 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

CORMIX1: Submerged Single Port Discharges End of Prediction File

11111111111111111111111111111111111111111111111111111111111111111111111111111
114

Figure C.5: Dye concentrations predicted by CORMIX1 plotted as a function of distance from right

bank in schematized channel

Figure C.6: Comparison of measured field dye distribution and CORMIX1 predictions within

cumulative discharge pattern
115

to improve the near-field mixing characteristics of Furthermore, a high initial dilution of 29.8 is

the existing discharge: (1) Utilization of a multiport attained in a short region (labeled the

diffuser to increase the initial entrainment of "acceleration zone", MOD271) following the high

ambient water into the multiple effluent jets, and velocity multiport discharge. These results are

(2) shifting of the discharge location toward the plotted in Figure C.8 using the graphics package

right bank to delay the contact with the left CMXGRAPH. In order to illustrate the capabilities

shoreline that -with the present installation- of the graphics program these plots include (a)

seems to occur at a downstream distance of 1000 the un-scaled plan view as it first appears on

ft. screen, (b) a re-scaled plan view that is

The design study is carried out for the low narrow plume shape and river stretch, and (c) a

flow ambient condition given by the 7Q10 side view of the near-field only with 1:2 vertical

discharge (285 cfs  8.1 m /s) as is typical for distortion. The user should explore the manifold 3

water quality studies on riverine sites. features of the graphics package.

Temperatures of the discharge and ambient and

channel roughness is assumed unchanged. The Obviously, predicted plan plume shapes

new local and average depth for this flowrate is

calculated to be  0.3 m from the formula given in

Section 4.3.1. 

State water quality regulations call for a

demonstration of plume concentrations at the

edge of a mixing zone that is limited to one fourth

(1/4) of the river width. With an average river

width of 250 ft, this corresponds to a width

limitation of 250/4  62 ft ( 19 m). (Note: The

actual width limitation must be handled within the

schematized cross-sections as specified. For the

schematic channel width of 50 m this represents

a 19/50 = 38% width limitation specification as

used in CORIMX2.)

Obviously, a number of design solutions,

with different diffuser configurations and

locations, need to be investigated. One of several

feasible solutions is presented in the following: A

15 m ( 49 ft) long diffuser consisting of 7 nozzles

is installed in perpendicular, co-flowing

arrangement centered at the 40% cumulative

discharge position. (Note: In the actual

coordinate position, this corresponds to a

distance of about 70 ft from the right bank; see

Figure C.1.) The nozzle diameter is 2.5 in (

0.0635 m).

The CORMIX2 simulation is summarized

in Figure C.7 (data preparation checklist), Table

C.2 (session report), and Table C.3 (prediction

file). 

Inspection of the session record and

prediction file shows that the plume becomes

rapidly mixed over the very shallow water depth.

undistorted (1:1) to show the actual long and

should be interpreted with the cumulative

discharge method. The far-field plume locator

FFLOCATR (Section 6.2) is designed for exactly

that purpose. The two data files examples in

Section 6.2 (input: Table 6.4, output: Table 6.5)

are, in fact, applications for the present design

case. Hence, the results of Table 6.5 when

plotted on the river plan view with the cumulative

discharge isolines are shown in Figure C.9 and

exhibit realistic plume shapes. After the rapid

initial mixing in the near-field the plume is growing

only very slowly in the far-field (MOD261). At the

1000 ft transect, the plume stays clear of the left

bank.

The concentration distribution along the

plume centerline is plotted in Figure C.10 for the

near-field only, as very slow additional mixing

occurs at larger distances (see Table C.3). As

regards the regulatory mixing zone (RMZ) the

prediction results indicate that it will be

encountered at a considerable distance

downstream, at about 354 m ( 1200 ft), i.e.

outside the region plotted in Figure C.10. The

dilution at that location is 33.5, corresponding to

a local centerline concentration value of 3.0 %.

Finally, it is illuminating to compare the

performance of the proposed multiport diffuser

design with the existing single port situation, both

under 7Q10 low flow. This is also included in

Figure C.10 by plotting the plume centerline

concentrations. (Note: The data sheet, session

record, and output file for this CORMIX1

application are omitted for space reasons.)

Clearly, the multiport design achieves much more
116

rapid initial mixing by capturing more of the single plume out of the 7-nozzle arrangement to

ambient entrainment flow as the diffuser is spread provide more detail in the near-field; the user has

over portion of the river width. Figure C.10 also been prompted by several messages within

includes an additional CORMIX1 prediction for a CORMIX2 to perform this additional prediction. 



120

Table C.3

CORMIX2 Prediction File for B-Plant discharge into Shallow River with multiport diffuser

CORMIX2 PREDICTION FILE:

22222222222222222222222222222222222222222222222222222222222222222222222222222

 CORNELL MIXING ZONE EXPERT SYSTEM

Subsystem CORMIX2: Subsystem version:

 Submerged Multiport Diffuser Discharges CORMIX_v.3.00__________July_1994

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

CASE DESCRIPTION

 Site name/label: B-PLANT^SHALLOW-RIVER 

 Design case: LOW-FLOW^7Q10 

 FILE NAME: cormix\sim\SAMPLE2 .cx2

 Time of Fortran run: 06/24/95--22:36:15 

ENVIRONMENT PARAMETERS (metric units)

 Bounded section

 BS = 50.00 AS = 15.00 QA = 8.10 ICHREG= 2

 HA = .30 HD = .30

 UA = .540 F = .105 USTAR = .6199E-01

 UW = 2.000 UWSTAR= .2198E-02

 Uniform density environment

 STRCND= U RHOAM = 998.2051

DIFFUSER DISCHARGE PARAMETERS (metric units)

 Diffuser type: DITYPE= unidirectional_perpendicular 

 BANK = RIGHT DISTB = 20.00 YB1 = 12.50 YB2 = 27.50

 LD = 15.00 NOPEN = 7 SPAC = 2.50

 D0 = .064 A0 = .003 H0 = .09

 Nozzle/port arrangement: unidirectional_without_fanning 

 GAMMA = 90.00 THETA = .00 SIGMA = .00 BETA = 90.00

 U0 = 4.150 Q0 = .092 = .9200E-01

 RHO0 = 997.7714 DRHO0 = .4337E+00 GP0 = .4260E-02

 C0 = .1000E+03 CUNITS= PERCENT 

 IPOLL = 1 KS = .0000E+00 KD = .0000E+00

FLUX VARIABLES - PER UNIT DIFFUSER LENGTH (metric units)

 q0 = .6133E-02 m0 = .2545E-01 j0 = .2613E-04 SIGNJ0= 1.0

 Associated 2-d length scales (meters)

 lQ=B = .001 lM = 28.81 lm = .09

 lmp = 99999.00 lbp = 99999.00 la = 99999.00

FLUX VARIABLES - ENTIRE DIFFUSER (metric units)

 Q0 = .9200E-01 M0 = .3818E+00 J0 = .3920E-03

 Associated 3-d length scales (meters)

 LQ = .15 LM = 24.53 Lm = 1.14 Lb = .00

 Lmp = 99999.00 Lbp = 99999.00

NON-DIMENSIONAL PARAMETERS

 FR0 = 1653.66 FRD0 = 252.28 R = 7.68

 (slot) (port/nozzle)

FLOW CLASSIFICATION

 222222222222222222222222222222222222222222

 2 Flow class (CORMIX2) = MU2 2 

 2 Applicable layer depth HS = .30 2

 222222222222222222222222222222222222222222

MIXING ZONE / TOXIC DILUTION / REGION OF INTEREST PARAMETERS

 C0 = .1000E+03 CUNITS= PERCENT 

 NTOX = 0

 NSTD = 0

 REGMZ = 1

 REGSPC= 2 XREG = .00 WREG = 19.00 AREG = .00

 XINT = 1000.00 XMAX = 1000.00

X-Y-Z COORDINATE SYSTEM:

 ORIGIN is located at the bottom and the diffuser mid-point:

 20.00 m from the RIGHT bank/shore.

 X-axis points downstream, Y-axis points to left, Z-axis points upward.

NSTEP = 20 display intervals per module

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD201: DIFFUSER DISCHARGE MODULE 
121

 Due to complex near-field motions: EQUIVALENT SLOT DIFFUSER (2-D) GEOMETRY

 

 Profile definitions:

 BV = Gaussian 1/e (37%) half-width, in vertical plane normal to trajectory

 BH = top-hat half-width, in horizontal plane normal to trajectory

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 X Y Z S C BV BH

 .00 .00 .09 1.0 .100E+03 .00 7.50

END OF MOD201: DIFFUSER DISCHARGE MODULE 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD271: ACCELERATION ZONE OF UNIDIRECTIONAL CO-FLOWING DIFFUSER 

 In this laterally contracting zone the diffuser plume becomes VERTICALLY FULLY 

 MIXED over the entire layer depth (HS = .30m).

 Full mixing is achieved after a plume distance of about five

 layer depths from the diffuser.

 Profile definitions:

 BV = layer depth (vertically mixed)

 BH = top-hat half-width, in horizontal plane normal to trajectory

 S = hydrodynamic average (bulk) dilution

 C = average (bulk) concentration (includes reaction effects, if any)

 X Y Z S C BV BH

 .00 .00 .09 1.0 .100E+03 .00 7.50

 .38 .00 .09 11.2 .894E+01 .08 7.39

 .75 .00 .10 15.4 .649E+01 .15 7.30

 1.13 .00 .10 18.6 .536E+01 .23 7.22

 1.50 .00 .10 21.4 .468E+01 .30 7.15

 1.88 .00 .11 23.8 .420E+01 .30 7.09

 2.25 .00 .11 26.0 .385E+01 .30 7.04

 2.63 .00 .11 28.0 .358E+01 .30 6.99

 3.00 .00 .11 29.8 .335E+01 .30 6.95

 3.38 .00 .12 29.8 .335E+01 .30 6.91

 3.75 .00 .12 29.8 .335E+01 .30 6.87

 4.13 .00 .12 29.8 .335E+01 .30 6.84

 4.50 .00 .13 29.8 .335E+01 .30 6.82

 4.88 .00 .13 29.8 .335E+01 .30 6.80

 5.25 .00 .13 29.8 .335E+01 .30 6.78

 5.63 .00 .14 29.8 .335E+01 .30 6.76

 6.00 .00 .14 29.8 .335E+01 .30 6.75

 6.38 .00 .14 29.8 .335E+01 .30 6.74

 6.75 .00 .14 29.8 .335E+01 .30 6.74

 7.13 .00 .15 29.8 .335E+01 .30 6.74

 7.50 .00 .15 29.8 .335E+01 .30 6.73

 Cumulative travel time = 11. sec

END OF MOD271: ACCELERATION ZONE OF UNIDIRECTIONAL CO-FLOWING DIFFUSER 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD251: DIFFUSER PLUME IN CO-FLOW 

 Phase 1: Vertically mixed, Phase 2: Re-stratified

 Phase 1: The diffuser plume is VERTICALLY FULLY MIXED over the

 entire layer depth.

 This flow region is INSIGNIFICANT in spatial extent and will be by-passed.

----------------------------------------------------------------------------- 

 Phase 2: The flow has RESTRATIFIED at the beginning of this zone.

 This flow region is INSIGNIFICANT in spatial extent and will be by-passed.

END OF MOD251: DIFFUSER PLUME IN CO-FLOW 

----------------------------------------------------------------------------- 

** End of NEAR-FIELD REGION (NFR) **

 

 The initial plume WIDTH values in the next far-field module will be 

 CORRECTED by a factor 1.24 to conserve the mass flux in the far-field!

----------------------------------------------------------------------------- 

BEGIN MOD241: BUOYANT AMBIENT SPREADING 

 Discharge is non-buoyant or weakly buoyant.

 Therefore BUOYANT SPREADING REGIME is ABSENT.
122

END OF MOD241: BUOYANT AMBIENT SPREADING 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD261: PASSIVE AMBIENT MIXING IN UNIFORM AMBIENT 

 Vertical diffusivity (initial value) = .372E-02 m^2/s

 Horizontal diffusivity (initial value) = .930E-02 m^2/s

 The passive diffusion plume is VERTICALLY FULLY MIXED at beginning of region.

 Profile definitions:

 BV = Gaussian s.d.*sqrt(pi/2) (46%) thickness, measured vertically

 = or equal to layer depth, if fully mixed

 BH = Gaussian s.d.*sqrt(pi/2) (46%) half-width,

 measured horizontally in Y-direction

 ZU = upper plume boundary (Z-coordinate)

 ZL = lower plume boundary (Z-coordinate)

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 Plume Stage 1 (not bank attached):

 X Y Z S C BV BH ZU ZL

 7.50 .00 .30 29.8 .335E+01 .30 8.37 .30 .00

 57.13 .00 .30 30.4 .329E+01 .30 8.53 .30 .00

 106.75 .00 .30 30.9 .323E+01 .30 8.68 .30 .00

 156.38 .00 .30 31.5 .318E+01 .30 8.83 .30 .00

 206.00 .00 .30 32.0 .313E+01 .30 8.98 .30 .00

 255.63 .00 .30 32.5 .308E+01 .30 9.13 .30 .00

 305.25 .00 .30 33.0 .303E+01 .30 9.27 .30 .00

 354.88 .00 .30 33.5 .298E+01 .30 9.42 .30 .00

 ** REGULATORY MIXING ZONE BOUNDARY **

 In this prediction interval the TOTAL plume width meets or exceeds

 the regulatory value = 19.00 m.

 This is the extent of the REGULATORY MIXING ZONE.

 404.50 .00 .30 34.0 .294E+01 .30 9.56 .30 .00

 454.13 .00 .30 34.5 .290E+01 .30 9.69 .30 .00

 503.75 .00 .30 35.0 .286E+01 .30 9.83 .30 .00

 553.38 .00 .30 35.5 .282E+01 .30 9.96 .30 .00

 603.00 .00 .30 36.0 .278E+01 .30 10.10 .30 .00

 652.63 .00 .30 36.4 .275E+01 .30 10.23 .30 .00

 702.25 .00 .30 36.9 .271E+01 .30 10.36 .30 .00

 751.88 .00 .30 37.3 .268E+01 .30 10.48 .30 .00

 801.50 .00 .30 37.8 .265E+01 .30 10.61 .30 .00

 851.13 .00 .30 38.2 .262E+01 .30 10.73 .30 .00

 900.75 .00 .30 38.7 .259E+01 .30 10.86 .30 .00

 950.38 .00 .30 39.1 .256E+01 .30 10.98 .30 .00

 1000.00 .00 .30 39.5 .253E+01 .30 11.10 .30 .00

 Cumulative travel time = 1828. sec

 Simulation limit based on maximum specified distance = 1000.00 m.

 This is the REGION OF INTEREST limitation.

END OF MOD261: PASSIVE AMBIENT MIXING IN UNIFORM AMBIENT 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

Because of the fairly LARGE SPACING between adjacent risers/nozzles/ports,

 the above results may be unreliable in the immediate near-field of 

 the diffuser.

A SUBSEQUENT APPLICATION OF CORMIX1 IS RECOMMENDED to provide more detail

 for one of the individual jets/plumes in the initial region 

before merging.

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

CORMIX2: Submerged Multiport Diffuser Discharges End of Prediction File

22222222222222222222222222222222222222222222222222222222222222222222222222222
123

Figure C.8: CORMIX2 prediction for B-Plant multiport diffuser discharge in Shallow River. Examples

of different graphics plots: a) Plan view over entire reach, b) equivalent undistorted plan view, and c) side

view of near-field only.
124

Figure C.9: Results of cumulative discharge interpretation of CORMIX2 prediction for B-Plant multiport

diffuser discharge in Shallow River

Figure C.10: Predicted plume centerline concentrations for multiport diffuser design (CORMIX1) in

comparison to single port design (CORMIX2)
125

Appendix D

CORMIX3: Buoyant Surface Discharge In An Estuary

Estuarine conditions are characterized by surface discharge plume for this situation will be

highly variable ambient conditions during the tidal quite variable in appearance and mixing

cycle. This case study provides a short characteristics due to the tidal reversal, a steady

application example for a buoyant surface state simulation will be performed to illustrate the

discharge from a large manufacturing plant basic CORMIX3 application in a time invariant

discharging its process water into an estuary. ambient receiving water. Furthermore, this

D.1 Problem Statement

A manufacturing plant (C-Plant) is using

process water at a capacity of 2.2 m /s ( 50 3

mgd). The process water is essentially fresh

water with a discharge temperature of 20.0 Co

and contains copper at a concentration of 80 μg/l.

The plant is located at the shore of an

estuary. Figure D.1 shows the bottom bathymetry

at the plant location; two transects have been

measured and show a relatively rapid drop-off

from the MSL line to a depth of about 5 m below

MSL. It is proposed to build a discharge channel

with a bottom elevation of about 1.0 m below MSL

and a width of 2.0 m. Thus, given the tidal

variation at the discharge location indicated in

Figure D.1, the actual channel depth will vary from

a maximum of about 1.8 m at MHW to a minimum

of about 0.5 at MLW, with corresponding

adjustments in the discharge velocity.

Figure D.2 shows data from

oceanographic field surveys near the discharge

site with ambient velocity variations from about

+0.7 m/s for flood tide and to about -0.7 m/s for

ebb tide. Figure D.2 also shows the tidal

elevation variations from -.7 m above MLW at ebb

to +1.1 m above MLW at flood. The estuary has

brackish water with mean salinity of about 26 ppt,

yielding a density of about 1018 kg/m (see Figure 3

4.3 as an aid).

State regulations specify a mixing zone of

about 250 m extending in any direction from the

discharge point. The CMC and CCC values for

copper are 25 and 15 μg/l, respectively.

D.2 Steady State Simulation (for reference)

Although it is to be expected that the

simulation will be used as a basis for comparison

in the next selection, where tidal CORMIX

simulations are appropriately performed in order

to determine the time evolution in this highly

unsteady environment.

Assume that the conditions one hour after

low water slack tide (t = 11.7 h) represent that in

a large steady river (see condition (b), Figure

D.2). This design condition is represented by a

water level 0.35 m below MSL and an ambient

velocity of 0.22 m/s. As shown in Figure D.1, the

ambient water body is schematized as

unbounded, with an average depth of 6 m at MSL,

a local depth of 2.5 m at MSL (1.5 m below the

discharge channel mouth), and a bottom slope of

11°.

Figure D.3 presents the input data

checklist and Table D.1 shows the CORMIX3

prediction file (the session report is omitted here

for brevity) for the steady state reference

condition one hour after low water slack (LWS). 

The shallow discharge channel (depth of 0.65 m)

produces a relatively weak free jet (flow class

FJ1). After only 4.5 m offshore distance, the initial

jet momentum is overwhelmed by the high

discharge buoyancy, and forms a surface plume

which is weakly deflected by the ambient

crossflow (MOD313). In this region, buoyant

forces rapidly thin and spread the plume

horizontally. Both the CCC and CMC are met

within this region, (and also within the regulatory

mixing zone) as is displayed by CORMIX in the

prediction file. The plume then becomes strongly

deflected (MOD323) and finally contacts the

shoreline some 1560 m downstream. The plume

then becomes attached to the shoreline, and

spreads through passive ambient diffusion and

weak buoyant forces (MOD341), until the end of

the region of interest (2000 m). Figure D.4 shows

the above behavior.
126

Figure D.1: Bathymetric conditions in Estuary in vicinity of C-Plant surface discharge

Figure D.2: Oceanographic data for Estuary showing tidal elevation and current. A complete tidal

analysis might include simulations for all time instances labeled a to g.

128

Table D.1

CORMIX3 Prediction Steady-Sate Prediction File for Surface Buoyant Discharge

CORMIX3 PREDICTION FILE:

33333333333333333333333333333333333333333333333333333333333333333333333333333

 CORNELL MIXING ZONE EXPERT SYSTEM

Subsystem CORMIX3: Subsystem version:

 Buoyant Surface Discharges CORMIX_v.3.10__________June_1995

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

CASE DESCRIPTION

 Site name/label: C-PLANT^ESTUARY 

 Design case: STEADY^SIMULATION^ONE^HOUR^AFTER^SLACK 

 FILE NAME: cormix\sim\SAMPLE3 .cx3

 Time of Fortran run: 06/24/95--22:32:20 

ENVIRONMENT PARAMETERS (metric units)

 Unbounded section

 HA = 5.65 HD = 5.65

 UA = .220 F = .025 USTAR = .1230E-01

 UW = 2.000 UWSTAR= .2198E-02

 Uniform density environment

 STRCND= U RHOAM = 1018.0000

DISCHARGE PARAMETERS (metric units)

 BANK = RIGHT DISTB = .00 Configuration: flush_discharge 

 SIGMA = 90.00 HD0 = 2.15 SLOPE = 11.00

 Rectangular channel geometry:

 B0 = 2.000 H0 = .650 A0 = .1300E+01 AR = .325

 U0 = 1.692 Q0 = 2.200 = .2200E+01

 RHO0 = 998.2051 DRHO0 = .1979E+02 GP0 = .1907E+00

 C0 = .8000E+02 CUNITS= MUG-P-L 

 IPOLL = 1 KS = .0000E+00 KD = .0000E+00

FLUX VARIABLES (metric units)

 Q0 = .2200E+01 M0 = .3723E+01 J0 = .4195E+00

 Associated length scales (meters)

 LQ = 1.14 LM = 4.14 Lm = 8.77 Lb = 39.40

NON-DIMENSIONAL PARAMETERS

 FR0 = 3.62 FRCH = 4.80 R = 7.69

FLOW CLASSIFICATION

 333333333333333333333333333333333333333333

 3 Flow class (CORMIX3) = FJ1 3 

 3 Applicable layer depth HS = 5.65 3

 333333333333333333333333333333333333333333

MIXING ZONE / TOXIC DILUTION / REGION OF INTEREST PARAMETERS

 C0 = .8000E+02 CUNITS= MUG-P-L 

 NTOX = 1 CMC = .2500E+02 CCC = CSTD

 NSTD = 1 CSTD = .1500E+02

 REGMZ = 1

 REGSPC= 1 XREG = 250.00 WREG = .00 AREG = .00

 XINT = 2000.00 XMAX = 2000.00

X-Y-Z COORDINATE SYSTEM:

 ORIGIN is located at the WATER SURFACE and at center of discharge

 channel/outlet: .00 m from the RIGHT bank/shore.

 X-axis points downstream

 Y-axis points to left as seen by an observer looking downstream

 Z-axis points vertically upward (in CORMIX3, all values Z = 0.00)

NSTEP = 20 display intervals per module

----------------------------------------------------------------------------- 

 TRJBUO TRJATT TRJBND TRJNBY TRJCOR DILCOR

C 3.401 1.000 1.000 1.000 3.400 1.000

----------------------------------------------------------------------------- 

BEGIN MOD301: DISCHARGE MODULE 

 Efflux conditions:

 X Y Z S C BV BH

 .00 .00 0.00 1.0 .800E+02 .65 1.00

END OF MOD301: DISCHARGE MODULE 
129

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD302: ZONE OF FLOW ESTABLISHMENT 

 Control volume inflow:

 X Y Z S C BV BH

 .00 .00 0.00 1.0 .800E+02 .65 1.00

 Profile definitions:

 BV = Gaussian 1/e (37%) vertical thickness

 BH = Gaussian 1/e (37%) horizontal half-width, normal to trajectory

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 Control volume outflow:

 X Y Z S C BV BH

 .13 4.11 0.00 1.4 .576E+02 1.09 1.41

 Cumulative travel time = 2. sec

END OF MOD302: ZONE OF FLOW ESTABLISHMENT 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD311: WEAKLY DEFLECTED JET (3-D) 

 Surface JET into a crossflow

 Profile definitions:

 BV = Gaussian 1/e (37%) vertical thickness

 BH = Gaussian 1/e (37%) horizontal half-width, normal to trajectory

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 X Y Z S C BV BH

 .13 4.11 0.00 1.4 .576E+02 1.28 1.65

 .13 4.14 0.00 1.4 .575E+02 1.28 1.66

 .13 4.16 0.00 1.4 .574E+02 1.28 1.66

 .13 4.18 0.00 1.4 .573E+02 1.28 1.66

 .13 4.20 0.00 1.4 .572E+02 1.29 1.66

 .14 4.23 0.00 1.4 .571E+02 1.29 1.67

 .14 4.25 0.00 1.4 .570E+02 1.29 1.67

 .14 4.27 0.00 1.4 .569E+02 1.29 1.67

 .14 4.29 0.00 1.4 .568E+02 1.30 1.67

 .15 4.32 0.00 1.4 .567E+02 1.30 1.68

 .15 4.34 0.00 1.4 .566E+02 1.30 1.68

 .15 4.36 0.00 1.4 .565E+02 1.30 1.68

 .15 4.38 0.00 1.4 .564E+02 1.30 1.68

 .15 4.41 0.00 1.4 .563E+02 1.31 1.69

 .16 4.43 0.00 1.4 .562E+02 1.31 1.69

 .16 4.45 0.00 1.4 .561E+02 1.31 1.69

 .16 4.47 0.00 1.4 .560E+02 1.31 1.69

 .16 4.50 0.00 1.4 .559E+02 1.32 1.70

 .17 4.52 0.00 1.4 .558E+02 1.32 1.70

 .17 4.54 0.00 1.4 .558E+02 1.32 1.70

 .17 4.56 0.00 1.4 .557E+02 1.32 1.70

 Cumulative travel time = 3. sec

END OF MOD311: WEAKLY DEFLECTED JET (3-D) 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD313: WEAKLY DEFLECTED PLUME 

 Surface PLUME into a crossflow

 Profile definitions:

 BV = Gaussian 1/e (37%) vertical thickness

 BH = Gaussian 1/e (37%) horizontal half-width, normal to trajectory

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 X Y Z S C BV BH

 .17 4.56 0.00 1.4 .557E+02 1.32 1.70

 .41 6.86 0.00 2.3 .343E+02 .82 4.48

 .67 9.16 0.00 2.9 .279E+02 .66 6.76

** CMC HAS BEEN FOUND **

 The pollutant concentration in the plume falls below CMC value of .250E+02

 in the current prediction interval.

 This is the extent of the TOXIC DILUTION ZONE.
130

 .96 11.46 0.00 3.3 .244E+02 .58 8.88

 1.28 13.76 0.00 3.6 .220E+02 .52 10.93

 1.62 16.05 0.00 4.0 .202E+02 .48 12.95

 1.99 18.35 0.00 4.3 .188E+02 .45 14.94

 2.38 20.65 0.00 4.5 .177E+02 .42 16.93

 2.80 22.95 0.00 4.8 .167E+02 .40 18.92

 3.25 25.25 0.00 5.0 .159E+02 .38 20.91

 3.72 27.54 0.00 5.3 .152E+02 .36 22.90

** WATER QUALITY STANDARD OR CCC HAS BEEN FOUND **

 The pollutant concentration in the plume falls below water quality standard

 or CCC value of .150E+02 in the current prediction interval.

 This is the spatial extent of concentrations exceeding the water quality 

 standard or CCC value.

 4.22 29.84 0.00 5.5 .146E+02 .35 24.90

 4.75 32.14 0.00 5.7 .140E+02 .33 26.92

 5.30 34.44 0.00 5.9 .135E+02 .32 28.93

 5.87 36.74 0.00 6.1 .131E+02 .31 30.96

 6.48 39.03 0.00 6.3 .126E+02 .30 33.00

 7.11 41.33 0.00 6.5 .123E+02 .29 35.05

 7.76 43.63 0.00 6.7 .119E+02 .28 37.11

 8.44 45.93 0.00 6.9 .116E+02 .28 39.18

 9.15 48.23 0.00 7.1 .113E+02 .27 41.25

 9.88 50.52 0.00 7.2 .110E+02 .26 43.34

 Cumulative travel time = 248. sec

END OF MOD313: WEAKLY DEFLECTED PLUME 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD323: STRONGLY DEFLECTED PLUME 

 Profile definitions:

 BV = top-hat thickness,measured vertically

 BH = top-hat half-width, measured horizontally in Y-direction

 S = hydrodynamic average (bulk) dilution

 C = average (bulk) concentration (includes reaction effects, if any)

 X Y Z S C BV BH

 9.88 50.52 0.00 7.2 .110E+02 .26 43.34

 84.15 123.86 0.00 7.5 .107E+02 .23 60.96

 158.42 154.39 0.00 7.8 .103E+02 .22 77.07

 232.69 176.11 0.00 8.1 .985E+01 .22 92.39

 ** REGULATORY MIXING ZONE BOUNDARY **

 In this prediction interval the plume distance meets or exceeds

 the regulatory value = 250.00 m.

 This is the extent of the REGULATORY MIXING ZONE.

 306.96 193.50 0.00 8.6 .934E+01 .22 107.24

 381.23 208.23 0.00 9.1 .876E+01 .23 121.77

 455.50 221.14 0.00 9.8 .815E+01 .25 136.02

 529.77 232.70 0.00 10.7 .750E+01 .26 150.02

 604.04 243.21 0.00 11.7 .685E+01 .28 163.77

 678.31 252.88 0.00 12.9 .621E+01 .30 177.26

 752.58 261.87 0.00 14.3 .560E+01 .32 190.49

 826.84 270.29 0.00 15.9 .504E+01 .34 203.46

 901.11 278.21 0.00 17.7 .452E+01 .36 216.17

 975.38 285.70 0.00 19.7 .406E+01 .39 228.65

 1049.65 292.82 0.00 21.9 .365E+01 .41 240.91

 1123.92 299.61 0.00 24.4 .328E+01 .44 252.95

 1198.18 306.11 0.00 27.1 .295E+01 .47 264.79

 1272.45 312.34 0.00 30.0 .267E+01 .50 276.45

 1346.72 318.34 0.00 33.1 .241E+01 .54 287.93

 1420.99 324.11 0.00 36.5 .219E+01 .57 299.25

 1495.25 329.69 0.00 40.1 .199E+01 .61 310.43

 Cumulative travel time = 7000. sec

END OF MOD323: STRONGLY DEFLECTED PLUME 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

** End of NEAR-FIELD REGION (NFR) **

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD341: BUOYANT AMBIENT SPREADING 

 Profile definitions:

 BV = top-hat thickness,measured vertically

 BH = top-hat half-width, measured horizontally from bank/shoreline

 S = hydrodynamic average (bulk) dilution

 C = average (bulk) concentration (includes reaction effects, if any)
131

 Plume Stage 1 (not bank attached):

 X Y Z S C BV BH

 1495.25 329.69 0.00 40.1 .199E+01 .63 319.79

 1498.55 329.69 0.00 40.3 .199E+01 .63 320.29

 1501.84 329.69 0.00 40.5 .198E+01 .63 320.79

 1505.13 329.69 0.00 40.6 .197E+01 .63 321.29

 1508.42 329.69 0.00 40.8 .196E+01 .63 321.79

 1511.72 329.69 0.00 41.0 .195E+01 .64 322.29

 1515.01 329.69 0.00 41.1 .195E+01 .64 322.78

 1518.30 329.69 0.00 41.3 .194E+01 .64 323.28

 1521.59 329.69 0.00 41.5 .193E+01 .64 323.78

 1524.89 329.69 0.00 41.6 .192E+01 .64 324.27

 1528.18 329.69 0.00 41.8 .191E+01 .64 324.77

 1531.47 329.69 0.00 42.0 .191E+01 .65 325.27

 1534.77 329.69 0.00 42.1 .190E+01 .65 325.76

 1538.06 329.69 0.00 42.3 .189E+01 .65 326.26

 1541.35 329.69 0.00 42.5 .188E+01 .65 326.75

 1544.64 329.69 0.00 42.6 .188E+01 .65 327.25

 1547.94 329.69 0.00 42.8 .187E+01 .65 327.74

 1551.23 329.69 0.00 43.0 .186E+01 .65 328.23

 1554.52 329.69 0.00 43.2 .185E+01 .66 328.73

 1557.81 329.69 0.00 43.3 .185E+01 .66 329.22

 1561.11 329.69 0.00 43.5 .184E+01 .66 329.71

 Cumulative travel time = 7299. sec

----------------------------------------------------------------------------- 

 Plume is ATTACHED to RIGHT bank/shore.

 Plume width is now determined from RIGHT bank/shore.

 Plume Stage 2 (bank attached):

 X Y Z S C BV BH

 1561.11 .00 0.00 43.5 .184E+01 .66 659.39

 1583.05 .00 0.00 44.6 .179E+01 .67 662.33

 1605.00 .00 0.00 45.7 .175E+01 .69 665.27

 1626.94 .00 0.00 46.8 .171E+01 .70 668.21

 1648.89 .00 0.00 48.0 .167E+01 .71 671.16

 1670.83 .00 0.00 49.1 .163E+01 .73 674.11

 1692.78 .00 0.00 50.3 .159E+01 .74 677.06

 1714.72 .00 0.00 51.4 .156E+01 .76 680.01

 1736.66 .00 0.00 52.6 .152E+01 .77 682.97

 1758.61 .00 0.00 53.8 .149E+01 .78 685.92

 1780.55 .00 0.00 55.0 .146E+01 .80 688.88

 1802.50 .00 0.00 56.2 .142E+01 .81 691.83

 1824.44 .00 0.00 57.4 .139E+01 .83 694.79

 1846.39 .00 0.00 58.6 .136E+01 .84 697.75

 1868.33 .00 0.00 59.9 .134E+01 .85 700.71

 1890.28 .00 0.00 61.1 .131E+01 .87 703.67

 1912.22 .00 0.00 62.4 .128E+01 .88 706.62

 1934.17 .00 0.00 63.6 .126E+01 .90 709.58

 1956.11 .00 0.00 64.9 .123E+01 .91 712.54

 1978.05 .00 0.00 66.2 .121E+01 .93 715.50

 2000.00 .00 0.00 67.5 .118E+01 .94 718.46

 Cumulative travel time = 9294. sec

 Simulation limit based on maximum specified distance = 2000.00 m.

 This is the REGION OF INTEREST limitation.

END OF MOD341: BUOYANT AMBIENT SPREADING 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

CORMIX3: Buoyant Surface Discharges End of Prediction File

33333333333333333333333333333333333333333333333333333333333333333333333333333
132

Figure D.4: CORMIX3 prediction of surface discharge from C-Plant into Estuary using a steady-state

simulation. a) Plume shape in near- and far-field, and b) concentration along plume centerline.
133

D.3 Detailed Tidal Simulations

A high variation in both ambient velocity

and tidal elevation occurs during the tidal episode

shown in Figure D.2. The changing water height

produces a discharge velocity which varies from

0.61 m/s (at high water slack) to 2.2 m/s (at low

water slack). When combined with the large

buoyancy flux, this produces flows which change

from momentum dominated jets to highly buoyant

plumes in a short period of time. Simultaneously,

the time-variant ambient velocity (which ranges

from stagnant to 0.75 m/s) produces flows which

are free and unattached at slack tide, yet become

strongly shore-hugging at maximum flood or ebb

currents.

In such highly time-variant ambient

conditions, it is recommended that several

CORMIX predictions be performed at critical

tidal conditions throughout a reversal episode.

These critical tidal conditions are identified as:

1) Shortly after slack tide: Effects of reentrainment of discharge from the

previous half-cycle are greatest.

However, the flow is evolving rapidly in

time, causing CORMIX tidal predictions to

be limited in spatial extent. Several

predictions should be made at hourly or

half hourly intervals following the reversal.

2) Maximum flood and ebb currents:

These represent extremes of along-shore

extent and shoreline interaction. Reentrainment will be less important at these

times.

For the present scenario, it is suggested that up

to seven simulations be performed at the times

indicated on Figure D.2 by the letters a-g. In the

following section, a detailed simulation is

performed corresponding to time b, one hour after

slack tide. The results are contrasted for that

case to the steady-state assumption simulated in

the preceding.

D.4 Tidal simulation one hour after slack tide

A detailed example of the tidal simulation

capability of CORMIX is presented in this section,

using conditions corresponding to those in

Section D.2 (see Figure D.2, time b). To perform

a CORMIX tidal simulation, four additional pieces

of data are required:

1) the tidal period (usually 12.4 hours for

a semi-diurnal tidal cycle)

2) the time of simulation (in hours relative

to slack tide)

3) the ambient velocity at the time of

simulation

4) the maximum velocity which occurs

during the tidal cycle

From this data, CORMIX calculates the rate of

reversal (du /dt) and related unsteady length a

scales (L , T , [ L ] , see Table 5.4), and u u m min

determines the spatial extent of CORMIX

applicability and the re-entrainment and build-up

caused by the reversal of ambient current. (Note:

If a simulation is performed at slack tide, then the

time of simulation is t = 0 h, and the ambient

velocity is set to u = 0 m/s.) However, in order to a

calculate the reversal rate, CORMIX requires

input of the ambient velocity at an other time near

reversal (for example, at one hour before or after

slack tide). This information is only used to

determine the limit of spatial applicability for the

slack tide simulation.

For this application, the time of simulation

is one hour after slack tide. The ambient velocity

at this time is u = 0.22 m/s, and the ambient and a

discharge channel depths are the same as in

Section D.2. The maximum ambient velocity

during the tidal cycle is 0.75 m/s. For this

simulation, the data preparation checklist is given

in Figure D.5.

Table D.2 lists the CORMIX session report

and Table D.3 the CORMIX3 prediction file for

this tidal application. Two important

consequences are evident when comparing Table

D.3 and Table D.1 (corresponding steady-state

simulation): 1) a concentration build-up in the

near-field, and 2) the termination of the plume

prediction after some distance. The latter

distance is the region over which a reasonably

steady-state plume can establish itself within the

time-varying tidal environment. The theoretical

background for these procedures is given in the

report on recent CORMIX enhancements (8).



137

Table D.3

CORMIX3 Prediction File for C-Plant discharge into Estuary with unsteady tidal conditions

CORMIX3 PREDICTION FILE:

33333333333333333333333333333333333333333333333333333333333333333333333333333

 CORNELL MIXING ZONE EXPERT SYSTEM

Subsystem CORMIX3: Subsystem version:

 Buoyant Surface Discharges CORMIX_v.3.10__________June_1995

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

CASE DESCRIPTION

 Site name/label: C-PLANT^ESTUARY 

 Design case: TIDAL^SIMULATION^ONE^HOUR^AFTER^SLACK 

 FILE NAME: cormix\sim\SAMPLE3T.cx3

 Time of Fortran run: 06/24/95--22:34:03 

ENVIRONMENT PARAMETERS (metric units)

 Unbounded section

 HA = 5.65 HD = 5.65

 Tidal Simulation at TIME = 1.000 h

 PERIOD= 12.40 h UAmax = .750 dUa/dt= .220 (m/s)/h

 UA = .220 F = .025 USTAR = .1230E-01

 UW = 2.000 UWSTAR= .2198E-02

 Uniform density environment

 STRCND= U RHOAM = 1018.0000

DISCHARGE PARAMETERS (metric units)

 BANK = RIGHT DISTB = .00 Configuration: flush_discharge 

 SIGMA = 90.00 HD0 = 2.15 SLOPE = 11.00

 Rectangular channel geometry:

 B0 = 2.000 H0 = .650 A0 = .1300E+01 AR = .325

 U0 = 1.692 Q0 = 2.200 = .2200E+01

 RHO0 = 998.2051 DRHO0 = .1979E+02 GP0 = .1907E+00

 C0 = .8000E+02 CUNITS= MUG-P-L 

 IPOLL = 1 KS = .0000E+00 KD = .0000E+00

FLUX VARIABLES (metric units)

 Q0 = .2200E+01 M0 = .3723E+01 J0 = .4195E+00

 Associated length scales (meters)

 LQ = 1.14 LM = 4.14 Lm = 8.77 Lb = 39.40

 Tidal: Tu = .2229 h Lu = 39.347 Lmin = 2.573

NON-DIMENSIONAL PARAMETERS

 FR0 = 3.62 FRCH = 4.80 R = 7.69

FLOW CLASSIFICATION

 333333333333333333333333333333333333333333

 3 Flow class (CORMIX3) = FJ1 3 

 3 Applicable layer depth HS = 5.65 3

 333333333333333333333333333333333333333333

MIXING ZONE / TOXIC DILUTION / REGION OF INTEREST PARAMETERS

 C0 = .8000E+02 CUNITS= MUG-P-L 

 NTOX = 1 CMC = .2500E+02 CCC = CSTD

 NSTD = 1 CSTD = .1500E+02

 REGMZ = 1

 REGSPC= 1 XREG = 250.00 WREG = .00 AREG = .00

 XINT = 2500.00 XMAX = 3500.00

X-Y-Z COORDINATE SYSTEM:

 ORIGIN is located at the WATER SURFACE and at center of discharge

 channel/outlet: .00 m from the RIGHT bank/shore.

 X-axis points downstream

 Y-axis points to left as seen by an observer looking downstream

 Z-axis points vertically upward (in CORMIX3, all values Z = 0.00)

NSTEP = 20 display intervals per module

----------------------------------------------------------------------------- 

 TRJBUO TRJATT TRJBND TRJNBY TRJCOR DILCOR

C 3.401 1.000 1.000 1.000 3.400 1.000

----------------------------------------------------------------------------- 

BEGIN MOD301: DISCHARGE MODULE 

 Efflux conditions:

 X Y Z S C BV BH

 .00 .00 0.00 1.0 .800E+02 .65 1.00
138

END OF MOD301: DISCHARGE MODULE 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD302: ZONE OF FLOW ESTABLISHMENT 

 Control volume inflow:

 X Y Z S C BV BH

 .00 .00 0.00 1.0 .800E+02 .65 1.00

 Profile definitions:

 BV = Gaussian 1/e (37%) vertical thickness

 BH = Gaussian 1/e (37%) horizontal half-width, normal to trajectory

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 Control volume outflow:

 X Y Z S C BV BH

 .13 4.11 0.00 1.4 .586E+02 1.09 1.41

 Cumulative travel time = 2. sec

END OF MOD302: ZONE OF FLOW ESTABLISHMENT 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD311: WEAKLY DEFLECTED JET (3-D) 

 Surface JET into a crossflow

 Profile definitions:

 BV = Gaussian 1/e (37%) vertical thickness

 BH = Gaussian 1/e (37%) horizontal half-width, normal to trajectory

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 X Y Z S C BV BH

 .13 4.11 0.00 1.4 .586E+02 1.28 1.65

 .13 4.14 0.00 1.4 .585E+02 1.28 1.66

 .13 4.16 0.00 1.4 .584E+02 1.28 1.66

 .13 4.18 0.00 1.4 .583E+02 1.28 1.66

 .13 4.20 0.00 1.4 .582E+02 1.29 1.66

 .14 4.23 0.00 1.4 .581E+02 1.29 1.67

 .14 4.25 0.00 1.4 .580E+02 1.29 1.67

 .14 4.27 0.00 1.4 .580E+02 1.29 1.67

 .14 4.29 0.00 1.4 .579E+02 1.30 1.67

 .15 4.32 0.00 1.4 .578E+02 1.30 1.68

 .15 4.34 0.00 1.4 .577E+02 1.30 1.68

 .15 4.36 0.00 1.4 .576E+02 1.30 1.68

 .15 4.38 0.00 1.4 .575E+02 1.30 1.68

 .15 4.41 0.00 1.4 .574E+02 1.31 1.69

 .16 4.43 0.00 1.4 .573E+02 1.31 1.69

 .16 4.45 0.00 1.4 .572E+02 1.31 1.69

 .16 4.47 0.00 1.4 .571E+02 1.31 1.69

 .16 4.50 0.00 1.4 .571E+02 1.32 1.70

 .17 4.52 0.00 1.4 .570E+02 1.32 1.70

 .17 4.54 0.00 1.4 .569E+02 1.32 1.70

 .17 4.56 0.00 1.4 .568E+02 1.32 1.70

 Cumulative travel time = 3. sec

END OF MOD311: WEAKLY DEFLECTED JET (3-D) 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD313: WEAKLY DEFLECTED PLUME 

 Surface PLUME into a crossflow

 Profile definitions:

 BV = Gaussian 1/e (37%) vertical thickness

 BH = Gaussian 1/e (37%) horizontal half-width, normal to trajectory

 S = hydrodynamic centerline dilution

 C = centerline concentration (includes reaction effects, if any)

 X Y Z S C BV BH

 .17 4.56 0.00 1.4 .568E+02 1.32 1.70

 .41 6.86 0.00 2.3 .354E+02 .82 4.48

 .67 9.16 0.00 2.8 .291E+02 .66 6.76

 .96 11.46 0.00 3.1 .256E+02 .58 8.88

** CMC HAS BEEN FOUND **

 The pollutant concentration in the plume falls below CMC value of .250E+02
139

 in the current prediction interval.

 This is the extent of the TOXIC DILUTION ZONE.

 1.28 13.76 0.00 3.4 .233E+02 .52 10.93

 1.62 16.05 0.00 3.7 .216E+02 .48 12.95

 1.99 18.35 0.00 3.9 .203E+02 .45 14.94

 2.38 20.65 0.00 4.2 .192E+02 .42 16.93

 2.80 22.95 0.00 4.4 .184E+02 .40 18.92

 3.25 25.25 0.00 4.5 .176E+02 .38 20.91

 3.72 27.54 0.00 4.7 .170E+02 .36 22.90

 4.22 29.84 0.00 4.9 .164E+02 .35 24.90

 4.75 32.14 0.00 5.0 .159E+02 .33 26.92

 5.30 34.44 0.00 5.2 .155E+02 .32 28.93

 5.87 36.74 0.00 5.3 .151E+02 .31 30.96

** WATER QUALITY STANDARD OR CCC HAS BEEN FOUND **

 The pollutant concentration in the plume falls below water quality standard

 or CCC value of .150E+02 in the current prediction interval.

 This is the spatial extent of concentrations exceeding the water quality 

 standard or CCC value.

 6.48 39.03 0.00 5.4 .147E+02 .30 33.00

 7.11 41.33 0.00 5.6 .144E+02 .29 35.05

 7.76 43.63 0.00 5.7 .141E+02 .28 37.11

 8.44 45.93 0.00 5.8 .138E+02 .28 39.18

 9.15 48.23 0.00 5.9 .136E+02 .27 41.25

 9.88 50.52 0.00 6.0 .134E+02 .26 43.34

 Cumulative travel time = 248. sec

END OF MOD313: WEAKLY DEFLECTED PLUME 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

BEGIN MOD323: STRONGLY DEFLECTED PLUME 

 Profile definitions:

 BV = top-hat thickness,measured vertically

 BH = top-hat half-width, measured horizontally in Y-direction

 S = hydrodynamic average (bulk) dilution

 C = average (bulk) concentration (includes reaction effects, if any)

 X Y Z S C BV BH

 9.88 50.52 0.00 6.0 .134E+02 .26 43.34

 84.15 123.86 0.00 4.9 .163E+02 .23 60.96

 158.42 154.39 0.00 4.6 .174E+02 .22 77.07

 232.69 176.11 0.00 4.5 .178E+02 .22 92.39

 ** REGULATORY MIXING ZONE BOUNDARY **

 In this prediction interval the plume distance meets or exceeds

 the regulatory value = 250.00 m.

 This is the extent of the REGULATORY MIXING ZONE.

 282.05 187.67 0.00 4.5 .177E+02 .22 102.26

 Cumulative travel time = 1485. sec

 CORMIX prediction has been TERMINATED at last prediction interval.

 Limiting distance due to TIDAL REVERSAL has been reached. 

END OF MOD323: STRONGLY DEFLECTED PLUME 

----------------------------------------------------------------------------- 

----------------------------------------------------------------------------- 

CORMIX3: Buoyant Surface Discharges End of Prediction File

33333333333333333333333333333333333333333333333333333333333333333333333333333

The results of the tidal simulations are at the edge of the RMZ (compare Figure D.4b and

shown graphically in Figure D.6. The most D.6b at a distance of 250 m downstream) in the

obvious difference in the tidal CORMIX prediction tidal application as a result of tidal re-entrainment.

at this time is that the maximum predicted As a result, the copper concentration at the RMZ

downstream distance is limited to 275 m in the x- is 18 μg/L as opposed to 10 μg/L for the steady

direction. Furthermore, a significant increase in state simulation, which exceeds the CCC at this

the pollutant concentration (copper) is observed distance.
140

Figure D.6: CORMIX3 prediction of surface discharge from C-Plant into Estuary using a unsteady tidal

simulation. a) Plume shape in near-field only (prediction is terminated after this region), and b)

concentration along plume centerline.
141

Appendix E

Two Applications of CORJET

Two case studies are presented here in the same direction, i.e. along the coastline.

illustrating the application of the post-processing The water depth at the discharge location is of the

model included within CORMIX, namely CORJET, order of 30 m.

the Cornell buoyant jet integral model. As

discussed in Section 6.1 is an important tool for The CORJET data preparation checklist

predicting additional details within the near-field of for this design case is given as Figure E.1.

a submerged discharge. Both case studies are Density data is specified in this case via

included in the normal CORMIX installation temperature and salinity. The program computes

package. internally the actual density distribution using the

It is repeated here that CORJET, as any noted that in case of multiple ambient levels

jet integral model, if used alone and by an CORJET assumes outside the specified range

inexperienced analyst, is not a safe

methodology for mixing zone analysis. It is

advised to use it only in conjunction with the more

comprehensive CORMIX system. Therefore, in

case of engineering design applications, CORJET

should be employed after prior use of the

expert system CORMIX has indicated that the

buoyant jet will not experience any

instabilities due to shallow water or due to

attachment to boundaries.

E.1 Submerged multiport diffuser in deep

water

A short diffuser consisting of 11 ports and

a total length of 20 m is discharging fresh water at

a temperature of 30 C into the stratified coastal o

ocean. The diffuser ports are each 0.5 m in

diameter and well-rounded in their internal

hydraulic design so that no further exit flow

contraction will occur. The nozzles are oriented

with a vertical angle of 45 upward and a o

horizontal angle of 45 pointing into the ambient o

crossflow (see multiport diffuser definition

diagram, Figures 4.6 and 4.7). The diffuser has

an alignment of 60 with respect to the ambient o

current. The discharge flow has a concentration

of 100 % of some conservative substance.

Detailed measurements in the water

column give the distribution of temperature,

salinity and current velocity as a function of

vertical distance. The current at each level flows

full (UNESCO) equation of state. It should be

(e.g. above 15 m in this case) that the data are

linearly continued from the last specified interval.

If uniform ambient conditions exist only a single

level must be specified. 

The port height H0 in the input data

specification is set to 0.0 m; thus, the coordinate

system is conveniently set at the discharge

height. Another value for the actual height above

the water bottom could be used too, but

remember that CORJET, as all integral models,

does not compute actual bottom interaction

effects (see Section 6.1.1). A maximum

computation height of 30 m and distance of 200

m is specified to stop the computation. The

number of print intervals is set to 10, in order to

provide sufficient detail.

A prior application of CORMIX (using a

linear density approximation Type A) has shown

that a stable multiport diffuser flow class MS

results for this case. The reader is encouraged to

ascertain that! Thus, CORJET is indeed

applicable for this case.

Table E.1 shows the input data file as

prepared externally using a line editor. The

CORJET prediction file is shown in Table E.2.

The file echoes the input data, but also lists the

computed density values, and all important

parameters and non-dimensional numbers. Note

that all parameters and scales are referenced to

the values of ambient conditions at the level of

discharge. The second half of the output table

gives the predicted plume conditions. 

143

Table E.1

CORJET input data file for multiport diffuser discharge into stratified coastal waters

#CORJET INPUT FILE

#Title line (50 characters max.):

Case5: MULTIPORT DIFFUSER: STRATIFIED, VARIABLE CURRENT

#Fluid (1=water,2=air), Density option (1=calculate,2=specify directly):

#Fluid (1⁄2): Density option (1⁄2): Ambient levels (1-10): 

1 1 3

#Ambient conditions (if d.o.=1, fill in TA+SA; if 2, fill in RHOA):

#Level ZA TA SA RHOA UA TAUA

1 0. 12. 30. 0.5 0.

2 5. 15. 29.5 0.8 0.

3 15. 20. 28. 1.2 0.

#Discharge conditions (T0+S0, or RHO0 as above; if NOPEN=1: set LD=0,ALIGN=0):

#NOPEN D0 H0 U0 THETA0 SIGMA0 C0 KD T0 S0 RHO0 LD ALIGN

11 0.5 0. 3.0 45. 45. 100. 0. 30. 0. 20. 60.

#Program control:

#ZMAX ZMIN DISMAX NPRINT

30. 0. 200. 10

Table E.2

CORJET prediction file for multiport diffuser discharge into stratified coastal waters

 CORJET PREDICTION FILE:

 JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ

 CORJET: CORNELL BUOYANT JET INTEGRAL MODEL Version 4.1, April 1996

 ----------------------------------------------------------------------------

 FILE NAME: post\cj\case5mpd.OUT 

 Label/identifier: Case5: MULTIPORT DIFFUSER: STRATIFIED, VARIABLE CU

 Time of CORJET run: 4/13/96--15:56:58

 Ambient conditions: No. of levels: 3 Fluid: Water Density option: 1

 LEV ZA TA SA RHOA UA TAUA

 1 .00 12.00 30.00 1022.71 .50 .00

 2 5.00 15.00 29.50 1021.74 .80 .00

 3 15.00 20.00 28.00 1019.43 1.20 .00

 

 Discharge conditions (metric): For each port: 

 D0 H0 U0 THETA0 SIGMA0 C0 KD T0 S0 RHO0

 .500 .00 3.00 45.00 45.00 .10E+03 .00E+0 30.0 .0 995.65

 MULTIPORT DIFFUSER conditions:

 NOPEN LD SPAC ALIGN Q0total

 11 20.00 2.00 60.00 6.480 = .6480E+01

 

 Program control:

 ZMAX ZMIN DISMAX NPRINT

 30.00 .00 200.00 10

 

 Flux variables (based on ambient at discharge level): For each port:

 Q0 = .589E+00 M0 = .177E+01 J0 = .153E+00 GP0 = .259E+00

 QT0 = .106E+02 QS0 = -.177E+02

 For multiport diffuser (per unit length):

 q0 = .324E+00 m0 = .972E+00 j0 = .841E-01

 

 Length scales (m) and parameters: For each port:

 LQ = .44 LM = 3.92 Lm = 2.66 Lb = 1.22

 Lmp = 5.61 Lbp = 6.71

 For multiport diffuser (per unit length):

 lQ=B = .108 lM = 5.07 lm = 3.89 lq* = .74

 lmp = 8.16 lbp = 10.37

 FR0 = 8.33 FR02 = 17.92 Fa = 1.14 R = 6.00

 (port) (2-D slot)

 Zone of flow establishment (m): 

 LE = 1.30 XE = .75 YE = .62 ZE = .86

 THETAE= 38.34 SIGMAE= 34.00 GAMMAE= 49.43

 ----------------------------------------------------------------------------

 CORJET PREDICTION: Stepsize = .2659 Printout every 10 steps

 Individual jet/plumes before merging:

 X Y Z Sc Cc B | DIST Save Gpc dTc dSALc

 .00 .00 .00 1.0 .100E+03 .25| .00 1.0 .26E+00 18.0-30.0

 .75 .62 .86 1.0 .100E+03 .25| 1.30 1.4 .27E+00 20.8-34.7

 2.80 1.50 2.27 3.0 .333E+02 .64| 3.96 4.6 .83E-01 5.2 -9.9

 Merging of individual jet/plumes to form plane jet/plume:
144

 Horizontal jet/plume half-width BH = B + 10.00

 4.26 1.78 2.85 4.5 .223E+02 .82| 5.55 6.6 .54E-01 3.1 -6.5

 5.31 1.84 3.01 6.3 .159E+02 .90| 6.62 6.4 .38E-01 2.1 -4.7

 7.96 1.88 3.22 7.4 .136E+02 1.09| 9.27 7.5 .32E-01 1.6 -3.9

 10.61 1.89 3.41 8.4 .118E+02 1.27| 11.93 8.6 .28E-01 1.3 -3.4

 13.26 1.89 3.59 9.5 .105E+02 1.45| 14.59 9.7 .24E-01 1.1 -3.0

 15.91 1.89 3.77 10.6 .940E+01 1.63| 17.25 10.7 .21E-01 .8 -2.7

 18.57 1.89 3.94 11.7 .852E+01 1.81| 19.91 11.8 .19E-01 .6 -2.4

 21.22 1.89 4.11 12.8 .779E+01 1.99| 22.57 12.9 .17E-01 .5 -2.2

 23.88 1.89 4.27 13.9 .717E+01 2.17| 25.23 14.0 .15E-01 .3 -2.0

 26.53 1.89 4.43 15.1 .664E+01 2.34| 27.89 15.1 .14E-01 .2 -1.8

 29.18 1.89 4.58 16.2 .619E+01 2.51| 30.54 16.1 .13E-01 .1 -1.7

 31.84 1.89 4.73 17.2 .580E+01 2.68| 33.20 17.2 .12E-01 .0 -1.6

 34.49 1.89 4.87 18.3 .545E+01 2.85| 35.86 18.2 .11E-01 -.1 -1.5

 37.15 1.89 5.01 19.4 .515E+01 3.02| 38.52 19.3 .97E-02 -.2 -1.4

 39.80 1.89 5.15 20.5 .488E+01 3.18| 41.18 20.3 .89E-02 -.2 -1.3

 42.46 1.89 5.28 21.5 .464E+01 3.34| 43.84 21.4 .82E-02 -.3 -1.2

 45.11 1.89 5.41 22.6 .443E+01 3.49| 46.50 22.4 .75E-02 -.3 -1.1

 47.77 1.89 5.53 23.6 .424E+01 3.64| 49.15 23.4 .69E-02 -.4 -1.0

 50.43 1.89 5.65 24.6 .407E+01 3.79| 51.81 24.3 .63E-02 -.4 -1.0

 53.08 1.89 5.77 25.6 .391E+01 3.94| 54.47 25.3 .58E-02 -.5 -.9

 55.74 1.89 5.88 26.5 .377E+01 4.08| 57.13 26.2 .54E-02 -.5 -.9

 58.39 1.89 5.99 27.5 .364E+01 4.22| 59.79 27.1 .49E-02 -.6 -.8

 61.05 1.89 6.09 28.4 .352E+01 4.35| 62.45 28.0 .45E-02 -.6 -.8

 63.71 1.89 6.20 29.3 .342E+01 4.48| 65.11 28.9 .42E-02 -.6 -.7

 66.36 1.89 6.29 30.1 .332E+01 4.61| 67.77 29.7 .38E-02 -.7 -.7

 69.02 1.89 6.39 31.0 .323E+01 4.73| 70.42 30.5 .35E-02 -.7 -.7

 71.68 1.89 6.48 31.8 .315E+01 4.85| 73.08 31.3 .32E-02 -.7 -.6

 74.34 1.89 6.57 32.6 .307E+01 4.96| 75.74 32.1 .29E-02 -.8 -.6

 76.99 1.89 6.65 33.3 .300E+01 5.07| 78.40 32.8 .27E-02 -.8 -.6

 79.65 1.89 6.74 34.1 .293E+01 5.17| 81.06 33.5 .24E-02 -.8 -.6

 82.31 1.89 6.81 34.8 .287E+01 5.27| 83.72 34.2 .22E-02 -.9 -.5

 84.97 1.89 6.89 35.5 .282E+01 5.37| 86.38 34.9 .20E-02 -.9 -.5

 87.62 1.89 6.96 36.1 .277E+01 5.46| 89.03 35.5 .18E-02 -.9 -.5

 90.28 1.89 7.03 36.7 .272E+01 5.54| 91.69 36.1 .16E-02 -.9 -.5

 92.94 1.89 7.09 37.3 .268E+01 5.62| 94.35 36.6 .14E-02 -.9 -.5

 95.60 1.89 7.16 37.8 .264E+01 5.70| 97.01 37.1 .12E-02 -1.0 -.4

 98.26 1.89 7.22 38.3 .261E+01 5.77| 99.67 37.6 .11E-02 -1.0 -.4

 100.91 1.89 7.27 38.8 .258E+01 5.83| 102.33 38.1 .93E-03 -1.0 -.4

 103.57 1.89 7.33 39.2 .255E+01 5.89| 104.99 38.5 .80E-03 -1.0 -.4

 106.23 1.89 7.38 39.6 .252E+01 5.95| 107.65 38.9 .67E-03 -1.0 -.4

 108.89 1.89 7.43 40.0 .250E+01 6.00| 110.30 39.2 .56E-03 -1.1 -.4

 111.55 1.89 7.47 40.3 .248E+01 6.04| 112.96 39.5 .45E-03 -1.1 -.4

 114.20 1.89 7.51 40.6 .246E+01 6.08| 115.62 39.8 .35E-03 -1.1 -.4

 116.86 1.89 7.55 40.8 .245E+01 6.11| 118.28 40.0 .26E-03 -1.1 -.3

 119.52 1.89 7.59 41.0 .244E+01 6.13| 120.94 40.2 .17E-03 -1.1 -.3

 122.18 1.89 7.62 41.1 .243E+01 6.15| 123.60 40.3 .94E-04 -1.1 -.3

 124.84 1.89 7.65 41.2 .243E+01 6.16| 126.26 40.3 .23E-04 -1.1 -.3

 125.90 1.89 7.66 41.2 .243E+01 6.15| 127.32 40.3 -.35E-05 -1.1 -.3

 Terminal level in stratified ambient has been reached. PROGRAM STOPS!

 ----------------------------------------------------------------------------

 END OF CORJET PREDICTION: Total number of integration steps = 475

 JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ

 Note: CORJET has been used outside the CORMIX system, assuming unlimited

 receiving water. Carefully examine all results for possible boundary

 effects due to surface, bottom, or lateral boundaries!
145

The CORJET program when called within discharge has a diameter of 3 m and an exit

the normal CORMIX installation after its execution velocity of 10 m/s. A discharge concentration of

automatically links to the graphics package 100 % exists for a fairly rapidly decaying

CMXGRAPH so the user can inspect the substance with a decay rate of 1 per 10 min or

predicted plume, rather than looking at the output 0.0028 /s.

file. Many graphics options (see Section 5.3)

exist to fully evaluate the plume geometry and Typical measurements, for example using

concentration distributions. Three examples of a tracked rising balloon, give the distribution of

graphics output are shown in Figures E.2 and E.3. temperature and wind velocity as a function of

Figure E.2 shows the plan view, side view, CORJET data preparation checklist given as

and side view along the trajectory, respectively, of Figure E.4. Density data is specified in this case

the plume, all with a plot scale fixed to 1:1, i.e. as air temperature, the program will convert

undistorted. All these figures have been density inputs internally to potential density as a

produced with the Postscript-file print option (I) of function of temperature. The wind velocity vector

CMXGRAPH (in contrast to all the figures in with increasing height deviates increasingly from

Appendices B to D that were made with the the direction at ground level. In this example the

screen print (C) option). Such an undistorted is coordinate system has been set at ground level

always preferable for the viewer of such plots in so that the chimney (i.e.“port”) height is equal to

order to get an unbiased picture of the mixing 40 m.

pattern. Note the merging of the individual jets in

the plan view. Figure E.3 gives the concentration Table E.3 shows the input data file for this

distribution along the plume centerline trajectory, case, while Table E.4 is the CORJET prediction

showing the rapid drop-off in this jet mixing file. The file echoes the input data, but also lists

process. the potential density values, and all important

E.2 Smoke plume in stratified atmosphere

with skewed wind velocity

As mentioned in Section 6.1 CORJET is

also applicable for atmospheric conditions in

which case the concept of potential density based

on the perfect gas equation with adiabatic

conditions is employed. Furthermore, the wind

conditions in the lower atmospheric boundary

layer with its greater freedom laterally often has a

skewed velocity distribution with different wind

directions at different levels above the ground.

This is the topic of this case study. 

An industrial chimney with a height of 40

m above ground discharges hot gases at a

temperature of 200 C into the atmosphere. The o

height above the ground. This is shown in the

parameters and non-dimensional numbers. 

Predicted plume properties are shown

graphically as Figures E.5 and E.6. Figure E.5

shows the plan view and the side view,

respectively, of the plume, both with a plot scale

fixed to 1:1, i.e. undistorted. The plan view shows

that the plume follows the variable direction of the

wind as it rises to higher levels. 

Figure E.6 gives the concentration

distribution along the plume centerline trajectory.

The added effect of plume decay would be

discernible only in the detailed output file (Table

E.4) where the centerline concentration is not

merely the inverse of the hydrodynamic centerline

dilution (the effect of pure mixing) but lower

because of the internal chemical decay effect.
146

Figure E.2: CORJET prediction for multiport diffuser discharge into stratified coastal waters as plotted

with graphics package. a) Plan view, b) side view, and c) side view along trajectory both with plot scale

fixed at 1:1 (undistorted).
147

Figure E.3: CORJET prediction for multiport diffuser discharge into stratified coastal waters as plotted

with graphics package. Concentration along centerline trajectory.

149

Table E.3

CORJET input data file for chimney discharge into stratified atmosphere 

with skewed wind

#CORJET INPUT FILE

#Title line (50 characters max.):

Case3: CHIMNEY, STRATIFIED AIR, VARIABLE WIND

#Fluid (1=water,2=air), Density option (1=calculate,2=specify directly):

#Fluid (1/2): Density option (1/2): Ambient levels (1-10): 

2 1 4

#Ambient conditions (if d.o.=1, fill in TA+SA; if 2, fill in RHOA):

#Level ZA TA SA RHOA UA TAUA

1 0. 12.0 2.0 0.

2 50. 12.0 5.0 15.

3 100. 12.5 6.0 25

4 200. 13.0 6.5 30.

#Discharge conditions (T0+S0, or RHO0 as above; if NOPEN=1: set LD=0,ALIGN=0):

#NOPEN D0 H0 U0 THETA0 SIGMA0 C0 KD T0 S0 RHO0 LD ALIGN

1 3.0 40. 10.0 90. 0. 100. .0028 200. 0. 0.

#Program control:

#ZMAX ZMIN DISMAX NPRINT

200. 0. 1000. 30

Table E.4

CORJET prediction file for chimney discharge into stratified atmosphere 

with skewed wind

 CORJET PREDICTION FILE:

 JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ

 CORJET: CORNELL BUOYANT JET INTEGRAL MODEL Version 4.1, April 1996

 ----------------------------------------------------------------------------

 FILE NAME: post\cj\case3air.OUT 

 Label/identifier: Case3: CHIMNEY, STRATIFIED AIR, VARIABLE WIND 

 Time of CORJET run: 4/13/96--16:12:15

 Ambient conditions: No. of levels: 4 Fluid: Air Density option: 1

 LEV ZA TA SA RHOA UA TAUA

 1 .00 12.00 .00 1.24 2.00 .00

 2 50.00 12.00 .00 1.24 5.00 15.00

 3 100.00 12.50 .00 1.24 6.00 25.00

 4 200.00 13.00 .00 1.23 6.50 30.00

 

 Discharge conditions (metric): SINGLE PORT

 D0 H0 U0 THETA0 SIGMA0 C0 KD T0 S0 RHO0

 3.000 40.00 10.00 90.00 .00 .10E+03 .28E-0 200.0 .0 .75

 Program control:

 ZMAX ZMIN DISMAX NPRINT

 200.00 .00 1000.00 30

 

 Flux variables (based on ambient at discharge level):

 Q0 = .707E+02 M0 = .707E+03 J0 = .275E+03 GP0 = .390E+01

 QT0 = .133E+05 QS0 = .000E+00

 

 Length scales (m) and parameters: 

 LQ = 2.66 LM = 8.26 Lm = 6.04 Lb = 3.23

 Lmp = 11.97 Lbp = 14.42

 FR0 = 2.92 R = 2.27

 Zone of flow establishment (m): 

 LE = .00 XE = .00 YE = .00 ZE = 40.00

 THETAE= 41.69 SIGMAE= 12.00 GAMMAE= 41.69

 ----------------------------------------------------------------------------

 CORJET PREDICTION: Stepsize = .6042 Printout every 30 steps

 Single jet/plume:

 X Y Z Sc Cc B | DIST Save Gpc dTc dSALc

 .00 .00 40.00 1.0 .100E+03 1.50| .00 1.0 .39E+01188.0 .0

 .00 .00 40.00 1.0 .100E+03 1.50| .00 1.4 .41E+01204.4 .0

 15.18 3.42 49.21 4.5 .221E+02 3.53| 18.13 6.6 .12E+01 41.6 .0

 31.38 7.54 56.20 9.6 .104E+02 5.18| 36.25 13.8 .63E+00 19.5 .0

 47.86 12.09 62.22 15.8 .634E+01 6.64| 54.38 22.5 .39E+00 11.8 .0

 64.47 16.97 67.60 22.7 .440E+01 7.96| 72.51 32.2 .27E+00 8.1 .0
150

 81.13 22.13 72.51 30.3 .330E+01 9.18| 90.64 42.8 .20E+00 6.0 .0

 97.83 27.54 77.06 38.4 .260E+01 10.30| 108.76 54.0 .16E+00 4.7 .0

 114.52 33.18 81.30 47.0 .213E+01 11.36| 126.89 65.8 .13E+00 3.8 .0

 131.21 39.03 85.29 55.9 .179E+01 12.35| 145.02 78.1 .11E+00 3.1 .0

 147.88 45.08 89.05 65.1 .154E+01 13.29| 163.15 90.7 .90E-01 2.6 .0

 164.52 51.31 92.63 74.5 .134E+01 14.18| 181.27 103.7 .77E-01 2.3 .0

 181.14 57.72 96.03 84.2 .119E+01 15.02| 199.40 116.9 .67E-01 2.0 .0

 197.71 64.29 99.27 94.0 .106E+01 15.83| 217.53 130.4 .58E-01 1.7 .0

 214.26 71.02 102.38 103.9 .963E+00 16.60| 235.66 144.1 .52E-01 1.5 .0

 230.77 77.88 105.37 113.8 .879E+00 17.35| 253.78 157.8 .47E-01 1.4 .0

 247.25 84.85 108.25 123.7 .808E+00 18.06| 271.91 171.7 .42E-01 1.2 .0

 263.71 91.92 111.04 133.8 .747E+00 18.75| 290.04 185.6 .39E-01 1.1 .0

 280.14 99.07 113.75 143.9 .695E+00 19.42| 308.17 199.6 .35E-01 1.0 .0

 296.56 106.30 116.39 154.1 .649E+00 20.07| 326.29 213.7 .32E-01 .9 .0

 312.96 113.58 118.96 164.4 .608E+00 20.71| 344.42 228.0 .30E-01 .9 .0

 329.34 120.93 121.47 174.7 .572E+00 21.33| 362.55 242.3 .27E-01 .8 .0

 345.70 128.34 123.91 185.1 .540E+00 21.93| 380.67 256.7 .25E-01 .7 .0

 362.05 135.79 126.30 195.6 .511E+00 22.52| 398.80 271.1 .23E-01 .7 .0

 378.39 143.29 128.64 206.1 .485E+00 23.10| 416.93 285.7 .22E-01 .6 .0

 394.72 150.83 130.92 216.6 .462E+00 23.66| 435.06 300.2 .20E-01 .6 .0

 411.03 158.41 133.16 227.2 .440E+00 24.21| 453.18 314.8 .19E-01 .5 .0

 427.33 166.03 135.35 237.8 .421E+00 24.75| 471.31 329.5 .17E-01 .5 .0

 443.62 173.69 137.49 248.4 .403E+00 25.28| 489.44 344.1 .16E-01 .5 .0

 459.90 181.39 139.58 259.0 .386E+00 25.80| 507.57 358.8 .15E-01 .4 .0

 476.17 189.11 141.64 269.6 .371E+00 26.31| 525.69 373.5 .14E-01 .4 .0

 492.43 196.87 143.65 280.3 .357E+00 26.80| 543.82 388.1 .13E-01 .4 .0

 508.68 204.66 145.62 290.9 .344E+00 27.29| 561.95 402.7 .12E-01 .3 .0

 524.92 212.48 147.54 301.4 .332E+00 27.76| 580.08 417.3 .11E-01 .3 .0

 541.15 220.33 149.43 312.0 .321E+00 28.23| 598.20 431.9 .10E-01 .3 .0

 557.37 228.20 151.28 322.5 .310E+00 28.68| 616.33 446.4 .95E-02 .3 .0

 573.58 236.11 153.10 333.0 .300E+00 29.13| 634.46 460.9 .88E-02 .3 .0

 589.79 244.03 154.87 343.5 .291E+00 29.57| 652.59 475.2 .81E-02 .2 .0

 605.98 251.98 156.61 353.8 .283E+00 30.00| 670.71 489.6 .74E-02 .2 .0

 622.17 259.96 158.31 364.2 .275E+00 30.42| 688.84 503.8 .68E-02 .2 .0

 638.36 267.96 159.98 374.4 .267E+00 30.83| 706.97 517.9 .63E-02 .2 .0

 654.53 275.98 161.61 384.6 .260E+00 31.23| 725.09 532.0 .57E-02 .2 .0

 670.69 284.03 163.21 394.8 .253E+00 31.62| 743.22 545.9 .52E-02 .2 .0

 686.85 292.09 164.77 404.8 .247E+00 32.01| 761.35 559.7 .47E-02 .1 .0

 703.01 300.18 166.30 414.8 .241E+00 32.39| 779.48 573.4 .42E-02 .1 .0

 719.15 308.28 167.79 424.6 .235E+00 32.76| 797.60 587.0 .38E-02 .1 .0

 735.29 316.41 169.25 434.4 .230E+00 33.12| 815.73 600.4 .34E-02 .1 .0

 751.42 324.56 170.68 444.1 .225E+00 33.47| 833.86 613.8 .30E-02 .1 .0

 767.54 332.72 172.08 453.6 .220E+00 33.82| 851.99 626.9 .26E-02 .1 .0

 783.66 340.90 173.44 463.1 .216E+00 34.16| 870.11 639.9 .22E-02 .1 .0

 799.77 349.10 174.77 472.5 .212E+00 34.49| 888.24 652.8 .18E-02 .1 .0

 815.88 357.32 176.07 481.7 .208E+00 34.81| 906.37 665.5 .15E-02 .0 .0

 831.98 365.55 177.34 490.8 .204E+00 35.13| 924.50 678.0 .12E-02 .0 .0

 848.07 373.80 178.57 499.8 .200E+00 35.43| 942.62 690.3 .87E-03 .0 .0

 864.16 382.07 179.78 508.6 .197E+00 35.73| 960.75 702.5 .57E-03 .0 .0

 880.24 390.35 180.95 517.4 .193E+00 36.03| 978.88 714.5 .29E-03 .0 .0

 896.32 398.65 182.09 525.9 .190E+00 36.31| 997.01 726.2 .15E-04 .0 .0

 897.39 399.20 182.17 526.5 .190E+00 36.33| 998.21 727.0 -.19E-05 .0 .0

 Terminal level in stratified ambient has been reached. PROGRAM STOPS!

 ----------------------------------------------------------------------------

 END OF CORJET PREDICTION: Total number of integration steps = 1653

 JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ
151

Figure E.5: CORJET prediction for chimney discharge into stratified atmosphere with skewed wind

profile as plotted with graphics package. a) Plan view, and b) side view along trajectory both with plot

scale fixed at 1:1 (undistorted).
152

Figure E.6: CORJET prediction for chimney discharge into stratified atmosphere with skewed wind

profile as plotted with graphics package. Concentration along centerline trajectory.