NOAA Technical Memorandum GLERL-148

Final Report: Computational Modeling of Ballast 

Water Tanks to Improve Understanding and Maximize 

Effectiveness of Management Practices and Treatment 

Mechanisms. Phase II -- Extension of Laboratory Study

Peter A. Chang III1

, Wesley Wilson1, Jason Carneal1, Paisan Atsavapranee1, 

Stephan Verosto1, David F. Reid2, and Philip T. Jenkins3

1

Naval Surface Warfare Center-Carderock Division, West Bethesda, MD

2

NOAA, Great Lakes Environmental Research Laboratory, Ann Arbor, MI

3

Philip T. Jenkins and Associates, LTD, Fonthill, ON, Canada

September 2009

UNITED STATES

DEPARTMENT OF COMMERCE

Gary Locke

Secretary

NATIONAL OCEANIC AND

ATMOSPHERIC ADMINISTRATION

Jane Lubchenco

Under Secretary for Oceans & Atmosphere

NOAA Administrator
NOTICE

Mention of a commercial company or product does not constitute an endorsement 

by the NOAA. Use of information from this publication concerning proprietary 

products or the tests of such products for publicity or advertising purposes is not 

authorized. This is GLERL Contribution No. 1532.

This publication is available as a PDF file and can be downloaded from GLERL’s 

web site: www.glerl.noaa.gov. Hard copies can be requested from GLERL

Information Services, 4840 S. State Rd., Ann Arbor, MI 48108.

pubs.glerl@noaa.gov.

NOAA’s Mission – To understand and predict changes in Earth’s environment 

and conserve and manage coastal and marine resources to meet our nation’s 

economic, social, and environmental needs 

NOAA’s Mission Goals:

•	 Protect, restore and manage the use of coastal and ocean resources through an

ecosystem approach to management.

•	 Understand climate variability and change to enhance society’s ability to plan

and respond.

•	 Serve society’s needs for weather and water information.

•	 Support the Nation’s commerce with information for safe, efficient, and

environmentally sound transportation.

•	 Provide critical support for NOAA’s Mission.

Suggested Citation: Chang, P.A., III, W. Wilson, J. Carneal, P. Atsavaprance, S. Verosto, D.F. Reid, and

P. Jenkins. Final Report: Computational Modeling of Ballast Water Tanks to Improve Understanding and

Maximize Effectiveness of Management Practices and Treatment Mechanisms, Phase II -- Extension

of Laboratory Study. NOAA Technical Memorandum GLERL-148. NOAA Great Lakes Environmental 

Research Laboratory, Ann Arbor, MI and NSWCCD-50-TR-2009/028, Naval Surface Warfare Center 

Carderock Division, West Bethesda, MD, 78 pp. (2009). 

ftp://ftp.glerl.noaa.gov/publications/tech_reports/glerl-148/tm-148.pdf
CONTENTS 

ERRATA......................................................................................................... i 

NOMENCLATURE......................................................................................... ii 

EXECUTIVE SUMMARY .............................................................................. iii 

ABSTRACT .................................................................................................... 1 

ACKNOWLEDGEMENTS.............................................................................. 2 

ADMINISTRATIVE INFORMATION........................................................... 3 

INTRODUCTION .......................................................................................... 3 

EXPERIMENTAL METHODOLOGY .......................................................... 7 

 Scaling ........................................................................................................ 7 

 Ballast Water Facility................................................................................ 8 

 Experimental Test Plan and Test Procedure............................................. 9 

 Measurement Techniques and Experimental Setup ................................... 12 

 LIF Setup.............................................................................................. 12 

 Fluorimeter Setup and Calibration....................................................... 13 

 Conductivity sensor setup and calibration ........................................... 13 

 Data Processing.......................................................................................... 15 

 LIF data processing ............................................................................. 15 

 Image Renormalization ........................................................................ 16 

 Volume Fraction and Mixedness ......................................................... 17 

 Spatial and Temporal Filtering ........................................................... 17 

 Fluorimeter data processing ................................................................ 18 

 Conductivity sensor data processing ................................................... 18 

EXPERIMENTAL RESULTS ........................................................................ 19 

 Laser Induced Fluorescence........................................................................ 19 

 General flow features............................................................................ 19 

 Mixedness .................................................................................................. 22 

 Saltwater Volume Fraction - Experimental Data ...................................... 24 

 Fluorimeter Results - Effluent Data ......................................................... 26 

 Conductivity Sensors ................................................................................. 26 

 Discussion Regarding Experiments ........................................................... 27 

COMPUTATIONAL METHODOLOGY ....................................................... 29 

ONE-THIRD SCALE CFD RESULTS .......................................................... 29 

 Exchange Efficiency (EE)........................................................................... 31 

 SW Effluent Volume Fraction (SWEVF) ............................................ 34 
 Saltwater Volume Fraction - Predicted vs. Experiments ..................... 39 

 Mixedness - Predicted vs. Experiments................................................ 43 

 Discussion Regarding Comparison of CFD Predictions to Experimental 

 Results ................................................................................................. 49 

FULL-SCALE CFD SIMULATIONS.............................................................. 50 

 Discussion of Full-Scale Results ................................................................. 56 

SUMMARY AND CONCLUSIONS ................................................................ 58 

APPENDIX A: UNCERTAINTY ANALYSIS................................................ 60 

 LIF Measurements...................................................................................... 60 

 Mixedness and Volume of Fluid Measurements .................................. 60 

REFERENCES................................................................................................ 65 

FIGURES 

1. Drawing of test tank and LIF camera planes. The compartment 

designations are as follows: lower left: DB1, upper left: DB2, lower 

right: HST1, upper right: HST2................................................................. 8 

2. CAD rendering and photographs of the modified ballast water facility 

at NSWCCD............................................................................................... 9 

3. LIF experimental setup .............................................................................. 12 

4. Fluorimeter setup and calibration curves. Ordinate is fluorimeter 

voltage (lower curve) or power (upper curve)............................................ 14 

5. Conductivity sensor setup and calibration curves. Ordinate is voltage ..... 15 

6. Example LIF raw data image from Camera 3 for Condition 2 .................. 16 

7. Mixedness as a function of MgSO4 volume fraction................................... 17 

8. Example raw fluorimeter data for Condition 1 .......................................... 18 

9. Mixing layers in the LIF raw data at t* = 0.5. Mixing layers are the 

lighter gray regions..................................................................................... 19 

10. Jet exiting the manhole (left side of each figure) for each test 

condition at t* = 1..................................................................................... 20 

11. Jet impingement on side of HST1 for each condition. Flow enters 

from top left corner of each figure. ........................................................... 21 

12. Hideout for (left) Condition 1 (center), Condition 2 and (right) 

Condition 3................................................................................................. 22 

13. Experimental mixedness results for all conditions (a) Camera 1, (b) 

Camera 2, (c) Camera 3 and (d) Camera 4. The ordinate is 

mixedness and the abscissa is non-dimensional time, t*............................ 23 

14. Experimental SWVF time histories for all conditions, from (a) 

Camera 1, (b) Camera 2, (c) Camera 3, and (d) Camera 4. The 

ordinate is SWVF and the abscissa is non-dimensional time, t* ............... 25 
15. Experimental SWEVF (ordinate) as function of non-dimensional 

time, t*, for all conditions.......................................................................... 26 

16. Conductivity sensor measurements of MgSO4 concentration..................... 27 

17. Grid details for 1/3-scale model ................................................................. 30 

18. Three-dimensional views of 1/3-scale tank showing contours of 

SWVF from CFD simulations of Condition 1; from upper left, 

proceeding clockwise: t*=0.086, 1, 2 and 3. Blue represents SW, red 

is FW.......................................................................................................... 30 

19. Three-dimensional views of 1/3-scale tank showing contours of 

SWVF from CFD simulations of Condition 2; from upper left, 

proceeding clockwise: t*=0.086, 1, 2 and 3. Blue represents SW, red 

is FW.......................................................................................................... 31 

20. Three-dimensional views of 1/3-scale tank showing contours of 

SWVF from CFD simulations of Condition 3; from upper left, 

proceeding clockwise: t*=0.086, 1, 2 and 3. Blue represents SW, red 

is FW.......................................................................................................... 32 

21. Predicted and measured EE (ordinate) for test conditions 1, 2, and 3...... 33 

22. EE (ordinate) from experiments (left) and predicted by CFD (right) 

for all test conditions.................................................................................. 35 

23. SWEVF (ordinate) time histories comparing experiment and CFD 

predicted values; (a) Condition 1, (b) Condition 2 and (c) Condition 

3.................................................................................................................. 36 

24. SWEVF (ordinate) time histories for all test conditions; (a) from 

experiment and (b) predicted by CFD....................................................... 38 

25. Area-averaged experimental and CFD SWVF time histories 

(logarithmically scaled) for Condition 1; (a) Camera 1, (b) Camera 2 

and (c) Camera 3 ....................................................................................... 41 

26. Area-averaged experimental and CFD SWVF time histories 

(logarithmically scaled) for Condition 2; (a) Camera 1, (b) Camera 2 

(c), Camera 3 and (d) Camera 4................................................................ 42 

27. Area-averaged experimental and CFD SWVF (ordinate) time 

histories for Condition 3; (a) Camera 1, (b) Camera 2 , (c) Camera 3 

and (d) Camera 4....................................................................................... 44 

28. Area-averaged experimental and CFD mixedness time histories for 

Condition 1; (a) Camera 1, (b) Camera 2, (c) Camera 3 and (d) 

Camera 4.................................................................................................... 45 

29. Area-averaged experimental and CFD mixedness time histories for 

Condition 2; (a) Camera 1, (b) Camera 2, (c) Camera 3, and (d) 

Camera 4.................................................................................................... 46 

30. Area-averaged experimental and CFD mixedness time histories for 

Condition 3; (a) Camera 1, (b) Camera 2, (c) Camera 3 and (d) 

Camera 4.................................................................................................... 47 

31. Area-averaged experimental and CFD mixedness (ordinate) time 

histories for all conditions .......................................................................... 48 
32. Drawing of bulk carrier tank. Three tanks are shown: lower left: 

double bottom tank (DBT); lower right: hopper tank (HT) and 

upper: topside tank (TT) ........................................................................... 51 

33. Inlet bay detail for full-scale tank. ............................................................. 52 

34. Full-scale SWVF contours at t* = 0.016 (60secs); left: with stringers 

and right: without stringers ....................................................................... 54 

35. EE time history for full-scale tank showing theoretical perfect mixing 

and plug flow filling lines ........................................................................... 54 

36. SWEVF time history for full-scale simulations showing theoretical 

perfect mixing and plug flow filling curves ................................................ 56 

TABLES 

1. Experimental test plan............................................................................... 10 

2. Correspondence between non-dimensional time, t*, and dimensional 

time in secs, for the three test conditions .................................................. 10 

3. Alcohol solution preparation ...................................................................... 11 

4. MgSO4 solution preparation ....................................................................... 12 

5. SWEVF at selected times during exchange, comparing CFD and 

experimental values.................................................................................... 37 

6. Comparison of EE and SWEVF predicted with CFD................................ 39 

7. Full scale tank dimensions ......................................................................... 50 

8. Computational details for 1/3-scale and full-scale simulations.................. 53 

9. Exchange efficiencies (full-scale), calculated from CFD simulation 

data ............................................................................................................ 55 

10. Bias error sources for measured intensity for a single pixel ....................... 62 

11. Bias error sources for measured intensity for a single pixel ....................... 62 

12. Relative uncertainties for LIF measurement regions.................................. 63 
ERRATA 

 

Technical errors identified in this document will be documented and corrected 

here. This section will be updated as appropriate in the on-line version of this 

Technical Memorandum. 

(09-2009) Pages 50 and 51: Table 7 and Figure 32 both erroneously label the 

hopper side tank (HST) and the wing tank (WT) as “HT” and “TT” (topside tank) 

respectively. 

i 
NOMENCLATURE 

B tank beam, m 

H tank height, m 

L tank length, m 

Q flow rate, m3

/sec 

T temperature, o

C 

v volume fraction 

Vo tank volume, m3

D density, kg/m3

F standard deviation 

ABBREVIATIONS 

BrW brackish water 

BWE ballast water exchange 

CFD computational fluid dynamics 

DBT double bottom tank 

EE exchange efficiency 

FPS frames per second 

FW fresh water 

FS full scale 

GLERL Great Lakes Environmental Research 

Laboratory 

HST hopper side tank 

LIF laser-induced fluorescence 

MH manhole 

NOAA National Oceanic and Atmospheric 

Administration 

NSWCCD Naval Surface Warfare Center - 

Carderock Division 

SW saltwater 

SWEVF saltwater effluent volume fraction (volume fraction of SW in the effluent at the 

tank outlet pipe) 

SWVF saltwater volume fraction (at locations 

within the tank) 

TVE tank volumes exchanged 

VF volume fraction 

V&V verification and validation 

ii 
Final Report: Computational Modeling of Ballast Water Tanks to Improve 

Understanding and Maximize Effectiveness of Management Practices and 

Treatment Mechanisms, Phase II -- Extension of Laboratory Study 

September 2009 

 

P.A. Chang III, W. Wilson, J. Carneal, P. Atsavapranee, S. Verosto, 

D.F. Reid, and P.T. Jenkins 

 

EXECUTIVE SUMMARY 

INTRODUCTION 

Mid-ocean ballast water exchange (BWE) is presently the primary 

management practice with widespread acceptance for reducing or preventing 

the spread of nonindigenous aquatic species via ballast water. Attempts to 

determine the efficiency of BWE via on-board experiments have generally 

produced inconsistent and unreliable results. Such experiments are labor 

intensive and difficult to run, so reproducibility is difficult to demonstrate for 

the same ship and tank structure. In addition, on-board experiments involving 

flow-through exchange generally relied on measurements taken at the overflow 

outlet of the tank, which may not represent the actual volume mixture that 

remains in the ballast tank. Given the complex structural nature of ballast 

tanks and the difficulty of obtaining direct experimental verification from inside 

ballast tanks, development of a computer-based model of the flow and mixing 

dynamics in ballast tanks during flow-through exchange can provide several 

advantages over on-board experimental approaches, and can also help interpret 

such experimental results. The NOAA Ballast Water Technology 

Demonstration Program provided funding for GLERL and NSWCCD to design 

and build a 1/3-scale model BWE facility and to develop a computational 

model for predicting BWE efficacy. In Phase I of this effort, documented in 

Wilson et al.1

 a 1/3-scale physical model facility was built at NSWCCD. 

In this report the (physical) scale-model experimental setup and 

measurement techniques used in Phases I and II of this project are described. 

Then, the results and the two-fluid physics that were observed during the entire 

3-TVE are shown. In the CFD section the methodology is described followed 

by comparisons of the CFD predictions with the measured quantities from the 

 

1

 Wesley Wilson, Peter A. Chang, Stephan Verosto, Paisan Atsavapranee, David Reid, and Phil 

Jenkins. Computational and experimental analysis of ballast water exchange. In Maritime 

Environmental Engineering Symposium (MEETS 2006), Crystal City, VA, 2006. ASNE. 

iii 
physical scale-model experiments. Additionally, full-scale simulations are 

documented and an Appendix shows the uncertainty analysis. 

EXPERIMENTAL METHODOLOGY 

In Phase I of this program, 1/3-scale model experiments were performed at 

a single flow rate and maximum density difference (freshwater ballast vs. 

influent seawater) for a single tank-volume-exchange (TVE). Also in Phase I 

the detailed CFD studies necessary for maximizing the accuracy while 

minimizing the run times of the computational model were performed. For 

Phase II, the capacity of the facility was increased to allow experiments over 

three-TVE and three different exchange conditions were tested: 1) 3-TVE 

BWE with saltwater (salinity = 35) being pumped at 4.1 l/sec (65 gpm, equal 

to 1,012 gpm equivalent flow rate at full scale) into a ballast tank filled with 

freshwater; 2) saltwater (salinity = 35) being pumped into a ballast tank filled 

with brackish water (salinity = 20) at the same flow rate; and 3) saltwater 

(salinity = 35) being pumped into a ballast tank filled with brackish water 

(salinity = 20) at 6.9 l/sec (110 gpm, equal to 1,700 gpm equivalent flow-rate 

at full scale). 

Laser-induced fluorescence (LIF) was used to capture planar images of flow 

and mixing in the up to four regions of interest during each experimental run. 

LIF images were analyzed to calculate volume fraction (the relative amount of 

saltwater at each pixel location) and mixedness (the amount of mixing at each 

pixel or averaged over each data plane) within the imaged regions for 

comparison against CFD model simulations of the same conditions. In 

addition, a fluorimeter was positioned in a horizontal section of the model’s 

outlet piping to record the two-fluid composition of the outflow over time. This 

mimics the location where samples used to calculate exchange efficiency (EE) 

have been taken during on-board flow-through exchange experiments. 

EXPERIMENTAL RESULTS (SCALE MODEL BWE EXPERIMENTS) 

The raw LIF images showed turbulent structures, areas of hideout, and the 

level of mixing within the planar areas imaged. Examples are provided and the 

features represented are discussed, along with a qualitative assessment of how 

changing the density and flow rate changed the observed flow and mixing 

dynamics. Graphs of the mixedness function and the saltwater volume fraction 

(SWVF) at each LIF image plane in the experimental tank versus time (TVE), 

and the saltwater effluent volume fraction (SWEVF) measured by the 

fluorimeter in the outlet pipe for each experimental condition are presented and 

interpreted. The LIF data show that a decrease in density difference between 

iv 
the original ballast water and the exchanging saltwater allows increased mixing 

throughout the ballast tank. Increases in inlet flow rate also increase the 

amount of mixing throughout the tank. Increases in density difference between 

the original fluid and the incoming exchange fluid can lead to increasing 

hideout of original fluid if the incoming flow does not have sufficient 

momentum to scour the pockets of trapped fluid from the tank tops. The 

effluent time histories suggest that exchanging fluids with large differences in 

density approaches the behavior of plug flow, whereas fluids of closer density 

approach a pure mixing condition as density difference is decreased and flow 

rate is increased. 

COMPUTATIONAL METHODOLOGY 

CFD simulations were performed using the commercial viscous flow solver, 

Fluent (developed by Ansys, Inc.). The setup of the code parameters and 

model grid structure is described and discussed. 

ONE-THIRD SCALE CFD RESULTS 

Graphical comparisons of the 1/3-scale model experimental data and CFDpredicted values for each of the three test conditions over the full 3-TVE 

exchange, are presented and discussed. 

SWEVF and EE: EE is an integral measure of the volume of the two fluids 

within the tank at a given time and therefore is a reflection of the volume of 

each of the two fluids that exit the tank. CFD values of EE are computed 

directly by a spatial integration of the SWVF over all grid cells within the CFD 

tank model, whereas experimental EE values are computed indirectly as the 

difference between the volume of SW entering the tank and the volume that 

has exited the tank, the latter based on the fluorimeter data (SWEVF) 

collected in the outlet pipe. It is shown that the CFD-predicted EE match the 

expected physical trends: as mixing increases, due to either an increase in flow 

rate or decrease in density difference, the EE at the end of three tank volumes 

increases. The computational predictions fall within the 95% uncertainty 

intervals for the EE computed from experimental data. However, we suggest 

that SWEVF as a basis for estimating EE can be problematic as it does not 

take into account the spatial inhomogeneities that may exist within the tank 

during BWE, and can under-predict the EE early on and over-predict EE 

during the latter stages of BWE. For the case where the density differences are 

small, SWEVF can start to approach EE in the mid- to later stages of an 

exchange. 

v 
SWVF: The saltwater volume fraction (SWVF) averaged over the camera 

data planes from each experiment (Conditions 1-3) over the complete 3-TVE 

exchange and that predicted by CFD are presented graphically and compared 

and interpreted, as are the CFD-predicted vs. experimental Mixedness 

parameter. The comparisons show that the CFD can predict the volume 

fraction (SWVF) quite well implying that the mass movement of the two fluids 

throughout the tank is well-predicted. 

The CFD comparisons of mixedness are on the whole, quite good, 

particularly for conditions 1 and 2, which involve less mixing, but for condition 

3, the mixing is under-predicted. This appears to be due to the highly energetic 

mixing caused by overturning gravity waves and turbulence in the bellmouth 

bay. 

Since the 1/3-scale tank is limited to two bay lengths, we suggest that the 

relative amount of energy available for mixing and scouring in the two adjacent 

bays of the 1/3-scale model is much higher than it will be across the entire fullscale tank with 10 bays. In a full-scale tank the far downstream energy levels 

should approach quiescent, and mixing should approach zero, no matter what 

the flow rate and density difference. 

FULL-SCALE CFD SIMULATIONS 

Full-scale CFD simulations were performed for a complete ballast tank from 

a typical 35,000 dwt handysize bulk carrier. The complete tank consists of 

interconnected double bottom tank (DBT), hopper side tank (HST), and wing 

tank (WT), each segmented into ten bays (27 m total length). The WT is 

connected to the HST via two 20.3 cm (8 in) diameter connection pipes. The 

incoming fluid is pumped into the DBT via a single inlet bellmouth. There are 

two exits that were modeled as flush with the tank top directly above the two 

connection pipes through which the overflow exits the tank during BWE. The 

tank floor openings and stiffeners were modeled based on tank drawings 

provided by Fednav International. The total volume of the tank (with 

longitudinal stringers) is 705 m3 (186,250 gals). The inflow rate was 11.4 

m3

/min (3000 gpm), meaning that a one tank volume exchange takes 62 min 

(real time). The tank is initially full of freshwater and exchanged (flow-through) 

with mid-ocean saltwater giving a density difference equivalent to a salinity 

difference of 35. 

Some previous applications of CFD to ballast tank flow were performed 

without some of the structural detail, especially the longitudinal stringers along 

the bottom and sometimes the top of ballast tanks to for strength. The 

inclusion of the structural detail such as stringers has a significant impact on 

the computational resources and time required to perform such simulations. In 

vi 
order to investigate the influence of stringers on the simulation outcomes, two 

separate representations (grids) were developed for the full-scale tank, one with 

all of the tank structure and one that omits the longitudinal stringers. 

The inclusion of longitudinal stringers in the computational geometry had a 

profound impact on the two-fluid mixing in the tank and on the EE. Without 

stringers the two fluids in the inlet bay are completely mixed, with highly 

mixed fluid regions thereafter quickly dispersing throughout the tank. With the 

stringers the flow is much less mixed, with almost pure SW forming overturning 

waves in the vicinity of the bellmouth and moving along the tank bottom. We 

believe the most important effect is in the stringers ability to restrain mixing in 

the transverse direction. With this limitation, the amount of mixing is 

dramatically reduced and the SWEVF and EE time histories approach that for 

plug flow filling. 

In the full-scale CFD simulations BWE did not reach the required 95% EE 

for the tank configuration and combination used here, but the difference at 3- 

TVE is not statistically different than 95%. It appears that the primary cause 

for loss of EE is trappage of water in the tank tops. However, neither the CFD 

nor the experimental model included the quarter-round vent holes at the top of 

the tank bays in the actual ballast tank. These would allow a small flow of 

water across the tank top toward the exit pipes, and should act to decrease 

possibility of water trappage, and possibly increase the calculated EE. 

SUMMARY AND CONCLUSIONS 

The combined experimental and computational approaches provide new 

insights into the physics of BWE. Significant findings are: 

1. The predicted values of EE fall within the experimental error bands, 

showing that the CFD model has been validated. 

2. Comparisons between CFD and experimental SWEVF and mixedness data 

within the tank show that the CFD predicts these quantities reasonably 

well. One shortcoming is the under-prediction of the amount of mixing with 

a higher flow rate and lower density difference. 

3. The exclusion of the quarter-round vent holes at the top of the tank bays 

might have led to a slight lowering of the calculated EE. However, due to 

size of a full-scale tank, the kinetic energy at the interface and the pressure 

forces pushing the flow through these holes would be very small. 

4. Longitudinal stiffeners (LS) are very effective at decreasing the extent of 

mixing within the inlet bay. With LS the early exchange approaches plug 

flow filling. The latter stages of exchange approach the perfect mixing case, 

vii 
viii 

but the maximum EE is reduced by FW hideout in the tank top. This result 

shows that in a full-scale tank there is insufficient kinetic energy to scour 

water trapped at the tank top (water hideout). 

5. Not including the LS in the CFD model allows nearly homogenous and 

instantaneous mixing to occur across the entire inlet bay. The EE curve 

approaches that for perfect mixing, especially near 3-TVE. 

6. These simulations indicate that if mixing in the inlet bay can be 

substantially reduced, AND the quarter-rounds at the tank tops are effective 

in reducing the water hideout in the tank tops, it may be possible to 

perform a 95% exchange in significantly less than 3-TVs. 

CFD allows examination of a wide range of ballast exchange conditions 

across any tank architecture. It allows evaluation of the effects of various 

parameters and small scale tank architecture on the outcomes of exchange. One 

aspect of ballast water exchange not incorporated into the present model is the 

effects of ship motion on the exchange process - ballast water exchange must be 

conducted on the high seas. Additional work on this application of CFD 

modeling should incorporate equations of motion that account for roll and pitch 

of a moving vessel. 

We conclude that CFD modeling is a very useful approach for investigating 

and understanding ballast tank flow and that use of CFD model-based 

calculations of EE can be a practical alternative to on-board experiments. 

However, appropriate resolution of tank structure and CFD cell grid densities 

must be allowed for maximum benefit. 

APPENDIX A: UNCERTAINTY ANALYSIS 

Appendix A provides an analysis of the uncertainty associated with 

determination of the mixedness parameter and the fluid volume fractions. 

Based on this analysis, the relative uncertainty in the LIF measurements on 

which mixedness and volume fractions of fluids are based is approximately 

0.66% over the whole field, while for a single pixel measurement the relative 

uncertainty approaches 9.84%. Our calculations of mixedness and volume 

fractions of fluids over an entire bay has a very low uncertainty due to the large 

number of points interrogated simultaneously by the LIF technique. It should 

be noted that in future studies the linearity of the LIF (CCD) sensor response 

versus dye concentration should be determined experimentally in order to 

better estimate the error associated with the assumption of linear response. 
Final Report: Computational Modeling of Ballast Water Tanks to Improve 

Understanding and Maximize Effectiveness of Management Practices and 

Treatment Mechanisms, Phase II -- Extension of Laboratory Study 

September 2009 

 

P.A. Chang III, W. Wilson, J. Carneal, P. Atsavapranee, S. Verosto, 

D.F. Reid, and P.T. Jenkins 

 

 

ABSTRACT 

Ballast water exchange (BWE) has been the most common method for 

reducing the transport and discharge of nonindigenous aquatic species 

associated with ballast tanks of ships traveling around the world. To reduce the 

spread of nonindigenous aquatic species, vessels exchange coastal ballast water 

with mid-ocean seawater, aiming for a minimum of 95% volume replacement. 

Measuring the exchange efficiency on board operating ships is extremely 

difficult and subject to large variances. Here we examine the use of 

computational fluid dynamics (CFD) to model ballast tank water flow and 

predict the exchange efficiency (EE). 

In order to compare and validate the model with experimental data, flow 

and exchange experiments were performed with a one-third scale fourcompartment model of section of a bulk carrier ballast tank that includes two 

double-bottom and two hopper side compartments. The experiments were run 

for a full three-tank-volume exchange (3-TVE). In order to mimic the 

conditions of most concern to the North American Great Lakes, the tank was 

initially filled with fresh or brackish (equivalent density) water and the 

incoming (exchanging) fluid was a salt, alcohol, and water mixture adjusted to 

approximate the density of 35 ppt seawater. Experiments were performed with 

two density differences and two flow rates that scale to those typically used in 

ballast water exchange. 

Transient, two-fluid CFD simulations were developed for the one-third scale 

model as well as for a full-scale bulk carrier ballast tank. Data from the fourcompartment 1/3-scale CFD model simulations is compared with the 

experimental data. Comparisons of the data within the tank are quite good. 

CFD predictions of EE show that the CFD can predict the right trends and 

falls within the experimental error bands. Two full-scale CFD simulations were 

run to determine the CFD model’s sensitivity to relatively small structures 

(longitudinal stringers). The results show that these structures are very 

important to the physics of two-fluid mixing and lead to significant changes in 

the EE. 

1 
2 

We conclude that CFD modeling is a very useful approach to understand 

ballast tank flow and that use of CFD model-based calculations of EE could be 

a practical alternative to on-board experiment. 

 

ACKNOWLEDGEMENTS 

This Technical Memorandum is the final report by the NOAA Great Lakes 

Environmental Research Laboratory (Ann Arbor, MI) for a multi-year, multiinstitutional research project to investigate the potential use of computer 

modeling to understand mixing and flow dynamics in commercial ship ballast 

tanks during flow-through ballast water exchange. The project was funded by 

the NOAA Ballast Water Technology Demonstration Program (Dorn Carlson, 

Program Manager). 

Fednav International (Montreal, Quebec, Canada) provided detailed ship 

information and ballast tank blueprints needed for accurate creation of the 

physical and CFD models. 

This document substantially incorporates final project report NSWCCD-50-

TR–2009/028 submitted by the Naval Surface Warfare Center – Carderock 

Division to the NOAA Great Lakes Environmental Research Laboratory in 

fulfillment of Award #01-3WCA90018. 
ADMINISTRATIVE INFORMATION

This was a joint project between the NOAA Great Lakes Environmental Research

Laboratory (Ann Arbor, MI) and the Naval Surface Warfare Center, Carderock Division (West Bethesda, MD). It was sponsored by the NOAA Ballast Water Technology

Demonstration Program (Dr. Dorn Carlson, Program Manager) and carried out at the

Naval Surface Warfare Center — Carderock facilities.

INTRODUCTION

Mid-ocean ballast water exchange (BWE) is presently the primary management

practice with widespread acceptance for reducing or preventing the spread of nonindigenous aquatic species via ballast water. BWE is the process whereby coastal

ballast water, which contains the unwanted organisms, is flushed from the ballast tanks

through the introduction of mid-ocean seawater. One method to achieve this is called

flow-through ballast water exchange and is the subject of this research. Flow-through

BWE is accomplished by overflowing a filled or partially filled ballast tank by pumping

seawater into the tank via the normal ballast intake lines. On most existing ships, seawater enters at the bottom of the tank and displaces and/or dilutes the coastal ballast

water. If perfect mixing is assumed, then 3 tank volumes of seawater are necessary

to achieve a 95% exchange efficiency (EE).7 EE is the proportion of the original tank

water that is replaced by the influent seawater.

While ballast exchange by itself is not the method of choice in the long-term, it is

likely to remain in use until there is both widespread acceptance of specific ballast water

biological discharge standards and widespread availability of more effective, technologybased, treatment approaches that meet those standards. The IMO Convention on

Ballast Water Management1 proposed discharge standards and set a very aggressive

agenda to establish on-board treatment of all ballast water by 2016, but this schedule is

unlikely to be achievable and has already been delayed by a year. No technologies for onboard treatment of ballast water discharge have been verified for routine shipboard use

in U.S. waters, although there are a number of systems in various stages of development

and IMO approval.2 Thus it is likely that BWE will continue in the foreseeable future

as a (or the) primary ballast water management practice with widespread availability

and use. Therefore, it is useful to understand the ballast water exchange process, the

flow dynamics inside a ballast tank during exchange, and how tank architectures affect

the outcome.

Past attempts to determine the efficiency of BWE via on-board experiments have

produced inconsistent and generally unsatisfactory results. Many of the direct on-board

experiments conducted in the past suffered from design and/or implementation deficiencies exacerbated by the complex structure, inaccessibility of typical ballast tanks, and

the fact that experimentalists did not usually have control of the ship (the test platform). These difficulties limited the experimental design and resolution of sampling to

determine exchange effectiveness related to coastal organisms. However, well-planned

and controlled experiments by the Smithsonian Environmental Research Center8 showed

3
that properly conducted BWE can be highly effective at replacing coastal ballast water

with mid-ocean water (88-99% replacement of original water) and flushing out or killing

coastal planktonic organisms (80-95% reduction in concentration) across ship types,

when conducted according to guidelines and regulations. However, such experiments

are labor intensive and difficult to run, so reproducibility is difficult to demonstrate for

the same ship and tank structure. In addition, such on-board experiments generally

rely on measurements taken at the overflow outlet of the tank and may not represent

the volume mixture that remains in the ballast tank. Given the complex structural nature of ballast tanks and the difficulty of obtaining direct experimental verification from

inside ballast tanks, development of a computer-based model of the flow and mixing

dynamics in ballast tanks can provide several advantages over on-board experimental

approaches, and can also help interpret such experimental results.

A successful model, one that has been fully validated and verified, will predict ballast water EE, is portable and can be tailored to different tank types and geometries,

different exchange flow rates, and different initial conditions. There is no need to wait

for another transoceanic voyage to retest or run a test on the same tank under different

conditions. The validated and verified model will provide insight into the flow and

mixing dynamics in the inaccessible recesses of a ballast tank, and can thus identify

hidden areas of the tank that may contain low fluid velocities (commonly referred to

as dead spots), or the occurrence of short-circuiting, where a stream of influent water

moves from inlet to outlet by the most direct route, never mixing throughout the tank.

Identifying and understanding phenomena such as dead spots and short-circuiting provides the basis for developing approaches and improvements to the overall effectiveness

and consistency of the exchange process. A verified model can also be used to test

the effects of modifications to internal tank structures and cutouts. A verified fluid

flow model can be expanded to incorporate modules to examine the behavior of passive

“particles,” such as phytoplankton or sediment, and possibly even active particles, such

as zooplankton. Such models can help understand why ballast water exchange may not

be as efficient for biological exchange as it is for water exchange, and under what conditions this is true, as well as possible solutions. Areas of sediment deposition may also

be identified and proposed modifications to tank structures can be tested using computer modeling prior to making any actual modifications to operational tank design, to

determine if there are ways to decrease sediment deposition and compaction.

An accurate CFD simulation of BWE must incorporate flows through complicated

tank structures that include an inlet bellmouth (the bottom of the inlet pipe is usually

flaired, appearing like an inverted funnel, and is called the bellmouth), longitudinal

stringers, transverse and longitudinal floors, manholes, limber holes and air vent holes.

Longitudinal stringers are the framing found along the tops and bottoms of the tanks.

Floors are the vertical partitions that divide the tank into compartments. Manholes

are openings in the floors that allow for human access and fluid flow between compartments. Limber holes are the smaller 6-inch diameter circular drain holes between the

compartments. Air vents are the very small (100 − 150 mm full scale radius) half- and

quarter-round air vent openings in the top of the tanks to allow passage of air and fluid

4
along the top of the tank. Drain holes are the very small (100 − 150 mm full scale

radius) half- and quarter-round openings in the bottom of the tanks to allow drainage

of fluid along the bottom of the tank.

Accurate CFD simulations also involve the simulation of two fluids, the initial ballast

water and the influent seawater, which, depending on the salinity, may be at different

starting densities. Thus, CFD models must successfully model the displacement of

one fluid by another, and must simulate the mixing of one fluid into another. CFD

efforts have taken a step-by-step approach to solving the problem. The first published

efforts were by Holdo, Armstrong and Rose5 who performed CFD calculations on a

double bottom tank with a simplified geometric arrangement, using steady state singlefluid simulations. They showed where in the tank mixing should occur and where the

flow is stagnant and would resist being flushed out. Kent and Parsons6 used twofluid modeling, performing simulations on J-type ballast tanks with single and dual

outlet ports, and hopper side/upper wing tank ballast tanks. However, while useful,

their results are limited by use of relatively coarse grids, tank geometries that did not

include longitudinal stringers, and the lack of validations with experimental data.

In order to assess the validity of any computational model it is important to validate

it against physical experimental data. While it would be ideal to obtain test data

during full-scale BWE, such experiments are very expensive and access to the interior

ballast tank structure difficult. Although sensors could be placed at various locations

throughout the tank, it would be difficult if not impossible to obtain the data resolution

necessary for understanding the two-fluid flow and mixing physics within the tank.

The NOAA Ballast Water Technology Demonstration Program provided funding for

GLERL and NSWCCD to design and build a model-scale BWE facility and to develop a

computational model for predicting BWE efficacy. In Phase I of this effort, documented

in Wilson et al.,9 a 1/3-scale model facility was built at NSWCCD. The tank models four

bays of a typical bulk-carrier double bottom and side hopper tank and is built to a 1:3

geometric scale. In Phase I the experiments were performed at a flow rate that scales to

1100 gpm full-scale. The most important mixing flows in the vicinity of the bellmouth

are scaled such that the ratio of buoyancy to inertial forces (Richardson number) is

the same at model- and full-scale. Experiments were performed at a single flow rate

and maximum density difference (freshwater ballast vs. influent seawater) for a single

tank-volume-exchange (TVE). Also in Phase I the detailed CFD studies necessary for

maximizing the accuracy while minimizing the run times of the computational model

were performed. These studies included the effects of time-stepping and advectivedifferencing schemes, turbulence modeling and grid refinement. The shortcoming of

Phase I is that it only included the first TVE whereas BWE requirements are based on

a three-TVE. While the most energetic mixing events occur in the first TVE, the second

and third TVE are important because they lead to the final two-fluid configuration at

the end of BWE. The physics of the second- and third-TVE are assumed to be that of

tank top scouring, but really are not clearly understood.

In this report the 1/3-scale model experimental setup and measurement techniques

used in Phases I and II of this project are described. Then, the results and the two5
fluid physics that occur during the entire three-TVE are shown. In the CFD section

the methodology is described followed by comparisons of the CFD predictions with the

measured quantities. Additionally, full-scale simulations are documented and finally

conclusions and recommendations for follow-on work are made. An appendix shows the

uncertainty analysis.

6
EXPERIMENTAL METHODOLOGY

Scaling

Full-scale bulk carrier ballast tanks are on the order of 10’s of meters long, with

exchange rates of up to 3000 gpm. Obviously it is not possible to build such a large

model or obtain such large flow rates and the resulting velocities in a model-scale facility.

However, it may be possible to model correctly some of the most important two-fluid

mixing events. From earlier work with ships compensated fuel/ballast it was discovered

that most of the two-fluid mixing occurs at the inlet jet and inflows through manholes.4

For stratified shear flows, the Richardson number (the ratio between the buoyancy and

inertial forces), is the most important parameter for two-fluid mixing. Low Richardson

numbers imply that the buoyancy force is relatively small and a large amount of mixing

will occur. As Richardson number increases, the flows become increasingly stable and

mixing decreases.3

Equating model- and full-scale Richardson numbers for the radial flow from the

bellmouth along the tank floor, it is possible to show that the volume inflow rates are

related by the 5/2-power of the scale ratio. Using this relationship it is possible to

show that the flows between the longitudinal stiffeners and through the manholes are

Richardson scaled. The scale ratio of 3 was chosen because it would give a tank with

a volume of 1.433 m3 (378 gal), allowing the use of readily available 1.9 m3 (500 gal)

supply and waste tanks for the initial one-TVE experiment.

The Reynolds number is the ratio between inertial and viscous forces and may also be

an important parameter as it gauges the amount of turbulent activity present. For small

Reynolds numbers, the viscous forces dominate and below certain thresholds, dependent

upon geometry, the flow will be laminar. As Reynolds numbers increase the inertial

forces dominate and the flow is susceptible to small disturbances and becomes turbulent.

Turbulent flow is comprised of eddies which will tend to increase the entrainment of

one fluid into the other. The Reynolds number of the inflow jet scales as the 3/2-power

of the scale ratio. A 1/3-scale model would provide a pipe Reynolds number that was

fully turbulent. The Reynolds numbers throughout the tank however, may not be fully

turbulent as the velocity magnitude decreases away from the bellmouth jet —though

this may occur in the full-scale tanks as well. For full-scale tanks the range of Reynolds

numbers between the bellmouth and far reaches of the tanks will be on the order of

106 with flows ranging from highly turbulent near the bellmouth jet to laminar in far

reaches of the tank. In this model scale tank, the Reynolds number at the bellmouth

is much smaller than for full-scale, yet because only four compartments are modeled,

the range of Reynolds number found in the tank will be much less. Therefore, at model

scale there may be a relatively large amount of turbulent activity in the “downstream”

bays that may not occur in full-scale downstream bays. In fact, as the results show,

there is a large amount of tank top scouring that takes place at model scale that may

not actually take place in a full-scale geometry.

7
Ballast Water Facility

The test tank, shown in Figure 1, is a 1/3-scale model of four compartments of a

bulk carrier ballast tank, including two double bottom (abbreviated as DB1 and DB2)

and two hopper side tank (HST1 and HST2) compartments. The tank has features

similar to those found in full-scale tanks, including the bellmouth, the longitudinal

stringers along the top and bottom of the tank, the transverse and longitudinal floors,

manholes, limber holes and the exit pipe. Thus, the test tank contains all the structural

features found in full-scale tanks and therefore, would have many of the same types of

flow features. The test tank does not have air vent or drain hole openings in the tops

and bottoms of the tanks, respectively.

Figure 1. Drawing of test tank and LIF camera planes. The compartment

designations are as follows: lower left: DB1, upper left: DB2,

lower right: HST1, upper right: HST2.

The test tank was constructed of 1.905 cm (3/4 in) thick acrylic and has a capacity

of approximately 1.433 m3 (378 gals). This is the same test tank used for CFD Phase I,

which allowed only one-TVE experiments. For Phase II, the capacity of the facility was

increased to allow experiments over three-TVE. The modified facility has two 3.8 m3

(1000 gal) supply tanks, one 1.9 m3 (500 gal) premix tank, and two 1.9 m3 (500 gal)

waste tanks, providing sufficient capacity for three-TVE experiments. The two 3.8 m3

(1000 gal) supply tanks supply the 12.6 #/sec (200 gpm) centrifugal pump through

5.08 cm (2 in) tank outlets combined through a (5.08 cm × 7.62 cm × 5.08 cm) (2 in ×

3 in×2 in) tee. This unique configuration provides for a more even pump suction head

allowing more precise flow control. The pump discharge is regulated by a 7.62 cm (3 in)

diaphragm valve. The facility is plumbed primarily with the 7.62 cm (3 in), Schedule

8
80, PVC pipe with a 6.99 cm (2.75 in) inner diameter, which scales satisfactorily for

the actual 20.3 cm (8 in) tank feeder pipes of a full-scale tank.∗ “Quick” disconnects

and flexible hoses allow for relatively easy change outs of plumbing components. A

schematic of the test facility is shown in Figure 2. Flow rates are measured using a

vortex shedding flowmeter equipped with local indication and 4 − 20 mA output for

data recording. It has an accuracy of ±1% flow and a repeatability of 0.2%.

Figure 2. CAD rendering and photographs of the modified ballast water

facility at NSWCCD.

Experimental Test Plan and Test Procedure

In order to provide a comprehensive dataset for CFD validation, experiments were

performed at a variety of flow rates and conditions as listed in Table 1. The experiments

performed during the course of this work were intended to study the dynamics of ballast

water exchange between two fluids of varying density in a model scale environment.

∗At full scale, the 20.3 cm (8 in) diameter tank feeder pipes are fed by main feeder pipes with a

diameter of 30 cm (12 in)

9
Since the utilization of true ocean water was impractical, a solution of magnesium

sulfate (MgSO4) was used to simulate seawater with a density equivalent to salinity =

35 in order to simplify the water preparation procedure and provide a stably stratified

fluid interface. In order to match the index of refraction of the MgSO4 solution and

provide the desired density differences, ethanol was added to the freshwater that initially

filled the tank.

A total of three conditions were tested. Condition 1 simulated a ballast water

exchange process with 35 parts-per-thousand (ppt) saltwater being into pumped into a

tank full of freshwater at a flow rate of 4.1 #/sec (65 gpm model scale = 1, 012 gpm

full scale). This is the flow rate used in the Phase I work documented in Wilson

et al.9 Condition 2 simulates a ballast water exchange with salinity = 35 saltwater

being pumped into a tank full of salinity = 20 brackish water at the same flow rate.

In condition 3, the flow rate was increased to 6.9 #/sec (110 gpm) for the saltwater

(salinity = 35) to brackish (salinity = 20) water exchange, which corresponds to a full

scale flow rate of 1700 gpm. The correspondence between the non-dimensional times

and the times in seconds are listed in Table 2.

Table 1. Experimental test plan.

Condition Q (gpm) Target∆ ρ ρM gSO4 ρEthanol n Sim’d Exchange

1 65 0.025 1.014 0.989 1.3361 SW to FW

2 65 0.010 1.005 0.995 1.3343 SW to BrW

3 110 0.010 1.005 0.995 1.3343 SW to BrW

Table 2. Correspondence between non-dimensional time, t

∗, and dimensional time in secs, for the three test conditions.

t

∗ Condition

1 2 3

0.02 7.0 7.0 3.5

0.05 17.4 17.4 8.7

0.086 30.0 30.0 15.0

0.1 35 35 17

0.2 70 70 35

0.5 174 174 87

1 349 349 174

2 698 698 349

3 1047 1047 523

The waste and supply tanks, supply and waste lines, and the ballast tank model

were all cleaned thoroughly prior to experimentation. The 1.9 m3 (500 gal) supply tank

10
for the alcohol and two 1.9 m3 (500 gal) waste tanks were filled with water through a

5 μm filter. MgSO4 (“salt”) was added to the water in the two waste tanks with the

mixers engaged to ensure a homogenous solution. The saltwater tanks were iterated

independently to the desired test condition as listed in Table 1 by adding incremental

amounts of salt and testing the density and index of refraction between iterations. The

saltwater preparation process was repeated for the second 3.8 m3 (1000 gal) supply

tank. Once the 3.8 m3 (1000 gal) supply tanks were filled with the salt solution, both

the fresh- and salt-water were left overnight to de-gas. The next morning, alcohol was

added to the freshwater supply tank and iterated to produce the desired density and

index of refraction as listed in Table 1. Ice was added to the freshwater supply tank to

match the temperature of the saltwater. Sample alcohol and MgSO4 solution iterations

from the Condition 1 test are shown in Table 3 and Table 4.

Once the indices of refraction were matched at the desired density difference, Rhodamine6G dye was added to the freshwater and the tank was thoroughly stirred to ensure

proper mixing of the dye. The scale-model ballast tank was then initially filled with

dyed freshwater from the 1.9 m3 (500 gal) supply tank. The saltwater was pumped in

recirculation mode until the desired flow rate was obtained and the test was ready to

start. To initiate the test, the model valve was opened simultaneously with the closing

of the recirculation valve, and the salt solution was introduced into the test tank. Data

was collected until three TVE had occurred [approximately 4.3 m3 (1136 gals)]. For the

4.1 #/sec (65 gpm) and 6.9 liter/sec (110 gpm) cases, this translated to approximately

17.5 mins and 10.4 mins, respectively. During the course of the data acquisition, the

actual flow rate was manually read every thirty seconds to confirm uniform and steady

flow during the experiment. After data acquisition was completed, the pump was shut

down and the model was drained. The model was then filled with pure salt solution,

and dark images were taken of the solution with no dye for data processing purposes.

The test procedure was repeated for each condition listed in Table 1.

Table 3. Alcohol solution preparation.

Iter ρ n T(oC) Alc. Added (gal.)

0 1 0

1 0.995 15

2 0.992 14.5 27

3 0.9895 15.0 30

4 0.9915 13.5 30

5 0.9905 13.5 33

6 0.9890 1.3364 14.0 36

7 0.9900 1.3363 14.0 36

8 0.9901 1.3362 14.0 36

9 0.9905 1.3361 14.0 36

11
Table 4. MgSO4 solution preparation.

Iter ρ n T(oC) Alc. Added (gal.)

0 1.00 0

1 — 175

2 1.014 14.0 250

3 1.017 1.3364 14.5 275

4 1.015 1.3362 14.5

Measurement Techniques and Experimental Setup

LIF Setup

The LIF experimental setup is shown in Figure 3 and camera plane locations in the

test tank are shown in Figure 1. Planar images in the regions of interest were taken

with four progressive-scan CCD (charge-coupled device) cameras (Hitachi model #KP120CL) with a spatial resolution of 1392 pixels × 1040 pixels and a full frame rate of

15 Hz. Cameras 1, 2 and 3 were fitted with 50 mm C-mount lens, and camera 4 was

fitted with a 25 mm lens for a larger field of view. Filters were placed on each camera

in order to filter out the laser source and record only fluoresced light. Images from all

cameras were captured using a data-acquisition computer capable of streaming images

from four cameras simultaneously at the full camera frame rate onto a real-time disk

array system with a capacity of 625 gigabytes. For system redundancy, images can also

be optionally captured to 1.8 gigabytes of RAM.

Figure 3. LIF experimental setup.

12
Illumination of the flow field was provided by a dual-head Nd:YAG laser (Big Sky

model #CFR-400), operating at 532 nm. Each head of the pulse laser operates with

a maximum optical energy output of 250 mJ per pulse, at a rate of 15 Hz. For our

experiments, a single laser head was used since the data collection rate was 15 Hz. This

data collection rate was chosen to provide sufficient information on the flow field while

allowing timely processing of the collected data.

The output beam from the laser was steered using a series of mirrors so that the

laser beams ran parallel to the test tank bottom. The energy of the beams was split

into two using a dichroic beamsplitter, and each resulting beam was reflected into a

vertical path underneath each measurement region using a mirror. Each beam was

then passed through a plano-spherical lens (1000 mm) and a cylindrical lens (25 mm)

to create the two laser sheets, illuminating the regions of interest for each camera. The

laser sheet illuminating the field of view of cameras 1 and 2 was centered under the

measurement region and oriented vertically, and the laser sheet illuminating the fields of

view of cameras 3 and 4 was located outboard and oriented at an angle into the curved

portion of the model to avoid blockage by the supporting structure. Rhodamine-6G

dye was added to the freshwater (initial tank volume) to provide fluoresced light during

the experiment. All interrogation regions were placed parallel to the plane of the center

of the inlet pipe. Cameras 1 and 2 interrogate the bay upstream of the manhole as

shown in Figure 1. Camera 3 interrogates the flow exiting the manhole, and Camera

4 captures the impingement of the jet from the manhole on the curved surface of the

ballast water tank.

Fluorimeter Setup and Calibration

The fluorimeter was installed in a horizontal section of the model’s outlet piping.

It was calibrated in-vivo by inserting various solutions of known dye concentration into

the test section. Between measurement points, the test section was rinsed thoroughly

with clean water by filling and draining twice. Successive measurements were made

to gain calibration curves of both voltage and intensity versus dye concentration. A

picture of the fluorimeter setup and the calibration data obtained are shown in Figure

4. The R2 value of the linear fits ranged from 0.9985 to 0.9987, which demonstrated

the linearity of the fluorimeters response.

Conductivity sensor setup and calibration

The conductivity sensors were mounted in compartment DB2 using a support structure as shown in Figure 5. The conductivity sensors were calibrated using mixtures of

pure alcohol and pure saltwater solutions encountered during the experiment. The calibration curve for one of the conductivity sensors is shown in Figure 5 (bottom). The

conductivity sensors were designed to measure salinity in an ocean environment and

therefore had maximum sensitivity in seawater conditions. As expected, the calibration

curve in Figure 5 (bottom) shows that the conductivity sensors only respond to the

higher range of MgSO4 encountered in this set of experiments and that below a certain

concentration threshold, they cannot detect conductivity variations. This means that

13
Figure 4. Fluorimeter setup and calibration curves. Ordinate is fluorimeter

voltage (lower curve) or power (upper curve).

14
the conductivity sensors can only track the salinity changes during the latter portions

of the experiment when water exiting the tank is at near-saltwater conductivity.

Figure 5. Conductivity sensor setup and calibration curves. Ordinate is voltage.

Data Processing

LIF data processing

The magnitude of data collected using LIF techniques requires a large amount of

data processing to provide concentration history, estimates of mixing (mixedness), and

volume of fluid calculations. The data processing calculations were performed on five

dual-processor Pentium Xeon 3.0 GHz machines with 1.0 GB of RAM each. In order

15
to perform the necessary calculations, in-house-developed MatLAB† software was used

to normalize the images and calculate the mixedness and volume of fluid levels. The

separate data processing procedures are described in the following sections.

Image Renormalization

The raw LIF images were first normalized using information from the reference (full

dye) and dark (no dye) images. The reference images and dark images were averaged

over 100 frames to give statistically valid averages for each pixel. Each pixel in the raw

data series was then renormalized from an 8-bit integer to a 16-bit integer ranging from

0 to 10,000 using the following equation,

N(x, y) = S I(x, y) − DF(x, y)

BF(x, y) − DF(x, y) (1)

where N(x, y) is the normalized value at each pixel, S is the scaling factor (10, 000), I

is the intensity at each pixel, DF is the dark field value at each pixel, and BF is the

reference value (full dye) at each pixel. An example raw data image is shown in Figure

6.

Figure 6. Example LIF raw data image from Camera 3 for Condition 2.

†#c The MathWorks, Inc.

16
Volume Fraction and Mixedness

Volume fraction (v), defined as the relative amount of saltwater at each pixel location

(x, y), is given by the following equation,

v(x, y) = N(x, y)

S (2)

where v(x, y) ranges from 0 (pure freshwater) to 1 (pure saltwater). v is calculated for

every pixel in the interrogation region, and averaged to obtain the spatially averaged v

in each measurement region.

While v gives the relative amounts of each of the fluids at each pixel location or

averaged over each of the data planes, it provides no information about whether the

two fluids are stratified or mixed. Mixedness, M(x, y), quantifies the amount of mixing

at each pixel or averaged over each data plane and is defined by,

0 ≤ v(x, y) < 0.5 : M(x, y)=2v (3)

0.5 ≤ v(x, y) ≤ 1.0 : M(x, y) = 2(1 − v). (4)

(5)

The mixedness function is shown in Figure 7. In a region that is purely stratified, the

regions of pure freshwater or saltwater will have VF values of 0 or 1, respectively, which

gives M = 0 in both cases. On the other hand, v = 0.5 will result in M = 1. At each

time step, M is averaged over the entire data plane, resulting in a single value of M

for each time step. The time series of these spatially averaged mixedness values are

compared with the CFD simulation data.

MgSO4 volume fraction

Mixedness

0 0.2 0.4 0.6 0.8 1 0

0.2

0.4

0.6

0.8

1

Figure 7. Mixedness as a function of MgSO4 volume fraction.

Spatial and Temporal Filtering

The data shown in Figure 6 contains small-scale turbulent structures that make

comparison to computational fluid dynamic (CFD) codes difficult. The raw LIF data

17
was spatially and temporally averaged to provide a smoothed experimental dataset for

CFD comparisons. Spatial filtering was accomplished by applying a Gaussian filter

(σ = 32, bin size 16). while temporal averaging was applied over a 2-second period

centered at the measurement time.

Fluorimeter data processing

To process the fluorimeter data, dark data was collected prior to testing in order to

provide a reference for background noise and a zero dye concentration measurement.

The fluorimeter data collected at the beginning of the test were assumed to be pure

alcohol solution. The data from the fluorimeter during the test were fit to a linear curve

between the zero measurement and the pure alcohol solution measurement, assuming

that the pure alcohol concentration had a value of 1 (or 100%) at the beginning of the

test. This fit was performed in each test because the dye concentration was not identical

throughout the test plan, and reference data were needed before each experiment. A

sample fluorimeter voltage plot is shown in Figure 8.

Figure 8. Example raw fluorimeter data for Condition 1.

Conductivity sensor data processing

To process the conductivity sensor data, the reading level when the tank was filled

with pure MgSO4 solution was used as a reference. A reading of zero was assumed for

zero salinity, since an actual value of zero MgSO4 was below the sensitivity threshold

of the instrument. A linear dependence, confirmed by calibration, was assumed. All

data below the sensitivity cutoff of the instrument were ignored.

18
EXPERIMENTAL RESULTS

Laser Induced Fluorescence

Figure 9. Mixing layers in the LIF raw data at t

∗ = 0.5. Mixing layers are

the lighter gray regions.

General flow features

Several qualitative observations can be made from the raw LIF data, as turbulent

structures, hideout, and the level of mixing within are readily visible. Mixing is one of

the most important physical phenomena in ballast water exchange and the mixing layer

between the two fluids is where the mixing takes place. Figure 9 shows renormalized

images that have been enhanced to show the mixing layer for each test condition. The

bright region at the top of each image represents the layer of freshwater remaining in the

ballast tank whereas the shaded regions represent sections of the tank that are mixed

with saltwater, with darker areas containing higher concentrations of saltwater. The

tank top is also clearly visible. The mixing layer is much more dispersed in condition

2 than in condition 1, the latter being much thinner and localized. This stems from

the larger density difference in condition 1, which inhibits mixing of the two fluids and

creates a much more stable interface than in condition 2. This implies that decreasing

the density difference between two fluids enhances the mixing process in the ballast

water exchange process.

The effects of increasing flow rate can also be seen in Figure 9. When the flow rate

is increased from 4.1 #/sec (65 gpm) to 6.9 #/sec (110 gpm) (condition 2 to condition

19
3), even more mixing is visible. This occurs because the incoming flow has much more

turbulent energy with higher energy turbulent eddies that generate mixing, advecting

mixed regions away from the interface. It should also be noted that as density difference

decreases from condition 1 to condition 2, the layer of original fluid at the top of the

ballast tank is much thinner. This is because the buoyancy forces between the two fluids

are smaller requiring less energy to lift the regions of heavier fluid above the interface,

where it remains in large part due to turbulent mixing processes.

Figure 10. Jet exiting the manhole (left side of each figure) for each test

condition at t

∗ = 1.

The flow structure of the jet exiting the manhole is shown in Figure 10 at t

∗ = 1.

For condition 1, the large density difference causes the jet to spill through the manhole

and fall quickly toward the bottom of the ballast tank. When the density difference is

decreased (condition 2), the jet exits the manhole but has a larger horizontal component.

When the flow rate is increased (condition 3), the jet exits the manhole and propagates

20
almost horizontally through the field of view. Another interesting observation is the

composition of the fluid inside the jet. In condition 1, the jet is comprised mostly

of incoming saltwater. In condition 2, the fluid inside the jet is more mixed, and in

condition 3 the fluid inside the jet is almost completely mixed. The impingement of

Figure 11. Jet impingement on side of HST1 for each condition. Flow enters

from top left corner of each figure.

the manhole jet (Camera 4) on the rounded side of HST1 for each condition is shown

in Figure 11. In condition 1, the jet impinges upstream of the stringer very close to

the manhole, as expected with the large density difference. The jet in condition 2

impinges near the center of the field of view on the curved surface of the tank, and is

also much more mixed than the jet in condition 1. For condition 3, the jet impinges

further downstream and exhibits an even greater level of mixing.

21
Another important phenomenon encountered in BWE is hideout. Hideout is defined

as the amount of pure original fluid trapped at the top of the tank at the end of an

exchange. Figure 12 shows the LIF images for all three conditions at t

∗ = 3. It is evident

that condition 1 exhibits the largest amount of hideout in this bay. For condition 2,

the amount of hideout is decreased slightly. However, for condition 3, the hideout has

been completely scoured from the bay due to a large increase in turbulent energy at

the fluid interface due to the increased flow rate.

Figure 12. Hideout for (left) condition 1 (center) condition 2 and (right) condition 3.

Mixedness

Figure 13(a) shows the mixedness as a function of time for camera 1 for all conditions. Figure 13(a) shows that for condition 1, the mixedness level starts at zero,

increases rapidly due to energetic mixing from the bellmouth jet and from the flow

over the longitudinal stringer and persists for a much longer portion of the exchange

than for conditions 2 and 3, not reaching a level of zero until t

∗ = 2.8. The mixing

persists in condition 1 because a small mixing layer persists in camera 1 even as the

dense fluid pushes the lighter fluid out of the field of view. When the density difference

is decreased in condition 2, and the flow rate increased in condition 3, the initial mixing

peak is much more pronounced reaching levels of almost 0.9. This is as expected because

the decrease in density and increase in flow rate both increase two fluid mixing. For

conditions 2 and 3 (Camera 1) the mixing decreases rapidly to zero at approximately

t

∗ = 1.1 signifying that either the camera 1 region has become completely stratified or

has become completely flushed of freshwater. As can be seen in the SWVF plot, Figure

14(a), the latter is the case, as the SWVF also goes to a value of 1 at t

∗ = 1.2. It should

be noted that a mixedness value of one is not realized because the LIF measurement is

an average of the entire field of view. Single pixels may reach a mixedness level of one,

22
but on average the entire measurement region never reaches the maximum mixedness

value in the time frame of the experiments.

Figure 13(b) shows the mixedness as a function of time for camera 2 for all conditions. Camera 2 interrogates the upper portion of the bay upstream of the manhole as

shown in Figure 1. Figure 13(b) shows trends that are very consistent with the trends

seen in Figure 13(a). For condition 1, the mixedness values barely reach 0.3 indicating

a highly stratified flow. Thus, condition 1 acts more like a plug flow, where the heavier

liquid, saltwater, pushes the lighter fluid, freshwater, up and out of the tank, like a

piston, with a minimum of mixing. In conditions 2 and 3, the mixedness reaches value

of 0.6 and 0.8, respectively, due to mixed layers that are much thicker than for condition

1. For conditions 2 and 3 the mixedness falls more quickly than condition 1 to lower

levels as the original fluid is diluted more quickly and the freshwater is more quickly

removed from this region.

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

EXP Cond 1 Cam 1

Expt Cond 2 Cam 1

Expt Cond 3 Cam 1

Expt

All Conditions

Camera 1

(a)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

EXP Cond 1 Cam 2

Expt Cond 2 Cam 2

Expt Cond 3 Cam 2

Expt

All Conditions

Camera 2

(b)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

Expt Cond 1 Cam 3

Expt Cond 2 Cam 3

Expt Cond 3 Cam 3

Expt

All Conditions

Camera 3

(c)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

Expt Cond 1 Cam 4

Expt Cond 3 Cam 4

Expt

All Conditions

Camera 4

(d)

Figure 13. Experimental mixedness results for all conditions (a) Camera 1

(b) Camera 2 (c) Camera 3 and (d) Camera 4. The ordinate is

mixedness and the abscissa is non-dimensional time, t

∗.

Figure 13(c) shows the mixedness as a function of time for camera 3 for all experimental conditions. Camera 3 interrogates the flow exiting the manhole as shown in

Figure 1. Figure 13(c) shows trends that are very consistent with the trends seen in

Figure 13(a). In condition 1, as seen in Figure 10 the jet exiting the manhole has a

23
high SWVF, which falls vertically as soon as it exits the manhole. This results in a

mixed region that persists throughout the exchange, as the jet impacts and fills the

bay from the bottom of the tank. The jet mixing layer provides energy for mixing the

fluid in the region between the original fluid and the incoming fluid, but it does not

contain enough energy to mix the entire interrogation region. For condition 2, as seen in

Figure 10, the jet exiting the manhole is much more mixed due to the enhanced mixing

upstream. The jet propagates throughout much of the interrogation region, providing a

large mixing region that spans most of this section of the tank. This allows the fluid to

mix much more readily, and after a period of time the fluid is diluted and approaches

v = 0.95 at t

∗ = 1.6. In condition 3, the mixing occurs at a faster rate, as turbulent

mixing structures dominate the mixing phenomenon. The persistence of mixing seen

in condition 3 is most likely due to local trappage, and mixing of original fluid at the

bottom of the tank throughout the exchange.

Figure 13(d) shows the mixedness as a function of time for camera 4 for conditions 1

and 3. Camera 4 interrogates the region in which the jet from the manhole impinges on

the curved portion of the bay. In this region for both conditions, the mixedness reaches

values greater than 0.8 which are of the same magnitude as those reached in camera 1

shown in Figure 13(a) . This shows that the waterfall impingement on the curved side

of the hopper side tank creates as much mixing as that generated near the bellmouth.

Saltwater Volume Fraction — Experimental Data

Figure 14(a) shows the SWVF in the lower portion of the bay upstream of the

manhole. The slopes of the SWVF curves are very steep indicating that the saltwater

is very effectively replacing the freshwater. Also, at this time (early in the exchange),

essentially only the inlet bay is getting filled. In condition 2 (Figure 14(b)) the slopes of

the SWVF curves for t

∗ < 1 are much less than for camera 1 indicating that freshwater

is exiting much more slowly, which is due to the SW/FW interface reaching the bottom

of the manhole and the saltwater beginning to flow into succeeding compartments, thus

slowing the rate of interface rise. For t

∗ > 1 the slope of the curves approach asymptotic

values determined by the amount of hideout at the tank tops. Condition 1 has the most

hideout, whereas the conditions 2 and 3 have successively less. The higher flow rates

and smaller density difference create more mixing that scours the freshwater out of the

tank top.

The SWVF behavior at the top of HST1, downstream of the manhole, is shown in

Figure 14(c). The SWVF reflects first the mixed fluids entering HST1 (conditions 2

and 3, t

∗ < 0.4). For t∗ > 0.4, it shows the subsequent rise in the interface level at the

manhole, with condition 1 and 2 having steeper slopes perhaps because the interface is

sharper and condition 3 having the smallest slope because of the fuzzy interface between

the SW and FW. Again we see for t

∗ > 1 the curves approaching asymptotic values,

with condition 1 having a significant volume of hide out.

Figure 14(d), the SWVF at the bottom of HST1, shows that for conditions 1 and

3 the curves have relatively steep slopes due to fact that the increase in SWVF is due

to the filling of the HST from the waterfall flow through the manhole. The rate should

24
t

*

Avg SWVF

0 1 2 3 0

0.2

0.4

0.6

0.8

1

EXP Cond 1 Cam 1

Expt Cond 2 Cam 1

Expt Cond 3 Cam 1

Expt

All Conditions

Camera 1

(a)

t

*

Avg SWVF

0 1 2 3 0

0.2

0.4

0.6

0.8

1

EXP Cond 1 Cam 2

Expt Cond 2 Cam 2

Expt Cond 3 Cam 2

Expt

All Conditions

Camera 2

(b)

t

*

Avg SWVF

0 1 2 3 0

0.2

0.4

0.6

0.8

1

Expt Cond 1 Cam 3

Expt Cond 2 Cam 3

Expt Cond 3 Cam 3

Expt

All Conditions

Camera 3

(c)

t

*

Avg SWVF

0 1 2 3 0

0.2

0.4

0.6

0.8

1

Expt Cond 1 Cam 4

Expt Cond 3 Cam 4

Expt

All Conditions

Camera 4

(d)

Figure 14. Experimental SWVF time histories for all conditions, from (a)

Camera 1 (b) Camera 2 (c) Camera 3 and (d) Camera 4. The

ordinate is SWVF and the abscissa is non-dimensional time, t

∗.

25
be somewhat less than for camera 1, since when the inlet flow is diverted at this time

into multiple bays, not just the inlet bay as for camera 1. The slope for condition 3 is

less than for condition 1 because the two fluids are much more mixed.

Fluorimeter Results — Effluent Data

t

*

SWEVF

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

Cond 1 Expt

Cond 2 Expt

Cond 3 Expt

All conditions

Experiment

Figure 15. Experimental SWEVF (ordinate) as function of non-dimensional

time, t

∗, for all conditions.

Effluent concentration was measured in order to provide the saltwater volume fraction in fluid exiting the ballast tank as a function of time throughout the exchange.

This is the type of measurement that could be taken during a full-scale shipboard experiment. The SWEVF is shown in Figure 15 for all of the experimental conditions.

For all conditions there is a finite lag of about t

∗ = 0.2 before any SW reaches the exit.

Condition 3 reaches the exit first because of the high levels of mixing in the inlet bay.

SW reaches the exit last for condition 1 because it has the least amount of mixing in the

inlet bay. However, for condition 1 once SW begins to arrive by t

∗ = 0.5, the increase

in SWEVF is very steep as there is very little mixing and the curve reflects a rapid

transition from almost all FW to almost all SW. Conditions 2 and 3 have successively

smaller slopes due to increasing amounts of mixing which provides a longer transition

time between the two almost-pure fluids. All curves eventually flatten out due to the

scouring of FW that is trapped at the tank tops.

Conductivity Sensors

The conductivity sensors used in this experiment were intended as a proof of concept

for possible use during full-scale experiments in the future. As mentioned previously,

26
only the latter portions of the experiment, where theMgSO4 concentrations were relatively high, produced salinity readings greater than zero. The sensors tracked the

salinity time history in compartment DB2. The normalized concentration of MgSO4

solution as a function of time obtained by one of the conductivity sensors for conditions 1 and 3 is shown in Figure 16. It shows that for condition 1 there is an almost

instantaneous increase in salinity at t

∗ = 0.35. CFD animations show that this is due

to arrival of a very sharp two-fluid interface. Prior to this the salinity levels in the

mixture above the interface are too low to register. After the interface goes above the

sensor there is a slow increase in salinity as the two-fluid mixture beneath the interface

becomes increasingly saline. The curve for condition 3 shows a later arrival (in terms of

t

∗) of the interface at about t∗ = 0.7 while the average slope of the curve up to t∗ = 1 is

slightly less than for condition 1 indicating that there is more two fluid mixing beneath

the interface than for condition 1. The CFD animations show that the interface is much

more diffuse for condition 3 than for condition 1. It can be concluded that the behavior

of the sensors matches up very well with the two fluid condition within the tanks, and

such subtleties as the amount of mixing can be deduced.

Figure 16. Conductivity sensor measurements of MgSO4 concentration.

Discussion Regarding Experiments

Several important conclusions can be drawn from these experiments. The LIF data

show that a decrease in density difference between the original ballast water and the

exchanging saltwater allows increased mixing throughout the ballast tank. Increases in

inlet flow rate also increase the amount of mixing throughout the tank. Increases in

density difference can lead to increasing hideout of original fluid if the incoming flow

does not have sufficient momentum to scour the pockets of trapped fluid from the tank

tops. The effluent time histories suggest that exchanging fluids with large differences in

density approaches the behavior of plug flow, whereas fluids of closer density approach

a pure mixing condition as density difference is decreased and flow rate is increased.

27
The salinity probes appear to accurately track the qualitative two fluid condition within

the tank.

28
COMPUTATIONAL METHODOLOGY

The CFD simulations were performed using the commercial viscous flow solver,

Fluent.‡ The code uses a cell-centered finite volume approach to solving the governing

equations of mass and momentum. In addition, a transport equation is solved for the

volume fraction of one of the fluids, with the algebraic constraint that the volume fraction of both fluids must sum to unity. The convection terms were discretized using a

second order upwind method, while the diffusion terms were discretized using the second order accurate central differencing scheme. The turbulence closure used the RNG

k − $ model. In order to solve for the physical and temporal distribution of the two

fluids, the mixture multi-phase model is used. This is appropriate for this type of problem, where the two fluids are miscible, and have densities that are nearly equal. The

time derivative terms were discretized using the first order backward implicit scheme.

Currently this is the only method available for temporal discretization of the volume

fraction equation. The PISO (Pressure-Implicit with Splitting of Operators) pressurevelocity coupling method was used, and the discretized equations were solved using

Pointwise Gauss-Seidel iterations, with an algebraic multi-grid method to accelerate

the solution convergence. A series of calibration runs were performed in order to arrive

at the optimal set of run parameters. These were determined based on a comparison of

the accuracy of the predicted mass flow of the incoming fluid relative to the theoretical

value (equal to the inlet volumetric flow rate multiplied by the total elapsed time).

In order to facilitate flexibility in handling the complex geometries in ballast tanks,

an unstructured grid was developed to represent the physical tank model. A cut plane

through the experimental model framework at the inlet pipe centerline showing the twodimensional grid structure is shown in Figure 17. Only the inlet pipe, bellmouth, and

exit pipe are modeled using structured hexahedral cells. This is for improved accuracy

in predicting the inflow and outflow of the two fluids since the flow direction is mostly

aligned vertically. The remainder of the domain volume is discretized using unstructured tetrahedral cells. The grid is also focused in regions of interest, such as near the

inlet pipe and bellmouth and through the tank floor openings (e.g., manholes, limber

holes) for improved resolution. The complete three-dimensional domain is composed of

approximately 1.3 million cells in total.

ONE-THIRD SCALE CFD RESULTS

Figure 18 shows the predicted SWVF in the 1/3-scale tank for condition 1 across two

cut planes (in color) through the experimental model ballast tank framework (gray). It

shows that after 30 seconds (t

∗=0.086) the SW is just beginning to fill the bottom of

the inflow bay. At t

∗=1.0 pure FW has been relegated to the tank tops, though there

are large regions of mixed fluid. At t

∗=2.0 the mixed regions have been flushed out of

the tank and FW has been trapped in the tops of most of the bays. Finally, at t

∗=3.0,

much of the trapped FW (red) has been scoured away.

‡Fluent is developed by Ansys, Inc.

29
Figure 17. Grid details for 1/3-scale model.

Figure 18. Three-dimensional views of 1/3-scale tank showing contours of

SWVF from CFD simulations of condition 1; from upper left,

proceeding clockwise: t

∗=0.086, 1, 2 and 3. Blue represents SW,

red is FW.

30
Figure 19 shows SWVF contours for condition 2 in which the density difference is

lower than in condition 2. At t

∗=0.086 it can be seen that the mixing region surrounding

the bellmouth is less stratified than for condition 1. At t

∗=1.0 the FW layers trapped

in the tank are somewhat reduced from condition 1, particularly above the bellmouth,

and upstream of the double-bottom/hopper side tank floor. Times t

∗=2 and 3 show

that the tank top has been scoured more completely than for condition 1.

For condition 3, Figure 20, at t

∗=0.086, the influent SW flows completely to the

tank top in the vicinity of the bellmouth. This leads to vigorous mixing and, as shown

at t

∗=1.0, the SWVF is much higher in the vicinity of the tank exit. At times t∗=2

and 3 the FW trappage is much less than for conditions 1 and 2, with only a single bay

containing visible FW at t

∗=3.

Figure 19. Three-dimensional views of 1/3-scale tank showing contours of

SWVF from CFD simulations of condition 2; from upper left,

proceeding clockwise: t

∗=0.086, 1, 2 and 3. Blue represents SW,

red is FW.

Exchange Efficiency (EE)

Figure 21 shows comparisons of EE from the CFD and experimental data for the

three test conditions. EE is defined as the volume of SW in the tank divided by the

tank volume. The CFD values of EE are computed directly by a spatial integration

of the SWVF over all grid cells within the CFD tank model. On the other hand, the

31
Figure 20. Three-dimensional views of 1/3-scale tank showing contours of

SWVF from CFD simulations of condition 3; from upper left,

proceeding clockwise: t

∗=0.086, 1, 2 and 3. Blue represents SW,

red is FW.

32
t

*

EE

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

1.2

Condition 2 CFD

EXP Condition2

Condition 2

(b)

t

*

EE

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

1.2

Condition 1 CFD

EXP Condition 1

Condition 1

(a)

t

*

EE

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

1.2

CFD Condition 3

EXP Condition 3

Condition 3

(c)

Figure 21. Predicted and measured EE (ordinate) for test conditions 1, 2, and 3.

33
experimental EE values are computed indirectly as the difference between the volume

of SW entering the tank and the volume that has exited the tank:

EE(t) = V (t)

Vo

= 1

Vo

!

V (t = 0) + Qt −

" t

0

Qφ(τ )dτ

#

(6)

where Q is the volume flow rate, V is the volume of SW in the tank, Vo is the volume

of the tank, φ is the SWVF at the tank exit and τ is the dummy integration variable.

The first term can be assumed to be zero since the tank initial condition is pure FW;

the second term, for constant Q, is linear in time and the third term is the mixing term.

If no mixing were to take place in the tank, then only FW would exit the tank, φ = 0 ,

and the mixing term would be zero. In this case EE = 1 would be achieved in a single

TVE in what is called plug-flow filling. Since mixing does occur in the tank, φ ≥ 0

for much of the exchange and the term then represents the deviation of the exchange

from plug-flow filling. The minimum value of uncertainty for the experimental values

of EE are estimated to be 0.06, since that is the amount by which the Condition 3

experimental values of EE exceed the theoretical upper limit, 1.0. A formal uncertainty

analysis should be performed in the future. Superimposed on the experimental curves

are 10% uncertainty intervals. The CFD results are within these uncertainty intervals.

The curves show that in the linear region (up to about t

∗=0.50) CFD and experiment

agree almost exactly. During this time the change in EE is proportional to the flow

rate since there is no mixing and only freshwater is exiting the tank. For condition

1, the experiment and CFD agree until about t

∗=1.2, after which the CFD predicts

lower values, with a value of EE=0.93 at t

∗=3.0. For condition 2, the experiment

and CFD agree only to about t

∗=0.60, after which the CFD predicts greater EE, with

EE=0.96 at t

∗=3.0. That CFD predicts higher values of EE for condition 2 than

condition 1 makes physical sense because in condition 2 the mixing is much greater

meaning that the volume of mixed fluid trapped in the tank tops will be less due to

more energetic scouring. This is shown most clearly by comparing Figure 18 and Figure

19. For condition 3, the experiment and CFD agree to about t

∗=0.80 after which the

experimental EE values are much larger than the CFD EE values, with experimental

EE increasing to a value greater than 1.0, which is physically impossible.

Figure 22 shows the EE results with the experimental curves and the CFD curves

compared side-by-side. The CFD curves (right) show that the EE increases from condition 1 to 2 and again from 2 to 3. This must be due to the increased scour of the fluid

trapped at the tank tops. The experimental curves, Figure 22(left) show a decrease

from condition 1 to 2 and then a large increase from condition 2 to condition 3. This

does not make physical sense. The differences between experimental and CFD model

results and possible causes are discussed in the following sections.

SW Effluent Volume Fraction (SWEVF)

Figure 23 shows the SWEVF time histories comparing experimental and CFD values

for each of the conditions. The uncertainty margin for the experimental data is shown.

It appears that for condition 1, the CFD and experiment agree very closely up until t

∗ =

34
t

*

Exchange Efficiency

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

1.2

EXP Condition 1

EXP Condition2

EXP Condition 3

All Conditions

Experiment

t

*

Exchange Efficiency

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

1.2

CFD Condition 1

CFD Condition 2

CFD Condition 3

All Conditions

CFD

Figure 22. EE (ordinate) from experiments (left) and predicted by CFD

(right) for all test conditions.

1.0, after which the CFD values become higher, though remain within the experimental

uncertainty band. After t

∗ = 1.0 SWEVF is a reflection of the amount of scouring

that is occuring between the FW trapped in the tank tops and the SW flowing to the

exit. Less scouring will result in a SWEVF value closer to 1.0. More scouring would

be indicated by values further from 1. Since scouring reduces the amount of FW in the

tank, it will result in higher EE. In Figure 23(a) for t

∗ > 1.0 CFD predicts SWEVF

closer to 1 than the experiments. Following the above reasoning, the cause of this

must be that the CFD is predicting less scouring of the fluid trapped in the tank top,

resulting in more freshwater trapped in the tank and less EE. Figure 21 shows that this

is indeed the case i.e., after t

∗ = 1 the CFD EE curve is lower than the experimental

curve indicating a greater volume of mixed fluid trapped in the tank top.

Figure 23(b), the SWEVF for condition 2, shows that early in the exchange (t

∗ <

1.00) the CFD is significantly lower than the experimental values. This indicates that

the CFD is predicting less mixing during the early stages of the exchange than the

experiment. During that middle stage of the exchange (1.0 < t∗ < 2.00) the CFD

and experiment agree almost exactly. Later in the exchange (t

∗ > 2) the experimental

concentration is larger than the CFD predictions and goes slightly larger than the

physical limit of 1.0.

Figure 23(c), the SWEVF time history for condition 3, shows that the experiment

and CFD agree well for t

∗ < 0.7, after which the CFD predicts higher values than the

experiment. This indicates that the CFD has less scouring of tank tops (and thus more

mixed-fluid trappage) during the later parts of the exchange, and therefore, will predict

less EE than the experiment. Figure 21(c) shows that this is the case, although the

35
t

*

SWEVF

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

Cond 3 CFD

Cond 3 Expt

Condition 3

(c)

t

*

SWEVF

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

Cond 2 CFD

Cond 2 Expt

Condition 2

(b)

t

*

SWEVF

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

Cond 1 CFD

Cond 1 Expt

Condition 1

(a)

Figure 23. SWEVF (ordinate) time histories comparing experiment and

CFD predicted values (a) condition 1 (b) condition 2 and (c)

condition 3.

36
experimental values of EE for condition 3 are well above 1.0, which is the physical limit

(maximum value) for EE. Table 5 summarizes the SWEVF values at integer multiples

of t

∗.

Table 5. SWEVF at selected times during exchange, comparing CFD and

experimental values.

t

∗

Condition 1 2 3

1 Expt 0.71 0.92 0.97

CFD 0.71 0.94 0.98

2 Expt 0.68 0.96 1.01

CFD 0.69 0.94 0.98

3 Expt 0.59 0.90 0.96

CFD 0.63 0.94 0.98

Figure 24(b), the CFD predictions of SWEVF vs. t

∗ for the three conditions, shows

that the three curves behave consistently with respect to the mixing that occurs in tank.

For condition 1, which should have the least amount mixing due to the lower flow rate

and higher density difference, the CFD predicts the latest arrival of SW at the tank exit

(t

∗ = 0.4) of the three cases. For conditions 2 and 3 the first arrival of SW at the tank

exit occurs at about t

∗ = 0.25, with condition 3, which has the highest flow rate and

lowest density difference, having the highest SW concentration. The energetic mixing

in the inlet bay results in mixed volumes that quickly advect to the tank exit. The

order of the curves changes at t

∗ = 0.65 indicating that the cases with higher mixing

early on have less mixing later on. At this point in the exchange, experimental movies

show that the two fluids are highly stratified and the primary means of mixing is due to

horizontal shear flows at stratified shear layers. Condition 1, with lower velocities and

higher density differences will have less scouring at the two-fluid interfaces, meaning that

the SW will pass through the tank with less freshwater contamination, and thus, show

higher values of SWEVF at the exit. On the other hand, condition 3, with the highest

velocities and lowest density differences, had the lowest values of SWEVF since it has

increased mixing and FW contamination, leading to lower values of SW concentration

at the exit. Condition 2 should be between conditions 1 and 3. At the later stages of

the exchange (t

∗ > 2) the three conditions have identical SW concentrations, indicating

that the CFD model, despite the differences in flow velocity and density difference, is

predicting identical scouring between the SW and the FW hideout in the tank tops.

The experimental curves for the three conditions are shown in Figure 24(a). The

curves for conditions 1 and 3 are consistent with respect to the two-fluid mixing that

occurs in the tank as discussed in the previous paragraphs. Mixing in the inlet bay

early in the exchange leads to early arrival of SW at the exit, with the highest mixing

condition 3 arriving the earliest (t

∗ ∼ 0.2); after t∗ > 0.65 condition 1, with less mixing

37
t

*

SWEVF

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

Cond 1 CFD

Cond 2 CFD

Cond 3 CFD

All conditions

CFD

(b)

t

*

SWEVF

0 0.5 1 1.5 2 2.5 3 0

0.2

0.4

0.6

0.8

1

Cond 1 Expt

Cond 2 Expt

Cond 3 Expt

All conditions

Experiment

(a)

Figure 24. SWEVF (ordinate) time histories for all test conditions; (a) from

experiment and (b) predicted by CFD.

at stratified interfaces, has higher values of SWEVF because the SW passes through the

tank with reduced levels of FW contamination. The curve for condition 2 is inconsistent

with these physics — after the first arrival of SW at the exit, the experimental condition

2 curve has SWEVF levels significantly higher than condition 3 for which the highest

levels of mixing are expected. Even after the flows are completely stratified (t

∗ > 1)

the condition 2 curve is higher than the condition 1 curve. Very late in the exchange

(t

∗ > 1.5) condition 2 has higher levels than the other two conditions indicating that

nearly pure SW is exiting the tank. This is inconsistent with the physics — if any

condition is likely to have pure SW exiting the tank at that time, it would be condition

1. Furthermore, the experimental (measured) SWEVF for condition 2 actually went

greater than 1.0, which is physically impossible. Thus, it is hypothesized that the

experimental SWEVF for condition 2 has a positive bias error leading to a greater

magnitude for the mixing term, φ, in the evaluation of the EE, which results in lower

than expected EE values, as shown in Figure 22(left).

Full-scale shipboard experiments often use SWEVF to approximate EE. SWEVF is

relatively simple to obtain since it is a point measurement whereas actual EE should be

calculated by integrating the entire tank volume or by a time integration of the measured

SWEVF. The following discussion addresses whether this is an accurate prediction

methodology. A comparison of the EE and SWEVF as predicted with CFD is shown

in Table 6. If perfect and instantaneous mixing occurred throughout the tank then the

EE and SWEVF would be equal. The table shows that early in the exchange (t

∗ = 1)

the EE values, calculated by CFD integrated over the entire tank, are significantly

higher than the SWEVF. Even though energetic mixing is occurring in and around the

38
inlet bay, the mixed regions take a finite time to reach the tank exit and therefore,

the SWEVF will be primarily FW during the early stages of the exchange, and it is

not a good indicator for the integrated SWVF within the tank. Later in the exchange

(t

∗ = 2), it can be seen that the EE and SWEVF compare very well, particularly for

conditions 2 and 3 that have lower density differences and/or higher flow rates. Finally

at end of the exchange (t

∗ = 3) the EE are less than the SWEVFs for conditions 1 and

2, due to the hideout, whereas they are practically the same for condition 3 due to lack

of hideout. It can be concluded that the using SWEVF to approximate EE does not

take into account the spatial inhomogeneities with in the tank, underpredicting the EE

early on and over-predicting EE later on. For the case where the density differences

are small, however, SWEVF can start to approach EE, in the mid- to later stages of an

exchange.

Table 6. Comparison of EE and SWEVF predicted with CFD.

t

∗

Condition 1 2 3

1 EE 0.79 0.90 0.94

SWEVF 0.71 0.94 0.98

2 EE 0.78 0.92 0.96

SWEVF 0.69 0.94 0.98

3 EE 0.79 0.95 0.99

SWEVF 0.63 0.94 0.98

Saltwater Volume Fraction — Predicted vs. Experiments

The saltwater volume fraction (SWVF) averaged over the camera data planes from

each experiment (Conditions 1-3) and that predicted by CFD are shown in Figures

25-27. SWVF is a measure of the relative amount of exchanged SW in a given area

averaged over the data plane of the camera. The saltwater may arrive at the data plane

either through a stratified flow along the tank bottom or in the form of a mixture.

Condition 1. Figure 25 shows the SWVF for Condition 1. Videos from the experiments show that the SW flows over a stringer into the Camera 1 data plane first as

a highly diffuse mixture consisting of complex turbulent eddies beginning at t

∗ = 0.04

and then begins pouring over the stringer at about t

∗ = 0.10, increasing to full strength

t

∗ = 0.3. Finally, at t∗ = 0.3 Camera 1 becomes full of mixed fluid and the interface

disappears. In Figure 25(a), the experiment and CFD both record the arrival of SW

t

∗ = 0.04 with a mild slope, indicating a diffuse mixture. At t∗ = 0.10 the slope in the

CFD predictions increases indicating the arrival of the interface into the data plane.

The experimental slope remains fairly constant. This difference in slope indicates that

the CFD is predicting a less diffuse solution filling the bottom of the data plane, whereas

the experimental data indicates a more diffuse mixture. We can deduce that the computations have under-predicted the amount of mixing that occurs upstream of the data

39
plane, presumably at the inlet. The predictions have much smoother spatial VF distributions because the turbulent eddies have been modeled. It appears, however, that

the higher values of VF for the predictions are because the SW flow over the stringer

is a stronger coherent jet in the predictions while the experiment shows a weaker more

diffuse jet flow. This discrepancy persists until well into the filling, t

∗ = 2, when both

the experiment and predictions converge to 1.0, i.e., when the entire data plane consists

of SW.

Camera 2, Figure 25(b), tracks the SWVF in the top of DB1 upstream of the

manhole between DB1 and HST1. From the experimental videos it can be seen that

the first significant SW intrusions begin at the bottom of Camera 2 at about t

∗ = 0.1; at

about t

∗ = 0.2 the flow becomes stratified with a thick and wavy mixed layer between

the SW and FW regions; at about t

∗ = 0.7 the mixed layer has disappeared and the SW

and FW regions are separated by a sharp, quiescent interface. These same features are

also seen in CFD animations. The predictions have the same slope as the experiments

though they have a small constant offset. The offset indicates that the CFD may be

predicting a thinner mixed layer at first (thus, greater amount of SW in the Camera

plane) than is measured in the experiments.

The Camera 3 data plane is directly downstream of the MH between DB1 and HST1.

Experimental videos show that the first trace amounts for SW start flowing through

the MH at t

∗ = 0.1 and the bulk interface begins pouring through the MH at about

t

∗ = 0.4. The jet through the manhole is turned downward by gravity having a smooth

interface until it turns about 450, where transition from a laminar to turbulent interface

takes place. The videos show that HST1 fills from the bottom with a very diffuse mixed

mixture never displaying a sharp interface. The jet through the MH is surrounded by

a mixture of constantly increasing SW which decreases the gravity force on the jet, so

that the downward component of the jet eventually disappears at about t

∗ = 1.5. CFD

animations show that the gross flow features of the computations compare very well

with experiments. In Figure 25(c), the CFD has a very small slope from t

∗ = 0.08 until

about t

∗ = 0.4 which is due to the inflow of a very diffuse mixture. After this, the

slope increases rapidly, so that it has a constant slope past t

∗ = 1. However, overall the

CFD predicts significantly higher VF than is measured in the experiments. As the VF

in the HST1 is a complex result of mixing in DB1, mixing at the interface of the MH

jet and impingement of the jet on the bottom of HST1, it is difficult to pinpoint any

one cause for the discrepancy. In view of the fact that the trends in the experimental

SWVF are different than for the other three conditions, it may be the case that there

is a systematic error in the experimental Camera 3, Condition 1 results.

Condition 2. Condition 2 has a smaller density difference between the two fluids

but the same flow rate as Condition 1. Therefore, we expect the SWVF time histories

to reflect greater mixing.

Figure 26(a) shows the SWVF time histories for Camera 1. We see that for Cameras

1 and 2 the experiment and CFD compare very well. This suggests that the CFD is

better at simulating the greater mixing allowed by the smaller density difference. For

Camera 3, the curves are parallel but offset, with the experimental SWVF greater than

40
t

*

Avg SWVF

10-1 100 0

0.2

0.4

0.6

0.8

1

EXP Cond 1 Cam 1

CFD Cond 1 Cam 1

Condition 1

Camera 1

(a)

t

*

Avg SWVF

10-1 100 0

0.2

0.4

0.6

0.8

1

EXP Cond 1 Cam 2

CFD Cond 1 Cam 2

Condition 1

Camera 2

(b)

t

*

Avg SWVF

10-1 100 0

0.2

0.4

0.6

0.8

1

Expt Cond 1 Cam 3

CFD Cond 1 Cam 3

Condition 1

Camera 3

(c)

t

*

Avg SWVF

10-1 100 0

0.2

0.4

0.6

0.8

1

Expt Cond 1 Cam 4

CFD Cond 1 Cam 4

Condition 1

Camera 4

(c)

Figure 25. Area-averaged experimental and CFD SWVF time histories (logarithmically scaled) for condition 1; (a) Camera 1 (b) Camera 2

and (c) Camera 3.

41
t

*

Avg SWVF

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 2 Cam 1

CFD Cond 2 Cam 1

Condition 2

Camera 1

(a)

t

*

Avg SWVF

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 2 Cam 2

CFD Cond 2 Cam 2

Condition 2

Camera 2

(b)

t

*

Avg SWVF

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 2 Cam 3

CFD Cond 2 Cam 3

Condition 2

Camera 3

(c)

t

*

Avg SWVF

10-1 10

0 0

0.2

0.4

0.6

0.8

1

CFD Cond 2 Cam 4

Condition 2

Camera 4

(d)

Figure 26. Area-averaged experimental and CFD SWVF time histories (logarithmically scaled) for condition 2; (a) Camera 1 (b) Camera 2

(c) Camera 3 and (d) Camera 4.

42
the CFD results. This suggests that HST1 fills faster in the experiment than in the

CFD simulation. From the VF alone it is not possible to ascertain why. This will be

discussed later in light of the mixedness results.

Condition 3. Figure 27 shows the SWVF time histories for Condition 3. The

comparisons for Cameras 1 and 2 are very good over almost the entire filling. For

Camera 3 the slope of the CFD is steeper than the experiment and the experimental

data are approximately linear for t

∗ < 1.6. It is unclear as to the reasons for this

behavior. Camera 4, on the other hand compares very well. The experimental data

behavior is not consistent with Conditions 1 and 2.

Mixedness — Predicted vs. Experiments

Figure 28 is the mixedness for Condition 1 averaged over each of the four camera

planes (see Figure 1). It shows that the experiment and CFD are, for the most part,

in very good agreement, especially for the shape of the curves, and the magnitude and

timing of the peaks. Camera 1, Figure 28(a), which is in the bottom of the inlet bay upstream of a manhole quickly receives highly mixed fluid due to mixing at the bellmouth.

Camera 2, Figure 28(b), is above camera 1, upstream of and in direct alignment with

a manhole. Arrival of mixed fluid is delayed, and the maximum mixedness is smaller

because the flow has stratified after reaching the level of the manhole. Camera 3, Figure

28(c), is directly downstream of the manhole and almost the same height off the bottom

as Camera 2. The CFD predicts slightly higher maximum mixedness than measured in

the experiment. Camera 4, Figure 28(d) is where the manhole flow strikes the side of

the tank, which causes high levels of mixing.

For condition 2, Figure 29, the CFD and experiment compare very well except at

Camera 3, Figure 29(c), where the CFD mixedness peak has the same magnitudes

but lags in time. There is no experimental data for Camera 4. Cameras 1 and 2

have significantly higher levels of mixing than Condition 1, due to the smaller density

difference between the two fluids. Interestingly, for Cameras 3 and 4 in HST1 the

mixedness for Condition 2 is only slightly higher than for Condition 1. It is reasoned

that the more stratified water fall through the MH impacting the bottom of HST1 for

Condition 1 acts as an energetic mixing mechanism, whereas for Condition 2, the water

fall is much more benign since the flow through the MH is already mixed.

For condition 3, Figure 30, the experiment and CFD curves are in agreement in all

four camera planes with respect to the general shape of the curves and approximate

timing of the peaks. However, the CFD predicts smaller peak values and generally

under-predicts mixedness. The reason could be that the CFD model does not adequately represent the complex, turbulent mixing associated with the higher flow rate

and the smaller density difference.

A sense of the physical trends between the three conditions can be seen in Figure 31

which plots all the conditions in a single plot for each camera plane in linear-linear space.

The experimental data are found in the left column; the CFD data in the right column.

For Camera 1 it can be seen that a high level of mixing occurs very early during the

exchange, with the magnitude of the peak increasing with increasing flow rate and/or

43
t

*

Avg SWVF

10-1 100 0

0.2

0.4

0.6

0.8

1

Expt Cond 3 Cam 1

CFD Cond 3 Cam 1

Condition 3

Camera 1

(a)

t

*

Avg SWVF

10-1 100 0

0.2

0.4

0.6

0.8

1

Expt Cond 3 Cam 2

CFD Cond 3 Cam 2

Condition 3

Camera 2

(b)

t

*

Avg SWVF

10-1 100 0

0.2

0.4

0.6

0.8

1

Expt Cond 3 Cam 4

CFD Cond 3 Cam 4

Condition 3

Camera 4

(d)

t

*

Avg SWVF

10-1 100 0

0.2

0.4

0.6

0.8

1

Expt Cond 3 Cam 3

CFD Cond 3 Cam 3

Condition 3

Camera 3

(c)

Figure 27. Area-averaged experimental and CFD SWVF (ordinate) time

histories for condition 3; (a) Camera 1 (b) Camera 2 (c) Camera

3 and (d) Camera 4.

44
t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

EXP Cond 1 Cam 1

CFD Cond 1 Cam 1 Mix

Condition 1

Camera 1

(a)

t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

EXP Cond 1 Cam 2

CFD Cond 1 Cam 2 Mix

Condition 1

Camera 2

(b)

t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 1 Cam 4

CFD Cond 1 Cam 4 Mix

Condition 1

Camera 4

(d)

t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 1 Cam 3

CFD Cond 1 Cam 3 Mix

Condition 1

Camera 3

(c)

Figure 28. Area-averaged experimental and CFD mixedness time histories

for Condition 1; (a) Camera 1 (b) Camera 2 (c) Camera 3 and

(d) Camera 4.

45
t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

CFD Cond 2 Cam 4 Mix

Condition 2

Camera 4

(d)

t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 2 Cam 3

CFD Cond 2 Cam 3 Mix Condition 2

Camera 3

(c)

t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 2 Cam 2

CFD Cond 2 Cam 2 Mix Condition 2

Camera 2

(b)

t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 2 Cam 1

CFD Cond 2 Cam 1 Mix Condition 2

Camera 1

(a)

Figure 29. Area-averaged experimental and CFD mixedness time histories

for Condition 2; (a) Camera 1 (b) Camera 2 (c) Camera 3 and

(d) Camera 4.

46
t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 3 Cam 1

CFD Cond 3 Cam 1 Mix Condition 3

Camera 1

(a)

t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 3 Cam 2

CFD Cond 3 Cam 2 Mix Condition 3

Camera 2

(b)

t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 3 Cam 3

CFD Cond 3 Cam 3 Mix Condition 3

Camera 3

(c)

t

*

Avg Mixedness

10-1 10

0 0

0.2

0.4

0.6

0.8

1

Expt Cond 3 Cam 4

CFD Cond 3 Cam 4 Mix Condition 3

Camera 4

(d)

Figure 30. Area-averaged experimental and CFD mixedness time histories

for Condition 3; (a) Camera 1 (b) Camera 2 (c) Camera 3 and

(d) Camera 4.

47
t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

CFD Cond 1 Cam 2 Mix

CFD Cond 2 Cam 2 Mix

CFD Cond 3 Cam 2 Mix

CFD

All Conditions

Camera 2

(b)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

EXP Cond 1 Cam 1

Expt Cond 2 Cam 1

Expt Cond 3 Cam 1

Expt

All Conditions

Camera 1

(a)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

EXP Cond 1 Cam 2

Expt Cond 2 Cam 2

Expt Cond 3 Cam 2

Expt

All Conditions

Camera 2

(c)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

Expt Cond 1 Cam 3

Expt Cond 2 Cam 3

Expt Cond 3 Cam 3

Expt

All Conditions

Camera 3

(e)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

Expt Cond 1 Cam 4

Expt Cond 3 Cam 4

Expt

All Conditions

Camera 4

(g)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

CFD Cond 1 Cam 1 Mix

CFD Cond 2 Cam 1 Mix

CFD Cond 3 Cam 1 Mix

CFD

All Conditions

Camera 1

(b)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

CFD Cond 1 Cam 2 Mix

CFD Cond 2 Cam 2 Mix

CFD Cond 3 Cam 2 Mix

CFD

All Conditions

Camera 2

(d)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

CFD Cond 1 Cam 3 Mix

CFD Cond 2 Cam 3 Mix

CFD Cond 3 Cam 3 Mix

CFD

All Conditions

Camera 3

(f)

t

*

Avg Mixedness

0 1 2 3 0

0.2

0.4

0.6

0.8

1

CFD Cond 1 Cam 4 Mix

CFD Cond 2 Cam 4 Mix

CFD Cond 3 Cam 4 Mix

CFD

All Conditions

Camera 4

(h)

Figure 31. Area-averaged experimental and CFD mixedness (ordinate) time

histories for all conditions.

48
decrease in density difference. The CFD and experiment are remarkably well matched

with regards to the peak height. However, later in the exchange, the experiment result

for condition 1 exhibits a long tail that reflects higher average mixedness (more mixing)

than conditions 2 and 3. This is an anomaly in the measurements because after t

∗ = 1,

the flow is highly stratified for both the conditions 2 and 3, which should result in less

mixing than condition 1. The CFD data show what should be the correct physical

trend.

For Camera 2, the experimental data show that there is a dramatic increase in peak

height between Conditions 1, 2 and 3, which seems to be physically correct because of

the increase in mixing in the inlet bay, due first to the decrease in density difference

(between conditions 1 and 2) and then the increase in flow rate (between conditions 2

and 3). On the other hand, the CFD results show only an increase between Conditions

1 and 2/3 with Conditions 2 and 3 having almost the same peak magnitude. In this

case the CFD is probably under-predicting the amount of mixing associated with an

increase in flow rate (condition 3).

For Camera 3, the experiment shows that the peak value of mixedness occurs first

for condition 3, then 2 and then 1. The CFD has a similar trend. The peak values

for CFD and experiments compare well for condition 2. The CFD predicts a higher

peak value for condition 1 and a slightly lower peak value for condition 3 compared

with experiments. CFD results for Camera 4 compare very well with the experiments,

indicating that the CFD correctly captures the mixing due to the impingement of a jet

into the rounded side of the tank.

Discussion Regarding Comparison of CFD Predictions to Experimental

Results

The ultimate objective of this multi-phase project is to develop a computational

tool for predicting whether a given tank design is likely to meet exchange requirements

(e.g., predict whether or not it will have 95% EE after 3 TVE). It is shown that the

predicted EE match the expected physical trends: as mixing increases, due to either

an increase in flow rate or decrease in density difference, the EE at the end of three

tank volumes increases (see Figure 21). The computational predictions fall within the

95% uncertainty intervals for the EE computed from experimental data. The EE is an

integral measure of the volume of the two fluids within the tank at a given time and

therefore is a reflection of the volume of each of the two fluids that exit the tank.

Detailed two-fluid data in four data planes in the physical ballast tank model were

collected to obtain a basic understanding of the mixing that occurs in the tank. Here,

the experimental uncertainty is much less than it is for EE and it is possible to assess the

accuracy with which the CFD model predicts the movement of two fluids throughout the

tank and two-fluid mixing. The comparisons show that the CFD can predict the volume

fraction quite well implying that the mass movement of the two fluids throughout the

tank is well-predicted. The CFD comparisons of mixedness are on the whole, quite

good, particularly for the conditions 1 and 2, which involve less mixing. For condition

3, the mixing is under-predicted, particularly due to the mixing in the bellmouth bay.

49
This type of mixing is highly energetic due to overturning gravity waves and turbulence.

Under-prediction of early-stage mixing, especially during the first TVE, will result in

less SWVF in the mixture carried to the exit and a greater VF of freshwater being

pushed out of the exit. The end result would be slightly higher EE during the first tank

volume.

That the EE is higher for the increased mixing conditions 2 and 3 is primarily

due to the scouring of freshwater trapped in the tank tops. Small, quarter-round vent

holes that are included in the upper corners of the actual tank top structure have not

been included in either the experiment tank or CFD model. Undoubtedly, they will

contribute to increased EE, but their significance is unknown at this time. One of the

limitations of the 1/3-scale model program is that the extent of the 1/3-scale tank is

only a fraction of a full-scale tank (i.e., a typical bulk carrier tank has ≈ 10 rows of bays,

whereas the 1/3-scale model only has two). This has implications for any conclusions

drawn from the EE results: since the 1/3-scale tank is limited to two bay lengths,

the relative amount of energy available for mixing and scouring in the two adjacent

bays is much higher than across the entire full-scale tank. In the full-scale tank, it is

hypothesized that far downstream the energy levels approach quiescent and mixing, no

matter what the flow rate and density difference, approaches zero. We follow next with

results of CFD simulations for the full-size 705 m3 (186, 250 gals) tank that will shed

some light on this concern.

FULL-SCALE CFD SIMULATIONS

Full-scale CFD simulations were performed on interconnected ballast tanks from a

typical 35, 000 dwt handysize bulk carrier. The tanks, shown in Figure 32 consist of a

total of ten rows of interconnected double bottom tank (DBT), hopper side tank (HST),

and wing tank (WT) bays. The dimensions of the tanks are listed in Table 7. The WT

bays are connected to the HST bays via two 8 in (0.203m) (ID) connection pipes. The

incoming fluid is pumped into the DBT via a single inlet bellmouth as shown in Figure

33.

Table 7. Full scale tank dimensions.

Tank L (m) B (m) H (m) V (m3)

DBT 27 3.3 1.4 11.5

HT 27 1.9 5.0 17.4

TT 27 5.2 4.7 41.4

There are two exits that were modeled as flush with the tank top (not shown) directly

above the two connection pipes to simulate an overflow condition. The tank floor openings and stiffeners were modeled based on tank drawings provided by Fednav International. The total volume of the tank (with longitudinal stringers) is 705 m3(186, 250gals).

The inflow rate was 11.4 m3/min (3000 gpm), meaning that a one tank volume takes

50
Figure 32. Drawing of bulk carrier tank. Three tanks are shown: lower left:

double bottom tank (DBT); lower right: hopper tank (HT) and

upper: topside tank (TT).

51
Figure 33. Inlet bay detail for full-scale tank.

52
62 min (physical time). The tank is initially full of freshwater with influent mid-ocean

saltwater giving a density difference equivalent to a salinity difference of 35 ppt.

In an earlier work, Kent and Parsons6 concluded that the EE was not affected

by the presence of the longitudinal stringers. These structural elements are small in

relation to the total tank volume and it is reasonable to assume that they would not

affect the EE. Their inclusion imposes a large computational burden meaning that

simulations could be performed much quicker without them. In order to investigate

the influence of the longitudinal stringers, two separate grids were developed for the

full-scale tank, one with all of the tank structure as shown in Figure 32 and one that

omits the reinforcing stringers. The grid that did not include the stringers needed

approximately 1.3 million cells, while the grid that included the finer structural details

required approximately 5.5 million cells. The inclusion of the stringers had a significant

impact on the computational resources and time required to perform the simulations

as shown in Table 8.

Table 8. Computational details for 1/3-scale and full-scale simulations

1/3-Scale FS (no stringers) FS (with stringers)

Total Volume (m3) 1.43 711 705

Total Volume (gals) 378 187,825 186,250

Total no. Cells 1.3 × 106 1.2 × 106 5.4 × 106

Avg Cell Size (cm) 1.0 8.5 5.0

Platform NSWCCD ARL

banyan banyan fcs

No. of cpus 12 12 48

Total Flow Time (secs) 1,050 12,000 12,000

No. of Time Steps 3,830 7,300 17,500

Total Wall Time (hr) 51.4 64.2 412

A close-up comparison of the predicted SWEVF very early (t

∗ = 0.016) in the

exchange, at several cut planes near the inlet pipe are shown in Figure 34. The figure

shows that the stringers cause a large difference in the mixing that takes place. Without

stringers the two fluids in the inlet bay are completely mixed, with highly mixed fluid

regions thereafter quickly dispersing throughout the tank. With the stringers the flow

is much less mixed, with almost pure SW forming overturning waves in the vicinity

of the bellmouth and moving along the tank bottom. A series of waterfall flows are

occurring, much like in the 1/3-scale tank. The exchange efficiencies for the two cases

are shown in Figure 35 as compared with the theoretical lines for perfect mixing and

plug flow filling. Perfect mixing occurs if the influent volume fraction in the tank is

spatially homogeneous i.e., as the influent enters the tank it is instantaneously mixed.

With perfect mixing EE obeys an exponential relationship

η = 1 − exp−t∗

(7)

53
Figure 34. Full-scale SWVF contours at t

∗ = 0.016 (60secs); left: with

stringers and right: without stringers.

t

*

Exchange Efficiency

0 1 2 3 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Full-Scale Tank CRS NO STRINGERS

Full-Scale WITH STRINGERS

Perfect Mixing Assumption

Plug Flow Filling

Tank Top Water Hideout

Figure 35. EE time history for full-scale tank showing theoretical perfect

mixing and plug flow filling lines.

54
such that only 95% EE can be obtained after three tank volumes, with 100% not

theoretically possible. Plug flow filling occurs when absolutely NO mixing occurs and

the influent pushes the original fluid out like a piston. In this case, EE obeys the simple

linear relationship

η = t

∗ (8)

Only a single tank volume is necessary to obtain 100% EE. The horizontal line in

Figure 35 is the EE due to water hideout in the tank tops. The theoretical maximum

volume of FW that could be trapped by the longitudinal stringers is 7.2% of the total

tank volume, giving an EE of 92.8% if all the freshwater except that in the tank tops is

flushed from the tank. Figure 35 shows that without stringers the EE curve follows the

perfect mixing line, after which it falls off significantly, reaching only 88% EE at t

∗=3.

On the other hand, the case with stringers follows the plug flow filling line until about

t

∗=0.8, after which it falls off rapidly, reaching the hideout line (93% EE) at t∗=2.6.

This implies that the FW trapped in the tank tops is only partially scoured. The

explanation for the drastically different behavior in the EE early on in the exchange is

due to the fact that the stringers localize the most energetic mixing from the bellmouth

and limit the transverse spread to the width of the stringer spacing. This limits the

extent of mixing that takes place and the SW water remains in the bottom of the tank

while advecting through the tank in a series of buoyant flow events. The EE curve is

linear because only the FW is exiting the tank. On the other hand, in the no stringer

case, the SW from the bellmouth is allowed to spread and mix transversely, as well

as longitudinally, which, apparently leads to near-perfect mixing in the inlet bay. The

mixed region quickly advects throughout the entire tank, carrying SW out the exit. If

the influent SW is exiting the tank, the rate of EE increase, i.e., the accumulation of

SW in the tank, is reduced.

Table 9 lists the EE values at integer values of t

∗for the stringer and no stringer

cases, as well as the two theoretical curves. From the table it can be seen that in both

cases, the EE does not reach the mandated 95% level at t

∗=3. The table emphasizes

the fact that if plug flow can be achieved 100% EE can be obtained at t

∗=1.

Table 9. Exchange efficiencies (full-scale), calculated from CFD simulation data.

t

∗ Exchange Efficiency

Plug flow Perfect mixing w/ stringers w/o stringers

1 1 0.63 0.82 0.63

2 1 0.86 0.91 0.81

3 1 0.95 0.93 0.88

Figure 36 is a plot of the SWEVF for the full-scale CFD simulations with the

theoretical curves for plug flow and perfect mixing. Note that SWEVF from two exits is

shown with outlet 1 being at the top of a bay close to the inlet and outlet 2 being the one

at the far end of the tank (see Figure 32). Figure 36 shows that, as compared with the

55
perfect mixing case, the no stringer case has a time lag before any SW mixture reaches

either of the outlets. The SWEVF then increases rapidly due to the transport of highly

mixed fluid from the inlet bay. The rate of SWEVF increase flattens out and eventually

converges with the perfect mixing case. The case with stringers is more similar to the

plug flow filling curve, with (except for a small spike early on, explained below) a much

longer time before appreciable amounts of SW reach the exits. Surprisingly, the SWEVF

in both the outlets act in tandem implying that the mixed water moves first through

the double bottom and hopper side tanks, before being transported into the upper wing

tank and outlets. This is because the stringers guide the SW to move longitudinally

across the tank more easily than transversely in the early stages of BWE.

t

*

SWEVF

0 1 2 3 0

0.2

0.4

0.6

0.8

1

FS NO STRING OUTLET 1

FS NO STRING OUTLET 2

FS WITH STRING OUTLET 1

FS WITH STRING OUTLET 2

Perfect Mixing

Plug Flow Filling

Figure 36. SWEVF time history for full-scale simulations showing theoretical perfect mixing and plug flow filling curves.

The small spike in the SWEVF at around t

∗ = 0.3 is due to the mixing event that

occurs at the start of the exchange procedure, as the incoming saltwater mixes with

the freshwater in the inlet bay. After this initial mixing event, the mixed fluid is then

transported downstream ahead of the bulk fluid motion. Later in the exchange there is

significant mixing that occurs as larger amounts of the incoming fluid passes up through

the vertical connection pipes and mixes with the fluid in the upper wing bays. As the

amount of incoming fluid passing through the connection pipes increases, the effluent

concentration profile reflects the large increase in the amount of incoming fluid that is

exiting the tank (around 1 TVE).

Discussion of Full-Scale Results

These simulations (Figure 35 and Table 9) indicate that the ballast tank configuration used in bulk carriers may not reach the required 95% EE, however, we cannot say

56
that at 3 TVE the EE is statistically different than 95%. It appears that the primary

cause for loss of EE is trappage of water in the tank tops. The case with stringers

approaches 93% EE, which is the limit if water above the level of the tank top structures (overhead longitudinal stringers) remains trapped. The case without stringers is

about 5% lower. In these calculations the quarter-round vent holes in the tops of the

structure were not included. Since they would allow for some movement of the trapped

water along the top of the tank, their addition in the model would probably increase

the calculated EE somewhat, though to what extent remains to be seen. The addition

of longitudinal stringers to the computational geometry has a profound impact on the

two-fluid mixing in the tank and the EE. It is believed that the most important change

is in the stringers ability to restrain mixing in the transverse direction. With this limitation, the amount of mixing is dramatically reduced and the SWEVF and EE time

histories approach that for plug flow filling. These results would seem to contradict

the findings of Kent and Parsons,6 who performed similar CFD calculations of BWE

and concluded that the finer structural details, such as stringers, could be neglected

and still achieve sufficiently accurate predictions of the EE. Their study, however, was

performed with limited computational resources. The predictions of the J-type bottom/side ballast tank, which is a similar tank arrangement to the geometry used in

this study, were performed using only 276,000 cells. The assessment of the impact of

the finer structural details was not performed on representative overall tank geometry.

Instead, their simulations that included the stringers simply focused on a region of only

the double bottom tank bays, which would not account for the mixing that occurs in

the hopper tank and topside tank sections where the vertical separations between the

structures is also important.

57
SUMMARY AND CONCLUSIONS

BWE experiments on a 1/3-scale section of a ballast water tank and CFD model

simulations for both the 1/3-scale tank and a full-scale ballast tank were performed

for three tank volumes of exchange flow. Experiments were conducted under three

different conditions: Condition 1: SW flow-through exchange with FW at 4.2 m3/min

(1100 gpm); Condition 2: SW flow-through exchange with brackish water at 4.2 m3/min

(1100 gpm); and Condition 3: SW flow-through exchange with brackish water at

6.4 m3/min (1700 gpm). A wealth of qualitative and quantitative data were collected

from areas of important mixing events within the tank, as well as from the exit pipe,

and used to validate the CFD model. These data are also very valuable for understanding the two-fluid flows that occur during BWE. Model scale computations and

simulations were performed for the three conditions. The combined experimental and

computational approaches have given us new insights into the physics of BWE. Significant findings are:

1. The predicted values of EE fall within the experimental error bands, showing that

the CFD model has been validated.

2. Comparisons between CFD and experimental SWEVF and mixedness data within

the tank show that the CFD predicts these quantities reasonably well. One shortcoming is the under-prediction of the amount of mixing for condition 3.

3. Neither the CFD nor the experimental model included the quarter-round vent

holes that are at the top of the tank bays. These would allow a small flow of the

water across the tank top toward the exit pipes, and should act to decrease the

water hideout and therefore possibly increase the calculated EE. However, due to

size of a full-scale tank, the kinetic energy at the interface and the pressure forces

pushing the flow through these holes would be very small.

4. Longitudinal stiffeners (LS) are very effective at decreasing the extent of mixing

within the inlet bay. With LS the early exchange approaches plug flow filling. The

latter stages of exchange approach the perfect mixing case, but the maximum EE

is reduced by FW hideout in the tank top. This result shows that in a full-scale

tank there is insufficient kinetic energy to scour water trapped at the tank top

(water hideout).

5. Not including the LS in the CFD model allows nearly homogenous and instantaneous mixing to occur across the entire inlet bay. The EE curve approaches that

for perfect mixing and is lower than the case including LS.

6. These simulations indicate that if mixing in the inlet bay can be substantially

reduced, AND the quarter-rounds at the tank tops are effective in reducing the

water hideout in the tank tops, it may be possible to perform a 95% exchange in

significantly less than 3 TVs.

58
CFD allows examination of a wide range of ballast exchange conditions across any

tank architecture. It allows evaluation of the effects of various parameters and smallscale tank architecture on the outcomes of exchange. One aspect of ballast water

exchange not incorporated into the present model is the effects of ship motion on the

exchange process – ballast water exchange must be conducted on the high seas. Additional work on this application of CFD modeling should incorporate equations of motion

that account for roll and pitch of a moving vessel. We conclude that CFD modeling is a

very useful approach to understand ballast tank flow and that use of CFD model-based

calculations of EE can be a practical alternative to on-board experiments. However,

appropriate resolution of tank structure and CFD cell grid densities must be allowed

for maximum benefit.

59
APPENDIX A: UNCERTAINTY ANALYSIS

LIF Measurements

Mixedness and Volume of Fluid Measurements

The mixedness at a point (x, y) is given by the following equations:

N(x, y) =







> S : M(x, y)=0

≥ S

2 : M(x, y) = 12 [S − N(x, y)]

< S

2 : M(x, y) = 12 [N(x, y)]

(9)

where the normalized intensity N(x, y) is given by:

N(x, y) = S I(x, y) − DF(x, y)

BF(x, y) − DF(x, y) (10)

The mixedness is proportional to the quantity N(x, y). If the parameters∆ Id and∆ Ic

and their associated uncertainties are defined as follows:

∆Id = I(x, y) − DF(x, y) (11)

∆Ic = BF(x, y) − DF(x, y) (12)

U∆Id = UI + UDF (13)

U∆Ic = UBF + UDF (14)

(15)

The normalized intensity N(x, y) now becomes:

N(x, y) = S ∆Id

∆Ic

(16)

The uncertainty in N is governed by the following equation:

(UN

N

)2

=

* S

N

δS

δN

+2 (US

S

)2

+

*

∆Id

N

δN

δ∆Id

+2 (U∆Id

∆Id

)2

+

*

∆Ic

N

δN

δ∆Ic

+2 (U∆Ic

∆Ic

)2

(17)

Since S is a constant scaling factor, the first term on the right hand side of the above

equation vanishes. Using the equations for the uncertainties in∆ Id and∆ Ic , the

uncertainty in N becomes:

(UN

N

)2

= U2

I + U2DF

∆I2

d

+

U2

BF + U2DF

∆I2

c

(18)

Since M(x, y) is a function of the constant S and 1

2N(x, y) , the relative uncertainty in

M(x, y) is given by the following equation:

(UM

M

)2

=

(UN

N

)2

= U2

I + U2DF

∆I2

d

+

U2

BF + U2DF

∆I2

c

(19)

60
Since the volume of fluid is directly related to the quantity N(x, y), the relative uncertainty in the volume of fluid measurement at each point can be written as:

(UV OF

V OF )2

=

(UN

N

)2

= U2

I + U2DF

∆I2

d

+

U2

BF + U2DF

∆I2

c

(20)

Therefore, the relative uncertainty of the volume of fluid measurement is identical to

the relative uncertainty of the mixedness. The uncertainties in the data, bright field,

and dark field intensities can be expressed in the form:

U2

I = B2I + P2

I = B2

I + 2S2I (21)

U2

BF = B2BF + P2BF = B2BF + 2S2

BF (22)

U2

DF = B2DF + P2DF = B2DF + 2S2DF (23)

(24)

The bias (or systematic) error in the intensity measurements depend on several factors,

including the response time of the fluorescent dye, the repeatability of the laser intensity

from frame to frame, and the pixel discretization of the intensity by the CCD cameras.

The intensity measured by a pixel in the CCD camera can be estimated by the following

equation, where Ip is the measured intensity, $ is the fluorescence efficiency of the dye,

L is the light emitted by the laser source,∆ t is the exposure time of the camera, and

A is the area of the measured area:

Ip ∝ D

($L∆t

A

)

(25)

Therefore, bias uncertainty of the measured intensity Ip can be expressed as:

B2

IP = B2! + B2L + B2∆t + B2A + B2D (26)

The dye response time is considered in this work to have little effect on the uncertainty

in the intensity measurement, since the camera exposure time is much greater than the

response time of the dye molecules. In addition, the dye efficiency is assumed in this

work to be constant throughout the fluid medium. Therefore, the term B! vanishes in

the above equation. This assumption is supported by the fact that the variation in the

laser light dominates the collected intensity. In addition, characterizing the stability of

the collected light will also include effects from dye performance. This work also assumes

that the errors due to CCD leakage are small since the intensities collected were well

below saturation values for the CCD sensors, and that the error in the measured area

is extremely small since the optics used do not move with respect to the target plane.

Therefore, the term BA disappears and the only remaining significant terms are those

originating from laser intensity, discretization error, and camera exposure time. The

repeatability of the laser intensity was measured using the bright field images. The

average intensity in the measurement region was calculated for each frame taken during

a bright field run, and the standard deviation of the measured average intensity was used

as the laser intensity uncertainty. For pixel discretization, an uncertainty of one pixel

61
was used as the uncertainty in intensity. The bias errors resulting from each systematic

source are listed in Table 10. As shown in Table 10, the uncertainty in the exposure

time is extremely small in comparison to the variations in laser illumination, and the

bias error on a single pixel basis is approximately 2.73%. The random uncertainty of the

Table 10. Bias error sources for measured intensity for a single pixel.

Error Source BL (counts) BD (counts) B∆t(sec) BIP (counts)

Absolute Value 1.1755 1 0.1 × 10−6 1.5433

Relative 0.0046 0.003922 1.5 × 10−6 0.00605

bright field and dark field images was calculated by sampling single pixels in the bright

and dark field run and calculating the standard deviation of the measured intensity. For

the intensity during data collection, pixel histories in the images at full concentration

at the beginning of an experimental run were analyzed in order to quantify the random

error in the measured intensity during a run to include the effects of moving fluid. The

bias errors PDF, PBF, and PI are listed in Table 11. The values listed in Table 11 are

Table 11. Bias error sources for measured intensity for a single pixel.

Quantity DF BF I

Mean Value (counts) 4.6217 50.669 37.6473

Relative Random Error 0.4601 0.0661 0.0802

on a pixel by pixel basis. The mixedness and volume of fluid measurements reported

in this work represent an average over the interrogation area. Therefore, in order to

characterize the measurement uncertainty properly, the uncertainty of the measurement

must be calculated for each camera. Using the calculated values and equations above,

the calculated relative uncertainties for each interrogation region are listed in Table 6.

The single point random uncertainty PM is used to calculate PM ̄ based on the number

of points in the corresponding interrogation region. Based on this uncertainty analysis,

the relative uncertainty in the LIF measurements of mixedness and volume of fluid are

approximately 0.66% over the whole field, while for a single pixel measurement the

relative uncertainty approaches 9.84%. Therefore, the LIF measurement of mixedness

and volume of fluid over an entire bay has a very low uncertainty due to the large

number of points interrogated simultaneously. It should be noted that in future studies

the linearity of the CCD sensor response versus dye concentration will be performed

experimentally in order to better estimate the error associated with the assumption of

linear response.

62
Table 12. Relative uncertainties for LIF measurement regions.

Quantity BM PM No. of pts. PM ̄ UM

M

UV OF

V OF

Cam 1 0.006614 0.09815 1388400 8.330E-05 0.006615 0.006615

Cam 2 0.006614 0.09815 1325768 8.524E-05 0.006615 0.006615

Cam 3 0.006614 0.09815 1429785 8.208E-05 0.006615 0.006615

Cam 4 0.006614 0.09815 1299047 8.612E-05 0.006615 0.006615

63
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