COMPUTATIONAL FLUID DYNAMIC MODELLING OF PARTICLE ... · conducted used Laser Doppler Anemometry...

COMPUTATIONAL FLUID DYNAMIC MODELLING OF PARTICLE DEPOSITION IN HUMAN

UPPER AIRWAYS

by

Toby Lai

A thesis submitted for the degree of

DOCTOR OF PHILOSOPHY

in

The Faculty of Engineering and Industrial Sciences

Swinburne University of Technology

2011

i

Declaration

This thesis contains no material which has been accepted for the award of any degree or

diploma, except where due reference is made in the text of the thesis. To the best of my

knowledge, this thesis contains no materials previously published or written by another

person except where due reference is made in the text of the thesis.

Signed________________________

Date _________________________

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Abstract

This thesis documents a Doctoral research program whose objective was the study of

particle deposition in the human lung, based upon a computational fluid dynamics (CFD)

modelling. Research in this field started as early as 1960 with the general aim of

understanding how various particle sizes can cause lung diseases and how the delivery of

aerosolized drugs is more effectively deposited in the human lung. These early studies,

however, focused heavily on experimental in vitro methods, at least until advancements in

computing technology facilitated the use of CFD as a tool in engineering applications with

high degree of accuracy. However, even after more than a half century of research, data

on particle deposition in the human lung was less than ideal, and hence there was still a

need to develop a holistic approach to this problem. The holistic approach was the main

theme of this Doctoral research.

The first part of this thesis presents background information about the human respiratory

system; mechanisms of particle deposition and the governing equations. This information

is then used for defining the model domain and the boundary initial conditions, as well as

to provide support and physical interpretation of the numerical predictions.

The second part of the thesis documents an in vitro experimental study whose objective

was to determine the validity/veracity of the results. The experiments that were

conducted used Laser Doppler Anemometry (LDA) to measure steady fluid flow under

various operating conditions. Then a one to one simulation was created using a

commercial CFD program (known as CFX), with the aid of Computer Aided Design (CAD).

The LDA data obtained in vitro was used to validate the numerical prediction and build

confidence in using CFX as a CFD tool for fluid flow and particle deposition simulation. A

good agreement was obtained between the experimental and numerical predictions.

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The third section of this thesis is related to the fluid flow in a four generation bifurcation,

in which the results were related to the upper section of the human lung. Flow fields

along the plane and cross section planes were investigated. The findings from this part of

the study showed a secondary flow downstream with imbalanced mass flow rate, upon

using a zero relative pressure at the outlets. This section demonstrated how important

the boundary condition was to obtaining realistic results. Moreover, an important aspect

of CFD analysis was the quality of the mesh generation. Without a proper refinement of

the mesh, the end results were of limited accuracy.

The fourth section of the thesis consists of information on how to develop and create

realistic human airway model, using the commercial package Solidworks, and how to

refine the mesh using the advanced meshing tool ANSYS ICEM. A grid independence test

was performed to ensure that the mesh generated can produce accurate results without

compromising computational time.

The final section of this thesis is related to the analysis of the particle depositions in

human airways under various operating conditions. Particle deposition simulation was

first studied on a symmetrical model and was later extended to asymmetrical airways and

transient conditions. The findings showed that the particles which entered each of the five

lung lobes were different and the deposition efficiency was found to be a proportional to

the Stokes Number which, in turn, related to the size, density, and the velocity of the

particle. Moreover, the results also showed how the entry position of a particle changed

the location and possibility of deposition within the lung.

The thesis concludes with a discussion of how the research findings contributed to

research related to particle deposition in the human lung. Particular emphasis was also

given to the simulation conditions that should be used in the analysis of particle

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deposition in the human lung, and how to generate meshes that could be used for

accurately simulating bifurcating flow.

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Table of Contents

Chapter. 1 Introduction ..................................................................................................... 1

1.1 Background and Objectives ..................................................................................... 2

1.2 Research Significance .............................................................................................. 4

1.3 Perceived Contributions of the Research ................................................................ 6

1.4 Thesis Structure ....................................................................................................... 7

Chapter. 2 Literature Review ............................................................................................. 9

2.1 Overview of Literature Review Process................................................................. 10

2.2 The Human Respiratory System ............................................................................ 12

2.3 Particle Deposition in the Human Respiratory System ......................................... 21

2.4 Related Studies of Particle Deposition in the Human Respiratory System ........... 31

2.5 Computational Fluid Dynamics and Modelling ..................................................... 38

2.6 Application of CFD to Modelling of Biological Systems ........................................ 53

2.7 Conclusions and Research Directions .................................................................... 58

Chapter. 3 In-Vitro Experimental Study Modelling Human Airways ............................... 60

3.1 Introduction ........................................................................................................... 61

3.2 Experimental Apparatus ........................................................................................ 62

3.3 Principles of Laser Doppler Anemometers (LDAs) ................................................ 64

3.4 Experimental Set Up .............................................................................................. 66

3.5 Initial Numerical Experimentation ........................................................................ 74

3.6 Results and Observations ...................................................................................... 78

3.7 Discussion .............................................................................................................. 86

Chapter. 4 Numerical Analysis In A Four Generation Airway Under Steady Flow .......... 87

4.1 Introduction ........................................................................................................... 88

4.2 Methodology ......................................................................................................... 89

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4.3 Numerical Method ................................................................................................ 95

4.4 Results and Discussion .......................................................................................... 97

4.5 Conclusion ........................................................................................................... 117

Chapter. 5 Numerical Analysis on Particle Deposition in Symmetrical Human Upper

Airways Under Steady Conditions ...................................................................................... 118

5.1 Particle Deposition Modelling using CFD ............................................................ 119

5.2 Model Validation ................................................................................................. 121

5.3 Geometric Model ................................................................................................ 125

5.4 Domain and Boundary Conditions ...................................................................... 125

5.5 Results ................................................................................................................. 128

5.6 Deposition Efficiency vs. Particle Density ........................................................... 131

5.7 Deposition Efficiency vs. Particle Size ................................................................. 135

5.8 Deposition Efficiency vs. Local Stokes Number ................................................... 140

5.9 Conclusion ........................................................................................................... 142

Chapter. 6 Creation of Asymmetric Airways Model ...................................................... 144

6.1 Introduction ......................................................................................................... 145

6.2 Geometry Creation and Software Tools .............................................................. 149

6.3 Geometry Creation using Solidworks .................................................................. 154

6.4 Meshing ............................................................................................................... 162

6.5 Meshing with ANSYS ICEM .................................................................................. 164

6.6 Physical Definition and Boundary Conditions ..................................................... 178

6.7 Grid Independence Test ...................................................................................... 180

6.8 Results for 5 different mesh configurations ........................................................ 181

6.9 Conclusion ........................................................................................................... 187

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Chapter. 7 Numerical Analysis on Particle Deposition in Asymmetrical Human Upper

Airways under Steady and Transient Conditions ............................................................... 188

7.1 Introduction ......................................................................................................... 189

7.2 Airways Geometry model .................................................................................... 190

7.3 Fluid and Particles Properties .............................................................................. 191

7.4 Boundary conditions of the model Airways ........................................................ 192

7.5 Turbulence model ............................................................................................... 197

7.6 Fluid flow Results ................................................................................................. 199

7.7 Particle deposition Results .................................................................................. 214

7.8 Conclusions .......................................................................................................... 236

Chapter. 8 Conclusions and Recommendations for Further Research .......................... 237

8.1 Conclusions .......................................................................................................... 238

8.2 Recommendations for future research ............................................................... 241

Appendix A ......................................................................................................................... 243

References ................................................................................................................................i

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List of Figures

Figure 2-1 Overall structure of the respiratory system – Reproduced from Sherwood [13]

.............................................................................................................................................. 14

Figure 2-2 Number and dimensions of airways in adult lung and the structure of the airway

wall – Reproduced from Hickey [14] .................................................................................... 16

Figure 2-3 Generations and Zones of the whole human lung airway (West [12]) .............. 17

Figure 2-4 Illustration of particle transport mechanisms onto airway surfaces (Martonen

[20]) ...................................................................................................................................... 26

Figure 2-5 Fluid element for conservation laws .................................................................. 42

Figure 2-6 Mass flows in and out of fluid element. ............................................................. 44

Figure 2-7 Stress components on three faces of fluid element ........................................... 47

Figure 2-8 Stress components in the x-direction ................................................................. 47

Figure 3-1 Laser Doppler Anemometry at Swinburne University of Technology ................ 63

Figure 3-2 Dual beam optical system and fringe pattern .................................................... 64

Figure 3-3 LDA system setup ................................................................................................ 66

Figure 3-4 Measurement Volume ........................................................................................ 67

Figure 3-5 Schematic diagram for the experimental setup ................................................. 68

Figure 3-6 Actual equipment setup at Swinburne Fluid Lab ................................................ 69

Figure 3-7 Glass bifurcation model ...................................................................................... 70

Figure 3-8 Dimension of bifurcation model mimicking the human airways ....................... 71

Figure 3-9 LDA measurements ............................................................................................. 71

Figure 3-10 Mesh of the bifurcation geometry ................................................................... 74

Figure 3-11 Solution converges for all the velocity investigated variables ......................... 75

Figure 3-12 Boundary conditions for the bifurcation model ............................................... 77

Figure 3-13 Velocity for Station 1 to 4 at Reynolds number 518 ........................................ 79

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Figure 3-14 Differences between Simulation model and Experimental model .................. 80

Figure 3-15 Velocity for Station 1 to 4 at Reynolds number 1036 ...................................... 83

Figure 3-16 Velocity for Station 1 to 4 at Reynolds number 2089 ...................................... 85

Figure 4-1 (a) In-plane (b) off-plane geometries and (c) shows two perpendicular planes in

off-plane bifurcation model ................................................................................................. 90

Figure 4-2 Computational domain for in-plane model with dimensions and boundary

conditions. ............................................................................................................................ 91

Figure 4-3 Mesh of the Gen 3 & Gen 4 showing the density increase near flow divider (in

plane model) Generated by author using CFX-5.7 ............................................................... 95

Figure 4-4 Mesh of the Gen 3 & Gen 4 showing the density increase near flow divider (off

plane model) Generated by author using CFX-5.7 ............................................................... 96

Figure 4-5 Comparison between experimental results with numerical results at Re = 1036

.............................................................................................................................................. 98

Figure 4-6 Comparison between numerical results with Liu, et al. [54] numerical results at

the end of the second-generation tube in a three-generation airway with (a) Re = 200, (b)

Re=800 and (c) Re=1400. ................................................................................................... 100

Figure 4-7 Velocity Plot in the main Trachea (Generation 0). ........................................... 103

Figure 4-8 Velocity patterns for the in-plane configuration .............................................. 104

Figure 4-9 Velocity patterns in the off-plane configuration (a) Plane A and (b) Plane B .. 105

Figure 4-10 Velocity Vector Plots for Generation 2 cross section planes at Re=500 (in-plane

model). ............................................................................................................................... 108


model). ............................................................................................................................... 109


model). ............................................................................................................................... 110

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Figure 4-13. Mass flow rates comparison between all the outlets P11 – P18 for different

Reynolds Number. .............................................................................................................. 113

Figure 4-14 Mass flow rate percentages for Reynolds Number at each outlet................. 114

Figure 4-15 Variations of the pressure drop coefficient with Re....................................... 116

Figure 5-1 Validation of Current model ............................................................................. 124

Figure 5-3 Regions of the lung model. ............................................................................... 129

Figure 5-4 Tracks for particles deposited at Generation 1 ................................................ 130

Figure 5-5 Re = 500, Particle size = 3 micron ..................................................................... 132

Figure 5-6 Re = 500, Particle size = 9 micron ..................................................................... 133

Figure 5-7 Re = 500, Particle size = 15 micron ................................................................... 133



Figure 5-10 Re = 2000, Particle size = 15 micron ............................................................... 134

Figure 5-11 Re = 500 Particle Density = 350 kg/m3 ......................................................... 136

Figure 5-12 Re = 500 Particle Density = 1000 kg/m3 ....................................................... 136




Figure 5-16 Re = 2000 Particle Density = 1000 kg/m3 ..................................................... 138



Figure 5-19 Log-log plot of particle deposition efficiency in the first for generations vs.

Local Stokes number calculated from the mean velocity at the specific generation. ....... 141

Figure 5-20 Bifurcations with different outside curvature, with the same diameter ratios.

............................................................................................................................................ 142

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Figure 6-1 Somso Anatomy Model GS4-3

(http://www.somso.de/deutsch/anatomie/gs4_3.htm) ................................................... 151

Figure 6-2 Default planes in Solidworks. ............................................................................ 154

Figure 6-3 Top Plane with dimensions of trachea ............................................................. 155

Figure 6-4 Extrusion of the trachea ................................................................................... 156

Figure 6-5 Guiding sketch for construction of generation 1 .............................................. 157

Figure 6-6 Building of Plane for Generation 1 ................................................................... 158

Figure 6-7 Circle for Generation 1 ...................................................................................... 158

Figure 6-8 Lofting for generation 1 into a body ................................................................. 159

Figure 6-9 Completed Bifurcation ...................................................................................... 160

Figure 6-10 Upper Airways Model ..................................................................................... 161

Figure 6-11 Geometry imported into ANSYS ICEM ............................................................ 165

Figure 6-12 Hexelements generated by sweeping - Reproduced from Owen [96] ........... 166

Figure 6-13 Mesh of a tube by sweeping, reproduced from ANSYS Documentation [99] 166

Figure 6-14 Initial blocking in ICEM .................................................................................... 167

Figure 6-15 Block associated with the geometry ............................................................... 169

Figure 6-16 Cuboid is the ideal block for sweeping ........................................................... 169

Figure 6-17 Blocks has been split and nodes has been moved to create uniform blocks . 170

Figure 6-18 Ogrid feature in ICEM ..................................................................................... 172

Figure 6-19 The mesh quality without Ogrid. Top figure is Angle, mid figure is Determinant

3x3x3, bottom figure is the quality .................................................................................... 172

Figure 6-20 The mesh quality with Ogrid. Top figure is Angle, mid figure is Determinant

3x3x3, bottom figure is the quality .................................................................................... 174

Figure 6-21 Setting mesh parameters for parts ................................................................. 176

Figure 6-22 Resultant mesh for Extra Coarse Mesh .......................................................... 176

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Figure 6-23 End view of Extra Coarse and Fine Mesh ........................................................ 177

Figure 6-24 Branch name denoted as lower case letter and Horsfield generation number is

labelled inside the bracket. (Coordinate system is also shown in figure) ........................ 181

Figure 6-25 Locations of 12 stations and top right hand corner has the cross section of a

measurement station viewed from proximal position. ..................................................... 183

Figure 6-26 Station 1A ........................................................................................................ 184

Figure 6-27 Station 1C ........................................................................................................ 184

Figure 6-28 Station 2A ........................................................................................................ 184

Figure 6-29 Station 2C ........................................................................................................ 184

Figure 6-30 Station 3A ........................................................................................................ 184

Figure 6-31 Station 3C ........................................................................................................ 184

Figure 6-32 Results of station 4 ......................................................................................... 186

Figure 7-1 Airway model for transient particle deposition simulation. ............................. 190

Figure 7-2 Measured resting breathing cycles ................................................................... 192

Figure 7-3 Measured light exercise cycles ......................................................................... 193

Figure 7-4 Measured heavy exercise cycles ....................................................................... 193

Figure 7-5 Boundary flow conditions during inhalation phase. ......................................... 195

Figure 7-6 Flow profile for Station 3, 4 and 5 at T=0.4s ..................................................... 201

Figure 7-7 Flow profile for Station 3, 4 and 5 at T=0.8 ...................................................... 201



Figure 7-10 Flow profile for station 6, 7 and 8 at T=0.4..................................................... 204




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Figure 7-14 Flow profile for station 9 and 10 at T=0.4 ...................................................... 206




Figure 7-18 Flow profile for station 11 and 12 at T=0.4 .................................................... 208




Figure 7-22 Vector plots of slice at different station showing secondary flow ................. 211

Figure 7-23 Stokes number vs time for resting condition ................................................. 215

Figure 7-24 Stokes number vs time for light exercise condition ....................................... 216

Figure 7-25 Stokes number vs time for heavy exercise condition ..................................... 216

Figure 7-26 Transient particle deposition fractions for different particle size at a full

inhalation cycle under resting condition. .......................................................................... 218


inhalation cycle under light exercise.................................................................................. 219


inhalation cycle under heavy exercise. .............................................................................. 220

Figure 7-29 Upper airways generation labels and colour codes. ...................................... 222

Figure 7-30 Particle tracks at time = 0.1154s for heavy exercise and 10 micron particles

conditions ........................................................................................................................... 223


conditions ........................................................................................................................... 224


conditions ........................................................................................................................... 225

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Figure 7-33 Particle tracks at time = 1.0963s for light exercise and 10 micron particles

conditions ........................................................................................................................... 226

Figure 7-34 Snap shot of release position at time step t = 1.7907s under light exercise

breathing conditions with 10 micron particles. ................................................................. 228

Figure 7-35 Release positions for different particle sizes under light exercise condition at t

= 1.79s ................................................................................................................................ 230

Figure 7-36 Release position for deposited particles of 6 micron under heavy exercise at

different time steps. ........................................................................................................... 231

Figure 7-37 Comparison of release position for two different breathing at 6 micron at time

step 11. ............................................................................................................................... 232

Figure 7-38 5 different exit location for particles .............................................................. 233

Figure 7-39 Release position of exit particles for 10 micron under light exercise. ........... 234

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List of Acronyms and Abbreviations

BSL: Baseline CAD: Computer Aided Design CFD: Computational Fluid Dynamics CPFD: Computational Particle Fluid Dynamics COPD: Chronic Obstructive Pulmonary Disease CT: Co-axial Tomography DE: Deposition Efficiency DES: Detached Eddy Simulation DF: Deposition Fraction EM: Empirical Model GP: General Practitioners ICRP: International Commission on Radiation Protection IN: Inlet LDA: Laser Doppler Anemometers LES: Large Eddy Simulation LL: Left Lower LRR: Launder, Reece and Rodi Isotropization of Production model LU: Left Upper MPM: Multiple Path Model PD: Particle Dynamics QI: Quasi-Isotropic model RANS: Reynolds Averaged Navier-Stokes RL: Right Lower RM: Right Middle RSM: Reynolds-Stress Models RU: Right Upper SMC: Second Moment Closure SPM: Single Path Model TGLD: Task Group on Lung Dynamics

xvi

Nomenclature

Re: Reynolds Number Stk: Stokes Number : Womersley Number : Density of fluid (kg/m) U: Mean Velocity (m/s) U: Velocity Vector U(x,y,z)

_

m : Mass flow rate (m3/s) Vmean: Average velocity (m/s) CDp: Particle drag coefficient Qmedial: Mass flow rate in the medial branch

: Angular frequency (=2f)

f : Fringe separation

: Laser wavelength

: Laser beam intersection angle fD: Doppler shift frequency

: Dynamics viscosity

: Kinematic viscosity P: Pressure

pc : Pressure drop coefficient

: Particle deposition efficiency

xvii

Acknowledgments

The work reported in this thesis was initiated by Prof. Y. Morsi, my supervisor. I wish to

express gratitude for his courage; guidance and constructive criticism throughout the

research without him this work would not have been completed.

Thanks to Australia Research Council (ARC) for providing funding for this research in the

first three years since 2002.

Special thanks to Dr M. Singh for reading and provide suggestions on improving the quality

of this thesis. I also would like to express my appreciation to Dr S. Das for his help during

the final stage of study.

xviii

Publications Arising from this Thesis

[1] T. Lai, Y. S. Morsi, W. Yang, and J. Mazumdar, "Flow through Bifurcation - Study

Particle Deposition in Human Lung," presented at International Congress On

Biological And Medical Engineering 2002, Singapore, pp. 2002.

[2] Lai, T., Morsi, Y., Mazumdar, J. “Modelling and Simulation of Particles Deposition in

the Human Lung”, Profiles in Industrial Research Knowledge and Innovation 2002,

Edited by Dario Toncich, ISBN 1 876 567 04 X., 313-327.

[3] Lai, T., Morsi, Y., “Particle Deposition in the Human Lung – Experimental Design”,

Profiles in Industrial Research Knowledge and Innovation 2003, Edited by Dario

Toncich., ISBN 1 876 567 05 8, 325-332.

[4] I.J. Freshwater, Y.S. Morsi, and T. Lai, “The effect of angle on wall shear stresses in

a LIMA to LAD anastomosis: numerical modelling of pulsatile flow”, Journal of

Engineering in Medicine, 743-757, 2006.

[5] T.C. Lai, Y.S. Morsi, M. Singh, “Numerical characterization of the flow field in a four

generation airways”, Journal of Mechanics in Medicine and Biology, Vol. 8, No. 1,

55-74, 2008.

1

Chapter. 1 Introduction

2

1.1 Background and Objectives

The principal objective of this research was to study and model the deposition of particles

within the human lung through the application of modern engineering approaches.

The pursuit of this research was considered to be significant because rapid increase in

population and industrial growth had accentuated air pollution, particularly within

factories and their surrounding areas. The inhalation of pollutants, and their subsequent

impact on humans, had become an important social issue. Understanding the impact of

particle deposition in the human lung was therefore is the key to understanding the

impact of pollutants.

The inhalation of hazardous pollutants can cause a variety of pulmonary injuries and

diseases such as asthma, bronchitis, chronic obstructive pulmonary disease (COPD) and

increase in lung and nasal cancer risks caused by inhalation of various harmful particles

(Martonen [1], Sussman, et al. [2], Sussman, et al. [3]). In extreme cases, ultra-fine

particles can get into blood stream through alveolar sac, deep inside the lung, causing

damage to other organs such as the kidneys and liver. It was well documented that the

particle concentration inhaled can have an adverse effect on human health. As reported

by Nemmar, et al. [4], pollution by particulates had been consistently associated with

increased cardiovascular morbidity and mortality.

According to the Australian Bureau of Statistics [5], each year lung disease was related to

some 19,200 deaths in Australia. Some of the lung disease risk factors included:

Smoking and passive smoking;

Exposure to environmental agents, including indoor and outdoor air pollutants;

Occupational dusts and chemicals (McKenzie, et al. [6]).

3

According to the Australian Lung Foundation[7], lung disease had annually caused 350,000

hospitalisations in Australia, while upper respiratory tract infections accounted for 3-4

million visits to general practitioners (GPs) each year – an average of six percent of all GP

consultations- with an estimated cost of more than $150 million Australian dollars in

direct costs alone[7]. These figures indicate the importance of this research topic. The

research conducted in this thesis is partly funded by Australian Research Council (ARC),

Swinburne University and a private company called BJJS Associates in Australia.

On the other hand, particulate inhalation can also have positive attributes, especially

when it is used as a means of delivering therapeutic agents to the human body. Inhalation

was gaining an increased acceptance as a convenient, reproducible, and non-invasive

method of drug delivery to the lung tissue and systemic circulation.

Therefore, gaining an understanding of particle depositions in the human lung was

important for both risk assessment related to air quality and for delivery of medication.

The ability to model particle deposition was the key to acquiring this understanding and

hence there was a significant impetus for this research.

4

1.2 Research Significance

It was noted in Section 1.1 that inhaled particles, deposited in the lung, could cause a

variety of pulmonary injuries and diseases. Thus, to assess the potential risk to human

health from inhaled particles, an accurate estimate of initial particle deposition along the

respiratory tract and lung was significant and necessary.

In-vitro and in-vivo particle deposition experimental studies typically employed laboratory

and animal models. However, there were significant interspecies differences in deposition.

To extrapolate the results of such studies to humans, dosimetry models for laboratory

animals and humans had to be developed so that an adequate regional respiratory tract

resolution could be obtained. This was a key objective of this Doctoral research. The

research aimed to create an efficient numerical and commutative model to calculate

lobar-specific and airway-specific deposition of mono-disperse and poly-disperse aerosols

in the human respiratory tracts.

Many earlier studies (Zhao and Lieber [8], Martonen, et al. [9], Zhang and Kleinstreuer

[10]) commonly idealized the airway tree structure to consist of symmetrical and

dichotomous branching networks. The use of this symmetrical structure had led to a

typical-path formulation that allowed for simulating average regional deposition only, and

could not account for heterogeneities in a real human lung system. For a human lung, a

full multiple-path model could not be implemented due to the lack of a complete

measurement data of the conducting airway. Major asymmetries exist in the upper

portion of the human. These asymmetries lead to different particle deposition patterns in

the human airways, as well as in the apportionment of airflow to the different lung lobes.

However, the lower airways of the human lung can be reasonably characterized in a

symmetric fashion (Raabe, et al. [11]).

5

This Doctoral research set out to develop and test a new model, termed the limited

multiple-path model, which combined asymmetry and symmetry. The first three

generations used asymmetrical structure to match real dimensions of the human lung, to

lead to five lung lobes. From each lobe to their terminal alveolar sacs, the individual

symmetrical and dichotomous branching network were employed. This was the first time

that such a model had been proposed and it represents a novel method of determining

particle deposition in the human lung. This new model will assist in monitoring

atmospheric quality and assess the risks associated with the deposition of particles. In

addition, the commercial code that was developed could potentially lead to a marketable

software package.

6

1.3 Perceived Contributions of the Research

The research presented in this Doctoral dissertation is perceived to have made a number

of specific contributions to the field. These are:

(i) A detailed review of literature in the field of particle deposition and its modelling

and measurement.

(ii) Development of the modelling process based upon a commercial computational

fluid dynamics software system. The modelling process included geometry creation,

mesh generation; determination and application of appropriate boundary

conditions, and detailed analysis of the results.

(iii) Conduct of an experimental study into fluid flow in bifurcating tubes which can be

used to provide a fundamental background for computer simulation.

(iv) Detailed analysis of the grid independence test to ensure that the applied model

had a very fine mesh suitable for high resolution analysis.

(v) Publication of five research papers, including two in international (peer reviewed)

refereed journals and one in an international conference.

7

1.4 Thesis Structure

This Doctoral thesis is composed of eight chapters, including this one. The content of the

chapters that follow on is summarized below:

Chapter 2 provides the background information and impetus for this research

program, through a detailed literature review on particle deposition in the human

lung, including an explanation of the human respiratory system. The review also

covers the use of CFD in both generalised applications and those specific to this

research.

Chapter 3 presents experimental results of fluid flow in bifurcating airway models.

The results of different flow rates (hence different Reynolds Numbers) are

presented.

Chapter 4 presents numerical results of fluid flow in bifurcating airway models. The

results are validated against the experimental results.

Chapter 5 provides an in depth analysis of the numerical results of Chapter 4 and

applies the symmetric airways model by simulating the model with particle

deposition. The results are validated against other studies.

Chapter 6 details the creation of a CAD model of realistic asymmetric airways. The

model is then meshed using a commercial package, known as ANSYS ICEM. The

meshing techniques applied in industry are described in detail. Grid independence

tests are performed to confirm that the mesh is adequate for accurate simulation

results.

Chapter 7, which is the key to this research, presents the numerical simulation

results of particle deposition in a realistic airways model. Extensive analysis is

carried out to show the importance of the results of particle deposition.

8

Chapter 8 presents the conclusions of this research, including an assessment of its

strengths and weaknesses. It also puts forward recommendations for further

research.

9

Chapter. 2 Literature Review

10

2.1 Overview of Literature Review Process

The purpose of this literature review is to provide the background to (and justification for)

the directions pursued during this research. The core objective of this research, restated

here, was to deploy computational fluid dynamics (CFD) to investigate particle deposition

in the human lung.

The review documented in this chapter is based upon a range of literature including text

books, referred journal papers, conference proceedings and internet web sites from

credible institutions.

This chapter commences with a review of literature providing basic background

information on human respiratory systems. An understanding of this physiology was

critical to determining the boundary conditions of the model that was deployed in this

research. The human respiratory system and the research undertaken into it had,

unsurprisingly, been extensively documented in many medical text books, and

measurements of the geometry of the human lung had also been extensively documented

by many researchers.

Following the background discussions, a more specific review of research into particle

deposition in human respiratory systems documents some of the studies in the field. This

is followed up with an in-depth review of various experimental studies and research

programs that have been undertaken by many researchers around the world.

A core element of this Doctoral research involved the deployment of computational fluid

dynamics (CFD), and so this literature review examines the relevant aspects – specifically,

The origins of CFD

Applications of CFD in conventional engineering applications

11

The application of CFD in biomedical science applications

This leads to a review of research into the application of CFD in particle deposition in the

human lung.

This chapter concludes with a summation of all the basic elements garnered from the

literature review and shows how these led to a natural progression for the Doctoral

research undertaken and documented herein.

12

2.2 The Human Respiratory System

2.2.1 Background

An understanding of the human respiratory system is essential to the study of particle

deposition in the human lung. An inhaled particle travels together with the air flow, while

the air flow into the lung is guided by the human lung morphology. Understanding the

system and its morphology was therefore fundamental to this research.

The respiratory system and its morphology had been heavily documented over many

years. Much of the work had already moved beyond research papers and had reached

book and textbook publications – some of it could be classified as basic medical

knowledge but needs to be included herein for completeness, given that this research

program spans both medical and engineering phenomena.

This section is based on readings undertaken from a number of scholarly books,

specifically the book by West [12]. In situations where specific elements have been

abstracted from authors, these are individually referenced.

2.2.2 Structure and function of the normal lung

The human respiratory system is a closed loop system. The primary function of the lungs is

to exchange oxygen with carbon dioxide – this is referred to as gas exchange. The process

of gas exchange is controlled by the central nervous system; the movement of the

diaphragm and chest wall musculature – the blood circulation system allows the gas

exchange to occur efficiently.

13

Alveolar level of the human lung is where gas exchange occurs (CO2 exchange O2); the

inspired air and the blood flow inside small blood vessel are separated only by a thin

tissue layer. The duration of the gas exchange performed by the red blood cells takes only

0.25 seconds. In a healthy human adult, the entire blood volume of the whole body passes

through the lung at resting condition in order to achieve 5 litres per minute. The total

surface of the human lung walls from trachea to alveolar level is approximately 80 square

metres (Sherwood [13]).

Human lung is filled with air (O2, CO2 and other gases) and blood, only about 10% of the

lung is solid tissue. The outer surface of the human lung is supported by rib cage to

maintain architectural integrity while the tissue deep inside the lung is delicate enough to

allow gas exchange. The functional structure of the lung can be divided into:

Conducting airways (dead air space).

Gas exchange portions.

The human lung conducting airways are fairly rigid and the shape is maintained during the

breathing cycle, the rigidness is supported by cartilage rings that wraps around the airway

tube. Only the gas exchange portions where the walls for the air passage will be closed

during exhalation. The two plumbing systems are:

Airways for ventilation.

The circulatory system for perfusion.

Both of these are under low pressure. Figure 2-1, which has been reproduced from

Sherwood [13], shows the overall structure of the human lung. It is important here to

note that breathing is driven by pressure differences because this is one of the main

boundary conditions for the computer simulation.

14

Figure 2-1 Schematic illustration of the overall structure of the respiratory system –Sherwood [13]

A typical normal human adult lung weight is about 300-400 grams. Upper and middle

lobes are anterior meaning that they are at the front of the body. Lower lobes are

posterior meaning that they are at the back of the human body.

Each lung lobe has more than 20 bronchopulmonary segments, they are relatively

constant in size. Physiopathology behind this human lung formation is for defending

diseases such as tuberculosis. The conducting airways will be covered in more detail in

Section 2.2.3.

15

2.2.3 The conducting airways

From the first generation of the human airways, trachea, the respiratory tree divides into

paired branches of uneven length and diameter. Therefore, it is described as having an

arborizing branching pattern of irregular dichotomy in medical terms. The internal

diameter of a branch is related to the number of alveoli at the end of that branch. The

longer airways, with more branches and more alveoli, usually have a wider lumen

diameter that allows greater airflow, such that newly inspired air reaches all of the alveoli

throughout both lungs at the same time and in approximately the same amount. This

results in an equal distribution of inspired air throughout all five lung lobes in a given

period of time. In total, there are approximately 23 airway divisions (generations) from

trachea to the level of the alveoli. These divisions include:

Main bronchi.

Lobar bronchi.

Segmental bronchi (to designated bronchopulmonary segments).

The smallest bronchioles that do not have alveoli are lined completely by bronchial

epithelium, the terminal bronchioles as shown in Figure 2-2, which has been reproduced

from Hickey [14]. Although the base airway diameter decreases with branching, the

overall or total cross-sectional area increases significantly so that peripheral airway

resistance decreases. This means air flow deep inside the lung is a lot slower compare to

the airflow near trachea.

16

Figure 2-2 Schematic illustration of the number and dimensions of airways in adult lung and the structure of the airway wall – Hickey [14]

2.2.4 Human lung morphology

Knowledge of human lung morphology is essential to the study of particle deposition in

the airways as the fluid flow and the transportation of the particles are guided by the

geometry of the human airways. The lengths, diameters and bifurcating angles will affect

the fluid flow pattern significantly thus altering the particle deposition pattern. Figure 2-3,

reproduced from West [12], shows the various generations and zones of the entire human

lung airway. There are three main zones within the human lung; they are conducting,

transitional and respiratory zone.

17

One of the earliest adopted models of airway anatomy was the Weibel [15] model. Weibel

[15] book on the morphometry of the human lung summarised all the studies on

dimensions of human lung since 1844. He described in detail his approach to measuring

the dimensions of the human lung from trachea (generation 0) to alveolar level

(generation 20-23). Weibel constructed two models labelled as “Model A” and “Model B”.

These were based on regular dichotomy (bifurcating) and irregular dichotomy respectively.

Figure 2-3 Generations and Zones of the whole human lung airway (West [12])

In “Model A”, Weibel has disregarded the irregularities and focus on the regular features.

As the branching is regular, the number of elements in each generation z is zzn 2 . The

airways of this lung model has 23 generations (as shown in Figure 2-3). Generation 0 to 16

is the conductive zone, generations 17 to 19 (respiratory bronchioles) and 20 to 23

(alveolar ducts and sacs) are the transitory zone and bear alveoli as shown in Figure 2-3.

The diameter, length and cross section area for each generation are listed in Table 2-1

which has been reproduced from Weibel [15]. The airway model refers to an average sized

adult human lung at a degree of ¾ maximal inflation. It has a total air volume of about

4800 ml of which 66% is contained in the alveoli.

18

In “Model B”, Weibel [15] attempted to account for the irregular dichotomy of the lung by

applying a binomial distribution to the occurrence of airways with 2mm diameters with

respect to generation number. The distance from the root of the trachea, at which these

2mm bronchi occurred, was then described by a normal distribution with a mean of 24.5

cm. Asymmetries for the smaller airways (1.0-and 0.5-mm diameters) were then

estimated based on the assumption of normal distributions analogous to those used for

the 2mm-diameter airways. Thus, a model accounting for airway diameter and length

asymmetries had been developed. However, there were no defined measurements of the

irregular dichotomy in “Model B”.

Table 2-1 Dimensions of Weibel “Model A" – Reproduced from Weibel [15]

Name of Airway Gen no.

Number per generation Diameter [cm] Length [cm]

Cross section area [mm^2]

Trachea 0 1 1.8 12 0.785398163

Main bronchus 1 2 1.22 4.76 3.141592654

Lobar bronchus 2 4 0.83 1.9 12.56637061

Lobar bronchus 3 8 0.56 0.76 50.26548246

Seg. bronchus 4 16 0.45 0.64 201.0619298

Seg. bronchus 5 32 0.35 1.07 804.2477193

Bronchus 6 64 0.28 0.9 3216.990877

Bronchus 7 128 0.23 0.76 12867.96351

Bronchus 8 256 0.186 0.64 51471.85404

Bronchus 9 512 0.154 0.54 205887.4161

Bronchus 10 1024 0.13 0.46 823549.6646

Term. Bronchus 11 2048 0.109 0.39 3294198.658

Term. Bronchus 12 4096 0.095 0.33 13176794.63

Bronchiole 13 8192 0.082 0.27 52707178.53

Bronchiole 14 16384 0.074 0.23 210828714.1

Bronchiole 15 32768 0.066 0.2 843314856.5

Ter. Bronchiole 16 65536 0.06 0.165 3373259426

Res. Bronchiole 17 131072 0.054 0.141 13493037705

Res. Bronchiole 18 262144 0.05 0.117 53972150818

Res. Bronchiole 19 524288 0.047 0.099 2.15889E+11

Alv. Duct 20 1048576 0.045 0.083 8.63554E+11

Alv. Duct 21 2097152 0.043 0.07 3.45422E+12

Alv. Duct 22 4194304 0.041 0.059 1.38169E+13

Alv. Duct 23 8388608 0.041 0.05 5.52675E+13

19

Horsfield, et al. [16] subsequently presented a more realistic model of the human lung by

considering asymmetry in the lung model. They measured the geometry of a resin cast of

a normal human bronchial tree down to branches of 0.7mm in diameter. The authors

suggested that airways asymmetry could be important in situations where it was

necessary to analyse the flow to different regions of the lung or to examine the effects of

gravity. The information obtained both from the original measurements and the

subsequent analysis was used to construct two mathematical models. These models

enabled the calculation of physiologic variables to be made while taking asymmetry into

account. Horsfield, et al. [16] measured branching angles and radius of curvature at the

origin of daughter branch, and calculated the flow percentage in the asymmetrical model.

It is important to note that in terms of lung morphology, the asymmetry occurs mostly for

the first four generations of the airways. The application of an asymmetrical model makes

the problem significantly more complex but, if the asymmetry for the lung is taken into

account, the deposition model will be more accurate.

The first approach in this research was to study the fluid flow and particle deposition in

the symmetrical geometry, as this in turn would be useful for airways after the 4th

generations. After the symmetrical study, then the Horsfield model would be applied to

increase the accuracy of the particle deposition analysis.

20

Table 2-2 Horsfield airways model dimensions – Reproduced from Horsfield, et al. [16] Branch No. Order Diameter, mm Length, mm E Flow, % of trachea Branching Angle R/d R

0 31 16 100 216544 100.0000%

1 28 12 50 98432 45.4559% 73 4.5 54

2 27 7.5 16 44416 20.5113% 48 3.5 26.25

3 26 7.3 1 30592 14.1274% 65 1.5 10.95

4 25 5 9 13760 6.3544% 28 0.5 2.5

5 24 5.5 11 13824 6.3839% 25 1.2 6.6

6 27 8 11 54016 24.9446% 44 6.3 50.4

7 26 6.5 18 43840 20.2453% 28 3 19.5

8 25 7 4.5 27008 12.4723% 17 2.7 18.9

9 24 5.5 7.5 16832 7.7730% 33 6.2 34.1

10 30 11.1 22 118112 54.5441% 35 3 33.3

11 26 7.3 15.6 47008 21.7083% 63 1.7 12.41

12 25 8.5 6.4 23776 10.9798% 18 4 34

13 29 8.9 26 71104 32.8358% 15 2.3 20.47

14 25 5.2 21 20800 9.6054% 61 8 41.6

15 28 6.4 8 50304 23.2304% 15 5.9 37.76

16 27 6 8.4 35392 16.3440% 8 11 66

17 26 6.2 14.8 27520 12.7087% 0 12.7 78.74

20 24 5.3 13.5 16832 7.7730% 14 4 21.2

23 23 3.5 11.5 7872 3.6353% 28 15.1 52.85

24 22 3.5 7.5 5952 2.7486% 8 8.7 30.45

25 20 5.5 8.5 10176 4.6993% 70 2.2 12.1

26 24 5 11.5 16832 7.7730% 36 18 90

28 20 5 8.5 10176 4.6993% 31 6 30

30 24 4 2 16832 7.7730% 40 4.2 16.8

31 19 4 13.4 6944 3.2067% 10 4 16

32 25 5.5 17 23232 10.7285% 33 1.9 10.45

33 24 4 10 10400 4.8027% 35 15.5 62

34 24 4.4 9.6 10400 4.8027% 18 13.1 57.64

35 21 4.4 6.2 14912 6.8864% 54 12.3 54.12

36 23 3.2 6.2 7872 3.6353% 58 14 44.8

37 25 4.8 6.8 13760 6.3544% 31 11.1 53.28

38 25 5.8 10.6 13760 6.3544% 35 8.9 51.62

21

2.3 Particle Deposition in the Human Respiratory System

2.3.1 Overview

This section describes some of the general studies on particle deposition in the human

respiratory system. In literature, there were numerous published studies related to the

prediction of deposition of particles in the lung system. These were based on models

could be classified into three types:

Empirical Model (EM) – Sussman, et al. [3].

Single-path model (SPM) – also known as the typical-path model – Yeh and Schum

[17].

Multiple-path model (MPM) –Asgharian and Anjilvel [18].

The Empirical Model was based on data obtained experimentally, where the deposition of

loss particles in the lung was correlated to various loss parameters such as impaction,

sedimentation and diffusion. However, empirical models were considered crude in

computing the deposition of the particles and were generally only useful for quick and

simple calculations. This was particularly so because the true breathing parameters were

not included in the empirical model, as it employed limited particle matter (PM) risk

assessments.

The single-path model (SPM) employed an idealized geometry of the lung, which used one

typical pathway to represent the entire lung, as in Yeh and Schum [17]. By using various

loss formulae to calculate deposition in each region, the SPM enabled the simulation of

average regional deposition patterns. The lower airways of the human lung could be

reasonably assumed to be symmetrical, but there were major asymmetries in the upper

airways of the human tracheobronchial tree. Therefore, if one adopted this symmetrical

approach, it could result in incorrect deposition patterns and inaccurate apportionment of

22

airflow to the different lung lobes – this, in turn, could lead to inaccurate calculation of

particle deposition within the airways.

A multiple-path module (MPM) was developed by Asgharian and Anjilvel [18]. This model

incorporated the correct asymmetry of the airways in the lung branching structure and

calculated deposition at the individual airway level. The MPM could be used to predict

particle losses at specific sites or locations in the lung. However, the mathematical

formulation of this model for calculating particle losses was similar to the one employed in

SPM.

Particle deposition in human respiratory systems had generally been researched with two

major objectives.

(i) To study pharmaceutical drug delivery into the human respiratory system

(ii) To study the local deposition of pollutants with the aim of determining the cause

of lung diseases

The determination of the deposition of pharmaceuticals had been reported widely in

literature, including books. One of the books that summarized some of the major research

was edited by Hickey [14]. Hickey’s work was divided into three key components,

specifically:

Aerodynamic behaviour of particles in human airways

Biological considerations of the aerosols describing how the drug interact with

human airways

The pharmaceutical technology related to particle generation

The first chapter of Hickey’s book was authored by Martonen and Yang [19]. Their

objective was to demonstrate how aerosolized drugs could be targeted to relatively well-

23

defined regions within the human respiratory tract. This was achieved by understanding

the relative roles of the factors that affected airborne motion and subsequent deposition

of inhaled particles.

As described by Martonen and Yang [19], particles were transported convectively with air

intake. All particles experienced a non-zero chance of being deposited during the course

of their path from nasal or mouth sources down to the alveolar sacs. The deposition

patterns of inhaled particles could be expressed as a function of three variables:

Aerosol characteristics

Ventilatory parameters (Breathing pattern)

Respiratory tract morphologies.

The aerosol characteristics were the properties of the particles being inhaled into the lung.

The particle size, material, density, shape, porosity were all factors related to the aerosol

characteristics. The ventilatory parameter was the breathing pattern, but there were

minimal variations in breathing pattern for an individual person – in general air flow

follows a sine curve form.

2.3.2 Particle deposition at head and throat

Although particle deposition at the head and throat is not a primary interest in this

research, it is important to have an insight into estimates of the number of particles that

pass through the nasal and throat. At the head and throat airways, Martonen and Yang

24

[19] has proposed that the head and throat acted as a filter through which particles could

transport into the trachea – this is described as a mathematical function.

[ ( )][ ( )] 2-1

where

M is the mass of inhaled aerosol

Mi is the quantity that penetrates to the trachea

p(m) and p(l) are the particle deposition efficiencies within the oropharygeal

region and larynx respectively.

Empirical formulations for p(m) and p(l) were presented by Martonen [20]. Most particles

in pollutants are normally deposited at the oropharyngeal and larynx region as it is the

first defence mechanism for the human lung to avoid pollutant particles. This applies to

drug particles as well – however, it is generally the case that the instructions for using

inhalers are to take a deep breath, which causes more pharmaceutical particles to transfer

into the lung.

2.3.3 Mechanisms of particle deposition

The actual transport mechanism and the manner in which particles are deposited

depended on the forces acting on the particles. The methods for particles being

deposited onto the airway surface can therefore be described by the transport

mechanisms.

25

The major transport mechanisms acting on particles in the respiratory system are:

Impaction due to inertia of particles.

Sedimentation due to gravitational forces.

Diffusion related to the Brownian motion of surrounding gases as illustrated in

Figure 2-4 which has been reproduced from Martonen [20].

These forces causes particles to diverge or separate from airflow streamlines and thereby

touch the airway surfaces lined with mucus, causing particles to stick onto the airway’s

wall resulting particle deposition. There are other minor mechanisms that can cause

deposition (Chan and Yu [21], Chan, et al. [22], Versteeg and Malalasekera [23]), such as:

Cloud motion.

Interception.

Electric charge effects.

In general, hazardous and pharmaceutical particles were not heavily charged and

therefore particle transport of these in the human respiratory tract was primarily

governed by mechanical transport.

26

Figure 2-4 Illustration of particle transport mechanisms onto airway surfaces (Martonen [20])

The types of mechanisms transfer are as:

(i) Inertial Impaction Transport - In branching network of airways, the inspired air is

changing its velocity and direction of motion all the time while it is penetrating into

the lungs. Particles carried with the air are therefore exposed to inertial forces all

the time. For particles of sufficient mass, these forces result in an inertial

displacement and thus in a particle transport toward airway surfaces. Due to the

27

velocity-dependence nature of inertial impaction transport mechanism, it is

anticipated that inertial deposition of particles in the respiratory tract occurs

mainly in regions of maximum airflow velocity such as in large airways. This is the

major study of this thesis.

(ii) Sedimentation Transport - Particles of sufficient mass maybe sedimentated due to

gravity when residence times within airways are large. Because of the time-

dependence nature of sedimentation particle transport, it is anticipated that

gravitational deposition of particles occurs mainly in lung regions of maximum

residence time of the tidal air such as small airways and the lung periphery.

(iii) Diffusion Transport - Aerosol particles of dimensions comparable with the mean

free path of gas molecules (about 0.06 m) recognize their gaseous surroundings

as composed of individual molecules, and every collision of a particle with a gas

molecule changes its kinetic energy and direction of motion; as a result, the

particle moves at random through the gas (Brownian motion or diffusion). The

random displacement of a particle covers by diffusion transport increases with

time and with decreasing particle diameter. It is independent of the particle

density. In the human respiratory tract, only ultrafine particles (particles with

diameter smaller than 0.1 m) are deposited solely due to diffusion. For all

ultrafine particles of the same size, deposition is the same regardless of their

density. As a result of the time-dependence of diffusion particle transport, it is

anticipated that diffusion deposition of ultrafine particles occurs mainly in lung

regions of maximum residence time of the tidal air such that in small airways and

in the lung periphery.

These three deposition mechanisms need to be considered when studying particle

deposition in human lung. It is true that in the upper airways, where the air flow velocity is

high, the chance for inertial transport deposition will be the highest.

28

2.3.4 Mathematical Particle Deposition Models

There is a history of respiratory modelling in relation to particle deposition which is well

described by Swift [24]. In general, early models were simple formulation and became

more detailed as they were improved over years of research.

An early mathematical model was presented by Findeisen [25]. He divided the respiratory

tract into nine generations only. His model began with the trachea, progressing through

three orders of bronchi and two orders of bronchioles and terminating with alveolar ducts

and sacs. Findeisen [25] assumed branching factors, dimensions, flow speeds and transit

times for each generation. He assumed a normal breathing pattern of two seconds

inhalation and two seconds of exhalation with a tidal volume of 400 cm3 leading to a

constant flow rate of 200 cm3 per second. Findeisen assumed simple expressions for the

deposition of particles in each generation resulting from the three mechanisms described

in 2.3.3. He assumed that the particles were spherical in shape and their density was 1 g/

cm3. He calculated deposition in each generation for seven particle diameters:

0.03 µm

0.1 µm

0.3 µm

1.0 µm

3.0 µm

10 µm

30 µm.

For the three smallest sizes, the total deposition fraction in the respiratory tract was

respectively 68%, 35% and 34%, the deposition being essentially confined to the last two

29

generations. For 1.0 µm diameter particles, Findeisen calculated 97.4% total deposition,

while for the two largest diameters the deposition was 100%. For 1 µm diameter,

deposition was still primarily in the last two generations, but as particle diameter

increased, the site of deposition moved proximally with the 30 µm diameter particles all

being deposited in the 1st generation trachea.

Over the years, the model by Findeisen was improved by researchers including Landahl

[26] and Beekmans [27]. Generally the improvements occurred through consideration of

an increased number of generations and inclusion of the nasal and oral passage.

Subsequent research led to a model of particle deposition that had wider use and was

documented in the report by the Task-Group-on-Lung-Dynamics [28] (TGLD) to the

International Commission on Radiation Protection (ICRP). This was because, at the time,

radiation impact on human health was a major concern. The model employed a slightly

modified version of the Findeisen [25] lung morphology, while having the additional

compartment of nasopharyngeal airway. The empirical equation used was developed by

Pattle [29] for the inspiratory nasal deposition

( ) 2-2

where

=particle density, gcm-3;

dp=particlde diameter, µm,

Q=flow rate, cm3sec-1.

The Task Group lung deposition model was intended for radiation protection purposes but

it was widely applied in other situations including outdoor pollutant particles and

occupationally related aerosols.

30

Mathematical particle deposition modelling is useful in determining the particle efficiency

in general. The drawbacks of the models are that they only provide overall deposition.

Therefore, risk assessment of inhaled particles is difficult to achieve because it requires

information on local deposition patterns with lung regions. In fact, creating a

mathematical model also requires enormous amounts of data and making assumptions on

limited amounts of particle sizes and breathing parameters in specific human subject.

There were other methods, however, that facilitated the determination of the local

deposition, either by lung cast experiment or by using computational models (discussed

later in this chapter).

31

2.4 Related Studies of Particle Deposition in the Human Respiratory

System

2.4.1 Overview

Particle deposition in the human respiratory system was a very broad topic, covering

many areas. Studies that were indirectly related to particle deposition were those

examining the fluid flow in the human respiratory system. Of these, the studies that were

of relevance here were the mathematical models, experimental studies and

computational studies. This section will describe the studies of fluid flow in human

airways and specific experimental studies of particle deposition.

2.4.2 Fluid flow studies in the view to study particle deposition

One of the pioneering works undertaken on fluid flow in human airways was by Dekker

[30] who studied the transition between laminar and turbulent flow in the human trachea.

This study focused on measuring the critical velocity where turbulence would appear in 21

transparent human lung casts using water and air as the medium. The results showed that

the critical flow velocity of air moving through tracheal casts (without the larynx) averaged

approximately 350ml of air per second. With the glottis opened into a more natural

position, the critical inspiratory flow velocity was higher, approximately by 100 ml of air

per second. The conclusion was that air flow in the trachea of most individuals was

probably turbulent during the greater part of normal respiratory activity.

Schroter and Sudlow [31] studied the fluid flow phenomena in two successive generations

of large scaled symmetrical models of typical junctions of human bronchial tree. The

32

symmetrical Y-shaped scale models were manufactured using Perspex. Flow visualisation

experiments were conducted on a single junction for Reynolds Numbers in the range from

50 to 4500 by using fine tracers of smoke. Details of velocity profile measurements were

taken for flow through two generations of bifurcation for Reynolds Numbers of 100-1500

using hot wire probes. Secondary flows were also observed at all flow rates for both

inspiration and expiration regardless of the form of the entry profile. For inspiration, a pair

of vortices resulted at the daughter tube. For the expiration case, the impinging flows

merged from daughter tubes causing the flow to form four vortices in the parent tube.

The studies concluded that flow patterns in the bronchial tree were found to be complex

and the assumption of laminar flow was not reasonable. They also found that each

junction disturbed the flow, and the disturbances might not be dissipated before the next

junction. Flow separation had been observed for the model where the outer wall

curvature was small. However, no discussion was given on the effect of Reynolds Number

on flow separation.

Most of the early experimental work had studied one or two generation symmetric

bifurcations to model human airways. Chang and Masry [32] constructed a four

generation asymmetric model of the human central airways using the lung geometry

reported by Horsfield, et al. [16]. Chang and Masry [32] used the same model to study the

steady axial velocity profiles; the secondary flow characteristics (Isabey and Chang [33]),

and velocity profiles during oscillatory flows (Menon, et al. [34]). The model was a 3:1

scale rigid model of the first 3-4 generations of human central airways from the trachea to

the five lobar bronchi. The model had been constructed from blocks of clear acrylic plastic

and circular tubes.

In the first part of their study Chang and Masry [32] employed two steady tracheal flow

rates of 5.0 L/sec and 1.2 L/sec corresponding to Reynolds Numbers of 2123 and 8846 at

the trachea. Comprehensive results of the velocity profile for both inspiratory and

33

expiratory flow were measured using hot wire probes. They also compared different flow

entrance conditions – one of these was flat entrance inviscid flow, and the other was

narrow jet (modelling the glottic aperture). These inlet conditions showed that the

inspiratory flow velocity profiles in the frontal plane developed a high degree of

asymmetry in all branches, with peak velocities near the inner wall of the bifurcation.

During expiratory flow, the velocity profiles were nearly symmetric, exhibiting a single

peak near the centre in the bifurcation plane and almost flat in the normal plane. These

flow characteristics were found to be independent of Reynolds Number but very

dependent on the local geometry. Flow separation was observed in the right upper lobar

bronchus. The authors suggested that the right upper lobar bronchus was a more likely

site for particle deposition than other branches due to flow separation. In the second part

of their studies, Isabey and Chang [33] concluded that secondary motion was also highly

sensitive to geometrical asymmetry. In the geometry they employed, the secondary flows

never exceeded 21.5% of the mean axial flow in either the expiratory direction or the

inspiratory direction. The maximum secondary velocities were observed near the wall.

Isabey and Chang also noted that more investigation of velocities in the boundary layer

was required in order to gain insight on secondary motion, as the measurements of

secondary flow using hot wire anemometry posed a problem for small velocity values.

Early studies of airflow dynamics in the airways were generally based on highly idealized

geometries and steady flow. Menon, et al. [34] in Part III, studied the velocity profiles

under oscillatory flow on the same physiology realistic asymmetry airway model. The

oscillatory flow they used was a sinusoidal flow.

One of the important parameters that dictated the effect of the periodically imposed

pressure gradient was the Womersley Number defined as

34

2d

2-3

where

d is diameter of the tube,

is angular frequency (=2f),

f is the frequency of the breathing,

is the kinematic viscosity of the fluid.

At a low Womersley Number, the flow is quasi-steady, such that the fluid particles

everywhere in the tube respond instantaneously to the applied pressure gradient. When

the value of the Womersley Number is large, the motions of the laminae close to the tube

wall follow the pressure gradient more closely than the laminae in the tube core which

show phase lags to the imposed pressure gradient.

Menon, et al. [34] also studied the influence of the oscillatory flow on the axial growth of

the viscous boundary layer. In general, the viscous boundary layer developed faster with

an oscillatory flow. Many of the previous studies (including Schroter and Sudlow [31],

Chang and Masry [32], Isabey and Chang [33]) argued that, for normal quiet breathing,

the airflow in the central airways should be quasi-steady. One of the objectives of the

study of Menon, et al. [34] was to validate the previous measurements, which used steady

flows, and to establish the criteria under which oscillating flows could be approximated by

steady flow. The measurements using hot wired probes indicated that the entry flow

profile into the model during oscillatory flow was flat. For low frequencies, the velocity

profile at peak flow rate resembled the profiles seen under steady flow conditions at the

corresponding Reynolds Number. As the frequency increased the velocity profiles

throughout most branches tended to flatten, except in the right upper lobar bronchus

35

where the skewed velocity profiles persisted even at the highest frequencies studied, due

to the sharp bend of the airway geometry.

Menon, et al. [34] determined that the nature of the velocity profile was strongly

influenced by the airway geometry under oscillatory flow. The critical value for the

Womersley Number was 16, where the velocity profiles resembled steady flow profiles at

comparable Reynolds Numbers for steady flow. However, their model had not simulated

normal and exercised breathing. The simulated curve was a sinusoidal curve that had not

taken into account the exact breathing cycle curve.

With the advances in Laser technology, Zhao and Lieber [8] were the first to use Laser

Doppler Anemometry to study fluid flow bifurcation. They employed inspiratory flow

(Zhao and Lieber [8]), expiratory flow (Zhao and Lieber [35]) and oscillatory flow (Lieber

and Zhao [36]) inside a symmetric bifurcation model.

As noted in Zhao and Lieber [35] in their expiratory flow paper, in contrast to inspiration,

the expiratory phase had received much less attention, and only fragments of information

regarding flow patterns in a typical junction during this phase of the respiration cycle were

available. They (Zhao and Lieber [35]) also noted that secondary motion acquired

momentum from the axial flow and with the added complexity of colliding streams

bringing about interesting flow phenomena. A detailed understanding of secondary flow

patterns could help to explain the deformation of axial velocity profiles and provide useful

information for determining the fate of airborne particles that were deposited in the

airways during expiration. Their experiment (Zhao and Lieber [35]) employed a model of

symmetric bifurcation to simulate steady expiratory flow in the upper part of the human

central airways. A two colour, two component laser Doppler anemometer was used to

measure both the axial flow and the secondary flow at three different Reynolds Numbers

of 518, 1036, 2089, corresponding to Dean Numbers of 98, 196, and 395 respectively.

36

2.4.3 Experimental study of particle deposition

Experimental studies related to particle deposition in human airways are rare. This is due

to the complexity of the air flow condition, difficulties with the generation of particles and

obtaining a lung cast.

Early experimental studies (Ferron [37],Myojo [38], Myojo [39],Kim and Iglesias [40], Kim

and Garcia [41], Kim and M.Fisher [42]) employed a simple bifurcation model with the

idealised geometry from Weibel [15] to determine the particle deposition patterns. These

studies were useful in understanding the flow pattern and deposition mechanisms. As

mentioned previously, however, the application of an idealised geometry will not facilitate

the determination of particle distribution for each lung lobe.

Another collection of particle deposition experiments (Sussman, et al. [2], Chan, et al. [22],

Schlesinger and Lippmann [43], Schlesinger, et al. [44], Gurman, et al. [45], Cohen, et al.

[46], Cheng, et al. [47]) used realistic airway replicas made from human cadavers.

Deposition data obtained from lung cast experiments suffered from large variations

however, and the data was more difficult to interpret or formulate into a model. The

results highlighted the degree of difference that arose when comparing experimental

results with theoretical models.

More recent studies were conducted by Zhou and Cheng [48] and these used a real

replication of the human airways that included the oral cavity, pharynx, larynx, trachea

and four generations of bronchi. Zhou and Cheng studied nine different sizes of

monodispersed, polystyrene latex fluorescent particles, ranging from 0.93 to 30 microns

at three different constant flow rates of:

15

30

37

60 litres per minute.

Zhou and Cheng formulated the deposition efficiency as a function of the Stokes Number.

In their study they created a lung cast from a cadaver, using a small-scale powder

disperser. An empirical model was developed for the particle deposition efficiency in the

tracheobronchial region based on their experimental data.

In general, experimental studies involve significant time, effort and cost. The lung casting

and supporting experimental equipment are expensive and it is also costly to vary

conditions in a physical system. For this reason, in this research, the use of computational

fluid dynamics for the modelling of particle deposition was seen to be a more effective

and flexible approach.

38

2.5 Computational Fluid Dynamics and Modelling

2.5.1 Overview

Computational Fluid Dynamics (CFD) is a computer-based tool for simulating the

behaviour of systems involving fluid flow, heat transfer, and other related physical

processes. It works by solving the equations of fluid flow (in a special form) over a region

of interest, with specified (known) conditions on the boundary of that region.

In the biomedical field, there are many applications involve fluid flow, heat exchange and

particles tracking in the human body and in biomedical devices. Some typical examples are:

aerosol drug delivery;

blood pumps;

artificial heart valves;

blood oxygenators;

filtration devices;

needles and catheters;

tubing;

diagnostic equipment.

Transport processes can include the effects of:

electrical fields;

osmosis;

multiple phases;

39

deposition of particles;

deformation of solid regions surrounding fluids;

chemical reactions.

CFD analysis offers details of fluid pressures, velocities, solute or particle concentrations,

temperatures, stresses, and heat/mass fluxes throughout the flow domain by solving the

governing equations using specified boundary conditions. At the post processing stage,

computation results on flow parameters can be displayed in different formats, this

including color-coded graphics, contour charts, vector diagrams, which helps to provide

insight into physical mechanisms affecting the operation of a particular device. CFD results

can also be exported in excel data to perform 2D analysis. CFD software users can readily

modify model geometry, boundary conditions, or physical material properties to

determine the effects on the system due to different conditions. As a result, CFD is

suitable for conducting parametric studies, making it possible to evaluate design

alternatives than the build and test method, in this manner allowing for faster

performance optimization, significant reduction of design cycle time, reduction of the cost

while improving the time to the market depending on the products.

Experiments using physical (in vitro) and animal models (in vivo) will continue to have a

dominant role in testing design of medical devices in the near future as of 2011 due to the

fact that medical devices are interfacing with human, it is far more convincing to

demonstrate physical experimental results than CFD analysis, however, it has some

significant disadvantages that explain the increasing emphasis many major medical device

manufacturers are placing on computer simulation. One example is that experiments

which take a long period of time to perform are expensive and may involve risk to animal

or even human subjects. For these reasons, medical device manufacturers are turning to

40

computer simulation for evaluating the relative performance of various design

alternatives to ensure that the most effective ones reach the market.

Another major drawback with physical experiment concerns the limited quantity and

quality of the data that is generated. Such data is obtained only at particular locations

where measurements can be made. On the other hand, computer simulations can provide

as many calculations, as many relevant parameters, and as many locations as the analyst

requires to improve the product during the design phase. Numerical simulation also

eliminates the problem of data scatter caused by difficulties in maintaining uniform

experimental conditions.

One of the classic example of the uses of CFD is demonstrated by Medtronic Incorporation

is the design of blood handling devices by Pederson and Karlsen [49]. This case study is

extracted from ANSYS CFX (commercial CFD software package) User Manual. According to

ANSYS Documentation [50] Medtronic utilize ANSYS CFX as their integral part of the

design optimization process for blood pumps (heart) and oxygenators (lung) used in open-

heart surgery. One design objective for such devices is to minimize mechanical and

thermal stresses that can cause damage to blood cells in the artificial circulation. The

BioMedicus Biopump, type of blood pump manufactured by Medtronic, is composed of

three rotating cones that produce a centrifugal effect for drawing blood from an inlet port.

Optimization of the blood pump performance required prediction of magnitude and

distribution of pressure, temperature, and shear stress fields, and residence time of fragile

blood cells within the pump cavity. Flow in the BioMedicus Biopump was simulated using

a geometrically accurate computational domain to determine the critical flow parameters.

After six months of utilizing CFD technology, Medtronic claimed that the hardware and

software expenses were recovered through improvements in product design efficiency

and a major decrease in time-to market for new product designs. The ability to modify late

in the design cycle using CFD results was therefore valuable because rebuilding and

41

conducting physical testing of prototypes at this stage was a very expensive process. This

shows that the significant of CFD technology plays an important role in product design

phase, this is not limiting CFD technology for Biomedical devices, this also applies for

many different engineering applications. The next section will describe some of the theory

behind CFD technology.

2.5.2 Governing equations of fluid flow in human airways

This section presents the derivation of the governing equations of fluid flow which are the

equations that are required to be solved in the simulations presented in later chapters.

The derivation presented here is largely based on a reading of Versteeg and Malalasekera

[23]. The governing equations of fluid flow represent two statements of conservation laws

of physics.

(i) Conservation of mass of the fluid – mass cannot be create or destroyed

(ii) Conservation of momentum – sum of the forces on a fluid particle equals to rate of

change of momentum (Newton’s second law).

The analysis of fluid flow being considered is at macroscopic level at 1m where molecular

structure and molecular motions are ignored. The fluid considered is a continuous

medium. At macroscopic level, the fluid element contains properties such as pressure,

velocity, density, temperature and their space and time derivatives. Consider a small

element of fluid with sides x, y, z as shown in Figure 2-5.

42

Figure 2-5 Fluid element for conservation laws

The fluid element has six faces, North (N), South (S), East (E), West(W), Top (T) and Bottom

(B). The right-handed Cartesian system is used and the positive direction is shown in the

figure. The fluid element centre is located at position (x,y,z). Consider the fluid properties

are functions of space and time, each of the property can be written as:

(x,y,z,t).

p(x,y,z,t).

T(x,y,z,t).

u(x,y,z,t).

for the density, pressure, temperature and the velocity vector respectively.

The fluid properties at the faces can be expressed accurately by a 2nd degree Taylor series

polynomial by assuming the fluid element is finitely small. Taking the pressure at the East

43

(E) and West (W) faces in which they are both at a distance of

from the element

centre can be expressed as

xxpp

21

xxpp

21

2.5.3 Mass conservation in three dimensions

The rate of increase of mass in the fluid element is defined as:

zyxt

zyxt

2-4

In Equation 2-4, the mass of the fluid element changes in time depending on the density

of the fluid element multiply by the volume of the element. Assuming there is mass flow

rate across the fluid element, this is given by the product of area, density and the average

velocity component normal to the face. As shown in Figure 2-6, the mass flow rate in and

out of the fluid element across its boundaries is given by:

44

yxzzwwyxz

zww

zxyyvvzxy

yvv

zyxxuuzyx

xuu

21

21

21

21

21

21

2-5

Figure 2-6 Mass flows in and out of fluid element.

Mass flow in and out must be balance with the rate of increase of mass in the fluid

element. By equating equation 2-4 and 2-5 and divide both sides with zyx , the

equation will become:

0

zw

yv

xu

t

2-6

Or in more compact vector notation

45

0

u divt 2-7

Equation 2-7 is the called the unsteady, three-dimensional mass conservation or

continuity equation at a point in a compressible fluid. The first term of the equation is the

rate of change in time of the density (mass per unit volume). The second term of the

equation describes the net flow of mass out of the element across its boundaries and is

called the convective term. For an incompressible fluid, the density is constant with

respect to time. Equation (2-7) then becomes

0u div or 0u 2-8

Or in longhand notation

0

zw

yv

xu

2-9

46

2.5.4 Momentum equation in three dimensions

Assume that the common properties such as density, pressure, temperature and velocity

of the particle are function of the position (x, y, z) of the particle and time t. Let the value

of a property per unit mass be denoted by . The total derivative of property with

respect to time can be written as D/Dt, where it represents:

dtdz

zdtdy

ydtdx

xtDtD

2-10

Newton’s second law states that sum of the forces on the particle equals to the rate of

change of momentum of a fluid particle. The rates of increase of x-, y- and z- momentum

per unit volume of a fluid particle are given by

DtDu

DtDv

DtDw

2-11

There are two types of forces acting on the fluid particles. Surface forces are pressure and

viscous forces. Body forces are gravity, centrifugal, Coriolis and electromagnetic.

On each face of the fluid element, there is one normal stress p (pressure) component and

three viscous stress component. There are in total of 9 different viscous stress as shown

in Figure 2-7. The suffix notation of the viscous stress ij is applied to indicate the direction

of the viscous stresses. The suffices i and j in ij indicate that the stress component acts in

the j-direction on a surface normal to the i-direction.

47

Figure 2-7 Stress components on three faces of fluid element

Consider only the x component of the forces due to pressure p and stress components xx ,

yx and zx as shown in Figure 2-8. Therefore in x-direction, the net force is the sum of

the force components acting in that direction on the fluid element.

Figure 2-8 Stress components in the x-direction

On the East (E) and West (W) faces, the sum of forces is:

48

zyxxx

p

zyxx

xxpp

zyxx

xxpp

xx

xxxx

xxxx

21

21

21

21

2-12

On the North (N) and South (S) faces, the sum of forces is:

zyxy

zxyy

zxyy

yxyxyx

yxyx

21

21

2-13

Finally, on the Top (T) and Bottom (B), the sum of forces is:

zyxz

yxzz

yxzz

zxzxzx

zxzx

21

21

2-14

The total force per unit volume on the fluid due to these surface stresses is equal to the

sum of (2-12), (2-13) and (2-14) divided by the volume zyx :

zyx

p zxyxxx

2-15

Assuming MxS is the source term containing the body forces. The suffix Mx denotes it is

the x-momentum per unit volume per unit time. The x-component of the momentum

equation is found by setting the rate of change of x-momentum of the fluid particle (2-11)

equal to the total force in the x-direction on the element due to the surface stress (2-15)

plus the rate of increase of x-momentum due to sources:

49

Mx

zxyxxx Szyx

pDtDu

2-16

Same apply to y direction and z direction:

My

zyyyxy Szy

pxDt

Dv

2-17

Mz

zzyzxz Szp

yxDtDw

2-18

The source terms MxS , MyS and MzS in equations 2-16, 2-17 and 2-18 are component of the

body forces only. For example, to model the body force due to gravity, 0MxS , 0MyS

and gSMz .

2.5.5 Navier-Stokes equations for a Newtonian fluid

In a Newtonian fluid, the viscous stresses are proportional to the rates of deformation.

Newton’s Law of Viscosity for compressible flows contains two constants of

proportionality and they are:

Dynamic viscosity, , to relate stress to linear deformations

Viscosity, , to relate stresses to the volumetric deformation.

The nine viscous stress components are:

50

udivxu

xx

2

udivyv

yy

2

udivzw

zz

2

xv

yu

yxxy

xw

zu

zxxz

yw

zv

zyyz

2-19

For gases a good approximation can be obtained by taking the value

32

.

Liquids are incompressible so the mass conservation equation is

0udiv

and the viscous stress are twice the local rate of linear deformation times the dynamic

viscosity. Substituting the shear stress equations (2-19) into (2-16, 2-17 & 2-18) produces

the Navier Stokes Equations:

51

MxSxw

zu

z

xv

yu

ydiv

xu

xxp

DtDu

u2

MySyw

zv

z

divyv

yxv

yu

xyp

DtDv

u2

MzSdivzw

z

yw

zv

yxw

zu

xzp

DtDw

u

2 2-20

To reduce the long mathematic terms, it is often rearrange by grouping viscous stress

terms, for x-component, the equation can become:

MxSxx

wzx

vyx

ux

zu

zyu

yxu

x

xw

zu

zxw

yu

yxu

x

u

u

u

graddiv

div

div2

The viscous stress balance for y- and z component can be written in the same form.

However to simplify the equation further, the insignificant viscous stress term can be

considered inside the source term:

MMM sSS 2-21

52

Where

xw

zu

zxv

yu

ysM

To help the development of the finite volume method, the Navier-Stokes equations can be

written in this form:

MxSxp

DtDu

ugraddiv

MySyp

DtDv

vgraddiv

MxSzp

DtDw

wgraddiv

2-22

These are the most important transport equations which governs the fluid flow inside the

human airways.

53

2.6 Application of CFD to Modelling of Biological Systems

2.6.1 Overview

At the time this research program commenced, the application of CFD to the modelling of

biological systems had already become widespread, largely due to the increased

availability of computing power and the relative cost and flexibility advantages over the

creation of physical models and experimental rigs. The results of CFD modelling were

generally regarded as highly accurate.

2.6.2 CFD modelling of fluid flow in human airways

In the field of fluid flow in human airways, there tended to be more articles that combined

the study of particle deposition together with fluid flow, rather than having fluid flow

studied in isolation. This section here will only describe numerical studies which looked at

fluid flow in the airways.

One of the early numerical studies which had been cited by many researches was

undertaken by Wilquem and Degrez [51]. They numerically studied a steady inspiratory

airflow through a three-generation model of human airways in two dimensions. The

three-generation model correspond to the fifth to seventh generation of Weibel [15]’s

model. Their study was restricted to two dimensions because of the lack of available

computer power. As noted in their study, Wilquem and Degrez had great difficulty in

generating grids for the bifurcation model. They overcame the problem by adapting a non-

overlapping multi-block technique. Their two dimensional simulation results did not,

however, replicate realistic human airway fluid flow as they concluded that flow

54

separation exists with low Reynolds Numbers that range from 200 to 1200. Similar studies

done by Gatlin, et al. [52] demonstrated different results because their computational

model was three dimensional.

Around the same era, Elad, et al. [53] created a computational model of oscillatory airflow

in a bronchial bifurcation. Their system or model parameters were time-dependent and

were extracted from laboratory studies of airway models and physiological measurements.

This was one of the first models that uses Computational Fluid Dynamics (CFD) to study

fluid flow in airways until Calay, et al. [54].

Calay, et al. [54] utilised CFD to study the unsteady respiratory airflow dynamics within

the human airways. The three dimensional asymmetric bifurcation model that they

employed was based on the morphological data given by Horsfield, et al. [16]. The CFD

simulation used two breathing conditions – that is, resting and exercise. They found that

flow separation occurred for the maximal exercise condition where the Reynolds Number

was with the Womersley Number α at 4.747.

Subsequently, Liu, et al. [55] performed similar simulations to Calay, et al. [54] with the

addition of the pressure drop analysis, where a correlation between pressure drop

coefficient and Reynolds Number was found. Later, they published another paper which

considered the asymmetric human lung airways in Liu, et al. [56].

As noted by Calay, et al. [54], fluid flow in human airways during exercise will become

turbulent flow. Luo, et al. [57] used large eddy simulations (a type of turbulence model

inside a commercial package called Fluent [58] to model the fluid flow in a simple airway

model. They concluded that LES was one of the feasible CFD modelling techniques to

model the fluid flow in human airways and they validated their results with Martonen, et

al. [9].

55

More recently, studies on this topic were performed by Leong, et al. [59]. This was

another study of fluid flow in a double bifurcation, and while the findings yielded no

surprises, the unique element of their study was that they utilised Particle Image

Velocimetry (PIV) to measure velocity data in the double bifurcation. This was one of the

newer sets of published experimental data.

Another more recent study was undertaken by Freitas and Schröder [60], who also used a

CFD technique. However, the solver employed the Lattice-Boltzmann method (LBM)

rather than finite volume method, thereby demonstrating that the LBM can be used as an

alternative to solve the fluid flow equations in human airways.

There were also a large number of numerical studies on fluid flow in the smaller airways

deeper inside the lung (e.g., Sharan and Singh [61], Hammersley, et al. [62]) which only

indirectly related to the current topic.

To conclude, fluid flow plays an important role in particle transportation and deposition.

The studies cited here provided valuable information on how fluid flow behaves in human

airways in both steady and oscillatory flow. The manner in which particles behave in the

human airways will be described in Section 2.6.3.

56

2.6.3 CFD modelling of particle deposition in human airways

At the time this research was undertaken, numerical methods had been used to model

particle deposition in the human airways. The flow field; particle trajectory and

deposition have been calculated by means of solving corresponding equations. Earlier

studies considered the flow field as steady flow (e.g., Diu and Yu [63], Gradon and Orlicki

[64], Lee and Goo [65], Asgharian and Anjilvel [18], Zhang, et al. [66], Comer, et al. [67]).

The numerical results for fluid flow and particle deposition had been reported by Zhang,

et al. [66], and Comer, et al. [67], but these simulations were carried out using a steady

flow, and the particles were injected at a constant rate. The problem was that human

breathing was not a constant flow process, so it was important to study the transient

effects on particle deposition. These factors were partially addressed by the recent work

of Li, et al. [68] and Zhang and Kleinstreuer [10]. At the time of compiling this review, CFD

modelling of particle deposition had primarily been conducted by a single group of

research from the North Carolina State University. These researchers had been using CFX

as the computer simulation tool as described in Zhang and Kleinstreuer [10], Kleinstreuer,

et al. [69]. However, their research had not evolved significantly over the decade since

their first CFD modelling paper till this review was conducted.

A more recent study by Comerford, et al. [70] used a co-axial tomography (CT) scan to

create the lung geometries and employed fluid structure interaction simulations.

Comerford’s study was patient specific and it considered only nanoparticles – it did not

formulate a generic particle deposition which facilitated the generalisation of the result to

the average adult. Therefore, a more comprehensive study was still necessary in order to

determine the transient particle patterns in a real model of human airways – this was the

basis of the research presented herein.

As there was a gap in relation to CFD studies in the area of particle deposition in the

human respiratory system, it was logical in this research to endeavour to use CFD as the

57

main approach. The novelty of the CFD approach in this research program was to be that

new assumptions were to be used – for example, how boundary conditions should be set,

and the type of turbulence model to be used.

58

2.7 Conclusions and Research Directions

The literature review provided both basic information on the structure of the human

respiratory system as well as research into modelling flow and particle deposition through

various techniques, including physical experimentation and simulation modelling through

CFD. The review highlighted earlier work and achievements as well as gaps that previous

researchers had identified. This research was structured to endeavour to address some of

these gaps.

In summary, a reading of basic literature on the respiratory system leads to the

understanding that the human lung is composed of bifurcating networks. The first

generation of the bifurcating network is the trachea, which is referred to as Generation 0

and it splits into two child branches called the main bronchus which are referred to as

Generation 1 of the airways. The interesting point about human airways is that the

velocity increases from Generation 0 to Generation 3, then monotonically decreases down

the generations. The Reynolds Number decreases monotonically down the generations.

If the Stokes Number is calculated with the same density and size along the human

airways, assuming a particle to be travelling at the speed of the flow, the maximum Stokes

Number is at generation 5. The key point of emphasis here is that it is onerous to relate

particle efficiency with just the Reynolds Number and Stokes number, as the airway

geometry is very complex.

It is also clear from the reviewed literature that it is difficult and costly to conduct full

particle deposition experiments using a lung cast, and the flexibility of experiments is

limited. The literature reported many attempts at developing computer based modelling

techniques as a more efficacious approach. This research program endeavoured to

pursue a simulation approach based on CFD modelling.

59

The first step in the modelling process in this research was therefore to create a simple

bifurcation model that had sufficient similarity to the human lung bifurcation. When

compared against existing experimental data, this could then be used to validate the CFD

model of the human lung. In fact, a more general particle deposition empirical formula

was additionally required for the upper airways.

In this research, a detailed computer simulation was to be developed for particle

deposition in the human upper airways for the first four generations. Model geometry was

to be built using Solidworks and the flow field and particle trajectories in the model

geometry calculated using CFX based on a finite volume method. The aim was to study the

factors affecting the deposition efficiency that included break down of the dimensionless

number, in view of the particle efficiency with changes in:

particle size

particle density

fluid flow rate.

It was deemed that by performing such an analysis, it would then be possible to

determine the factors which had the maximum influence on deposition efficiency, based

on considerations of a realistic particle diameter and density.

60

Chapter. 3 In-Vitro Experimental Study Modelling Human Airways

61

3.1 Introduction

In this chapter, the experimental work which was performed on fluid flow through a

bifurcating airway model is presented. The human lung airway system is composed of

bifurcating networks and the experiments in this study investigated the fluid flow in

bifurcations.

The primary objective of this work was to form a basis on which to validate the results

obtained using computational fluid dynamics code provided by CFX ANSYS CFX v11 [71].

The model used was basic as the aim was mainly to build confidence in the numerical

code and validate some selected data.

The experiments employed Laser Doppler Anemometry (LDA) to measure velocity profiles

at various locations inside the parent tubes and daughter tubes of bifurcation. The results

obtained were used for the validation of the numerical data given later in this chapter.

The experiments conducted in this chapter were carried out under steady flow, and the

medium used for velocity measurements was water.

62

3.2 Experimental Apparatus

LDAs are non-contact optical instruments for the investigation of fluid flow structure in

gases and liquids. These instruments can also measure surface velocities of solids. LDAs

have some unique advantages in comparison with other fluid flow instrumentation such

as hot-wired probe.

(i) Non-contact optical measurement – This is the major advantage of LDA as LDAs

probe the flow with focused laser beams and can sense the velocity without any

disturbance to the flow in the measuring volume. The necessary conditions

(sometimes considered as drawbacks) are a transparent medium with a suitable

concentration of seeding particles (or tracer particles) and optical access to the

flow through transparent windows, or via a submerged optical probe. In some

Engineering application, it can become economically costly to generate seeding

particles for airflow measurements.

(ii) No calibration is required – LDAs have unique intrinsic response to fluid velocity

therefore, it is absolute linearity. LDA measurement is based on the stability and

linearity of optical electromagnetic waves and is only slightly affected by other

physical parameters such as temperature, density, pressure of the flow medium.

(iii) Well defined directional response – The velocity measurement by LDA is the exact

directional projection response of the flow. Meaning that measuring the velocity in

x-direction will not contain velocity component from y- or z- component.

(iv) High spatial and temporal resolution – High intensity laser beam allows LDA to able

to define a very tiny measuring volume. This provides high spatial resolution and

allows local measurement of Eulerian velocity. With the advance in fast signal

processing electronics nowadays and since the measuring volume is small; this

63

permits high bandwidth, time-resolved accurate measurements of fast fluctuating

velocities.

(v) Multi-component bi-directional measurements at the same time – with the

installation of frequency shifting apparatus to the laser system, the laser can be

split into multi component. Two or more velocity component can be measured at

the same time.

The properties of LDAs made them an attractive proposition for measurements in this

research. As is often the case, however, optimization of the performance of a system with

respect to certain parameters can influence other performance characteristics negatively.

Figure 3-1 shows the 2D Laser Doppler Anemometry facility made available for this

research. Swinburne University of Technology has utilised this Laser Doppler Anemometry

for many research projects (Morsi, et al. [72],Morsi, et al. [73]).

Figure 3-1 Laser Doppler Anemometry at Swinburne University of Technology

64

3.3 Principles of Laser Doppler Anemometers (LDAs)

The LDA measuring technique was first proposed by Yeh and Cummings [74]. The principle

of the LDA technique is based on the fact that the light scattered by particles in a flow is

Doppler shifted. The frequency of the Doppler-shift is directly proportional to the velocity

of the particles. A different combination of optical set up is designed to measure the

Doppler shift frequencies, and the most common optical system is the so-called dual beam

or fringe mode system. In a dual beam arrangement system, two Gaussian beams of equal

intensity are crossing each other in the flow field using a focusing lens to produce an

ellipsoid shaped measurement volume. Therefore, a fringe pattern is generated at this

point in the same plane as the beams. Figure 3-2 shows the schematic diagram of the dual

beam optical system with the fringe description.

Figure 3-2 Dual beam optical system and fringe pattern

The fringe separation f , is defined as,

65

2sin2

f

3-1

where is the laser wavelength and is the laser beam intersection angle. A particle

passing through the dark and the light fringe pattern will scatter light whose intensity will

vary. Assuming that the Doppler shift frequency is fD, then the particle velocity component,

U, normal to the fringe in the same plane is given by,

2sin2

D

DfffU

3-2

This model provides an accurate expression for the velocity of particles in the flow field,

and requires no calibration since the wavelength and intersection angle are constants

once the colour of the laser beam is chosen and the optical arrangement is fixed. The

component of velocity must always be measured normal to the fringes, regardless of the

direction of the flow.

66

3.4 Experimental Set Up

The experimental work presented here made use of the LDA shown in Figure 3-1. The

two-component LDA system is a transmitted based Fibre Flow system with high

transmission efficiencies from the laser source to the measuring volume. As show in

Figure 3-3, the system consists of a laser source, the Aerometrics Fibre Drive connected

with a fibre optic probe and signal processors together with a data acquisition system.

Figure 3-3 LDA system setup

The Argon-Ion laser was functioning in the fundamental optic mode of the cylindrical laser

cavity mode which provides a Gaussian distribution of its intensity at all cross sections

along the beam. The laser source of the LDA system was a Spectra-Physics Stabilite 2017

Argon-Ion laser with overall output power of 5W for all continuous lines of wavelength

from 351.nm to 528.7nm, particularly with approximately 1.5W power of the blue beam

at 488 nm wavelength and the green beam at 514.5 nm wavelength. These blue and green

67

beams were the two colour beams used for the optical arrangement of the two

component LDA system.

The fibre optic probe had a lens of 100mm focal length and the beam diameter of 3.5mm

which produced an ellipsoidal measurement volume. Figure 3-4 shows the measuring

volume is an ellipsoid due to the Gaussian intensity distribution in the beams. dx is the

height, dy is the width and dz is the length of the measuring volume and f is the

wavelength of the beam.

Figure 3-4 Measurement Volume

The probe volume dimensions recorded from signal analyser is shown in Table 3-1.

Table 3-1 Probe volume dimensions

dx (m) dy (m) dz (m)

U – Velocity Green beam

0.00181 0.00177 0.00898

V – Velocity Blue beam

0.00190 0.00187 0.00947

Acquisition of LDA data is achieved on the computer with high speed to digital converters.

The software called DATAVIEW was used to collect data from the signal analysers. In the

68

experiment, 5µm silver coated pearl particles were used as the seeding particles due to

the high reflection rate. These particles were found to track the flow accurately and

generate sufficient scattered light from the laser for the photo detector to detect (Owida

[75]).

A schematic diagram of the fluid flow equipment is shown in Figure 3-5.

Figure 3-5 Schematic diagram for the experimental setup

Actual physical setup of all the equipment is shown in Figure 3-6. The pump is located

under the water tank

69

Figure 3-6 Actual equipment setup at Swinburne Fluid Lab

Each component of the setup is described below:

Water tank – 0.252 m3 in volume, the water tank provided a reservoir of water

with filler to provide water flow for the whole circuit without air bubbles. Very fine

particles were deployed into the water tank for the whole system. These seeding

particles were used for LDA measurements.

Pump – A pump was used to provide work to drive the water from the tank

through the circuit. This pump was capable of producing 33 L/ min of flow.

Ball valve – The ball valve was used for adjusting flow rates.

70

Flow meter – The flow meter was used for measuring the flow rates along the main

tube and the bifurcation model.

Pressure gauge – Pressure gauge is used to measure the water pressure entering

the bifurcation model.

Bifurcation model – The bifurcation model was made out of glass, as shown in

Figure 3-7. The model was mounted onto a Perspex box such that the laser could

shine onto a flat surface before entering the model. The Perspex box is filled with

liquid (glycerine) that has a similar refractive index as glass. The reasons for having

the Perspex box are:

1. To reduce optical noise as laser light scatters when shine onto curved

surface on the glass tube.

2. To maintain the laser refractive indices such that the laser beam would not

bend (change direction) when the laser pass through curved surface.

Figure 3-7 Glass bifurcation model

71

The dimensions of the model are shown Figure 3-8.

Figure 3-8 Dimension of bifurcation model mimicking the human airways

Figure 3-9 shows an example of how the LDA measures the velocity of the water flow

inside the bifurcation glass model.

Figure 3-9 LDA measurements

Three different steady flow rates were measured in the experiment. These represented

Reynolds numbers (Re) of

72

518

1036

2089

at the inlet to the bifurcation model. Reynolds number is a dimensionless number that is

the ratio of the inertial forces to viscous forces. Reynolds numbers are commonly used to

determine the characteristic of the flow regimes.

3-3

where

is the density (property of the flowing fluid)

U is the mean velocity of the flow (can be computed from flow meter

measurement)

D is the hydraulic diameter (diameter of the glass tube)

µ is the dynamic viscosity (property of the flowing fluid)

It is well known that there are three types of fluid flow in pipes, they are laminar,

transitional and turbulent. The flow is

Laminar when Re < 2300

Transitional when 2300 < Re < 4000

Turbulent when Re > 4000

The LDA equipment is only capable of capturing fluid flow when it is under laminar

condition. Therefore the selection of the Reynolds number for conducting the experiment

73

is limited, so the Reynolds number chosen are 518, 1036 and 2089. The results were

measured at four different locations inside the bifurcation mode. As per Figure 3-12,

Station 1 was at the inlet; Station 2 was at the point before the flow divider; Station 3 was

at the point after the flow divider, and Station 4 was at the outlet.

At each station, 20 equally spaced points were selected to conduct LDA measurements.

The LDA probe was placed on a high precision X-Y axis adjustable table. In order to

determine the location of the wall, the LDA probe was moved at the step of 0.05mm until

a non-zero velocity were recorded. Then the LDA probe was moved in an increment of

0.013m allowing 19 measurements for Station 1 & 2 and 17 measurements for Station 3 &

4. At each point location for measurements, the average velocity was calculated based on

measurement from 10,000 sample particles.

Section 3.5 describes how the experimental setup was modelled numerically, and the

results obtained will subsequently be presented together.

74

3.5 Initial Numerical Experimentation

3.5.1 Overview

The experimental set up described in 3.4 was simulated numerically using computational

fluid dynamics to build some degree of confidence in the numerical code. First, the

bifurcation model was created using CFX-Build. CFX-Build was a program that was part of

CFX version 5.6. CFX-Build was a geometry creation software packaged that enabled users

to create complex two or three dimensional geometry from points and lines. Meshing was

performed after geometry creation. Figure 3-10 shows the mesh created by CFX-Build

using tetrahedral elements.

Figure 3-10 Mesh of the bifurcation geometry

The specification of the flow physics, boundary conditions, initial values and solver

parameters was all performed in CFX-Pre. CFX-Pre could import mesh files produced by

75

CFX-Build, or from a range of other mesh generation software packages. From a problem

specification generated in CFX-Pre, the CFX-5 Solver solved for all the solution variables for

the simulation. When the residual of the variable reached a limiting value, a solution was

obtained. Figure 3-11 shows the residual of variables

P-Mass

U-Mom

V-Mom

W-Mom

reaching below 0.0001, thus providing the required solution for each variable.

Figure 3-11 Solution converges for all the velocity investigated variables

76

An important feature of CFX-5 is its use of a coupled solver, in which all the hydrodynamic

equations are solved as a single system. The coupled solver is faster than the traditional

segregated solver, and thus less iteration is required to obtain a converged flow solution.

CFX-Post is a post-processing graphics tool which is employed to analyse and present the

results from CFX-5 simulations.

3.5.2 Simulation Physics Specification

The fluid considered here was incompressible air at 25C with viscosity, = 1.831E-05

(kg/m-s) and density, = 1.185 (kg/m3). The solutions were obtained for a large range of

Reynolds Numbers (Re = 500 to 2000) at steady inspiration rate. The governing equations

were:

The continuity equation:

0 U 3-4

The momentum equation:

Tp1 UUUU

3-5

77

Where

is the density

p is the static pressure

U is the vector of velocity U (x, y, z).

is the kinematic viscosity

The inlet condition for the bifurcation was the measured mass flow rate by the flow meter

in the experimental setup. The outlet condition was by setting relative static pressure to

zero. The wall was set to no slip boundary.

Figure 3-12 Boundary conditions for the bifurcation model

78

3.6 Results and Observations

3.6.1 Overview

This section presents three sets of results for Reynolds Numbers at

518

1036

2089

respectively. In each set of results, there were 4 locations of velocity measurements as

shown in Figure 3-12. The location A-A’ denotes Station 1, the location B-B’ denotes

Station 2, the location C-C’ denotes Station 3 and the location D-D’ denotes Station 4.

3.6.2 Case 1: Reynolds Number at 518

The velocities Vmean at four locations are plotted in Figure 3-13 for a Reynolds Number of

518. On the graph, the triangle symbols represent simulations results and the hollow

square symbols represent the experimental results. The agreement is quite good at

Station 1. At Station 1, the maximum velocity reaches 0.024 m/s. At Station 2, the

simulation still presents a very smooth parabolic profile while the actual experimental

results velocities showed decreased velocity on the side walls, and the peak velocity was

lower than simulation result. The maximum experimental velocity recorded was 0.0158

m/s at x=0.0106 m from the left wall of the tube. While the maximum simulation velocity

recorded was 0.0174m/s.

79

Station 1

Station 2

Station 3

Station 4

Figure 3-13 Velocity for Station 1 to 4 at Reynolds number 518

The differences between the experimental and simulation results could be attributed to

the manufacturing defects of the glass model. The round tubes of glass were melted and

joined together by a professional glass blower and, at the inner side of the joint, there

X (m)

Vel

ocity

(ms- 1)

0 0.01 0.02 0.030

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0.024

X (m)

Vel

ocity

(ms- 1)

0 0.01 0.02 0.03

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

X (m)

Velo

city

(ms^

-1)

0 0.01 0.02

0

0.005

0.01

0.015

X (m)

Velo

city

(ms^

-1)

0 0.01 0.02

0

0.005

0.01

0.015

80

existed some roughness on the surface, as shown in Figure 3-14, causing the velocity

profile differences for other stations. There were also other inaccuracies in experimental

data which were due to the imperfections of the experimental model. Apart from the wall

having rough surfaces, within the glass model, it was also unavoidable that the glass

model had air bubbles created during the blowing process at low velocity. When the laser

light passed through the air bubbles inside the glass, the laser light was bent and caused

measurement errors. This error mainly affected Station 2 and Station 3.

Figure 3-14 Differences between Simulation model and Experimental model

At Station 3, the simulation showed a very smooth skewed parabolic shape and was

somewhat different from the experimental results. This was due to the effect of the

differences in geometry of the two models. It is important to note that major differences

are more noticeable near the wall. At Station 3, maximum experiment velocity was

located at x=0.01995 m with 0.016299 m/s while maximum simulation velocity was

located at x=0.0019 m with 0.01613 m/s which they both were located closely with similar

value. At station 4, the error had slightly reduced as the flow developed again into a

parabolic profile. The experiment measured values were all lower than simulation, one of

the assumptions that were made at the construction of the experimental rig was that the

81

flow rate should be equal for the both outlet. If the flow resistance were different

downstream after the flow divider, the flow would not be equal in each branch of outlet

especially when the mass flow rate is low. Another point to note with the results was the

velocity measured was by the magnitude of 0.016 m/s equivalent to 1.6 cm/s, which was a

very small velocity and the errors would increase due to the capability of the LDA

equipment.

82


The velocities Vmean for Reynolds Number at 1036 are plotted in Figure 3-15. The

experimental results at Station 1 (inlet) matched very closely with the simulation results.

The simulation velocity profiles were quite similar for Station 1 and Station 2. The

experimental results at Station 2 had a parabolic trend except at x=0.02. This was because

of errors in the reading of experimental measurements. At Station 3, the results looked

promising as the experimental results matched with the simulation results. The

differences between the experimental results and simulation results were greatest near

the wall. At Station 4, the simulation results remained as a smooth curve when the flow

started to redevelop – however, the two peaks of the skewed velocity profile from the

experimental results were higher than the simulation result. This could be contributed by

the wall roughness as explained in Section 3.6.2.

83

Station 1

Station 2

Station 3

Station 4


X (m)

Vel

ocity

(ms- 1)

0 0.01 0.02 0.030

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

X (m)

Vel

ocity

(ms- 1)

0 0.01 0.02 0.030

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

X (m)

Vel

ocity

(ms- 1)

0 0.01 0.020

0.005

0.01

0.015

0.02

0.025

0.03

0.035

X (m)

Vel

ocity

(ms- 1)

0 0.01 0.020

0.005

0.01

0.015

0.02

0.025

0.03

0.035

84


The velocities Vmean for Reynolds Number at 2089 are plotted in Figure 3-16. The results in

this case are similar to Case 2. At Station 1, the parabolic shape was matched in both

experimental and simulation results. However, in this case, the peak of the profile at

Station 1 was flatter. This was because when the Reynolds Number was 2089, it reached

the transition region from laminar flow to turbulent flow and the profile demonstrated a

fairly turbulent profile. At Station 2, the experimental results were lower compared to the

simulation. This may have been because the cross section area at Station 2 in the

experimental model was larger than the simulation model and the error value in the

experimental results may also be due to the wall roughness. At Station 3, the results

matched reasonably well. The experimental results in this station showed a slight double

peak, which was shown again in the simulation results at Station 4. At Station 4, the

simulation results were quite similar to experimental results.

85

Station 1

Station 2

Station 3

Station 4


X (m)

Vel

ocity

(ms- 1)

0 0.01 0.02 0.030

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

0.07

X (m)

Vel

ocity

(ms- 1)

0 0.01 0.02 0.030

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

0.07

X (m)

Vel

ocity

(ms- 1)

0 0.01 0.02

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

0.07

X (m)

Vel

ocity

(ms- 1)

0 0.01 0.020

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

86

3.7 Discussion

All the results show a parabolic profile at the inlet (as shown in Figure 3-13, Figure 3-15

and Figure 3-16). As the flow reached Station 2 which was close to the flow divider of the

bifurcation, the flow started to slow down, due to the larger cross sectional area. After

the flow divider, the flow became skewed as the velocity at the inner wall was larger than

the velocity at the outside wall. This was logical because, as the parabolic profile split into

two streams, the high velocity was divided into two daughter tubes downstream. The

high velocity was at the inside wall, and as the fluid flowed further downstream, the

velocity started to redevelop a laminar tube flow profile. Therefore, peak velocity was

only on one side and the peaks started to move from wall to middle downstream as

shown in the plots of Station 3 to Station 4. Reynolds number is a function of density,

velocity, diameter of the pipe divided by the viscosity of the fluid. As the Reynolds number

increases, as the other parameters are the same, this means only the velocity is faster. As

the velocity increases, after the flow divider, the velocity profile recovers faster and

develops back to the parabolic profile. At Station 4, in all cases, the flow was starting to

redevelop to become laminar. When the flow was skewed, the pressure along the profile

was uneven – on one side with high velocity, the pressure was low and on the other side

with low velocity, the pressure was high – as the flow started to redevelop, a skewed M

shape was produced.

The case for Re=2089 was slightly different, for the skewed M shape profiles earlier in

Station 3.

Overall, despite some anomalies, the simulation results showed similar trends to the

experimental results. The computational fluid dynamics code could thus be used to model

a practical situation with some accuracy.

87

Chapter. 4 Numerical Analysis In A Four Generation Airway Under

Steady Flow

88

4.1 Introduction

The objective of this chapter is to document the more detailed numerical simulation work

that was undertaken by extending the previously developed model from one to four

generations while the fluid flow conditions remained at steady flow.

The literature review highlighted several pieces of research into air flow in bifurcation

models, with relatively in simpler geometries than encountered here. In fact, both

numerical (Wilquem and Degrez [16], Zhao et al. [21], Liu et al. [18]) and experimental

(Schroter & Sudlow 1969, Chang & Masry 1982, Isabey and Chang, Zhao & Lieber 1994)

models had been reported in two decades prior to the undertaking of this research. The

studies, noted above, generally concluded that there existed a skewed velocity profile at

the outlet of the bifurcation and the subsequent development of the secondary flow along

the downstream towards the daughter branches.

Wilquem & Degrez (1997) used two dimensional steady air flow using a three generation

airway. They determined that velocity profiles downstream of the first junction were

highly skewed, thus leading to an important imbalance in the flow distribution

downstream of the second junction. Zhao et al. (1997) reported his two generation

airways model for laminar flow and validated the results with his experimental findings. It

was clear from the knowledge gained from the earlier literature that there were

significant differences between symmetric and asymmetric geometries. Moreover, that a

two dimensional representation of human airways failed to represent actual phenomena

due to the dominance of radial components in the daughter branches.

The previous chapter documented a numerical simulation that was carried out to validate

the accuracy of the numeric method in comparison with experimental data. In this chapter,

the focus is on documenting the ensuing numerical simulation. Herein, the model is

extended from one to four generations while the fluid flow condition stays at steady flow.

89

4.2 Methodology

4.2.1 Overview

In this section, the geometry of the models considered is provided along with the

equations governing the simulation. Details on the numerical method to solve the

equations are also specified. The laboratory experiment to collect the field data is also

explained in detail.

4.2.2 Geometry of the model

In the analysis here, both in-plane and off-plane geometries were considered for four

generation airways – see Figure 4-1. The in-plane geometry was one where all bifurcations

were in one single plane, similar to that of Liu, et al. [55]. In the off-plane case, the

bifurcated branches were perpendicular to each other and symmetric about their parent

branch, typically a Weibel [15] geometric model (Figure 4-1c). The computational domain

(Figure 4-2) involved a mother branch and a set of symmetrically configured lateral and

medial branches. Downstream of the mother branch, there existed two bifurcation points

symmetric to the mother branch centreline. The principal dimensions and the angles for

the model considered here are given in Table 4-1.

90

Figure 4-1 (a) In-plane (b) off-plane geometries and (c) shows two perpendicular planes in off-plane bifurcation model

(a) (b)

(c)

91

Figure 4-2 Computational domain for in-plane model with dimensions and boundary conditions.

L0

L1

L2

L3

D2 D3

D4

D0

D1

P1

P2

P4

P3 P5

P6

P8

P13

P7

P11

P12

P9 P10 P14

P15 P16 P17

P18

R0

R1

R2 R3

Ux = 0; Uy Re; Uz = 0;

p =0

y

x

92

Table 4-1 Dimension of the airways geometry of the model Name of airway Gen.

No. Number per Gen

Diameter [mm]

Length [mm]

Curvature [mm]

Trachea 0 1 D0 18 L0 120 R0 1.9D0 Main bronchus 1 2 D1 12.2 L1 47.6 R1 1.2D1 Lobar bronchus 2 4 D2 8.3 L2 19 R2 0.9D2 Lobar bronchus 3 8 D3 5.6 L3 7.6 R3 1.2D3 Segmental bronchus

4 16 D4 4.5 L4 12.7 R4 -

The geometries were constructed with the following assumptions:

The wall is smooth and the cartilage ring does not pose significant disturbances.

The curvature for the bifurcation is calculated such that smooth transition from

one generation to the next can be achieved.

The bifurcation is symmetrical with bifurcating angle 70.

4.2.3 The equations

The fluid considered here was incompressible air at 25C with viscosity = 1.81e-5 (kg/m s)

and density = 1.29 (kg/m3). The solutions were obtained for a large range of Reynolds

Numbers (Re = 500 to 2000) at steady inspiration rate. The conservation law of mass and

momentum are given below.

Continuity Equation:

0 U 4-1

93

Momentum Equation:

Tp UUUU

1

4-2

Where

is the density




4.2.4 Fluid Domain Conditions

A full cycle of breathing is a transient process such that the flow varies with time, but the

foci are given to the overall view of the flow characteristics such as flow field and

secondary flow inside a four generation airways model. The transient simulation was not

deemed to be essential as the effect of transition of flow characteristics in transient

simulation were not significant. Hence, steady state flow was assumed in the simulation.

Forced ventilation was a condition where air was pushed into the airways such that

velocity was assigned at the inlet of the simulation. In the available literature, forced

ventilation was assumed in the simulated models. The control volume of the fluid began

from the start of trachea (Gen 0) and finished at the segmental bronchus (Gen 4, Figure

94

4-2). Assuming the fluid was incompressible and the air went into the trachea it would all

pass through to segmental bronchus. Therefore mass flow rate at the inlet equals that at

the outlet. Table 4-2 lists the mass flow rate at different Reynolds Numbers.

Table 4-2 Breathing flow rate and mass flow rate at trachea for each different Reynolds Number

Reynolds Number (Re) Breathing flow rate at trachea [L/min]

Mass flow rate at trachea [kg/min]

500 6.55 0.43

750 9.83 0.64

1000 13.11 0.86

1250 16.38 1.07

1500 19.66 1.29

1750 22.94 1.50

2000 26.21 1.72

At the trachea inlet, the mass flow rate was assigned to the cross section area as:

tconsUAminlet tan

4-3

At the segmental bronchus outlet, the static relative pressure was assigned to zero. This

implied that all outlets did not provide resistance. This boundary condition was also

applied in Wilquem and Degrez [51]:

0relativep 4-4

A no-slip boundary condition was specified in all rigid smooth walls as shown in Figure 4-2.

95

4.3 Numerical Method

In light of the symmetry of the problem, only one quarter of the geometry needed to be

considered for the numerical analysis. This reduced the computation time by a factor of

four, while the results could be determined for the other mirror images regardless.

The density of the mesh varied across the cross-section - more nodes were placed near

the flow divider for better resolution in the results because the high velocity flow collided

with the wall near the flow divider. Figure 4-3 and Figure 4-4 demonstrate that the mesh

density increases near the flow divider. The figures also show that as the diameter

decreases through the generation, the size of the element also decreases to maintain a

good resolution.

Figure 4-3 Mesh of the Gen 3 & Gen 4 showing the density increase near flow divider (in plane model) Generated by author using CFX-5.7

96

Figure 4-4 Mesh of the Gen 3 & Gen 4 showing the density increase near flow divider (off plane model) Generated by author using CFX-5.7

In near-wall regions, boundary layer effects gave rise to velocity gradients which were

maximum normal to the face. Hence, inflation layers were applied on all walls to make the

model more computationally efficient. A grid independence test was carried out for

maximum steady flow condition (Re=2000) and the same grid was used for all simulations.

97

4.4 Results and Discussion

4.4.1 Overview

In this section, first step is to discuss the validation of the model based on the numerical

simulation and experimental data. Following validation of the model, velocity patterns for

Reynolds Numbers 500-2000 and for different generations are provided. The behaviour of

secondary flow is also considered.

4.4.2 Numerical Code Validation with Experimental Results

As it is typical with other numerical simulations, validation of proposed model is the first

step towards simulating a computationally difficult problem. In order to validate the code,

initially a simpler model of branching tube is considered for both numerical and

experimental analysis. Figure 4-5 shows the schematic view of the model and shows the

comparison of LDA (Laser Doppler Anemometry) data with our numerical data at Re =

1036. The validation process was described in Lai, et al. [76].

The results clearly showed the boundary layer growth as the flow passed the divider (from

parent tube to daughter tubes) indicating no separation zone at a given bifurcation angle

and Reynolds number. Zhao and Lieber [8] had also reported similar experimental results

on symmetric bifurcated tubes having 70o bifurcation angle.

98

Figure 4-5 Comparison between experimental results with numerical results at Re = 1036

99

4.4.3 Model Validation

The objective of this research was to model and simulate air flow through multiple

generations of the human airways, and hence further validation against a multiple

generation model was required. The exact same model as defined in Liu, et al. [55] was

reproduced with the same dimensions. The dimensions of this model are listed in Table

4-3 Geometric parameters for the fifth and sixth bifurcation in the human airways model

used in Liu, et al. [55]’s simulation. The diameter of the mother branch was 35.1mm and

the total cross-sectional area of the two daughter branches was the same as that of the

mother branch. The junction radius of curvature was seven times the diameters of the

daughter branches, and the bifurcation angle was 70.

Agreement between the calculations here and numerical results from Liu, et al. [55] was

quite good, including the skewed axial velocity profile towards the inner wall in the

bifurcation plane as shown in Figure 4-6. Although the model here was reproduced

according to the dimensions given in Liu, et al. [55], it needs to be noted that these were

two dimensional only, in the mid plane of the model. The small discrepancies in the results

may then be attributed to the effect of the three dimensional parameters, such as the wall

curvatures, on how the flow divider was modelled here.

The results also compared well against calculations in a 180 pipe bend by So, et al. [77]

and experimental measurements by Zhao and Lieber [78].

Table 4-3 Geometric parameters for the fifth and sixth bifurcation in the human airways model used in Liu, et al. [55]’s simulation

I D (mm) L (mm) R (mm) 2 () ()

5 3.5 10.7 7D6 70

1803

6

RL

6 2.8 9.0 7D7 70

1803

7

RL

7 2.3 7.6

100

Figure 4-6 Comparison between numerical results with Liu, et al. [55] numerical results at the end of the second-generation tube in a three-generation airway with (a) Re = 200, (b) Re=800 and (c) Re=1400.

XVe

loci

ty(D

imen

sion

less

)-1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4Liu's ResultCFX Result

X

Velo

city

(Dim

ensi

onle

ss)

-1 -0.5 0 0.5 10

0.2

0.4

0.6

0.8

1

1.2


X

Velo

city

(Dim

ensi

onle

ss)

-1 -0.5 0 0.5 10

0.2

0.4

0.6

0.8

1

1.2


(a)

(b)

(c)

101

4.4.4 Velocity Flow Field for in-plane and off-plane model

A four generation model of the airway system was developed and computations were

carried out for Reynolds Numbers in the range from 500 – 2000, by using the same

numerical code that was validated in Sections 3.1 and 3.2. These flow rates represented

the situation where a human breathes quietly at different stages from normal breathing to

medium exercise. Although the actual flow within such a bronchial network was time

dependent, a steady inspiratory flow analysis was carried out with the aim of

understanding the flow characteristics, particularly the secondary flow growth at the

fourth-generation stage both in-plane and off-plane configurations.

As the flow passed the first generation of bifurcation, along the downstream, it showed

the existence of skewed velocity patterns, creating an asymmetric flow that featured in all

the previous numerical models developed previously - Wilquem and Degrez [51], Calay, et

al. [54], Liu, et al. [55], Zhao, et al. [79]. The axial velocity profile underwent a dramatic

change in terms of the development of the secondary flows as it passed from the main

trachea to successive branches.

Figure 4-7 shows the velocity profile for different Reynolds Numbers for the first

generation (G0). It is evident from the figure that, with an increase in Reynolds Number,

the skewed velocity profiles became more significant in the vicinity of the inner wall of the

bifurcation. The similar skewed profile near the inner wall was also observed in our

experimental model of a single bifurcation tube. This was mainly attributed to the non-

linear contribution from the inertial terms that became significant at higher Reynolds

Numbers and a higher radius of curvature. The skewed nature of the flow became more

apparent as flow passed the 2nd, 3rd and 4th generation of the bronchial airways.

It is important to note that if the resultant area (cross-sectional area of the all out going

branches) of the branching tubes is equal (or less than) the main trachea, the flow will

exhibit severe skewed velocity profile (in first few generations of airways). Further

102

downstream, the total cross-sectional area of the branching tube increases due to the

large number of generations, which decreases the mass flow rate per branch and, in turn,

reduces the dominance of the skewed profile. However, in the first few generations of the

bronchial tree, each daughter tube of the same branch will have different air flow rates

due to skewed upstream velocity patterns.

The velocity patterns plotted for all 3rd and 4th generations of airways for both in-plane

and off-plane geometry are shown in Figure 4-8 and Figure 4-9. The air stream splits at

each bifurcation and develops a new boundary layer along the inner wall of the successive

daughter tube. The skewed profile, with a maximum axial velocity near the inner wall,

increases along the downstream. However, flow reversal was not observed even with a

higher Reynolds Number (Re = 2000) in the entire branching model. This may be due to

the inertial forces that are insufficient to provide an adverse pressure gradient (large

enough) to cause the shear gradient to change direction. This contributes to the

persistence of a strong boundary layer growth near the inner wall.

Figure 4-8 shows the effect of increasing Reynolds Numbers on flow patterns. Figure 4-9

illustrates the velocity vector for off-plane configuration. In off-plane configuration the

flow will be symmetrical at the first generation branching tube because of its position.

However, the flow loses its symmetry in the second generation. In comparison with the in-

plane configuration, the flow loses its symmetry after the first generation. This is because

of the differences between the configurations as shown in Figure 4-8 and Figure 4-9.

103

Figure 4-7 Velocity Plot in the main Trachea (Generation 0).

(a)

(b)

(c)

104

Figure 4-8 Velocity patterns for the in-plane configuration

Re = 500

Re = 1000

Re = 2000

105

Figure 4-9 Velocity patterns in the off-plane configuration (a) Plane A and (b) Plane B

Re = 500

Re = 1000

Re = 2000

106

4.4.5 The Secondary flow

According to Zhang, et al. [80], Zhang, et al. [81], flow near the divider depended on a

number of geometric parameters, including:

The diameter of daughter branches relative to the corresponding parent branch.

The angle of bifurcation.

The angle of curvature of the outside wall.

When the flow splits in the divider, the fluid in the middle of the airway moves along the

diameter, impinges the inner wall and turns outward (towards the centreline) further

downstream. This behaviour of the flow is potentially the major source that could

generate the secondary flow patterns in the angular direction (i.e., near the vicinity of the

inner wall).

Velocity vectors in the cross-sectional plane were plotted for both in-plane and off-plane

configurations and are shown in Figure 4-10, Figure 4-11 and Figure 4-12. Two distinct and

symmetric secondary vortices appeared at the upper and lower side of the tube.

P1 and P2 (Figure 4-10) show the velocity vector plots as the flow immediately passed the

first generation of branching and approached the 2nd generation branching. The secondary

flow in Figure 4-10 clearly indicated the flow towards the inner wall in P1. In P3 and P4 (in

the second generation), the flow was not symmetrical because of the velocity profile

before the second generation tube was skewed. Thus, in P4, it was expected to have more

mass flow relative to P3. The most interesting situation arose when the secondary flow in

these two cross-sections was compared.

In P3 the flow was towards the inner wall (i.e., in the same direction as in P2 and P1).

Sections, P7, P9, P11, P13, P15 and P17, as shown in Figure 4-11 and Figure 4-12, had

similar flow patterns. However, in P4, when the flow moved towards the inner wall

107

opposing the secondary flow that existed in the branch previously it resulted in a

completely different flow pattern to that of P3. Hence, a similar flow pattern as P4 will be

expected in P8, P10, P12, P14, P16 and P18, as shown in Figure 4-11 and Figure 4-12. In

the off plane configuration the flow exhibited completely different patterns due to the

combined effects of secondary flow dominance (towards the inner wall and 90 degree

offset from the centreline). The diametral symmetry was affected significantly.

In summary, the secondary flow propagated throughout the whole model after the first

bifurcation. The strength of secondary flow increased with Reynolds Number. Repeated

trends could be found at different locations in the whole model. The secondary flow

weakened as the flow started to redevelop downstream of the flow divider.

108

Figure 4-10 Velocity Vector Plots for Generation 2 cross section planes at Re=500 (in-plane model).

P1

P2

P3 P4

109


P7

P8

P9

P10

110


P18 P17

P16 P15

P14 P13

P12 P11

111

4.4.6 Flow Distribution

After the first flow divider, the velocity profiles of the flow became skewed with a higher

velocity along the inside wall and low along the outside wall. This skewed velocity profile

was further divided into two streams of flow. This led to an unbalance in the flow

distribution throughout the model and hence there was more flow in the medial branch

(P4 in Figure 4-8) than lateral branch (P3 in Figure 4-8).

Studies were carried out to correlate mass flow rate ratio between the medial and lateral

branch and the Reynolds Number of the parent branch. Wilquem and Degrez [51]

presented the relationship as:

02.1Re1090.7Re1032.6 426_

lateral

medial

QQ

m 4-5

Where Qmedial and Qlateral were the mass flow rates, respectively passing through the

medial and lateral branches.

Liu, et al. [55] had also suggested the same correlation. For their in-plane bifurcation

model, the Re_

m relation was given by:

227.0_

Re36.0m 4-6

In the simulation here, it was found that _m did not vary with Re as greatly as it did in the

work of Wilquem and Degrez [51] and Liu, et al. [55].

The model in this research produced the Re_m relation as:

112

09.1Re00002.0_

m 4-7

The main difference between the previous correlations and that presented here is that the

model here used dimensions from Generation 0 to 2, rather than Generation 5 to 7, which

implied that there could be limited application of the Rem relation – specifically

because it did not take into account the length of the middle generation. In this research,

the length of the first generation was not taken into account and the skewed velocity

profiles may have redeveloped into a more parabolic flow profile. In the Liu, et al. [55]

model, Generation 6 was shorter than in the model here, and the skewed profile did not

have the length to develop before the next flow divider, implying that more mass would

flow into the medial branch than the lateral branch.

The mass flow rates at Generation 4 across P11 to P18, for the in-plane model, are shown

in Figure 4-13. The results indicate that the mass flow rate is higher at P12, P13, P16 and

P17 than at P11, P14, P15 and P18, which may be attributed to the skewed velocity profile

developed as shown in Figure 4-8.

In order to show the variation in the flow distributions with Reynolds Numbers, the

percentage of the mass flow rates for each outlet and for different Reynolds Numbers was

calculated. When the Re was low, the flow distribution was more even compared to the

higher Reynolds Numbers, as shown in Figure 4-14. Moreover, there was more flow to the

outer branches, P11 and P18, when the Re was low. This meant that during breathing,

depending on the branch orientation, there could be a change in local velocity as the flow

rate increased and the mass flow to each branch changed.

113

Figure 4-13. Mass flow rates comparison between all the outlets P11 – P18 for different Reynolds Number.

Location

Air

mas

sflo

wra

te[k

g/s]

P11 P12 P13 P14 P15 P16 P17 P180

5E-06

1E-05

1.5E-05

2E-0520050075010001250150017502000

Re

114

Figure 4-14 Mass flow rate percentages for Reynolds Number at each outlet.

Location

Air

mas

sflo

wra

tepe

rcen

tage

[%]

P11 P12 P13 P14 P15 P16 P17 P188

9

10

11

12

13

14

15

16

17 20050075010001250150017502000

Re

115

4.4.7 Pressure drop behaviour

Pressure drop in the bifurcating airways plays an important role in the respiratory process.

The respiratory process can only take place continually and normally when the alternative

contraction and expansion of the respiratory muscles overcomes the pressure drop due to

viscous loss. The pressure drop coefficient pc is defined as

dynamic

totaltotal

dynamic

totalp P

PPPPc

,0

,4,0

,0

4-8

Where

totalP ,0 is the mass-weighed integral of the total pressure over the inlet section of

generation 0.

totalP ,4 is the mass-weighed integral of the total pressure over the eight outlet

section of generation 4

dynamicP ,0 is the mass-weighed integral of the dynamic pressure over the inlet

section of generation 0.

The values for the total and dynamic pressure can be obtained easily by Post processing

software. From the analysis in this Doctoral research, the pc versus Re are plotted in

Figure 4-15. The relation can be fitted by

cp = 123.32Re-0.58 4-9

This relationship was valid for Re between 200 to 2000. This relationship was very similar

to other simulations conducted by other researchers. For example, Liu, et al. [55]

calculated the exponent to be -0.497, and Wilquem and Degrez [51] in their two

dimensional simulation had the resulting exponent to be -0.61. The simulation results

116

here also showed similarity with the experimental results conducted by Snyder and Olson

[82] and Pedley [83] who had produced the pc vs Re relation with exponent to be -0.5.

Figure 4-15 Variations of the pressure drop coefficient with Re.

Re

Cp

0 500 1000 1500 20000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

117

4.5 Conclusion

In this chapter, computational fluid dynamics was used to determine the flow field

patterns in a four-generation bifurcation airway model. The velocity profiles for various

flow rates were presented and discussed. Selected results were compared with

experimental and published data and good agreement was achieved.

From the flow distribution analysis, the flow partition in the third generation in-plane

model was found to be unbalanced. Moreover, a linear rather than exponential

correlation was found between the mass flow ratios of the medial and lateral branches

and Reynolds Numbers. This was attributed to the fact that the length of the generation

investigated in this study was longer than the ones considered in previously published

studies.

From the pressure drop analysis, the pressure coefficient pc was found to vary with Re

according to cp = 123.32Re-0.58. The value of the exponent was found to be in general

agreement with experimental data and results of other published numerical simulations (-

0.497 to -0.61). Currently research is continuing to determine the effect of transient flow

and particle deposition in the same model presented here.

The extension to the computation work documented in this chapter was the study of

particle deposition in the four generation model. This will be discussed in the next

chapter.

118

Chapter. 5 Numerical Analysis on Particle Deposition in

Symmetrical Human Upper Airways Under Steady Conditions

119

5.1 Particle Deposition Modelling using CFD

It has already been noted herein that, at the time this research was undertaken, numerical

methods had been commonly applied to model particle deposition in the human airways.

The flow field and particle trajectory and deposition had been calculated by means of

solving corresponding equations.

Early studies considered the flow field as steady flow (Diu and Yu [63], Gradon and Orlicki

[64], Lee and Goo [65], Asgharian and Anjilvel [18], Zhang, et al. [66], Comer, et al. [67]).

Particle deposition was also studied extensively in these examples. The results showed

good agreement with experimental work. In subsequent studies, the steady flow model

was extended to an oscillatory flow (Zhang, et al. [84]). This highlighted that, relative to

the steady flow, the transient flow model revealed an increased particle deposition

efficiency – based upon comparisons using the same mean Reynolds Numbers. However,

most of these studies focused on geometry in Generation 3 onwards in the human airways,

although the non-dimensional parameters of the Stokes and Reynolds Numbers were

applied. However, there were parameters that could have an impact on particle efficiency

that were not considered within these numbers. Stokes Number is a dimensionless

number corresponding to the behaviour of the particles interacting with a fluid.

DUd

Stk pp

18

2

5-1

Where

p is the density of a spherical particle

pd is the particle diameter

U is the mean velocity of the fluid

120

is the dynamic viscosity

D is the diameter of the tube (airway)

A human lung is composed of bifurcating networks. The first generation of the bifurcating

network is the trachea – this is referred to as Generation 0 and it splits into two child

branches called the Main bronchus, which are Generation 1 of the airways. The

interesting point to note about human airways is that the flow velocity increases from

Generation 0 to Generation 3, then monotonically decrease down the generations. The

Reynolds Number, however, only decreases monotonically down the generations. Further,

if the Stokes Number is calculated with the same density and size along the airways

(assuming a particle to be travelling at the speed of the flow), the maximum Stokes

Number is at Generation 5. The point of emphasis here is that it is difficult to relate

particle efficiency with just Reynolds Number and Stokes Number, as the airway geometry

is very complex.

In fact, a more general particle deposition empirical formula is required for upper airways.

Therefore, in this chapter, a detailed computer simulation is presented for particle

deposition in the human upper airways for the first four generations.

Model geometry for the work documented in this chapter was built using Solidworks and

the flow field and particle trajectories in the model geometry were calculated using CFX,

based on a finite volume method. The objective was to study the factors affecting the

deposition efficiency that included the breakdown of the dimensionless number, in view

of the particle efficiency, with the changes in particle size, particle density, and fluid flow

rate. By doing this, it was possible to identify the factors which had the maximum

influence on deposition efficiency, based on realistic particle diameters and densities

under consideration.

121

5.2 Model Validation

This section documents the efforts made to verify the numerical model by first building a

model that had similar geometry to the one presented by Comer, et al. [67] and then

comparing the results with other available experimental data as well as numerical results.

Chan and Lippmann [85] produced an empirical formula for particle deposition in hollow

cast studies as:

0023.0803.0 Stk 5-2

The above formula is developed based on deposition in the first six generations of the

airways.

Kim and Iglesias [40] performed extensive experimental work on deposition in a single

generation bifurcation by varying different bifurcating angels, ranging from 15 degrees to

90 degrees. They arrived at two empirical formulae:

(i) For bifurcation half angle equal to 15, 30 and 45 degree,

342.1log694.0log09.0 2 StkStk ee

5-3

(ii) For bifurcation half angle equal to 60 and 90 degree.

263.1log495.0log041.0 2 StkStk ee

5-4

where Stk is Stokes Number defined as

122

DUd

Stk pp

18

2

5-5

and is the particle deposition efficiency.

Zhang, et al. [66] arrived at empirical formulae based on the Stokes Number and Reynolds

Number:

a) For Parabolic flow

sinRe7.55exp000654.0 31

954.0Stk 5-6

for Stk < 0.04

sinRe5.9exp193.019.0 31

565.1Stk 5-7

for Stk ≥ 0.04

b) Uniform flow

sinRe7.22exp000425.0 31

832.0Stk 5-8

for Stk < 0.07

sinRe28.3exp194.019.0 31

585.1Stk 5-9

123

for Stk ≥ 0.07

The comparison between the model in this Doctoral research, and various experimental

and numerical models, as shown in Figure 5-1, predicts the particle efficiency of the model

here lower than others when the Stokes Number is below 0.09, but the difference is

relatively small. In fact, the model in this research shows a very similar trend to the

results found in Comer, et al. [67]. The results show the differences in the particle

efficiency are lower by around 3% each Stokes number tested. This could mainly due to

the slight variations in model geometry, meshing algorithms and drag coefficient.

124

Figure 5-1 Validation of Current model

Stokes Number

Par

ticle

Effi

cien

cy(%

)

0 0.05 0.1 0.15 0.20

5

10

15

20

25

30

35

40

45

Kim & Iglesias (1989)Zhang, Asgharian & Anjilvel (1997)Chan & Lippmann (1980)Present ModelComer (2000)

125

5.3 Geometric Model

After the validation of the model, the same numerical code for particle tracking was used

for the geometry from Generation 0 to Generation 4. The same geometric model used in

Chapter 4 is used for the particle tracking simulation. The dimension and cross section of

the geometry are shown in Table 4-1 and Figure 4-2 respectively.

5.4 Domain and Boundary Conditions

It was assumed that the transport medium, air, was an incompressible fluid. The flow was

assumed to be laminar. The simulation considered only inspiration particle deposition. The

start of Generation 0 was the inlet and the ends of Generation 4 were the outlets. The

continuity and momentum equations are given as

The Continuity equation

0 U 5-10

The Momentum equation

Tp UUUU

1

5-11

Where

is the density

126




The particles used for simulation were assumed to be spherical and non-interacting. This

meant particles did not transform into clouds. Employing an Eulerian – Lagrangian

approach, the particle trajectory equation is

pp

p Fdtxd

m 2

2

5-12

Where

mp is the mass of a single particle

xp is the displacement of the particle

t is time

Fp is the sum of all the forces acting on the particle.

In this simulation, the major force acting on the particle was the momentum by the fluid,

hence with total drag and the particle trajectory equation is

ppDppp

p vvvvCddtxd

m

22

2

81

5-13

Where

127

vp is the particle velocity

v is the fluid velocity

CDp is the drag coefficient of the particle

This simulation employed the Schiller Naumann Drag Model where the drag coefficient

CDp was given by:

687.0Re15.01Re24

pD

C 5-14

The particles distributed uniformly at the inlet. The number of particles placed at the inlet

was chosen to be 2000, because increasing the number of particles beyond 2000 was

unlikely to alter the particle deposition results. A particle’s trajectory ended when it had

either exited through the outlet or it had hit a wall - hence particles were assumed to stick

to the lung wall once they collided with it.

At the inlet, at Generation 0, a uniform fluid velocity was specified. At the outlet, a

uniform outlet pressure was specified. Due to the symmetry of the problem, there were

two symmetric planes, one along the XY plane and the other along the YZ plane.

In all, 24 simulations were performed and completed. The two different flow rates that

were tested were 6.55 L/min and 26.21 L/min which equates to Reynolds Numbers 500

and 2000 at the Generation 0 inlet. The three particle sizes chosen were 3, 9 and 15

microns.

These particles densities were 350, 1000, 3000 and 5000 kg/m3.

The numerical solution of the fluid flow equations (continuity and momentum equations)

and particle transport equation were carried out using a commercial finite-volume based

program CFX-5.7.

128

5.5 Results

The particle deposition efficiency is defined as:

%100_____

___[%] regionenteringparticlesofnumbertotal

depositedparticlesofnumber

5-15

The region identification is shown in Figure 5-2. There were a total of eight different

regions in the model being simulated. They were named according to the generation

number. After Generation 1, there was more than one branch at the same generation, so

an alphabetic character was assigned to each of these (e.g., 2A, 2B, 3A, 3B, 3C and 3D).

There were eight regions where the particle deposition efficiency was considered, as

shown in Figure 5-2.

129

Figure 5-2 Regions of the lung model.

The simulation here focused on particle deposition from Generation 0 to Generation 3

airways. As the velocities were high, the particle deposition was influenced more by

inertial impaction rather than sedimentation and diffusion. Figure 5-3 shows the tracks

for particles being deposited at Generation 1. It clearly shows that the particles travelled

with strong secondary flow due to the bifurcation geometry before deposition. Particle

deposition sites were similar to those found in Comer, et al. [67] and Zhang, et al. [66].

130

Figure 5-3 Tracks for particles deposited at Generation 1

131

5.6 Deposition Efficiency vs. Particle Density

The graphs in this section (Figure 5-4 - Figure 5-9) show how the deposition efficiency

varied with particle density at different flow rates and different particle sizes at various

generations. The Reynolds Number, specified in Figure 5-4, applied to the inlet of

Generation 0 only. The local Reynolds Number varied depending on the variations of the

velocity in different generations and different branches.

As shown in Figure 5-4 and Figure 5-7, particle deposition remained similar regardless of a

change in density when the particle size was 3 microns. For particle sizes larger than 3

microns, as shown in Figure 5-5, Figure 5-6, Figure 5-8 and Figure 5-9, the particle

deposition efficiency showed significant increases with increase in particle density.

132

Figure 5-4 Re = 500, Particle size = 3 micron

Particle density [kg/m3]

Dep

ositi

onE

ffici

ency

[%]

0 1000 2000 3000 4000 50000

0.5

1

1.5

2 Gen 0Gen 1Gen 2AGen 2BGen 3AGen 3BGen 3CGen 3D


Dep

ositi

onE

ffici

ency

[%]

0 1000 2000 3000 4000 50000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7Gen 0Gen 1Gen 2AGen 2BGen 3AGen 3BGen 3CGen 3D

133





Dep

ositi

onE

ffici

ency

[%]

0 1000 2000 3000 4000 50000

5

10

15

20

25



Dep

ositi

onE

ffici

ency

[%]

0 1000 2000 3000 4000 50000

1

2


134




Dep

ositi

onE

ffici

ency

[%]

0 1000 2000 3000 4000 50000

5

10

15

20

25

30

35

40

45



Dep

ositi

onE

ffici

ency

[%]

0 1000 2000 3000 4000 50000

10

20

30

40

50

60


135

5.7 Deposition Efficiency vs. Particle Size

The graphs in this section (Figure 5-10 - Figure 5-17) show how the deposition efficiency

varied with particle size at different flow rates and different particle densities at various

generations. The trend was similar to how deposition efficiency varied with particle

density. At low particle density, the particle size did not really impact on the deposition

efficiency as shown in Figure 5-10. In Figure 5-11, when particle density was 1000 kg/m^3,

the deposition did not vary greatly when particle size increased from 5 microns to 10

microns. However, the change was noticeable when particle size increased from 10

microns to 15 microns. This trend is also shown in Figure 5-12, Figure 5-13, Figure 5-14,

Figure 5-15 and Figure 5-16 at different Reynolds Numbers. In Figure 5-17, there is a sign

that the deposition for the early generation is too high (over 50%) - therefore the

deposition efficiency dropped off in later generations such as 2A and 3C.

136

Figure 5-10 Re = 500 Particle Density = 350 kg/m3


Particle Size [m]

Dep

ositi

onE

ffici

ency

[%]

0 5E-06 1E-05 1.5E-050

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8


Particle Size [m]

Dep

ositi

onE

ffici

ency

[%]

0 5E-06 1E-05 1.5E-050

0.5

1

1.5

2

2.5


137



Particle Size [m]

Dep

ositi

onE

ffici

ency

[%]

0 5E-06 1E-05 1.5E-050

2

4

6

8

10

12


Particle Size [m]

Dep

ositi

onE

ffici

ency

[%]

0 5E-06 1E-05 1.5E-050

2

4

6

8

10

12

14

16

18

20

22

24

26


138



Particle Size [m]

Dep

ositi

onE

ffici

ency

[%]

0 5E-06 1E-05 1.5E-050

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Particle Size [m]

Dep

ositi

onE

ffici

ency

[%]

0 5E-06 1E-05 1.5E-050

5

10

15

20

25

30


139



Particle Size [m]

Dep

ositi

onE

ffici

ency

[%]

0 5E-06 1E-05 1.5E-050

5

10

15

20

25

30

35

40

45

50

55

60

65


Particle Size [m]

Dep

ositi

onE

ffici

ency

[%]

0 5E-06 1E-05 1.5E-050

5

10

15

20

25

30

35

40

45

50

55

60


140

5.8 Deposition Efficiency vs. Local Stokes Number

Stokes Numbers were expected to be the most influential parameters on deposition

efficiency. Figure 5-18 shows the deposition at various Stokes Numbers at different

branches and at different Reynolds Numbers. The results in the graph are shown for

Reynolds Numbers of 500 and 2000 at the inlet. The Reynolds Numbers shown in Figure

5-18 were in fact slightly lower because the Reynolds Numbers were calculated near the

flow divider area. This decreased the flow as the cross section started getting larger.

From these result, by relating purely the Stokes Number with deposition, using the Least

Squares method, the equation can be written as:

3844.2231.50% Stk 5-16

This equation is in agreement with the results of particle deposition of hollow cast studies

of the respiratory system for the first six generations reported by Chan and Lippmann [85].

141

Figure 5-18 Log-log plot of particle deposition efficiency in the first for generations vs. Local Stokes number calculated from the mean velocity at the specific generation.

Stk Number

Dep

ositi

onE

ffici

ency

[%]

10-3 10-2 10-1 10010-2

10-1

100

101

102

Gen 0 Local Re = 394Gen 1 Local Re = 351Gen 2A Local Re = 256Gen 2B Local Re = 224Gen 3A Local Re = 224Gen 3B Local Re = 174Gen 3C Local Re = 192Gen 3D Local Re = 174Gen 0 Local Re = 1593Gen 1 Local Re = 1397Gen 2A Local Re = 1043Gen 2B Local Re = 889Gen 3A Local Re = 741Gen 3B Local Re = 763Gen 3C Local Re = 738Gen 3D Local Re = 696

142

5.9 Conclusion

It was recognized that particle deposition in airways was different from generation to

generation within the model of the first four generations. This was because of the change

in the inlet conditions and the particle distribution. Some geometric factors could be

responsible for the changes in particle deposition at different generations. One such factor

was the outside curvature of the bifurcation. Figure 5-19 shows two bifurcations sharing

the same diameter ratio with different outside curvature. The outside curvature impacts

upon the fluid flow pattern quite significantly.

Figure 5-19 Bifurcations with different outside curvature, with the same diameter ratios.

By performing simulations with two different curvatures, it was determined that more

particles deposited in the model with a small outside curvature. This was because the

flow changes were more rapid, and therefore particles had less opportunity to change

directions even when they carried the same momentum in both the models. In fact, there

were 322 depositions in the large curvature model and 373 depositions for the smaller

143

curvature when 2000 particles were deployed. The local Stokes Number and Reynolds

Number were 0.125 and 2000.

The main finding that emerges in this chapter was that the computation simulation model

produced results that were in line with other researchers in the literature (Kim and

Iglesias [40], Zhang, et al. [66], Comer, et al. [67], Chan and Lippmann [85])

The empirical formulation between particle deposition and Stokes number was related by:

3844.2231.50% Stk 5-17

This equation provided a very rough estimation for particle deposition for the first 4

generations using the Weibel [15] symmetric model. It was possible that the relationship

might not apply to the lower respiratory systems and this required further investigation.

Therefore, the next chapter documents the asymmetrical human respiratory model that

was created to provide a more realistic airway model which could be used to represent

the upper respiratory system of a human.

144

Chapter. 6 Creation of Asymmetric Airways Model

145

6.1 Introduction

The data which was acquired and presented in Chapter 5 showed that a symmetrical

model did not accurately represent realistic human airways. At this point it is therefore

opportune to review why it was necessary to study the particle deposition in asymmetrical

airway models.

Knowledge of air flow characteristics in the tracheo-bronchial tree was essential to the

understanding of airway resistance, intrapulmonary gas mixing and deposition of airborne

particles. While imaging techniques were capable of determining the particle deposition

patterns in the airways with a reasonable degree of accuracy, this form of experimental

data represented averages over many individual airway branches (Schroter and Sudlow

[31], Chang and Masry [32]). Moreover, in vitro experiments could only measure and

analyse one set of data at a time – for example, the velocity field. On the other hand,

computational fluid dynamics (CFD) had proven to be an acceptable method for

determining detailed deposition patterns in a cost effective way, and it had been widely

used to simulate various bio-engineering problems.

Analysis techniques had often incorporated straightforward numerical approximations

(Wilquem and Degrez [51], Liu, et al. [55], Leong, et al. [59], Zhao, et al. [79], Leong, et al.

[86]) or experimental set ups (Zhao and Lieber [8], Schroter and Sudlow [31], Chang and

Masry [32]). Many earlier studies had also demonstrated the existence of a skewed

velocity profile at the outlet of a bifurcation, and the subsequent development of a

secondary flow – downstream towards the daughter branches. For example, Wilquem and

Degrez [51] used two dimensional steady air flow in a three generation airway. Wilquem

determined that velocity profiles downstream of the first junction were highly skewed,

thus leading to an important imbalance in the flow distribution downstream of the second

junction. Zhao, et al. [79] reported his two generation airways model for laminar flow and

validated the results with his experimental findings. However, in general, the literature

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indicated clearly that there were significant differences between symmetric and

asymmetric geometries. Moreover, two dimensional (2D) representations of human

airways, which many researchers had deployed, had inadequately represented actual

phenomena because of the dominance of a radial component in the daughter branches.

Specifically, a significant difference was found in between the flow patterns predicted by

the symmetric and the asymmetric models, and also between two dimensional (2D) and

three dimensional (3D) models using CFD.

The existence of separation regions, occurring at the outer walls of a bifurcation (flow

divider), in the 2D models by Wilquem and Degrez [51], was not apparent in the 3D model

studied by Gatlin, et al. [87] – this was primarily due to 3D effects, because the swirling

flow along a tube could not be simulated in a 2D model. Other work by Lee and Goo [65]

and Asgharian and Anjilvel [88] used a square cross-section model to calculate the inertial

deposition of particles in a three-generation bifurcation model. These researchers found

that the corners of their models introduced more flow disturbances because of the

existence of corner vortices.

Much of the work uncovered during the course of the literature review, undertaken for

this Doctoral research, had been for a system of central or smaller airway junctions within

the lung, and subject to laminar flow. However, more realistic, 3D CFD multiple junction

models, in laminar flow, by Liu, et al. [55] were validated with the velocity profile

measurements of Zhao and Lieber [78]. It should also be noted that flow within the

trachea and major bronchi was turbulent for the normal range of flow-rates Luo, et al.

[57]. Flow in the upper airway, during heavy breathing, could have a Reynolds Number (Re)

as high as 9300, and therefore presented turbulent features. Although turbulence was

known to have a significant effect on the airflow and other transport processes in the

bronchial tree, numerical studies had generally assumed the flow to be laminar. However,

more recent CFD work had been undertaken on a multiple junction model, employing

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more realistic, curved bronchi, compared transient velocity profiles with a validated single

bifurcation - Calay, et al. [54].

The studies, cited above, incorporated one- or two-generation idealized bifurcations but

little research had been focused on the asymmetry of the bronchial tree. In one example,

Liu, et al. [55] had modelled an asymmetric airway extracted from the 5th–11th branches

of the model of Weibel [15]. However, the geometry deployed in this research did not

represent the actual geometry of the human airways. Additionally, the study was primarily

focused on how flow characteristics changed with the asymmetric airways. Green [89], on

the other hand, modelled a four-generation asymmetric model of the human central

airways in accordance with the lung geometry reported by Horsfield, et al. [90]. However,

Green’s study was merely expiratory peak-flow wall shear stress – the inspiratory flow and

flow fields were not examined. More recent work by Freitas and Schröder [60] considered

a sixth generation model using steady flow (with Re = 1250), and simulated using the

Lattice-Boltzmann Method, which was another method for solving the Navier Stokes

equation. Again, this was a steady flow which did not consider any transient effects or

particle deposition.

The numerical results for fluid flow and particle deposition had been reported by Zhang,

et al. [91], and Comer, et al. [67], but these simulations were carried out using a steady

flow, and the particles were injected at a constant rate. The problem was that human

breathing was not a constant flow process, so it was important to study the transient

effects on particle deposition. These factors were partially addressed by the more recent

work of Li, et al. [68] and Zhang and Kleinstreuer [10]. Another recent study by Comerford,

et al. [70] used a co-axial tomography (CT) scan to create the lung geometries, and

employed fluid structure interaction simulations. Comerford’s study was patient specific

and it considered only nanoparticles – it did not formulate a generic particle deposition

which facilitated the generalisation of the result to the average adult. Therefore, a more

comprehensive study was still necessary in order to determine the transient particle

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patterns in a real model of human airways – this was the basis of the Doctoral research

presented herein.

The aim of the research here was to provide quantitative information concerning the fluid

dynamics and particle deposition in the human central airways, with realistic geometry

based on the model of Horsfield, et al. [90]. This chapter documents the creation of the

CAD model and the meshing of the model using an advanced (commercial) meshing

software tool (ANSYS ICEM). A detailed explanation on advance meshing will be provided

herein.

A number of different mesh densities were generated to perform the grid independent

test and are documented here. This enabled an optimal mesh to be deployed for further

complex simulation, such as particle tracking, multiphase flow, fluid structure interaction

(future studies). The application of an optimal mesh had the effect of reducing

computation times without compromising the accuracy of the results.

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6.2 Geometry Creation and Software Tools

In previous chapters, only symmetric airway geometries had been considered in detail. As

described in Chapter 2, the Weibel [15] geometry was an idealised geometry of the human

airways. In this chapter, the asymmetric geometry of the airways is considered. Table 6-1

describes all the dimensions of the Horsfield, et al. [16] model. Comparing the Horsfield et

al. model with Weibel [15] model, shows that the former is considerably more detailed

and has provided dimensions for 38 different branches.

From Table 6-1, it was noted that the non symmetrical portion of human airways located

mainly at the first four generation. This chapter documents the building of a computation

model that was asymmetrical for the first four generations, and the study of the fluid flow

using it in the view to test out what grid size is the most efficient for the particle

deposition study.

The airways geometry defined by Horsfield was very complicated (see Table 6-1), so it was

necessary to make the assumption that the first four generations of bifurcation were

branched in the same plane. Moreover, in addition to the Horsfield, et al. [16] model, a

lung cast model by Somso Anatomy model [92] (Figure 6-1) was acquired as a reference

guide to creating a realistic airways model.

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Table 6-1 Horsfield airways model dimensions Horsfield, et al. [16]

Branch No. Order Diam, mm Length, mm E Flow, % of trachea Branching Angle R/d R 0 31 16 100 216544 100.0000%

1 28 12 50 98432 45.4559% 73 4.5 54

2 27 7.5 16 44416 20.5113% 48 3.5 26.25

3 26 7.3 1 30592 14.1274% 65 1.5 10.95

4 25 5 9 13760 6.3544% 28 0.5 2.5

5 24 5.5 11 13824 6.3839% 25 1.2 6.6

6 27 8 11 54016 24.9446% 44 6.3 50.4

7 26 6.5 18 43840 20.2453% 28 3 19.5

8 25 7 4.5 27008 12.4723% 17 2.7 18.9

9 24 5.5 7.5 16832 7.7730% 33 6.2 34.1

10 30 11.1 22 118112 54.5441% 35 3 33.3

11 26 7.3 15.6 47008 21.7083% 63 1.7 12.41

12 25 8.5 6.4 23776 10.9798% 18 4 34

13 29 8.9 26 71104 32.8358% 15 2.3 20.47

14 25 5.2 21 20800 9.6054% 61 8 41.6

15 28 6.4 8 50304 23.2304% 15 5.9 37.76

16 27 6 8.4 35392 16.3440% 8 11 66

17 26 6.2 14.8 27520 12.7087% 0 12.7 78.74

20 24 5.3 13.5 16832 7.7730% 14 4 21.2

23 23 3.5 11.5 7872 3.6353% 28 15.1 52.85

24 22 3.5 7.5 5952 2.7486% 8 8.7 30.45

25 20 5.5 8.5 10176 4.6993% 70 2.2 12.1

26 24 5 11.5 16832 7.7730% 36 18 90

28 20 5 8.5 10176 4.6993% 31 6 30

30 24 4 2 16832 7.7730% 40 4.2 16.8

31 19 4 13.4 6944 3.2067% 10 4 16

32 25 5.5 17 23232 10.7285% 33 1.9 10.45

33 24 4 10 10400 4.8027% 35 15.5 62

34 24 4.4 9.6 10400 4.8027% 18 13.1 57.64

35 21 4.4 6.2 14912 6.8864% 54 12.3 54.12

36 23 3.2 6.2 7872 3.6353% 58 14 44.8

37 25 4.8 6.8 13760 6.3544% 31 11.1 53.28

38 25 5.8 10.6 13760 6.3544% 35 8.9 51.62

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Figure 6-1 Somso Anatomy Model GS4-3 (http://www.somso.de/deutsch/anatomie/gs4_3.htm)

At the time this research was undertaken, significant time and effort was devoted to

investigating the best software options for creating the 3D airways geometry. Some of the

software packages that were reviewed as part of this research included:

Pro/Engineer

Rhino

CFX-Build

Solidworks.

http://www.somso.de/deutsch/anatomie/gs4_3.htm

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This software comparison study was conducted early in the Doctoral research program (in

2002) as the basis of decision making for this research, and so the descriptions here are

the ones that were used in order to determine the most suitable package. Clearly, given

the time lapse between the original decision making and writing of this dissertation, the

descriptions here will have changed as a result of upgrades to each of these packages. In

summary, however, the characteristics of each, as they were when the comparisons were

performed, is as follows:

(i) PTC Pro/ENGINEER [93]– this was a mechanical engineering and design CAD tool

capable of creating complex 3D models, assemblies, and 2D measured drawings.

Pro/ENGINEER offered many useful featuring tools – however, its deployment to

create an airways geometry with curvatures (and changes in the diameters of the

airways) would have been a complex task.

(ii) Rhinoceros NURBS modeling for Windows [94] – this was a stand-alone,

commercial NURBS-based modelling tool, originally a plug-in for Autodesk's

AutoCAD. The software was commonly used for industrial design, architecture,

marine design, jewellery design, CAD / CAM, rapid prototyping, reverse

engineering as well as in the multimedia and graphic design industries. Rhino 3D

specialized mainly in free-form NURBS modelling. Users would be able to create

airway geometries using the surfacing tools in Rhino 3D. However, after exporting

these as IGES files, there existed gaps between different surfaces. These gaps

created compatibility problems with the meshing tools available (CFX-build or

ICEM).

(iii) CFX-Build (Available only on CFX 5.6, not available after integrated with ANSYS

benchtop) – this was a geometry creation tool for modelling. It created geometry

from points and curves – by joining multiple curves, surfaces could be formed.

Creating airway geometry this way was not a complex task. A single bifurcation of

the airways was created using CFX-Build as a trial. However, as the geometry was

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created by using points and curves, it was difficult to build multiple generations of

the airways.

(iv) "Solidworks (3D CAD Design Software)" [95] – this was a 3D computer-aided

design (CAD) program that executed on Microsoft Windows platforms. In the

SolidWorks 3D modelling environment, the creation of a solid or surface typically

began with the definition of a 2D or 3D sketch. There existed many similarities

between Solidworks and Pro/Engineer - however, one of the key features that was

used for creating the airway geometry was the lofting function. The lofting

functionality enabled a solid body to be created between two sketches in 3D

spaces (with or without guiding curves).

Considering the functionality of all of these packages, it was ultimately decided to deploy

Solidworks to create the geometry of the airways model. The version used at the time was

Solidworks 2002.

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6.3 Geometry Creation using Solidworks

This section describes how the airways geometry was created through the Solidworks

application.

As a first step, one had to consider how the geometry was oriented within global

coordinates. In Solidworks, by default, there were three planes, TOP, FRONT and RIGHT

(Figure 6-2). Let us say that the trachea Generation 0 was to be created along the Y axis.

The objective was to create a sketch on the TOP plane first - with the dimensions of the

trachea (Figure 6-3)

Figure 6-2 Default planes in Solidworks.

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Figure 6-3 Top Plane with dimensions of trachea

The next step was to extrude the sketch to create the length of the pipe (Figure 6.4). At

this point the dimensions of this part did not matter as the dimensions would need to

change once the geometry was created.

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Figure 6-4 Extrusion of the trachea

As the geometry of the lofting was unknown at the start, the next step was to create a

guiding sketch primarily for use in construction. The construction sketch is built on to the

Front plane (Figure 6.5).

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Figure 6-5 Guiding sketch for construction of generation 1

A plane was defined at the end of the construction sketch, such that the circle of

Generation 1 could be drawn. By default, the name for the plane was Plane 1 (Figure 6-6).

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Figure 6-6 Building of Plane for Generation 1

A sketch of the circle for Generation 1 was created on Plane 1 (Figure 6-7).

Figure 6-7 Circle for Generation 1

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The Lofting feature was applied by joining two circles - one circle from the extruded

section and the other on Plane 1. In addition, the start and end constraints were set to

“Normal” to the profile so that the lofting process could produce a smooth transition. A

solid curved tube was created with the start having the dimensions of Generation 0

(16mm) and end having the dimensions of Generation 1 (12mm) – Figure 6-8.

Figure 6-8 Lofting for generation 1 into a body

The same process was followed for a branch on the other side in order to complete the

bifurcation. Note that the length and curvature had to be adjusted to take into account

the fact that practical human airways may not be smooth. A completed bifurcation is


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Figure 6-9 Completed Bifurcation

Applying the above process, together with the dimensions from Horsfield model, and with

Somso Anatomy model [92] as a reference point, the full first four generations of the

airways model were completed as shown in Figure 6-10. This was one of the first models

created to study the air flow and particle deposition.

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Figure 6-10 Upper Airways Model

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6.4 Meshing

6.4.1 Overview

In previous chapters, meshing was created using CFX Build or ANSYS Workbench. Both of

these software packages provided good tetrahedral meshing as shown in Figure 3-10. The

model validation in section 3.6 reflected that the quality of the mesh. However, there

were disadvantages in using a tetrahedral grid that lacked user control when laying out

the mesh. Further, tetrahedral grids tended to require more processing memory and

longer execution times because tetrahedrals required more elements than hexahedrals. It

was therefore important to evaluate different meshing methods for the airways model.

This section will firstly overview tetrahedral meshing – then the meshing of the

asymmetrical model, using quad elements, will be described in detail such that the

research undertaken in this Doctoral program can be extended in subsequent research.

6.4.2 Meshing methods available

Mesh generation is the practice of generating a polygonal or polyhedral mesh that

approximates a geometric domain. It is commonly referred to as “grid generation”. There

was a group of literature (Thompson, et al. [96], Thompson [97]) and software that could

be used to create structured meshing. Strictly speaking, a structured mesh could be

recognized by the characteristic that all interior nodes of the mesh had an equal number

of adjacent elements. In general, structured grid generators produced quads or

hexahedrals. In order to align elements with boundaries and physical domains, generally

the generation of a structured mesh involved complex iterative smoothing techniques and

algorithms. “Block-structuring” techniques were used when the boundaries were non-

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trivial, because blocking could divide the domain into topological blocks where structured

mesh could then be produced.

Structured meshes were generally used for Computational Fluid Dynamics (CFD)

simulations where strict alignment of elements could be required for the analysis code in

the solver or it where it was necessary to capture physical phenomena.

Unstructured mesh generation relaxed the node valence requirement which allowed any

number of elements to meet at a single node. An unstructured (or irregular) grid was a

tessellation of a part of the Euclidean plane (or Euclidean space) by simple shapes, such as

triangles or tetrahedra, in an irregular pattern. Triangle and Tetrahedral meshes were

most commonly thought of when referring to unstructured meshing, although

quadrilateral and hexahedral meshes could also be unstructured.

While there was certainly some overlap between structured and unstructured mesh

generation technologies, the main feature which distinguished the two fields was the

unique iterative smoothing algorithms employed by structured grid generators.

In previous chapters, the computational model was meshed using unstructured mesh (see

Figure 3-10, Figure 4-3, Figure 4-4)Owen [98] – the mesh only contained tetrahedral,

prism (on flat end) and quad (elements on the round wall) elements. This chapter will

develop further into the creation of a more sophisticated mesh in order to generate a

more efficient, accurate model to be used for studying the particle deposition in the

asymmetric airways model. It was a challenge to create such a model, which was both

computationally efficient and capable of producing feasible results. Significant effort was

expended on this element of the research in order to learn about different meshing

methods; how to improve the mesh by smoothing, refinement and cleaning up the

geometry.

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6.5 Meshing with ANSYS ICEM

ANSYS ICEM was a commercial engineering software package, and its primary

functionality was to convert a CAD model to a mesh model for analysis. ANSYS ICEM

provided:

Sophisticated geometry acquisition

Mesh generation

Mesh editing

A wide variety of solver outputs and post-processing.

ANSYS ICEM CFD was the only universal pre-processor for analysis including FEA, CFD and

other CAE applications (e.g., particle transport and computational electro-magnetics).

When applied in engineering applications, such as CFD and structural analysis, ANSYS

ICEM CFD's mesh generation tools offered the capability to parametrically create grids

from geometry in multi-block structured; unstructured hexahedral; tetrahedral, and

hybrid grids consisting of hexahedral, tetrahedral, pyramidal and prismatic cells – and

Cartesian grid formats combined with boundary conditions.

The algorithms for mesh generation and smoothing in ANSYS ICEM will be described

together with the meshing process. For tetrahedral meshing, ANSYS ICEM consisted of

Delaunay and advancing front as well as Laplacian smoothing. However, the specific

details of the mesh generation process were not generally made available to public users.

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6.5.1 Importing the CAD geometry

The first step of the mesh generation process required a user either to create or import

the basic geometry. One of the features of ANSYS ICEM was the advanced CAD geometry

reader and repair tools to enable a user to quickly progress to a variety of geometry

tolerant meshers and produce high quality volume or surface meshes with minimal effort.

Some of the common formats that ANSYS ICEM supported included IGES, ParaSolid, STL,

Solidworks SLD.

Earlier in this chapter, the Horsfield model had been created in Solidworks as a SLD file.

This model was imported directly into ANSYS ICEM (in some older versions of ICEM, it was

necessary for a user to export CAD file into IGES format before importing into ICEM).

Figure 6-11 shows the imported geometry model into ANSYS ICEM.

Figure 6-11 Geometry imported into ANSYS ICEM

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6.5.2 Blocking of the geometry

A block may or may not be necessary for tetrahedral generation, depending on the type of

elements that need to be meshed. However, tetrahedral elements tended to be more

difficult to control and to use to perform studies in relation to convergence. Therefore,

hexahedral elements were chosen to be used for this Horsfield model.

A block is a rectangular box that is placed and associated with geometry such that ICEM

knows how to plaster the hexahedral elements into that geometry. ICEM can then apply

an algorithm called sweeping to generate the hexahedra mesh. Sweeping was a type of

mapped hexahedral meshing, sometimes was referred as 2½ D meshing. Quadrilateral

surface mesh could be swept through a space along the block, and regular layers of

hexahedra then created at specified intervals (by user) using the same topology as the

quadrilateral surface mesh. Sweeping technique could be universal to mesh a large variety

of volumes by defining a source and target surfaces. Provided the source and target

surface had comparable topology and the surfaces were connected by a set of meshable

surfaces into a block, the quad surface elements of the source area could be swept

through the volume to generate hexahedra as shown in Figure 6-12.

Figure 6-12 Hexelements generated by sweeping - Reproduced from Owen [98]

Attention had to be taken in locating internal nodes during the sweeping process,

numerous research papers (Staten, et al. [99], Lai, et al. [100]) had been presented

addressing this issue. An example of the meshing of a tube (airway like shape) by sweep is


Figure 6-13 Mesh of a tube by sweeping, reproduced from ANSYS Documentation [50]

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It was important to ensure that a block was not distorted too much – otherwise the

elements in that specific block were also distorted causing a poor quality mesh. In this

research it was decided to choose and create blocks as shown in Figure 6-14. However, at

this stage, the blocks were not associated with the geometry and it can be seen that the

lines did not lie on the surface of the geometry. Meshing would only be successful once

the blocks were associated with the geometry.

Figure 6-14 Initial blocking in ICEM

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To associate the block with the geometry, ICEM brought the points to match with the

surface of the geometry. Figure 6-15 shows the blocks associated with the geometry, but

the blocks had many sharp corners. Notice, in the first bifurcation, on the right branch,

the block is highly distorted; meaning the angle between one surface and another is very

small. An ideal block was to have a shape like a cuboid, where all sides were 90 degrees to

each other as in Figure 6-16. This was because any topology for the source surface

sweeping through the cuboid would also produce a cuboid shape.

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Figure 6-15 Block associated with the geometry

Figure 6-16 Cuboid is the ideal block for sweeping

Therefore the objective here was to create blocks that were rectangular, and where all the

edges were almost perpendicular at the joining node. If the block was too long and it

crossed over large amount of surface, it was possible to split it into smaller blocks and the

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nodes followed the geometry closer. In Figure 6-17 the blocks have been split and the

nodes have been moved to create a better blocks.

Figure 6-17 Blocks has been split and nodes has been moved to create uniform blocks

After the blocks were refined properly, according to ANSYS Documentation [50], the

quality should not fall below a tolerance value of 0.3 – 0.4. The tolerance value was a

measurement of the distortion of a block. With the revised blocking, the tolerance values

for quality were all above 0.4, which is desirable for the next step. However, to further

improve the mesh, a technique called Ogrid was applied.

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6.5.3 Apply Ogrid to the geometry

Ogrid was a feature in ICEM that enabled the internal elements to be rectangular, by

placing an internal rectangular block inside the existing block. Ogrid subdivided selected

blocks into a configuration of one central block surrounded by radial blocks. In other

words, Ogrid creation capability was simply a modification of a single block (rectangular)

to a five sub-block topology. It arranges grid lines into an “O” shape to reduce skew,

where a block corner lay on a continuous curve or surface. It was recommended for

cylindrical type geometries to avoid bad internal angles at block corners (which was the

case for the lung model). Figure 6-18 shows the Ogrid of one of the bifurcation ends. The

middle of the circle now has a rectangular shape and the outer has a parallelogram.

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Figure 6-18 Ogrid feature in ICEM

It was known that using Ogrid could improve mesh quality significantly. Figure 6-19 shows

the main major pre mesh quality calculations without Ogrid. There were many elements

that had small angles, and the determinant 3x3x3 calculated was not acceptable to

produce sound results. The overall quality calculation showed that there were many

elements that fell below the value of 0.4.

Figure 6-19 The mesh quality without Ogrid. Top figure is Angle, mid figure is Determinant 3x3x3, bottom figure is the quality

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The checks shown in Figure 6-21 are summarized as follows:

The angle quality evaluated the maximum internal angle deviation from 90

degrees for each element. Various solvers had different tolerance limits for the

internal angle check. If the elements were distorted, and the internal angles were

small, the accuracy of the solution would decrease.

The determinant check computed the deformation of the elements in the mesh by

first calculating of the Jacobian of each hexahedron, and then normalizing the

determinant of the matrix. A value of one represented a perfect hexahedral cube,

while a value of zero was a totally inverted cube with a negative volume.

The mesh quality, measured on the x-axis, of all elements would be in the range

from zero to one. If the determinant value of an element was zero, the cube had

one or more degenerated edges. In general, determinant values above 0.3 were

acceptable for most solvers. The Quality histogram represented the overall quality

of all the elements.

Once the Ogrid was introduced to the block, the pre mesh quality increased significantly

as shown in Figure 6-20. All the elements were now over a 23 degree angle, the

determinant 3x3x3 calculations were all over 0.55, and the overall quality of all elements

was over 0.4. It was therefore very useful to create meshes with Ogrid when the

geometry contained cylindrical surfaces.

As well as using Ogrid, ANSYS ICEM contained smoothing and clean up algorithm to

improve the quality of the mesh. Further details on exact smoothing and clean up

procedures can be found in ANSYS Documentation [50].

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Figure 6-20 The mesh quality with Ogrid. Top figure is Angle, mid figure is Determinant 3x3x3, bottom figure is the quality

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6.5.4 Meshing hexahedral elements

Once the pre mesh quality became reasonable, then the mesh could be produced. As the

lung geometry had different diameters for different generations, it was important to take

this into account when meshing. The model was divided into 9 generations, with each

generation having a different element size. Five different element sizes were defined here

for performing the grid independence test as shown in Table 6-2.

Table 6-2 Five different element sizes for grid independance test

Branch No. Extra Coarse Coarse Medium Fine Ultra Fine

0 2.67 1.78 1.33 1.07 0.94

1 2.00 1.33 1.00 0.80 0.71

2 1.25 0.83 0.63 0.50 0.44

6 1.33 0.89 0.67 0.53 0.47

10 1.85 1.23 0.93 0.74 0.65

11 1.22 0.81 0.61 0.49 0.43

13 1.48 0.99 0.74 0.59 0.52

14 0.87 0.58 0.43 0.35 0.31

15 1.07 0.71 0.53 0.43 0.38

The element size was calculated by dividing the generation diameter by the following

numbers:

Extra coarse mesh: 6.

Coarse mesh: 9

Medium mesh: 12

Fine mesh: 15

Ultra fine mesh: 18.

These were entered into ICEM through setting mesh parameters by parts as shown in

Figure 6-21.

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Figure 6-21 Setting mesh parameters for parts

By using the mesh parameters above, the resultant mesh is shown in Figure 6-22.

Figure 6-22 Resultant mesh for Extra Coarse Mesh

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To demonstrate the grid mesh size differences clearly, Figure 6-23 shows the end view of

the extra coarse and fine mesh. Note that the mesh around the wall is much denser

compare to the internal geometry. This was important because fine resolution was

required for capturing the changes occurring inside the boundary layer between the flow

and the wall. Once the mesh was created, it was possible to export the mesh from ICEM

to different commercial packages, in this case is CFX. This mesh could also be used for FEA

and other analysis if required.

Figure 6-23 End view of Extra Coarse and Fine Mesh

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6.6 Physical Definition and Boundary Conditions

Two steady tracheal flow rates were used in this study:

5.0 L/sec

1.2 L/sec.

These represented resting and moderate exercise conditions. The tracheal flow was

distributed among the five lobar bronchi according to the approximate lobar volumes at

75% TCL as reported by Horsfield, et al. [16]. This is shown in Table 6-3. This tracheal flow

rate had also been used in the experiment conducted by Chang and Masry [32] in their

acrylic constructed model.

Table 6-3 Tracheal Flow Distribution

Lobe Right Upper

Right Middle

Right Lower

Left Upper

Left Lower

Total

Static lung volume at 75% 19 10 26 19 26 100

Horsfield lung model 21 9 25 20 25 100

These flow percentages were useful as they made it possible to calculate the boundary

conditions for the five outlets to each lobe. As noted earlier, most of the CFD simulations

conducted by other researchers (such as Liu, et al. [56]) generally used forced ventilation,

as only the velocity or the mass flow rate at the inlet was known. The approach here was

to make use of the flow percentages and assign the mass flow rate at the outlet. This way,

natural ventilation was assumed and the flow field would be more realistic. At the trachea

inlet, it was assumed the pressure was similar to the atmospheric pressure. Therefore, we

set:

0relp 6-1

179

The wall was assumed to be no slip wall. It was decided to leave the cartilage rings study

for further research as it would require a large amount of computing power and

significant time to get realistic measurements of the cartilage rings. Further information

this assumption can be found in Musante and Martonen [101] who studied the flow field

of a pipe with some artificial addition of cartilage rings, and which lacked realistic

measurements. Therefore, here, we assumed the wall to have zero velocity.

0wallv 6-2

For each outlet, we assigned the flow percentage multiplied by the mass at the inlet.

6-3

This condition would make the air flow become natural ventilation rather than forced

ventilation.

180

6.7 Grid Independence Test

A “grid independence test” was carried out to ensure that the results were insensitive to

the size of grid. Only the inspiratory flow was used for investigating the grid

independence for a single bifurcation model (for a steady flow) because inspiratory flow

was more prone to the onset of turbulence than expiratory flow.

There were five different meshes on which to run the grid independence test. Table 6-4

shows the statistics of the five different mesh configurations. The mesh elements used in

this test were hexahedral as they could be controlled (compared to tetrahedral). Also,

when running simulations with hexahedral elements, the same convergence could be

achieved with fewer elements.

Table 6-4 Five different mesh configurations

Nodes Elements Computing Time

Extra Coarse 47720 43750 31minutes

Coarse 173543 164288 1 hour13 minutes

Medium 430060 413215 1 hour 53 minutes

Fine 862875 836136 3 hours 15 minutes

Ultra Fine 1262133 1227776 4 hours 51 minutes

From Table 6-4, it became evident that the nodes and elements increased in a quadratic

manner. Also the nodes and elements had a one to one ratio because this was a

hexahedral elements mesh. The grid independence test was performed using the steady

flow rate of 5.0L/sec - this corresponded to maximum air intake during a breathing cycle.

181

6.8 Results for 5 different mesh configurations

In this section, the results for the five different meshes are presented. The results will be

compared station by station. The model was labelled in the same fashion as Chang and

Masry [32] - see Figure 6-24. Also the station locations were defined in a similar way to

Chang and Masry [32] experiments as in

Figure 6-24 Branch name denoted as lower case letter and Horsfield generation number is labelled inside the bracket. (Coordinate system is also shown in figure)

182

Table 6-5 Locations of the stations of measurement

Station No. Branch Horsfield Generation No.

Diameter d (mm)

Distance from bifurcation l (mm)

1 a 0 16 74

2 a 0 16 44

3 a 0 16 16

4 b 1 12 10

5 c 10 11.1 5.6

6 b 1 12 40

7 d 2 7.5 16.2

8 e 6 8 12.5

9 f 13 8.9 16

10 g 11 7.3 12

11 h 15 6.4 7.1

12 i 14 5.2 20

There were a total of 12 stations located in nine different branches as shown in Figure

6-25. Stations 1-3 had two lines - one line representing the horizontal, one line

representing vertical. The other stations had two additional lines representing the

diagonal.

To understand exact location of the cross section lines A-A’, B-B’, C-C’ and D-D’, consider

Station 1 as an example. The cross section is viewed from bottom to top, while line A-A’

represents a line on the front plane A corresponding to the left, and A’ corresponding to

the right. Line C-C’ represents the line into the page where C is closer to the reader. This

convention is important when analysing the results for each station as it will be referred

to regularly. The velocities on these lines were compared for each different mesh. A final

conclusion was drawn as to which mesh size was the best for the simulation, considering

both accuracy and computing time.

183

Figure 6-25 Locations of 12 stations and top right hand corner has the cross section of a measurement station viewed from proximal position.

The results from Station 1 to Station 3 are shown in Figure 6-26. The results for the five

different mesh configurations produced very similar results. This was because the results

were in the same plane.

184

Figure 6-26 Station 1A

Figure 6-27 Station 1C





X

Vel

ocity

(m/s

)

0 0.2 0.4 0.6 0.8 10

1

2

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Extra CoarseCoarseMediumFineUltra Fine

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(m/s

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185

Figure 6-32 shows the results at Station 4. This was the first station after the bifurcation.

The results showed significant differences between the four different cross sections for

each of the mesh configurations. It can also be seen that the results from the coarse mesh

produced significantly different results from either the fine or ultra-fine mesh.

As shown in each of the charts in Figure 6-32, it seemed that the results for the coarse

mesh did not contain the full detail. However, and as the mesh got finer and finer, the

actual characteristics of the flow started to become visible. It was noticeable that the

results between fine and ultra-fine mesh configurations only differed by 2% - as this was

minimal, it meant that further refinement of the mesh would not produce significantly

better results.

In summary, it was feasible to use the “fine” mesh which was sufficient for the

computational exercises for the rest of the simulations - for both fluid flow and particle

deposition.

186

4A

4B

4C

4D

Figure 6-32 Results of station 4

X

Vel

ocity

(m/s

)

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7

8

9Extra CoarseCoarseMediumFineUltra Fine

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ocity

(m/s

)

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187

6.9 Conclusion

This chapter has documented the creation of a more realistic airway lung model based on

Horsfield, et al. [16]. The purpose of this chapter was to enunciated the exact steps

involved in creating the geometry using a commercial CAD software package Solidworks.

The CAD model was then imported into commercial mesh generation software called

ANSYS ICEM. Step by step meshing procedures were explained such that further

improvement and extension of the work could be undertaken. Significant effort was put

in to creating the correct mesh as this was a very important aspect of CFD. The quality of

the mesh impacted upon both results accuracy and computation time.

A grid independence test demonstrated that there was very little variation between the

fine mesh and ultra-fine mesh, so the fine mesh was utilised for particle deposition

simulation.

188

Chapter. 7 Numerical Analysis on Particle Deposition in

Asymmetrical Human Upper Airways under Steady and Transient

Conditions

189

7.1 Introduction

In Chapter 6, a substantial amount of documentation was provided to illustrate how a new

asymmetrical model was created successfully and optimized for simulation purposes. This

chapter documents how the newly created model was used in order to study particle

deposition in the human upper airways.

190

7.2 Airways Geometry model

The numerical simulation used the airways model created in Chapter 6 (shown in Figure

7-1). The geometry for the asymmetric model was created by closely following the values

defined by Horsfield, et al. [16]. This model was only an in-plane model, meaning that all

bifurcation branches split along the same plane. However, it was felt that the branching

angle would capture the important aspects relating to how particle were being deposited

inside the airways.

There were two major reasons why the model being used was in-plane only. Firstly, the

exact out-of-plane model was not well described in the literature. Secondly, the results

that were available were difficult to analyse. These reasons constrained the simulation to

focus on in-plane geometry.

Figure 7-1 Airway model for transient particle deposition simulation.

191

7.3 Fluid and Particles Properties

The fluid for the airways domain was air at 25C with the following properties:

Density at 25C = 1.185 [kg m3]

Dynamic viscosity = 1.831 e-5 [kg /ms].

The particles that were injected into the model at each time step were solid particles,

namely “Aerosol”. The density of the “Aerosol” was 350 [kg/m^3] which was similar to

the density of many common fibres, dust particles and smoke particles. There were, in

total, 50,000 particles entering the domain each second. The number of particles entering

at each time step was the total number of particles divided by the number of time steps in

each second.

There were, in total, 5 simulations, each with a different particle diameter being injected

at the inlet. The simulations conducted involved 2, 4, 6, 8 and 10 micron particles.

Changing the diameter of the particle implied a change of Stokes Number and, in turn,

enabled the analysis of particle deposition versus Stokes Numbers.

The air was inhaled by the lung and it was driven by pressure - the particles were carried

by the air. Therefore, there was no buoyancy effect on the particles or on the air, so the

buoyancy properties of the particles and air were not used. The theory behind the particle

tracking and the particle transport theory are described in ANSYS Documentation [50].

Each of the parameters discussed here will affect the formulation to the momentum

transfer equation.

192

7.4 Boundary conditions of the model Airways

For transient simulation, the fluid flow condition at the inlet had to be known for the

whole breathing cycle. The realistic human inhalation waveforms used in the simulations,

documented in this chapter, were the three breathing patterns from Zhang and

Kleinstreuer [10] – these being for resting, light exercise and heavy exercise.

The mean volume air flow rate against time is plotted in Figure 7-2 to Figure 7-4 with the

results as in Table 7-1.

Table 7-1 Inhalation Results

Condition Inhalation Cycle (Seconds)

Maximum Flow (L/Sec)

Exhalation Cycle (Seconds)

Reynolds Number at Max flow rate

Resting 2 0.33 2.3 1510.71

Light Exercise 1.8 0.7 2.0 3204.54

Heavy Exercise 1.18 1.35 1.2 6180.19

Figure 7-2 Measured resting breathing cycles

193

Figure 7-3 Measured light exercise cycles

Figure 7-4 Measured heavy exercise cycles

In the work of Li, et al. [68], at each time step, an analytical expression of the transient,

developed flow in a straight tube was employed to calculate the inlet velocity profiles.

According to Buchanan [102] and Womersley [103], having a parabolic-like inlet condition

was more realistic than a constant velocity at the inlet. This was true because the work of

194

Li, et al. [68] assumed uniform pressures at all exits - the inlet condition and the geometry

had significant effects on the outlets. The major issue with their work was that the flow

for each outlet was controlled by the geometry. This assumption may not realistically

determine the actual flow characteristics inside the human airways. The human lung is

composed of five major lung lobes, two on the left and three on the right. The flow is

driven by pressure differences - therefore, assuming uniform pressures for each lobe, all

the outlets will not be simulating the flow of the human lung because it is possible that

the pressures at the outlets are all different in actual human lungs.

Learning from these simulations, the work documented in this chapter takes another

approach. The geometry of the lung model here was constructed based on the model of

Horsfield, et al. [16]. In their published work, these authors measured the flow

percentage to each branch (Table 6-1). These flow percentages could be used as a

boundary condition. The assumption here was that the flow to each lung lobe was the

same throughout the breathing cycle. In the simulation, the flow at the inlet is 100%

distributed as:

20.5% to Left Upper (LU)

25% to Left Lower (LL)

21.7% to Right Upper (RU)

9.6% to Right Middle (RM)

23.2% to Right Lower (RL).

The flow direction during the inhalation phase is shown in Figure 7-5. Each one of the five

outlets had their own percentage of fluid passing through at each time step. The boundary

condition used mass flow rate, which was the specific percentage multiplied by the mass

flow at the inlet.

195

Figure 7-5 Boundary flow conditions during inhalation phase.

Rather than enforcing the trachea as an inlet boundary, meaning the flow direction has to

be flowing into the domain, instead, an opening boundary was used because the flow may

not always be flowing into the domain when the flow is very slow. In fact, this is The

opening boundary condition was set with an opening pressure boundary with zero relative

pressure. That is:

0relp 7-1

The flow direction was normal to the boundary, meaning that there were no swirls in the

flow.

196

The Reynolds Number in the airways did not exceed 2000 within the full inhalation cycle.

Therefore, a reasonable amount of “medium” (Intensity = 5%) turbulence was applied for

this opening boundary condition.

This simulation simulated particle depositions where particles were injected at the

opening uniformly. Particles were equally spaced at the trachea opening. Zero slip

velocity was applied between the particles and the continuous phase at the opening

boundary. This meant that the particles were travelling at the same velocity as the air

when they entered the domain.

For each simulation, the total number of particles being injected into the inlet was

100,000. The simulation divided the flow into 40 time steps – therefore each time step

would have 2,500 particles being injected. The particle sizes being simulated were 2, 4, 6,

8 and 10 microns. All of these diameters assumed that the particles were spherical in

shape.

The walls of the trachea and bronchi were lined with mucus, therefore no slip boundary

was applied to all the walls. The carinal rings were not considered in the simulation as the

structure of the model would be too complex to create. However, there was literature

describing the effect of carinal rings, as studied by Martonen, et al. [104].

The wall could be the end trace for some of the particles - the walls had moisture, and

particles would stick to them and not bounce off. The parallel and perpendicular

restitution coefficients, which described the action of particles when they hit a wall, were

both set to zero. This meant that all the kinetic energy that a particle carried would be

absorbed by the wall. This simulation focused on the particle paths rather than the effect

of particle clouding or clotting of the airways. Therefore, once a particle had collided with

the wall, the particle was assumed to have exited the domain.

197

7.5 Turbulence model

During the peak flow of the inhalation cycle, the Reynolds Number reaches over 2300 in

magnitude, therefore, turbulence model is required for the transient simulation.

According to ANSYS Documentation [50], ANSYS CFX has numerous models to

approximate turbulence based on Reynolds Averaged Navier-Stokes (RANS) equations.

There are in total of at least 16 turbulence models (more can be found in later version of

ANSYS CFX) that can be used and they can be categorized into four groups.

1. Laminar model.

2. Eddy-viscosity models.

3. Reynolds-Stress Models (RSM).

4. Large Eddy Simulations (LES) and Detached Eddy Simulation (DES).

According to ANSYS Documentation [50], because the fluid flow inside the human airways

geometry is a flow with strong streamline curvature and it contains secondary flow.

Reynolds Stress Models had shown superior predictive performance in comparison with

eddy-viscosity models. Therefore, the simulations documented in this chapter adopted

the BSL Reynolds Stress model as it was better suited to the flow conditions under

consideration.

Appendix A contains the output file for the ANSYS CFX Solver (in the CFX Expression

Language). The file contains all the parameters related to:

Boundary conditions.

Fluid properties.

Particle properties.

Time steps.

198

Turbulence model.

Convergence criteria.

199

7.6 Fluid flow Results

7.6.1 Airflow patterns under transient flow with particles

The airflow patterns in the lung airways are primarily determined by

The fluid properties.

The inlet condition.

The geometric characteristics.

The airflow patterns in the airways have been covered and documented in considerable

detail in the preceding chapters. However, a brief recap of the fluid flow pattern is

presented herein in order to compare the results of the transient model to those of the

steady state, as well as the laminar model with the turbulence model.

7.6.2 Fluid Flow Velocity Profile

In Chapter 4, the velocity profiles for different stations were recorded in the symmetric

airways model. Here, the velocity profiles are recorded in a similar manner. The

simulation that was used for this analysis was the resting condition. Snap shots of the fluid

flow were taken at time equals to

0.4s

0.8s

1.2s

1.6s.

200

The reason for taking snap shots at these times was because at time of 0.4s and 0.8s, the

flow was under acceleration. The maximum flow rate at trachea was at a time of 1.2s. The

snap shot at 1.6 was taken to study the flow under deceleration. The Reynolds Numbers

at the trachea for each of these times is listed in Table 7-2.

Table 7-2 Reynolds Number at time at 0.4, 0.8, 1.2 and 1.6s

Time (s) Flow rate at the

trachea (l/s) Volume flow rate (m^3/s)

Average velocity (m/s) Re at trachea

0.4 0.24 0.000240 0.943140 1098.699334

0.8 0.322 0.000322 1.265380 1474.088273

1.2 0.335 0.000335 1.316467 1533.601154

1.6 0.295 0.000295 1.159277 1350.484598

The profiles are on the mid plane (XY Plane) of the model which were denoted by A-A’ in

Figure 7-1. These profiles should be sufficient to study the flow characteristic.

Figure 7-6 to Figure 7-9 shows the flow profile at Stations 3, 4 and 5. This figure clearly

shows that with an asymmetric airways model, the flow divided unevenly, which would be

the same in the case of a realistic human lung. However, even though the flow was highly

skewed, in all 4 time steps, no reverse flow was noticed, meaning that no flow separation

occurred.

201

Figure 7-6 Flow profile for Station 3, 4 and 5 at T=0.4s

Figure 7-7 Flow profile for Station 3, 4 and 5 at T=0.8

202



203

Figure 7-10 to Figure 7-21 show the fluid flow profile at Stations 6-12 at different time

steps. From all these snap shots, there was no significant difference at each of the time

steps, apart from different magnitude of the flow. It is also important to note that the

flow characteristic at T=1.6 was very similar to the flow characteristic at T=0.4. This shows

that it was difficult to detect the differences between the flow acceleration and

deceleration.

204

Figure 7-10 Flow profile for station 6, 7 and 8 at T=0.4


205


T=1.6


206

Figure 7-14 Flow profile for station 9 and 10 at T=0.4


207


T=1.6


208



209



210

7.6.3 Secondary flow profile under transient flow

In Chapter 4, the study of secondary flow in a symmetrical airway model was presented.

Secondary flow was also exhibited in the simulation. This was because the angle of the

bifurcation was large enough to cause the flow to have empty vicinity near the outside

wall downstream after the bifurcation. Due to this empty vicinity, flow was drawn side

ways – this was the main cause of the secondary flow.

After comparison, the secondary flow did not vary significantly at different time steps.

The noticeable differences were the magnitude only, and a small shift in the centre of the

vortex. Therefore, the results of only one time step at t=1.2 is presented here (Figure

7-22). The camera view for all the vector plots are from viewed from the downstream.

Station 3

Station 4

Station 5

Station 6

211

Station 7

Station 8

Station 9

Station 10

Station 11

Station 12

Figure 7-22 Vector plots of slice at different station showing secondary flow

212

Figure 7-22 shows all the vector plots for Station 3 to Station 12. Stations 1 and 2 are

omitted because their plots are the same as those for Station 3.

The observations for the various stations are as follows:

(i) Station 3 shows the flow starting to have the streamline direction by the

bifurcation - the vectors are pointing outwards from the vertical middle line.

(ii) Station 4 shows the flow has two vortices, the top one is clockwise and the bottom

one is anti-clockwise. As discussed earlier, when the flow is divided at the

bifurcation, the volume near the outside wall of the bend will have to be filled.

Therefore, flow will transverse to the side and this is the main cause of the

secondary flow. The same principle can be applied to Station 5, which is a mirror

image to Station 4.

(iii) Station 6 shows that, after a short relatively straight distance, the secondary flow

starts to disappear. However, the vortices still exist in the vector plot at Station 6.

From Chapter 4, the simulation of fluid flow under steady conditions proved that if

there were vortices in the vector plot before a bifurcation, the secondary flow of

the downstream station will have double vortices. This is also the case for Station 7

and Station 8. Due to the asymmetric bifurcation, the locations of the vortex

centres are different between the two stations.

(iv) The bifurcation on the left side of Station 5 branches off slightly differently

compare to the ones previously described. On the second bifurcation, the Station 9

plane is the branch that is branched off, while Station 10 is the straight tube from

Station 5. From this, it is expected that Station 9 will have secondary flow, while

Station 10 will have small vortices due to the vortices that exist in Station 5. Station

9 has double vortices which are inherited from Station 5.

213

(v) While Station 10 does not have strong secondary flow, Station 11 and Station 12’s

secondary flow mainly exhibit a single mirror vortex rather than the double vortex

similar to Station 4 and Station 5.

In summary, during the first few generations of the airways, notably different secondary

flows were recorded in different branches. None of the branches had more than double

vortices.

214

7.7 Particle deposition Results

7.7.1 Overview

Particle deposition during transient inhalation (focusing on both relations between release

time and deposition fraction (DF) as well as release position and deposition sites) was

analysed. The results are presented in this section for all three breathing patterns. The

first analysis will examine the relationship between deposition fraction and Stokes

Number. The second analysis will investigate the release position in relation to deposited

location.

7.7.2 Stokes Number Analysis to predict particle deposition fraction

The Stokes Number is defined as:

DUd

Stk pp

18

2

7-2

Where

p is the density of a spherical particle

pd is the particle diameter

U is the velocity

is the dynamic viscosity

D is the diameter of the tube

215

The Stokes Numbers (St) for the inlet, for different conditions, are plotted in Figure 7-23 to

Figure 7-25. Stokes Number is a dimensionless number corresponding to the behaviour of

the particles interacting with a fluid. It is defined as the ratio of the stopping distance of a

particle to a characteristic dimension of the obstacle. The Stokes Number equation above

is defined for particles travelling inside circular tube.

For Stokes Numbers greater than one, particles will continue in a straight line as the fluid

turns around the obstacle - therefore particles will hit the wall and deposit onto the wall.

For Stokes Numbers less than one, particles will follow the fluid flow very closely.

Figure 7-23 Stokes number vs time for resting condition

Time/Total Time

Sto

kes

Num

ber

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

0.25

0.3 2 micron4 micron6 micron8 micron10 micron

216

Figure 7-24 Stokes number vs time for light exercise condition

Figure 7-25 Stokes number vs time for heavy exercise condition

Time/Total Time

Sto

kes

Num

ber

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55


Time/Total Time

Sto

kes

Num

ber

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1


217

From Figures 7-11 to 7-13, the Stokes Number for 2 micron particles was less than 0.01,

therefore minimal particles were deposited. On the other hand, the Stokes Number for 10

micron particles, under the heavy exercise condition, exceeded the value of one, and

therefore a large deposition of particles occurred.

7.7.3 Transient Deposition Fraction

Deposition fraction in a transient simulation is defined as:

%100______

___ttimeatenteringparticlesofnumber

particlesdepositedofnumbertDF 7-3

The dependence of DF on particle-release times for a range of different particles from 2

microns to 10 microns are presented in Figure 7-26 to Figure 7-28.

218

Figure 7-26 Transient particle deposition fractions for different particle size at a full inhalation cycle under resting condition.

For the resting condition, the particle deposition did not start until a time of 0.1 into the

inhalation cycle. This was due to the short period of time for particles released at time

step zero before reaching down into the first bifurcation. As the flow was under

acceleration, the particle depositions increased with time, with the maximum deposition

fraction reaching approximately 3% for all particles sizes being simulated. The deposition

fraction fluctuated from time step to time step. The trend line for the variation shows

that the deposition fraction was related to the Stokes Number. The figure also

demonstrated that, during the acceleration phases of the inhalation, the deposition

fraction was higher compared the deceleration phase.

Time/Total Time

Dep

ositi

onFr

actio

n

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

42 micron4 micron6 micron8 micron10 micron

219

Figure 7-27 Transient particle deposition fractions for different particle size at a full inhalation cycle under light exercise.

For the light exercise condition, the particle deposition occurred slightly earlier than it did

in the resting condition. For the 10 micron particle case, the deposition fraction increased

to 4% very rapidly. However, the deposition peaked at a time of 0.6 of the time scale,

reaching 5%. As expected, the deposition fraction increased with increase in particle size.

Once again, the trend line for the deposition fraction mimicked the shape of the flow

curve - in turn, the shape of the Stokes Number vs time relationship.

Time/Total Time

Dep

ositi

onFr

actio

n

0 0.2 0.4 0.6 0.8 10

2

4


220

Figure 7-28 Transient particle deposition fractions for different particle size at a full inhalation cycle under heavy exercise.

For heavy exercise, the deposition behaved slightly differently to the previous two

conditions. The deposition fraction had a sudden increase from zero to 5%. However, the

trend for the deposition fraction increased over time – for the 10 micron particle’s case,

the deposition fraction increased from 5% and peaked at time 0.7, reaching 13.5%. The

deposition fraction followed the trend of the Stokes Number vs time graph.

Overall, it was observed that the deposition fractions were strongly influenced by the

particle release times for a given inhalation waveform. As can be expected, for all Stokes

Numbers and flow rates, the DF was low if particles were released in the early stage of the

inhalation period and then increased with higher airflow rates.

Time/Total Time

Dep

ositi

onFr

actio

n

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12

14


221

Especially for large mean Stokes numbers, say,

1meanSt ,

tDF followed tinRe qualitatively.

This implied that the magnitude of DF was strongly influenced by the Stokes Number. For

a small Stokes Number (e.g., 05.0meanSt ) DF was less dependent on the Stokes Number’s

variation. As the particle size increased, the transient effect was more important. This was

because particle deposition was not a linear function of Stokes Number, and particle

deposition could increase dramatically at larger flow rates due to impaction.

When particles were released at different time levels, with their associated instantaneous

flow rates, their residence times and Stokes Number ranges varied. In summary, the

Stokes Number dominated particle deposition, while at high Stokes Numbers the inlet

waveform strongly influenced the tDF distribution. The turbulence effect on particle

deposition was minor, probably because the influence of turbulence was small close to

the wall.

The tDF results from the simulation, when compared to Li, et al. [68], appeared to be

lower for all cases. However, direct comparisons were not made here as the turbulence

model, geometry, particle size range and breathing pattern were all different.

Overall, the drawback of using the deposition fraction for analysis was the lack of

consideration of local particle deposition. The results did not show the walls to which the

particles were being deposited. For this reason, local deposition and release position will

be investigated in Section 7.7.4.

222

7.7.4 Overall Particle Deposition Pattern

The overall particle deposition was an important phenomenon to understand as this

would provide insight into how geometry affected particle deposition. The particle

deposition results were in 3D and it is difficult to present the same level of detail in print.

To clarify the display of the results, colours are used to display the particle tracks. The

particle tracks for the deposited particle will use the specified colours as shown in Figure

7-29.

Figure 7-29 Upper airways generation labels and colour codes.

Figure 7-30 shows the particle tracks at time = 0.1154s, where particles had just started

depositing. At this time step, the majority of particles were deposited onto the walls of

Gen 1, Gen 6, Gen 11 and Gen 14 - because these were the walls that had the greatest

change in geometry. For example, comparing Gen 10 to Gen 1, Gen 1 had a stronger

branching angle of 48, while Gen 10 branching angle is only 35 - therefore more particles

deposited onto Gen 1’s wall while Gen 10 had minimal deposition.

223

Gen 2, Gen 13 and Gen 15 did not have any particle deposition at this time step. This was

either because the branching angle was small or the particles still hadn’t arrived at the

branch.

Figure 7-30 Particle tracks at time = 0.1154s for heavy exercise and 10 micron particles conditions

At time = 0.5193, as shown in Figure 7-31, there were many more particles being

deposited, because the flow rate from the inlet was very high, and because this was close

to the peak flow rate for heavy exercise. Notice that because of the acceleration of the

flow, the particle deposition did not just occur at the region that was close to the flow

divider. For Gen 1, there were particles being deposited on the upper side - away from

224

the flow divider. As expected, because the branching angles were small for Gen 10, Gen

13 and Gen 15, they all had very little particle deposition. From the results, one could

conclude that the branching angle was a major factor from the geometry that affected the

deposition.


At time = 1.0963s (Figure 7-20), the results showed more particles being deposited, and

they were, in their distribution, more spread out compare to time = 0.5193s. Note that in

Gen 1, there were more particles being deposited on the wall that was away from the flow

divider. The diagram suggests that the particles may have travelled very close to the wall

225

before their deposition in many cases. Again, Gen 10, Gen 13 and Gen 15 showed minimal

deposition.


The results for light exercise conditions (Figure 7-21) were very similar to those in the

heavy exercise conditions, but sparser because of the lower flow rate (which meant a

lower Stokes Number). The main point of interest was at Gen 14, where some particles

travelled backwards slightly before deposition, meaning that, in Gen 14, there was a small

reverse flow occurring. From this analysis, it was evident that the particle deposition and

226

the geometry had a close relationship where branching angle is the major factor causing

particle deposition.

2 Micron

6 Micron

10 Micron

Figure 7-33 Particle tracks at time = 1.0963s for light exercise and 10 micron particles conditions

227

The analysis has only looked at the results qualitatively. A quantitative analysis is

documented in Sections 7.7.5 and 7.7.6.

7.7.5 Release Position of Deposited Particle

Another component of the analysis in the transient simulation was the release position of

the deposited particle. Understanding the release position of deposited particles had

major implications for inhaled drug aerosol targeting.

The snapshots of the release position of particles for light exercise conditions, with

particle sizes of 10 microns are shown in Figure 7-34. The cross section is taken at the top

view of the trachea. The colour denotes the specific wall to which a particle deposits – as

per previous sections.

228

Figure 7-34 Snap shot of release position at time step t = 1.7907s under light exercise breathing conditions with 10 micron particles.

229

For the light exercise condition, the release positions of particle depositions in different

lung generations were confined to key areas. For example, the release positions of

particles depositing in Gen 0, Gen 1 and Gen 10 regions were mainly at the centre and

along the wall. For particles depositing in the second bifurcation region, for example Gen

6, their release areas were along two curved lines - some rare locations were close to the

top and bottom walls. Particles depositing in Gen 2 were fewer than those in Gen 6. The

release positions only contributed to part of the Gen 6 particle release positions - near the

centre only.

The release positions of particles depositing in Gen 11 and Gen 13 were very similar - they

formed two curved lines on the left, and those curved lines were closer to the outer wall

compare with the particles depositing in Gen 6. This was because Gen 10 is a lot shorter

than Gen 1.

The release positions of particles depositing in Gen 14 were on two curved lines with

lower curvature than those in Gen 11 and Gen 13. Those lines were also located closer to

the centre. Gen 15 only had two circular spots on the two curved lines of Gen 14, as Gen

15 had minimal deposition in comparison.

To compare how the particle sizes would affect the release position, Figure 7-35 shows

the release position snap shots for 3 different particle sizes, under the same time and

condition. From the figure, it is apparent that there were no significant differences.

230

2 micron

6 micron

10 micron

Figure 7-35 Release positions for different particle sizes under light exercise condition at t = 1.79s

For the heavy exercise condition, it should be noted that at t = 0.5193s, inhalation took

place during the acceleration period and, at t=1.0963s, it was in the deceleration phase

(Figure 7-24). Although the DFs were different at these two particular times, the particles

which were released from the same inlet position deposited basically at close proximity.

231

t = 0.5193

t = 1.0963

Figure 7-36 Release position for deposited particles of 6 micron under heavy exercise at different time steps.

Comparing the release position of deposited particles for two different breathing

conditions (Figure 7-25), the results showed very similar patterns with minor overall

differences. For the heavy exercise conditions, there were more particles deposited in Gen

0 - this was due to the high flow rate, meaning higher turbulence along the wall. The

shape of the curve lines for Gen 14 was slightly different – in the case of light exercise, the

curve appeared to be a bell shape curve. Also, notice that overall, the release location for

heavy exercise appeared to expand and was closer to the outer wall.

232

Light exercise

Heavy exercise

Figure 7-37 Comparison of release position for two different breathing at 6 micron at time step 11.

From this exercise, the results showed that the release position did not vary significantly

with change in particle size and time. However, the release positions changed slightly with

different breathing conditions.

7.7.6 Particle Continuation into Lower Airways

While most of the previous analyses focused on the particle deposition, another aspect

that was important was that related to the particles that continued further down the

airways. This section will study the release position for particles being exited and will also

study the particle exit pattern.

Figure 7-38 shows the five different exit location for particles. They are named as:

233

Left Upper (LU)

Left Lower (LL)

Right Upper (RU)

Right Mid (RM)

Right Lower (RL).

In order to distinguish the different exit particles, colour was used to separate the

differences. Figure 7-39 shows the five release position regions where particles were

being exited.

Figure 7-38 5 different exit location for particles

234

The results for different particles sizes and different time steps are not presented here

because they were all largely similar. This meant that if a particle was released in the RL

region, the chance of this particle being exited in the Right Lower lung lobe was very high.

However, as can be seen in the diagram, there were regions where particle release

positions overlapped or were very close to one another. Those were the areas where

particles were deposited as well - by comparing those curves with the region boundary.

Figure 7-39 Release position of exit particles for 10 micron under light exercise.

Another way to analyse the results is to study the exit proportion. Table 7-3 shows the

three different particle sizes exit to different lung lobes under light exercise. In

percentage terms, there was little variation when comparing the particle percentage with

the fluid flow percentage. As stated in Section 7.3, the fluid flow percentages were:

20.5% to Left Upper (LU)

235

25% to Left Lower (LL)

21.7% to Right Upper (RU)

9.6% to Right Middle (RM)

23.2% to Right Lower (RL).

This meant that the percentage amount of particle exiting could also be estimated by the

amount of fluid flow to each of the lung lobes.

Table 7-3 Exit proportion under light exercise

LL LU RL RM RU Total

Light 2 micron 23046 17869 20240 8600 19796 89551

25.74% 19.95% 22.60% 9.60% 22.11% 100.00%

Light 6 micron 23245 17445 20298 8850 19265 89103

26.09% 19.58% 22.78% 9.93% 21.62% 100.00%

Light 10 micron 23411 16603 20436 9093 18111 87654

26.71% 18.94% 23.31% 10.37% 20.66% 100.00%

236

7.8 Conclusions

This chapter documented the full investigation of particle deposition under realistic

transient inlet conditions. The BSL Reynolds Stress Model was used for all the simulations.

When compared to other published research, the deposition fraction results were slightly

different, but this was potentially due to a number of factors related to the model –

including:

Geometry

Flow rate

Turbulence model.

Further (more detailed) investigation and comparison would be required as part of further

research in order to determine the specific cause of the variations.

Overall, the particle deposition patterns demonstrated that there were more depositions

at certain walls – specifically, if the branching angle was large, the chance of high

deposition was very high.

The release position of deposited particles and exited particles was also investigated. The

study showed that the release position did not vary significantly at different time steps or

with changes in particle size. However, the release position for particles being deposited

would vary with breathing pattern.

237

Chapter. 8 Conclusions and Recommendations for Further Research

238

8.1 Conclusions

The human lung has been evolving for many thousands of years and, in engineering terms,

its major function has always been gas exchange. During human evolution, however, the

lung has also evolved to adapt its changing environment - for human survival. The blood-

gas barrier has a very large area and is extremely thin, which makes it ideal for rapid

diffusion of oxygen and carbon dioxide. In addition, the branching airway structure is very

efficient, with little unevenness of ventilation, and a relatively small dead space compared

with the total lung volume. The mucociliary escalator and the alveolar macrophage system

are effective in keeping the lung clean.

The research work presented in this thesis was conducted in order to gain a greater

understanding of particle deposition in the human lung, by using both experimental and

computer simulation. This may lead us to understand why the human lung has evolved in

the way that it has, and how that evolution has helped it to adapt to its environment. The

benefits of this understanding are manifold and include applications related to:

Understanding particle contaminant and pollutant effects on the human

respiratory system

Delivery of pharmaceutical products through the respiratory system through

aerosols and other means.

With these points in mind, the key achievements in this research included the following:

(i) Chapter 2 provided the background information and research related to the

human lung and its analysis. This information provided a detailed review of

literature in the field and was required for both experimental and computer

simulation. The morphology of the human lung was presented together with

fluid flow theory and the principle of particle behaviour in human airways.

239

(ii) Chapter 3 documented the experimental results of fluid flow in bifurcation.

The experiments conducted used Laser Doppler Anemometry to measure the

fluid flow of three different Reynolds Numbers (518, 1036, and 2089)

conditions. An initial numerical simulation was conducted using CFX-5.5 with

the correct boundary conditions as the experiment. This validated that the

simulation could match experimental results closely and built confidence in

the numerical simulation analysis using CFX.

(iii) Chapter 4 extends the simulation from Chapter 3 to a four generation

bifurcation flow. The geometry of the model used came from Weibel [15], and

the CAD model was created using Solidworks 2004. The velocity flow profile,

secondary flow, flow distribution and pressure drop behaviour were presented

and compared with other researchers. Insights into fluid flow behaviour were

gained from this exercise. From the velocity flow profile analysis, it was

demonstrated that the profiles become skewed after a fully developed flow

had been divided by the first flow divider (i.e., after first bifurcation). The

skewness of the flow inherits to the children branches.

(iv) From the secondary flow analysis, the results demonstrated that secondary

flows existed in the cross section of the airways. Because the model was

symmetrical, symmetrical vortices could be observed downstream from the

bifurcation.

(v) Due to the geometry, the flow distribution at the outlets was uneven. This

information was used to justify the need to change the boundary conditions of

the subsequent simulation.

(vi) The CFD simulations conducted to this point were using tetrahedral meshing

models. From testing and evaluation, hexahedral elements were preferred,

and could lead to more accurate results.

240

(vii) In Chapter 5, in order to validate the particle deposition simulation with CFX-

11, a symmetrical airway model was used to validate the particle tracking

simulation code. Results of the particle deposition were compared to other

researchers. The particle deposition efficiency relating to the Stokes Number

was found to be 3844.2231.50% Stk

(viii) In Chapter 6, a new CAD airways model was created, based on Horsfield, et al.

[16], using Solidworks 2005. ICEM was then used to mesh the model using

hexahedral elements. The meshing was fine-tuned and a grid independence

test was conducted and fine mesh model was used for the later chapters.

(ix) In Chapter 7, which was the core of this thesis, a full transient inhalation

particle tracking simulation was conducted using the asymmetrical model

generated in Chapter 5. Full transport theory was presented and the

justification of the boundary conditions and turbulence model were given.

From the fluid flow analysis, secondary flow was noticeable as with steady

asymmetrical fluid simulation. Correlation could not be achieved at this stage

because of the number of variables involved in the asymmetrical transient,

with different breathing conditions and particle sizes. However, visual analyses

were presented instead.

241

8.2 Recommendations for future research

The research undertaken during this Doctoral program is open-ended and ongoing – it is

one element in a long chain of research and development that has been under way for

many decades.

This specific research endeavoured to address a range of topics related to particle

deposition in the human lung. During the course of this Doctoral work, a number of areas

that require further/ongoing investigation were noted and are listed here:

A fundamental future research goal needs to be the simulation of the full human airways

from mouth or nose; passing external nares, nasopharynx, pharynx, then larynx into

human lung from Trachea down to alveoli level. This basic research is important in

understanding particle deposition in the human lung because the inlet flow conditions at

this stage are unknown without the precursor work. Also, this work would be important

in gaining a holistic picture on the state of the flow, as well as the amount of particles that

are able to pass through the first particle filtering system, the nose. There are also two

ways of human breathing (i.e., nasal and oral). In this thesis, nothing has been mentioned

regarding the type of breathing because the boundary conditions here start from the

trachea. Therefore studying the two ways of breathing would help to establish meaningful

inlet conditions for the trachea. The difficulty in performing such research is that the

geometry of the nasal, nasopharynx and larynx are not well defined in the literature –

therefore, creating a CAD model and producing the mesh for the volume will be an issue.

The second half of the particle deposition analysis that was not covered here was the

suspended particles inside the tidal volume after the inhalation. A simulation is required

for simulating the exhalation of those particles. Again, this is related to the first point

where the lung model deep inside the lung is not defined – the number of particles

remaining suspended in the air inside the tidal volume remains unknown. With

242

advancements in computing power, it will be possible to create a whole lung model to

simulate the exhalation of the particles.

With advances in imaging technology, there need to be techniques applied to extract high

resolution images of the human lung from Trachea to the small Alveoli. Journal papers

have already been published on using micro CT on the human lung by Watz, et al. [105].

The results from the simulation can be used as a benchmark for particle deposition. From

an engineering perspective, the problem of using images from CT scan or MRI is that it will

take a very long time to smooth the surfaces before one can be meshed with reasonable

mesh size.

In Chapter 7, a number of different turbulence models were presented. The BSL Reynolds

Stress Model was chosen because of its characteristics. Conversely, there are other

turbulence model that may be more suitable and which were not examined here. For

instance, it may be necessary to create a new transition model as, at times, the fluid flow

of the inhalation cycle is laminar - using a transition model can produce more accurate

simulation results.

Throughout this thesis, the commercial CFD simulation software package used was CFX.

There are numerous other CFD simulation software packages in the market which could

be explored to replicate the work here

Particle deposition will remain a research topic for some decades. Further research and

modelling of the lung and airways could also provide new information on the cause of

lung diseases due to particle deposition. Particle deposition analysis may also ultimately

aid in the design of an artificial human lung.

243

Appendix A

This appendix contains a sample of the CFX output file that contains all the settings and

parameters that was used in the transient particle deposition computation in Chapter 7.

This run of the CFX-11.0 Solver started at 1:31:28 on 14 Dec 2009 by

user Toby on TOBY-WS (intel_xeon64.sse2_winnt) using the command:

"C:\Program Files\ANSYS Inc\v110\CFX\bin\perllib\cfx5solve.pl"

-stdout-comms -batch -ccl -

Installed patches:

* Service Pack 1

*

Setting up CFX Solver run ...

+--------------------------------------------------------------------

+

|

|

| CFX Command Language for Run

|

|

|

+--------------------------------------------------------------------

+

LIBRARY:

CEL:

EXPRESSIONS:

AerosolDensity = 350[kg/m^3]

InhaleCycle = 1.154[s]

InletMassFlow = 0.000474[kg/s]

LLArea = 5.02655E-05[m^2]

LUArea = 4.41786E-05[m^2]

ParticleDiameter = 0.000008[m]

TotalParticles = 100000

VolumeOfParticle = 4*pi*((ParticleDiameter/2)^3)/3

ParticleMassFlow = \

VolumeOfParticle*AerosolDensity*TotalParticles/InhaleCycle

RLArea = 3.21699E-05 [m^2]

RMArea = 2.12372E-05 [m^2]

244

RUArea = 4.18539E-05 [m^2]

StepsPerCycle = 40

END

FUNCTION: MassFlowRateAtInlet

Argument Units = s

Option = Interpolation

Result Units = kg/s

INTERPOLATION DATA:

Data Pairs = \

0,0.0000010000,0.055814,0.0003341700,0.111628,0.0006079050,0.167442\

,0.0009112650,0.223256,0.0011067900,0.27907,0.0012383250,0.

334884,0\

.0013177200,0.390698,0.0013793400,0.446512,0.0014326650,0.5

02326,0.\

0014859900,0.55814,0.0015215400,0.613953,0.0015559050,0.669767,0.00\

15831600,0.725581,0.0015831600,0.8,0.0015653850,0.863,0.0015120600,\

0.932,0.0013994850,0.988,0.0012478050,1.05,0.0009645900,1.093,0.000\

5978444,1.154,0.0000010000,1.216,-0.0007027050,1.292,-

0.0013698600,\

1.323,-0.0015215400,1.36,-0.0016092300,1.39535,-

0.0016447800,1.4511\

6,-0.0016815150,1.50698,-0.0016909950,1.56279,-

0.0016732200,1.6186,\

-0.0016424100,1.67442,-0.0016009350,1.73023,-

0.0015298350,1.78605,-\

0.0014409600,1.84186,-0.0013354950,1.89767,-

0.0012288450,1.95349,-0\

.0011233800,2.0093,-0.0009906600,2.06512,-

0.0008401650,2.12093,-0.0\

006991500,2.17674,-0.0005664300,2.23256,-

0.0004194900,2.28837,-0.00\

02784750,2.34419,-0.0001469400,2.4,-

0.0000010000,2.45581,0.00033417\

00,2.51163,0.0006079050,2.56744,0.0009112650,2.62326,0.0011067900,2\

.67907,0.0012383250,2.73488,0.0013177200,2.7907,0.001379340

0,2.8465\

1,0.0014326650,2.90233,0.0014859900,2.95814,0.0015215400,3.01395,0.\

0015559050,3.06977,0.0015831600,3.12558,0.0015831600,3.1814,0.00156\

53850,3.23721,0.0015120600,3.29302,0.0013994850,3.34884,0.001247805\

0,3.40465,0.0009645900,3.46047,0.0005978444,3.51628,0.0000010000,3.\

57209,-0.0007027050,3.62791,-0.0013698600,3.68372,-

0.0015215400,3.7\

245

3953,-0.0016092300,3.79535,-0.0016447800,3.85116,-

0.0016815150,3.90\

698,-0.0016909950,3.96279,-0.0016732200,4.0186,-

0.0016424100,4.0744\

2,-0.0016009350,4.13023,-0.0015298350,4.18605,-

0.0014409600,4.24186\

,-0.0013354950,4.29767,-0.0012288450,4.35349,-

0.0011233800,4.4093,-\

0.0009906600,4.46512,-0.0008401650,4.52093,-

0.0006991500,4.57674,-0\

.0005664300,4.63256,-0.0004194900,4.68837,-

0.0002784750,4.74419,-0.\

0001469400,4.8,-

0.0000010000,4.85581,0.0003341700,4.91163,0.0006079\

050,4.96744,0.0009112650,5.02326,0.0011067900,5.07907,0.0012383250,\

5.13488,0.0013177200,5.1907,0.0013793400,5.24651,0.0014326650,5.302\

33,0.0014859900,5.35814,0.0015215400,5.41395,0.0015559050,5.46977,0\

.0015831600,5.52558,0.0015831600,5.5814,0.0015653850,5.6372

1,0.0015\

120600,5.69302,0.0013994850,5.74884,0.0012478050,5.80465,0.00096459\

00,5.86047,0.0005978444,5.91628,0.0000010000,5.97209,-

0.0007027050,\

6.02791,-0.0013698600,6.08372,-0.0015215400,6.13953,-

0.0016092300,6\

.19535,-0.0016447800,6.25116,-0.0016815150,6.30698,-

0.0016909950,6.\

36279,-0.0016732200,6.4186,-0.0016424100,6.47442,-

0.0016009350,6.53\

023,-0.0015298350,6.58605,-0.0014409600,6.64186,-

0.0013354950,6.697\

67,-0.0012288450,6.75349,-0.0011233800,6.8093,-

0.0009906600,6.86512\

,-0.0008401650,6.92093,-0.0006991500,6.97674,-

0.0005664300,7.03256,\

-0.0004194900,7.08837,-0.0002784750,7.14419,-

0.0001469400,7.2,-0.00\

00010000

Extend Max = No

Extend Min = No

Option = One Dimensional

END

END

END

MATERIAL: Aerosol

Material Group = User

Option = Pure Substance

Thermodynamic State = Solid

PROPERTIES:

246

Option = General Material

EQUATION OF STATE:

Density = AerosolDensity

Molar Mass = 1.0 [kg kmol^-1]

Option = Value

END

END

END

MATERIAL: Air at 25 C

Material Description = Air at 25 C and 1 atm (dry)

Material Group = Air Data, Constant Property Gases

Option = Pure Substance

Thermodynamic State = Gas

PROPERTIES:

Option = General Material

Thermal Expansivity = 0.003356 [K^-1]

ABSORPTION COEFFICIENT:

Absorption Coefficient = 0.01 [m^-1]

Option = Value

END

DYNAMIC VISCOSITY:

Dynamic Viscosity = 1.831E-05 [kg m^-1 s^-1]

Option = Value

END

EQUATION OF STATE:

Density = 1.185 [kg m^-3]

Molar Mass = 28.96 [kg kmol^-1]

Option = Value

END

REFERENCE STATE:

Option = Specified Point

Reference Pressure = 1 [atm]

Reference Specific Enthalpy = 0. [J/kg]

Reference Specific Entropy = 0. [J/kg/K]

Reference Temperature = 25 [C]

END

REFRACTIVE INDEX:

Option = Value

Refractive Index = 1.0 [m m^-1]

END

SCATTERING COEFFICIENT:

Option = Value

Scattering Coefficient = 0.0 [m^-1]

END

SPECIFIC HEAT CAPACITY:

Option = Value

Specific Heat Capacity = 1.0044E+03 [J kg^-1 K^-1]

Specific Heat Type = Constant Pressure

END

THERMAL CONDUCTIVITY:

Option = Value

Thermal Conductivity = 2.61E-02 [W m^-1 K^-1]

247

END

END

END

END

FLOW:

SOLUTION UNITS:

Angle Units = [rad]

Length Units = [m]

Mass Units = [kg]

Solid Angle Units = [sr]

Temperature Units = [K]

Time Units = [s]

END

SIMULATION TYPE:

Option = Transient

EXTERNAL SOLVER COUPLING:

Option = None

END

INITIAL TIME:

Option = Automatic with Value

Time = 0 [s]

END

TIME DURATION:

Option = Total Time

Total Time = InhaleCycle

END

TIME STEPS:

Option = Timesteps

Timesteps = InhaleCycle/StepsPerCycle

END

END

DOMAIN: Airways

Coord Frame = Coord 0

Domain Type = Fluid

Fluids List = Air at 25 C

Location = SOLID

Particles List = Aerosol

BOUNDARY: IN

Boundary Type = OPENING

Location = IN

BOUNDARY CONDITIONS:

FLOW DIRECTION:

Option = Normal to Boundary Condition

END

FLOW REGIME:

Option = Subsonic

END

MASS AND MOMENTUM:

Option = Opening Pressure and Direction

Relative Pressure = 0 [Pa]

END

TURBULENCE:

248

Option = Medium Intensity and Eddy Viscosity Ratio

END

END

FLUID: Aerosol


MASS AND MOMENTUM:

Option = Zero Slip Velocity

END

PARTICLE DIAMETER DISTRIBUTION:

Diameter = ParticleDiameter

Option = Specified Diameter

END

PARTICLE MASS FLOW RATE:

Mass Flow Rate = ParticleMassFlow

END

PARTICLE POSITION:

Option = Uniform Injection

Particle Locations = Equally Spaced

NUMBER OF POSITIONS:

Number per Unit Time = TotalParticles/InhaleCycle

Option = Direct Specification

END

END

END

END

END

BOUNDARY: LL

Boundary Type = OUTLET

Location = LL


FLOW REGIME:

Option = Subsonic

END

MASS AND MOMENTUM:

Mass Flow Rate = 0.25*MassFlowRateAtInlet(t)

Option = Mass Flow Rate

END

END

END

BOUNDARY: LU


Location = LU


FLOW REGIME:

Option = Subsonic

END

MASS AND MOMENTUM:



END

END

END

249

BOUNDARY: RL


Location = RL


FLOW REGIME:

Option = Subsonic

END

MASS AND MOMENTUM:



END

END

END

BOUNDARY: RM


Location = RM


FLOW REGIME:

Option = Subsonic

END

MASS AND MOMENTUM:



END

END

END

BOUNDARY: RU


Location = RU


FLOW REGIME:

Option = Subsonic

END

MASS AND MOMENTUM:



END

END

END

BOUNDARY: WallGen00

Boundary Type = WALL

Location = GEN00


WALL INFLUENCE ON FLOW:

Option = No Slip

END

END

FLUID: Aerosol


VELOCITY:

Option = Restitution Coefficient

Parallel Coefficient of Restitution = 0

250

Perpendicular Coefficient of Restitution = 0

END

END

END

END

BOUNDARY: WallGen01


Location = GEN01



Option = No Slip

END

END

FLUID: Aerosol


VELOCITY:




END

END

END

END

BOUNDARY: WallGen02


Location = GEN02



Option = No Slip

END

END

FLUID: Aerosol


VELOCITY:




END

END

END

END

BOUNDARY: WallGen06


Location = GEN06



Option = No Slip

END

END

FLUID: Aerosol


VELOCITY:

251




END

END

END

END

BOUNDARY: WallGen10


Location = GEN10



Option = No Slip

END

END

FLUID: Aerosol


VELOCITY:




END

END

END

END

BOUNDARY: WallGen11


Location = GEN11



Option = No Slip

END

END

FLUID: Aerosol


VELOCITY:




END

END

END

END

BOUNDARY: WallGen13


Location = GEN13



Option = No Slip

END

END

FLUID: Aerosol

252


VELOCITY:




END

END

END

END

BOUNDARY: WallGen14


Location = GEN14



Option = No Slip

END

END

FLUID: Aerosol


VELOCITY:




END

END

END

END

BOUNDARY: WallGen15


Location = GEN15



Option = No Slip

END

END

FLUID: Aerosol


VELOCITY:




END

END

END

END

DOMAIN MODELS:

BUOYANCY MODEL:

Option = Non Buoyant

END

DOMAIN MOTION:

Option = Stationary

END

253

MESH DEFORMATION:

Option = None

END

REFERENCE PRESSURE:

Reference Pressure = 1 [atm]

END

END

FLUID MODELS:

COMBUSTION MODEL:

Option = None

END

HEAT TRANSFER MODEL:

Option = None

END

THERMAL RADIATION MODEL:

Option = None

END

TURBULENCE MODEL:

Option = BSL Reynolds Stress

END

TURBULENT WALL FUNCTIONS:

Option = Automatic

END

END

FLUID PAIR: Air at 25 C | Aerosol

Particle Coupling = Fully Coupled

MOMENTUM TRANSFER:

DRAG FORCE:

Option = Schiller Naumann

END

PRESSURE GRADIENT FORCE:

Option = None

END

TURBULENT DISPERSION FORCE:

Option = None

END

VIRTUAL MASS FORCE:

Option = None

END

END

END

FLUID: Aerosol

FLUID MODELS:

MORPHOLOGY:

Option = Dispersed Particle Transport Fluid

END

END

END

FLUID: Air at 25 C

FLUID MODELS:

MORPHOLOGY:

Option = Continuous Fluid

254

END

END

END

END

INITIALISATION:

Option = Automatic

INITIAL CONDITIONS:

Velocity Type = Cartesian

CARTESIAN VELOCITY COMPONENTS:

Option = Automatic

END

EPSILON:

Option = Automatic

END

K:

Option = Automatic

END

STATIC PRESSURE:

Option = Automatic

END

END

END

OUTPUT CONTROL:

PARTICLE TRACK FILE:

Keep Track File = On

Option = All Track Positions

Track Positions = Element Faces

END

RESULTS:

File Compression Level = Default

Option = Standard

END

TRANSIENT RESULTS: Transient Results 1

File Compression Level = Default

Include Mesh = No

Option = Selected Variables

Output Variables List = Courant Number,Pressure,Reynolds \

Stress,Velocity,Wall Shear,Yplus

OUTPUT FREQUENCY:

Option = Time Interval

Time Interval = InhaleCycle/10

END

END

END

SOLVER CONTROL:

ADVECTION SCHEME:

Option = High Resolution

END

CONVERGENCE CONTROL:

Maximum Number of Coefficient Loops = 30

Timescale Control = Coefficient Loops

END

255

CONVERGENCE CRITERIA:

Residual Target = 0.00001

Residual Type = RMS

END

PARTICLE CONTROL:

PARTICLE INTEGRATION:

First Iteration for Particle Calculation = 1

Iteration Frequency = 30

Option = Forward Euler

END

PARTICLE SOURCE SMOOTHING:

Option = Smooth

END

END

TRANSIENT SCHEME:

Option = Second Order Backward Euler

TIMESTEP INITIALISATION:

Option = Automatic

END

END

END

END

COMMAND FILE:

Version = 11.0

Results Version = 11.0

END

EXECUTION CONTROL:

INTERPOLATOR STEP CONTROL:

Runtime Priority = Standard

EXECUTABLE SELECTION:

Double Precision = Off

END

MEMORY CONTROL:

Memory Allocation Factor = 1.0

END

END

PARALLEL HOST LIBRARY:

HOST DEFINITION: tobyws

Remote Host Name = TOBY-WS

Host Architecture String = winnt-amd64

Installation Root = C:\Program Files\ANSYS Inc\v%v\CFX

END

END

PARTITIONER STEP CONTROL:

Multidomain Option = Independent Partitioning



Use Large Problem Partitioner = Off

END

MEMORY CONTROL:


END

256

PARTITIONING TYPE:

MeTiS Type = k-way

Option = MeTiS

Partition Size Rule = Automatic

Partition Weight Factors = 0.125, 0.125, 0.125, 0.125, 0.125,

0.125, \

0.125, 0.125

END

END

RUN DEFINITION:

Definition File = \

E:/PhD/Simulation/FullModel/FineMesh/Transient/ParticleTrackingNov2009

/\

FineMeshHighResolutionTransientInspiratoryParticleTrackingHeavy.def

Initial Values File = \

E:/PhD/Simulation/FullModel/FineMesh/Transient/ParticleTrackingNov2009

/\

FineMeshHighResolutionSteadyInspiratoryParticleTracking_001.res

Interpolate Initial Values = Off

Run Mode = Full

END

SOLVER STEP CONTROL:



Double Precision = Off

END

MEMORY CONTROL:


END

PARALLEL ENVIRONMENT:

Number of Processes = 8

Start Method = PVM Local Parallel

Parallel Host List = tobyws*8

END

END

END

+--------------------------------------------------------------------

+

| Warning!

|

|

|

| Both the Definition File and the Initial Values File contain a

|

| mesh. The mesh in the Definition File will be ignored.

|

257

+--------------------------------------------------------------------

+

+--------------------------------------------------------------------

+

|

|

| Partitioning

|

|

|

+--------------------------------------------------------------------

+

+--------------------------------------------------------------------

+

|

|

| ANSYS CFX Partitioner 11.0

|

|

|

| Version 2007.08.08-23.01 Wed Aug 8 23:43:11 GMTDT 2007

|

|

|

| Executable Attributes

|

|

|

| single-int32-64bit-novc6-optimised-supfort-noprof-nospag-lcomp

|

|

|

| Copyright 1996-2007 ANSYS Europe Ltd.

|

+--------------------------------------------------------------------

+

+--------------------------------------------------------------------

+

| Job Information

|

258

+--------------------------------------------------------------------

+

Run mode: partitioning run

Host computer: TOBY-WS

Job started: Mon Dec 14 01:31:40 2009

+--------------------------------------------------------------------

+

| Memory Allocated for Run (Actual usage may be less)

|

+--------------------------------------------------------------------

+

Data Type Kwords Words/Node Words/Elem Kbytes Bytes/Node

Real 4608.9 5.34 5.51 18003.6 21.37

Integer 34259.5 39.70 40.97 133826.3 158.82

Character 2501.2 2.90 2.99 2442.6 2.90

Logical 65.0 0.08 0.08 253.9 0.30

Double 1200.5 1.39 1.44 9378.9 11.13

+--------------------------------------------------------------------

+

| Mesh Statistics

|

+--------------------------------------------------------------------

+

Domain Name : Airways

Total Number of Nodes =

862875

Total Number of Elements =

836136

Total Number of Hexahedrons =

836136

Total Number of Faces =

52472

+--------------------------------------------------------------------

+

| Partitioning Information

|

+--------------------------------------------------------------------

+

259

Partitioning of domain: Airways

- Partitioning tool: MeTiS multilevel weighted k-way algorithm

- Number of partitions: 8

- Number of graph-nodes: 862875

- Number of graph-edges: 5122764

Partitioning information for domain: Airways

+-----------+---------------------+-----------+--------

+

| Elements | Vertices (Overlap) | Faces | Weight

|

+-------------+-----------+---------------------+-----------+--------

+

| Full mesh | 836136 | 862875 | 52472 |

|

+-------------+-----------+---------------------+-----------+--------

+

| Part. 1 | 105566 | 111996 4.9% | 7278 | 0.125

|

| Part. 2 | 109853 | 116579 5.4% | 6995 | 0.125

|

| Part. 3 | 110993 | 118214 7.5% | 5490 | 0.125

|

| Part. 4 | 108904 | 115125 5.7% | 5813 | 0.125

|

| Part. 5 | 106637 | 114283 8.4% | 5593 | 0.125

|

| Part. 6 | 99701 | 104997 2.8% | 7454 | 0.125

|

| Part. 7 | 108003 | 113264 2.1% | 7951 | 0.125

|

| Part. 8 | 109633 | 115943 4.7% | 7007 | 0.125

|

+-------------+-----------+---------------------+-----------+--------

+

| Sum of part.| 859290 | 910401 5.2% | 53581 | 1.000

|

+-------------+-----------+---------------------+-----------+--------

+

CPU-Time requirements:

- Preparations 1.997E+00

seconds

- Low-level mesh partitioning 9.828E-01

seconds

- Global partitioning information 2.028E-01

seconds

- Vertex, element and face partitioning information 4.368E-01

seconds

260

- Element and face set partitioning information 1.560E-01

seconds

- Summed CPU-time for mesh partitioning 6.380E+00

seconds

+--------------------------------------------------------------------

+

| Job Information

|

+--------------------------------------------------------------------

+


Job finished: Mon Dec 14 01:31:49 2009

Total CPU time: 8.018E+00 seconds

or: ( 0: 0: 0: 8.018 )

( Days: Hours: Minutes: Seconds )

Total wall clock time: 9.000E+00 seconds

or: ( 0: 0: 0: 9.000 )

( Days: Hours: Minutes: Seconds )

+--------------------------------------------------------------------

+

|

|

| Solver

|

|

|

+--------------------------------------------------------------------

+

+--------------------------------------------------------------------

+

|

|

| ANSYS CFX Solver 11.0

|

|

|

| Version 2007.08.08-23.01 Wed Aug 8 23:43:11 GMTDT 2007

|

|

|

| Executable Attributes

|

261

|

|

| single-int32-64bit-novc6-optimised-supfort-noprof-nospag-lcomp

|

|

|

| Copyright 1996-2007 ANSYS Europe Ltd.

|

+--------------------------------------------------------------------

+

+--------------------------------------------------------------------

+

| Job Information

|

+--------------------------------------------------------------------

+

Run mode: parallel run (PVM)


Par. Process: Master running on mesh partition: 1



Par. Process: Slave running on mesh partition: 2

















262




+--------------------------------------------------------------------

+

| Memory Allocated for Run (Actual usage may be less)

|

+--------------------------------------------------------------------

+

Allocated storage in: Kwords

Words/Node

Words/Elem

Kbytes

Bytes/Node

Partition | Real | Integer | Character| Logical | Double

----------+------------+------------+----------+----------+----------

1 | 38035.5 | 9563.2 | 2951.2 | 65.0 | 1208.0

| 339.61 | 85.39 | 26.35 | 0.58 | 10.79

| 360.30 | 90.59 | 27.96 | 0.62 | 11.44

| 148576.0 | 37356.1 | 2882.0 | 63.5 | 9437.5

| 1358.46 | 341.55 | 26.35 | 0.58 | 86.29

----------+------------+------------+----------+----------+----------

2 | 39090.6 | 9858.7 | 2951.2 | 65.0 | 1208.0

| 335.31 | 84.57 | 25.31 | 0.56 | 10.36

| 355.84 | 89.74 | 26.86 | 0.59 | 11.00

| 152697.7 | 38510.7 | 2882.0 | 63.5 | 9437.5

| 1341.26 | 338.27 | 25.31 | 0.56 | 82.90

----------+------------+------------+----------+----------+----------

3 | 39158.7 | 9885.1 | 2951.2 | 65.0 | 1208.0

| 331.25 | 83.62 | 24.96 | 0.55 | 10.22

| 352.80 | 89.06 | 26.59 | 0.59 | 10.88

| 152963.5 | 38613.8 | 2882.0 | 63.5 | 9437.5

| 1325.01 | 334.48 | 24.96 | 0.55 | 81.75

----------+------------+------------+----------+----------+----------

4 | 38599.6 | 9740.4 | 2951.2 | 65.0 | 1208.0

| 335.28 | 84.61 | 25.63 | 0.56 | 10.49

| 354.44 | 89.44 | 27.10 | 0.60 | 11.09

| 150779.5 | 38048.4 | 2882.0 | 63.5 | 9437.5

| 1341.14 | 338.43 | 25.63 | 0.56 | 83.94

----------+------------+------------+----------+----------+----------

5 | 38079.9 | 9577.5 | 2951.2 | 65.0 | 1208.0

| 333.21 | 83.81 | 25.82 | 0.57 | 10.57

| 357.10 | 89.81 | 27.68 | 0.61 | 11.33

| 148749.5 | 37412.3 | 2882.0 | 63.5 | 9437.5

| 1332.83 | 335.22 | 25.82 | 0.57 | 84.56

----------+------------+------------+----------+----------+----------

6 | 36429.6 | 9131.6 | 2951.2 | 65.0 | 1208.0

| 346.96 | 86.97 | 28.11 | 0.62 | 11.51

263

| 365.39 | 91.59 | 29.60 | 0.65 | 12.12

| 142303.3 | 35670.3 | 2882.0 | 63.5 | 9437.5

| 1387.84 | 347.88 | 28.11 | 0.62 | 92.04

----------+------------+------------+----------+----------+----------

7 | 38676.7 | 9753.7 | 2951.2 | 65.0 | 1208.0

| 341.47 | 86.12 | 26.06 | 0.57 | 10.67

| 358.11 | 90.31 | 27.33 | 0.60 | 11.18

| 151080.8 | 38100.6 | 2882.0 | 63.5 | 9437.5

| 1365.90 | 344.46 | 26.06 | 0.57 | 85.32

----------+------------+------------+----------+----------+----------

8 | 39006.9 | 9841.1 | 2951.2 | 65.0 | 1208.0

| 336.43 | 84.88 | 25.45 | 0.56 | 10.42

| 355.80 | 89.76 | 26.92 | 0.59 | 11.02

| 152370.7 | 38441.7 | 2882.0 | 63.5 | 9437.5

| 1345.73 | 339.51 | 25.45 | 0.56 | 83.35

----------+------------+------------+----------+----------+----------

Total | 307077.4 | 77351.4 | 23609.5 | 520.0 | 9664.0

| 355.88 | 89.64 | 27.36 | 0.60 | 11.20

| 367.26 | 92.51 | 28.24 | 0.62 | 11.56

| 1199521.1 | 302153.9 | 23056.1 | 507.8 | 75500.0

| 1423.51 | 358.58 | 27.36 | 0.60 | 89.60

----------+------------+------------+----------+----------+----------

+--------------------------------------------------------------------

+

| Mesh Statistics

|

+--------------------------------------------------------------------

+


Total Number of Nodes =

862875

Total Number of Elements =

836136

Total Number of Hexahedrons =

836136

Total Number of Faces =

52472

Minimum Orthogonality Angle [degrees] = 27.7

ok

Maximum Aspect Ratio = 31.9

OK

Maximum Mesh Expansion Factor = 23.1 !

+--------------------------------------------------------------------

+

264

| Initial Conditions Supplied by Fields in the Input Files

|

+--------------------------------------------------------------------

+


Absolute Pressure

Aerosol.Averaged Volume Fraction

Aerosol.Particle Momentum Source

Aerosol.Particle Momentum Source Coefficient

Courant Number

Pressure

Pressure.Gradient

Shear Strain Rate

Specific Volume

Total Pressure

Velocity

Velocity.Beta

Velocity.Gradient

Volume Porosity

+--------------------------------------------------------------------

+

| Average Scale Information

|

+--------------------------------------------------------------------

+


Global Length = 3.2046E-

02

Minimum Extent = 1.5999E-

02

Maximum Extent = 1.4850E-

01

Density =

1.1850E+00

Dynamic Viscosity = 1.8310E-

05

Velocity = 3.3664E-

03

Advection Time =

9.5192E+00

RMS Courant Number =

1.3047E+01

Maximum Courant Number =

1.0068E+02

Reynolds Number =

6.9818E+00

+--------------------------------------------------------------------

+

265

| ERROR #002100004 has occurred in subroutine Out_Scales_Flu.

|

| Message:

|

| The Reynolds number is outside of the range expected based on the

|

| Option selected for the TURBULENCE MODEL. Check this setting,

|

| the values of the properties, mesh scale, consistency of units

|

| and solution values in the input file. Execution will proceed.

|

+--------------------------------------------------------------------

+

+--------------------------------------------------------------------

+

| Writing transient file 48.trn

|

| Name : Transient Results 1

|

| Type : Selected Variables

|

| Option : Time Interval

|

+--------------------------------------------------------------------

+

+--------------------------------------------------------------------

+

| The Equations Solved in This Calculation

|

+--------------------------------------------------------------------

+

Subsystem : Wall Scale

Wallscale

Subsystem : Momentum and Mass

U-Mom

V-Mom

W-Mom

P-Mass

Subsystem : Reynolds Stress and TurbFreq

uu-RS

vv-RS

ww-RS

uv-RS

uw-RS

266

vw-RS

O-TurbFreq

+--------------------------------------------------------------------

+

| Particle Transport Equations Solved in This Calculation

|

+--------------------------------------------------------------------

+

Domain Type : Airways

x-Mom-Aerosol

y-Mom-Aerosol

z-Mom-Aerosol

CFD Solver started: Mon Dec 14 01:34:59 2009

+--------------------------------------------------------------------

+

| Convergence History

|

+--------------------------------------------------------------------

+

======================================================================

| Timestepping Information

|

---------------------------------------------------------------------

-

| Timestep | RMS Courant Number | Max Courant Number

|

+----------------------+----------------------+----------------------

+

| 2.8850E-02 | 13.05 | 100.68

|

---------------------------------------------------------------------

-

======================================================================

TIME STEP = 49 SIMULATION TIME = 2.8850E-02 CPU SECONDS =

8.376E+01

(THIS RUN: 1 2.8850E-02

8.376E+01)

---------------------------------------------------------------------

-

| SOLVING : Wall Scale

|

267

---------------------------------------------------------------------

-

| Equation | Rate | RMS Res | Max Res | Linear Solution

|

+----------------------+------+---------+---------+------------------

+

| Wallscale | 0.00 | 7.7E-04 | 4.2E-03 | 21.5 5.5E-01

ok|

+----------------------+------+---------+---------+------------------

+

| Wallscale | 0.68 | 5.2E-04 | 1.3E-02 | 21.5 2.1E-01

ok|

+----------------------+------+---------+---------+------------------

+

| Wallscale | 0.41 | 2.1E-04 | 5.4E-03 | 21.5 2.6E-01

ok|

+----------------------+------+---------+---------+------------------

+

| Wallscale | 0.53 | 1.1E-04 | 4.4E-03 | 21.5 2.6E-01

ok|

+----------------------+------+---------+---------+------------------

+

| Wallscale | 0.57 | 6.5E-05 | 2.5E-03 | 21.5 2.5E-01

ok|

+----------------------+------+---------+---------+------------------

+

| Wallscale | 0.60 | 3.9E-05 | 1.7E-03 | 21.5 2.4E-01

ok|

+----------------------+------+---------+---------+------------------

+

| Wallscale | 0.63 | 2.4E-05 | 1.2E-03 | 21.5 2.1E-01

ok|

+----------------------+------+---------+---------+------------------

+

| Wallscale | 0.65 | 1.6E-05 | 8.9E-04 | 21.5 1.9E-01

ok|

+----------------------+------+---------+---------+------------------

+

| Wallscale | 0.67 | 1.1E-05 | 6.4E-04 | 21.5 1.6E-01

ok|

+----------------------+------+---------+---------+------------------

+

| Wallscale | 0.68 | 7.2E-06 | 4.6E-04 | 21.5 1.3E-01

ok|

+----------------------+------+---------+---------+------------------

+

---------------------------------------------------------------------

-

COEFFICIENT LOOP ITERATION = 1 CPU SECONDS =

3.930E+02

---------------------------------------------------------------------

-

268

| Equation | Rate | RMS Res | Max Res | Linear Solution

|

+----------------------+------+---------+---------+------------------

+

| U-Mom | 0.00 | 6.0E-04 | 8.4E-03 | 4.0E-02

OK|

| V-Mom | 0.00 | 6.6E-04 | 1.1E-02 | 2.5E-02

OK|

| W-Mom | 0.00 | 2.3E-04 | 8.2E-03 | 1.7E-01

ok|

| P-Mass | 0.00 | 6.9E-05 | 6.1E-03 | 23.3 3.8E-01

ok|

+----------------------+------+---------+---------+------------------

+

| uu-RS | 0.00 | 1.5E-03 | 1.1E-02 | 16.3 7.6E-02

OK|

| vv-RS | 0.00 | 1.8E-03 | 1.9E-02 | 16.3 7.0E-02

OK|

| ww-RS | 0.00 | 8.0E-04 | 1.0E-02 | 11.2 6.5E-02

OK|

| uv-RS | 0.00 | 5.3E-02 | 5.1E+00 | 6.1 7.8E-02

OK|

| uw-RS | 0.00 | 3.1E-02 | 2.9E+00 | 6.1 9.3E-02

OK|

| vw-RS | 0.00 | 4.1E-02 | 2.9E+00 | 6.1 7.8E-02

OK|

| O-TurbFreq | 0.00 | 1.3E-01 | 1.0E+00 | 8.6 1.1E-02

OK|

i

References

[1] T. B. Martonen, "Aerodynamic size measurement of airborne fibers and health effects implications.", Advanced Powder Technology, vol. 3, pp. 311-317, 1992.

[2] R. G. Sussman, B. S. Cohen and M. Lippmann, "Asbestos fiber deposition in human tracehobronchial cast. I. Experimental.", Inhalation Toxicology, vol. 3, pp. 146-160, 1991.

[3] R. G. Sussman, B. S. Cohen and M. Lippmann, "Asbestos fiber deposition in human tracehobronchial cast. I. Empirical model", Inhalation Toxicology, vol. 3, pp. 161-179, 1991.

[4] A. Nemmar, P. H. M. Hoet, B. Vanquickenborne, D. D. M. Thomeer, M. F. Hoylaerts, H. Vanbilloen, L. Mortelmans and B. Nemery, "Passage of Inhaled Particles Into the Blood Circulation in Humans", Journal of the American Heart Association - Circulation, vol. 105, pp. 411-414, 2002.

[5] Australian Bureau of Statistics - Underlying causes of deaths in Australia., 2009

[6] D. K. McKenzie, P. A. Frith, J. G. Burdon and G. I. Town, "The COPDX Plan: Australian and New Zealand Guidelines for the management of Chronic Obstructive Pulmonary Disease 2003.", The Medical Journal of Australia, vol. 178, pp. 7-39, 2003.

[7] The Australian Lung Foundation. Respiratory infections disease burdens in Australia. , http://www.lungfoundation.com.au/lung-information/statistics

[8] Y. Zhao and B. B. Lieber, "Steady inspiratory flow in a model symmetric bifurcation", J Biomech Eng, vol. 116, pp. 488-496, 1994.

http://www.lungfoundation.com.au/lung-information/statistics

ii

[9] T. B. Martonen, X. Guan and R. R. Shreck, "Fluid dynamics in airway bifurcations: I. Primary flows", Inhalation Toxicology, vol. 13, pp. 261-279, 2001.

[10] Z. Zhang and C. Kleinstreuer, "Transient airflow structures and particle transport in a sequentially branching lung airway model.", Physics of Fluids, vol. 14, pp. 862, 2002.

[11] O. G. Raabe, H. C. Yeh, G. M. Schum and R. F. Phalen, Tracheobronchial geometry: human, dog, rat, hamster, Lovelace Foundation Report 1976

[12] J. B. West, "Respiratory Physiology: The Essentials", Lippincott Williams & Wilkins, 2000

[13] L. Sherwood, "Human Physiology: From Cells to Systems", Wadsworth Pub Co, 1997

[14] A. J. Hickey, "Inhalation Aerosols",Physical and Biological Basis for Therapy, Informa Healthcare, 2006

[15] E. R. Weibel, "Morphometry of the Human Lung", Springer, 1963

[16] K. Horsfield, G. Dart, D. E. Olsen, G. F. Filley and G. Cumming, "Models of the human bronchial tree", Journal of Applied Physiology, vol. 31, pp. 207-217, 1971.

[17] H. C. Yeh and G. M. Schum, "Models of human lung airways and their application to inhaled particle deposition", Bulletin of Mathematical Biology, vol. 42, pp. 461-480, 1980.

iii

[18] B. Asgharian and S. Anjilvel, "Inertial and Gravitational Deposition of Particles in a Square Cross Section Bifurcating Airways", Aerosol Science and Technology, vol. 20, pp. 177-193, 1994.

[19] T. Martonen and Y. Yang, "Deposition Mechanics of Pharmaceutical Particles in Human Airways", Inhalation Aerosols, vol. 221, 2006.

[20] T. B. Martonen, "Deposition of inhaled particulate matter in the upper respiratory tract, larynx, and bronchial airways: a mathematical description.", Journal of Toxicology Environment Health, vol. 12, pp. 787-795, 1983.

[21] T. L. Chan and C. P. Yu, "Charge Effects on Particle Deposition in the Human Tracheobronchial Tree", The Annals of Occupational Hygiene, vol. 26, pp. 65-75, 1982.

[22] T. L. Chan, M. Lippmann, V. R. Cohen and R. B. Schlesinger, "Effect of Electrostatic Charges on Particle Deposition in a Hollow Cast of the Human Larynx-tracheobronchial Tree", Journal of Aerosol Science, vol. 9, pp. 463-468, 1978.

[23] H. K. Versteeg and W. Malalasekera, "An introduction to computational fluid dynamics The finite volume method", Longman Scientific & Technical, 1995

[24] D. L. Swift, "Use of Mathematical Aerosol Deposition Models in Predicting the Distribution of Inhalded Therapeutic Aerosols", Inhalation Aerosols, vol. 221, 2006.

[25] W. Findeisen, "Uber das Absetzen kleiner, in der Luft suspendierter Teilchen in der menschlichen Lunge bei der Atmung.", Arch Ges Physiol, vol. 236, pp. 367-379, 1935.

[26] H. D. Landahl, "On the removal of airborne droplets by the human respiratory tract. I. The lung.", Bulletin of Mathematic Biophys, vol. 12, pp. 43-56, 1950.

iv

[27] J. M. Beekmans, "The deposition of aerosols in the respiratory tract.", Canadian Journal of Physiology and Pharmacology, vol. 43, pp. 157-172, 1965.

[28] Task-Group-on-Lung-Dynamics, "Deposition and retention models for internal dosimetry of the human respiratory tract.", Health Physics, vol. 12, 1966.

[29] R. E. Pattle, "The retention of gases and particles in the human nose.", Inhaled PArticles and Vapours, vol., pp. 301-311, 1961.

[30] E. Dekker, "Transition between laminar and turbulent flow in human trachea", Journal of Applied Physiology, vol. 16, 1961.

[31] R. C. Schroter and M. F. Sudlow, "Flow patterns in models of the human bronchial airways", Journal of Respiration Physiology, vol. 7, pp. 341-355, 1969.

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