PURDUE UNIVERSITY

GRADUATE SCHOOL

Thesis Acceptance

This is to certify that the thesis prepared

By

Entitled

Complies with University regulations and meets the standards of the Graduate School for originality

and quality

For the degree of

Final examining committee members

, Chair

Approved by Major Professor(s):

Approved by Head of Graduate Program:

Date of Graduate Program Head's Approval:

Liangzhu Wang

 Coupling of Multizone and CFD Programs for Building Airflow and Contaminant

Transport Simulations

Doctor of Philosophy

Qingyan Chen

James E. Braun

Albert J. Heber

Jayathi Y. Murthy

February 28, 2007

Qingyan Chen

Anil K. Bajaj

Graduate School ETD Form 9

(01/07)
COUPLING OF MULTIZONE AND CFD PROGRAMS FOR BUILDING AIRFLOW 

AND CONTAMINANT TRANSPORT SIMULATIONS 

A Dissertation 

Submitted to the Faculty 

of 

Purdue University 

by 

Liangzhu Wang 

In Partial Fulfillment of the 

Requirements for the Degree 

of 

Doctor of Philosophy 

May 2007 

Purdue University 

West Lafayette, Indiana 
ii

 

To my mother and father, Juncai Li and Tingtang Wang, who devotes their whole lives to 

raising and educating my two sisters and me; to the memory of my step-grandmother and 

my grandfather, Qingmei Ji and Wenyi Wang, who reminds me to be always strong and 

optimistic; to my beloved wife, Jinxia Liu, who always stands by my side throughout the 

ups and downs of those past years. 
iii

ACKNOWLEDGMENTS 

My thanks and appreciation first goes to Dr. Qingyan (Yan) Chen for his perseverance 

with me as my advisor to complete this research and write the dissertation, and for his 

thoroughness and promptness in guiding my work in progress. Without his on-going 

encouragement, it would have been impossible to complete the project and to maintain 

the standard of scholarship that the project required. I am also grateful to him for the 

opportunity to work under his supervision at Purdue University, which was one of the 

most important and formative experiences in my life. 

I would like to express my gratitude to the members of my dissertation committee, Dr. 

Andrew Persily from U.S. National Institute of Standards and Technology, Dr. James 

Braun, Dr. Albert Heber, and Dr. Jayathi Murthy from Purdue University, who have 

generously given their time and expertise to better my work. My thanks also go to George 

Walton, Stuart Dols, and Steven Emmerich at U.S. National Institute of Standards and 

Technology for their encouragement and valuable contributions to the research. I also 

owe thanks to Dr. Patricia Davies, the director of Ray W. Herrick Laboratories, who 

shared with me the wisdom of life and encouraged me throughout my studies. 

I must acknowledge as well my many friends and colleagues, especially Zhipeng Zhong, 

Jinsong Zhang, Zhiqiang (John) Zhai and Jennifer Gosselin, for their friendship and 

knowledge. I also appreciate the great help from all the technicians and secretaries at Ray 

W. Herrick Laboratories. Finally, my special thanks go to the kindly sponsorships from 

Indoor Air Quality and Ventilation Group of U.S. National Institute of Standards and 

Technology under the grant of 70NANB5H1051, and the contracts of SB1341-04-Q0771 and RFQ-03-Q-9537. 
iv

TABLE OF CONTENTS 

Page 

LIST OF TABLES............................................................................................................ vii

LIST OF FIGURES............................................................................................................ix

NOMENCLATURE.........................................................................................................xiv

ABSTRACT ......................................................................................................................xx

CHAPTER 1. INTRODUCTION........................................................................................1

1.1. General Statement of the Problem.............................................................................1

1.2. Current Design Tools for Building Ventilation and IAQ Analyses ..........................4

1.2.1. Individual Building Ventilation and IAQ Analysis Tools..................................4

1.2.2. Integrated Building Ventilation and IAQ Analysis Tools ................................10

1.3. Research Objectives and Thesis Outline .................................................................13

CHAPTER 2. MAJOR LIMITATIONS OF MULTIZONE MODELS AND 

REMEDY STRATEGIES ATTAINED BY COUPLING MULTIZONE 

AND CFD PROGRAMS...................................................................................................16

2.1. Major Assumptions of Multizone Models...............................................................16

2.1.1. Description of Wind Pressures around Buildings.............................................18

2.1.2. Buoyancy-driven Airflows with Temperature Gradients .................................20

2.1.3. Indoor Airflows with Strong Momentum Effects.............................................22

2.1.4. Indoor Airflows with Contaminant Concentration Gradients...........................24

2.2. Remedy Strategies by Coupling CONTAM and CFD0-C ......................................26

2.3. Summary..................................................................................................................29

CHAPTER 3. COUPLING CONTAM AND CFD0 FOR AIRFLOW 

AND CONTAMINANT TRANSPORT AROUND AND IN BUILDINGS....................31

3.1. Indirect/Virtual Coupling of CONTAM and CFD0-C for 

the Non-uniform Distribution of Wind Pressure around Buildings ...............................31

3.1.1. Indirect Coupling of CONTAM and CFD0-C by the Wind Pressure 

and Contaminant (WPC) Link ....................................................................................32

3.1.2. Indirect Coupling of CONTAM and CFD0-C by the 

Wind Pressure Profile (WPP) Link.............................................................................33

3.2. Direct Coupling of CONTAM AND CFD0-C for Non-uniform 

Distributions of Momentum, Temperature, and Contaminant Concentrations 

in Buildings ....................................................................................................................35

3.2.1. Direct Coupling Controller and Coupling Data Interface.................................35

3.2.2. Direct Coupling Algorithms for Different Simulation Types...........................37

3.2.3. Coupling Solution Existence and Uniqueness..................................................40

3.2.4. Different Coupling Methods.............................................................................51
v

Page 

3.2.5. Selection of the Best Coupling Method by the Scarborough Criterion ............52

3.2.6. Selection of the Best Coupling Method by Numerical Stability Analysis .......53

3.2.7. Numerical Experiments ....................................................................................56

3.3. Summary..................................................................................................................68

CHAPTER 4. VALIDATIONS.........................................................................................70

4.1. Part I – Validation of CFD0-C ................................................................................70

4.1.1. Flow through a 90-degree Planar Branch .........................................................71

4.1.2. Buoyancy-driven Airflows in a Stairwell .........................................................73

4.1.3. Displacement Ventilation .................................................................................77

4.1.4. Cross Ventilation in a 4-zone Building Model .................................................82

4.1.5. External Airflow around a Building Model in a Wind Tunnel.........................84

4.2. Part II – Validations of Coupled Program...............................................................87

4.2.1. Experimental Design.........................................................................................87

4.2.2. Non-Uniform Momentum Distributions...........................................................90

4.2.3. Non-Uniform Contaminant Concentration Distributions.................................97

4.2.4. Non-Uniform Temperature Distributions.......................................................101

4.3. Summary................................................................................................................107

CHAPTER 5. APPLICATIONS......................................................................................108

5.1. Demonstration of the Indirect Coupling for Outdoor Airflow Simulations..........108

5.1.1. Demonstration of the Indirect Coupling by the Wind Pressure 

and the Contaminant (WPC) Link ............................................................................108

5.1.2. Demonstration of the Indirect Coupling by the Wind Pressure 

Profile (WPP) Link ...................................................................................................112

5.2. Demonstration of the Direct Coupling for Indoor Airflow 

and Contaminant Transport Simulations......................................................................118

5.2.1. Simulation of Steady Airflow and Steady Contaminant Transport ................118

5.2.2. Simulation of Steady Airflow and Transient Contaminant Transport............125

5.2.3. Simulation of Transient Airflow and Transient Contaminant Transport........127

5.3. Summary................................................................................................................132

CHAPTER 6. CFD ZONE SELECTIONS FOR COUPLED 

CONTAM-CFD0 SIMULATIONS.................................................................................133

6.1. CFD Zone Selection for Non-Uniform Momentum Distributions........................133

6.1.1. CFD Zone Selection for Channel Flow with Strong Momentum Effect ........134

6.1.2. CFD Zone Selection for Jet Flow with Strong Momentum Effect .................136

6.2. CFD Zone Selection for Non-uniform Contaminant Concentration 

Distributions.................................................................................................................139

6.3. CFD Zone Selection for Non-uniform Temperature Distributions.......................145

6.4. Summary................................................................................................................149

CHAPTER 7. CONCLUSIONS AND FUTURE WORK ..............................................152

7.1. Conclusions ...........................................................................................................152

7.2. Challenges for Future Studies................................................................................155

LIST OF REFERENCES.................................................................................................161 

APPENDICES 

Appendix A. Manual for CFD0-C................................................................................170
vi

Page 

A.1 Installation and Execution of CFD0-C ..............................................................170

A.2 Inputs and Outputs.............................................................................................173

A.3 Preparation of an Input File for CFD0-C...........................................................173

A.4 Result Analyses from Outputs...........................................................................185

A.5 Program Structure of CFD0-C...........................................................................187

A.6 Description of Variables Used in the CFD0-C Code.........................................190

A.7 Description of Formats of Binary Output Files .................................................194

Appendix B. Manual for the Coupled CONTAM-CFD0C Program............................196

B.1 Preparation of an Definition File for a Coupled Simulation..............................196

B.2 The Output File of a Coupled Simulation..........................................................200

B.3 Modifications in CONTAMX and CFD0-C for the Coupled Program..............203

Appendix C. Examples of Input Files ..........................................................................208

VITA................................................................................................................................247
vii

LIST OF TABLES 

Table Page 

1.1: Comparison of computational costs among different CFD methods (Jiang, 2002). ....8

1.2: Comparison of simulation characteristics among multizone, zonal, and CFD 

RANS models. (√=Good, √√=Better, √√√=Best). ...........................................10

2.1: Pressure distribution at the window opening..............................................................20

2.2: Measured results and their comparison with calculated airflow rates 

by CONTAM. .............................................................................................................22

2.3: Fractional flow rate in main branch as a function of Reynolds number 

(Kelka and Choudhury, 2000). ...................................................................................24

2.4: Concentration values at different locations for different models 

(Schaelin et al., 1994). ................................................................................................25

3.1: Atmospheric boundary layer parameters (ASHRAE, 2005). .....................................34

3.2: Simulation types for airflow and contaminant simulations in CONTAM. ................37

3.3: Stability conditions for the three coupling methods...................................................55

3.4: The fluctuation terms of different coupling methods for Scenarios A and B 

for the pressure gradient flows in an office suite........................................................60

4.1: Measured air parameters of the buoyancy-driven flow in a stairwell. .......................74

4.2: Comparison of airflow rates through openings O1 and O2 by the 

measurement and by the coupled simulation (m3/s). ................................................100

4.3: Actual flow conditions from the two air supplies. ...................................................103

5.1: Opening locations, the relative wind pressures computed by CFD0-C, 

and airflow rates computed by CONTAM under the wind speed of 6 m/s...............110

5.2: Prescription of boundary conditions when the wind direction is “θ” 

from the Xmax plane for airflows around a low-rise house........................................114

6.1: Verification of the suggestion for the CFD zone selection for jet 

flows by Case 1: pressure gradient flows in an office suite and 

Case 2: cross ventilation in a four-zone building model in Chapter 3......................138

6.2: Verification of the suggestion for the CFD zone selection for jet flows by 

Case 3: the chamber experiment of non-uniform momentum distributions 

in Chapter 4.2.2.........................................................................................................139

6.3: The parameters required to calculate dimensionless Ar number in order 

to judge when the CFD is required for the cases of a 4-zone chamber, 

a 3-story building, displacement ventilation in an office, and mechanical 

ventilation in a house. ...............................................................................................143 
viii

Table Page 

6.4: The parameters required to calculate dimensionless temperature ................................ 

in order to judge when CFD is required for the cases of a stairwell model, 

a 4-zone chamber, and a light well model. ...............................................................147 

Appendix Table 

A.1: Input and output files of CFD0-C............................................................................173

A.2: The source code files of CFD0-C............................................................................188

A.3: The description of CFD0-C functions. ....................................................................190
ix

LIST OF FIGURES 

Figure Page 

2.1: Plan view of a single-level apartment. .......................................................................20

2.2: Schematic diagram of the half-scale stairwell model.................................................21

2.3: Geometry and grid of 90-degree planar branch (Kelka and Choudhury, 2000)........24

2.4: (a) Contaminant values in a multizone model. (b) Contaminant values 

in CFD (Schaelin et al., 1994). ...................................................................................25

2.5: A conceptual illustration of the indirect coupling of CONTAM and 

CFD0-C for outdoor airflow simulations in a three-story building 

with a large atrium. .....................................................................................................27

2.6: A conceptual illustration of the direct coupling of CONTAM and CFD0-C 

for indoor airflow and contaminant transport simulations in a three-story 

building with a large atrium........................................................................................28

2.7: Coupling strategies for coupled simulations of non-uniform distributions 

of wind pressure, momentum, temperature, and contaminant concentration. ............29

3.1: The schematic of the indirect coupling attained by using the WPC link 

(Walton and Dols, 2003).............................................................................................33

3.2: The schematic of the indirect coupling attained by using the WPP link....................35

3.3: The schematic of the direct coupling attained by using the coupling 

controller and the coupling data interface..................................................................36

3.4: Three coupling schemes for the coupled CONTAM and CFD0-C simulations.........39

3.5: Coupling schematic in a portion of a three-story building with an atrium.................42

3.6: Solution existence and uniqueness analysis of the curves of Pd,ic-Pu,ic.......................50

3.7: Schematic of the coupling procedure at the coupling iteration k. ..............................54

3.8: The layout of an office suite with four offices and one hallway. ...............................57

3.9: Airflow rates calculated with different coupling methods 

(a) airflow rate through door 1 in Scenario A by Methods 1 and 3; 

(b) airflow rate through door 3 in Scenario B by Methods 1 and 2............................59

3.10: Comparisons of calculated airflow rates through different openings in 

an office suite with and without coupling (a) Scenario A and (b) Scenario B............61

3.11: Airflow patterns and pressure distributions with coupling in the office suite 

(a) Scenario A with closed windows a, b, c, and d; 

(b) Scenario B with open windows a, b, c, and d........................................................63

3.12: The 4-zone building model (a) section (top) and plane (bottom) of 

the wind tunnel laboratory (Sawachi et al., 2003); (b) the three-dimensional 

view of the building model. ........................................................................................64
x

Figure Page 

3.13: The coupled simulation in a four-zone house model with cross ventilation 

(a) the measured velocity field of the four-zone house model; 

(b) the velocity and pressure fields by the coupled simulations.................................66

3.14: Airflow rate through path B during the iteration with the 

three coupling methods in a four-zone building model with cross ventilation...........67

4.1: Streamline lines in the 90-degree planar branch: (a) Re=10, (b) Re = 400................72

4.2: Fractional flow rates in main branch as a function of the Reynolds number. ............73

4.3: Comparison of mass flow rates of CFD0-C, Experiment and 

CONTAM for the buoyancy-driven flow in a stairwell..............................................75

4.4: The flow pattern in the experiment. ...........................................................................76

4.5: The flow patterns by the numerical simulation by CFD0-C for 

the input power of 300 W. ..........................................................................................77

4.6: The layout of the displacement ventilation simulated and tested 

in the chamber (inlet -1, outlet -2, person -3, table -4, window -5, 

fluorescent lamps -6, cabinet -7, computer -9, tracer gas sources -10). .....................78

4.7: The air distribution for the displacement ventilation case. (a) computed velocity 

in a middle section, (b) computed velocity in a horizontal section, 

(c) computed temperature in a middle section, and (d) airflow pattern 

observed by smoke visualization in a middle section.................................................79

4.8: The comparison of the velocity profiles at nine positions in the room 

between the calculated and measured data for the displacement ventilation 

case. Z = height, H = total room height, V = velocity, Vin = inlet velocity, 

H = 2.43 m, Vin = 0.086 m/s. .....................................................................................80

4.9: The comparison of the temperature profiles at nine positions in 

the room between the calculated and measured data for 

the displacement ventilation case. Z = height, H = total room height, 

θ = (T-Tin/Tout-Tin), H = 2.43 m, Tin = 17.0 oC, Tout = 26.7 oC. .............................81

4.10: The comparison of the contaminant profiles (ppm) at nine positions 

in the room between the calculated and measured data for the 

displacement ventilation case. Z = height, H = total room height, 

χ= (C-Cin/Cout-Cin), H = 2.43m, Cin = 0.0, Cout = 0.421. ......................................82

4.11: Comparison of calculated and measured flow field with 

the wind coming perpendicular to the opening (a) The CFD0-C model, 

(b) CFD0-C flow field, (c) flow visualization in the test model, 

and (d) measured airflow field....................................................................................83

4.12: Measured wind velocity distribution (m/s) at the wind supply opening 1. ..............85

4.13: Comparison of (a) measured wind pressure coefficients with 

(b) calculated wind pressure coefficients by CFD0-C when 

wind direction is zero degree. .....................................................................................86

4.14: The environment chamber of Ray W. Herrick Laboratories....................................88

4.15: Example of the sensors used for air velocity, air temperature, 

and flow rate measurements and their locations.........................................................89

4.16: The scheme of the four-zone chamber used to study 

non-uniform momentum distribution in zone 1..........................................................91
xi

Figure Page 

4.17: Airflow and pressure distributions in the four-zone chamber facility 

(a) calculated by CONTAM and (b) calculated by the coupled CONTAM 

and CFD0 program. ....................................................................................................92

4.18: Comparison of measured airflow rates with different simulated results..................93

4.19: The pressure distribution at 1.66 m from the floor in the four-zone 

chamber calculated by CFD0......................................................................................94

4.20: The plan view of the four-zone facility with the nine measuring poles. ..................95

4.21: Comparison of air velocities at P7, P8, and P9 in zone 1 with 

non-uniform momentum distribution (H=2.44m; υ =U/Uin, non-dimensional 

velocity when Uin=2.281 m/s is the supply air velocity and the supply rate 

is 0.105 m3/s................................................................................................................96

4.22: The chamber schematic used for contaminant transport study 

and the contaminant source locations. ........................................................................97

4.23: Comparison of measured and simulated SF6 concentrations (ppm) 

in zones 2 and 3. .........................................................................................................98

4.24: SF6 concentration distribution at openings 1 and 2 height in 

the four-zone chamber facility calculated by the coupled CONTAM 

and CFD0 program. ....................................................................................................99

4.25: Comparison of measured and computed SF6 concentrations (ppm) at 

P7, P8, and P9 in Zone 1 for the non-uniform contaminant distribution case..........101

4.26: Schematic of the case used to study non-uniform temperature distribution. .........102

4.27: Comparison of airflow and pressure distributions for the case 

with non-uniform temperature distribution by (a) CONTAM and by 

(b) the coupled CONTAM and CFD0. .....................................................................103

4.28: Comparison of airflow rates for the case with different methods. .........................105

4.29: Comparison of the air temperatures at the three poles in zone 2 for 

the non-uniform temperature distribution when the surface temperature 

of the heated box was 35 °C (H=2.44m; τ = (T-Tin)/ (Tout -Tin) is 

non-dimensional temperature where Tin=18.2 °C was the supply air temperature 

and Tout=24.3 °C was the exhaust air temperature). .................................................106

5.1: Building plane view and CONTAM results using the WPC File. ............................109

5.2: Pressure contours (Pa) and velocity fields around a building, 

as computed by CFD0...............................................................................................110

5.3: (a) CFD0-C mesh, (b) the internal zone configuration of the low-rise house 

with a sloping roof, and (c) plane view of the CFD0-C domain. .............................113

5.4: The profile of mean wind velocity V for inflows. ..................................................115

5.5: Comparison of calculated wind pressure coefficient by the WPP link 

with measured data at Path 3 of the house for the relative wind direction 

to the surface with Path 3 (θ =0° ~ 360°). ................................................................116

5.6: Comparison of calculated infiltration rates by CONTAM, the WPP Link, 

and using measured non-uniform wind pressure coefficients when θ = 60°............117
xii

Figure Page 

5.7: Views of the three-story building. (a) Three-dimensional outside view 

with the external walls removed; (b) Three-dimensional internal view; 

and (c) Plan view in CONTAM with the contaminant of C1. ..................................119

5.8: Comparison of airflow rates with and without coupling..........................................121

5.9: Velocity fields and temperature contour at the section of Y=5.5m..........................122

5.10: Comparison of C1 concentrations with and without coupling at 

(a) Plane 1 (P1); (b) Plane 2 (P2); (C) Plane 3 (P3); and (d) Plane 4 (P4). ..............123

5.11: Velocity distribution at the cross section of X=30m...............................................124

5.12: Comparison of transient C1 concentration with and without coupling for 

(a) zones 1 through 8 except 4 at Level 1; (b) zone 4 at Level 1..............................126

5.13: Emergency ventilation, control systems, and airflow distribution 

when the emergency ventilation is on at (a) the first floor 

and (b) the top of the 3-story building. .....................................................................128

5.14: Concentration history of zone 1-4 for three sensor locations before 

and after the emergency ventilation system is on. ....................................................129

5.15: Airflow and C1 concentrations at 10 minutes after the release of C1 

for the sensor locations of (a) Sensor #3 and (b) Sensor #1. ....................................131

5.16: Personal exposures to the C1 concentration and to the incremental C1 

magnitude when occupants evacuate through paths 1 and 2. ...................................132

6.1: Illustration of airflow patterns/types into a room.....................................................134

6.2: The errors caused by neglecting airflow momentum effects under different 

Reynolds numbers for channel flows........................................................................136

6.3: Illustration of airflows inside a room for jet flows...................................................137

6.4: Illustration of airflow and contaminant transport in a room with 

an internal partition...................................................................................................141

6.5: The correlation of Ar ~ m for the cases of a 4-zone chamber, 

a 3-story building, displacement ventilation in an office, and mechanical 

ventilation in a house. ...............................................................................................144

6.6: Illustration of the non-uniform distribution of temperatures in a room. ..................146

6.7: The errors caused by the assumption of uniform temperature for 

dimensionless temperature gradient for the case of a stairwell model, 

a 4-zone chamber, and a light well mode. ................................................................148

6.8: Procedure to judge when CFD is required by the suggestions for 

non-uniform distribution of air momentum effect, air temperature, and 

contaminant concentration........................................................................................150

7.1: Asymmetric results caused by the difference of multizone and CFD methods 

and the inappropriate selection of CFD zones (Axley, 2006)...................................158 

Appendix Figure 

A.1: The Graphic User Interface (GUI) of CFD0-C .......................................................173 

A.2: The window for registration of CFD0-C.................................................................173 

A.3: Run CFD0-C from the CFD0-C GUI ......................................................................173 

A.4: Run CFD0-C from WINDOWS Console ................................................................174 

A.5: Instant help in the CFD0-C GUI..............................................................................176 

A.6: Program structure of SIMPLE algorithm in CFD0-C .............................................191 
xiii

Figure Page 

A.7: The flow domain inside the dashed box is output to create the EWC, WDB, 

and CDB files (note that Point O is the origin of the output domain, at which 

xref, yref, zref is the ordinates relative to the whole CFD domain) .........................197 

B.1: Program structure of CONTAMX 2. ......................................................................209 

 
xiv

NOMENCLATURE 

a coefficient of an unknown variable 

A area of an opening; cross-sectional area of a room 

Ar the Archimedes number 

b source term in a mass continuity equation 

'

b

source term in the linear form of mass continuity equation for a zone in a 

multizone program 

B vector of source terms in an assembled momentum conservation equation 

Bc vector of source term in an assembled species conservation equation 

Be vector of source terms in an assembled energy conservation equation 

B1 vector of the source terms in the assembled total matrix equation for Method 1 

c index of CFD zones 

C

nonlinear flow coefficient; ratio of inflow opening area to the cross-sectional area 

of a room; contaminant concentration 

C average contaminant concentration 
xv

C coefficient matrix in an assembled total matrix equation 

Cc coefficient matrix in an assembled species conservation equation 

C1 coefficient matrix in the assembled total matrix equation for Method 1 

Cm coefficient matrix in an assembled momentum conservation equation 

Ce coefficient matrix in an assembled energy conservation equation 

C system equations for a CFD program 

CL linear flow coefficient 

Cp heat capacity at constant pressure 

d

difference between the local pressure of a flow path and the pressure of the zone, 

to which the path connects 

F air mass flow rate; volumetric airflow rate 

F vector of unknown flow rates through interface paths and cells 

f airflow rate through the face of a CFD cell, perpendicular to the flow direction 

g acceleration of gravity 

Gr the Grashof number 

h height 

H reference height 
xvi

i index of the zones for a multizone program; input parameter for C

ic index of the flow paths linking zone i and zone c 

ij index of the flow paths linking zone i and zone j 

j index of the zones for a multizone program 

L characteristic length 

m index of non-uniformity of contaminant 

M system equations for a multizone program 

M vector of species concentration of an assembled species conservation equation 

n flow exponent 

N total number of sample cells/points 

p pressure at a grid point 

P pressure of a zone; index of grid points or cells 

P vector of unknown pressures of multizone and CFD cells 

Pd downwind total pressure of an airflow path 

PH undisturbed wind pressure at the reference height H 

PS pressure difference due to density and elevation differences 
xvii

Pu upwind total pressure of an airflow path 

PW pressure difference due to wind; wind pressure 

Q heat input in w 

Q vector of heat inputs in an assembled energy conservation equation 

r input parameter for M

Re the Reynolds number 

S source term 

S vector of source terms in an assembled species conservation equation 

St the Stanton number 

T temperature 

T vector of temperatures in an assembled energy conservation equation 

U wind velocity; velocity in X direction 

U vector of airflow velocity through an opening 

UH wind velocity at the reference height H 

V velocity; volume; velocity in Y direction 

V velocity vector 
xviii

V average wind velocity 

W width; velocity in Z direction 

a exponent for wind velocity profile 

b Volumetric thermal expansion coefficient 

d atmospheric boundary layer thickness 

θ azimuth direction 

r air density 

t dimensionless temperature gradient 

υ air kinematic viscosity 

Δ difference 

f general variable 

Γ diffusion coefficient forf 

Subscripts 

av average 

b bottom 
xix

exp experiment 

i index of the zones of a multizone program; index of CFD cell 

ic index of the flow paths linking zone i and zone c 

ij index of the flow paths linking zone i and zone j 

in inflow 

j index of the zones of a multizone program; coordinate direction 

k index of coupling iterations 

met meteorological 

nb neighboring 

P index of grid points or cells 

r room 

s building surface 

t top 

w wind 
xx

ABSTRACT 

Wang, Liangzhu. Ph. D., Purdue University, May, 2007. Coupling of Multizone and CFD 

Programs for Building Airflow and Contaminant Transport Simulations. Major Professor: 

Dr. Qingyan (Yan) Chen, School of Mechanical Engineering. 

Building ventilation designs and Indoor Air Quality (IAQ) analyses are important to 

provide a safe, healthy, and comfortable indoor environment, and to improve the energy 

savings and substantiality of buildings. However, current design tools have their own 

merits and drawbacks. Multizone programs can achieve a fast computing speed, but they 

are still limited to the predictions of the average characteristics of airflows and 

contaminant distributions due to the various assumptions that revolve around them. CFD 

programs can provide more accurate results, yet they demand higher computing costs. An 

integrated program of multizone-CFD methods can combine the merits of both programs 

while eliminating their drawbacks. This thesis thus investigates the fundamentals, 

strategies, implementations, validations, and applications of coupling a multizone 

program, CONTAM, with a CFD program, CFD0-C, for building airflow and 

contaminant transport simulations. 

This research first identifies the situations, where the major assumptions of multizone 

models become problematic: non-uniform distributions of wind pressures, momentum 

effects, temperatures, and contaminant concentrations. Two coupling strategies have been 

developed to improve CONTAM assumptions. For non-uniform wind pressure 

distributions on a building surface, this study develops an indirect coupling strategy, 

which exchanges wind pressures indirectly between CONTAM and CFD0-C. For the 

cases with non-uniform distributions of momentum effects, temperatures, and 
xxi

contaminant concentrations, a direct coupling scheme is employed to exchange iteratively 

information between CONTAM and CFD0-C. Theoretical analyses then prove that the 

direct coupling scheme has a solution, which is a unique one. This study also finds that 

for the direct coupling, the most stable method is to exchange pressure boundary 

conditions between the multizone and CFD programs. 

This research conducted experiments in a test chamber to validate the coupled 

CONTAM-CFD0 program. This study shows that the calculations of the coupled 

program are reasonably accurate, while preserving acceptable computing costs. The 

performances of the coupled program are also demonstrated by several case studies, 

illustrating how the coupled CONTAM-CFD0 program can effectively improve 

CONTAM simulations. Finally, dimensional analyses are conducted to provide 

suggestions on when multizone assumptions become problematic and thus CFD methods 

are needed. 
1

CHAPTER 1. INTRODUCTION 

1.1. General Statement of the Problem

People in developed countries spend about 90% of their lifetime indoors (U. S. EPA, 

1995). With properly controlled air temperature, humidity, and velocity, people feel 

comfortable and are productive in an indoor environment. An uncomfortable indoor 

environment and poor indoor air quality (IAQ) can lead to low productivity at work, 

resulting in significant economic loss (Raw et al., 1990; Mendell, 1993; Wolkoff, 1995). 

Conservatively estimated, the loss of productivity due to impoverished IAQ can be up to 

6% (Dorgan et al., 1998). In US commercial buildings, the corresponding economic 

losses could be about $20 to $160 billion per year (Fisk, 2000). 

Issues related to indoor environments do not only involve comfort, but also encompass 

people's health. Long periods of exposure to poor IAQ can cause various health 

problems. If building occupants repeatedly report a complex range of vague and 

subjective health complaints, they are experiencing what is called “Sick Building 

Syndrome” (SBS). Serious SBS can lead to morbidity, disability, disease, and even death 

in extreme cases (Ren, 2002). The current increase of indoor pollutants is resulting in 

more frequent cases of SBS. In developing countries, more than 2,000,000 people, 

mainly women and children, die yearly because of the deadly mixture of pollutants 

resulting from the burning of biomass, especially when cooking indoors (Sundell, 2004). 

In developed countries, more and more synthetic building materials are being used in 

building insulations, internal furnishings, and craft materials. Many sources of 

contaminants, such as volatile organic compounds (VOCs), are being introduced into 

indoor working and living environments. Some VOCs can cause eye, nose, and throat 

irritation, as well as damage to the liver, kidney, and the central nervous system. Studies 
2

have found that the VOC levels are 2 to 5 times higher indoors than outdoors. Especially 

after the immediate use of materials containing VOCs, such as those used during paint 

stripping, for example, the VOC levels can be 1,000 times higher than outdoor levels (U. 

S. EPA, 1995). Buildings have become sources of contamination and are often more 

polluted than their surroundings (Spengler and Chen, 2000). 

Moreover, highly populated buildings can become dangerous if the building ventilation 

system performs poorly during emergencies. Between November 2002 and June 2003, 

the severe acute respiratory syndrome (SARS) epidemic caused unprecedented 

international panic. SARS is primarily transmitted by bio-aerosol droplets or direct 

personal contact. Originating in China, SARS spread to the rest of the world when an 

infected medical doctor stayed in a hotel at Hong Kong. The medical doctor was later 

treated in a hospital, where the ventilation and air-conditioning system were later found 

to be highly possible causes of a large SARS outbreak (Li et al., 2005b). The most 

serious reported community SARS outbreak worldwide was at the Amoy Gardens of 

Hong Kong, with a total of 329 infected cases and 42 deaths. Li et al. (2005a) found that 

natural ventilation might have played an important role in circulating the SARS virus at 

the Amoy Gardens. Such an incident showed the importance of proper ventilation designs 

in high-rise residential buildings. 

Some other types of emergencies also show the importance of building ventilation 

designs and IAQ analysis. The September 11, 2001 terrorist attacks on New York City 

and Washington D.C. and the following anthrax dispersion by mail have spawned 

concerns about various possible forms of terrorism, including airborne/aerosolized 

chemical and biological warfare agent (CBWA) attacks. The events have confirmed that 

the attacks are no longer a hypothesis but a reality. Most CBWAs are highly poisonous. 

A small amount of CBWA can seriously affect one’s health or even threaten lives. For 

instance, one may suffer a mild injury, a serious injury, and death, respectively, while 

inhaling as little as 0.9, 10, and 15 milligrams of the lethal nerve agent VX gas, according 

to the US Army Chemical Biological Defense Command (Zhai et al., 2003). Once the 
3

terrorists and rogue nations own weapons such as CBWA, they could deliver small 

packages to an embassy, military facility, or a building with a high civilian population 

density (Arvelo et al., 2002). Another type of potential warfare agents is radiological 

materials, which may cause less instant damage but more serious long-term effects than 

CBWAs. In 1995, a TV reporter was directed by Chechnya rebels to a park in central 

Moscow, where she found a package with a small amount of explosives and something 

else: Cesium-137, a radioactive isotope. This was the debut of what has become a 

household word: a dirty bomb. The explosives in a dirty bomb are not the true threat, but 

Cesium-137, which is very dispersible, like talc powder, is very dangerous. With typical 

air speed, it could travel six miles, if unobstructed, in half an hour. The resultant 

radioactive contamination will be deposited on building walls, plants, and soils. Unless it 

is cleaned up, this radioactivity, with the potential of damaging human DNA, will stay in 

place for decades (Higginson, 2003). 

The concept of a building design that is immune toward these potential chemical, 

biological, and radiological warfare agent (CBRWA) attacks has gained wide attention in 

recent years. To design an immune building, it is very important to understand the 

transport physics of CBRWAs, especially their transport phenomena with air movement. 

Thus, an appropriate design of building ventilation system does not only mean supplying 

air with a suitable temperature and velocity to achieve a comfortable and healthy indoor 

environment. The ventilation system must be designed in such a way that during 

emergencies, enough clean (or fresh) air is distributed in a properly controlled manner to 

dilute or remove various types of hazardous pollutants in a timely and effective fashion. 

The planned amount of clean air, however, hinges on other factors, including, for 

example, energy and sustainability concerns. Buildings consume a lot of energy. In 

Western Europe, 52% of energy is delivered to maintain acceptable climate conditions 

within buildings (Clarke and Maver, 1991). In the US, buildings account for one-third of 

all used energy and two-thirds of all electricity consumption (U.S. EIA, 1995). Recently, 

the shortage in crude oil caused an increase in the price of gas, which caused people to 
4

worry about a recurrence of the 1970's energy crisis. Building ventilation designs thus 

have to consider sustainability. One of the popular strategies is to use natural ventilation, 

which can provide occupants with good IAQ and less energy costs than conventional 

mechanical ventilation (Allard and Inard, 1992; Etheridge and Sandberg, 1996). 

However, the design of natural ventilation cannot be successful without a proper design 

tool. In conclusion, building ventilation designs and IAQ analyses should consider the 

relationship between various aspects, including the safety, health, and comfort of people, 

and the energy consumption and sustainability of buildings. Sophisticated design tools 

are therefore required. 

1.2. Current Design Tools for Building Ventilation and IAQ Analyses

The traditional method to design building ventilation systems is the paper-and-pencil 

method, which is based on design handbooks and engineering experiences. With the 

invention of computers, computer programs can now carry out the tedious manual 

calculations. In the last three decades, many computer design models and tools have been 

developed. According to underlying design regimes and calculation methods, one can 

classify the design tools as “individual building ventilation and IAQ analysis tools” and 

“integrated building ventilation and IAQ analysis tools.” 

1.2.1. Individual Building Ventilation and IAQ Analysis Tools 

Although all building ventilation and IAQ analysis tools are designed for predictions of 

airflow distribution and contaminant transport, they serve different purposes when used 

individually. Some tools focus on the average characteristics of infiltration airflows, 

contaminant distribution, and lower computational costs, such as multizone airflow 

network (multizone) models. These models often employ many assumptions in order to 

achieve fast computing speed. Some other tools use much less assumptions and are able 

to obtain detailed spatial values of airflow and contaminant concentrations. Nevertheless, 

these tools demand more computing time than multizone models, e.g. computational fluid 

dynamics (CFD) models. A third type of model is the zonal model, which is a simplified 
5

form of CFD models. Zonal models normally demand less computational time than CFD 

models while providing more detailed results than multizone models. Zonal models, 

however, have their own drawbacks. The merits and drawbacks of these models are 

compared in detail in the following section. 

Multizone airflow network models

Multizone airflow network models have been used as a research and design tool for over 

twenty years (Emmerich, 2001). A 1992 survey reported that nearly fifty multizone 

models are available (Feustel and Dieris, 1992). They are widely used in such areas as air 

distribution analysis, smoke controls, and building pressurization tests, etc. The simulated 

building types include residential buildings (Persily, 1998; Emmerich et al., 2002), 

commercial buildings (Salemi et al., 1996), and industrial buildings (Li et al., 2000). 

Multizone models calculate the airflow and contaminant transport between the rooms of a 

building and between the building and the outdoors. The rooms of a building are typically 

represented as zones, with homogeneous air properties and contaminant concentrations. 

Airflows pass through the paths interconnecting the various zones, and they have userdefined leakage characteristics (Musser, 2001). The airflow rates through paths and the 

average contaminant concentrations are calculated based on the mass balance. Since 

multizone models solve only mass and contaminant balance equations for each room, the 

computational time is much less than that required by other models, such as a 

computational fluid dynamics (CFD) program. 

To achieve a fast computing speed, multizone models use a number of assumptions, 

which can lead to some problems. The key assumptions of the multizone network models 

are (Persily, 2003): 

• Uniform pressure, temperature and species concentration in each zone 

• Quiescent or still air in zones; airflow through zones does not impact zone 

pressure 

• Kinetic energy and momentum not accounted for by flow path models 
6

• Instantaneous contaminant transport along each flow path, e.g. no delays in 

ductwork 

Note that multizone models in fact assume that pressure is hydrostatically distributed in 

each zone. Here by meaning uniform pressure, we refer to the total pressure of each zone 

without the hydrostatic part, which is consistent with the custom of CFD methods. These 

assumptions may compromise the accuracy of the results obtained. In addition, multizone 

models cannot provide the spatial parameters of airflow and the transport of contaminant. 

To reduce the assumptions used, and to obtain more detailed indoor airflow information, 

some other models should be used, such as the zonal airflow models. 

Zonal airflow models

The development of zonal models aims to obtain approximate but faster simulation 

methods than the CFD ones to predict a building's airflow and the transport of 

contaminant (Mora et al., 2003). The first zonal model was proposed by Lebrun (1970), 

who divided a single zone into sub-zones based on the characteristics of the main driving 

flows. Instead of a uniform temperature, a rough estimate of thermal stratification was 

calculated for the zone. Since Lebrun’s pioneering work, various zonal models (Inard, 

1988; Li et al., 1998b; Haghighat et al., 2001) have been developed for different 

applications, e.g. flows with plumes, jets, and boundary layers etc. Grelat (1987), Bouia 

and Dalicieux (1991), and Wurtz (1995) generalized the zonal models by developing a 

so-called pressure zonal model, in which a room is divided into sub-zones with nonuniform pressures. The pressures are then solved by imposing mass balances to each subzone. 

Zonal models introduce more dynamics into the prediction of mean flows, compared to 

multizone airflow network models. By using a mesh to divide the room air into control 

volumes, zonal models provide more information than multizone models and require less 

computing power than the CFD models (Zhai, 2003). However, current zonal models also 

have many limitations. One of the problems is the method of dividing a room into subzones, namely the zoning method. Most zoning methods use regular hexahedrons, in 
7

which air properties and contaminant concentrations are assumed homogeneous. Airflow 

patterns and contaminant concentration distributions often have to be known before a 

room can be correctly divided into sub-zones. Presently, zonal models only provide 

airflow patterns for some typical indoor airflow problems; thus, their applications are 

limited. Furthermore, Griffith (2002) found that many zonal models are not numerically 

stable. Even if zonal models are numerically stable, the pressure variable solved in zonal 

models is really an internal variable used to balance the flow equations, and has no 

physical significance (Musy, 1999). 

Computational fluid dynamics (CFD) models 

Over the past half century, computational fluid dynamics (CFD) has become an important 

methodology for attacking the complex problems in fluid mechanics and heat transfer 

(Tannehill et al., 1997). CFD techniques have achieved encouraging results for diverse 

indoor environmental and HVAC studies (Emmerich, 1997; Ladeinde and Nearon, 1997; 

Nielsen, 1998; Spengler and Chen, 2000). Compared to multizone and zonal airflow 

models, CFD is the most sophisticated method. It calculates the detailed spatial 

distribution of air velocity, temperature, and contaminant concentrations by solving the 

Navier-Stokes and species-conservation equations. CFD can be further divided into direct 

numerical simulation (DNS), large eddy simulation (LES), and the Reynolds averaged 

Navier-Stokes equations with turbulence models (RANS). 

Direct numerical simulation is to compute the turbulent flow and the contaminant 

dispersion by solving the highly reliable Navier-Stokes equations without 

approximations. Very fine grid resolution is required to capture the smallest eddies in the 

turbulent flow at very small time steps, even for a flow at steady state. It would take years 

of computing time for DNS to predict contaminant dispersion in buildings. 

Large eddy simulation (Deardorff, 1970) separates turbulent motion into large eddies and 

small eddies. The large eddies corresponding to the three-dimensional time-dependent 

equations can be directly simulated, while small eddies are modeled. It has been 
8

successfully applied to study airflow in a single space (Emmerich and McGrattan, 1998; 

Jiang and Chen, 2001; Jiang, 2002). Although large eddy simulation requires a much 

smaller computer capacity and is much faster than direct numerical simulation, large 

eddy simulation, for predicting the airflow and contaminant dispersion in a building, 

demands a large computer memory capacity (1010-byte memory) and a long computing 

time (weeks), which is not practical. 

The Reynolds Averaged Navier-Stokes (RANS) equations with turbulence models solve 

the statistically averaged Navier-Stokes equations by using turbulence transport models 

to simplify the calculation of the turbulence effect. The use of turbulence models leads to 

some errors, but can significantly reduce the need for computer memory and speed. The 

RANS modeling provides detailed information on airflow and contaminant concentration 

distributions. The method has been successfully applied to a building's indoor airflow, as 

well as to thermal comfort and indoor air quality analysis, as reviewed by Emmerich 

(1997), Ladeinde and Nearon (1997), and Nielsen (1998). The RANS modeling can be 

easily used to study the airflow and contaminant dispersion in a room. 

Table 1.1 Comparison of computational costs among different CFD methods (Jiang, 

2002). 

Grid Computational time CFD methods Building Airplane Building Airplane 

RANS 1051072 hours 200 hours 

LES 106108100 hours 1 year 

DNS 1011 1016 105years 1012years 

Table 1.1 compares grid resolutions and computational costs when the three CFD 

methods are used in the airflow simulations of buildings and airplanes. The RANS 

method requires the fewest number of grids and is the fastest CFD method. It is very 

difficult to apply LES and DNS to real design practices due to their enormous 

computational costs. Currently, RANS is the most commonly used CFD method in 

building ventilation design and IAQ analysis. 
9

However, CFD methods have their own drawbacks when compared to multizone and 

zonal models. Although the RANS method is the fastest CFD method, it still requires 

much more computational cost than multizone and zonal models. Although two hours 

seem acceptable for a building with 105grids in Table 1.1 when simulated by RANS, 

multizone models only need several seconds for the same problem. The difference in 

computational costs between CFD and multizone models will be even more significant 

for transient simulations over a long period of time. Thus, the CFD method is seldom 

used for a whole-year building simulation. Presently, CFD models also face some 

challenges in building ventilation design and IAQ analysis. It is hard for CFD methods to 

simulate air infiltrations or exfiltrations, especially when the locations of building cracks, 

through which filtrations occur, cannot be identified. For simulations of buoyancy-driven 

flows with pressure boundary conditions, under-relaxation factors must be carefully 

selected for convergence. Sometimes, multiple runs are required to test different CFD 

parameters for convergence. CFD methods, therefore, normally need more expertise and 

experience than other methods for a successful simulation. 

Above all, when multizone, zonal, and CFD methods are used individually, they have 

different merits and drawbacks, as summarized and compared in Table 1.2. The 

multizone model is the fastest method with many assumptions, whereas the CFD is the 

most accurate, with the most computational costs. Zonal methods stand between these 

two models in terms of accuracy and computational time. For simulation capacities, each 

method has its own merits when applied to different problems. Multizone models can 

provide average characteristics of airflow and contaminant transport, while CFD and 

zonal methods can calculate the spatial distributions of these parameters. Therefore, an 

integration of multizone, zonal, and CFD methods is supposed to combine the merits and 

avoid the drawbacks of each of these methods. 
10

Table 1.2 Comparison of simulation characteristics among multizone, zonal, and CFD 

RANS models. (√=Good, √√=Better, √√√=Best). 

1.2.2. Integrated Building Ventilation and IAQ Analysis Tools 

Most of the current integrated tools are coupled multizone and zonal models, or coupled 

multizone and CFD models. Although some studies (Peng and Paassen, 1995; Kato et al., 

1998) extracted CFD information for their simulations by zonal models, their studies did 

not integrate zonal and CFD methods. In fact, as a simplified form of CFD, zonal models 

Items Multizone Zonal CFD 

Simulation assumptions 

Perfect mixing in each room √

Quiescent or still air in each room √

Neglect of air resistance in each room √

Neglect of inflow momentum effect, if any √

Instantaneous contaminant transport inside a room √

Airflow driven only by pressure difference √ √

Hydrostatic distribution of pressure inside a room √

Simulation potentials 

Ductwork design √

Building energy calculation √ √√

Distribution of airflow and contaminant concentration √ √√

Wind pressure profile around buildings √

Popularity in whole building simulation √√√ √ √√

Popularity in yearly dynamic simulation √√√ √ √√

Modeling capacity of orifice type openings √√√ √√ √

Modeling capacity of large openings √ √√ √√√

Modeling of large spaces √ √√ √√√

Integration capacity with building controls √

Modeling of building infiltrations √√√ √√ √

Evaluation of ventilation efficiency √ √√

Evaluation of personal exposure inside a room √ √√

Miscellaneous items 

Simulation accuracy √ √√ √√√

Computational speed √√√ √√ √

Numerical convergence and stability √√√ √ √√

Adaptability √√√ √ √√

Less simulation skills required √√√ √√ √
11

do not need to be integrated with CFD models. By using coupled multizone and zonal 

models, or multizone and CFD models, one of the major motivations is to remedy the 

well-mixing assumption of multizone models. 

 

Since zonal models can provide non-uniform distributions of pressures and airflow 

patterns, they are useful in improving the accuracy of multizone model simulations. 

Stewart and Ren (2003) nested zonal models within a multizone model – COMIS 

(Feustel, 1999) and developed a new program called CoWZ, for “COMIS with subzones.” Although CoWZ was able to improve the accuracy of contaminant distributions 

calculated by COMIS, the zonal models of CoWZ can only be applied to single rooms 

with a limited set of driving forces (Ren, 2002). Based on a more robust simulation 

environment of zonal models – SPARK, Buhl et al. (1993) and Mora (2003) also tried to 

couple zonal and multizone models. However, the limitations of zonal models themselves 

prevented the application of a coupled multizone-zonal model. Musy (1999) pointed out 

that the pressure variable solved in zonal models is really an internal variable used to 

balance the flow equations, which should not be confused with the pressure variable 

solved in multizone models. So Mora et al. (2003) concluded that when zonal models are 

coupled with multizone models, the pressure predictions by zonal models should be 

ignored, and only the airflows should be used at the interfaces shared by the two models. 

Mora et al. therefore suggested that Computational Fluid Dynamics (CFD) should be an 

alternative to zonal models for coupling with multizone models in building air 

distribution simulations. 

Although the idea of the coupling of multizone and CFD models in building airflow 

simulations was proposed fairly early (Schaelin et al., 1994), literature reviews show that 

not many coupling studies have been conducted. Schaelin et al. proposed a method called 

"method of detailed flow path values," in which the well mixing assumptions of 

multizone models were remedied, providing detailed pressures, velocities, and 

contaminant concentrations of flow paths from the CFD. This study, however, only 

implemented the coupling of contaminant concentrations and did not actually perform the 
12

coupling in airflow simulations. The coupling procedure was also an external or 

“manual” iteration. 

Moreover, Clarke et al. (1995a), and Negrao (1998) implemented an automatic airflow 

coupling inside ESP-r (Clarke, 1985) with the CFD. However, in their studies, different 

coupling methods resulted in dramatically different results for the same airflow problem, 

which indicated multiple solutions of airflow coupling. Bartak et al. (2002) recently 

refined the CFD module of ESP-r and adopted a "conflation controller" (BeausoleilMorrison, 2002) to improve the simulation capacities of the CFD module of ESP-r. In the 

airflow coupling, however, their evaluation of possible coupling methods was incomplete. 

The conflation controller by default only transfers the CFD-calculated airflows to the 

multizone model. They did not explain why the CFD-calculated pressures should be 

ignored. Musser (2001), Srinivas (2001), and Yuan and Srebric (2002) compared results 

from multizone and CFD programs for contaminant transport simulations. However, all 

of them avoided the problem of coupled airflow simulations by using predefined airflow 

rates in contaminant transport simulations. Recently, Jayaraman et al. (2004) tried to 

develop an algorithm for coupled multizone and CFD programs for airflow simulations, 

demonstrating the algorithm on a two-dimensional building with a large space. Their 

preliminary study showed that coupling CFD with a multizone model could result in 

more realistic predictions of airflow and contaminant transport in buildings with large 

spaces. The details of their algorithm, however, were not provided in the literature. 

Among the past coupling endeavors in building ventilation simulations, the coupling of 

multizone and CFD models is considered the most sophisticated (Musser, 2001). As 

reviewed above, current design tools of coupled multizone and CFD programs still have 

many limitations. Several issues remain unsolved, e.g. the development of an appropriate 

coupling algorithm and a stable coupling method, and the study of the solution 

characteristics, validations, and applications of such a coupled program to real problems. 

This thesis aims to tackle these challenges to develop a new design tool by coupling a 

multizone and a CFD program. 
13

1.3. Research Objectives and Thesis Outline

Previous sections of this chapter show that building ventilation design and IAQ analysis 

are essential for providing people with a safe, healthy, and comfortable indoor 

environment. Current design tools, e.g. multizone, zonal, and CFD models, have their 

own merits and drawbacks when used individually. Integrated tools can combine the 

merits of the individual tools and avoid their drawbacks. By comparing current integrated 

models in previous studies, we find that the coupled multizone and zonal models have 

many limitations due to the restrictions of current zonal models. The coupled program of 

multizone and CFD models is promising, although many questions remain unsolved. 

With the aim to develop a new design tool integrating multizone and CFD programs, this 

thesis tries to 

● evaluate the assumptions of multizone models and identify the major limitations, 

pointing to the areas in which the multizone assumptions are inappropriate, thus 

verifying the need for CFD models; 

● develop coupling strategies to remedy the multizone assumptions in these situations, 

and implement the coupling algorithms in a coupled program of multizone and CFD 

models; 

● analyze the solution existence and uniqueness of the coupled program, and evaluate 

the numerical performance of the coupling methods for the implementation of the 

coupling algorithms; 

● verify the CFD model and validate the coupled program through experimental data 

for the situations in which the multizone assumptions are inappropriate; 

● apply the coupled program to realistic cases of building ventilation and IAQ analysis; 

and 
14

● investigate under what conditions the multizone assumptions become inappropriate 

and provide suggestions for selection of CFD zones for a coupled multizone-CFD 

simulation. 

This thesis is organized as follows: 

● CHAPTER 2 first selects CONTAM (Walton and Dols, 2003), a multizone program, 

and CFD0-C, a CFD program, for the current study. The chapter then evaluates the 

major assumptions of CONTAM, which could become problematic in both outdoor 

and indoor airflow situations. The situations include the description of wind 

pressures around buildings, buoyancy-driven flows with temperature gradient, winddriven flows with momentum effect, and indoor airflows with contaminant 

concentration gradient. To remedy the CONTAM assumptions, the current study 

discusses the concepts of two coupling strategies: the indirect coupling for outdoor 

airflow simulations, and the direct coupling for indoor airflow and contaminant 

transport simulations. 

● CHAPTER 3 develops the coupling schemes to carry out the indirect and the direct 

coupling strategies. The indirect coupling employs two coupling schemes, the Wind 

Pressure and Contaminant (WPC) link, and the Wind Pressure Profile (WPP) link, to 

predict the non-uniform distribution of wind pressures for CONTAM. To remedy the 

assumptions associated with indoor airflow and contaminant transport simulations, 

the direct coupling provides coupling algorithms for three types of CONTAM 

simulations: steady airflow and steady contaminant transport, steady airflow and 

transient contaminant transport, and transient airflow and transient contaminant 

transport. This chapter then conducts theoretical analyses on the solutions and the 

coupling methods of the direct coupling algorithms. The analyses involve the 

existence and uniqueness of a coupled airflow simulation, and the numerical 

convergences and stabilities of different coupling methods. With the aim to find the 

most stable coupling method, this chapter then verifies the theoretical study by two 
15

numerical experiments: one is the pressure-gradient flows in an office suite, and the 

other is cross ventilation in a four-zone building model. 

● CHAPTER 4 verifies the capabilities of CFD0-C by comparing the numerical results 

with the published data for indoor and outdoor airflows. Indoor airflows include 

airflow through a 90-degree planar branch, natural ventilation in a stairwell, 

displacement ventilation, and cross ventilation in a 4-zone building model. Outdoor 

airflow verification includes external airflow around a building model and wind 

pressure and airflow distribution of a low-rise house with a slope roof. To validate 

the coupled program of CONTAM and CFD0-C, experimental measurements are 

conducted in a chamber facility for three cases: non-uniform distributions of 

momentum effects, contaminant concentrations, and temperatures. 

● CHAPTER 5 demonstrates the indirect coupling in a simulation of outdoor airflows 

around a cubic building. The direct coupling algorithms are applied to simulations of 

natural ventilation in a three-story building with a large atrium. The simulations 

include three direct coupling algorithms: steady airflow and steady contaminant 

transport, steady airflow and transient contaminant transport, and transient airflow 

and transient contaminant transport. 

● CHAPTER 6 conducts dimensionless analyses on the conditions, under which the 

multizone assumptions of uniform air momentum effect, air temperature, and 

contaminant concentration become inappropriate. Based on these conditions, this 

thesis develops a judging procedure for selection of CFD zone in a coupled 

CONTAM-CFD0 simulation. 

● CHAPTER 7 summarizes the conclusions from the current investigation, identifies 

remaining challenges and points out recommendations for future work. 
16

CHAPTER 2. MAJOR LIMITATIONS OF MULTIZONE MODELS AND REMEDY 

STRATEGIES ATTAINED BY COUPLING MULTIZONE AND CFD 

PROGRAMS 

2.1. Major Assumptions of Multizone Models

One of the major motivations informing the development of an integrated multizone-CFD 

program is to remedy the limitations characterizing current multizone models. The major 

limitations of current multizone network models are associated with many of their 

assumptions. Due to these assumptions, multizone programs should be used only to 

predict building infiltrations/exfiltrations and the average values of contaminant 

concentrations. For other situations, where the assumptions become inappropriate, 

multizone programs may provide inaccurate results. 

For example, multizone network models are based on the assumption that each room of a 

building is a zone with a uniform temperature and pressure. They also neglect the airflow 

momentum preserved inside a zone. These assumptions may compromise the accuracy of 

the results obtained for the simulations. Previous studies have noticed the problems 

inherent in multizone assumptions. Murakami et al. (1991) found that current multizone 

network models fail to account for the preservation of the kinetic energy of the airflow. 

Schaelin et al. (1994) thought that the local variables near the flow paths within each 

zone, e.g. air velocity and temperature, could have a strong influence on multizone model 

predictions. Later, Upham (1997) pointed out that, for non-uniform distributions of 

contaminant concentrations, the results of using a multizone contaminant dispersion 

model are questionable. Clarke (2001) also noted that current buildings' airflow 

modeling-by-network approach has significant limitations: because momentum effects 

are neglected, intra-room airflow and temperature distribution cannot be correctly 

determined. Recently, Gao and Chen (2003) found that multizone models produce 
17

incorrect results if the preserved momentum within a zone is neglected. Yuan (2002) 

further showed, through his on-site experiments of a zone with a contaminant source, the 

shortcomings of the well-mixing assumption of contaminants in multizone models. 

Such previous studies and the analysis of Persily (2003) summarize the major 

assumptions and limitations linked to multizone models as: 

1. wind pressures on a building's surface are uniform by default; 

2. room pressures, temperatures, and concentration of species are uniform in each zone; 

3. the transport of contaminants along each flow path or within a room is instantaneous; 

4. momentum and kinetic energy are not accounted for by flow path models; 

5. air is quiescent or still in each zone, so the airflow through zones does not impact 

zone pressures. 

Assumption 1 could cause problems when the wind pressures vary dramtically with the 

different locations on a building’s surface. Assumptions 2 and 3 are also called the wellmixing assumption, which could be problematic for simulations with poorly mixed air 

parameters and contaminant concentrations. Some common examples are buoyancydriven airflows with temperature gradients, and the transport of contaminant with poorly 

mixed contaminant concentrations. For airflows with strong inflow momentum effects, 

which could influence pressure and airflow distributions inside a zone, Assumptions 4 

and 5 will become inapplicable. 

The above assumptions can be summed up as uniform distributions of wind pressures, 

temperatures, momentum effects, and contaminant concentrations, respectively. These 

assumptions can become critical for the following problems: 

1. Description of wind pressures around buildings 

2. Buoyancy-driven airflows with temperature gradient 

3. Indoor airflows with strong momentum effect 

4. Indoor airflows with contaminant concentration gradients 
18

Cases 1-3 are closely related to natural ventilation designs, and Cases 3 and 4 to 

ventilation designs during emergencies, e.g. the emergency ventilation design that dilutes 

polluted air during a CBRWA attack. 

On the other hand, nearly fifty multizone models have been developed during the past 

twenty years (Feustel and Dieris, 1992). It is hard to evaluate every multizone program 

for the above cases. This chapter therefore focuses on CONTAM (Walton and Dols, 

2003), a public-domain multizone program from the National Institute of Standard and 

Technology (NIST), USA. The discussions in this chapter, however, are not limited to 

CONTAM since most multizone programs use similar assumptions. 

CFD0-C, a three-dimensional CFD code, is selected as the CFD program to be coupled 

with CONTAM. Srebric et al. (1999) developed CFD0, which is also called CFD0-F, 

since it was written in FORTRAN. With many new capabilities, the CFD0-C is upgraded 

from CFD0-F through the conversion of FORTRAN to C. The conversion makes the 

coupling much easier because CONTAM is written in C. CFD0 utilizes SIMPLE 

algorithm and the solver of line-by-line TDMA (Patankar, 1980). Turbulence is 

accounted for by the indoor zero-equation eddy-viscosity model (Chen and Xu, 1998). 

2.1.1. Description of Wind Pressures around Buildings 

For buildings with natural ventilation, wind pressure is the most important driving force 

for airflow through the building envelope. The wind pressure is a function of wind speed, 

wind direction, building configuration, and local terrain effects (ASHRAE, 2005). In 

versions prior to CONTAM 2.1, users can account for the effects of wind pressure by 

three options. One can choose to ignore the effects of wind, define wind pressure to be 

constant, or implement variable wind pressures for each envelope penetration. CONTAM 

provides a general approach for handling the variable effects of wind on the building 

envelope. This approach requires users to provide CONTAM with a local wind pressure 

coefficient, Cp, for the building surface (Walton and Dols, 2003). A wind pressure profile 
19

is required, which contains surface-averaged pressure coefficients for each building 

surface. 

In fact, air movement around buildings is a three-dimensional turbulent flow. A more 

accurate approach than surface-averaged pressure coefficient is to account for variations 

in wind pressure coefficients by location over a building surface. Swami and Chandra 

(1988) presented a correlation of wind pressure coefficients for high-rise buildings, where 

the value of Cp was determined for a specific point on the building façade instead of 

being averaged over the entire façade. Since it may only apply to high-rise buildings and 

cannot represent average ones, the correlation has not been incorporated into CONTAM. 

The most reliable means of determining Cp for a specific building are through on-site 

measurements or wind tunnel studies (Persily and Ivy, 2001). However, the 

measurements can be expensive, and are often associated with technical difficulties. 

Hence, the CFD simulation of turbulent flows around buildings seems a better option to 

obtain wind pressures. 

Gao (2002) has used a single-story apartment, as shown in Fig. 2.1, to demonstrate that 

CFD can supply specific wind pressure for each opening on a building envelope. Table 

2.1 shows the wind pressures for different windows of the building when the wind speed 

is 3 m/s at 10m above the ground. Without reliable information, the CONTAM user 

might specify the same wind pressure coefficients for windows 2, 3, and 5, and for 

windows 7 and 8. Because the relative wind direction, as well as the difference of the 

wall azimuth angle and the wind azimuth angle is the same for windows 2, 3, and 5, the 

calculated pressure would be the same. As shown in Table 2.1, the wind pressures 

calculated by a CFD program vary a lot at different locations on the same building 

surface. Uniform wind pressure coefficients may cause significant errors for windows 2, 

3, and 5. The same conclusion could be applied for windows 7 and 8. 

Gao’s study reveals that CFD can be used to provide non-uniform wind-pressure 

distributions on building surfaces. CHAPTER 3 of this thesis will develop a coupling 
20

method, applying it to CONTAM and CFD0-C, in which CFD0-C calculates non-uniform 

distributions of wind pressures to improve the calculations of natural ventilation in 

CONTAM. 

Table 2.1 Pressure distribution at the window opening. 

 

Fig. 2.1 Plan view of a single-level apartment. 

2.1.2. Buoyancy-driven Airflows with Temperature Gradients 

Besides the effects of wind pressures, buoyancy-driven airflows are also common in 

natural ventilation. In simulations of buoyancy-driven flows, zone temperature is a 

crucial factor. Since the current version of CONTAM does not include the calculation of 

energy conservation, a uniform temperature must be manually specified for each zone. 

An improper setting of the zone temperature may result in inaccurate or even wrong 

results. The temperature can also stratify along the height of a zone and the assumption of 

a uniform temperature does not hold. 

To illustrate the importance of temperature and temperature gradient in CONTAM 

calculations, this investigation uses a case studied by Zohrabian et al. (1990). They 

conducted a series of measurements of buoyancy-driven airflows between the two 

Window # Pressure from CFD 

(Pa) 

1 7.43 

2 7.055 

3 7.215 

4 7.215 

5 3.769 

6 1.983 

7 0.008 

8 -6.5 
21

compartments of a stairwell, as shown in Fig. 2.2. The study focused on the dependence 

of the buoyancy-induced flows on parameters such as heating, outside temperature, and 

heat losses through walls and inlet/outlet openings. 

Fig. 2.2 Schematic diagram of the half-scale stairwell model. 

The stairwell had two small openings at A and F. The throat area was indicated by DD ́

and the sidewall was defined by ACDEFGHIA (Zohrabian et al., 1990). 

The current study models the stairwell in CONTAM as a single zone by using the 

measured results, as shown in Table 2.2. Temperatures from the experiment are averaged 

as inputs for the CONTAM simulation. By using average zone temperatures, CONTAM 

cannot consider the temperature gradient, which is important to obtain correct airflow 

results for buoyancy-driven flows. Table 2.2 illustrates that in the current case, the 

measured vertical temperature gradient can be 7°C for 300 W and 17°C for 900 W. As a 

result, the calculated airflow rates by CONTAM are quite different from the measured 

ones. 
22

Table 2.2 Measured results and their comparison with calculated airflow rates by 

CONTAM. 

The above analysis shows that the temperature and temperature gradient are very 

important parameters for buoyancy-driven flows. CONTAM users could obtain the 

temperature and temperature gradient by carrying out certain experiments, but such a 

process may not be easy. Even if the temperature gradient obtained from experiments is 

available, it cannot be used by CONTAM due to the well-mixing assumption. Thus, 

obtaining zone temperatures when experimental data is unavailable and assessing the 

temperature gradient in buoyancy-driven flows are two of the major problems facing 

CONTAM. 

2.1.3. Indoor Airflows with Strong Momentum Effects 

CONTAM assumes that the air in a zone is quiescent or still, and the airflow through a 

zone does not have an impact on zone pressure. The assumption is valid for the cases, in 

which air velocity through openings is low enough to be immediately dissipated or 

distributed after entering the zone. This is commonly true in the case of infiltration 

through small openings. 

However, a strong momentum effect may be preserved, contributing to spatial variations 

in zone pressure, such as airflows provided by large openings in the case of a building's 

natural ventilation. Murakami et al. (1991) used a multizone network model to study 

cross ventilations with an open window. The airflow preserved a large part of its mean 

kinetic energy when it remained inside the room. They found that current multizone 

network models could not account for the preservation of the airflow's kinetic energy. So 

Q (power of 

the heater) 

(W) 

Measured 

vertical 

temperature 

gradient (°C) 

Measured 

average 

temperature 

(°C) 

CONTAM mass 

flow rate×103 

(kg/s) 

Experiment mass 

flow rate×103

(kg/s) 

300 7 29.6 2.850 4.484 

900 17 40.4 4.485 7.223 
23

the models tended to overestimate the pressure loss and underestimate the total pressure. 

Since natural ventilation design has become a new trend, it is important that CONTAM 

should be able to address such a flow. 

In order to further illustrate the problem concerning the neglect of the momentum effect 

in multizone models, the present study selects a case from Hayes et al. (1989), and Kelka 

and Choudhury (2000). They studied a 90-degree planar branch case, as shown in Fig. 

2.3. It should be noted that this study selects the 90-degree planar branch since it can be 

regarded as flow through corridors. The connection of two corridors is very similar to the 

planar branch so we can study how flow is distributed in two corridors. Table 2.3 further 

lists different fractional flow rates in the main branch, Φ, versus different Reynolds 

numbers. Since CONTAM neglects the momentum and the kinetic energy of airflow 

within the zone, the flow through the main branch will be the same as that through the 

side branch, so Φ will be always 0.5. As shown in Table 2.3, when the momentum is 

insignificant (or the Reynolds number is very small), Φ is approaching 0.5. As the 

Reynolds number increases, CONTAM would not produce acceptable results. 

The momentum effect becomes significant for airflow distributions in cases of natural 

ventilation or emergency ventilation, e.g. during a fire. The above case shows that since 

CONTAM neglects the preserved momentum effect inside a zone, it will provide 

inaccurate results for the study of airflow distributions. 
24

Fig. 2.3 Geometry and grid of 90-degree 

planar branch (Kelka and Choudhury, 2000).

2.1.4. Indoor Airflows with Contaminant Concentration Gradients 

CONTAM also assumes the existence of species concentrations in each zone to be 

uniform at all time steps. Within each time step, the contaminant is distributed throughout 

a zone with zero time delay. When the time scale for a zone is small compared to the total 

transport time concerned, e.g. in a whole building, this assumption may be acceptable. 

Otherwise, we must account for the time delay, which may be a crucial factor in some 

cases, e.g. when we need to compute the time required for a sensor to produce a control 

signal. 

Schaelin et al. (1994) noticed the possible errors caused by the assumption of uniform 

contaminant concentration. They illustrated a zone with three openings and a contaminant 

source in the zone, as in Fig. 2.4. The contaminant concentration distribution, indicated 

by the contour lines in Fig. 2.4, was not uniform in the zone. Table 2.4 shows that the 

contaminant concentration at the three openings could be very different, depending on the 

Table 2.3 Fractional flow rate in 

main branch as a function of 

Reynolds number (Kelka and 

Choudhury, 2000). 

Re (Reynolds 

number) 

Φ (Fractional 

flow rate in main 

branch) 

10 0.522 

100 0.725 

200 0.830 

300 0.883 

400 0.911 

V

W
25

airflow pattern and the position of the contaminant sources. CONTAM, however, would 

treat the contaminant transported to the neighbor zone with the same concentration for all 

the openings. 

The transport of contaminant from one zone to a neighboring space depends on the local 

concentrations at the flow paths. These local concentrations are influenced by the 

positions of heat and contaminant sources and of the resultant airflow pattern. Schaelin et 

al. applied CFD to calculate the airflow pattern and non-uniform contaminant 

concentration in the zone. Then they extracted local concentrations from the CFD results 

as inputs for the multizone program. The procedure was called a “ping-pong” technique, 

which was a one-iteration coupling between the CFD and the multizone model. Their test 

cases showed that the calculated concentrations from this technique differ by a factor of 

up to 2.5 from the pure multizone approach. Their results from the coupled simulation 

look more reasonable than those obtained from only multizone simulation. 

Recently, Yuan (2003) tried to consider the non-uniform contaminant concentration in 

CONTAM by using CFD results. He also validated the results with on-site experimental 

Table 2.4 Concentration values at different 

locations for different models (Schaelin et al., 

1994).

The case with 

wind 

Mean 

contaminant 

(ppm) 

Cdoor

(ppm) 

Cexh

(ppm)

a) Multizone 

only (perfect 

mixing) 

0.15 0.15 0.15 

b) Detailed 

flow path value 

method 

0.12 0.09 0.185 

Fig. 2.4 (a) Contaminant values in a multizone 

model. (b) Contaminant values in CFD 

(Schaelin et al., 1994). 
26

data and found that the CONTAM results could be improved. Although his approach was 

a manual coupling procedure, it is a good starting point for further studies. Inspired by 

such research, this study develops several strategies to integrate CONTAM with a CFD 

program, CFD0-C as discussed in the following sections. 

2.2. Remedy Strategies by Coupling CONTAM and CFD0-C

The above analysis shows some major limitations of multizone programs: 

● the assumption of uniform wind pressures around buildings could result in an 

inaccurate description of wind pressures on a building surface; 

● the assumption of uniform temperature distribution could not consider the 

temperature gradient in buoyancy-driven flows; 

● the assumption of neglecting inflow momentum fails to consider the momentum 

effect on airflow distributions; 

● the assumption of uniform contaminant concentration could cause inaccurate 

predictions when a contaminant is poorly mixed inside a zone. 

Depending on whether the above problems are airflow simulations around or in 

buildings, the current study develops different remedy strategies for the coupled 

CONTAM-CFD0 program. 

Indirect/Virtual coupling for outdoor airflow simulations

To remedy the assumption of uniform wind pressures on a building surface, an indirect 

(or virtual) coupling strategy should be used. The strategy uses CFD0-C to simulate the 

wind flow around a building, which can be illustrated by a three-story building in Fig. 

2.5. The building will be simulated as a solid block without internal zones, by the CFD0-

C. Then the CFD0-C calculates the wind pressures at different locations of the building 

as denoted by arrows in Fig. 2.5. CONTAM afterwards simulates airflows for all the 

internal zones by obtaining the calculated wind pressure information from the CFD0-C. 
27

Fig. 2.5 A conceptual illustration of the indirect coupling of CONTAM and CFD0-C for 

outdoor airflow simulations in a three-story building with a large atrium. 

Since the building is simulated in CFD0-C as a solid block, which is a common technique 

in CFD simulations (Jiang, 2002), no information is needed from the internal CONTAM 

zones. The information is exchanged between CFD0-C and CONTAM only once, 

through wind pressures. Thus, the above procedure is described as an indirect or virtual 

coupling, compared to the direct/dynamic coupling, which will be discussed next. 

Direct/Dynamic coupling for indoor airflow and the transport of contaminant simulations

For indoor airflow and contaminant transport simulations, CONTAM uses the 

assumptions of the uniform distribution of momentum effect, temperature, or 

contaminant concentration. A direct/dynamic coupling strategy is developed to remedy 

the assumptions. The strategy will divide a building's rooms into two types of zones. For 

zones where these assumptions are inappropriate, CFD0-C will be used and CONTAM is 

applied to the rest of the zones. Fig. 2.6 illustrates the direct coupling concept in the same 

building, as in the previous section. CFD0-C is used for the atrium, which is so large that 

air and contaminant properties apparently cannot be distributed uniformly. The rest zones 

are much smaller than the atrium and CONTAM can be used by rule of thumb. 

CONTAM Zones 

Wind Wind 
28

 

Fig. 2.6 A conceptual illustration of the direct coupling of CONTAM and CFD0-C for 

indoor airflow and contaminant transport simulations in a three-story building with a 

large atrium. 

The zones of CFD and CONTAM are connected by the airflow paths at their interfaces 

(hereafter, interface paths as designated by arrows in Fig. 2.6). Specifically, the solid 

cells in the CFD zone connect the atrium directly to the CONTAM zones. Due to these 

physical connections, the information of airflow and contaminant transport needs to be 

exchanged between the two programs. Compared to the indirect coupling, the direct 

coupling is an iterative procedure since CONTAM and CFD0-C often cannot reach 

convergence with only a one-time information exchange. Therefore, the direct coupling is 

also called the dynamic coupling of CONTAM and CFD0-C. 

Moreover, the direct coupling is also more complex than the indirect coupling. Given that 

the information is exchanged iteratively between CONTAM and CFD0-C, the coupling 

procedure might not reach stable solutions. Although stable solutions exist, another 

question is whether the solution is unique. In addition, the above analysis only 

conceptually illustrates the strategies of coupling CONTAM and CFD0-C. To integrate 

these two programs, each of which has its own program and data structure, appropriate 

coupling schemes also need to be developed. CHAPTER 3 will provide answers to these 

questions. 

The Atrium (CFD0-C zone) 

CONTAM 

Zones 

CONTAM 

Zones 
29

2.3. Summary

This chapter studies the situations, in which the major multizone assumptions could 

become problematic. When wind pressures vary with the locations of openings on a 

building surface, the assumption of uniform wind pressures of CONTAM is 

inappropriate. For indoor airflow simulations, the CONTAM assumptions could cause 

problems with non-uniform distributions of momentum effect and temperature gradient, 

as well as contaminant concentration. 

This chapter proposes the concept of an indirect coupling strategy for the problem 

associated with non-uniform wind pressure distribution and a direct coupling strategy for 

the remaining situations, as summed up in Fig. 2.7. 

Indirect coupling 

for airflow around 

buildings

Non-uniform

momentum 

distribution

Non-uniform 

temperature 

distribution

Non-uniform 

contaminant 

concentration 

distribution

Non-uniform

wind pressure 

distribution

Coupling

of CONTAM and 

CFD0

Direct coupling for 

airflow inside 

buildings

Fig. 2.7 Coupling strategies for coupled simulations of non-uniform distributions of wind 

pressure, momentum, temperature, and contaminant concentration. 
30

Fig. 2.7, however, only proposes the concepts about how to couple CONTAM and 

CFD0-C. CHAPTER 3 will develop the coupling schemes to implement the coupling 

strategies. More studies will also be conducted on the solution characteristics for coupled 

indoor airflow simulations. 
31

CHAPTER 3. COUPLING CONTAM AND CFD0 FOR AIRFLOW AND 

CONTAMINANT TRANSPORT AROUND AND IN BUILDINGS 

The coupling of CONTAM and CFD0-C is meant to integrate these two individual 

programs in a single coupled program. However, the program and data structures of 

CONTAM and CFD0-C are quite different from each other, as shown in Fig. A.6 and 

Fig. B.1 in the Appendices. The integration of the two programs should keep the 

programs' integrity and at the same time cause minimal modifications in each program. 

To be specific, the coupled program should be developed with knowledge of 

● what information needs to be exchanged between the two programs; 

● how the exchanged information should be formatted in one program to be directly 

accepted by the other; 

● where, when and how the information should be exchanged in both programs. 

To answer the above questions, this thesis thus develops different coupling schemes for 

the indirect and the direct coupling, as discussed next. 

3.1. Indirect/Virtual Coupling of CONTAM and CFD0-C for the Non-uniform 

Distribution of Wind Pressure around Buildings

The indirect coupling strategy only uses one-step, sequential runs of CFD0-C and 

CONTAM. First, the CFD0-C calculates the distribution of wind pressures or wind 

pressure coefficients on building surfaces, which are stored in a file. CONTAM then 

extracts these data from this file for simulations of indoor airflow and contaminant 

transport. Since wind pressure or wind pressure coefficient is exchanged between the 

CONTAM and the CFD0-C only once through the file, this process is an indirect or 

virtual coupling of the two programs. The indirect coupling is realized through two 
32

methods: a Wind Pressure and Contaminant (WPC) link, which provides wind pressures, 

and a Wind Pressure Profile link, which calculates wind pressure coefficients for 

CONTAM simulations. 

3.1.1. Indirect Coupling of CONTAM and CFD0-C by the Wind Pressure and 

Contaminant (WPC) Link 

To implement the indirect coupling, a coupling scheme specifying wind pressures in 

CONTAM is developed, as shown in Fig. 3.1. The scheme uses a Wind Pressure and 

Contaminant file (WPC file) to provide wind pressure data for each path on the building 

envelope, which are required by CONTAM. Note that CONTAMX in Fig. 3.1 is the 

solver and CONTAMW is the Graphic User Interface (GUI) of CONTAM. To create the 

WPC file, the CFD0-C first generates an intermediate file, External Wind pressure and a 

Contaminant (EWC) file, as well as a CFD0-formatted file with three-dimensional wind 

pressures. Due to the format differences of EWC and WPC files, a format-converting 

program, WPC translator, converts the EWC file into a WPC file by reading a Path 

Location Data (PLD) file, which provides path location information. The advantage of 

this method is that when the path location changes, wind pressure can be obtained easily 

without running CFD0-C again. 

On the other hand, wind pressure distribution also depends on terrain characteristics at a 

building site, wind direction and velocity. The WPC link needs to recalculate wind 

pressures when the wind direction and velocity vary or the building location is changed. 

The resultant computing time will be enormous especially under a transient weather 

condition. The WPC link can be improved by a method as discussed next. 
33

CONTAM

PLD File

CONTAMW

CONTAM

PRJ File

WPC File

Converter

External Wind 

Pressure and 

Contaminant File

CONTAMX

CONTAM

WPC File

CFD0

CFD0

INPUT File

Fig. 3.1 The schematic of the indirect coupling attained by using the WPC link (Walton 

and Dols, 2003). 

3.1.2. Indirect Coupling of CONTAM and CFD0-C by the Wind Pressure Profile (WPP) 

Link 

For the calculation of wind pressures under variable wind velocity and direction, one of 

the methods to reduce the computing cost of the WPC link is to use wind pressure 

coefficients. 

2

H

W H

P

U

2

1

P P

C

ρ

−

=

(3.1)

where CP is the wind pressure coefficient, PW is the wind pressure at the building surface, 

PH is the undisturbed wind pressure at the reference height H, and UH is the wind velocity 

at the reference height H. 
34

Eq. (3.1) shows that wind pressure coefficients are dimensionless and independent of 

wind velocity. Hence, wind pressures for a certain wind velocity can be obtained from 

previously calculated wind pressure coefficients without running CFD simulation again. 

The value of the wind pressure coefficient, CP, however, does depend on local terrain 

features (ASHRAE, 2005), which can be considered by the adjustment of wind velocity 

profile, UH, through the following equation. 

 

α α

δ

δ

= )

H

) (

H

U U (

met

met

met

H met

(3.2)

where Umet is the wind velocity at the height of Hmet, δmet is the atmospheric boundary 

layer thickness, αmet is the exponent, and Hmet is the reference height at the 

meteorological station; δ, H, and α are the corresponding values for the local terrain. 

These terrain features can be determined from Table 3.1. 

Table 3.1 Atmospheric boundary layer parameters (ASHRAE, 2005). 

Terrain Category α (Exponent) δ (m, Layer Thickness)

Large city centers 0.33 460 

Urban and suburban areas 0.22 370 

Open terrain with scattered 

obstructions 

0.14 270 

Flat, unobstructed areas 0.10 210 

The method of using wind pressures coefficients for the indirect coupling is called a 

Wind Pressure Profile (WPP) link, which includes two steps as illustrated by Fig. 3.2. In 

the first step, CFD0-C calculates a database of wind pressure coefficients, the WPP file, 

with specified terrain features by users. A format-converting program, the WPP 

converter, will then extract the wind pressure coefficients from the WPP file and create a 

CONTAM library file of CP values at each path of a building for variable wind directions. 

In Step 2, CONTAM will convert wind pressure coefficients to wind pressures, PW, 
35

through Eq. (3.1). Since the WPP link employs wind pressure coefficients instead of wind 

pressures, it can reuse the calculated wind pressure data and reduce computational cost. 

Step 1

Step 2

Path locations

UH

Users

Pld file

CONTAM

CFD0

Umet

Pw

Umet, Cp

WPP file

A flow

path

WPP

converter

Cp libary

Umet, Cp

Prj file

Fig. 3.2 The schematic of the indirect coupling attained by using the WPP link. 

The indirect coupling attained by using a WPC link and a WPP link is indeed a sequential 

run of CFD0-C and CONTAM. The wind pressures or wind pressure coefficients are 

exchanged only once between the two programs through the CONTAM WPC/WPP file. 

The procedure is straightforward and thus can be easily controlled. Nevertheless, this is 

not the case for the direct coupling. 

3.2. Direct Coupling of CONTAM AND CFD0-C for Non-uniform Distributions of 

Momentum, Temperature, and Contaminant Concentrations in Buildings

3.2.1. Direct Coupling Controller and Coupling Data Interface 

Compared to the one-step, sequential procedure of the indirect coupling, the direct 

coupling needs to exchange information iteratively until both CONTAM and CFD0-C 

reach convergence. Thus, the direct coupling is a multi-step, iterative procedure. “What”
36

are exchanged between the CONTAM and the CFD0-C can be airflow rates and 

pressures for airflow simulations, as well as contaminant concentrations for contaminant 

transport simulations. In order to manage the exchanged information easily, the direct 

coupling stores the exchanged information in the data interface of a computer's memory, 

as shown in Fig. 3.3. A coupling controller controls the locations, “where” the 

information should be exchanged, and the running sequences of the two programs. 

Appendix B.3 provides the locations in the CONTAM code, where the information is 

exchanged. It also shows that by using the coupling controller and the data interface, the 

resultant modifications in CONTAM and CFD0-C are minimal. 

CONTAM

PRJ File CONTAM

Coupling

INPUT File

CFD0 

INPUT File

Coupling 

CONTROLLER

CFD0

CONTAM 

OUTPUT Files

Couplling 

OUTPUT Files

CFD0

OUTPUT Files

DATA from/to 

CFD0

DATA from/to 

CONTAM

Fig. 3.3 The schematic of the direct coupling attained by using the coupling controller 

and the coupling data interface. 
37

3.2.2. Direct Coupling Algorithms for Different Simulation Types 

In addition to deciding “where” the information is exchanged, the coupling controller in 

Fig. 3.3 also determines “when” the information is exchanged by following certain 

coupling algorithms, and “how” to exchange the information by using certain coupling 

methods. 

This study develops the coupling algorithms within the framework of different 

CONTAM solution methods. CONTAM has five solution methods for different 

combinations of airflow and contaminant transport simulations, as shown in Table 3.2 

(Walton and Dols, 2003). Since cyclic simulations are special cases of transient 

simulation, the current study only needs to develop coupling schemes for Types 1-3. The 

scheme for Type 2 can be used for Type 4, and Type 3 for Type 5. 

Table 3.2 Simulation types for airflow and contaminant simulations in CONTAM. 

Simulation Type Airflow Simulation Contaminant Simulation 

Type 1 Steady State Steady State 

Type 2 Steady State Transient 

Type 3 Transient Transient 

Type 4 Steady State Cyclic 

Type 5 Transient Cyclic 

This investigation has proposed three coupling algorithms for the coupled airflow and 

contaminant simulations. As shown in Fig. 3.4, the coupled program first reads a 

CONTAM project file to provide all the information for CONTAM and a coupling 

definition file for the coupling. The zones, where CFD0-C is applied to, are then “decoupled” from the airflow network of CONTAM. 

For steady-state airflow and contaminant transport (Type 1), the scheme will use 

previously calculated airflow data if it is available. The coupled program will import the 

airflow data from CFD0 and provide them directly to CONTAM. CONTAM will then 

calculate the transport of contaminants for a whole building and the results are used as 
38

boundary conditions for CFD zones. CFD0 will calculate contaminant distributions for 

the CFD zones and send back the contaminant data as corrected sources or sinks for the 

CONTAM zones. Without previously calculated airflow data, the coupled program needs 

to obtain airflow field. CONTAM will first calculate the pressures and airflow rates. 

Then the CFD0 will be called to calculate the airflow for the CFD zones. Iterations with 

CONTAM are necessary until convergence. With the converged airflow data, the 

contaminant distribution can be calculated in the same way stated above. 

For steady-state airflow and unsteady contaminant transport (Type 2), the calculation of 

airflow is the same as that for Type 1, which is framed by the dash line on the left of Fig. 

3.4. A transient coupling is then performed for contaminant transport. At each time step, 

a similar procedure to that of Type 1 can be applied. The coupling simulation continues 

until the maximum time specified for contaminant transport is reached. 

For transient airflow and transient contaminant transport (Type 3), similar procedures of 

coupling for airflow and contaminant simulations of Type 1 can be used for each time 

step, as shown in Fig. 3.4. 
39

End

Start

Read CONTAM PRJ file & 

coupling INPUT file

'De-couple' CFD zone

Coupling schems

Type 2. Steady airflow and transient 

contaminant transport

All zones by CONTAM

CFD0

Converge?

Yes

No

CONTAM

Airflow rates or 

pressures

CFD0

CONTAM

At time step n

CONTAM

CFD0

Converge?

Yes

No

CONTAM

CFD0

CONTAM

Contaminant 

concentrations

Start from a previous 

airflow field?

CFD0

CONTAM

Contaminant 

concentrations

Contaminant 

concentrations

Yes

No

At time step n

Move to next time step

n=n+1

Run coupled airflow simulation 

at steady state

CFD0

CONTAM

Contaminant 

concentrations

Coupled airflow 

simulation at 

steady state

Coupled airflow 

simulation at 

transient state

Maximum time?

Maximum time?

Type 1. Steady airflow and

steady contaminant 

transport

Type 3. Transient airflow 

and transient contaminant 

transport

Yes

No

No

Yes

Airflow rates or 

pressures

Airflow rates or 

pressures

Airflow rats or 

pressures

Move to next time step

n=n+1

Fig. 3.4 Three coupling schemes for the coupled CONTAM and CFD0-C simulations.
40

After deciding on the “what, where, and when” of the exchange of information in direct 

coupling, the coupling controller needs to follow certain coupling methods to determine 

“how” to exchange the information. Some previous studies (Negrao, 1998; Bartak et al., 

2002; Beausoleil-Morrison, 2002) developed several coupling methods. However, they 

found convergence and stability problems with some of the methods. In some cases, 

multiple coupling solutions could happen as well. Thus, it is necessary in this study to 

conduct theoretical analysis to answer the following questions: 

● Are there solutions to direct coupling? 

● If the solutions exist, is the solution unique? 

● If the solution is unique, which coupling method is the best, namely, which is the 

most stable method to obtain a unique solution? 

● If the solution is not unique, what reasons cause multiple solutions? 

3.2.3. Coupling Solution Existence and Uniqueness 

CONTAM and CFD0-C solve different sets of conservation equations. CONTAM only 

solves air mass and contaminant conservation equations, while CFD0-C solves the 

Reynolds Averaged Navier-Stokes equations. When the two programs are coupled, it is 

not known for certain whether there are solutions and if the solution is unique without 

relying on theoretical analysis. Unfortunately, not much work has been done on 

theoretical investigations, although previous studies (Schaelin et al., 1994; Negrao, 1998; 

Musser, 2001; Jayaraman et al., 2004) show promising numerical results. On the other 

hand, in the coupled building energy and CFD simulations, Clarke et al. (1995b) proved 

the existence of a coupling solution by analyzing a super-matrix of the coupling. Zhai and 

Chen (2003) investigated the uniqueness of the solution by performing parametric 

analysis for both energy simulation and CFD models. Inspired by their studies, this 

chapter uses an analogue methodology to investigate whether a coupled multizone and 

CFD program can have a solution for an airflow problem, and if the solution is unique. 
41

Basic equations and coupling principles

In order to analyze if a coupled multizone and CFD simulation has a solution and if the 

solution is unique, the analysis should start with the fundamentals of direct coupling. The 

idea behind multizone-CFD coupling is to apply a multizone program to most zones of a 

building while applying a CFD program to the zones, where the multizone assumptions 

are not appropriate. Fig. 3.5 illustrates the coupling schematic for natural ventilation in a 

portion of the three-story building illustrated in Fig. 2.6. The atrium is so large that the 

well-mixing assumption is inappropriate and zone c is thus chosen as the CFD zone, while 

the remaining zones are modeled with the multizone program. Although the zones 

modeled with the multizone program are connected to zone c by paths at their interfaces, 

the equations solved by the multizone and the CFD programs are quite different from 

each other. 

If path ij connects zone i and zone j and Fij is defined as the airflow rate through path ij, 

Fij is normally calculated in a multizone program by a power-law function of the pressure 

drop across path ij, 

n n ij ij Fij Cij ij ij i j S,ij W,ij = | ΔP | = C | P − P + + P P | (3.3) 

where Fij is the airflow rate, Cij is the flow coefficient, ΔPij is the pressure difference, PS,ij

is the pressure difference due to desity and elevation difference, PW,ij is the pressure 

difference due to wind through path ij; Pi and Pj is the total pressure of zone i and j, 

respectively. 
42

Fig. 3.5 Coupling schematic in a portion of a three-story building with an atrium. 

Suppose path ic connects zone i for the multizone program and zone c for the CFD 

program, and the flow rate through path ic is Fic, a mass continuity equation under a 

steady state condition can be obtained for zone i by the multizone program 

ij ic i

j

∑F − F = b (3.4)

where Fic is the airflow rate through path ic and bi is the mass source term of zone i. 

In the CFD program, a set of partial differential governing equations for mass, 

momentum, and energy conservation are solved. The equation can be written for steady 

state flow in a general form 

2 ∇(rVf f ) S − Γf f ∇ = (3.5)

path ij

path ic

Pj Pi

zone j zone i

CFD zone c

Cell 

Fic

Pu,i Pd,i
43

where f can be 1 for mass continuity, Uj for air velocity component in the j direction 

(j=x, y, z), and T for temperature. With the SIMPLER algorithm (Patankar, 1980) the 

mass continuity equation actually becomes a pressure equation. If path ic has n discrete 

grid points and we focus only on the grid point P (or cell P), the pressure equation for 

point P can be written in the following linear form 

nb nb P P P P ∑a p − a p + = f b (3.6)

where anb and pnb is the coefficient and pressure of the neighboring grid point, respecively; 

ap is the coefficient, pp is the pressure, fp is the net airflow rate through the face of a CFD 

cell, and bp is the mass source term at the grid point p in CFD. 

A linear form can also be obtained for non-linear Eq. (3.4) in a multizone program 

'

L,ij j i ic i

j

∑C (P − P ) − = F b (3.7)

where '

i i L,ij S,ij W,ij

j

b = b − + ∑C (P P ) , by defining a linear flow coefficient 

ij

L,ij

ij

F

C

P

=

Δ

(3.8)

Eqs. (3.6) and (3.7) show mathematically that Fic and fP are the only linkages between the 

multizone and the CFD equations. It is thus important to know how they are calculated in 

both programs and how they are related to each other. 

A CFD program calculates 

P

n

P P u,ic P L,P u,ic P f = C (P − p ) = − C (P p ) (3.9)
44

where Pu,ic= P d i + ic , which is the upwind total pressure of path ic if the airflow is from 

zone i to zone c; Cp, np and CL,p is nonlinear flow coefficient, exponent, and linear flow 

coefficient of the grid point p, respectively . In a multizone program 

ic n

Fic Cic u,ic d,ic L,ic u,ic d,ic = (P − P ) = − C (P P ) (3.10)

where Cic is the flow coefficient, nic is the exponent, CL,ic is the linear flow coefficient, 

and Pd,ic is the average downwind total pressure for path ic. Eq. (3.10) is actually the 

integral form of Eq. (3.9) and it comes 

n

ic P

P 1

F f

=

= ∑

(3.11)

where n is the total number grid points in CFD for path ic. 

An assembled total matrix equation can then be obtained by applying Eqs. (3.6) and (3.7) 

to all the zones in Fig. 3.5. 

CP + = F B (3.12)

where C is the flow coefficient maxtrix, P is the unknown pressure vector of zones and 

cells, F is the vector of unknown flow rates at the interface paths and cells, and B is the 

vector of source terms. To ensure that Eq. (3.12) is closed, two coupling principles must 

be followed. 

● Eq. (3.11) should be used as the convergence criterion of the coupled simulation. 

● The relationship of the flow rate and the pressure drop in Eq. (3.9) must be the 

known condition for each grid point of path ic. 

To implement Eq. (3.9) in the coupling program as the convergence criterion, a relative 

residue is defined by: 
45

m n

ic P k

k 1 P 1

inf low

(| F f |)

F

= =

−

≤

∑ ∑

ε

(3.13)

where k and m are the index and the total number of the interface paths, respectively, 

Finflow is the total inflow to the CFD zone, and ε is 1% in current study. 

With the above two principles and Eq. (3.12), we can examine important parameters 

linking the multizone and the CFD equations in the coupling. 

Parameter analysis

In the coupling, the important parameters are Pu,ic, Pd,ic and Fic for both multizone and 

CFD programs. In order to conduct theoretical analysis on these parameters, this 

investigation uses the following simplifications: 

● Flow coefficients CL,P, CL,ij, and CL,ic; the source terms, bi, 

'

i

b , dic, bP, and B; and the 

coefficients, aP and anb are constant from one coupling iteration to the next (one 

coupling iteration includes one call of multizone and one call of CFD). 

● In the CFD calculation, the flow coefficients, CL,P and aP, and the pressures, pP and 

pnb, are uniform at path ic. 

● The derivatives of Pd,ic and Fic over Pu,ic are existent and bounded. 

Although both problems formulated by multizone and CFD simulations are nonlinear, it 

is appropriate to assume mathematically the flow coefficients of the multizone method, 

CL,ij and CL,ic as defined by Eq. (3.8), to be constant. This assumption is valid as long as 

the change of pressure difference, ΔP , is small from one multizone call to the next 

during coupled iterations. If we focus on the vicinity of ΔP , the flow coefficients can 

shift slowly with ΔP so it can be considered constant. In CFD, the coefficients, CL,P, aP

and anb, can also be assumed to be constant as long as the boundary conditions do not 

change significantly from one CFD call to the next. Technically, this can be realized in 

the coupling program by under-relaxing the flow coefficients in both the multizone and 
46

CFD methods. Users can check how the flow coeffients are under-relaxed from the 

output file for a coupled simulation as discussed in Appendix B.2. On the other hand, for 

nonlinear problems, it is hard or sometimes impossible to conduct theoretical studies such 

as solution uniqueness and stability analysis. Thus, such simplifications are necessary for 

the nonlinear problem. 

 

From the above simplifications, we can obtain the following relationships for a multizone 

program by using Eqs. (3.7) and (3.10) 

L,ic L,ij L,ij j L,ij ic i

d,ic u,ic

L,ic L,ic

C C C P C d b

P P

C C

+ − − ′

= −

(3.14)

Fic CL,ijPu,ic + CL,ijPj CL,ijd b ic i = − − − ′ (3.15)

By using Eqs. (3.6), (3.9), (3.10) and (3.11) for a CFD program we have 

 

L,P nb nb P

d,ic u,ic

P L,P P L,P

C a p b

P P

a C a C

−

= +

+ +

∑ (3.16)

P L,ic L,ic nb nb P

ic u,ic

P L,P P L,P

a C C ( a p b )

F = P

a C a C

−

−

+ +

∑ (3.17)

These equations reveal the mathematical relationships of Pu,ic, Pd,ic, and Fic, which are 

exchanged between the two programs iteratively through boundary conditions. The 

existence and uniqueness of the solution to this iterative procedure can be investigated by 

studying the derivatives of these equations for a coupled simulation. 

Solution existence and uniqueness

Zhai (2003) successfully coupled a program for building energy simulation with a CFD 

program. This investigation uses a similar approach to their study to prove the existence 
47

and uniqueness of a solution for a coupled multizone and CFD program. The basic idea is 

to analogize pressure in coupled airflow simulations and air temperature in coupled 

energy simulations. 

Applying the derivatives over Pu,ic for both sides of Eqs. (3.14) - (3.17), we have 

 

L,ic L,ij L,ij j

L,ic L,ic i

d,ic

nb

u,ic nb

L,P u,ic

P L,P P L,P

C C C P

(multizone)

C C P

P

p

P a

C P

(CFD)

a C a C

  + ∂

−   ∂

∂

=   ∂

∂   ∂

+

+ +  

∑

(3.18)

j

L,ij L,ij

i

ic

nb

u,ic nb

P L,ic u,ic

P L,P P L,P L,ic

P

C C (multizone)

P

F

p

P a

a C P

(CFD)

a C (a C ) C

  ∂

− +   ∂

∂

=   ∂

∂   ∂

−

+ +  

∑

(3.19)

One of the conditions of unique solution to a steady-state airflow simulation in a 

multizone program is that increase of pressure in one zone should increase or maintain 

the net outflow to the neighboring zones (Lorenzetti, 2002). This implies that in Fig. 3.5, 

the increase of Pi should increase or maintain Pj

j

i

P

0

P

∂

≥

∂

(3.20)

In a CFD program, the increase of Pu,ic will increase or maintain the pressures of the 

nodes next to it and the flow rate through Path ic 
48

nb

u,ic

p

0

P

∂

≥

∂

(3.21a)

0

P

F

u,ic

ic ≥

∂

∂ (3.21b)

Furthermore, Pj and Pu,ic are calculated by multizone programs and their changes from 

one coupling iteration to the next can attribute to the change of the boundary pressure, 

Pd,ic from CFD programs. So 

j j j d,ic

i u,ic u,ic d,ic

P P P P

P P P P

∂ ∂ ∂ ∂

= =

∂ ∂ ∂ ∂

(3.22)

Applying the condition of unique solution in a multizone program to Path ic of Fig. 3.5, 

we obtain 

0

P

F

d,ic

ic ≤

∂

∂ (3.23)

0

P

P

d,ic

u,ic ≥

∂

∂ (3.24)

If applying the derivative over Pd,ic for both sides of Eq. (3.10) and also considering Eq. 

(3.23), we then get 

1

P

P

d,ic

u,ic ≤

∂

∂ (3.25)

We then apply Eqs. (3.23) – (3.25) for Path ij in Fig. 3.5 
49

1

P

P

P

P

u,ic

j

i

j

≤

∂

∂

=

∂

∂ (3.26)

Combining Eqs. (3.20) and (3.26), one can obtain for multizone programs 

1

P

P

0

i

j

≤

∂

∂

≤

(3.27)

Applying inequalities (3.21) and (3.23) to Eqs. (3.18) and (3.19), we finally have 

 

L,ic L,ij

d,ic L,ic

u,ic L,P

P L,P

C C

(1, ](multizone)

P C

P C

[ ,1)(CFD)

a C

  +

  ∂

=   ∂  

+  

(3.28)

L,ij

ic

P L,ic

u,ic

P L,P

[ C ,0)(multizone)

F

a C

P (0, ](CFD)

a C

  −

∂  

=   ∂   +  

(3.29)

Note that Eqs. (3.28) and (3.29) exclude the situation when ∂Pd,ic ∂Pu,ic = 1 and 

∂Fic ∂Pu,ic = 0 , which indicates that Fic is constant/known so the coupled simulation is 

not needed for Path ic. Eqs. (3.28) and (3.29) illustrate how Pd,ic and Fic change with Pu,ic

in multizone and CFD programs. The parenthesis indicates an open side of an interval 

and the bracket means closed side, e.g., in Eq. (3.28), for multizone method 

1 d,ic u,ic L,ic L,ij L,ic < (∂P ∂P ) ≤ + (C C ) C . The solution existence and uniqueness of a coupled 

simulation can then be studied through Eqs. (3.28) and (3.29). 

The Pd,ic - Pu,ic relations are plotted in Fig. 3.6. If there is a solution for the coupled 

multizone and CFD program, the two curves will intersect, as shown in Fig. 3.6. Eq. 
50

(3.28) shows that the derivative of Pd,ic over Pu,ic for multizone calculation is always 

greater than unity, while that of CFD is less than unity, as shown in Fig. 3.6(a). 

Therefore, both curves can at least intersect at one point, which indicates that at least one 

coupling solution exists. 

Fig. 3.6 Solution existence and uniqueness analysis of the curves of Pd,ic-Pu,ic. 

The method of reduction to absurdity is used to investigate the uniqueness of the coupling 

solution. For the Pd,ic - Pu,ic relations, Fig. 3.6(b) and Fig. 3.6(c) show two possible 

scenarios of multiple solutions. Suppose we already find a solution at Point 1 through the 

above analysis of solution existence. We can then assume that the Pd,ic - Pu,ic curves may 

intersect at other points. In the first scenario, as indicated by Point 2 in Fig. 3.6(b), the 

slope of CFD curve at Point 2 is less than unity, which satisfies Eq. (3.28). The slope of 

the multizone curve at Point 2, however, does not satisfy Eq. (3.28), so the first scenario 

is impossible and Point 2 cannot be a coupled solution. The second scenario shown in 

Fig. 3.6(c) is also impossible because one specific pressure boundary condition, Pu,ic in 

CFD, can have only one corresponding Pd,ic for a given situation (including given 

numerical models and techniques). Therefore, Points 2 and 3 cannot be coupled solutions 

and Point 1 is the only solution for multizone and CFD coupling. Please note that this 

conclusion is based on the assumption that both the CFD and multizone methods can 

have a unique solution. 

Pu,ic

Pd,ic=Pu,ic 

Multizone

CFD

(a) Analysis of solution existence 

Pd,ic

Pd,ic=Pu,ic 

Pu,ic 

Pd,ic

Multizone 

CFD

1 

2 

(b) Scenario of two solutions

Pu,ic 

Multizone 

CFD 

1

2

3

(c) Scenario of three solutions

Pd,ic Pd,ic=Pu,ic 
51

The analysis here only discusses the situation in which the airflow of path ic is from zone 

i to zone c, as shown in Fig. 3.5. It is easy to apply a similar analysis to prove the 

existence and uniqueness of a solution when the airflow of path ic is from zone c to zone 

i. In conclusion, there is thus one and only one solution for multizone and CFD coupling. 

The question now is how to obtain this unique solution. 

3.2.4. Different Coupling Methods 

The unique solution of airflow coupling can only be obtained by applying appropriate 

coupling methods, which determine how the boundary conditions are exchanged between 

multizone and CFD models. Negrao (1995) claimed that the pressure boundary condition 

was applicable to the cases, where the inlet momentum changes the flow locally but does 

not substantially affect the airflow pattern of the CFD zone. The velocity boundary 

condition should be used for inlet openings, where the momentum magnitude can 

significantly modify the zone airflow pattern and must be known in advance. 

Unfortunately, we could not find the details. 

This study investigates the coupling methods by studying the basic governing equations 

of airflow coupling. As shown in Fig. 3.5, when the airflow of path ic is from zone i to 

zone c, the upwind total pressure, Pu,ic, the downwind total pressure, Pd,ic, and the airflow 

rate, Fic, are the boundary conditions to be exchanged between the two programs. Three 

coupling methods are possible according to permutation and combination: 

● Method 1: multizone gives Pu,ic to CFD and CFD returns Pd,ic to multizone; 

● Method 2: multizone gives Pu,ic to CFD and CFD returns Fic to multizone; and 

● Method 3: multizone gives Fic to CFD and CFD returns Pd,ic to multizone. 

We find that the above three coupling methods will result in different assembled matrix 

equations. When pressure and airflow rate boundary conditions are used together, such as 

in Methods 2 and 3, the assembled matrix equation is in the form of Eq. (3.12). However, 

when only pressure boundary conditions are employed (Method 1), Eq. (3.12) becomes 
52

C1 1 P B= (3.30)

where C1 is the flow coefficient maxtrix for Method 1 and B1 is the vector of the source 

terms for Method 1. 

 

Different assembled matrix equations will not have the same numerical characteristics. 

The numerical performance of one matrix equation could be better than the other matrix 

equation. 

3.2.5. Selection of the Best Coupling Method by the Scarborough Criterion 

Scarborough (1966) established a convergent criterion for a Gauss-Seidel solution for a 

set of linear equations. The criterion is often used to evaluate CFD equations. In this 

study, multizone and CFD programs provide complementary boundary conditions and the 

coupled program tries to obtain a Gauss-Seidel solution of the assembled matrix 

equation. Thus, the Scarborough criterion could be used. 

For the Gauss-Seidel solution of a linear system like Eq. (3.31), a sufficient convergence 

condition, the Scarborough criterion, is to satisfy inequality (3.32): 

 

,P P ,nb nb af f f = + ∑a b f f

(3.31)

For all equations (3.32a)

,nb

,P

1

| a |

| a |

1

f

f

≤







<

∑

For at least one equation (3.32b) 

 

The Scarborough criterion concludes that Eq. (3.31) has a convergent solution if the 

matrix is "diagonally dominant." 
53

In a coupled simulation, inequality (3.32b) can always be satisfied so long as at least one 

zone connects directly to another with a constant pressure in Eq. (3.12) or (3.30). The 

multizone calculation itself actually requires that at least one zone with unknown pressure 

be connected to another with constant pressure. Otherwise, the airflow system in a 

multizone program will be singular and can have no unique solutions (Lorenzetti, 2002). 

The zone with constant pressure can be the ambient with zero pressure or a zone with 

constant pressure specified. Inequality (3.32b) is therefore satisfied automatically in a 

coupled simulation. 

Among the three methods, only Method 1 satisfies inequality (3.32a) since it solves Eq. 

(3.30), which is a combination of Eqs. (3.7) and (3.10) and where each independent offdiagonal pressure will introduce its coefficient to that of the diagonal pressure of the 

matrix. Methods 2 and 3 solve the matrices in the form of Eq. (3.12) and F is an 

independent vector. The coefficients of F do not contribute to those of the diagonal 

pressure in the matrix. The condition of "diagonal dominance" may not always be 

satisfied for Eq. (3.12). Method 1 therefore is the only one that satisfies the Scarborough 

criterion and is guaranteed to have a convergent solution. 

Since the Scarborough criterion is only a sufficient condition and the other two methods 

may still produce a convergent solution, it may be not convincing enough to conclude 

that Method 1 is the best method. A stability analysis should be performed to provide an 

in-depth investigation of the numerical performance of the coupling methods. 

3.2.6. Selection of the Best Coupling Method by Numerical Stability Analysis 

In order to investigate further the stability of the three coupling methods, we have 

examined the iterative procedure when exchanging boundary conditions between the 

multizone and CFD programs in a coupled simulation. Fig. 3.7 shows that, during a 

coupled solving procedure, the output of one program becomes the input of the other. 

When both inputs and outputs stabilize (their values do not change), the solution of the 

coupling is considered convergent. This iterative coupling procedure can be regarded as a 
54

closed-loop system. If r is the input parameter of a multizone program from CFD and rk is 

its value at the coupling iteration k, we can define the difference of r at this iteration 

as k k 1 k r | r r | Δ = − +. 

Fig. 3.7 illustrates that the system equation for a multizone program is M, and its solution 

at iteration k, ik, can be calculate as k k i = M{r } .Similarly, we have k 1 k r {i } + = C for the 

CFD program. 

Fig. 3.7 Schematic of the coupling procedure at the coupling iteration k. 

If k Δr can be expressed by the partial derivatives of M and C, we have 

k

k k 1 0 r | | r | | r

r i r i −

∂ ∂ ∂ ∂ Δ = × ×Δ = × ×Δ

∂ ∂ ∂ ∂

M C M C (3.33)

where Δrk is the difference of the input for multizone method between the coupling 

iteration k+1 and k, M is the system equations for a multizone program, C is the system 

equations for a CFD program, i is the input for a CFD program, r is the input for a 

multizone program, and Δr0 is the initial value of Δr. 

Then when k is sufficiently large, the coupled simulation will be stable and convergent 

only if 

| | 1

r i

∂ ∂ × ≤

∂ ∂

M C (3.34)

Multizone CFD 

rk M ik rk+1 {rk} C{ik}
55

Here, we call the term 

r i

∂ ∂

×

∂ ∂

| | M C the fluctuation term. The derivatives of M and C are 

shown in Eqs. (3.18) and (3.19). Table 3.3 compares the fluctuation terms among the 

three coupling methods. The last column provides the stability criteria for a coupled 

solution. 

 Table 3.3 Stability conditions for the three coupling methods. 

The stability criterion for Method 1 is satisfied unconditionally because CL,ic, CL,ij, CL,P

and ap are all positive and the derivatives of M and C are always less than one. Together 

with the convergence analysis, one can conclude that Method 1 can lead to convergent 

and stable solutions. In addition, it is also indicated that the greater CL,ij and ap are, the 

faster the coupled program reaches a convergent solution. 

The criteria for Methods 2 and 3 shows that the two methods are conditionally stable. 

With Method 2, the greater CL,ij and the smaller CL,ic are, the more stable the coupling. 

However, Method 3 requires a smaller CL,ij to reach a better stability in the coupled 

solution. Thus, Method 1 seems the best. This can be further proved by numerical 

experiments. 

Method i r 

r i

∂ ∂

×

∂ ∂

| | M C Stability Criteria 

1 Pu,ic Pd,ic

L,ic L,P

L,ic L,ij P L,P

C C

[ ,1)

C C a C

×

+ +

unconditionally stable for 

all CL,ic, CL,ij, CL,P, and aP

2 Pu,ic Fic

P L,ic

L,ij P L,P

a C

(0, ]

C (a +C )

L,ij L,P

L,ic P

C C 1,conditionally stable

(1 )

C a 1,stable

< _

+ = 

≥

3 Fic Pd,ic

L,ij L,P

P L,ij L,ic

C C

(0, ]

a (C + C )

P L,ic

L,P L,ij

a C 1,conditionally stable

(1 )

C C 1,stable

< −

+ = 

≥
56

3.2.7. Numerical Experiments 

The numerical experiment is designed with the following considerations: 

● The assumptions of multizone models is inappropriate for at least one zone, so that 

the airflow coupling with the CFD program for the zone is necessary; 

● The numerical experiments should be able to illustrate how non-uniform 

distributions of airflow variables, especially pressures, and airflow patterns affect 

building airflow distributions; 

● The numerical experiments should be as simple as possible so that it is easy to apply 

the theoretical analysis. 

Based on these considerations, this study investigates two types of flows: pressure 

gradient flows in an office suite and cross ventilation in a four-zone building model. In 

both cases, multizone network models cannot provide reasonable predictions of air 

distributions and therefore the coupled program is employed to improve the calculations. 

Pressure gradient flows in an office suite

The first case concerns isothermal pressure gradient flows at a steady state in an office 

suite with four offices and a long hallway, as shown in Fig. 3.8. For the sake of 

simplicity, this investigation offers a two-dimensional portrayal of the office suite in an 

X-Y plane. 

The hallway, 3 m (X) × 10 m (Y), is selected as the CFD zone. The open area of Doors 1 

and 2 is 0.5 m

2

each, and that of Doors 3 through 6 is 1 m

2

each. When windows a, b, c 

and d are closed, the crack area is estimated to be 0.0002 m

2

each. Other possible 

leakages in the office suite, e.g. cracks at wall joints, are neglected in the current 

simulation. When they are opened, the cross-sectional area is 1 m

2

each. The flow is 

assumed to be isothermal so that the pressure difference due to density difference is zero 

for every flow path and the wind pressure is the only driving force. At door 1, the wind 

pressure is assumed to be constant, at 1 Pa, and those of other doors are 0 Pa. This 

investigation studies two scenarios: 
57

● Scenario A: windows a, b, c and d are closed so that the airflow rates and thus the 

pressure drops through doors 3, 4, 5 and 6 are close to zero; 

● Scenario B: windows a, b, c and d are open so that the airflow rates and thus the 

pressure drops of doors 3, 4, 5 and 6 are non-zero. 

 

Fig. 3.8 The layout of an office suite with four offices and one hallway. 

For the two-dimensional CFD calculations, the convergence criterion is that the 

normalized residuals are less than 0.01 for all the variables solved and the grid of 21×42 

(X×Y) is used for the hallway. For multizone calculations, the non-linear equation solver 

of the simple trust region is used and the flow model of the orifice equation is applied to 

all flow paths of the multizone method. The total computing time of the coupled 

simulation of method 1 is 125s for Scenario A, and 53s for Scenario B on a Pentium 4 2.0 

GHz PC. The total computing time can be divided into three parts: multizone calls 

(multizone internal iterations), the iterative exchange of boundary conditions between 

multizone and CFD (external iterations), and CFD calls (CFD internal iterations). CFD 

internal iterations take most of the total computing time. At the early stage of the coupled 

simulation, each CFD call needs more than 1000 internal iterations to obtain an 

intermittent-converged CFD solution. At a later stage, when the coupled simulation tends 

hallway 

door 1 

door 2 

door 3 

door 4 

door 6 

window a 

window b 

window c 

window d 

door 5 

Xd
58

to converge, one internal iteration of CFD is sufficient for CFD convergence. Therefore, 

the exchange of boundary conditions between multizone and CFD programs gets more 

frequent when the coupled simulation is closer to the coupling convergence. 

Fig. 3.9 shows the changes of airflow rates with coupling iterations by the three coupling 

methods in these two scenarios. Fig. 3.9(a) is for door 1 in Scenario A, and Fig. 3.9(b) is 

for door 3 in Scenario B. Fig. 3.9(a) shows that with Methods 1 and 3, the coupled 

simulation converges after about 15 iterations. This means that the exchange of boundary 

conditions between multizone and CFD programs occurs for 15 times before the coupling 

convergence, as evaluated by Eq. (3.11). The calculated airflow rates are 0.367 kg/s with 

Method 1 and 0.372 kg/s with Method 3. The two numbers are close so they support the 

theory of the uniqueness of the solution. The small difference may be due to their 

different ways in applying boundary conditions in CFD calculations. In Method 1, a 

uniform boundary pressure is employed, while Method 3 assumes a uniform distribution 

of velocity for each path. Method 2 diverges after the first several iterations in Scenario 

A, even if very high under-relaxations are used. The calculated airflow rates by Method 2 

are too unrealistic, so the results of Method 2 are not plotted in Fig. 3.9. On the other 

hand, since door 1 is connected to the ambient with a known pressure, its airflow rate can 

be calculated directly from the local pressures of CFD calculation at each iteration. 

Therefore, for Method 3, only the convergence history of CFD0 (Method-3-CFD0) is 

shown because it is the same as that of CONTAM. 

Compared with Scenario A, the three coupling methods behave differently for Scenario 

B, as shown in Fig. 3.9(b), which shows the flow rates through door 3 during coupling. 

For Scenario B, Methods 1 and 2 can give a convergent solution and calculate the same 

flow rate through door 3. Method 3 diverges quickly and fails to produce reasonable 

airflow rates during the iteration. 

 
59

(a) 

(b) 

Fig. 3.9 Airflow rates calculated with different coupling methods (a) airflow rate through 

door 1 in Scenario A by Methods 1 and 3; (b) airflow rate through door 3 in Scenario B 

by Methods 1 and 2. 

Without coupling 

Without coupling 
60

The distinct numerical performances of the three coupling methods can be explained by 

studying their stability performance based on the stability criteria in Table 3.3. By 

calculating the coefficients, CL,ic, CL,P, CL,ij and aP, for Scenarios A and B, one can obtain 

the fluctuation terms 

r i

∂ ∂

×

∂ ∂

| | M C for all coupling methods, as shown in Table 3.4. The 

stability criteria require that the fluctuation terms must be smaller than 1.0, so Method 1 

is unconditionally stable for Scenarios A and B. Furthermore, the smaller the fluctuation 

term is, the faster the coupled simulation reaches convergence. This can be easily seen in 

Fig. 3.9, in which it took Method 1 four iterations in Scenario B to reach convergence, as 

opposed to 15 iterations in Scenario A. Furthermore, Table 3.4 illustrates that the 

fluctuation terms of Method 2 in Scenario B and Method 3 in Scenario A are much 

smaller than 1.0, which guarantee converged solutions. The instabilities of Method 2 in 

Scenario A and Method 3 in Scenario B can also be explained by their high fluctuation 

terms, as shown in Table 3.4. The fluctuation term can be greater than 1.0 during 

coupling iterations, which finally leads to divergences. 

Table 3.4 The fluctuation terms of different coupling methods for Scenarios A and B for 

the pressure gradient flows in an office suite. 

∂ ∂

×

∂ ∂

| |

r i

M C

Scenario A Scenario B 

Method 1 [0.5, 1) [0.002,1) 

Method 2 (0, 1879.7] (0, 0.003] 

Method 3 (0, 0.002] (0, 41.5] 

Fig. 3.9 also compares the calculated airflow rates with and without coupling (the results 

of the iterations versus those at Iteration 1). If a positive value means an inflow for the 

hallway, the relative differences can be 11% for door 1 in Scenario A. Fig. 3.10 provides 

comparisons with more detail. For Scenario A, as shown in Fig. 3.10(a), since windows a, 

b, c and d are closed, the flow rates of doors 3 through 6 are close to zero with coupling. 

The largest difference without and with coupling is around 30%. When windows a, b, c 

and d are open in Scenario B, the flow directions through doors 3 and 5 even change from 
61

outflows to inflows with coupling, as shown in Fig. 3.10(b). As a result, the airflow rates 

of other doors change dramatically in Scenario B. 

(a) 

(b) 

Fig. 3.10 Comparisons of calculated airflow rates through different openings in an office 

suite with and without coupling (a) Scenario A and (b) Scenario B. 
62

The dramatic changes of airflow rates with coupling in Scenario B provide clear evidence 

that, when the homogeneous assumption of multizone models are inappropriate, the 

airflow pattern plays an important role in building air distributions. Fig. 3.11 shows the 

airflow patterns in the hallway, calculated by CFD. For Scenario A, shown in Fig. 

3.11(a), a recirculation area forms at each side of door 1, whereas it is not big enough to 

affect doors 3 and 5. Moreover, the local pressures at doors 3 through 6 are almost the 

same so that the calculated airflow rates are close to each other. 

However, when windows a, b, c, and d are open in Scenario B, Fig. 3.11(b) shows that 

the airflow pattern changes dramatically. Compared with Scenario A, the airflow through 

door 1 has less flow resistance, and the flow momentum is preserved after entering the 

hallway. The recirculation areas therefore extend far enough to affect the local flow near 

doors 3 and 5. Instead of outflows calculated by CONTAM, air is induced through doors 

3 and 5 into the hallway. Fig. 3.11(b) also illustrates that the pressure distribution in 

Scenario B is non-uniform, which explains why the airflow rates of doors 4 and 6 change 

more with coupling than those in Scenario A. 

Fig. 3.10 and Fig. 3.11 show that CFD solutions were a little asymmetrical, e.g. for door 

3 and door 5 in Fig. 3.10(b), the flow rates were 0.013 and 0.01 respectively. One 

explanation is that the CFD convergence criterion in this case is that the CFD residual is 

less than 1%. The residual of CFD simulation can be roughly calculated as [(0.302-0.295) 

+ (0.013-0.01)]/ (0.763) ~ 0.01 (0.763 is the total inflow rate). So the small difference of 

flow rates is caused by simulation residuals. On the other hand, perfect symmetry 

normally is not easy to be achieved in CFD simulations (Chen and Jiang, 1992). 
63

Fig. 3.11 Airflow patterns and pressure distributions with coupling in the office suite (a) 

Scenario A with closed windows a, b, c, and d; (b) Scenario B with open windows a, b, c, 

and d. 

The numerical experiment for the pressure gradient flows in the office suite demonstrates 

that the coupled solution exists and is unique. Method 1 is indeed the best coupling 

method. Furthermore, the coupled program can improve the accuracy of the multizone 

models by considering the airflow patterns and non-uniform pressures inside the CFD 

zones. 

Cross ventilation in a four-zone building model

For the sake of simplicity, the numerical experiment for the office suite is conducted twodimensionally. Negrao (1995) found that the airflow coupling of multizone and CFD 

models may not work for three-dimensional cases. In order to test further the coupled 

program, a more complex three-dimensional problem, with cross ventilation in a fourzone building model, is studied. 

(a) 

1.0 m/s 

3 4 

1

5 6 

2

(b) 

1.0 m/s 

3 4 

1

5 6 

2
64

Fig. 3.12 The 4-zone building model (a) section (top) and plane (bottom) of the wind 

tunnel laboratory (Sawachi et al., 2003); (b) the three-dimensional view of the building 

model. 

(a)

(b)

A

B

C

zone F 

Xd 
65

Sawachi et al. (2003) used a full-scale building model in a wind tunnel to measure the 

discharge coefficients at the building openings under different wind directions. Fig. 

3.12(a) shows the wind tunnel sketch. The test model placed in the wind tunnel was a 

full-scale building model that was 5.53 m (X) × 5.53 m (Y) ×3.0 m (Z), and was divided 

into four sub-zones with the same size. The full-scale building model could be turned 

around to study the impact of different wind directions. This study only uses the case 

where the wind was perpendicular to the opening in the building model. Fig. 3.12(b) 

illustrates the three-dimensional view of the 4-zone building model. With a strong 

momentum, the wind flows into zone F through path A, the size of which is 0.86m (W)×

1.74m (H), and is distributed among the other three sub-zones through internal paths B 

and C, the size of which is 1.68m (W)× 2.5m (H) each. Zone F is therefore subject to the 

momentum effect of the incoming wind, and the coupled simulation selected zone F as 

the CFD zone. 

The same convergence criterion as the previous case is used for the three-dimensional 

CFD runs, and the grid in this case is 19×19×24 (X×Y×Z). The total computing time of 

the coupled simulation of Method 1 is 184 s on a Pentium 4 2.0 GHz PC, which is more 

than that of the previous case because of the increased grid numbers in the CFD 

simulation. 

Fig. 3.13(a) illustrates the experimental airflow pattern for the building model. It shows 

that, due to the preserved momentum of the incoming wind, the air in zone F mostly 

flowed from opening A through path C. Opening B has little flow. Obviously, the 

momentum effect was very significant for this case. Fig. 3.13(b) shows the calculated 

airflow pattern with coupling by Method 1, which is similar to that used in the 

experiment except that the calculated recirculation area is smaller. The difference is 

mainly caused by specifying the uniform distribution of velocities in opening A, which is 

not uniform in the experiment. On the other hand, since the coupled simulation applied 

the CFD simulation only to zone F, its prediction is a combination of the results of 
66

multizone and CFD simulations. Therefore, the calculated airflow pattern may be 

different from the experiment. 

Although the coupled simulation may not be as accurate as the application of CFD to all 

zones, it is still able to provide more reasonable airflow predictions than that provided by 

multizone models alone. When the flow rate through path A is 2.386 kg/s, CONTAM 

alone would calculate the same flow rate for paths B and C at 1.193 kg/s due to 

neglecting the preserved momentum inside zone F. However, the coupled program 

calculates the flow rate of 0.746 kg/s for path B and 1.640 kg/s for path C. The difference 

is around 60% between the solutions by CONTAM alone and by the coupled program. 

This is because the coupled program can capture the strong momentum at path A when 

applying CFD for zone F. 

Fig. 3.13 The coupled simulation in a four-zone house model with cross ventilation (a) 

the measured velocity field of the four-zone house model; (b) the velocity and pressure 

fields by the coupled simulations. 

3.0 m/s 

(b) 

A

B 

C

(a) 

A

B 

zone F C
67

Fig. 3.14 Airflow rate through path B during the iteration with the three coupling methods 

in a four-zone building model with cross ventilation. 

The above analysis uses the results obtained from Method 1 with and without coupling. 

By using Methods 2 and 3, we can also achieve converged solutions for this case. Fig. 

3.14 shows the airflow rates of path B during the coupled solution with the three 

methods. All the three methods have led to the same flow rate at path B, which again 

supports the theory of unique solution. Compared with Method 1, the coupling by 

Methods 2 and 3, however, fluctuates during iterations, as shown in Fig. 3.14. This 

further proves the conditional stability of the two methods. Due to the nonlinearity of the 

problem, the linear flow coefficients, CL,ij and CL,ic, can change during the iterative 

coupling. Although the overall trend of the coupling is convergent, the stability criteria in 

Table 3.3 may not always be satisfied at some iteration, which as a result causes the 

fluctuations. 

This investigation is for large openings, where CFD plays an important role and can 

improve the results. If cracks become very important, multizone models alone can handle 

it, where no coupling between the CFD and the multizone is required. This study does not 

address the coupling of CFD with multizone methods in the event that cracks exist. 

Without coupling 
68

3.3. Summary

This chapter develops the indirect coupling scheme for airflow simulations around 

buildings and the direct coupling for airflow and contaminant transport simulations in 

buildings. The coupling schemes decide “what” information, and “how”, “where”, and 

“when” the information should be exchanged between CONTAM and CFD0-C. 

The indirect coupling scheme uses the WPC link and the WPP link to provide calculated 

wind pressures and wind pressure coefficients, respectively, by CFD0-C for CONTAM. 

Since only one-time interaction of CONTAM and CFD0-C is involved, it is not a direct 

coupling but a virtual coupling procedure. 

The direct coupling scheme is used to solve the coupled simulations in buildings. This 

scheme will exchange airflow rates or pressures between CONTAM and CFD0-C, 

iteratively. To determine “where” and “when” the information should be exchanged, a 

direct coupling controller and three different coupling algorithms are developed, 

respectively. Three coupling methods are then proposed to decide “how” the direct 

coupling exchanges the information between a multizone network model and a CFD 

program (Fig. 3.5): 

● Multizone gives Pu,ic to CFD and CFD returns Pd,ic to multizone; 

● Multizone gives Pu,ic to CFD and CFD returns Fic to multizone; 

● Multizone gives Fic to CFD and CFD returns Pd,ic to multizone. 

Through theoretical analyses, this chapter has proven that the coupled program has a 

solution and the solution is unique, based on the three coupling methods. 

 

This investigation also uses the Scarborough criterion to evaluate the convergent 

performances and to analyze the stability of the three coupling methods during their 

iterative coupling processes. Method 1, which exchanges pressure boundary conditions 

between multizone and CFD programs, is unconditionally stable, while Methods 2 and 3 

are conditionally stable. Two numerical experiments are conducted to demonstrate the 
69

theory: one is pressure gradient flow in an office suite, and the other is cross ventilation 

in a four-zone building model. Numerical results show that the coupling solution is 

indeed unique and Method 1 is the most stable method. Thus, the theory analysis is 

correct and valid. 
70

CHAPTER 4. VALIDATIONS 

CONTAM could provide inaccurate results in the simulations with non-uniform 

momentum effect, temperature, and contaminant concentration. Before improving 

CONTAM by CFD0-C, it is necessary to check whether CFD0-C itself can perform 

better than CONTAM in the simulations, where CONTAM assumptions fail. Therefore, 

the validation of CFD0-C is needed. On the other hand, many uncertainties can be 

involved when the two programs are integrated, although the individual program has 

already been validated. It is important to compare the numerical solutions with the 

experimental data and to reveal the advantages of the coupled CONTAM and the CFD0-

C program over the individual CONTAM and CFD0-C program. Hence, this chapter first 

verifies CFD0-C through the data obtained from the literature, and then validates the 

coupled CONTAM and the CFD0-C program through the measured data from a series of 

chamber experiments. 

4.1. Part I – Validation of CFD0-C

The validation of CFD0-C is necessary because it is converted and upgraded from the 

FORTRAN version of CFD0, CFD0-F. Before validating the coupled program of 

CONTAM and CFD0-C, it is necessary to verify the conversion. The verification of the 

CFD0-C program is carried out by comparing the simulation results with published data. 

This study selects the following cases based on the facts that: 

1. a 90-degree planar branch case tests the CFD0-C's capability of using pressure 

boundary conditions, which is required by the coupling Method 1; 

2. a case of the buoyancy-driven airflows in a stairwell validates CFD0-C in the 

prediction of the buoyancy-driven flow with a non-uniform distribution of 

temperature; 
71

3. a 4-zone case of cross ventilation examines the capability of CFD0-C to simulate 

airflows with a non-uniform distribution of the momentum effect; 

4. a case of displacement ventilation reveals the ability of CFD0-C to predict airflows 

with a non-uniform distribution of temperatures and contaminant concentrations; and 

5. an external airflow around a building model in a wind tunnel validates the prediction 

of non-uniform wind pressures on a cubic house by CFD0-C. 

4.1.1. Flow through a 90-degree Planar Branch 

CHAPTER 3 has revealed that the best coupling method is Method 1, in which pressure 

boundary conditions are exchanged between the CONTAM and the CFD0-C. However, 

to describe pressure as a boundary condition is a new capability of CFD0-C. This section 

thus validates the ability of CFD0-C to handle pressure boundary conditions through a 

classic case, the airflow through a 90-degree planar branch. The case has been used to 

validate CFD simulations with pressure boundary conditions in several previous studies 

(Hayes et al., 1989; Kelka and Choudhury, 2000; Zhai et al., 2004). Although the 90-

degree planar branch is not a building, it is quite similar to a corridor. The current study 

therefore chooses it as a validation case. 

Fig. 4.1 illustrates the geometry of the branch. The flow domain is divided into 30×58 

grids by the CFD0-C. Uniform velocity is specified for the inlet, and zero pressure for the 

two outlets. As shown in Fig. 4.1, when the Reynolds number is small, e.g. Re=10, the air 

stream almost bifurcates equally between the two outlets. As the Reynolds number 

increases to 400, recirculation is observed at the elbow of the branch. The outflow to the 

straight or main branch is greater than the side branch. This is because the higher the 

Reynolds number is, the stronger the momentum effect. 
72

Fig. 4.1 Streamline lines in the 90-degree planar branch: (a) Re=10, (b) Re = 400. 

Hayes et al. (1989), Kelka and Choudhury (2000), and Zhai et al. (2004) have simulated 

the 90-degree planar branch using different CFD codes. Fig. 4.2 compares the results 

obtained by the CFD0-C with the three studies. The fractional flow rates of the main 

branch calculated by the CFD0-C are close to those obtained by the published results. 

Both the CFD0-C and MIT-CFD (Zhai, 2003) use the zero-equation turbulence model 

(Chen and Xu, 1998), which is different from the κ-ε model used by Hayes and Kelkar. 

MIT-CFD and CFD0-C use different implementation approaches for pressure boundary 

conditions: CFD0-C uses the method of Patankar (1980), and MIT-CFD uses the method 

of Versteeg and Malalasekera ( 1995). All of these factors could contribute to the 

differences in simulation results. However, the differences are insignificant. Therefore, 

this case verifies that pressure boundary condition in CFD0-C is implemented correctly. 
73

Fig. 4.2 Fractional flow rates in main branch as a function of the Reynolds number. 

4.1.2. Buoyancy-driven Airflows in a Stairwell 

For buoyancy-driven airflows, temperature variations play an important role in 

ventilation rates. This is because the directional buoyancy force has a large influence on 

the flow patterns within the space and on the nature of the exchange with the outside 

(Linden, 1999). In CHAPTER 2, we compare the results of CONTAM with experimental 

data in the buoyancy-driven flow in a stairwell. The CONTAM results are quite different 

from those obtained by the experiment due to the well-mixing assumption of uniform 

temperatures. Before improving the CONTAM results by coupling it with CFD0-C, it is 

necessary to validate the ability of CFD0-C to model buoyancy-driven flows. 

Fig. 2.2 in CHAPTER 2 shows the geometry of the stairwell model. Thirteen steps form 

the stairway and the width of the stairwell is 0.608 m. The circulation of air is maintained 

by a continuous supply of heat to the lower compartment. There are two small openings 

measuring 0.01 m×0.608 m, one in the lower and one in the upper compartment. The 

heater, a 1 kW Dimplex oil-filled electric radiator with 0.570 m×0.659 m dimensions 

(both sides are exposed to air), is placed in the corner of the lower compartment. 
74

In CFD0-C simulation, a fine grid number of 95×28×81 is used. Special attention is paid 

to the specification of boundary conditions. Zero pressure is applied at the two openings. 

The overall heat flux data is available and it may be specified as boundary conditions at 

the walls of the stairwell. Since this study does not calculate heat conduction in the walls, 

it needs to specify the convective heat fluxes instead of the overall heat fluxes. The 

convective heat fluxes are calculated based on the overall heat balance in the walls: 

c r q = − q q (4.1)

where c

q , rq , and q denote the convective, radiative, and total heat fluxes, respectively. 

It is assumed that the surfaces of the stairwell are opaque and gray bodies. This 

investigation further assumes that the medium (air) do not participate in radiative heat 

transfers (Mokhtarzadeh-Dehghan et al., 1994). 

Table 4.1 shows the measured air temperatures and temperature gradients for different 

input powers from the heater. With the increase in power, the differences in the 

temperature inside and outside the stairwell, and the vertical temperature gradient, 

increase dramatically. The vertical temperature gradient is 3.5 °C for 100 W and can 

reach 17 °C for 900 W. CONTAM cannot consider such high temperature gradients, as 

revealed in Fig. 4.3. 

Table 4.1 Measured air parameters of the buoyancy-driven flow in a stairwell. 

Q (power of the 

heater) (W) 

Ambient 

temperature 

Tamb (°C) 

Average inside 

temperature 

Tins (°C) 

Temperature 

differences 

∆T=Tamb-Tins (°C)

Vertical 

temperature 

gradient (°C) 

100 21.8 25.8 4 3.5 

300 23.7 29.6 5.9 7 

600 24.9 37.9 13 11 

900 24.9 40.4 15.5 17 
75

As we can see, the mass flow rates computed by CONTAM are all less than the measured 

results. When the temperature gradient is low, e.g. 3.5 °C for 100 W, the difference 

between CONTAM and the experimental results is not significant. With the increase of 

the temperature gradient, such a difference increases considerably. The huge discrepancy 

is found in the case of 900 W with the maximum temperature gradient. Therefore, the 

temperature gradient is important for buoyancy-driven flows, whereas CONTAM may 

provide inaccurate results due to its well-mixing assumption. 

Fig. 4.3 Comparison of mass flow rates of CFD0-C, Experiment and CONTAM for the 

buoyancy-driven flow in a stairwell. 

CFD0-C can consider a non-uniform distribution of temperatures with reasonable 

accuracy, as shown in Fig. 4.3. The calculated results obtained from the CFD0-C are 

close to the experiment, although the CFD0-C tends to overestimate the airflow rates. 

One reason for this overestimation is the method used in calculating the convective heat 

flux. Based on the results, it seems that the method might have overestimated the 

convective heat fluxes. Another possible reason is the reliability of the experimental data, 
76

which did not ascertain how the heat fluxes of walls are measured. It would be better if 

wall temperatures were available for the CFD0-C computations. 

Fig. 4.4 The flow pattern in the experiment. 

Fig. 4.4 shows the measured airflow pattern. The air rises along the heater due to 

buoyancy and two large vortices are formed in the upper compartment. The relatively 

cold air moves from the upper to the lower compartment along the stairs and then is 

reheated by the heater. The flow patterns computed by the CFD0-C are close to the 

measured one, as shown in Fig. 4.5. 

The study of the buoyancy-driven flows in a stairwell reveals that CFD0-C can predict 

airflow rates and temperature gradients with reasonable accuracy. The current study thus 

can use CFD0-C for the problems with a non-uniform distribution of temperature. 
77

Fig. 4.5 The flow patterns by the numerical simulation by CFD0-C for the input power of 

300 W. 

4.1.3. Displacement Ventilation 

In the previous two cases, we try to validate CFD0-C by comparing it with published 

results. Due to limited experimental data, we do not compare spatial distributions of air 

velocities and contaminant concentrations. More validations are required to check the 

reliability of CFD0-C to calculate spatial air and contaminant parameters. Hence, we 

selected the displacement ventilation case from the studies of Srebric et al. (1999) for 

further validation. 

Fig. 4.6 shows the displacement ventilation case. Conditioned air with the temperature of 

17 °C is supplied from a 0.53 m × 1.1 m air diffuser at the low air velocity of 0.086 m/s. 

The return is located at the ceiling through which the warm room air is released. The 

supply air spreads over the floor and then rises as it is heated by the heat sources in the 

occupied zone. Heat sources (e.g. persons or computers) in the occupied zone create 

upward convective flows in the form of thermal plumes. These plumes remove heat and 

contaminants that are less dense than the air from the surrounding occupied zone. 
78

Fig. 4.6 The layout of the displacement ventilation simulated and tested in the chamber 

(inlet -1, outlet -2, person -3, table -4, window -5, fluorescent lamps -6, cabinet -7, 

computer -9, tracer gas sources -10). 

Fig. 4.7(a) and Fig. 4.7(b) show the calculated air velocity plotted in two sections in the 

room. Fig. 4.7(d) illustrates the airflow distribution by smoke visualization. The 

computed results are in good agreement with the flow pattern observed, e.g. the 

recirculation in the lower part of the room is well captured. Fig. 4.7(b) also shows the 

upward plumes due to the buoyancy generated from the heat sources (the hot window, 

two computers, and two persons). A remarkable stratification of temperature can be 

observed in Fig. 4.7(c). The cold air at about 17 °C moves slowly along the floor, is 

heated by the heat sources, and finally leaves the room through the ceiling outlet with a 

temperature around 26.7 °C. 
79

Fig. 4.7 The air distribution for the displacement ventilation case. (a) computed velocity 

in a middle section, (b) computed velocity in a horizontal section, (c) computed 

temperature in a middle section, and (d) airflow pattern observed by smoke visualization 

in a middle section. 

Fig. 4.8, Fig. 4.9, and Fig. 4.10, respectively, show the comparison of measured and 

calculated velocity, temperature, and concentration of tracer-gas (SF6). The right bottom 

figure shows the floor plan of the room, where the measurements were carried out at nine 

positions. Fig. 4.10 also illustrates the positions of the tracer-gas sources, e.g. S1 and S2. 

The computed results are compared with the experimental data in different vertical 

sections in the room. Although some discrepancies are observed, e.g. temperatures near 

the ceiling in Fig. 4.9, the computed velocity and temperature distributions generally 

agree very well with the measured results. The comparison for concentration, however, is 

(a) (b)

(c) (d)
80

not as good as that for velocity and temperature. As shown in Fig. 4.10, both the 

concentration near the ceiling and the floor do not agree well with the experimental data, 

especially near the tracer-gas sources. The same problem has been found in similar 

studies. The most plausible reason is that the flow is not very stable and it is difficult to 

measure the time-averaged concentration. For each point, the concentration measurement 

took 30 seconds. It took six minutes to measure 12 points of the tracer-gas concentration. 

Fig. 4.8 The comparison of the velocity profiles at nine positions in the room between the 

calculated and measured data for the displacement ventilation case. Z = height, H = total 

room height, V = velocity, Vin = inlet velocity, H = 2.43 m, Vin = 0.086 m/s. 
81

Fig. 4.9 The comparison of the temperature profiles at nine positions in the room between 

the calculated and measured data for the displacement ventilation case. Z = height, H = 

total room height, θ = (T-Tin/Tout-Tin), H = 2.43 m, Tin = 17.0 oC, Tout = 26.7 oC. 

Nevertheless, the CFD0-C results are close to the experimental data, and the accuracy is 

acceptable. If a RMS value of the divergence of the calculated data from the measured 

results is calculated, it is 9.6% for air velocity, 3.2% for air temperature, and 13% for SF6

concentration. The RMS difference of SF6 concentration is higher than that of air velocity 

and temperature due to the above reasons. The CFD case and grid quality are also 

relevant to the accuracy of the simulation. As noted in Fig. 4.10, the source of tracer gas 

is originally modeled as a cube, the side of which is 20 cm. Later it is found that a cube 

with the side of 10 cm is more appropriate. Fine grids also improve the results. On the 

other hand, it seems more suitable to model the transfer-gas source as “Fluid” blockage, 

which allows air to flow through, than “Solid” blockage. Generally, the results of the 

CFD0-C are acceptable. 
82

Fig. 4.10 The comparison of the contaminant profiles (ppm) at nine positions in the room 

between the calculated and measured data for the displacement ventilation case. Z = 

height, H = total room height, χ = (C-Cin/Cout-Cin), H = 2.43m, Cin = 0.0, Cout = 0.421. 

4.1.4. Cross Ventilation in a 4-zone Building Model 

In addition to buoyancy-driven airflows, natural ventilation driven by wind is also very 

common. Cross ventilation is one of the popular ways to deal with hot indoor 

environment in summer and shoulder seasons. A strong momentum effect is often 

observed in airflows with cross ventilation. In order to validate CFD0-C in solving 

airflows with strong momentum effect, the current study selects a case of cross 

ventilation in a 4-zone building model. 
83

Fig. 4.11 Comparison of calculated and measured flow field with the wind coming 

perpendicular to the opening (a) The CFD0-C model, (b) CFD0-C flow field, (c) flow 

visualization in the test model, and (d) measured airflow field. 

Sawachi et al. (2003) designed a full-scale wind tunnel to measure the variable discharge 

coefficients of openings due to different wind directions. Fig. 3.12 in CHAPTER 2 shows 

the wind tunnel sketch. The test model placed in the wind tunnel is a full-scale room, 

5.53 m (L) × 5.53 m (B) ×3.0 m (H), divided into 4 sub-zones with the same size. 

Pressures and velocities are measured at many points around and inside the test model by 

differential pressure transducers and ultra-sonic three-dimensional anemometers. Laser 

(b) 

(c) 

(a) 

(d) 

Left Front

Top

Front

Left

Right 

Back 
84

light sheet and smoke generation are used to visualize the flow fields, as illustrated in 

Fig. 4.11(c) for the case in which the wind is perpendicular to the opening (zero degree). 

In this study, the flow boundary condition of the “air inlet 1” in Fig. 4.11(a) is specified 

with the uniform velocity of 3 m/s, and a zero pressure boundary is used for the outlet 4. 

The air flowing through opening A is at an angle due to a strong momentum effect, as 

shown in the measured flow field (Fig. 4.11(d)). Most of the flow goes into sub-zone D. 

The momentum of the air is still preserved even when leaving sub-zone C. Recirculation 

is observed in each of the sub-zones, some of which have caused two-way flows, such as 

across the two openings of sub-zone B. As shown in Fig. 4.11(b), the flow field 

calculated by CFD0-C is quite close to that measured. The recirculation in the left upper 

corner of sub-zone D, however, is not as obvious as the measured one. Reasons for the 

discrepancies could be insufficient grid resolution in that area and the isotropic 

assumption of turbulence in the turbulence model. 

When the wind angle is zero degree, the measured ventilation rate by Sawachi of this 4-

zone house was 8.2×103 m3/h. By integration over door 2 in Fig. 4.11(a), the CFD0-Ccalculated ventilation rate is about 7.158×103

 m3/h and the relative difference is 12.7%. 

Nishizawa et al. ( 2003) simulated the same case by a k -e model with a commercial 

CFD code, STREAM, and the ventilation rate they obtained was around 9.1×103 m3/h. 

Their relative difference was about 11.0%. Inadequate geometry data may be one reason 

for the high relative difference. 

4.1.5. External Airflow around a Building Model in a Wind Tunnel 

The previous sections have validated CFD0-C for indoor airflow and contaminant 

transport simulations, which are characterized by low air velocities and turbulence 

effects. Compared to indoor airflows, atmospheric airflows around buildings involve 

higher air speed, more turbulence separation, reattachment, and vortices (Cochran, 2000). 

Literature review shows that not many validation studies have been conducted for such 

outdoor simulations with the CFD zero-equation turbulence model. Therefore, it is 
85

necessary to examine the performance of CFD0-C for atmospheric airflows around 

buildings. 

This thesis chose the same building model of Sawachi et al. (2003), who also measured 

external wind pressure distribution except that doors 2 and 3 in Fig. 4.11 were completely 

closed to obtain a solid building block. Sawachi et al. also measured the wind velocities 

at opening 1 as shown in Fig. 4.12, which was not the normal power-law/logarithm 

distribution. To consider the non-uniform distribution of wind velocities, opening 1 was 

modeled by eight vertically-arranged openings, each of which has uniform velocity 

specified in CFD0-C. A minimum grid spacing of 300mm as suggested by Cochran 

(2000), which is a similar size to the separation vortex, was used for the building block 

and a total grid number of 57×63×42 (X×Y×Z) was created for the wind tunnel. 

Fig. 4.12 Measured wind velocity distribution (m/s) at the wind supply opening 1. 

CFD0-C illustrated variable performances for different building surfaces when simulating 

wind pressure distributions. Fig. 4.13 shows that for the front surface, which is under 

least flow separation, the predicted Cp values had a maximum of 20% difference from the 

measured data. However, the maximum difference could be 80% for the rest surfaces, 

which had strong turbulence separation and recirculation flows. Therefore, CFD0-C 

performs better for the surface with less turbulence separation and recirculation. In fact, 

the Reynolds Averaged Navier-Stokes (RANS) equations were found incapable to 

resolve the turbulence vortices and the curvature-sensitive separation flow features in 
86

wind flow around buildings (Cochran 2000). Better results could be obtained by Large 

Eddy Simulations (LES), which however cause more computing time than RANS 

models. For engineering applications, the calculated wind pressure coefficients by CFD0-

C may be enough to remedy the assumption of uniform wind pressures of CONTAM as 

illustrated by a demonstration case in CHAPTER 5.1.2. 

Fig. 4.13 Comparison of (a) measured wind pressure coefficients with (b) calculated wind 

pressure coefficients by CFD0-C when wind direction is zero degree. 

Note that to calculate Cp the reference wind velocity, UH in Eq. (3.1), was measured when 

there was no building model inside the wind tunnel, which was lower than the actual 

velocity for the wind tunnel with the building model. As a result, the maximum wind 

pressure coefficient became more than “1.0” in this case (Nishizawa et al., 2003). 

Front

Right 

Left

Back

Top 

(a) (b) 
87

4.2. Part II – Validations of Coupled Program

Even if CFD0-C and CONTAM may have been already validated individually, it cannot 

be guaranteed that the coupled CONTAM-CFD0 program will provide acceptable results. 

Since the coupled program only applies CFD0-C to some zones of a building, it will not 

be a surprise if the calculated results are not as accurate as those obtained by using 

CFD0-C for the whole building. However, the results from a coupled simulation should 

at least be better than CONTAM. Otherwise, there is no need to use the coupled program. 

It is therefore necessary to validate the coupled program to check how accurate the results 

are, when compared to a whole building simulation by only using CFD0, checking as 

well how well it can improve CONTAM calculations. 

4.2.1. Experimental Design 

In order to validate the coupled program and to show that the coupled program is superior 

to a multizone program, the experiment should be designed to study the situations where 

the CONTAM assumptions fail. As discussed previously, the situations include 

1. non-uniform air momentum distributions ; 

2. non-uniform contaminant concentration distributions; and/or 

3. non-uniform air temperature distributions. 

In this investigation, three experimental cases are designed for each of the above 

situation. The experiment uses an environmental chamber facility in the Ray W. Herrick 

Laboratories at Purdue University (Fig. 4.14(a)). The current study partitioned the facility 

further into four zones by a foam board, as shown in Fig. 4.14(b). All the cracks are 

sealed by duct tape to avoid filtrations. 

This investigation measures the wall temperatures, spatial distributions of air velocities 

and temperatures, contaminant concentrations simulated by sulfur hexafluoride (SF6), and 

airflow rates through the openings between the zones. Air velocities and temperatures are 

measured at 63 locations with omni-directional hot-sphere anemometers, as shown in Fig. 

4.15(a). Eighteen thermal couples are embedded in the walls for wall temperature 
88

measurements, supplemented with an infrared thermometer. Spatial SF6 concentration is 

measured at 45 locations by a tracer gas analyzer. 

(a) External view of the environmental chamber 

(b) Internal view of the environment chamber partitions inside the test chamber with the 

partition door removed for each zone 

Fig. 4.14 The environment chamber of Ray W. Herrick Laboratories. 

Foam partitions 

Test chamber 

Climate chamber 
89

 (a) Sensor location (b) Flow rate measurements 

Fig. 4.15 Example of the sensors used for air velocity, air temperature, and flow rate 

measurements and their locations. 

Fig. 4.15(b) shows three tracer-gas sampling tubes in an opening simulated by a window, 

used to measure the airflow rate through the window. The measurements were based on 

the steady-state tracer gas method. The equilibrium flow rate through an opening was 

calculated by: 

m Q = C

 (4.2)

where, Q = flow rate through an opening, 

m = tracer-gas source (SF6) flow rate, 

i i

i

C = ( C A )/A ∑ , the average SF6 concentration through the opening. 
90

4.2.2. Non-Uniform Momentum Distributions 

This section will first present the experimental conditions for airflow and contaminant 

transport in the four-zone chamber facility with non-uniform momentum distribution in a 

zone. The numerical results of CONTAM, CFD0, and the coupled simulations are then 

compared with the measurement data. 

We used mechanical ventilation through an air supply to create a strong non-uniform 

momentum effect in zone 1, as shown in Fig. 4.16. Zone 1 has two openings, one on the 

opposite side of the supply and the other far from the supply. Multizone models could not 

consider the non-uniform momentum effect in zone 1 created by the air supply. As a 

result, the airflow rate through the two openings, calculated by multizone models, would 

be the same. In reality, we know that opening 1 would have a higher flow rate caused by 

the momentum effect from the air supply than opening 2, as the zone geometry in the 

downstream was almost symmetrical. 

The supply opening size was 0.3 m × 0.2 m, with an effective area ratio of 0.77. The 

airflow rates used in the experiment were 0.034, 0.053, 0.105, 0.14, and 0.215 m3/s. The 

size of the openings 1 and 2 was 0.40 m × 0.20 m each and the other openings in zones 2 

and 3 (windows 1 and 2) were 0.65 m × 0.20 m. 

The case is simulated by three methods: 

● CONTAM simulations 

● Coupled CONTAM and CFD0 simulations in which 67 × 25 × 35 grids were used in 

zone 1 for CFD0 

● CFD0 simulations of all four zones with 67 × 71 × 35 grids 
91

(a) Physical conditions for zone 1 

(b) The geometric conditions of the four-zone chamber 

Fig. 4.16 The scheme of the four-zone chamber used to study non-uniform momentum 

distribution in zone 1. 

1 2 3 4 5 6 

x(m) 2.49 0.55 1.76 0.73 1.07 4.43 

y(m) 0.20 0.40 1.83 2.44 0.18 0.75 

z(m) 1.72 0.62 0.35 1.50 1.62 2.44 

supply

opening 1

zone 1 

y2 

y1 

y3(Xd) 

y4 

y5 

y6 

x1

x2

x3

x4 

x5

z1

z3

z2

supply z4

opening 1

opening 2 

window 1 

window 2

exhaust 

zone 1 

zone 2 

zone 3 

zone 4 

x6 

z5 

z6
92

(a) (b) 

Fig. 4.17 Airflow and pressure distributions in the four-zone chamber facility (a) 

calculated by CONTAM and (b) calculated by the coupled CONTAM and CFD0 program. 

Fig. 4.17 compares the airflow results of the CONTAM simulation with those of the 

coupled simulation for the case with 0.105 m3/s of air supply. The blue lines stand for 

airflow rates and the red lines for pressure differences across the airflow paths. A 

multizone model, such as CONTAM, could not consider the non-uniform momentum 

effect in zone 1 created by the supply air. As a result, the airflow rate through the two 

openings calculated by CONTAM would be the same, as shown in Fig. 4.17. In reality, 

opening 1 would have a higher flow rate than opening 2 caused by the momentum effect 

from the air supply, as the zone geometry in the downstream was almost symmetrical. 

Thus, the multizone model fails to calculate accurately airflow distribution for this case 

with non-uniform momentum flow. 

The measured airflow rates in Fig. 4.18 further verify that the airflows measured through 

openings 1 and 2 were not equal, although the geometry is symmetrical. The higher the 

zone 1 (CFD zone) zone 1 

opening 1 opening 2 

opening 1 opening 2 

supply supply 

zone 2 zone 3 

zone 4 zone 4 

zone 2 zone 3 
93

momentum (airflow rate) from the supply is, the higher the ratio of the flow through 

opening 1 over opening 2 will be. 

Fig. 4.18 Comparison of measured airflow rates with different simulated results. 

When the coupled CONTAM-CFD0 program was used, where CFD0 was applied to zone 

1 and CONTAM for the rest zones, Fig. 4.19 shows that the pressure near opening 1 was 

much greater than that near opening 2. Because of the non-uniform distribution of 

pressure in zone 1, the flow rate through opening 1 was greater than that through opening 

2. However, the discrepancies between the calculated results and the measured data were 

very significant as shown in Fig. 4.18. These results were consistent with different 

airflow rate and were unexpected. 
94

Fig. 4.19 The pressure distribution at 1.66 m from the floor in the four-zone chamber 

calculated by CFD0. 

By applying CFD0 to all the four zones, the calculated airflow ratios did not improve 

further, compared with those obtained with the coupled CONTAM-CFD0 program. Then, 

a commercial CFD program, Airpak (Fluent, 2002), was applied to all the four zones by 

using the same zero-equation turbulence model as that used in CFD0. The results 

obtained by Airpak were almost identical to those by CFD0. Clearly, for this particular 

case, the zero-equation model was unable to predict accurately the airflow in the fourzone facility, although the reason was not clear. 

If we replaced the zero-equation model by the standard k-ε model in Airpak and 

simulated all the four zones, the computed ratios of airflow rates of opening 1 over 

opening 2 were very close to the experimental data as also shown in Fig. 4.18. This 

further verified that the turbulence model played a very important role in this case. 

Finally, this investigation applied Airpak with the standard k-ε model to zone 1 and 

CONTAM to the other three zones. The computed results were in reasonable agreement 

with the experimental data and those obtained by using Airpak with the standard k-ε

opening 1 

opening 2 

zone 1

zone 2

zone 3

zone 4
95

model to all the zones. This validates that a coupled multizone and CFD program with the 

standard k-ε model can be used for the prediction of airflow in zones with non-uniform 

momentum distributions. 

For this case, the computation time is about 490 minutes for the simulation with CFD0 

for all the four zones and 185 minutes for the coupled CONTAM-CFD0 simulation for 

zone 1. The coupled simulation used less computing time than the CFD0 simulation since 

it applied CFD0 to zone 1 only. Although the computing cost was much greater than 

CONTAM, which only takes a few seconds, the coupled simulation provided more 

accurate results than CONTAM. The simulations with the standard k-ε turbulence model 

required more computing time than those with the zero-equation model. An Airpak 

simulation with the same grid number as CFD0 for the four zones by the standard k-ε

model costs 620 minutes, which doubled the simulation time with the zero-equation 

model in Airpak. 

Fig. 4.20 The plan view of the four-zone facility with the nine measuring poles. 

In addition to flow rates, our experiment also measured the air velocity and temperature 

in sixty-three locations in the chamber facility. The sixty-three locations were in nine 

poles, and each pole has seven points from the floor to the ceiling. Fig. 4.20 shows the 

positions of the nine measuring poles that were in Zones 1, 2, and 3. Fig. 4.21 compares 

P1

P2

P3

P7 P8 P9 

P6

P5

P4
96

the air velocities calculated by CFD0, the coupled CONTAM-CFD0, and the Airpak 

simulation of the four zones by the standard k-ε model for selected positions with the 

experimental data. Since the coupled CONTAM-CFD0 simulation applied CFD0 only to 

zone 1, the comparison can only be made for P7, P8, and P9. The Airpak simulation with 

the standard k-ε model provided the best results while the CFD0 results had some 

discrepancies from the experimental data. The discrepancies could be attributed to the 

turbulence model, as discussed previously. The calculated air velocities by the coupled 

program generally agree well with those by the CFD0, although similar degree of 

discrepancies was found. Even if the coupled simulation only applied CFD0 to one zone, 

the coupled CONTAM-CFD0 performed as well as CFD0 for all the zones. 

Fig. 4.21 Comparison of air velocities at P7, P8, and P9 in zone 1 with non-uniform 

momentum distribution (H=2.44m; υ=U/Uin, non-dimensional velocity when Uin=2.281 

m/s is the supply air velocity and the supply rate is 0.105 m3/s. 

The results from this case imply that 

● CONTAM could not consider a zone with a strong non-uniform momentum flow 

● The coupled CONTAM-CFD0 program performs better than the CONTAM 

● The coupled CONTAM-CFD0 program, where CFD0 was used for zone 1, is as 

good as CFD0 for all the zones, but with a major reduction in computing time 

● The CFD0 with the zero-equation model is as good as Airpak with the same model 

(a) P7 (b) P8 (c) P9
97

● The Airpak with a standard k-ε turbulence model gives better results, but also the 

longest computing time 

● The zero-equation model could not correctly simulate the airflow for zone 1 in this 

case. 

4.2.3. Non-Uniform Contaminant Concentration Distributions 

CONTAM assumed the instantaneous mixing of a contaminant in a zone. Such an 

assumption is acceptable if the zone is small and the mixing is intensive. In many cases, 

the mixing is not perfect. By applying CFD to such a zone, the non-uniform mixing can 

be considered so that the simulated results can be greatly improved. 

Fig. 4.22 The chamber schematic used for contaminant transport study and the 

contaminant source locations.

Source Location x (m) y (m) z (m) 

SF6 0.36 1.53 0 

SF6

zone 1 

zone 2 

zone 3 

zone 4 

opening 1 

opening 2 

supply 

exhaust 
98

This investigation has designed a case to study non-perfect contaminant mixing. The case 

was the same as Fig. 4.16 in previous section, except for adding a partition wall in front 

of the air supply in zone 1 to create non-uniform contaminant distributions, as shown in 

Fig. 4.22. This study created a non-uniform SF6 distribution in zone 1 by placing a 

contaminant source, which was simulated by SF6, behind the partition. 

It was possible to improve CONTAM results by separating the area behind the partition 

wall as another zone. However, the airflow between the new zone and the rest of zone 1 

could be multi-directional through the large opening. That creates a very challenging 

problem for CFD0. On the other hand, our aim is to demonstrate how CFD0 could be 

used to improve the airflow modeling not to demonstrate how we could do better by 

using CONTAM alone. 

0

0.2

0.4

0.6

0.8

1

Zone 2 Zone 3

S

F6 (ppm)

Experiment CONTAM Coupled simulation

Fig. 4.23 Comparison of measured and simulated SF6 concentrations (ppm) in zones 2 

and 3. 

Thus, if a CONTAM simulation is applied for the whole space of zone 1, it could not 

predict the non-uniform distribution of SF6 in zone 1. CONTAM also interprets the flow 

and geometrical conditions to be symmetrical, because it could not take the partition wall 

into account. As a result, CONTAM would predict the same SF6 concentration in zone 2 

and zone 3, as shown in Fig. 4.23. Without concerning about airflow models, the coupled 

CONTAM and CFD0 simulation, in which the CFD0 was applied to zone 1, could 

consider the non-uniform SF6 concentration in zone 1. Clearly, the zone next to the SF6
99

source had a high SF6 concentration than the other zone, although the geometry is 

symmetrical. The SF6 concentration in zone 2 was 0.977 ppm, which was obtained by 

averaging the SF6 concentration over the 15 locations along Poles 1-3. The average SF6

concentrations were 0.022 ppm for zone 1 and 0.018 ppm for zone 3. Most of the SF6 was 

transported to zone 2 so the average concentration in zone 1 was low. 

Fig. 4.24 SF6 concentration distribution at openings 1 and 2 height in the four-zone 

chamber facility calculated by the coupled CONTAM and CFD0 program. 

The huge difference in SF6 concentrations between zones 2 and 3 was caused by the nonuniform SF6 distribution in zone 1, as illustrated in Fig. 4.24. When SF6 is placed behind 

the partition, the partition wall confined the SF6 in a corner. As a result, the SF6

concentration near opening 1 was about 50 times higher than that near opening 2. The 

coupled program can correctly calculate the SF6 concentrations by predicting the detailed 

SF6 distribution in zone 1. 

opening 1 opening 2 

zone 1 

window 1 

Exhaust 

zone 2 zone 3 

zone 4 

SF6

window 2 
100

Fig. 4.24 also shows the airflow distributions from the coupled simulation. The blue lines 

stand for airflow rates and the red lines for pressure differences across the airflow paths. 

The partition board in front of the supply blocked the inflow so that air was almost 

equally distributed between openings 1 and 2. Table 4.2 illustrates that the calculated 

airflow rates through openings 1 and 2 were close to the measured data. 

Table 4.2 Comparison of airflow rates through openings O1 and O2 by the measurement 

and by the coupled simulation (m3/s). 

Experiment Coupled simulation 

opening 1 0.049 0.048 

opening 2 0.050 0.051 

Fig. 4.25 compares the SF6 concentrations in zone 1 obtained with different methods. The 

SF6 concentrations were measured at 45 locations at the same nine poles as in the 

previous case. When applying CFD0 to the entire flow domain (all the four zones), the 

CFD0 results were reasonably close to the experimental data, although some fluctuations 

of experimental data existed. Since it took 30 s to measure the SF6 concentration in one 

location, the data obtained between the two measurements that were two minutes apart 

may not be the same for the same location. The solid triangles show the mean SF6

concentration measured and the horizontal bars show the fluctuation. Our experience also 

shows that it is very difficult to obtain good agreement between CFD simulations and 

experimental measurements for tracer-gas concentration. The coupled CONTAM and 

CFD0 simulation predicted higher SF6 concentrations for Poles 7-9. This is probably 

caused by the inaccurate flow rate provided by CONTAM in other zones for the CFD0 as 

boundary conditions. 
101

Fig. 4.25 Comparison of measured and computed SF6 concentrations (ppm) at P7, P8, 

and P9 in Zone 1 for the non-uniform contaminant distribution case. 

4.2.4. Non-Uniform Temperature Distributions 

A multizone model, such as CONTAM, could consider the impact of temperature on the 

airflow between zones. However, the model assumes that the temperature is uniformly 

distributed in each zone. Therefore, the impact caused by the temperature gradient is 

normally not accounted for. Hence, this investigation designed another case with a high 

temperature gradient to examine the impact of the temperature gradient on the airflow 

rate calculated by CONTAM. 

(a) P7 (b) P8 (b) P9 
102

Fig. 4.26 Schematic of the case used to study non-uniform temperature distribution. 

Fig. 4.26 shows the schematic of the case design. Another supply was added in zone 1 to 

create a symmetrical flow-supply condition. However, as shown in Table 4.3, the flow 

rate and the supply of air temperature were not exactly symmetrical in the experiment. A 

heated box was placed in zone 2 and a non-heated box of the same size was 

symmetrically placed in zone 3. Because the heat from the box was highly concentrated, 

it generated a large temperature gradient in zone 2. This experiment also placed openings 

1 and 2 in the lower part of the partition. Because zone 2 was of a higher temperature 

than zone 3 due to the heat source, the stack effect created a higher flow into zone 2 than 

zone 3. 

x1 x2 x3 x4 x5 y1 z1 

0.81 0.26 0.76 0.21 0.97 2.04 1.2 

opening 1 

opening 2 

window 1 

window 2 

block with heat 

block without 

heat

supply 1 

supply 2 

zone 2

zone 3 

zone 1 

zone 4 

x1 x2

x3 x4 

x5 

y1 

z1 
103

Table 4.3 Actual flow conditions from the two air supplies. 

Air supply 1 Air supply 2 

Heat source Flow rates (m3

/s) Temperature (°C) Flow rates (m3/s) Temperature (°C) 

0 W 0.0477 18.5 0.0543 18.5 

288 W 0.0510 18.9 0.0467 18.7 

859 W 0.0514 18.5 0.0533 18.3 

CONTAM, the coupled CONTAM-CFD0, and CFD0 were used to simulate the case. Fig. 

4.27 shows the airflow and pressure distributions obtained by CONTAM (Fig. 4.27(a)) 

and by the coupled CONTAM-CFD0 (Fig. 4.27(b)). In the coupled simulation, CFD0 

was only applied to zone 2. There are differences in the results but they are not evident. 

Although not shown in this chapter, the detailed comparison of air velocity and 

temperature in the sixty-three locations in the room for this case is very similar to the 

other two cases. 

Fig. 4.27 Comparison of airflow and pressure distributions for the case with non-uniform 

temperature distribution by (a) CONTAM and by (b) the coupled CONTAM and CFD0. 

zone 2 

zone 2 

(CFD zone)

Opening 1 Opening 2 Opening 1 Opening 2 

(a) (b) 
104

Fig. 4.28 shows that the measured airflow ratios through opening 1 over opening 2 

increased with the stack effects in zone 2, which were caused by increasing the surface 

temperatures of the heated box. As shown in Fig. 4.28, CONTAM generally underpredicted the airflow ratios by 10%, although it could consider the stack effects caused by 

the temperature difference of zones 2 and 3. The reason was that CONTAM neglected the 

temperature gradients inside zone 2. To consider the temperature gradients, this study 

applied CFD to zone 2 and CONTAM to the other zones in the coupled CONTAM-CFD0 

simulations. The measured surface temperatures of the heated box were used as boundary 

conditions in the coupled simulations so that the temperature gradients could be correctly 

considered. Fig. 4.28 illustrates that the calculated airflow ratios by the coupled program 

were very close to the measured data except for the box surface temperature of 30°C. 

This study then used CFD0 to simulate all the four zones and found that the results of 

CFD0 were close to those of the coupled simulations for all the three cases. When the 

surface temperature was 30 °C, therefore, the discrepancy between the measured and 

calculated results could be attributed to the experimental errors. 

On the other hand, the assumption of uniform temperature in each zone seems to be 

tolerable in this case. The difference of 10% of CONTAM simulations from the 

experimental data was within the normal acceptable range of 20% for multizone 

simulations (Emmerich, 2001). Of course, the experiments provided CONTAM 

simulations a good estimation of air temperature for each zone. Otherwise, the difference 

of 10% may be difficult to obtain. 
105

Fig. 4.28 Comparison of airflow rates for the case with different methods. 

The moderate temperature gradients in this case explained why the assumption of 

uniform temperature was not crucial. Fig. 4.29 illustrates the temperature distribution of 

Poles 1-3 of zone 2 when the surface temperature of the heated box was 35 °C. The 

measured temperature gradient of the bulk air in zone 2 was as high as 3.7 °C, although 

the temperature gradient near the heated box could be higher. The temperature gradient 

could reach to 5.5 °C when the surface temperature of the heated box was 46 °C. Li et al. 

(1998a) also found that when the temperature gradient was moderate, there was 

reasonable agreement between the ventilation flow rates predicted by multizone and CFD 

approaches. However, when the temperature gradient was more than 10 °C, the 

calculated ventilation rates by multizone methods can differ from the measured data by 

more than 30% (Kotani et al., 2003). 
106

Fig. 4.29 Comparison of the air temperatures at the three poles in zone 2 for the nonuniform temperature distribution when the surface temperature of the heated box was 35 

°C (H=2.44m; τ = (T-Tin)/ (Tout -Tin) is non-dimensional temperature where Tin=18.2 °C 

was the supply air temperature and Tout=24.3 °C was the exhaust air temperature). 

Fig. 4.29 also compares the calculated temperature distributions of poles 1-3 with the 

measured data. Since the coupled simulation only applied CFD to zone 2, the calculated 

temperatures were quite different from the measured data, although the pattern of the 

temperature differences was similar to the data. The results could be improved if CFD0 

was applied to all the four zones as also shown in Fig. 4.29. However, the computing 

time of the CFD0 simulation for all four zones was one-order magnitude greater than the 

coupled program. When the accuracy of the spatial temperatures was not a primary 

concern, the coupled program provides acceptable results. 

Note that, for the purpose of experimental validation of the coupled CONTAM-CFD0 

program, the chamber experiments in this section used extreme cases of non-uniform air 

momentum effects and contaminant concentrations. For common cases, CHAPTER 6 

developed guidelines when and what case such coupling is needed. 

(a) P1 (b) P2 (c) P3
107

4.3. Summary

By comparing the numerical results with the experimental data, this chapter conducts 

extensive verifications and validations of the CFD0-C and the coupled program of 

CONTAM and CFD0-C. For most of the cases, it shows the calculated results are 

reasonably close to those of the experiments. 

The CFD0-C is verified by comparing its results with published data. It shows that 

CFD0-C performs reasonably well in solving the following problems: airflow with strong 

momentum effect and prescribed pressure boundary conditions, buoyancy-driven flows 

with temperature gradients, displacement ventilation with temperature and contaminant 

concentration gradients, and external airflow around a building model in a wind tunnel. 

Therefore, the upgrade of CFD0-C from CFD0-F is successful. 

To validate the coupled CONTAM and CFD0 program, a series of experiments were 

conducted in a chamber facility for airflows with non-uniform distributions of 

momentum, temperature, and contaminant concentrations. Although some discrepancies 

exist, the calculated results by the coupled program generally agree well with the 

experimental data. The coupled program thus can be used to improve CONTAM while 

costing less computational time than the simulation that only uses CFD0-C in the whole 

flow domain. 

Since the verifications and validations are only for steady-state problems and real design 

problems are often at a transient state, it is necessary to apply the coupled program to 

simulations with a transient airflow and a contaminant transport. CHAPTER 5 will 

demonstrate the coupled program through several realistic cases. 
108

CHAPTER 5. APPLICATIONS 

To use the coupled CONTAM and CFD0-C program as a design tool, it is important to 

apply the coupled program to realistic cases. Therefore, for coupled outdoor airflow 

simulations, this study demonstrates the WPC link to simulate the ambient airflow around 

a cubic building and the WPP link for the airflow around a low-rise house with a sloping 

roof. For building indoor airflows, although the numerical experiments in CHAPTER 3 

and the validation studies in CHAPTER 4 demonstrate the capabilities of the coupled 

program, the studies are limited to steady-state analysis. It is also essential to apply the 

coupled program to transient simulations, since most of the real cases are at transient 

state. For that reason, this chapter selects a realistic case, natural ventilation in a threestory building with a large atrium, to demonstrate how the coupling algorithms can be 

employed to improve CONTAM results. 

5.1. Demonstration of the Indirect Coupling for Outdoor Airflow Simulations

5.1.1. Demonstration of the Indirect Coupling by the Wind Pressure 

and the Contaminant (WPC) Link 

Fig. 3.1 in CHAPTER 2 illustrates that the indirect coupling needs a WPC translator for 

the WPC link of CONTAM and CFD0-C. At present, a WPC translator has been 

developed to find wind pressure data obtained from CFD0-C for specific openings in 

CONTAM simulation. Two simulations are performed to demonstrate how the translator 

converts the EWC files to WPC files, and how CONTAM uses the WPC files to calculate 

airflow in a building. A building with a cubic shape is selected because CONTAM 

developers use it as a typical case to demonstrate the WPC link. In order to show the 
109

impact of wind direction on wind pressure distribution, two types of wind direction are 

simulated. The first case involves wind blowing perpendicularly at a building wall, and in 

the other case, the wind blowing at an angle. 

Fig. 5.1 Building plane view and CONTAM results using the WPC File. 

The building is located in a place with 6 m/s wind velocity coming from the direction of a 

positive X-axis, as shown in Fig. 5.1. The building has four closed doors on its envelope, 

as labeled in the figure. Table 5.1 shows the door locations with the reference points of 

(0, 0, 0) in the lower-left corner of this building. 

Fig. 5.2 shows the pressure contours and the velocity field computed by CFD0-C, viewed 

from two different angles. Fig. 5.2A and Fig. 5.2B are for the case with the perpendicular 

wind and Fig. 5.2C and Fig. 5.2D are for the wind blowing at an angle. The small white 

box is the building simulated and the large one is the CFD computational domain. The 

zero reference pressure is at the line of ‘x=0, z=0’. 
110

Table 5.1 Opening locations, the relative wind pressures computed by CFD0-C, and 

airflow rates computed by CONTAM under the wind speed of 6 m/s. 

Openings 1 2 3 4 

Locations x, y, z (m) 5.0, 10.0, 1.0 0.0, 7.5, 1.0 0.0, 5.0, 1.0 0.0, 2.5, 1.0 

Wind pressure for 

perpendicular wind (Pa) -17.71 -21.17 -19.31 -21.65

Wind pressure for wind at an 

angle (Pa) -33.97 -27.3 -24.96 -26.29

Air exchange rate for 

perpendicular wind (ACH) 0.0229 0.0059 0.0034 0.0062 

Air exchange rate for wind at 

an angle (ACH) 0.0432 0.0087 0.0106 0.0095 

Fig. 5.2 Pressure contours (Pa) and velocity fields around a building, as computed by 

CFD0. 
111

Fig. 5.2A and Fig. 5.2C show a strong recirculation behind the building, but CFD0-C 

fails to calculate the recirculation on the roof. This is a well-known problem for CFD 

programs using the Reynolds Averaged Navier-Stokes (RANS) equations and the 

turbulence models. Fig. 5.2B shows no recirculation on the sidewalls of the building. 

Please note that the wind for these two cases is specified as a constant distribution instead 

of a parabolic distribution, and thus the velocity at the ‘sky’ (the top of the CFD domain) 

becomes smaller. The contours of Fig. 5.2B also indicate that wind pressure on paths 2, 3, 

and 4 are smaller than that on path 1, so there is inflow through path 1 (as shown in Fig. 

5.1A). 

These three-dimensional pressures shown in Fig. 5.2 are saved in EWC files. The WPC 

translator is used to read the PLD file that provides flow-path locations, and then link to 

the EWC file. The WPC translator searches for the needed pressure data in the EWC files 

and then creates the WPC files. 

Finally, CONTAM reads the WPC files for wind pressure data. Fig. 5.1 graphically 

shows the pressures and flow rates computed by CONTAM with the WPC file. Fig. 5.1A 

is for the case featuring the wind blowing perpendicularly at the wall, and Fig. 5.1B is for 

the case with the wind hitting the wall at an angle. The blue lines show the direction and 

scale of the airflow rate through the doors, and the red lines show the pressure drops. 

Since the wind pressure at door 1 is greater than the rest, and all the doors are located at 

the same height, the flow at door 1 is inwards. Table 5.1 shows the wind pressure 

computed by CFD0-C. Although wind speed is high (6 m/s), the airflow rate is small 

since all the doors are closed and this building is quite tight. 

The case in which the wind hits the wall at an angle uses the same building geometry and 

opening locations as the case in which the wind is perpendicular to the wall. However, 

wind velocity is 6 m/s in the x component and 3 m/s in the y component. Table 5.1, Fig. 

5.1, and Fig. 5.2 compare the results for this case with those of the previous one. 
112

Without the WPC link, CONTAM would calculate the same airflow rates through the 

openings 2-4 due to the assumption of uniform wind pressures on a building surface. 

Nevertheless, this study shows that the wind direction dramatically changes the pressure 

distribution on the building envelope in Fig. 5.2D, even though the wind angle change is 

less than 30o. These changes also alter the airflows inside the building. Table 5.1 shows 

that the calculated airflow rates of openings 2-4 by the WPC link are different from each 

other. It is more reasonable because Fig. 5.2 reveals that wind pressures should be nonuniform on a building surface. Therefore, wind pressure data is crucial for CONTAM 

simulations. The above two test cases demonstrate that the WPC translator was able to 

transfer the pressure distribution computed by CFD0-C for CONTAM use. 

5.1.2. Demonstration of the Indirect Coupling by the Wind Pressure 

Profile (WPP) Link 

Instead of calculating wind pressures as in the WPC link, the WPP link provides wind 

pressure coefficients for CONTAM so that CFD0-calculated airflow data can be reused if 

the wind velocity and/or building site change. To demonstrate the WPP link, this thesis 

selected another case to investigate the distributions of wind pressures and air infiltrations 

under different wind directions for a common low-rise house. 
113

Fig. 5.3 (a) CFD0-C mesh, (b) the internal zone configuration of the low-rise house with 

a sloping roof, and (c) plane view of the CFD0-C domain. 

Holmes (1986; 1994) measured wind pressure distribution on a low-rise house model for 

various wind directions in an open circuit, boundary-layer wind tunnel. Fig. 5.3(a) shows 

the house model after being scaled up to a full-sized house in CFD0-C simulation. To 

(a) 

α

Δx 

Δz 

Δy 

l 

w 

h

l = 15.5 m 

w = 7.4 m 

h = 3.0 m 

Δx = 4w 

Δy = 2l

Zmin

Zmax

(b) (c) 

Ymin

Ymax

Xmin Xmax

θ

3

1 2

4

5

6

7

10 9 8

15

14

13

12

11

3

N

S

W E
114

simulate atmospheric conditions around the house appropriately, this study carefully 

selected the size of the whole CFD domain through test runs so that the impacts of the 

domain size on the airflow pattern and the total grid number were minimal. The size of 

the flow domain was 15.5 m × 7.4 m × 3.0 m (l × w × h) and the total grid number was 74 

× 87 × 24 (X × Y × Z), as shown in Fig. 5.3(a). Slippery flow boundary conditions were 

applied for the Zmin and Zmax planes while a wind velocity profile was prescribed for 

“inflows” and a “free outflow” boundary condition for “outflows”. Table 5.2 shows the 

boundary conditions for the four open planes, Xmin, Xmax, Ymin, and Ymax, when the wind 

direction is “θ” to the Xmax plane, as shown in Fig. 5.3(c). 

Table 5.2 Prescription of boundary conditions when the wind direction is “θ” from the 

Xmax plane for airflows around a low-rise house. 

Flow planes Boundary conditions 

Xmax and Ymin U= − θ Vcos ; V= Vsinθ

Xmin and Ymax Free outflows 

The wind velocity, V , was defined by Eq. (5.1) and prescribed by a power-law profile in 

Fig. 5.4, which was for the urban and suburban area (ASHRAE, 2005), and is similar to 

that in the Holmes’ experiment. 

where V is the average wind velocity, U, V, and W is the wind veloicity in the X, Y, and 

Z direction, respectively. 

2 2 2 V = U + + V W (5.1)
115

Fig. 5.4 The profile of mean wind velocity V for inflows. 

The simulations were performed for the relative wind direction, θ, between 0° and 360°

with a step of 30°. As illustrated in Fig. 5.3(b), the relative wind direction to a building 

surface is the clockwise angle from the building surface azimuth direction to the wind 

azimuth direction (Walton and Dols, 2003), 

θ = θw - θs

(5.2)

where, θw is the wind azimuth direction, e.g. N = 0° and E = 90° etc.; θs is the building 

surface azimuth direction. 

Wind pressure coefficients at building surface change dramatically with wind directions. 

Fig. 5.5 shows that the surface-averaged wind pressure coefficient (Swami and Chandra, 

1987) varies between “-0.6” and “0.6” depending on wind directions. The wind pressure 

coefficient also depends on the path location at the building surface. Fig. 5.5 illustrates 

the local wind pressure coefficient measured by Holmes (1986; 1994) and calculated 
116

values by the WPP link at Path 3, as shown in Fig. 5.3. Apparently, the surface-averaged 

value cannot consider the dependence of wind pressure on the path location since the Cp

values are symmetric around “θ=180°”, which in fact could only happen for the middle 

point at a surface. If compared to the local wind pressure at Path 3, the average wind 

pressure also overestimated Cp between 0° and 90° while underestimating it from 270° to 

360°. 

Fig. 5.5 Comparison of calculated wind pressure coefficient by the WPP link with 

measured data at Path 3 of the house for the relative wind direction to the surface with 

Path 3 (θ =0° ~ 360°). 

The calculated Cp at Path 3 by the WPP Link generally agreed with the measured data 

except for the wind direction, from 180° to 270°. Due to the same reason as in the 

previous section, the discrepancy was caused by the inability of CFD0 to predict wind 

pressures correctly in the regions with strong turbulence separations and recirculation 

flows near Path 3. As a result, the WPP Link does not significantly improve the 

calculation of non-uniform distribution of wind pressure coefficients. The relative 
117

discrepancy of the WPP-calculated Cp was only 40% while the surface-averaged value 

was 50% from the measured local value at Path 3. 

Although the WPP link did not notably improve the calculation of wind pressure 

coefficients, it still considers the non-uniform distribution of wind pressures so that 

infiltrations can still be calculated more accurately than without it. To verify this effect, 

this study simulated the infiltrations through the low-rise house with fourteen zones and 

fifteen envelope paths, as shown in Fig. 5.3(b). The configuration of the zones was based 

on the manufacture house in Figure 14 of Chapter 34 in the ASHRAE Handbook (2005), 

except that the house was naturally ventilated. The leakages of airflow paths were 

adopted from Table 2 in the same chapter of ASHRAE Handbook. 

-1.00E-02

-5.00E-03

0.00E+00

5.00E-03

1.00E-02

1.50E-02

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Path

Flow Rates (kg/s)

CONTAM WPP Measured CP

Fig. 5.6 Comparison of calculated infiltration rates by CONTAM, the WPP Link, and 

using measured non-uniform wind pressure coefficients when θ = 60°. 

Fig. 5.6 illustrates the calculated infiltration values, of which the inflows are positive 

while the outflows are of negative values, by using three different prescription methods 

of Cp for θ = 60°: 
118

● Method 1: CONTAM method, which uses the surface-averaged wind pressure 

coefficient as provided by Swami (1987); 

● Method 2: WPP method, which uses the calculated local wind pressure coefficient by 

the WPP link; 

● Method 3: Measured Cp method, which uses the measured local wind pressure 

coefficients from Holmes (1986; 1994). 

Compared to the most accurate method, Method 3, the WPP link generally predicted 

better results than CONTAM. The average relative difference of calculated infiltrations is 

17% for the WPP link and 30% for CONTAM, compared to those obtained by Method 3. 

For wind directions other than θ = 60°, similar results were obtained. Therefore, the WPP 

link could improve CONTAM calculations by considering the non-uniform distribution 

of wind pressures. 

5.2. Demonstration of the Direct Coupling for Indoor Airflow and Contaminant Transport 

Simulations

5.2.1. Simulation of Steady Airflow and Steady Contaminant Transport 

To demonstrate the direct coupling for the simulation of steady airflow and steady 

contaminant transport, the first case uses a three-story building with a large atrium in the 

center and with natural ventilation. We use natural ventilation because the supply airflow 

rates in natural ventilation are not pre-defined, so it is more challenging to simulate such 

a case. Fig. 5.7 shows the three-dimensional views and the plan view of the building. The 

room dimensions are: 

● Rooms 1-8: 12 m×6 m×2.7 m 

● Rooms 9-12: 6 m×9 m×2.7 m 

● Rooms 13-14: 6 m×5 m×2.7 m 

● The atrium: 48 m ×11 m×10.8 m 
119

(a) 

(b) 

(c) 

Fig. 5.7 Views of the three-story building. (a) Three-dimensional outside view with the 

external walls removed; (b) Three-dimensional internal view; and (c) Plan view in 

CONTAM with the contaminant of C1. 

path 2 Sensor#3

Sensor#1

C1

Sensor#2

path 1

path 2

Windows Windows

63 64 65 66

78 79 80 81

69 70

73 74

75 76

R1 R2 R3 R4 

R5 

R9 

R10 

R11 

R12 

R13 

R6 R7 R8 

R14 

C1

Sensor#3
120

The floor plane is the same for the three stories, except for the atrium. All flow paths of 

the building are open windows with a height of 0.9 m and the width of the room. The 

west (-X) and the east (+X) windows on the top of the atrium are also open. The cooling 

load is set to 40 W/m2from the occupied zone (0 – 1.8 m above the floors) in the rooms 

and the atrium. The heat gain/loss from the building envelope is neglected. 

The mean wind speed was assumed to be at a constant of 10 km/hour from the west, the 

mean outdoor air temperature to be 15 oC, and the mean relative humidity to be 70%. 

This study also assumes that an imaginary contaminant (hereafter C1) is released in the 

northeast corner of the atrium on the ground floor, at a constant rate of 1.0×10-5 kg/s. 

Since the C1 concentration will be non-uniform for such a large space, the perfect mixing 

assumption would not work well so the case is selected as a demonstration case for the 

coupled CONTAM and the CFD0-C simulation. This study therefore selects the central 

atrium as the CFD zone and applies CONTAM to the rest of the zones. 

The central atrium is divided into a total grid of 104×27×40 (X×Y×Z) for the CFD 

simulation. For the CONTAM simulation, the orifice equation (Walton and Dols 2003) is 

applied to the airflow paths of all the CONTAM zones. The temperatures of the 

CONTAM zones are determined by the iterative calculation of energy conservation for 

each zone. 

The convergence criterion is 0.1% for CFD0 calculation and 1% for the coupled 

simulation. Twenty-five coupling iterations are required for convergence, and the total 

computing time is about 72 minutes on a Pentium 4 2.0 GHz PC. 
121

-5

-3

-1

1

3

5

7

Flow Path Number

Flow

Rates(kg/s)

With Coupling Without Coupling

Top Level 3 Level 2 Level 1

1

2

63

64

65

66

78

79

80

81

Fig. 5.8 Comparison of airflow rates with and without coupling. 

Fig. 5.8 compares the airflow rates with CONTAM only and with the coupled program 

for the 44 airflow paths (each floor had 14 paths and there were two paths at the top) of 

the three-story atrium. Except for the paths at Levels 2 and 3, the flow rates of some 

paths at Level 1 and the two paths at the atrium top (red numbers in Fig. 5.8) had changed 

significantly with the coupled program. If a positive value was for the inflow to the 

atrium and a negative one for the outflow, the inflow through path 1 (Fig. 5.7(a)) 

increases from 4.1 kg/s without coupling to 7.0 kg/s with coupling. The flow directions 

through Paths 63 through 66 and 78 through 81 change from inflow to outflow if 

simulated by the coupled program. 

Such changes of airflows with coupling could be explained by the temperature and 

pressure gradients inside the atrium. Fig. 5.9 illustrates the airflow and temperature 

distributions at section Y=5.5m in the atrium (CONTAM zones are also shown for 

comparison). Due to the buoyancy effect, the west wind with the temperature of 15 oC 

travels downwards after entering the atrium through path 1. The cold air then flows along 

69

70

73

74

75

76
122

the atrium floor and rises at the right end of the atrium so that a huge recirculation zone is 

formed. The temperature gradients are about 4 K in the horizontal direction and 3 K in 

the vertical direction. So the assumption of uniform temperature may not hold in this case 

and the flow rates through paths 1 and 2 change with the coupling. 

Fig. 5.9 Velocity fields and temperature contour at the section of Y=5.5m. 

The changes in airflow distribution with coupling, especially the change of flow 

directions, will greatly affect the contaminant transport. Fig. 5.10 illustrates the results of 

C1 concentrations with coupling at the four planes of the atrium. The positions of the 

planes are shown in Fig. 5.11. Without coupling, all the neighboring zones of the atrium 

in Fig. 5.10(a) have zero C1 concentrations because the atrium only has inflows from all 

the neighboring zones. With coupling, the flows at Paths 63 through 66 and 78 through 

81 become outflows for the atrium, so the C1 concentrations were non-zero for the 

neighboring zone 1 through 8. The closer the neighboring zone is to the source, the 

higher the C1 concentration of the neighboring zone. 
123

Fig. 5.10 Comparison of C1 concentrations with and without coupling at (a) Plane 1 (P1); 

(b) Plane 2 (P2); (C) Plane 3 (P3); and (d) Plane 4 (P4). 

Besides airflow directions, airflow patterns also play an important role for contaminant 

transport. Although the directions of airflows in Fig. 5.10(b) and Fig. 5.10(c) do not 

change with coupling, the airflow pattern inside the atrium makes the C1 concentration 

highly poor-mixed. The coupled simulation is thus required to calculate C1 

P1 

(a) (b) 

P2 

P3 P3 

P4 P4 

(c) (d) 

66 

C1 

C1

63 64 65 

78 79 80 81 

69 70 

73 74

75 76 

R9 R1 R2 R3 R4 

R13 

R11 

R10 

R14 

R5 R6 R7 R8 R12 

1 2
124

concentrations more accurately than CONTAM alone. The airflow pattern can also cause 

a discontinuous distribution of concentrations inside the atrium. The C1 concentration 

marked by the red circle in Fig. 5.10(c) is lower than the surroundings, which could be 

explained by the airflow pattern in Fig. 5.11. At the circled region in Fig. 5.10(c), the 

fresh air moves upwards so the concentration inside this region at P3 is lower than the 

surroundings. The same reason can be applied to the circled region in Fig. 5.10(b). The 

impact of airflow patterns on the distribution of C1 concentration can further be observed 

for the P4 plane in Fig. 5.10(d). The fresh air moves downwards after entering the atrium 

for about five meters and the air flows leftward at the right side of the atrium top (Fig. 

5.9). Therefore, the C1 concentration at the right of the atrium top is higher than that at 

the left. 

Fig. 5.11 Velocity distribution at the cross section of X=30m. 

The above analysis illustrates that the coupled simulation of a steady airflow and the 

steady contaminant transport can provide distributions of temperature, pressure, 

P1 

P2 

P3 

P4 

C1 Source 
125

contaminant concentration and airflow patterns for the CFD zones. As a result, the wellmixing assumption of CONTAM is remedied and the dispersion of airborne contaminants 

in a building can be well predicted. 

5.2.2. Simulation of Steady Airflow and Transient Contaminant Transport 

For the steady airflow and the transient transport of contaminants, multizone models 

assume that the contaminant transport along each flow path is instantaneous. This 

assumption becomes problematic when the transport of the contaminants from the source 

zone to the neighboring zones is not instant. For example, in the naturally ventilated 

three-story building of Fig. 5.7, the atrium is so large that the transport time from the C1 

source to the neighboring zones can be long. To calculate the transport time, the CFD 

simulation should be applied to the atrium. This study simulates the contaminant 

transport for 30 minutes with a time step of ten seconds, which is small enough to 

account for the transport time of C1 within the atrium. 

Fig. 5.12 compares the C1 concentrations with and without coupling for selected zones 

on the first floor. Without coupling, the neighboring zones on the first floor, zone 1 

through 8 in Fig. 5.12(a) (except zone 4, which is shown in Fig. 5.12(b) for a better 

comparison) has zero concentration all the time since the atrium only has inflows from 

the neighboring zones. With coupling, the C1 concentrations of zone 1 through 8 become 

non-zero due to the reversed airflow directions of Paths 63 through 66, and 78 through 

81, as shown in Fig. 5.8. 
126

0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0.04

0.05

0.05

0:00:00 0:05:00 0:10:00 0:15:00 0:20:00 0:25:00 0:30:00

Time

Concentrations(PPM)

Zone 1-1(with coupling) Zone 1-2(with coupling)

Zone 1-3(with coupling) Zone 1-5(with coupling)

Zone 1-6(with coupling) Zone 1-7(with coupling)

Zone 1-8(with coupling) All Zones at Level 1(without coupling)

(a) 

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0:00:00 0:00:10 0:00:20 0:00:30 0:00:40 0:00:50 0:01:00

Time

Concentrations(PPM)

Zone1-4 (without coupling) Zone 1-4(with coupling)

(b) 

Fig. 5.12 Comparison of transient C1 concentration with and without coupling for (a) 

zones 1 through 8 except 4 at Level 1; (b) zone 4 at Level 1. 

C1 

4

5

1 2 3

6 7 8

Level 1 

C1 

4

5

1 2 3

6 7 8

Level 1 
127

Fig. 5.12(a) shows that the transport time from the C1 source to most of the neighboring 

zones at Level 1 was rather long. For example, it takes ten minutes for zone 2 and 

twenty-five minutes for zone 5 to reach the C1 concentration of 0.01 ppm. On the other 

hand, Fig. 5.12(b) shows that it only takes twenty seconds for zone 4 to reach 0.01 ppm. 

Only selected zones at level 1 are discussed and similar analyses could be applied to the 

simulation results of Levels 2 and 3. When the assumption related to the instantaneous 

transport of contaminants along each flow path fails, the coupled simulation of 

CONTAM and CFD0 could predict the transport time from the source zone to the 

neighboring zones. Then the transient dispersion of a contaminant in a building could be 

calculated. 

5.2.3. Simulation of Transient Airflow and Transient Contaminant Transport 

In real cases, both airflow and contaminant transport can be at transient state, for 

example, when mechanical emergency ventilation is turned on during building 

evacuation. The coupled CONTAM-CFD0 program can model this type of transient 

events and provide important information required for the placement of contaminant 

sensors and the strategy of occupant evacuations. This study used the same building as 

the previous sections with the addition of systems of emergency ventilation and control 

networks to demonstrate the coupled program in the simulation of an emergency 

ventilation. 

As shown in Fig. 5.13, the emergency ventilation system was modeled in CONTAM as a 

Simple Air Handling System, which included a supply vent for each room and eight 

ceiling exhaust fans (EF) for the atrium. During emergencies, fresh air will be supplied 

from the room vent for pollution dilution and room pressurization. At the same time, the 

ceiling fans will exhaust polluted air from the atrium to create a “Pull-Push” effect. The 

emergency ventilation system was controlled by the building control network, which was 

comprised of a contaminant sensor in the atrium, a control link, a control node, and a 

control actuator. When the contaminant concentration at the sensor reached the set value, 
128

Cset, the sensor transferred an “ON” signal through control links to control nodes, which 

directed the actuators to turn on the room vents and ceiling fans. The emergency 

ventilation system continues running till all occupants evacuate the building. 

Fig. 5.13 Emergency ventilation, control systems, and airflow distribution when the 

emergency ventilation is on at (a) the first floor and (b) the top of the 3-story building. 

Cset Control node 

Supply

Emergency 

ventilation system

Sensor 

Actuator

(a) 

Path 1

Path 2 

A 

B

EF #1 EF #2 EF #3 EF #4

EF #5 EF #6 EF #7 EF #8

Path 1 Path 2

(b) 
129

The operating conditions of the emergency ventilation are 

● Cset = 0.1 ppm; 

● Designed airflow rate of room supply is 15 ACH; 

● Designed airflow rate of the atrium is 22 ACH. 

Three independent coupled simulations with different contaminant sensor locations as 

shown in Fig. 5.7 were studied. The best scenario was the location of Sensor #1, which 

was placed near the contaminant source and the worst case is Sensor #3 at the third floor, 

close to Path 1. The medium scenario was the location of Sensor #2 at the third floor 

close to Path 2. The transient simulations included a total time of ten minutes with a time 

step of one second. 

tCONTAM=64 s TAM=64 s

Fig. 5.14 Concentration history of zone 1-4 for three sensor locations before and after the 

emergency ventilation system is on. 
130

Fig. 5.14 illustrates the history of C1 concentration of Zone 1-4, which is the zone closet 

to the C1 source, for the three sensor locations. Without coupling, CONTAM predicted 

the sensor will respond at 64 s after the C1 release no matter where the sensors were 

placed. The coupled simulation provided more reasonable results than CONTAM. Before 

the set point was reached, the C1 concentrations of Zone 1-4 were the same for all sensor 

locations. At 8 s, Sensor #1 is the first to respond so that the C1 concentration started to 

drop in Zone 1-4. In comparison, it took 31 s for Sensor #2 and more than 10 minutes for 

Sensor #3 to take action. Since CONTAM calculated the concentration of Zone 1-4 to be 

zero, as shown in previous sections, it was not shown in Fig. 5.14. Note that the C1 

concentration dropped linearly due to the logarithm scale of Y-axis. 

Once the sensor responded, the control nodes activated the ceiling exhaust fans to pull the 

polluted air out of the atrium and the room supply vents to pressurize the rest zones. As 

shown in Fig. 5.13, fresh air would flow into the atrium through all airflow paths except 

the exhaust fans so that the ceiling fans exhausted the contaminant from the atrium. Fig. 

5.15 shows the importance of the ceiling fans by comparing the distribution of C1 

concentration with and without their running. When the sensor was placed at Sensor #3, 

the ceiling fans were not activated even at the end of 10 mins. Fig. 5.15(a) shows that the 

contaminant could disperse farther into the atrium from the source, endangering the 

occupants' safety. However, if the sensor was at the location of Sensor #1, the ceiling 

fans would be turned on at 8 s after the C1 release. Fig. 5.15(b) illustrates that the C1 

concentration at the plane of Y=10.5 m for Sensor #1 was far less than that for Sensor #3 

at the end of 10 mins. Thus, the “Push-Pull” effect of the emergency ventilation would 

effectively remove the contaminant from the atrium when the sensor was placed at 

Sensor #1. 
131

Fig. 5.15 Airflow and C1 concentrations at 10 minutes after the release of C1 for the 

sensor locations of (a) Sensor #3 and (b) Sensor #1. 

Besides the capability to evaluate the performance of the emergency ventilation system, 

the coupled simulation can also help to determine the occupants' evacuation strategies. 

Supposing that an occupant would evacuate the building through Door A by Path 1 or 

Door B by Path 2 at the first floor as shown in Fig. 5.13(a), his best survival scenario is 

that he starts to run at the time of zero when the sensor was at Sensor #1. Intuitionally, he 

should choose Door A since Path 1 is shorter than Path 2. In fact, Fig. 5.16 shows that the 

occupant will have more transient exposure if he follows Path 1 rather than Path 2, 

especially from 10 sec to 16 sec. Moreover, the accumulated exposure to the contaminant 

for Path 1 could be about twice higher than for Path 2, which indicates that the 

evacuation through Door B was the better choice. Although the determination of 

evacuation strategies in real cases could be more complicated than this example, this 

study shows that the coupled CONTAM-CFD0 simulation has the potential for the 

analyses of personal exposures and evacuation strategies. 

X = 42 m

Z = 10.4 m

Y = 10.5 m

X = 42 m

Z = 10.4 m

Y = 10.5 m

(a) (b) 
132

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

Time 2 4 6 8 10 12 14 16 18 20 22

Time (s)

Transie

nt Exposure(ppm)

0.0E+00

2.0E-02

4.0E-02

6.0E-02

8.0E-02

1.0E-01

1.2E-01

1.4E-01

1.6E-01

1.8E-01

2.0E-01

Acc

u

m

ulated Exposure(1e-3mg)

Transient Exposure_Path1 Transient Exposure_Path2

Accumulated Exposure_Path1 Accumulated Exposure_Path2

Fig. 5.16 Personal exposures to the C1 concentration and to the incremental C1 

magnitude when occupants evacuate through paths 1 and 2. 

5.3. Summary

This chapter applies the indirect and the direct coupling of CONTAM and CFD0-C to 

realistic cases. With the WPC link or the WPP link, the indirect coupling is able to 

provide a spatial distribution of wind pressures or wind pressure coefficients on a 

building surface so that the CONTAM obtains more realistic wind data. The direct 

coupling demonstrates the three coupling algorithms for indoor airflow and contaminant 

transport simulations. The algorithms are capable of improving CONTAM simulations by 

predicting non-uniform distributions of momentum, temperature, and contaminant 

concentration for real designs and analyses. The application studies also present more 

proof for the uniqueness of the solution. The coupled simulation will have a unique 

solution at each time step of a transient airflow simulation as long as the simulation is 

convergent and stable. 
133

CHAPTER 6. CFD ZONE SELECTIONS FOR COUPLED CONTAM-CFD0 

SIMULATIONS 

A coupled CONTAM-CFD0 simulation applies CFD0-C to the zones, where multizone 

assumptions fail, and CONTAM to the rest of the zones. In the previous chapters, we 

selected the CFD zones by either applying the “rule of thumb” or comparing CONTAM 

results with experimental or CFD0 data to find the problematic zones. When 

experimental and CFD results are unavailable, it is important to study the underlying 

principles of multizone assumptions and provide guidelines for the zone selection. By 

applying non-dimensional analyses among the cases from the previous chapters, this 

chapter provides suggestions of CFD zone selection for coupled simulations of nonuniform distributions of air momentum, contaminant concentration, and temperature. A 

selection procedure is also developed for users to use these suggestions. 

6.1. CFD Zone Selection for Non-Uniform Momentum Distributions

Multizone models assume quiescent air inside a zone, which could become problematic 

for zones with strong momentum effect and significant indoor air movement. If the 

momentum effect cannot be totally dissipated, the airflow distribution downwind can be 

greatly affected. We have shown this problem in the case of 90-degree planar branch in 

Chapter 2.1.3, the momentum-driven flows in Chapter 0, and the 4-zone chamber with 

the strong momentum effect in Chapter 4.2.2. The dissipation of airflow momentum 

effects depends on many parameters such as airflow pattern, inflow and outflow 

locations, inflow velocity, the size of the opening and zone, etc. 
134

The dissipation of the momentum effect first depends on the airflow pattern/type. Graça 

(2002) divided the airflow with strong momentum effects into three types, based on the 

ratio of inflow opening area to the cross-sectional area of room, C=Ar/Ain. 

Ain

Ar

C=Ar/Ain

Fig. 6.1 Illustration of airflow patterns/types into a room. 

As shown in Fig. 6.1, 

1.0 channel flow

C 1.0 recirculation flow

jet flow

2.0 combination of channel and recirculation flow





=  

 

 

:

?

:

This study combined the second and the third flow types since the flow becomes a jet 

flow when C is more than a unit. Different guidelines of CFD zone selection for channel 

and jet flows have been developed, as discussed next. 

6.1.1. CFD Zone Selection for Channel Flow with Strong Momentum Effect 

A channel flow occurs when the inflow opening area is close to the cross-sectional area 

of the room so that air will attach to the walls, as shown by the case of a 90-degree planar 

branch in Chapter 2.1.3. More examples can be found in a cross-ventilation flow through 

a long corridor or a vertical shaft with a strong chimney effect. The wall attachment of 

the channel flow causes easy penetration of inflow momentum into the zone and thus the 
135

assumption of quiescent air is invalid. The stronger the inflow momentum effect, the 

harder the inflow momentum gets dissipated. This study used the Reynolds number of the 

inflow to characterize the strength of the momentum effect. 

VW Re =

υ

(6.1)

where V is inflow velocity, W is channel width, and υ is air kinematic viscosity. 

For the channel flow in a 90-degree planar branch of Chapter 2.1.3, Fig. 6.2 shows the 

errors caused by neglecting the inflow momentum effects, compared to CFD results from 

Hayes (1989), Kelka (2000), and Zhai (2004). As expected, a higher Reynolds number 

caused greater errors, which was more than 20% if Re was greater than 30. Since an error 

of 20% is normally acceptable for most multizone simulations (Emmerich, 2001), CFD0 

is needed for channel flows when 

Re > 30 (6.2)

If the order of channel width, W, is “1 m”, the resultant inflow velocity will be in the 

order of 10-4 m/s for the Reynolds number of 30. Therefore, this conclusion indicates that 

CFD may be considered for most channel flows. 
136

Fig. 6.2 The errors caused by neglecting airflow momentum effects under different 

Reynolds numbers for channel flows. 

6.1.2. CFD Zone Selection for Jet Flow with Strong Momentum Effect 

Jet flow occurs more often than channel flow given that the inflow opening area is often 

less than that of the cross-sectional area of a room. Comprised by a jet expansion area 

and a recirculation area, as shown in Fig. 6.3, a jet flow is also more complicated than a 

channel flow. The jet expansion area can be further divided into four zones (ASHRAE, 

2005), depending on how much the jet is dissipated. 

● Zone 1: initial zone, where the maximum velocity and temperature remain constant 

● Zone 2: transition zone, where the initial jet flow is transforming into fully turbulent 

flow 

● Zone 3: fully developed turbulent flow 

● Zone 4: degradation/dissipation zone, where maximum air velocity and temperature 

drop rapidly and the jet is considered almost dissipated. 
137

Zone 1 Zone 2 Zone 3 Zone 4

Recirculation area

Tmax (maximum throw length)

1

2

3

Jet area

Uc

Xd

Zone 1 Zone 2 Zone 3 Zone 4

Recirculation area

Tmax (maximum throw length)

1

2

3

Jet area

Uc

Xd

Fig. 6.3 Illustration of airflows inside a room for jet flows. 

The 4-zone classification of a jet flow describes how the jet is expanded and dissipated 

inside a zone. The impact of jet momentum effect on airflow distribution downwind 

depends on the opening location about the four jet zones. If an opening is located outside 

the jet expansion zone, such as in openings 2 and 3 in Fig. 6.3, or in Zone 4, such as 

opening 1, the momentum effect of the jet will have minimal impact on the opening 

airflow. For the rest of the cases, an opening in Zone 1-3 will be subject to the 

momentum effect due to incomplete jet dissipation. 

Therefore, this study suggests using the distance from the inflow opening to Zone 4, i.e. 

the maximum jet throw length, to estimate jet dissipation, which was defined by 

ASHRAE (2005) as 

max

c d fa c

KQ T = 1.13

U C R A

(6.3)

where Tmax is the maximum throw length of the jet with the unit of m; K is 

proportionality constant, which is determined by the opening type and inflow velocity in 

Table 2, Chapter 33 of ASHRAE Handbook (2005); Q is the volumetric inflow rate, m3/s; 

Uc is the characteristic velocity in Zone 4, which is suggested to be 0.25 m/s; Cd is the 

discharge coefficient of the inflow opening, which is usually between 0.65 and 0.90; Rfa
138

is the ratio of free area to gross area of the inflow opening; Ac is the gross area of the 

inflow opening, m

2

. 

As illustrated in Fig. 6.3, CFD is needed when an opening is inside the zone with 

incomplete jet dissipation. 

Xd < Tmax (6.4)

where, Xd is the distance from the inflow opening to the opening downwind in the jet 

direction. Otherwise, the jet flow is considered dissipated so that it can be appropriate to 

neglect the momentum effect. 

Three cases with non-uniform momentum distributions in Chapter 0 were used to verify 

Inequality (6.4): 

● Case 1: pressure gradient flows in an office suite in Fig. 3.8, 

● Case 2: cross ventilation in a four-zone building model in Fig. 3.12 and 

● Case 3: jet flows in a four-zone chamber in Fig. 4.16. 

Table 6.1 Verification of the suggestion for the CFD zone selection for jet flows by Case 

1: pressure gradient flows in an office suite and Case 2: cross ventilation in a four-zone 

building model in Chapter 3. 

Cases Tmax (m) Xd (m) CFD required?

Case 1: an office suite 15.1 10.0 Yes 

Case 2: four-zone building model 45.2 2.8 Yes 

As shown in Table 6.1, the maximum throw length was 15.1 m for Case 1 and 45.2 m for 

Case 2. The distance from door 1 to door 2 in Fig. 3.8 and that from door A to door C in 

Fig. 3.12 was 10.0 m and 2.8 m, respectively, both less than the maximum throw length 

of the jets. Therefore, the inflow momentum could not be dissipated before exiting the 

zones, and CFD was required for both cases. 
139

Table 6.2 Verification of the suggestion for the CFD zone selection for jet flows by Case 

3: the chamber experiment of non-uniform momentum distributions in Chapter 4.2.2. 

Supply (m3/s) Tmax (m) Xd (m) Flow ratio Errors CFD 

required? 

0.0345 5.2 1.83 1.6 19% Yes 

0.0533 8.1 1.83 2.2 27% Yes 

0.1052 15.9 1.83 2.4 29% Yes 

0.1397 21.1 1.83 2.5 30% Yes 

0.2152 32.5 1.83 2.5 30% Yes 

0.0113 1.75 1.83 1.07 3% No 

Case 3 is the jet flow experiments in the 4-zone chamber in Chapter 4.2.2. The 

experiment tested different inflow momentum effects by changing the supply airflow 

rates from 0.0345 to 0.2152 m3/s, for which CFD0 was required. We applied Inequality 

(6.4) to explain why the momentum effects could not be neglected for the supply rates 

from 0.0345 to 0.2152 m3/s. Table 6.2 shows that the calculated maximum throw lengths 

for the supply of 0.0345 to 0.2152 m3/s were all greater than the distance from the supply 

to opening 1 in Fig. 4.16 so that air exited zone 1 directly with incomplete dissipation. To 

provide more proof of Inequality (6.4), we simulated the same case with the supply flow 

of 0.0113 m3/s, for which the calculated Tmax value became less than Xd, as shown by the 

italics in Table 6.2. In this case, the inflow momentum effect was considered dissipated 

and the error caused by neglecting the inflow momentum effect was only 3%. Therefore, 

CFD0 was not needed for the supply flow of 0.0113 m3/s. 

Note that these verifications used 0.25 m/s as the characteristic velocity for the jet 

degradation zone, as suggested by ASHRAE (2005). The characteristic velocity could be 

different if experimental results are available. 

6.2. CFD Zone Selection for Non-uniform Contaminant Concentration Distributions

Multizone models assume that the contaminant is perfectly mixed in a zone, which is 

often not true. In fact, the mixing of contaminants in a zone is dependent on the locations 

of the contaminant source, air inflow and outflow, and the local airflow pattern, the air 
140

velocity direction and magnitude, and the strength of turbulence effect. To find the 

relations of these parameters to contaminant mixing, previous studies tried to apply the 

mixing theory of mechanical turbines and agitation tanks to indoor contaminant transport. 

Baughman (1994) and Drescher (1995) successfully studied the mixing of an instantly 

released point source in a room with natural and forced convections, respectively. They 

found that the contaminant would be completely mixed after a certain amount of time, i.e. 

mixing time, in an unventilated space. Mora (2002) extended their studies to the potential 

mixing improvement by occupant activities, such as moving, breathing, and generating 

thermal plumes from the body. These findings implied that the CFD method should be 

used before the mixing time for an unventilated enclosure. 

The mixing theory for unventilated rooms, however, could not be applied to spaces with 

inflows and outflows (or so-called mechanically ventilated space) (Thatcher et al., 2004). 

Finlayson (2004) and Thatcher (2004) conducted experiments and CFD simulations to 

study the mixing of a continuously released point source in a mechanically ventilated 

space. It was found that the contaminant concentration was hardly well-mixed for a 

mechanically ventilated space, especially ones that had physical obstructions (Gadgil et 

al., 2003) such as partitions or people, as illustrated in Fig. 6.4. Some exceptions do exist, 

such as when the contaminant is brought in only by inflow air, which apparently will 

cause a uniform distribution of the contaminant. Another exception could be that the 

contaminant source is also a heat source so that the buoyancy effect could be strong 

enough to improve contaminant mixing in the space. This thesis, therefore, tried to study 

the condition under which the buoyancy effect can play a significant role for contaminant 

mixing. 
141

Fig. 6.4 Illustration of airflow and contaminant transport in a room with an internal 

partition. 

For a mechanically ventilated space with an internal heat source, Fig. 6.4, the 

Archimedes number characterizes the relative strength of the buoyancy force to the 

inertial force (Incropera and DeWitt, 2007) 

n

Gr Ar

Re

=

(6.5)

where Gr is the Grashof number, Re is the Reynolds number, and n is the exponent of Re, 

which is normally 2 (ASHRAE, 2005). 

For building simulations, it was suggested to weight more on the exponent of Re than 

“n=2” in Eq. (6.5), which was considered to underestimate the inertial force (Zhang et al., 

1993). Xue (1994) studied the airflow characteristics and the temperature stratification in 

a ventilated tunnel and suggested the exponent could be 2.5 (Xue and Shu, 1999). 

Reynolds (1986) found that the air motion inside a heated stairwell model could be better 

represented by a relation of 3 Gr ∝ Re . Combining these published results with the 

experimental data in this thesis, this study suggested that the exponent of 3 could be used 

in Eq. (6.5). 

3

Gr Ar

Re

=

(6.6)

(b) Case 3

Fin

Qin

Vroom 
142

In Fig. 6.4, 

3

in

2

P in

g Q L Gr=

C F

b

r u

(6.7)

and 

Fin Re

L

=

u

(6.8)

where g is the acceleration of gravity, b is the volumetric thermal expansion coefficient, 

and Qin is the heat input, L is the characteristic length of the room, which is 1/ 3 Vroom (Gadgil 

et al., 2003), Vroom is the total volume of the room, r is the air density, Cp is the heat 

capacity at constant pressure, Fin is the volumetric airflow rate into the room, and u is the 

kinematic viscosity of the air. 

An index of non-uniformity of contaminant was defined to evaluate the mixing level of 

contaminant. The greater the non-uniformity index is, the less uniform the contaminant 

will be. 

N

2

i i

i 1

N

i

i 1

(C C) V

m

V

=

=

−

=

∑

∑

(6.9)

and 

N

i i

i 1

N

i

i 1

C V

C

V

=

=

=

∑

∑

(6.10)
143

where m is the non-uniformity index, Ci is the contaminant concentration at sample 

cell/point i, C is the volumetric averaged contaminant concentration, Vi is the volume of 

sample cell i, and N is the total number of the sample cells. 

Table 6.3 The parameters required to calculate dimensionless Ar number in order to 

judge when the CFD is required for the cases of a 4-zone chamber, a 3-story building, 

displacement ventilation in an office, and mechanical ventilation in a house. 

Cases Ar Qin (w) Fin

(m3/s)

L (m) CFD 

required?

Case 1: indoor airflow with contaminant 

concentration gradient (Schaelin et al., 1994) in 

Chapter 2.1.4 

70 500 0.07 4.2 Yes 

Case 2: displacement ventilation in an office 

(Srebric et al., 1999) in Chapter 4.1.3 

24 173 0.05 3.5 Yes 

0 0 0.1 2.22 Yes 

200 400 0.018 2.22 Yes 

400 810 0.018 2.22 No 

Case 3: non-uniform contaminant concentration 

distribution in the 4-zone chamber in Chapter 

4.2.3 (cases in italics are the results from 

numerical simulations) 500 1000 0.018 2.22 No 

Case 4: natural ventilation in the 3-story building 

with a large atrium in Chapter 5.2.1 

0 0 13.6 17.7 Yes 

In order to find the correlation of Ar ~ m, this study used the cases from the previous 

chapters, as shown in Table 6.3, which also illustrates the parameters used to calculate 

Ar. Note that three new simulations, indicated by italics, were conducted for the case of 

the 4-zone chamber. 
144

Fig. 6.5 The correlation of Ar ~ m for the cases of a 4-zone chamber, a 3-story building, 

displacement ventilation in an office, and mechanical ventilation in a house. 

Fig. 6.5 shows the calculated Ar and m for the four cases. For the case of the 4-zone 

chamber, the non-uniformity index is more than the unit, and the contaminant 

concentration is highly non-uniform when Ar is zero. With the increase of the heat input, 

the buoyancy effect improved the contaminant mixing so that the value of m was less 

than 0.2 for Ar = 400. 

Compared to the case of the 4-zone chamber, the case of the 3-story building had a 

smaller value of m, although the building is much bigger than the chamber. This could be 

explained by the fact that the inflow rate of the building was much higher than the 

chamber so that the turbulence mixing was dominant. The non-uniformity index of the 

other two cases fell between the previous two cases, with a value of m about 0.3 and an 

Ar less than 100. 

The definition of the non-uniformity index in Eq. (6.9) is the RMS of the difference of 

local contaminant concentrations from the average value, which indicates the error 

caused by the assumption of uniform contaminant concentration. As already known, an 

error of 20% is normally considered acceptable for multizone simulations (Emmerich, 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 Ar 300 400 500

m

4-zone chamber 3-story building with a large atrium

Srebric et al. (1999) Schaelin et al. (1994)

m>1 
145

2001). This study therefore suggests that CONTAM results are acceptable and therefore 

the CFD0 is not needed when 

Ar > 400 (6.11)

When Ar is less than 400, especially when the Ar is zero, the buoyancy effect is not 

strong enough to improve contaminant mixing. As a result, the contaminant distribution 

can highly depend on the local airflow pattern, air velocity, internal partition, and the 

location of the contaminant source. The studies of Schaelin (1994), Yuan (2003), and Ren 

(2005) suggested that the CFD method should be used for the zone, which contains the 

contaminant source and where the contaminant concentration tends to be less uniform 

than the rest of the zones of a building. 

6.3. CFD Zone Selection for Non-uniform Temperature Distributions

Multizone models assume uniform temperature distribution in a zone, which could cause 

errors when the temperature gradient is significant, as shown by the case of the 

buoyancy-driven airflows in a stairwell in Chapter 2.1.2. Evidence was also found that 

the assumption of uniform temperature could become acceptable for a moderate 

temperature gradient, as in the case of the non-uniform temperature distribution in the 4-

zone chamber in Chapter 4.2.4. This chapter studied the conditions when the CFD 

method is needed, if the assumption of the uniform temperature fails. 

For the room in Fig. 6.6, the magnitude of temperature gradient could be defined by 

t b

av av

T |T T |

T T

Δ −

=

(6.12)

where ΔT is the temperature gradient, Tav is the average zone temperature, Tt is the 

temperature at the top of the zone, and Tb is the temperature at the bottom of the zone. 
146

Tt

t

Tbb

Tavav

Finin

h

A

Qinin

Tt

t

Tbb

Tavav

Finin

h

A

Qinin

Fig. 6.6 Illustration of the non-uniform distribution of temperatures in a room. 

A smaller value of ΔT Tav indicates a better mixing of temperature in a zone; for 

example, it is zero for a perfectly mixed zone. Reynolds (1986) found that for buoyancydriven airflows with internal temperature gradient, ΔT Tav could be related to the 

Reynolds number and the Stanton number 

1/ 3 2/3

av

T

Re St

T

Δ

∝ = t

(6.13)

where 

Fin Re

L

=

u

(6.14)

in

1/ 2

p av

Q

St

C T A(gh)

=

r

(6.15)

where t is the dimensionless temperature gradient, Fin is the volumetric inflow rate, L is 

the characteristic length of the room, which is 1/ 3 Vroom (Gadgil et al., 2003), Vroom is the total 

volume of the room, u is the kinematic viscosity of the air, Qin is the total heat input, A 
147

is the cross-sectional area of the room, and h is the height from the inflow opening to the 

outflow opening. 

We then defined the error caused by neglecting the temperature gradient as 

CONTAM exp

exp

F F

Error

F

−

=

(6.16)

where FCONTAM is the volumetric airflow rate predicted by CONTAM and Fexp is the 

volumetric flow rate from the experiment. 

Table 6.4 The parameters required to calculate dimensionless temperature in order to 

judge when CFD is required for the cases of a stairwell model, a 4-zone chamber, and a 

light well model. 

Cases τ Qin

(w)

Fin

(×102

m

3

/s) 

L 

(m) 

A 

(m2) 

h 

(m) 

Tav

(K)

CFD 

required?

0.015 100 0.24 1.43 0.46 1.22 299 No 

0.035 300 0.37 1.43 0.46 1.22 303 Yes 

0.061 600 0.52 1.43 0.46 1.22 311 Yes 

Case 1: buoyancy-driven 

airflows in a stairwell 

model (Zohrabian et al., 

1990) from Chapter 2.1.2 0.083 900 0.60 1.43 0.46 1.22 313 Yes 

0.011 300 5.8 2.45 6.01 2.44 296 No 

0.017 600 5.8 2.45 6.01 2.44 298 No 

Case 2: non-uniform 

temperature distribution in 

the 4-zone chamber from 

Chapter 4.2.4 

0.022 900 6.0 2.45 6.01 2.44 300 No 

0.035 10 0.035 0.2 0.021 0.48 299 Yes 

0.057 20 0.042 0.2 0.021 0.48 307 Yes 

0.077 30 0.048 0.2 0.021 0.48 313 Yes 

Case 3: natural ventilation 

through a light well model 

(Kotani et al., 2003) 

0.096 40 0.054 0.2 0.021 0.48 322 Yes 

Intuitionally, it was expected that a higher dimensionless gradient leads to more error by 

CONTAM assumption. To verify this claim, this study tried to find a correlation of 

“Error ~ τ” from two cases from the previous chapters, as listed in Table 6.4. To have 

more data, we also used Case 3, an experimental study of natural ventilation through a 

light well by Kotani (2003). 
148

Fig. 6.7 The errors caused by the assumption of uniform temperature for dimensionless 

temperature gradient for the case of a stairwell model, a 4-zone chamber, and a light well 

mode. 

Fig. 6.7 shows the correlation of “Error ~ τ” for the three cases. When t is less than 

0.03, the error is less than 20%, which implies that the CONTAM results are acceptable. 

For the rest of the cases, the temperature gradient in a room cannot be neglected so that 

the error can reach 30% ~ 50%. Therefore, this study suggests that it is necessary to use 

CFD0 when 

 

t > 0.03 (6.17)

Note that the above conclusion was based on the experimental data with the average zone 

temperature ranging from 296 K to 322 K. More verification studies should be needed if 

the zone temperature is outside this range. 

0%

10%

20%

30%

40%

50%

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Error

Stairwell (Zohrabian et al.,1990) 4-zone chamber

Lightwell (Kotani et al., 2003)

τ
149

6.4. Summary

This chapter conducted dimensionless analyses for simulations of non-uniform 

distributions of air momentum effects, air temperatures, and contaminant concentrations. 

By checking the errors caused by the well-mixing assumption of multizone models, 

several suggestions were provided about under what conditions the CFD method is 

required. 

● For airflows with non-uniform distribution of air momentum effect, the CFD is 

needed when 

● Re > 30 for channel flow 

● Xd < Tmax for jet flow, where Xd is the distance from the jet opening to the 

opening downwind in the jet flow direction, and Tmax is the maximum throw 

length of the jet 

● For airflows with non-uniform distribution of contaminant concentration, CFD is 

needed for the zone containing the contaminant source, except Ar > 400, when the 

contaminant source is also a heat source. 

● For airflows with non-uniform distribution of air temperatures, CFD is needed when 

the dimensionless temperature gradient, τ > 0.03. 
150

Building model

Run CONTAM simulation

Check airflow results for

non-uniform distribution

of air momentum

Channel flow or jet

flow?

Yes

No

Channel flow Jet flow

Re > 30?

End

L < Tmax? Yes

Check airflow results for

non-uniform distribution

of air temperature

t > 0.03? Yes

Check results for nonuniform distribution of

contaminant concentration

Ar > 400 ?

No

Yes

No

No

Coupled simulation

required

Fig. 6.8 Procedure to judge when CFD is required by the suggestions for non-uniform 

distribution of air momentum effect, air temperature, and contaminant concentration. 

The above suggestions for CFD zone selection can be used by following the procedure in 

Fig. 6.8, which is simply a combination of ordered criteria. Users should note that 

● To calculate the dimensionless numbers, i.e. Ar, Gr, Re, and St, it is necessary to 

perform a CONTAM simulation first to provide preliminary parameters. 

● The order of applying these suggestions could be different from that of the 

procedure, depending on the type of the simulation in question. 
151

Furthermore, the suggestions in this chapter were obtained through the analyses of 

limited data, which may only characterize certain airflows, temperature distributions, and 

contaminant transports. More verification studies and dimensionless investigations are 

necessary to evaluate multizone assumptions in the future. 
152

CHAPTER 7. CONCLUSIONS AND FUTURE WORK 

7.1. Conclusions

Building ventilation designs and indoor air quality analyses are essential to provide a 

safe, healthy, and comfortable indoor environment for a building's occupants. Current 

design and analysis tools, as well as multizones, CFDs, and zonal models have their own 

merits and drawbacks when used individually. Multizone models require the least 

computational time, but their applications are limited to the simulations, where many of 

their assumptions are applicable. Inaccuracies in simulated results or sometimes errors 

may happen when multizone assumptions fail. The literature review shows that the failed 

cases include airflows with 

● non-uniform distribution of wind pressures around buildings, 

● non-uniform distribution of momentum effects, 

● non-uniform distribution of temperatures, and 

● non-uniform distribution of contaminant concentrations 

For such cases, CFD programs can be coupled with multizone programs to improve their 

calculations. 

This study has investigated how to improve the accuracy of airflow and contaminant 

transport calculations in a multizone network model, CONTAM, by coupling it with a 

CFD program, CFD0-C. For the non-uniform distribution of wind pressures, the present 

study proposed an indirect/virtual coupling strategy to provide spatial distributions of 

wind pressures for CONTAM simulations. By using a Wind Pressure and Contaminant 

concentration (WPC) link or a Wind Pressure Profile (WPP) link in numerical tests, the 
153

proposed method could effectively improve the description of wind pressures around 

buildings. 

For the problems caused by well-mixing assumptions of air pressures, temperatures, and 

contaminant concentrations for simulations of indoor airflows and contaminant transport, 

CONTAM and CFD0-C were coupled through the airflow rates or pressure drops at the 

interfaces. Through theoretical analysis, this study has also proven that the coupled 

program has a solution and the solution is unique with the three coupling methods. 

In this investigation, we have studied three feasible coupling methods between 

CONTAM and CFD0-C for coupled indoor air simulations: 

1. CONTAM gives pressure to CFD0 and CFD0 returns the pressure to CONTAM; 

2. CONTAM gives pressure to CFD0 and CFD0 returns the flow rate to CONTAM; 

and 

3. CONTAM gives flow rate to CFD0 and CFD0 returns the pressure to CONTAM. 

The Scarborough criterion was used to evaluate the convergence of the numerical 

solutions and to analyze the stability of the three coupling methods during their iterative 

coupling processes. Method 1, which exchanges pressure boundary conditions between 

multizone and CFD programs, is unconditionally stable, while Methods 2 and 3 are 

conditionally stable. Two numerical experiments were conducted to demonstrate the 

theory: one was pressure gradient flow in an office suite and the other was cross 

ventilation in a four-zone building model. Although experimental data is either 

unavailable or limited for these two cases, numerical results show the theory to be valid. 

To validate the numerical simulations, this study first verified the conversion of CFD0-C 

from CFD0-F, the FORTRAN version of CFD0, by comparing the CFD0-C results with 

published data for six cases. CFD0-C was shown to provide results with reasonable 

accuracy. In order to validate the coupled program, this investigation then used a fourzone environmental chamber to measure the airflow rate and the distributions of air 
154

velocity, air temperature, and contaminant concentration simulated by SF6. The 

experiment was designed to study non-uniform distributions of momentum, contaminant, 

and the temperature gradient in a zone. CONTAM, the coupled CONTAM-CFD0, CFD0, 

and a commercial CFD program (Airpak) were used for the investigation. The results 

show that CONTAM could not consider the flow in a zone with strong non-uniform 

distributions of momentum and contaminant concentration. However, the impact of a 

non-uniform temperature gradient on CONTAM simulation is small, if the zone air 

temperature can be correctly estimated. In general, the coupled CONTAM-CFD0 

program performs better than the CONTAM for all the cases studied, and is as good as 

the CFD0 for all the zones but with a major reduction in computing time. Both the 

coupled CONTAM-CFD0 and the CFD0 programs can predict reasonably well the 

distributions of air velocity, temperature, and SF6 concentration in the chamber, but there 

are discrepancies. The discrepancies could be caused by the boundary conditions 

provided by CONTAM and by the zero-equation model used in CFD0. 

The validations also found the limitations of CFD0-C program. For airflows with strong 

momentum effects, CFD0-C could not predict the airflow distribution as well as the 

commercial software, such as Airpak, which uses the standard k-ε turbulence model. 

When used for outdoor airflow simulations, CFD0-C may perform unsatisfactorily for the 

surfaces with storng turbulence separation and recirculation flows. 

This study also proposed three algorithms for coupling CONTAM with CFD0-C for 

steady airflow and steady contaminant transport, steady airflow and transient contaminant 

transport, and transient airflow and transient contaminant transport. The three schemes 

were demonstrated by the simulations of natural ventilation in a three-story building with 

a large atrium, to which CFD0 was applied. The results show that the coupled program 

can give more realistic results than CONTAM. The coupled program could also help to 

evaluate emergency ventilation and control systems, and calculate personal contaminant 

exposure for the determination of evacuation strategies. 
155

Through dimesional analyses, this study also found correlation of simulation errors, 

which were caused by the multizone assumptions, to the mixing levels of air properties 

and contaminant concentrations in a zone. The assumption of uniform air temperatures is 

critical when a non-dimensional temperature gradient is higher than 0.03. The assumption 

of uniform air momentum effects could fail when the airflow with a strong momentum 

effect cannot be totally dissipated in a zone. The assumption of uniform contaminant 

concentrations can be invalid for the zone containing the contaminant source except that 

the contaminant source is also a heat source. The well-mixing assumption of contaminant 

concentration could be used if the new Archimedes number is greater than 400. 

7.2. Challenges for Future Studies 

In building airflow distribution and contaminant transport simulations, some challenges 

remain unsolved for coupling multizone and CFD programs. This section briefly outlines 

these challenges, which could be the bases of future studies. 

Atmospheric Contaminant Dispersion under Transient Weather Condition

Airflow and contaminant transport around buildings are always transient due to the 

unsteady feature of the weather. For transient airflow, this thesis used the Wind Pressure 

Profile (WPP) link of CONTAM and CFD0 to predict the distribution of wind pressure 

coefficients for variable wind speed. However, the WPP link was unable to predict 

atmospheric contaminant dispersion under transient weather, although it could simulate 

contaminant transport at a steady state for a certain wind direction. It is necessary to 

develop a method of contaminant dispersion under transient weather conditions, which is 

more realistic than the simulation at a steady state. 

The simulation of airflow and contaminant dispersion under a specific weather at 

transient state makes it hard to reuse the previously-calculated results. One alternative is 

to consider airflow at a quasi-steady state within one time step, and the contaminant 

transport to be always transient throughout all the time steps. This means that transient 

contaminant transport can be calculated by using pre-calculated steady-state airflow 
156

results at the same time step. When the wind velocity is different from that of the precalculated airflow results, a correction of airflow velocity can be applied, which is similar 

to the correction of wind pressure coefficients in the WPP link. By reusing pre-calculated 

airflow data, this method will save huge computational costs. Furthermore, since using 

airflow is relatively easier to reach steady state than using contaminant dispersion, it is 

reasonable to use airflow at a quasi-steady state within one time step for transient 

contaminant simulation. 

Single Solver for Integrated Multizone and CFD Equations for Airflow, Energy, and 

Contaminant Simulations 

This thesis studied the methods to run multizone and CFD programs separately while 

exchanging boundary conditions between them. It is desirable that a solver or a single 

program can be developed to calculate the assembled equations of multizone and CFD 

programs for airflow, energy, and contaminant transport. The single solver can avoid the 

convergence and stability problems associated with different coupling methods. The 

single solver also calculates integrated energy equations so that the zone temperature can 

be predicted instead of being specified by users. 

Chapter 3.2.3 showed an assembled matrix equation of multizone and CFD models for air 

mass conservation in Eq. (3.12). Similarly, a linearized assembled equation can also be 

written for momentum, energy, and contaminant/species conservations, which are 

combined with air mass conservation as: 

CP + = F B (Air mass conservation) (7.1)

where C is the flow coefficient maxtric, P is the vector of unkown pressures of multizone 

and CFD cells, F is the vector of unkown flow rates through interface paths and cells, and 

B is the vector of mass source term. 

Cm m U + Δ = P B (Momentum conservation) (7.2)
157

where Cm is the coefficient matrix in an assembled momentum conservation equation, U 

is the vector of unknown air velocities through an opening or CFD cell face, DP is the 

vector of pressure difference, Bm is the vector of source term in an assembled momentum 

conservation equation. 

Ce e T+ = Q B (Energy conservation) (7.3)

where Ce is the coefficient matrix in an assembled energy conservation equation, T is the 

the vector unknown temperatures, Q is the vector of heat inputs, and Be is the vector of 

the source terms in an assembled energy conservation equation. 

Cc c M + = S B (Contaminant/Species conservation) (7.4)

where Cc is the coefficient matrix in an assembled species conservation equation, M is 

the vector of species concentrations, S is the vector of species mass source terms, and Bc 

is the vector of source terms in an assembled species conservation equation. 

A point-to-point (cell-to-cell) linear solver can be used to solve Eqs. (7.1) – (7.4), such as 

the Gauss Seidel method, or faster linear Multi-grid solver. Note that the momentum 

conservation equation becomes airflow path resistance model in multizone methods. 

Furthermore, the integration of multizone and CFD methods links a spatially onedimensional model with a three-dimensional method. Therefore, some assumptions must 

be employed for the physical links/interfaces between the zones of the two methods. For 

example, it is often assumed that 

● tangential air velocity at an interface airflow path are zero, and 

● spatial distribution of pressures and velocities along the interface path are uniform. 

Under some situations, these assumptions could become critical, which thus cause 

simulation errors, as discussed next. 
158

Potential Asymmetric Problems Associated with Coupled Multizone and CFD 

Simulations

An integrated multizone and CFD simulation apply the CFD model to the zones, where 

multizone assumptions fail, and multizone models are applied to the rest of the zones of a 

building. The distinctions of multizone and CFD methods may cause asymmetrical 

results for a symmetrical problem, as illustrated in Fig. 7.1 (Axley, 2006). 

 

Fig. 7.1 Asymmetric results caused by the difference of multizone and CFD methods and 

the inappropriate selection of CFD zones (Axley, 2006). 

A 4-zone house with symmetrical configuration in Fig. 7.1 was solved asymmetrically 

when the CFD method was only applied to Zone 3. As a result, the airflow through Path 

12 was non-zero, which was apparently incorrect. The asymmetrical solution was caused 

by the assumption of zero tangential velocities at Path 5, which was otherwise 

unavailable from the multizone equations. Some researchers claimed that the 

asymmetrical solution was an intrinsic limitation for integrated macro-micro methods. 

This thesis, however, suggested two possible solutions for the asymmetrical results. One 

solution is to apply the CFD method to both Zone 1 and Zone 3 in order to capture the 

correct airflow directions at Paths 3 and 5. The other is to simulate both Zone 2 and Zone 

Zone 1 

Path 3 

Path 5 

Path 12
159

3 as a CFD zone, which will make the integrated simulation symmetrical. So far, it is not 

clear if these solutions could improve the results. Therefore, more studies on the 

asymmetrical problem related to the integrated methods and the impact of neglecting 

tangential velocities at the interface paths should be done in the future. 

Contaminant Mixing Level and Mixing Time

One of the major multizone assumptions is that the contaminant is perfectly mixed in a 

zone without time delay. As already discussed in this thesis, contaminant mixing depends 

on many factors such as contaminant source locations, local air velocities and flow 

patterns, and internal blockages. For contaminant transports at a transient state, it also 

takes time for contaminants to spread in a room. 

More theoretical and experimental studies are necessary for contaminant mixing level 

and mixing time in a room. This thesis already showed the possibility of applying 

dimensionless analyses to study the contaminant mixing enhanced by buoyancy effects, 

although it was limited to the situation, where the contaminant source was also a heat 

source. Experimental studies are also possible, such as the studies done on mixing time 

by Baughman (1994), Drescher (1995), Thatcher (2004), and Finlayson (2004). 

Applications of Multizone, CFD, or the Coupled Multizone-CFD Programs to Building 

Evacuations and Real-time Controls

This thesis has demonstrated the coupled CONTAM-CFD0 program for outdoor airflow 

simulations through the indirect/virtual coupling, and indoor simulations by the direct 

coupling, as shown in CHAPTER 5. It was shown that the coupled program was able to 

help evaluate the building evacuation strategies and the design of building control 

systems before and after building construction. One of the more important applications is 

simulation and control at real-time, which is especially important for designing safe and 

immune buildings. For example, with real-time inputs from sensor information, the 

simulation could predict safe evacuation routes before the contaminant concentration 

reaches lethal level. 
160

Several barriers exist, however, for real-time analyses and control. The computing time 

of the coupled multizone-CFD program is still too high for real-time applications. The 

multizone program itself seems a good alternative in terms of simulation time, but it may 

provide inaccurate answers due to its assumptions. More future studies should be done to 

further reduce the computational cost of CFD methods and to understand the applicability 

of multizone assumptions. Moreover, numerical simulations are often found to be at odds 

with the measured data. More studies could be conducted on how to use the real-time 

data from sensors to improve the simulation accuracy. 

As a whole, the current study developed a coupled CONTAM-CFD0 program for airflow 

distribution and contaminant transport simulations outside and inside buildings. 

Theoretical studies proved that the coupled program has a solution and the solution is 

unique. The coupled program was then validated by comparing the numerical results with 

experimental data. The demonstration of the coupled CONTAM-CFD0 program to real 

design problems illustrated that the coupled program could effectively improve the 

CONTAM calculations. This study also found that many challenges remain unsolved and 

pointed out several potential solutions, which could be used as bases for future studies. 
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142. 

 
APPENDICES 
170 

Appendix A. Manual for CFD0-C 

This appendix is a manual for using CFD0-C, C version of the CFD0. CFD0-C uses 

Cartesian coordinates, the SIMPLE algorithm, the upwind and power-law differencing 

schemes, the TDMA solver (Patankar, 1980), and the indoor zero-equation eddyviscosity turbulence model (Chen and Xu, 1998). A detailed description for the 

turbulence modeling of CFD0 can be found in ASHRAE RP-927 (Srebric et al., 1999). 

CFD0-C solves velocity component U in the x-direction, V in the y-direction, and W in 

the z-direction, air pressure: P, air temperature: T, species concentration (≤ 5): C, and 

turbulence effective viscosity: μ at steady state or transient state. 

Appendix A.1 - A.4 is for general-purpose usage of CFD0-C and Appendix A.5 -A.6 for 

advanced users with the aim of further development of CFD0-C. 

A.1 Installation and Execution of CFD0-C

The executable PC version of CFD0-C include a Graphic User Interface (GUI), which 

defines a CFD simulation, generates simulation meshes, creates CFD input file, and 

visualize CFD results, and a Windows Console program, CFD0C.EXE, which is the CFD 

solver. Fig. A.1 shows the GUI of CFD0-C. The GUI and the solver can be copied and 

run directly without further installation. Note that to run the GUI of CFD0-C, users need 

to obtain a “Registration Number” from Professor Qingyan (Yan) Chen by sending an 

email with a randomly generated “Information Number” to YANCHEN@PURDUE.EDU as 

shown in Fig. A.2. 
171 

Fig. A.1 The Graphic User Interface (GUI) of CFD0-C. 

Fig. A.2 The window for registration of CFD0-C. 

There are two methods to execute CFD0-C. One method is to run CFD0-C by choosing 

the CFD0C.EXE inside the CFD0C GUI as illustrated by Fig. A.3. 

Fig. A.3 Run CFD0-C from the CFD0C GUI. 
172 

Fig. A.4 Run CFD0-C from WINDOWS Console. 

The second method is to run CFD0C.EXE by double clicking the CFD0C.EXE in 

WINDOWS environment as shown in Fig. A.4. Users must specify the full path location 

of the CFD input file, “*.CFD”. 
173 

A.2 Inputs and Outputs

Table A.1 Input and output files of CFD0-C. 

Input 

• CFD the ASCII input file defining geometry, boundary conditions, control 

parameters etc.; 

Outputs 

• RET the ASCII output of CFD results of flow rates, spatial air velocities, 

temperatures, pressures, contaminant concentrations at grid points. 

• DAT the data file for post-processing in TECPLOT (compatible with TECPLOT 

360) 

• BAL outputs of convergence history, e.g. residues of calculations of velocities and 

temperatures etc. 

• VAR 

the binary file with the whole data of air pressures, velocities and temperatures 

for the calculations of airflow restart and the contaminant dispersion based on 

existent flow field. 

• OUT the output file for visualization in the CFD0C GUI 

Optional Outputs 

• EWC the binary file of wind pressures for the WPC link of CONTAM (optional) 

• CFDLOG the output of the simulation definition from a CFD input (optional) 

• WDB the binary file of wind pressure coefficients for the WPP link of CONTAM 

(optional) 

• CDB the binary file of contaminant concentrations from the simulations of 

atmospheric contaminant dispersion (optional) 

A.3 Preparation of an Input File for CFD0-C

The CFD0C input file, *.CFD, can be created either by the CFD0-C GUI or manual 

preparation by users. When preparing an input file from the GUI, users can use the 

instant help by resting the mouse arrow over where they want to get help. A green popup 

box with tips will show up as illustrated by Fig. A.5. 
174 

Fig. A.5 Instant help in the CFD0-C GUI. 

Since the input file is in ASCII format, which users can prepare or edit manually. All the 

input information is in SI units. Manual input must follow an exact format requirement as 

follows. It is suggested prepare a manual input file always by starting with a template 

input file to avoid format errors. Note that all the input data values in the following 

format must be separated by comma. 

Lines Input Data

The first line: User specified title of the case to be simulated in quotation marks 

The next two lines: Subtitle information 

The next four lines: Title of problem definition 

The next one line: Title of stead or unsteady control parameters of velocity and 

contaminant 

The next one line: stead or unsteady control parameters of velocity and contaminant, 

respectively (1=steady; 0=unsteady), respectively. Calculation for 

WPP link? (1=Yes; 0=No) 

(Only if Yes), Reference Height, Reference Wind Velocity, 

Atmospheric boundary layer thickness at a weather station, Wind 

profile exponent at a weather station, Atmospheric boundary layer 

thickness at local site, Wind profile exponent at local site, The first 
175 

calculated wind angle, The last calculated wind angle, The step of 

calculated wind angle. 

The next two lines: Title of Time step, maximum time, residual of contaminant and 

maximum iterations of contaminant computation 

The next one line: Time step, maximum time for unsteady contaminant computations, 

residual and maximum iterations for contaminant computations 

The next two lines: Title of the control parameter for energy computation 

The next one line: The control parameter for energy computation (1=solve energy 

equation; 0=not solve energy equation) 

The next two lines: Title of the control parameters for contaminant computation, 

number of contaminants computed and whether the computation 

starts from an existent file of flow field 

The next one line: The control parameter for contaminant computation (1=compute 

contaminants; 0=not compute contaminant), total number of 

contaminants involved in the computation (<=5), the control 

parameter for whether the contaminant computation starts from an 

existent *.VAR file of flow field (1=based on a flow field file; 

0=not based on a flow field file) 

The next two lines: Title of the residual and maximum iterations of velocity 

computation 

The next one line: The residual of velocity computation, the maximum iterations of 

velocity computation 

The next two lines: Title of the control parameter for flow regime 

The next one line: The control parameter for flow regime (F=turbulence flow; 

T=laminar flow) 

The next two lines: Title of turbulence models (if the flow regime is laminar, these two 

lines should be non-existent) 

The next one line: Variable of turbulence models (0=zero equation model; 1=κ-ε

model (not available in current version). if the flow regime is 

laminar, this line should be non-existent) 
176 

The next four lines: Title of the geometry data 

The next three lines: Explanation of the flow domain 

The next line: The flow domain size (m) in the x, y, and z direction (XX, YY, 

ZZ), respectively 

The next three lines: Grid size information 

The next line: The total number of control volumes (grid numbers) in the in x, y 

and z direction (NNX, NNY, NNZ), respectively 

The next two lines: Information of the control volume 

The next line: Title for the x-direction 

The next line(s): The size of the control volumes in the x-direction (DELX). The 

sum of these values must be equal to XX. 

The next line: Title for the y-direction 

The next line(s): The size of the control volumes in the y-direction (DELY). The 

sum of these values must be equal to YY. 

The next line: Title for the z-direction 

The next line(s): The size of the control volumes in the z-direction (DELZ). The 

sum of these values must be equal to ZZ. 

The next two lines: Title for the openings 

The next line: The number of inlet and outlet openings (NBIN, NBOUT) 

The next block: Exists only when NBIN > 0 

The next two lines: Title information for inlet opening(s) 

The next line: Title for the x-direction 

The next line: The first and last grid number of the opening 

in the x-direction 

The next line: Title for the y-direction 

The next line: The first and last grid number of the opening 

in the y-direction 

The next line: Title for the z-direction 

The next line: The first and last grid number of the opening 

in the z-direction 
177 

The next line: types of openings(1) (1=small opening; 

2=large openings), types of boundary 

conditions (1=velocity, 2=pressure), 

• (if =1, velocity boundary conditions) 

velocity in the x-direction (m/s), 

velocity in the y-direction (m/s), 

velocity in the z-direction (m/s), 

mass inflow (kg/s, set the mass 

inflow to a non-zero value, only 

when the momentum method is used 

for the inlet), temperature (oC) and 

total number of contaminants (must 

be <=5; if no contaminant 

computation, put ‘0’ or leave it 

blank), respectively. 

▪ (if total number of 

contaminants≠0) the next 

line: index of the contaminant 

(1-5), mass fraction of this 

contaminant. 

Repeat for all the 

contaminants 

• (if =2, pressure boundary conditions) 

pressure (Pa), mass flow coefficient 

(kg/s·Pan, if opening type is ‘2’, the 

flow coefficient and exponent 

specified here will not be used), flow 

exponent, temperature (oC) and total 

number of contaminants (must be 

<=5; if no contaminant computation, 

put ‘0’ or leave it blank), 

respectively. 

▪ (if total number of 

contaminants≠0) the next 

line: index of the contaminant 

(1-5), mass fraction of this 

contaminant. 

Repeat for all the 

contaminants 

Repeat for all the inlet openings 

The next block: Exists only when NBOUT>0 
178 

The next two lines: Title information for outlet opening(s) 

The next line: Title for the x-direction 

The next line: The first and last grid number of the opening 

in the x-direction 

The next line: Title for the y-direction 

The next line: The first and last grid number of the opening 

in the y-direction 

The next line: Title for the z-direction 

The next line: The first and last grid number of the opening 

in the z-direction 

The next line: types of openings [1] (1=small opening; 

2=large openings), types of boundary 

conditions (1=velocity, 2=pressure), 

• (if =1, velocity boundary conditions) 

velocity normal to the outlet (m/s), 

mass outflow (kg/s, from which 

CFD0 compute the outlet velocity 

internally), temperature (oC) and 

total number of contaminants (must 

be <=5; if no contaminant 

computation, put ‘0’ or leave it 

blank), respectively. 

▪ (if total number of 

contaminants≠0) the next 

line: index of the contaminant 

(1-5), mass fraction of this 

contaminant. 

 Repeat for all the 

contaminants 

• (if =2, pressure boundary conditions) 

pressure (Pa), mass flow coefficient 

(kg/s·Pan, if opening type is ‘2’, the 

user-specified flow coefficient and 

exponent will not be used), flow 

exponent, temperature (oC) and total 

number of contaminants (must be 

<=5; if no contaminant computation, 
179 

put ‘0’ or leave it blank), 

respectively. 

▪ (if total number of 

contaminants≠0) the next 

line: index of the contaminant 

(1-5), mass fraction of this 

contaminant. 

Repeat for all the 

contaminants 

Repeat for all the outlet openings 

The next two lines: Title for the blockage number 

The next line: The total number of the blockages 

The next block: Exists only when the total number of the blockages is greater than 

zero 

The next two lines: Title for the first blockage 

The next line: Title for the x-direction 

The next line: The first and last grid number of the 

blockage in the x-direction 

The next line: Title for the y-direction 

The next line: The first and last grid number of the 

blockage in the y-direction 

The next line: Title for the z-direction 

The next line: The first and last grid number of the 

blockage in the z-direction 

The next line: Title for blockage types, the heat flux and 

number of contaminant (if any) 

The next line: The blockage type (1=solid blockage; 

2=fluid blockage), The heat generation rate 

from the blockage, HSOU (W) and the total 

number of contaminants (if ≠0, must <=5; if 

=0, just leave it to blank) 

• (if total number of contaminants≠0) 

the next line: index of the 
180 

contaminant (1-5), mass generation 

rate of this contaminant[2] (kg/s). 

Repeat for all the contaminants 

Repeat for all the blockages. 

The next two lines: Title for non-adiabatic surfaces given by a constant temperature 

The next line: The total number of non-adiabatic surfaces with a constant 

temperature (NAWT) 

The next block: Exists only when NAWT>0 

The next two lines: Title for the first surface 

The next line: Title for the x-direction 

The next line: The first and last grid number of the surface 

in the x-direction 

The next line: Title for the y-direction 

The next line: The first and last grid number of the surface 

in the y-direction 

The next line: Title for the z-direction 

The next line: The first and last grid number of the surface 

in the z-direction 

The next line: Title for the temperature 

The next line: The surface temperature, TNAW (oC) 

Repeat for all the surfaces. 

The next two lines: Title for surface sources of heat (given by a constant heat 

generation rate) and of contaminant (given by a constant mass 

generation rate) 

The next line: The total number of surface sources with a constant heat rate or 

contaminant mass rate (NAWQ) 

The next block: Exists only when NAWQ>0 

The next two lines: Title for the first surface 

The next line: Title for the x-direction 

The next line: The first and last grid number of the surface 

in the x-direction 
181 

The next line: Title for the y-direction 

The next line: The first and last grid number of the surface 

in the y-direction 

The next line: Title for the z-direction 

The next line: The first and last grid number of the surface 

in the z-direction 

The next line: Title for the heat rate and mass rate 

The next line: The heat generation rate (QNAW (W), if no 

heat, just put ‘0’), the total number of 

contaminants (if ≠0, must <=5; if =0, just 

leave it to blank) 

• (if total number of contaminants≠0) 

the next line: index of the 

contaminant (1-5), mass generation 

rate of this contaminant[2] (kg/s). 

Repeat for all the contaminants 

Repeat for all the surfaces. 

The next four lines: Title for numerical and control parameters 

The next two lines: Title for differential schemes of U,V,W,T and C 

The next line: The differential schemes of U, V, W, T, C [3] (1=Upwind; 2=Power 

Law) 

The next two lines: Title for initial and reference temperature 

The next line: Initial temperature (oC) (TINIT) and reference temperature (oC) 

(TM) 

The next two lines: Title for buoyancy model 

The next line: Buoyancy model [4] (1=Bousinesq; 0=non-Bousinesq, density 

variable with temperature) 

The next two lines: Title for minimum and maximum values 

The next line: The minimum and maximum values for U velocity (m/s), V 

velocity (m/s), W velocity (m/s), and temperature (oC) (UMIN, 

UMAX, VMIN, VMAX, WMIN, WMAX, TMIN, TMAX), 

respectively 
182 

The next two lines: Title for under-relaxation 

The next line: The linear under-relaxation values [3] for U velocity, V velocity, W 

velocity, pressure, temperature, kinetic energy, dissipation rate and 

contaminant (URFU, URFV, URFW, URFP, URFT, URFEK, 

URFED, URFC) 

The next two lines: Title for false-time-steps 

The next line: The false-time steps [3] for U velocity, V velocity, W velocity, 

pressure, temperature, kinetic energy, dissipation rate and 

contaminant (DTU, DTV, DTW, DTT, DTKE, DTED, DTC) 

The next two lines: Title for change of false time step 

The next line: Set T if the change for the false time step is needed 

The next two lines: Exists only when ‘T’, Title for new false time step 

The next line: The iteration number when the new false time step is to be used 

(ISTEP) and the new false time steps [3] for U velocity, V velocity, 

W velocity, temperature, kinetic energy, dissipation rate and 

contaminant (CDTU, CDTV, CDTW, CDTT, CDTKE, CDTED, 

CDTC) 

The next two lines: Title for printing frequency 

The next line: Printing frequency for the residuals during the calculation to the 

PC monitor (PINTV) 

The next two lines: Title for monitoring point 

The next line: The grid number for the monitoring point in the x-, y-, and zdirection (IMON, JMON, KMON), respectively 

The next two lines: Title for reference point 

The next line: The grid number for the reference point in the x-, y-, and zdirection (IREF, JREF, KREF), respectively 

The next two lines: Title for printing frequency to the *.RET (text results) file 

The next line: The number of the first control volume, last control volume and 

interval for printing results in the x-direction (IP1, IP2, IPSTP) and 
183 

the number of the first control volume, last control volume and 

interval for printing results in the y-direction (JP1, JP2, JPSTP) 

The next two lines: Title for restarting the computation based on the results of the 

previous computation and output control parameter of EWC file 

and output control parameter for *.CFDLOG file 

The next line: Set to 0 if not starting from the previous results and set to 1 if 

starting from the previous results (ICOMPU), EWC output control 

parameter (EWCYN) (0=do not create EWC file; 1=create EWC 

file), output control parameter for *.CFDLOG file (DUMPLOG) 

(0=do not create *.CFDLOG file; 1=dump input data only; 

2=dump residuals of pressure correction equation only; 3=dump 

both input data and residuals of pressure correction equation for 

code checking) 

The next four lines: Title for ambient conditions and material properties 

The next two lines: Title for ambient pressure 

The next line: Ambient pressure (PAMB, (Pa)) 

The next line: Title for fluid reference density 

The next line: Reference density (REFDENS,(kg/m3), usually=1.2kg/m3 for air) 

The next line: Title for fluid operating density 

The next line: Operating density (OPERDENS, (kg/m3), usually= the ambient 

density) 

The next line: Title for kinematic viscosity 

The next line: Fluid kinematic viscosity (m2/s) (ANU) 

The next line: Title for thermal conductivity 

The next line: Fluid thermal conductivity (W/m K) (AK) 

The next line: Title for specific heat at constant pressure 

The next line: Fluid specific heat at constant pressure (J/kg K) (ACP) 

The next line: Title for Prandtl number 

The next line: Fluid Prandtl number (PRL) 
184 

NOTE

[1] Explanation of types of openings. If it is a small opening, the user-specified flow 

coefficients and exponents will be used for the pressure boundary conditions to 

characterize the opening resistance. If it is a large opening, these parameters will not be 

used. Instead, the conventional CFD method of handling the flow resistance of openings 

is used. For details refer to the section 2.1.2 of Chen and Wang (2005). 

[2] If the mass generation rate of a contaminant source is at the scale of 10-6 kg/s, for 

example 2.0×10-6 kg/s, 2.0 kg/s is suggested be used instead of 2.0×10-6 kg/s so that the 

computed mass fraction will be in the unit of PPM. Usually, a value of 2.0 kg/s also helps 

to avoid possible round-off errors, which may be caused by a value of 2.0×10-6 kg/s. 

[3] The setting of the input information requires experience and expertise in CFD 

simulations and it is recommended that the default values specified in the template input 

file of CFD should be used. 

[4] CFD0-C uses the Bousinesq buoyancy model, in which only the density in the W 

momentum equation is variable with temperature. 

[5] For the WPP link, CFD0-C will first check if there is an existent VAR file for a 

certain wind angle. If yes, CFD0-C will skip the calculation for this wind angle and 

continue to calculate the next wind angle. For example, for a simulation of “Case1.CFD”

of the wind angle from 0° ~ 360° with a step of 30°, a WPP calculation will skip the 

calculation for the wind of 90° if there is already a file with the name of “Case1-wind90.VAR”. The file name of “Case1-wind-90.VAR” is created automatically for each 

wind angle during a WPP calculation. 

[6] If a WPP simulation for a certain wind angle is not convergent (for example, more 

than 2000 iterations), CFD0-C will not create a VAR file for that wind angle. To get 
185 

convergence, users can adjust control parameters and restart the whole calculation. For 

previously-convergent wind angles, which already have their VAR file created, the restart 

will not calculate them again. CFD0-C will only calculate those which are not convergent 

at the previous run before user’s adjustment of the control parameters. 

A.4 Result Analyses from Outputs

The results of CFD0-C simulations can be screen outputs, which are for convergence 

monitoring, and file outputs, which are for visualization and further analyses. 

Monitoring Screen Outputs during CFD Calculation

During the calculation, several important parameters are displayed on the PC monitor, 

which monitors the calculation progress. These parameters are: 

• NITER: the index of iteration, 

• RESOU, RESOV, RESOW, RESOT, and RESOM: the relative residuals for the 

air velocity component of U, V, W, air temperature, and air mass continuity 

respectively, and 

• the location of the monitored grid point and the values of U, V, W and T at the 

monitored grid point. 

The output frequency of the screen monitoring can be specified in the CFD input file. 

CFD Result Analyses through Output Files

After CFD0-C simulations, several output files are created, i.e. *.BAL, *.RET, *VAR, 

*.DAT, *. OUT, and optional outputs, *.CFDLOG, *.EWC, *.WDB, and *.CDB. 

The BAL file contains residual values of air mass, T, U, V and W momentum equations 

at each iteration during the calculation, which is the same as the screen monitoring 

outputs during the calculation. It can help users to check the convergence after the 

completion of the calculation. 
186 

The RET file contains the results of the air velocity component of U, V, W, the mean 

scalar velocity, temperature, contaminant concentration, and effective turbulence 

viscosity. The output frequency in the X-direction (or I-direction) and the Y-direction (or 

J-direction) can be controlled in the CFD input file. 

The VAR file stores the whole airflow results in binary format after the completion of a 

CFD simulation. The results can be used to restart the airflow calculation, or calculate 

steady/transient contaminant dispersion. A format description of the binary VAR file can 

be found in Appendix A.7. 

The DAT file is in TECPLOT data file. TECPLOT is a post-processing program for 

visualization and analysis of the numerical data. The CFD0-C DAT file includes the 

following data: 

• the positions of the cell center (X, Y and Z) 

• the values of the velocity components at the cell center (UC, VC and WC) 

• averaged air velocity (VTT), pressure (P), temperature (T), contaminant 

concentration (C1, C2, ..., C5), total pressure (TP), wind pressure coefficient 

(CP), and effective turbulence viscosity (VIS) 

• control parameter for “Value Blanking” in TECPLOT of blockages (BLANK). To 

use “Value Blanking” in TECPLOT, users can choose “Blank entire cell” to be 

“when all corners are blanked”, “Constraint” to be “Blank When BLANK is less 

than or equal to 0”. This will make only solid blockages visible in TECPLOT 

visualization, e.g. building blocks, so that the calculated contour values on 

building surfaces can be shown. 

• name of CFD objects for “Object Labeling” in TECPLOT (OBJECTS). The 

“Object Labeling” will help users to identify the names of different objects in 

TECPLOT, which is very helpful for simulations with many inlets, outlets, or 

blockages. To use the “Object Labeling” in TECPLOT, users need to go to “Label 

Points and Cells” in TECPLOT’s PLOT Menu, Choose “Show Node Labels” and 

Select OBJECTS for “Show Variable Value”, then select “Number Format” to be 
187 

“Custom”. 

The OUT file is an ASCII file, which is required by the CFD0-C GUI for visualization 

purposes. It is a counterpart in the CFD0-C GUI as the DAT file in TECPLOT. The 

current version of the CFD0-C GUI can only visualize results of steady-state simulations. 

Users should use the DAT file in TECPLOT for transient simulations. 

The CFDLOG is an optional log file for the purpose of checking the input data of CFD0-

C and the residuals of pressure correction equation of each iteration for advanced users. 

The EWC file is an optional wind pressure data file in binary format for pressure 

information around a building to be used by CONTAM. A format description of the 

binary EWC file can be found in Appendix A.7. 

The WDB file is an optional file containing wind pressure coefficients in binary format 

for the WPP link of CFD0-C and CONTAM. A format description of the binary WDB 

file can be found in Appendix A.7. 

The CDB file is an optional file containing atmospheric contaminant concentrations in 

binary format for CONTAM. A format description of the binary CDB file can be found in 

Appendix A.7. 

A.5 Program Structure of CFD0-C

The source codes comprise of three C source files and six C header files as show in Table 

A.2. CFD0-C borrowed many valuable functions and ideas from CONTAM so that some 

new features were added since the FORTRAN version of CFD0, e.g. dynamic allocation 

of memory, which was developed by Mr. George Walton of NIST, USA. 

CFD0-C source codes can be compiled in two modes: a stand-alone CFD0-C program 

and a coupled program with CONTAMX source code. A macro with the name of 

‘FLOWC’ in the first line of flow.c defines the mode. For the default value of ‘1’, CFD0-
188 

C works as a stand-alone CFD program and the value of ‘0’ means that CFD0-C works in 

the mode of coupling with CONTAM. The most recent version to be coupled with CFD0-

C is CONTAM2.4b dated at August 2006. Fig. A.6 is the program structure of CFD0-C 

and Table A.3 describes each of CFD0-C functions. 

Table A.2 The source code files of CFD0-C. 

C Source Files 

flow.c: a CFD0 core file, containing all CFD functions; 

HeapCFD.c: 

a utility file and a counterpart of Heap.c in CONTAM, containing 

functions of dynamic allocation and deallocation of memories; 

UtilsCFD.c: 

a utility file and a counterpart of Utils.c in CONTAM, containing 

functions of management of input and output file names; 

C Header Files 

comflo.h: a header file, declaring all global variables in flow.c; 

fprtype.h: a header file, declaring all functions in flow.c; 

prtypCFD.h: 

a header file and a counterpart of prtyp.h in CONTAM, declaring 

functions in HeapCFD.c and UtilsCFD.c; 

sglobCFD.h: 

a header file and a counterpart of sglob.h in CONTAM, declaring 

variables about paths and names of input and output files; 

sxtrnCFD.h: 

a header file and a counterpart of sxtrn.h in CONTAM, declaring some 

temporary variables; 

typesCFD.h: 

a header file and a counterpart of types.h in CONTAM, defining types of 

variables. 
189 

NO

YES

NO

YES

Flow

Input

Prcase

Init

Niter=Niter+1

Ucompu

Vcompu

Wcompu

Ppcompu

Correc

Tcompu

Vistur1

 Converge?

Plotvt

Prvari

Coeffu

Tdmax

Tdmay

Tdmaz

Boundu

Coeffv 

Tdmax

Tdmay

Tdmaz

Boundv

Coeffw

Tdmax

Tdmay

Tdmaz

Boundw 

Coeffpp

Tdmax

Tdmay

Tdmaz

Coefft

Tdmax

Tdmay

Tdmaz

 Contaminant

calculation?

Computec

End

Fig. A.6 Program structure of SIMPLE algorithm in CFD0-C. 
190 

Table A.3 The description of CFD0-C functions. 

Flow Main program; 

Input Read CFD0-C input files; 

Prcase Create the RET file; 

Init Initialize CFD0-C simulations; 

Coeffu, Coeffv, Coeffw, 

Coefft, Coeffpp 

Calculate coefficients of X , Y , Z momentum equations, 

energy equation and pressure correction equation, 

respectively; 

Boundu, Boundv and 

Boundw 

Implement boundary conditions for X , Y and Z momentum 

conservation equations, respectively; 

Ucompu, Vcompu and 

Wcompu 

Solve U , V and W velocities through momentum 

conservation equations, respectively; 

Ppcompu Solve pressure correction equation; 

Correc 

Correct air velocities based on the results of pressure 

corrections; 

Tcompu Solve energy equation; 

Computec Solve species conservation equation; 

Vistur1 Update effective turbulence viscosities; 

Tdmax, Tdmay and 

Tdmaz 

Solve linear equations by TDMA algorithm in X, Y and Z 

directions, respectively; 

Plotvt Create TECPLOT data files; 

Prvari Output CFD results to the RET files. 

Note: Niter is the current number of iterations. 

A.6 Description of Variables Used in the CFD0-C Code

This section describes the global variables used in the source code of CFD0-C. 

• TITLE - a character variable, (dimension defined by LINELEN, default, up to 144 

characters), for the title of the simulated case. 

• XX, YY, ZZ - real variables for the flow domain in the X, Y, and Z direction, 

respectively. Note that the gravitational force is always in the negative z-direction. 

For a two-dimensional case, use 0.0 m for the third dimension, but the program 

will adjust it to 1.0 m automatically. 

• NNX, NNY, NNZ - the number of control volumes (grids) in the x-, y-, and zdirection, respectively. 

• DELX, DELY, DELZ - the arrays that store the dimension for each control 
191 

volume (grid size) in the X, Y, and Z direction, respectively. The sum of all the 

control volumes in the x-direction must be equal to XX. The same rule applies to 

YY and ZZ. 

• X, Y, Z - the arrays that contain the coordinates for the grid nodes (control 

volume centers). 

• AREX, AREY, AREZ - the arrays that store the surface area for each control 

volume normal to the x-, y-, and z-axis, respectively. 

• VOL - a three-dimensional array with volume size for each control volume. 

• NBIN - the total number of the inlet openings. This number should be equal or 

less than ten. 

• LBIN - an array to define the location of an inlet opening by the first and last 

control volume occupied by the inlet in the x-direction, the first and last control 

volume occupied by the inlet in the y-direction, and the first and last control 

volume occupied by the inlet in the z-direction, respectively. For a twodimensional inlet, the third direction is represented by the two same numbers. If 

the inlet opening is on the x=0 wall, use 1, 1 for instance. The inlet must be on a 

wall not in the flow domain. 

• UBIN, VBIN, WBIN - the arrays that store inlet velocities in the x, y and z 

direction, respectively. 

• AMASSIN - an array for the mass flows through the inlet. 

• TBIN - an array for the inlet temperature. 

• NBOUT - the total number of the outlet openings. This number should be equal or 

less than ten. 

• LBOUT - an array that defines location of the outlet openings in the same way as 

that for LBIN. Outlet openings are treated as two-dimensional objects that can be 

placed on the enclosure walls. Hence, rules explained for the definition of location 

for inlet openings also apply for the outlet opening. 

• VBOUT - an array for the outlet velocity. The values should be set in accordance 

with mass continuity. 

• TBOUT - an array for the outlet temperature. These values should be set as close 
192 

as possible to the real value. The outlet temperature and velocity have an impact 

on the convergence speed. 

• NBL - the total number of the blockages used in the flow field. The blockages are 

usually used for furniture, lights, occupants, partition walls, etc. This number 

should be equal or less than fifty. 

• IBL - an array that defines positions for each blockage in the same way as LBIN. 

The blockages are always three-dimensional and must be in the flow domain. 

• HSOU - an array that stores the heat generated by each blockage. 

• NAWT - the total number of the enclosure surfaces with a constant temperature. 

The maximum number of the non-adiabatic surfaces is fifty. 

• LNAW - an array that defines the positions for the surfaces in the same way as 

that for LBIN. The definition of the location has the same restrictions as for the 

inlets. 

• TNAW - an array for the temperature of the non-adiabatic walls. 

• NAWQ - the total number of enclosure surfaces with constant heat flux. The 

maximum number of the non-adiabatic surfaces is fifty. 

• LNAWQ - an array that defines the positions of the enclosure areas with heat 

flux. The definition of the location has the same restrictions as for inlet openings. 

• QNAW - an array for the heat from the non-adiabatic walls 

• NITMAX - the maximum iteration number for the run. 

• CRITE - a convergence criterion. The computation ends when the total residual is 

smaller than CRITE or when the maximum iteration number is reached. 

• LAMIN - a logical variable to identify if the flow is laminar (true) or turbulent 

(false) 

• ITUR - a parameter to select turbulence model. When ITUR=0, the zero-equation 

model is used. When ITUR=1, the standard k- model (Launder and Spalding 

1974) is used. However, the standard k- model may not work properly at 

present. 

• TINIT - an initial value for the temperature field. The initial velocities are 

internally set to zero. 
193 

• TM - the reference temperature 

• UMIN, UMAX, VMIN, VMAX, WMIN, WMAX, TMIN, TMAX - the minimum 

and maximum values for U, V, W, and T, respectively, during the solving 

procedure. This will help the solution because the values will not run out of 

control during the iteration. Those ranges, however, should be wide enough. 

• URFP, URFU, URFV, URFW, URFT - the linear under-relaxation factors for P, 

U, V, W, and T, respectively. The value of these factors should be between 0 and 

1. A value of 1 implies no relaxation. A lower value will slow the convergence 

but will stabilize the calculation. 

• DTU, DTV, DTW, DTT - the false time steps for U, V, W, and T, respectively. 

The false time steps work in a similar way as the linear under-relaxation factors. 

However, the range of the false time steps can be from 10-30 to 1030. A large 

value means no relaxation and a small value implies heavy relaxation. The false 

time steps can be increased one order higher or lower in the calculation to achieve 

a converged solution. 

• ISTEP - the iteration number when the new false time step to be used. In some 

cases, it is possible to speed up the convergence by changing values of the false 

time steps during the calculation. 

• CDTU, CDTV, CDTW, CDTT - new false-time-step values for U, V, W, and T, 

respectively. As a rule of thumb they can be used one order higher than those set 

for DTU, DTV, DTW, DTT. 

• PINTV - a real variable setting the printing frequency for the residuals during the 

calculation 

• IMON, JMON, KMON - the grid number in the x-, y-, and z-direction, 

respectively, for the monitoring point. When the values of the variables at the 

monitoring grid do not change significantly, a converged solution is reached. 

• IREF, JREF, KREF - the grid number for the reference point. It should not be 

inside a blockage. 

• IP1, IP2, IPSTP - The number of the first control volume, last control volume and 

interval for printing results in the x-direction. 
194 

• JP1, JP2, JPSTP - The number of the first control volume, last control volume and 

interval for printing results in the y-direction 

• ICOMPU - Set to 0 if not starting from the previous results and set to 1 if starting 

from the previous results 

• DENS - Fluid density (kg/m3) 

• ANU - Fluid kinematic viscosity (m2/s) 

• AK - Fluid thermal conductivity (W/m K) 

• ACP - Fluid specific heat at constant pressure (J/kg K) 

• PRL - Fluid Prandtl number 

A.7 Description of Formats of Binary Output Files

The following rules are used to describe the formats of the binary files. 

• There are no separations between any pair of data values, such as Space, Comma, 

and Period etc. 

• The description of data formats and other explanations are bracketed and are not 

output information of the binary file. 

The Format of the VAR File

(From the first grid in X direction, I1, to the last grid in X direction, IMAX, repeats the 

following) 

(From the first grid in Y direction, J1, to the last grid in Y direction, JMAX, 

repeats the following) 

(From the first grid in Z direction, Z1, to the last grid in Z direction, 

ZMAX, repeats the following) 

U (velocity in X direction at i, j, k; double) 

V (velocity in Y direction at i, j, k; double) 

W (velocity in Z direction at i, j, k; double) 

P (pressure at i, j, k; double) 

T (temperature at i, j, k; double) 
195 

VIS (effective turbulence viscosity at i, j, k; double) 

The Format of the EWC File

Fig. A.7 shows the output domain, for which CFD0-C creates the EWC, WDB, and CDB 

files. For a detailed explanation of the data format, please refer to the function in 

FLOW.C, void makeewc() . 

Fig. A.7 The flow domain inside the dashed box is output to create the EWC, WDB, and 

CDB files (note that Point O is the origin of the output domain, at which xref, yref, zref is 

the ordinates relative to the whole CFD domain). 

The Format of the WDB File

(The WDB file is created by the same function as that for the EWC file in FLOW.C, void 

makeewc(), except that “COUPLEWPP=1”. Please refer to the FLOW.C source code 

for the data and binary file format.) 

The Format of the CDB File

(The CDB file is created by the function in FLOW.C, void makecdb(), which uses very 

similar data and file formats to that of the WDB file. Please refer to the FLOW.C source 

code for details.) 

O (Reference point) 

nmax[2] 

nmax[0] CFD domain 

Output domain 
196 

Appendix B. Manual for the Coupled CONTAM-CFD0C Program 

The coupled CONTAM-CFD0C program will embed CFD simulations of selected zones 

in the multizone calculations of airflow network. The two programs can iteratively 

exchange airflow rates or pressure boundary conditions with each other. A resistance 

model can also be specified for the paths connecting multizone and CFD zones. A 

coupling definition file, *.CPL, is needed to provide required control parameters for a 

coupled simulation. The coupled program will also create an output file, *.CMO, which 

contains intermediate convergence information and final calculation results. Users can 

check the results also from CONTAMW or the output files of CFD0-C. 

B.1 Preparation of an Definition File for a Coupled Simulation

An ASCII coupling definition file, *.CPL, is required to specify which zone is the CFD 

zone, what methods should be used for airflow paths connecting multizone and CFD 

zones, and coupling control parameters. It can be prepared and edited manually by 

following the file format as the next. Users may want to edit the provided 

sample/template file for their own simulations. Note that all the input data values must be 

separated by comma. Some more explanations can be found in the notes at end of this 

section. 

Lines Input Data

The first three lines: Notation lines 

The next one line[NOTE1]: Total number of CFD zones, Running mode of the coupled 

simulation (0=Quasi coupling; 1=Dynamic coupling; 

2=Post-processing; 3=CFD only; 4=CONTAM only), 

Coupled contaminant transport simulation (0=No; 

1=Steady state; 2=Transient state), Contaminant index 

number in CFD simulation (only needed for coupled 

contaminant transport simulation), Calculate Contaminant 
197 

transport from a previously-calculated CFD airflow data 

file? (0=No; 1=Yes) 

Repeat the following section for each CFD zone 

{ 

The next two lines: Notation lines 

The next one line: Zone index number in CONTAM, Total number of coupled 

airflow paths for this zone (all airflow paths of the CFD 

zone should be included) 

 Repeat the following section for each coupled airflow path of this zone [NOTE2]

{ 

The next two lines: Notation lines 

The next one line: Airflow index number in CONTAM, large or small 

opening (1=Small; 2= Large), Type of boundary condition 

for CFD0 run provided by CONTAM (0=Constant mass 

airflow rate; 1=Mass airflow rate, which is variable during 

the coupling iteration; 2=Constant pressure condition; 

3=Pressure condition, which is variable during the coupling 

iteration), Type of boundary condition for CONTAM run 

provided by CFD0 (0=Change the flow coefficient in 

CONTAM, based on algorithm of Gao (2002; 2003); 

1=Pressure condition, which is local value near airflow 

path in the CFD zone; 2=Mass airflow rate, which is 

variable during the coupling iteration; 3=No feed back 

from CFD0 for CONTAM) 

} 

} 

The next two lines: Notation lines 

The next one line[NOTE3]: Reference zone (0=the ambient; index number if it is a zone 

other than the ambient zone) 
198 

The next two lines: Notation lines 

The next one line[NOTE4]: Maximum coupling iterations (for dynamic/direct coupling 

only); Output intermediate coupling results to the CMO 

file? (0=No; 1=Yes; 2=dump intermediate results of 

coupled transient contaminant dispersion simulations), 

Clear allocated internal memory for CFD0 simulation? 

(1=Yes; 0=No), Step for output the CMO file 

NOTE

[1] The current version of the coupled program is only tested for the coupled simulation 

with only one CFD zone. Further tests are needed for more than one CFD zones. 

Quasi coupling means the coupled program running in a mode of “CONTAM-CFD0-

CONTAM”, which involves no further coupling iterations between the two programs. 

Dynamic coupling is the direct coupling of CONTAM and CFD0, for which the running 

mode is “CONTAM-CFD0-CONTAM” with iterations until the coupling convergence 

criterion is met, i.e. the exchanged boundary conditions stabilize. 

The mode of Post-processing means “CONTAM-CFD0”, in which CFD0 simply obtains 

boundary conditions from CONTAM without feeding back information or further 

coupling iterations. 

In the CFD-only running mode, CFD0 will be run as a stand-alone program. That is to 

say, CFD0 will read the boundary conditions from the CFD input file, *CFD, instead 

obtaining them from CONTAM. There are no actual coupling between CONTAM and 

CFD0. 

In the CONTAM-only running mode, CONTAM will be run as a stand-alone program 

without calling CFD0. The modes of CFD-only and CONTAM-only are for advanced 

purposes such as debugging the codes etc. 
199 

Contaminant index number refers to the contaminant species simulated by the coupled 

simulation. Since the current version of the coupled program can simulate only one 

contaminant species at one time, users must specify which contaminant species needs to 

be calculated if multiple species (≤5) are defined in CFD0. 

Users can calculate contaminant transport from a previously-calculated CFD0 airflow 

data file, i.e. the VAR file. This is useful for coupled simulations of steady-state airflow 

and steady-state contaminant transport, or steady-state airflow and transient contaminant 

transport. For transient airflow and transient contaminant transport, this option means that 

the VAR file is used as an initial airflow conditions. 

[2] The coupled airflow paths must be defined in the CPL file in the same order as they 

are defined in the CFD input file, the CFD file. 

Large or small opening refers to how to consider the flow resistance in CFD0. For details, 

refer to the manual of CFD0-C. It is considered that for large openings, conventional 

CFD methods of implementing pressure boundary conditions should be used. That is to 

say, pressure boundary condition is looked at as stagnation pressure for inflow opening 

and as static pressure for outflow opening (Kelka and Choudhury, 2000). For small 

openings, a power-law resistance model can be specified for CFD0 simulation by flow 

coefficient and exponent, if it is considered necessary and appropriate. 

For CFD0 run, CONTAM can provide several different boundary conditions. Constant 

mass airflow rate is for fans or other devices with fixed mass flow rates. For the cases, 

where mass flow rates are calculated, variable mass flow rate condition should be used. If 

an airflow path of the CFD zone is connected to the ambient or a zone with known 

pressure, constant pressure condition should be used. For the rest cases with pressure 

boundary conditions, pressures are calculated so that variable pressure condition should 

be used. 
200 

For CONTAM run, CFD0 can feed back several boundary conditions too. The method of 

“change the flow coefficient” is suggested by Gao (Gao, 2002; 2003), which needs to be 

further validated. The rest two methods, “pressure condition” and “mass airflow rate”, are 

the methods suggested by this study, which should be used for common users. For 

example, the method of “Pressure-Pressure” coupling for a large opening with an index 

number 12 should use the following definition: 12,2,3,1 if it is not connected to the 

ambient, or 12,2,2,1 if it is connected to ambient or a zone with known pressure. One 

more example, for a fan with constant mass flow rate and index number 5 in CONTAM, 

users should use 5,1,1,3 or 5,2,1,3. Here, it is not important if the fan is considered large 

opening or small opening since there are no resistance model needed for a fan. 

[3] The specification of reference zone is needed to obtain reference temperature, 

reference density values for CFD simulations. It is suggested to use the ambient zone as 

the reference zone. 

[4] The maximum coupling iteration is used to end the coupled simulation if the coupling 

convergence criterion is not met after a long run. The output of intermediate results to the 

CMO file and The function of clearing allocated internal memory are for debugging 

purposes. It is suggested use No for both options. A frequent output to the CMO file will 

result in a big file size. Therefore, it is suggested to use a big value of the output step, for 

example, 50 or 100. 

B.2 The Output File of a Coupled Simulation

A output file, the CMO file, will be created to provide intermediate results for debugging 

purposes, and final results of convergence of a coupled simulation. 

Format Description of Intermediate Output in a CMO File (Optional Output)

● In a CMO file: Path, Outlet?, Flow1, Flow2, Pbc1, Pbc2, Coe, Exp 
201 

Explanation: 

Path: coupled airflow path index number; 

Outlet?: is it an outlet or inlet? 1=outlet; 0=inlet, as related to the CFD zone; 

Flow1: CONTAM-calculated mass airflow rate at the previous coupling iteration; 

Flow2: CONTAM-calculated mass airflow rate at the current coupling iteration; 

Pbc1: CONTAM-calculated pressure boundary conditions at the previous coupling 

iteration; 

Pbc2: CONTAM-calculated pressure boundary conditions at the current coupling 

iteration; 

Coe: linearized flow coefficient of the airflow path 

Exp: exponent of the resistance model of the airflow path 

● In a CMO file: FlowBC, Pbc, Coe, Exp, udrl

Explanation: 

FlowBC: boundary condition of mass flow rate, which is provided by CONTAM for 

CFD0 

Pbc: pressure boundary condition, which is provided by CONTAM for CFD0 

Coe: linear flow coefficient used in CFD0 simulation 

Exp: flow exponent of the resistance model used in CFD0 simulation 

udrl: under-relaxation factor used in exchanging boundary conditions 

● In a CMO file: Path, Outlet?, Cmass1, Cmass2, Pcfd1, Pcfd2, Coe, Exp, Mult, 

Crate1, Crate2

Explanation: 

Path: airflow path index number 

Outlet?: is it an outlet or inlet? 1=outlet; 0=inlet, as related to the CFD zone; 

Cmass1: CFD0-calculated mass flow rate at the previous coupling iteration; 

Cmass2: CFD0-calculated mass flow rate at the current coupling iteration; 
202 

Pcfd1: CFD0-calculated local pressure near the airflow path at the previous coupling 

iteration; 

Pcfd2: CFD0-calculated local pressure near the airflow path at the current coupling 

iteration; 

Coe: linear flow coefficient used in CFD0 simulation 

Exp: flow exponent of the resistance model used in CFD0 simulation 

Mult: correction of the multiplier for implementation of local pressures in CONTAM 

Crate1: CFD0-calculated contaminant mass flow rate through the airflow path at the 

previous coupling iteration; 

Crate2: CFD0-calculated contaminant mass flow rate through the airflow path at the 

current coupling iteration; 

● In a CMO file: CONTAM Time: XXX, CFD0 TIME: XXX 

 path XXX

 : XXXXXX[kg/s] XXXXXX[kg/kg] 

Explanation: 

CONTAM Time: current simulation time in CONTAM for debugging purposes; 

CFD0 Time: current simulation time in CFD0 for debugging purposes; 

path: airflow path index number involved in coupled contaminant dispersion 

simulation followed by CFD0-calculated contaminant mass flow rate [kg/s] 

transferred to CONTAM as contaminant source through the coupled airflow paths 

and CFD0-calculated local contaminant concentration [kg/kg] transferred to 

CONTAM. 

Format Description of Final Output in a CMO File (Normal Output)

● In a CMO file: Path CPL CFD0_NITER Coe_CONTAM Exp_CONTAM 

PressureB_CONTAM PressureB_CFD0 Mass_CONTAM Mass_CFD0 

PressureL_CFD0 Pressure_ext_CFD0 
203 

Explanation: 

Path: index number of coupled airflow path; 

CPL: Coupling iteration number 

CFD0_NITER: total internal iterations of CFD0 to achieve CFD convergence at 

current coupling iteration 

Coe_CONTAM: corrected flow coefficient at current coupling iteration in 

CONTAM for this path 

Exp_CONTAM: flow exponent of this path at current coupling iteration in 

CONTAM 

PressureB_CONTAM: pressure boundary condition calculated by CONTAMCFD0 

for CFD0 at current coupling iteration 

PressureB_CFD0: actual pressure boundary condition used in CFD0 simulation, 

which could be different from PressureB_CONTAM due to possible under-relaxation. 

By default, they are the same. 

Mass_CONTAM: mass flow rate calculated by CONTAM; 

Mass_CFD0: mass flow rate calculated by CFD0 

PressureL_CFD0: local pressure, i.e. pressure boundary condition, calculated by 

CFD0 

Pressure_ext_CFD0: flow coefficient should be corrected for the next CONTAM 

run in order to achieve the goal of Mass_CONTAM=Mass_CFD0. 

B.3 Modifications in CONTAMX and CFD0-C for the Coupled Program

Advanced users can compile the coupled source codes if needed. First, users need to 

change the first line of FLOW.C from “#define FLOWC 1” to “#define FLOWC 0”. 

Then, they can copy flow.c, comflo.h, fprtype.h and other two files, couple.c and 

interface.h, into the directory of the source codes of CONTAMX and recompiled all 

source files to get the executable of the coupled CONTAM-CFD0 program. Note that the 

version of coupled source codes works with the CONTAM version of CONTAM2.4b 

dated at August 2006 or prior ones. 
204 

This appendix shows the changes (in italic fonts) made to the CONTAMX source code 

for the coupling with CFD0-C. The purposes for these changes are explained in the 

brackets after the line number. Advanced users can always search “//coupling” through 

all the source code files to find where the modifications are needed in CONTAMX. 

• WndProc.c (for the WPC link in order to create the WPC file in the same directory 

with the EWC file, the following codes in ‘WndProc.c’ were changed in the 

CONTAM source codes) 

▪ Line 29 

I1 _wpcdrive[_MAX_DRIVE]; /* drive letter for WPC file */ 

I1 _wpcdir[_MAX_DIR]; /* directory path for WPC file */ 

▪ Line 1562 

if( streql( _PLDdat.WPCfile, "null" ) ) 

{ 

pathsplit(_PLDdat.EWCfile, _wpcdrive,_wpcdir,_string,_stringx); 

pathmerge( _PLDdat.WPCfile, _wpcdrive, _wpcdir, _prjname, ".WPC" ); 

} 

• contamx.c 

▪ Line 45: (the following line added to call function cplloop(), a function in 

coupling data interface, within CONTAMX) 

extern IX cplloop(); 

▪ Line 371: (the following line added a label in CONTAMX to form a coupling 

loop within CONTAMX together with the next changes in Line 482) 

L200:

▪ Line 482: (the following line and the previous Line 371 form a loop within 

CONTAMX for the coupling) 

if(COUPLE) 
205 

 { 

 if(cplloop()) goto L200; 

 } 

• heap.c (some new functions added for 3D arrays allocation in CFD0, they are: alc_ac, 

chk_ac and fre_ac ) 

▪ Functions of dynamic allocation of 3D arrays for CFD0 

• simulate.c 

▪ Line 35: (the following line added to call incontam_loc() in CONTAMX, a 

function to change the local pressure of the paths in the pressure-pressure 

coupling. Pressure-pressure coupling was tried but not stable so there are no too 

many discussions in this thesis.) 

extern void incontam_loc(); 

▪ Line 36: (the following line added to introduce a variable ‘_cpl’, which used to 

control whether to do coupling in CONTAMX) 

extern _cpl; 

▪ Line 728: (the following line added to run the function ‘incontam_loc()’ in 

CONTAMX for the pressure-pressure coupling) 

if(_cpl) incontam_loc(); 

▪ Line 748: (the following line added to run the function ‘incontam_loc()’ in 

CONTAMX for the pressure-pressure coupling, the difference between it and 

the last one is that this is for another case in CONTAMX, that is when the 

height difference of the path is less than 0.001) 

if(_cpl) incontam_loc(); 
206 

• prtyp.h 

▪ Line 85- Line 87: (the following lines added to declare the functions added in 

the heap.c, which are for 3D array allocations) 

void *alc_ac( IX, IX, IX, IX, IX, IX, IX, I1 * ); 

void chk_ac( void *, IX, IX, IX, IX, IX, IX, IX, I1 * ); 

void *fre_ac( void *, IX, IX, IX, IX, IX, IX, IX, I1 * ); 

 

• sglob.h 

▪ Line 278: (the following lines added to declare another control variable about 

whether to do coupling or not in CONTAMX. It is a global variable.) 

#define COUPLE 1 //couple or not?
207

CONTAMX

prj_read

(read PRJ file)

run_read

(read control /weather etc.)

leve l_read

(read leve l Data)

wind_read

(read wind data)

afe lmt_read

(read airflow and duct 

element data)

system_read

(read AHS data)

zone_read

(read zone data)

path_read

(read path data)

sim_data

(create simulation data)

mat_init

(allocate simulation arrays)

se t_usim&se t_usum

(open output file s)

sim_init

(simulation 

initialization/steady 

simulation)

solveAfstr

(solve building airflows)

calc_wP

(calculate wind pressure s)

calc_sP

(calculate stack pressure s)

init_Af

(initialize node pre ssures)

fillAf

(fill the Jacobian matrix)

solve_slae

([A] {X} = {B} update node and path 

pressure s)

return jacFacs

(return number of ite rations)

ChkCnvgAf

(converge?)

fillAf

(fill the Jacobian matrix)

ChkCnvgAf

(converge?)

jacFacs <= mat->itmax (max 

iterations reached?)

solve_DE

( solve steady contaminants)

simout

(simulation output)

de-allocate simulation 

arrays

End

transient?

sim_loop

(unsteady simulation)

START

No

Yes

Yes

Yes

No

No

No

Yes

return 0

(if no error)

return 1

(if no e rror)

First level

Second level

Third level

Note: a closed level forms a subroutine 

of the upper level

Second level Second level Third level

Fig. B.1 Program structure of CONTAMX 2.
208 

Appendix C. Examples of Input Files 

CFD0-C Input File for Flow in the 90-degree Planar Branch with Re=400 in Chapter 

4.1.1 

'2D-RE-400' 

------------------------------- 

------------------------------------- 

Problem Definition 

------------------------------------- 

Velocity steady? (1=YES,0=NO),Contaminant steady?(1=YES,0=NO) 

1, 1 

Time step, Max time, Residue of concentration computation, Maximum iterations 

1, 5, 0.000001, 2000 

Energy (compute energy equation?) 

0 

Contaminant (compute contaminant?); number of contaminants; start from a velocity 

file? 

0, 0, 0 

Convergence criterion for flow, The maximum iteration number 

 0.00001,10000 

Is the flow laminar? 

 T 
209 

------------------------------- 

GEOMETRY, MESH AND BOUNDARY CONDITIONS 

-------------------------------- 

Size of the enclosure 

X(L) Y(W) Z(H) 

 0.05, 0.093, 0. 

Number of control volumes in three directions 

 x y z 

 30, 58, 0 

Size of control volumes 

x direction 

.001 .001 .001 .001 .001 .001 .001 .001 .001 .001 

.002 .002 .002 .002 .002 .002 .002 .002 .002 .002 

.002 .002 .002 .002 .002 .002 .002 .002 .002 .002 

y direction 

.002 .002 .002 .004 .004 .004 .002 .002 .002 .002 

.002 .002 .002 .002 .002 .002 .002 .002 .002 

.001 .001 .001 .001 .001 .001 .001 .001 .001 .001 

.001 .001 .001 .001 .001 .001 .001 .001 .001 

.001 .001 .001 .001 .001 .001 .001 .001 .001 .001 

.002 .002 .002 .002 .002 .002 .002 .002 .002 .002 

z direction 

0.0 

Total number of openings 

 1, 2 
210 

THe control volumes covered by inlet opening 

in x direction 

1, 10 

in y direction 

1, 1 

in z direction 

1, 1 

Inlet velocity and temperature 

1,1,0, 0.6, 0, 0.0, 20 

The control volumes covered by outlet opening 

in x direction 

1, 10 

in y direction 

58, 58 

in z direction 

1, 1 

outlet velocity and temperature 

2,2,0.0,0.0,0.0,20. 

The control volumes covered by outlet opening 

in x direction 

30, 30 

in y direction 

21, 30 

in z direction 

1, 1 

outlet velocity and temperature 

2,2,0.0,0.0,0.0,20. 
211 

Total number of blockages 

2 

Block 1 

in x direction 

11, 30 

in y direction 

1, 20 

in z direction 

1, 1 

heat flux 

1,0 

Block 2 

in x direction 

11, 30 

in y direction 

31, 58 

in z direction 

1, 1 

heat flux 

1,0 

TOtal number of non-adiabatic walls given by T=const. 

 0 

Total number of non-adiabatic walls given by Q=const 

 0 

------------------------------- 
212 

CONTROL PARAMETERS 

------------------------------ 

Differential schems for u,v,w,t,c(1=Upwind,2=Power law) 

 1,1,1,1,1 

 

Inital value for T, reference value for T 

20.0, 20.0 

Buoyancy?(use Bousinesq?) 

1 

Limits UMIN,UMAX, VMIN,VMAX, WMIN,WMAX, TMIN,TMAX 

 -10.0,10.0, -10.0,10.0, -10.0,10.0, 0.0,80.0 

Linear relaxations URFU,URFV,URFW,URFP,URFT,URFEK,URFED,URFC 

 0.1, 0.1, 0.1, 0.9, 0.6, 1.0, 1.0,0.6 

False-time step DTU DTV DTW DTT DTEK DTED DTC 

.125, .125, .125, 30, 1E+30, 1E+30,30 

Is there step chance for the false-time step relaxation? 

T 

Step change: Iter., DTU, DTV, DTW, DTT, DTEK, DTED DTC 

 300, 2.0E00, 1.0E00, 2.0E00, 3.0E+2, 1.0E30, 1.0E30,300 

Printing frequency for the residuals during the calculation 

 5.0 
213 

Monitoring point during the calculation 

2,5,2 

Reference point 

21,5,5 

Printing Ifirst,Ilast,Istep, Jfirst,Jlast,Jstep 

 1, 20, 2 1, 18, 5 

Do you want to restart the calculation? (0-no, 1-yes), creat EWC file? create CFDLOG 

file? 

 0,0,1 

--------------------------- 

MATERIAL PROPERTIES FOR AIR 

--------------------------- 

 pressure ambient 

 101325.0 

 reference density 

 1.2 

 operating density 

 1.2 

 kinematic-visc. 

 1.513E-5 

 conductivity 

 0.0262 

 speficit heat at constant pressure 

 1005.6 

 laminar Prandtl number 
214 

 0.71 

CFD0-C Input File for Displacement Ventilation in Chapter 4.1.3

'DISPLACEMENT VENTILATION' 

------------------------------------- 

------------------------------------- 

Problem Definition 

------------------------------------- 

Velocity steady? (1=YES,0=NO),Contaminant steady?(1=YES,0=NO) 

1,1 

Time step, Max time, Residue of concentration computation, Maximum iterations 

1,100,0.000001,2000 

Engergy(compute energy equation?) 

1 

Contaminant (compute contaminant?); number of contaminants; start from a velocity 

file? 

1,1,0 

Convergence criterion for flow, The maximum iteration number 

 0.001, 3000 

Is the flow laminar? 

 F 
215 

Turbulence model: simple (0) or k-e model (1) 

 0 

 

------------------------------------- 

GEOMETRY, MESH AND BOUNDARY CONDITIONS 

-------------------------------------- 

Size of the enclosure 

X (L) Y(W) Z(H) 

 5.16, 3.65, 2.43 

Number of control volume in three directions 

x y z 

 25, 18, 16 

Size of control volumes 

 in x direction 

0.12 0.23 0.23 0.23 0.22 0.20 0.25 0.25 0.25 

0.20 0.20 0.20 0.20 0.15 0.20 0.20 0.20 0.20 

0.24 0.24 0.25 0.25 0.20 0.15 0.10 

 in y direction 

0.10 0.15 0.20 0.13 0.17 0.20 0.35 0.20 0.11 

0.21 0.22 0.31 0.35 0.20 0.30 0.20 0.15 0.10 

 in z direction 

0.10 0.25 0.25 0.10 0.05 0.09 0.10 0.16 0.14 

0.10 0.20 0.28 0.28 0.13 0.10 0.10 

Total number of openings 

 1, 1 
216 

The control volumes covered by inlet opening 

 in x direction 

 1, 1 

 in y direction 

 9, 11 

 in z direction 

 1, 8 

 Inlet velocity and temperature 

 2,1,0.086, 0.0, 0.0, 0.0, 17.0 

 

The control volumes covered by outlet opening 

 in x direction 

 12, 13 

 in y direction 

 10, 11 

 in z direction 

 16, 16 

 Outlet velocity and temperature 

 2,2,0.0,0.0,0.0,26.7 

 

Total number of blockages 

 16 

Table 1 

 in x direction 

 3, 12 

 in y direction 

 1, 5 

 in z direction 

 5, 5 
217 

 heatflux 

 1,0.0 Table 2 

 in x direction 

 15, 25 

 iny direction 

 15, 18 

 in z direction 

 5, 5 

 heatflux 

 1,0.0 Cabinet 1 

 in x direction 

 1, 2 

 iny direction 

 1, 4 

 in z direction 

 1, 10 

 heatflux 

 1,0.0 Cabinet 2 

 in x direction 

 21, 25 

 iny direction 

 1, 4 

 in z direction 

 1, 9 
218 

 heatflux 

 1,0.0 Computer 1 

 in x direction 

 10, 11 

 iny direction 

 2, 3 

 in z direction 

 6, 8 

 heatflux 

 1,108.5 Computer 2 

 in x direction 

 16, 17 

 iny direction 

 16, 17 

 in z direction 

 6, 8 

 heatflux 

 1,173.4 Person 1 

 in x direction 

 10, 11 

 iny direction 

 7, 7 

 in z direction 

 1, 8 
219 

 heatflux 

 1,75 Person 2 

 in x direction 

 16, 17 

 iny direction 

 13, 13 

 in z direction 

 1, 8 

 heatflux 

 1,75 Lamp 1 

 in x direction 

 6, 6 

 iny direction 

 2, 7 

 in z direction 

 15, 15 

 heatflux 

 1,34.0 Lamp 2 

 in x direction 

 12, 12 

 iny direction 

 2, 7 

 in z direction 

 15, 15 
220 

 heatflux 

 1,34.0 Lamp 3 

 in x direction 

 18, 18 

 iny direction 

 2, 7 

 in z direction 

 15, 15 

 heatflux 

 1,34.0 Lamp 4 

 in x direction 

 6, 6 

 iny direction 

 13, 17 

 in z direction 

 15, 15 

 heatflux 

 1,34.0 Lamp 5 

 in x direction 

 12, 12 

 iny direction 

 13, 17 

 in z direction 

 15, 15 
221 

 heatflux 

 1,34.0 Lamp 6 

 in x direction 

 18, 18 

 iny direction 

 13, 17 

 in z direction 

 15, 15 

 heatflux 

 1,34.0 

 Tracer

gas1 

 in x direction 

 11, 11 

 iny direction 

 6, 6 

 in z direction 

 9, 9 

 heatflux 

 2,0.0,1 

 1,0.013 

 Tracer

gas2 

 in x direction 

 17, 17 

 iny direction 

 16, 16 

 in z direction 
222 

 9, 9 

 heat flux 

 2,0.0,1 

 1,0.013 

 

Total number of non-adiabatic walls given by T=const. 

 12 

Ceiling - first part 

 in x direction 

 1, 12 

 in y direction 

 1, 18 

 in z direction 

 16, 16 

 temperature 

 25.3 

Ceiling - second part 

 in x direction 

 13, 25 

 in y direction 

 1, 18 

 in z direction 

 16, 16 

 temperature 

 26.0 

Floor - first part 

 in x direction 
223 

 1, 12 

 iny direction 

 1, 18 

 in z direction 

 1, 1 

 temperature 

 22.4 Floor - se

cond part 

 in x direction 

 13, 25 

 iny direction 

 1, 18 

 in z direction 

 1, 1 

 temperature 

 24.5 East wall

- parapet 

 in x direction 

 25, 25 

 iny direction 

 1, 18 

 in z direction 

 1, 7 

 temperature 

 24.4 East wall

-window 

 in x direction 
224 

 25, 25 

 iny direction 

 1, 18 

 in z direction 

 8, 13 

 temperature 

 27.7 

 E

astwall-abovethewindow 

 in x direction 

 25, 25 

 iny direction 

 1, 18 

 in z direction 

 14, 16 

 temperature 

 26.6 West wall

-abovetheinlet 

 in x direction 

 1, 1 

 iny direction 

 1, 18 

 in z direction 

 9, 16 

 temperature 

 25.4 North wall

-lower part 

 in x direction 
225 

 1, 25 

 iny direction 

 18, 18 

 in z direction 

 1, 7 

 temperature 

 23.9 North wall

- upper part 

 in x direction 

 1, 25 

 iny direction 

 18, 18 

 in z direction 

 8, 16 

 temperature 

 26.0 South wall

-lower part 

 in x direction 

 1, 25 

 iny direction 

 1, 1 

 in z direction 

 1, 7 

 temperature 

 23.9 South wall

- upper part 

 in x direction 
226 

 1, 25 

 in y direction 

 1, 1 

 in z direction 

 8, 16 

 temperature 

 26.0 

Total number of non-adiabatic walls given by Q=const. 

 0 

--------------------------------- 

CONTROL PARAMETERS 

--------------------------------- 

Differential schems for u,v,w,t,c(1=Upwind,2=Power law) 

 1,1,1,1,1 

Initial value for T, reference value for T 

 22.0, 22.0 

 

Buoyancy?(use Bousinesq?) 

1 

Limits UMIN,UMAX, VMIN,VMAX, WMIN,WMAX, TMIN,TMAX 

 -4.0, 4.0, -4.0, 4.0, -4.0, 4.0, 0.0, 80.0 

Linear relaxations URFU,URFV,URFW,URFP,URFT,URFEK,URFED,urfc 

 0.1, 0.1, 0.1, 0.9, 0.6, 1.0, 1.0,0.6 
227 

False-time step DTU, DTV, DTW, DTT, DTEK, DTED 

 2.0E-1, 1.0E-1, 2.0E-1, 3.0E+1, 1.0E30, 1.0E30,30 

Is there step change for the false-time step relaxation? 

T 

Step change: Iter., DTU, DTV, DTW, DTT, DTEK, DTED 

 300, 2.0E00, 1.0E00, 2.0E00, 3.0E+2, 1.0E30, 1.0E30,300 

Printing frequency for the residuals during the calculation 

 5.0 

Monitoring point during the calculation 

10,2,10 

Reference point 

10,12,10 

Printing Ifirst,Ilast,Istep, Jfirst,Jlast,Jstep 

 1, 25, 1 1, 18, 1 

Do you want to restart the calculation? (0-no, 1-yes), creat EWC file? create CFDLOG 

file? 

 0,0,3 

--------------------------- 

MATERIAL PROPERTIES FOR AIR 

--------------------------- 

 pressure ambient 
228 

 101325.0 

 reference density 

 1.2 

 operating density 

 1.2 

 kinematic-visc. 

 1.513E-5 

 conductivity 

 0.0262 

 speficit heat at constant pressure 

 1005.6 

 laminar Prandtl number 

 0.71 

CFD0-C Input File for Cross Ventilation in a 4-Zone Building Model in Chapter 4.1.4

'Momentum driven air flow in 4Zone with cross ventilation 0Degree' 

------------------- 

------------------------------------- 

Problem Definition 

------------------------------------- 

Velocity steady? (1=YES,0=NO),Contaminant steady?(1=YES,0=NO) 

1,1 

Time step, Max time, Residue of concentration computation, Maximum iterations 

1, 5, 0.000001, 2000 

Energy (compute energy equation?) 
229 

0 

Contaminant (compute contaminant?); number of contaminants; start from a velocity 

file? 

0, 0, 0 

Convergence criterion for flow, The maximum iteration number 

0.001, 7000 

Laminar Flow? 

F 

Turbulence model: simple (0) or k-e (1) 

0 

----------------------- 

GEOMETRY, MESH, AND BOUNDARY CONDITIONS 

------------------------- 

Size of the enclosure 

X(L) Y(W) Z(H) 

 16.1, 15.5, 9.0 

Number of control volumes in three directions 

 x y z 

 50, 54, 32 

Size of control volumes 

x direction 

0.42 .45 .84 .84 
230 

0.84 0.84 0.42 0.3 0.1 0.05 0.05 

0.05 0.13 0.3 

0.42 0.42 0.42 0.42 

0.3 0.18 

0.1 0.025 

0.025 0.1 

0.18 0.3 

0.42 0.42 0.42 0.42 

0.3 0.13 0.05 

0.05 0.05 0.1 0.3 0.21 .21 .42 .42 .42 .42 

.42 .42 .42 .42 .42 .42 .3 

y direction 

.285 .42 .42 .42 .42 .42 

.615 .225 .42 .42 .21 .21 .3 .1 .05 .05 

0.05 0.13 0.3 

0.42 0.42 0.42 0.42 

0.3 0.18 

0.1 0.025 

0.025 0.1 

0.18 0.3 

0.42 0.42 0.42 0.42 

0.3 0.13 0.05 

0.05 0.05 0.1 0.3 0.21 .21 .42 .42 .225 .615 

.42 .42 .42 .42 .42 .285 

z direction 

0.25 0.25 

0.35 0.3 0.3 0.3 0.3 

0.19 0.14 0.2 0.21 0.16 0.05 

0.05 0.05 0.1 0.3 0.21 0.21 0.42 0.66 0.18 0.42 

0.42 0.42 0.42 0.42 0.42 0.42 0.42 .23 .23 
231 

Total number of openings 

 1, 1 

west-inlet 

in x direction 

1, 1 

in y direction 

8, 47 

in z direction 

1, 21 

Inlet velocity and temperature 

2,1,3.0, 0.0, 0.0,0.0,21.8,0 

east-outlet 

in x direction 

50, 50 

in y direction 

1, 54 

in z direction 

1, 32 

Inlet velocity and temperature 

2,1,1.022, 0.0,21.8,0 

Total number of blockages 

22 

west1 

in x direction 

12, 12 
232 

iny direction 

17, 19 in z direction 

3, 13 heat flux 

1,0 

west2 

in x direction 

12, 12 in y direction 

20, 21 in z direction 

9, 13 heat flux 

1,0 

west3 

in x direction 

12, 12 in y direction 

22, 27 in z direction 

3, 13 heat flux 

1,0 

west4 

in x direction 

12, 12 
233 

iny direction 

28, 38 in z direction 

3, 13 heat flux 

1,0 

east1 

in x direction 

33, 33 in y direction 

17, 27 in z direction 

3, 13 heat flux 

1,0 

east2 

in x direction 

33, 33 in y direction 

28, 33 in z direction 

3, 13 heat flux 

1,0 

east3 

in x direction 

33, 33 
234 

iny direction 

34, 35 in z direction 

9, 13 heat flux 

1,0 

east4 

in x direction 

33, 33 in y direction 

36, 38 in z direction 

3, 13 heat flux 

1,0 

south1 

in x direction 

12, 22 in y direction 

17, 17 in z direction 

3, 13 heat flux 

1,0 

south2 

in x direction 

23, 33 
235 

iny direction 

17, 17 in z direction 

3, 13 heat flux 

1,0 

north1 

in x direction 

12, 22 in y direction 

38, 38 in z direction 

3, 13 heat flux 

1,0 

north2 

in x direction 

23, 33 in y direction 

38, 38 in z direction 

3, 13 heat flux 

1,0 

roof 

in x direction 

12, 33 
236 

iny direction 

17, 38 in z direction 

13, 13 heat flux 

1,0 

x1 

in x direction 

12, 14 in y direction 

27, 28 in z direction 

3, 12 heat flux 

1,0 

x2 

in x direction 

31, 33 in y direction 

27, 28 in z direction 

3, 12 heat flux 

1,0 

y1 

in x direction 

22, 23 
237 

iny direction 

17, 19 in z direction 

3, 12 heat flux 

1,0 

y2 

in x direction 

22, 23 in y direction 

36, 38 in z direction 

3, 12 heat flux 

1,0 

c1 

in x direction 

19, 22 in y direction 

27, 28 in z direction 

3, 12 heat flux 

1,0 

c2 

in x direction 

23, 26 
238 

iny direction 

27, 28 in z direction 

3, 12 heat flux 

1,0 

c3 

in x direction 

22, 23 in y direction 

24, 27 in z direction 

3, 12 heat flux 

1,0 

c4 

in x direction 

22, 23 in y direction 

28, 31 in z direction 

3, 12 heat flux 

1,0 

floor 

in x direction 

12, 33 
239 

in y direction 

17, 38 

in z direction 

1, 2 

heat flux 

1,0 

Total number of non-adiabatic walls given by T=const 

0 

Number of adiabatic walls given by Q-const. 

0 

------------------------------- 

CONTROL PARAMETERS 

------------------------------ 

Differential schems for u,v,w,t,c(1=Upwind,2=Power law) 

 1,1,1,1,1 

Inital value for T, reference value for T 

21.8, 21.8 

Buoyancy? 

1 

Limits UMIN,UMAX, VMIN,VMAX, WMIN,WMAX, TMIN,TMAX 

 -5.0,5.0, -5.0,5.0, -5.0,5.0, 0.0,80.0 

Linear relaxations URFU,URFV,URFW,URFP,URFT,URFEK,URFED,URFC 
240 

 0.1, 0.1, 0.1, 0.9, 0.6, 1.0, 1.0,0.6 

False-time step DTU DTV DTW DTT DTEK DTED DTC 

15, 15, 1, 30, 1E+30, 1E+30,30 

Is there step chance for the false-time step relaxation? 

t 

 

Step change: Iter., DTU, DTV, DTW, DTT, DTEK, DTED, DTC 

 2000, 2.0E00, 2.0E00, 2.0E00, 3.0E+2, 1.0E30, 1.0E30,300 

Printing frequency for the residuals during the calculation 

 5.0 

Monitoring point during he calculation 

10,2,1 

Reference point 

10,12,1 

Printing Ifirst,Ilast,Istep, Jfirst,Jlast,Jstep 

 1, 20, 2 1, 18, 5 

Do you want to restart the calculation? (0-no, 1-yes) 

 0,0,3 

--------------------------- 

MATERIAL PROPERTIES FOR AIR 

--------------------------- 

 pressure ambient 
241 

 101325.0 

 ref density 

 1.198 

 oper den 

 1.198 

 kinematic-visc. 

 1.513E-5 

 conductivity 

 0.0262 

 speficit heat at constant pressure 

 1005.6 

 laminar Prandtl number 

 0.71 

An Example of The CPL File

This appendix demonstrates an example of the CPL file, coupling definition file. The 

selected case is the natural ventilation in a 3-story building with a large atrium with 

steady-state airflow and transient contaminant transport as discussed in Chapter 5.2.2. 

Couple CFD0C and CONTAM 

--------------------------------------------------------------- 

Coupled zones and types 

1,1,2,1,1 

Zone names to be coupled; number paths 

35,44 

Definition of coupled airflow path 
242 

1,1,3,1 

Definition of coupled airflow path 

13,1,3,1 

Definition of coupled airflow path 

17,1,3,1 

Definition of coupled airflow path 

19,1,3,1 

Definition of coupled airflow path 

41,1,3,1 

Definition of coupled airflow path 

45,1,3,1 

Definition of coupled airflow path 

47,1,3,1 

Definition of coupled airflow path 

69,1,3,1 

Definition of coupled airflow path 

73,1,3,1 

Definition of coupled airflow path 

75,1,3,1 

Definition of coupled airflow path 

63,1,3,1 
243 

Definition of coupled airflow path 

64,1,3,1 

Definition of coupled airflow path 

65,1,3,1 

Definition of coupled airflow path 

66,1,3,1 

Definition of coupled airflow path 

70,1,3,1 

Definition of coupled airflow path 

74,1,3,1 

Definition of coupled airflow path 

76,1,3,1 

Definition of coupled airflow path 

78,1,3,1 

Definition of coupled airflow path 

79,1,3,1 

Definition of coupled airflow path 

80,1,3,1 

Definition of coupled airflow path 

81,1,3,1 
244 

Definition of coupled airflow path 

2,1,3,1 

Definition of coupled airflow path 

7,1,3,1 

Definition of coupled airflow path 

8,1,3,1 

Definition of coupled airflow path 

9,1,3,1 

Definition of coupled airflow path 

10,1,3,1 

Definition of coupled airflow path 

14,1,3,1 

Definition of coupled airflow path 

18,1,3,1 

Definition of coupled airflow path 

20,1,3,1 

Definition of coupled airflow path 

22,1,3,1 

Definition of coupled airflow path 

23,1,3,1 
245 

Definition of coupled airflow path 

24,1,3,1 

Definition of coupled airflow path 

25,1,3,1 

Definition of coupled airflow path 

35,1,3,1 

Definition of coupled airflow path 

36,1,3,1 

Definition of coupled airflow path 

37,1,3,1 

Definition of coupled airflow path 

38,1,3,1 

Definition of coupled airflow path 

42,1,3,1 

Definition of coupled airflow path 

46,1,3,1 

Definition of coupled airflow path 

48,1,3,1 

Definition of coupled airflow path 

50,1,3,1 
246 

Definition of coupled airflow path 

51,1,3,1 

Definition of coupled airflow path 

52,1,3,1 

Definition of coupled airflow path 

53,1,3,1 

Reference Zone (0 if it is ambient,index number if it is a specifed zone) 

0 

Maximum couple iterations (for dynamic only); Output intermediate 

results?(1=Yes,0=No) 

300,0,0,1 
VITA
247 

VITA 

Liangzhu Wang was born in Handan, China on January 15, 1977. He obtained his B.S. in 

Thermal Engineering from Tianjin Institute of Urban Construction in 1999. With the 

highest total grade in the graduate entrance exams for Tianjin University, he joined the 

school of Civil Engineering and conducted researches on Heating, Ventilating, and Air 

Conditioning with the emphasis of building simulations of indoor environment and 

energy consumption. In 2002, he was awarded his M.S. at Tianjin University, where he 

also met his classmate and wife, Jinxia Liu. 

In August 2002, Liangzhu Wang joined the doctoral program of the school of Mechanical 

Engineering at Purdue University and worked as a research and teaching assistant under 

the guidance of Dr. Qingyan (Yan) Chen. He conducted research on integrated building 

simulations of airflow and contaminant transport by using multizone and CFD models. 

After completing his Ph.D., he will work at National Institute of Standard and 

Technology (NIST) as a guest post-doctoral researcher beginning March 2007.