Modeling Air and Particle Transport in the Human

Upper and Tracheobronchial Airways using RANS

and LES by

Vivek Agnihotri

MTech, Mechanical Engineering, IIT Kanpur, 2007

Thesis submitted in fulfillment of the requirements for the award of the degree of Doctor in de Ingenieurswetenschappen (Doctor in Engineering)

At

Vrije Universiteit Brussel, February 2014

Promoter: Prof. Dr. Ir. Chris Lacor

Prof. Dr. Ir. Ghader Ghorbaniasl

Prof. Dr. Sylvia Verbanck

Print: Silhouet, Maldegem 2014 Vivek Agnihotri 2014 Uitgeverij VUBPRESS Brussels University Press VUBPRESS is an imprint of ASP nv (Academic and Scientific Publishers nv) Ravensteingalerij 28 B-1000 Brussels Tel. +32 (0)2 289 26 50 Fax +32 (0)2 289 26 59 E-mail: info@vubpress.be www.vubpress.be ISBN 978 90 5718 030 9 NUR 950 Legal deposit D/2014/11.161/034 All rights reserved. No parts of this book may be reproduced or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the author.

iii

Abstract

Attempts are being made from several researchers to understand aerosol transport inside

the human respiratory system. The basic goal of these studies is acquire an in-depth

knowledge of flow-particle transport with the ultimate aim to access local and total

particle deposition. The knowledge of which can then be used to make improved inhaler

designs or evaluate toxicological impact of inhaling toxic matter. The key to this

understanding depends mainly on three factors: human airway geometry, material

characteristics of inhaled aerosols (i.e. shape, size and mass) and knowledge of local flow

structures of carrier gas. Evaluation of aerosol deposition characteristics relies on

experiments and Computational Fluid Dynamics (CFD). The human airway geometry

varies significantly from person to person and as such realization of experiments is a time

consuming, and costly affair. Additionally, the inherent intricacies involved with the

airway geometry may render experiments unfeasible. It is to this end that CFD is a boon

to many biological studies. This work is concerned with the understanding of aerosol

deposition behavior in human airways using CFD.

The main goal of the present PhD research is to evaluate the existing flow-particle

modeling methods and propose more efficient CFD techniques in particulate flows.

The work described in this dissertation considers a sedentary breathing rate of 30 l/min

and 60 l/min corresponding to light activity. The particle sizes range from 2 m to 10

m. Two airway geometries, representing extrathoracic airway (consisting of oral,

pharynx, larynx and throat) and a 5-generation intrathoracic airway, are used for the

current research. The Eulerian or fluid part is solved by employing Reynolds Averaged

Navier-Stokes equations (RANS) and using Large Eddy Simulation (LES). Moreover, the

particle phase is represented in the Lagrangian frame and calculated by numerically

integrating the particle equation of motion.

iv

The main highlights of the current research are:

(i) Introduction of a Helicity based Eddy Interaction Model (HEIM) to account the effect

of turbulence on particles in the framework of RANS.

(ii) Implementation and validation of a new Rotational based Smagorinsky Model

(RoSM) developed at VUB, as a subgrid scale model for LES.

(iii) Introduction of an efficient multiple LES frozen field approach based on the proper

orthogonal decomposition method, for particle simulation.

v

Acknowledgement

Foremost, I would like to express my deepest acknowledgement to my two supervisors,

Prof. Dr. Ir. Chris Lacor and Prof. Dr. Ir. Ghader Ghorbaniasl. Their patience, wisdom

and constant encouragement were the key driving force behind this PhD research.

I would like to express my deepest gratitude and respect to Prof. Dr. Ir. Ghader

Ghorbaniasl who has been my advisor and the guiding beacon through four years of my

PhD research. I deeply owe to him for my intellectual gains and knowledge I learnt

during these years.

I would also like to thank my co-promoter Dr. Sylvia Verbanck for making me

understand the physiological aspects of the research project and giving vital suggestions

during the meetings.

I owe special gratitude for our system administrator Alain Wery for his everlasting

patience and support from day one of my VUB. Without his support this research

wouldnt have completed.

Special thanks go to our secretary Jenny Dhaes for helping me out in various

administrative tasks.

I would also like to thanks my colleagues, Leonidas Siozos-Rousoulis, Anna Sunol

Jimenez, Joo Duarte Miranda, Dinesh Kumar Verma, Khairy Elsayed for providing me

a good office environment with their good mood and humor. I would also thank my

former colleagues Matteo Parsani, Willem Diconinck, and Patryk Widera for making my

first two years at VUB truly fun and enjoyable. I have shared many laughs with them.

I would like to thank my family, specially mom, dad, brother and sister in law for their

constant love, motivation and unlimited support throughout my education. My gratitude

vi

also goes to my parents in law for their support and their unconditional belief in me.

Special word of affection goes to my nephew Akshat and my brother in law Pranjal.

Finally, I cannot end without thanking my wife Prachi. You came into my life at the most

important time of my PhD, my final year. I thank you for giving me your unending

support, motivation and the belief that success will eventually follow despite having the

rough time of 2013. Without your support and love this work couldnt have completed.

You bring the light to my life.

vii

Jury Members

President Prof. Johan Deconinck Vrije Universiteit Brussel

Vice-President Prof. Rik Pintelon Vrije Universiteit Brussel

Secretary Prof. Steve Vanlanduit Vrije Universiteit Brussel External Members Prof. Wolfgang Schroeder RWTH AAchen University Prof. Jan Vierendeels University of Ghent Advisors Prof. Chris Lacor Prof. Ghader Ghorbaniasl Prof. Sylvia Verbanck

viii

Contents

........................................................................................................................................... 1 CHAPTER 1

Human respiratory system and its interaction with aerosols Introduction ............................................................................................................................... 1 1.1 Anatomy of human respiratory system ........................................................................................ 2 1.2

Extra-thoracic region .......................................................................................................................... 3 1.2.1 Tracheobronchial region ..................................................................................................................... 5 1.2.2 Alveolar region .................................................................................................................................. 6 1.2.3

Aerosols .................................................................................................................................... 6 1.3 Aerosol particle dynamics .......................................................................................................... 7 1.4 Aerosol deposition mechanism ................................................................................................... 9 1.5 Factors affecting aerosol particle deposition ............................................................................ 12 1.6 Outline of the thesis ................................................................................................................. 13 1.7

......................................................................................................................................... 15 CHAPTER 2

Literature survey Airway modelisation ................................................................................................................ 15 2.1

Extrathoracic airway geometry ......................................................................................................... 16 2.1.1 Tracheobronchial geometry .............................................................................................................. 19 2.1.2

Modeling methods for aerosols transport ................................................................................. 24 2.2 Modeling fluid phase........................................................................................................................ 24 2.2.1 Modeling particle phase ................................................................................................................... 26 2.2.2

......................................................................................................................................... 29 CHAPTER 3

Governing equations Introduction ............................................................................................................................. 29 3.1 Importance of turbulence ......................................................................................................... 30 3.2 Incompressible Navier-Stokes equation .................................................................................... 31 3.3 Modeling turbulence ................................................................................................................ 32 3.4

Reynolds averaged Navier-Stokes equation ....................................................................................... 33 3.4.1

Two equation SST k EVM ..................................................................................................... 35 3.4.2

ix

Large eddy simulation ...................................................................................................................... 39 3.4.3 Smagorinsky model.......................................................................................................................... 41 3.4.4

Modeling particle phase ........................................................................................................... 45 3.5 Modeling assumptions...................................................................................................................... 46 3.5.1 Eulerian approach ............................................................................................................................ 47 3.5.2 Lagrangian approach ........................................................................................................................ 49 3.5.3 Eddy interaction model .................................................................................................................... 52 3.5.4

......................................................................................................................................... 55 CHAPTER 4

Particle deposition in an extrathoracic airway using RANS Introduction ............................................................................................................................. 55 4.1 Mathematical background ........................................................................................................ 57 4.2

EIM and correction functions ........................................................................................................... 59 4.2.1 Isotropic EIM .................................................................................................................................. 59 4.2.2 Wang and James EIM ...................................................................................................................... 59 4.2.3 Helicity EIM .................................................................................................................................... 60 4.2.4

Results and discussion ............................................................................................................. 63 4.3 Test geometry 1, 90 degree bend, Re=10000 ..................................................................................... 63 4.3.1 Test geometry 2, Simplified human upper airway model ................................................................... 66 4.3.2

Conclusions ............................................................................................................................. 72 4.4

......................................................................................................................................... 75 CHAPTER 5

Performance of helcity eddy interaction model Introduction ............................................................................................................................. 75 5.1 Simulation condition ................................................................................................................ 76 5.2 Results and discussion ............................................................................................................. 77 5.3

Inspiration ....................................................................................................................................... 77 5.3.1 Expiration ........................................................................................................................................ 79 5.3.2 Influence of inlet conditions and flow field data ................................................................................ 85 5.3.3

Conclusion .............................................................................................................................. 95 5.4

x

......................................................................................................................................... 99 CHAPTER 6

Rotational based Smagorinsky model Introduction ............................................................................................................................. 99 6.1 Description of RoSM model.................................................................................................... 101 6.2 Results and discussion ........................................................................................................... 107 6.3

Fully developed turbulent channel flow .......................................................................................... 108 6.3.1 Fully developed turbulent flow in a square duct .............................................................................. 113 6.3.2 Flow past a circular cylinder ........................................................................................................... 117 6.3.3 Application to UAM ...................................................................................................................... 122 6.3.4

Conclusions ........................................................................................................................... 126 6.4

....................................................................................................................................... 129 CHAPTER 7

Particle deposition in an extrathoracic airway using LES Introduction ........................................................................................................................... 129 7.1 Multiple LES frozen field approach ........................................................................................ 130 7.2 Mathematical background ...................................................................................................... 132 7.3

Discrete POD method..................................................................................................................... 133 7.3.1 Procedure to derive the optimal set of frozen fields ......................................................................... 136 7.3.2

Description of model geometry and sample data sets .............................................................. 139 7.4 Results and Condition ............................................................................................................ 140 7.5

Step 1, Evaluation of sampling period ............................................................................................. 140 7.5.1 Step 2, Evaluation of time interval .................................................................................................. 144 7.5.2

Particle deposition results ...................................................................................................... 147 7.6 Effect of SGS models ..................................................................................................................... 148 7.6.1 Accounting SGS motion ................................................................................................................. 150 7.6.2 Particle deposition comparison between RANS and LES ................................................................. 154 7.6.3

Conclusion ............................................................................................................................ 156 7.7

....................................................................................................................................... 159 CHAPTER 8

Particle deposition in a 5 generation intrathoracic airway using LES Introduction ........................................................................................................................... 159 8.1 Upper airway geometry.......................................................................................................... 160 8.2 Simulation condition .............................................................................................................. 161 8.3 Results and discussion ........................................................................................................... 163 8.4

Mesh convergence study ................................................................................................................ 163 8.4.1

xi

Flow dynamics............................................................................................................................... 165 8.4.2 Optimal set determination .............................................................................................................. 168 8.4.3 Particle deposition results ............................................................................................................... 171 8.4.4

Conclusions ........................................................................................................................... 175 8.5

....................................................................................................................................... 177 CHAPTER 9

Conclusion and furture work RANS ..................................................................................................................................... 177 9.1 LES ....................................................................................................................................... 178 9.2 Future work ........................................................................................................................... 179 9.3

Boundary condition ........................................................................................................................ 179 9.3.1 Detailed comparison of particle data in present tracheobronchial geometry ...................................... 180 9.3.2 Moving Larynx .............................................................................................................................. 181 9.3.3 Uncertainty quantification .............................................................................................................. 181 9.3.4

LIST OF PUBLICATIONS ................................................................................................................ 183

BIBLIOGRAPHY............................................................................................................................... 185

xii

Nomenclature

N-S Navier-Stokes

DNS Direct Numerical Simulation

RANS Reynolds Averaged Navier-Stokes

LES Large Eddy Simulation

SGS Subgrid Scale

DSM Dynamic Smagorinsky model

RoSM Rotational based Smagorinsky model

EVM Eddy Viscosity Model

SST Shear Stress Transport

EIM Eddy Interaction Model

HEIM Helicity Eddy Interaction Model

POD Proper Orthogonal Decomposition

UAM Upper airway Model

PDI Phase Doppler Interferometry

CT Computer tomography

Symbols

Re Reynolds number, dimensionless

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Pr Prandtl number, dimensionless

Fr Froude number, dimensionless

Stk Stokes number, dimensionless

Re p Particle Reynolds number

Ret Turbulent Reynolds number

tSc Turbulent Schmidt number

Fluid density, kg/m3

Fluid dynamic viscosity, kg/m-s

Fluid kinematic viscosity, m2/s

t Turbulent eddy viscosity, m2/s

p Particle density, kg/m3

dC Particle drag coefficient

iu Velocity component, m/s

u Velocity vector, m/s

g Gravity vector, m/s2

pu Particle velocity vector, m/s

x position vector, m

px Particle position vector, m

xiv

F Force vector, N

k Turbulent kinetic energy, (m/s)2

Dissipation

Specific dissipation

r Particle relaxation time, s

intt Particle interaction time

crosst Particle crossing through eddy, s

el eddy length scale, m

t time step, s

filter width

ijS strain rate tensor, s-1

ij stress tensor, N/m2

absolute value

time average

sC Smagorisnky constant

xv

Figures

FIGURE 1.1, HUMAN RESPIRATORY TRACT [1] ...................................................................................................... 3

FIGURE 1.2, SCHEMATIC OF EXTRATHORACIC REGION REPRESENTING DIFFERENT REGIONS ................................................ 3

FIGURE 1.3, DIFFERENT TYPES OF INHALERS ......................................................................................................... 7

FIGURE 1.4, DEPOSITION DUE TO INERTIAL IMPACTION ........................................................................................... 9

FIGURE 1.5, DEPOSITION DUE TO SEDIMENTATION .............................................................................................. 10

FIGURE 1.6, DEPOSITION DUE TO BROWNIAN MOTION ......................................................................................... 11

FIGURE 1.7, DEPOSITION PROBABILITY WITH RESPECT TO PARTICLE SIZE, [7]............................................................... 13

FIGURE 2.1, SIMPLIFIED LARYNX GEOMETRY BY KATZ AND MARTONEN [13] .............................................................. 16

FIGURE 2.2, LARYNX GEOMETRY USED BY CORCORAN AND CHIGIER [14] .................................................................. 17

FIGURE 2.3, EXTRATHORACIC AIRWAY DEVELOPED BY KLEINSTREUER AND ZHANG [15] ................................................. 18

FIGURE 2.4, EXTRATHORACIC AIRWAY DEVELOPED BY [20] .................................................................................... 18

FIGURE 2.5, (LEFT) REALISTIC GEOMETRY; (B) SIMPLIFIED EXTRATHORACIC GEOMETRY OF VUB. ..................................... 19

FIGURE 2.6, TRACHEOBRONCHIAL GEOMETRIES BASED ON WEIBEL A MODEL, (LEFT) ZHANG AND KLEINSTREUER [26], (MIDDLE)

LONGEST AND VINCHURKAR [27], (LEFT) VASCONCELOSET ET AL. [28] ............................................................ 21

FIGURE 2.7, TRACHEOBRONCHIAL GEOMETRY GENERATED BY VAN ERTBRUGGEN ET AL. [11] ......................................... 22

FIGURE 2.8, DOUBLE BIFURCATION GENERATION GENERATED BY HOLBROOK ET AL. [29]............................................... 23

FIGURE 2.9, CT-SCAN BASED UPPER RESPIRATORY AIRWAY GEOMETRY USED BY LIN ET AL. [30], (LEFT) EXTRATHORACIC REGION

DEPICTING VARIOUS REGIONS, (RIGHT) TRACHEOBRONCHIAL REGION ............................................................... 23

FIGURE 3.1, FLOW STRUCTURES INSIDE UAM AT 60 L/MIN ................................................................................... 31

FIGURE 3.2, CHARATERISTIC MAP FOR PARTICLE-FLOW COUPLING, [78] ................................................................... 47

FIGURE 4.1, 90 DEGREE TEST BEND. (LEFT) GEOMETRY DETAILS; (RIGHT) MESH CUT PLANE AT MIDDLE OF THE BEND. ........... 64

FIGURE 4.2, PARTICLE PROFILE AT THE INLET ...................................................................................................... 65

FIGURE 4.3, TOTAL DEPOSITION EFFICIENCY. (CONNECTED SYMBOLS) - SIMULATIONS; (DISCONNECTED SYMBOLS)

EXPERIMENTS; (LEFT) EXPLODED VIEW ..................................................................................................... 65

FIGURE 4.4, SIMPLIFIED UAM MODEL AND RESPECTIVE COMPARTMENTS USED IN UAM .............................................. 66

FIGURE 4.5, MESH AT DIFFERENT SECTION PLANES IN UAM .................................................................................. 67

FIGURE 4.6, COMPARISON OF NORMALIZED VELOCITY COMPONENT FOR DIFFERENT MESH COUNTS. SECTION (A), (B), (C) AND

(D) CORRESPONDS TO FIVE MM ABOVE EPIGLOTTIS AND ONE, TWO AND THREE TRACHEAL DIAMETERS DOWNSTREAM OF

GLOTTIS, RESPECTIVELY ........................................................................................................................ 68

xvi

FIGURE 4.7, INSPIRATORY TOTAL DEPOSITION EFFICIENCIES, (LEFT) 30 L/MIN AND (RIGHT) 60 L/MIN; PARTICLE SIZES RANGE

FROM 2 M-10 M; (CONNECTED SYMBOLS)-SIMULATIONS; (DISCONNECTED SYMBOLS)-EXPERIMENTS ................... 70

FIGURE 4.8, INSPIRATORY RELATIVE DEPOSITION EFFICIENCIES, (UPPER) 30 L/MIN AND (LOWER) 60 L/MIN; (LEFT) 3M AND

(RIGHT) 6M; (CONNECTED SYMBOLS) SIMULATIONS; (DISCONNECTED SOLID SQUARES,-EXPERIMENTS) ................. 71

FIGURE 5.1, SCHEMATIC OF AEROSOL DEPOSITION EXPERIMENTS, VERBANCK ET AL. [45].............................................. 77

FIGURE 5.2, INSPIRATORY TOTAL DEPOSITION EFFICIENCIES, (LEFT) 30 L/MIN AND (RIGHT) 60 L/MIN; PARTICLE SIZES RANGE

FROM 2M-10M; (CONNECTED SYMBOLS) SIMULATIONS; (DISCONNECTED SYMBOLS)-EXPERIMENTS ................... 78

FIGURE 5.3, INSPIRATORY RELATIVE DEPOSITION EFFICIENCIES, (UPPER) 30 L/MIN AND (LOWER) 60 L/MIN; (LEFT) 3M AND

(RIGHT) 6M; (CONNECTED SYMBOLS) SIMULATIONS; (DISCONNECTED SOLID SQUARES,-EXPERIMENTS) ................. 79

FIGURE 5.4, INSPIRATORY RELATIVE DEPOSITION EFFICIENCIES, (LEFT) 30 L/MIN AND (RIGHT) 60 L/MIN; ALL PANELS TOP TO

BOTTOM CORRESPOND TO 2, 4, 8AND 10 M ........................................................................................... 81

FIGURE 5.5, EXPIRATORY TOTAL DEPOSITION EFFICIENCIES, (LEFT) 30 L/MIN AND (RIGHT) 60 L/MIN; PARTICLE SIZES RANGE

FROM 2M-10M; (CONNECTED SYMBOLS)SIMULATIONS; (DISCONNECTED SQUARE SYMBOLS)-EXPERIMENTS ......... 82

FIGURE 5.6, EXPIRATORY RELATIVE DEPOSITION EFFICIENCIES, (UPPER) 30 L/MIN AND (LOWER) 60 L/MIN; (LEFT) 3M AND

(RIGHT) 6M; (CONNECTED SYMBOLS)SIMULATIONS; (DISCONNECTED SQUARE SYMBOLS)-EXPERIMENTS ................ 83

FIGURE 5.7, EXPIRATORY RELATIVE DEPOSITION EFFICIENCIES, (LEFT) 30 L/MIN AND (RIGHT) 60 L/MIN; ALL PANELS TOP TO

BOTTOM CORRESPOND TO 2, 4, 8AND 10 M; (CONNECTED SYMBOLS) SIMULATIONS ........................................ 84

FIGURE 5.8, (LEFT) UAM WITH CONNECTOR TUBING (SHOWN IN SHADED AREA) AT THE INLET FOR INSPIRATORY BREATHING

PHASE SETUP; (RIGHT) UAM WITH 900 ELBOW BEND CONNECTOR (SHOWN IN SHADED AREA) AT THE INLET FOR

EXPIRATORY BREATHING PHASE SETUP. THE ADDITIONAL MESH FOR THE CONNECTOR TUBINGS ARE (LEFT) 0.4 X 106 AND

(RIGHT) 0.8 *106 HEXAHEDRAL CELLS. .................................................................................................... 86

FIGURE 5.9, (TOP) TOTAL DEPOSITION EFFICIENCY FOR PARTICLE SIZES RANGING FROM 2-10M AT 60 L/MIN, (BOT-TOM)

RELATIVE DEPOSITION EFFICIENCY FOR 6M AT 60 L/MIN. (LEFT) INSPIRATION, (RIGHT) EXPIRATION. ....................... 87

FIGURE 5.10, IMPACT OF TOP HAT AND PARABOLIC INSPIRATORY VELOCITY PROFILES IMPOSED EITHER DIRECTLY AT UAM INLET

(UPPER AND MIDDLE PANELS) OR VIA CONNECTOR TUBING (BOTTOM PANEL). VELOCITY MAGNITUDE CONTOURS, FLOW

STREAMLINES IN THE CENTRAL SAGITTAL PLANE, AND PARTICLE DISTRIBUTION PROFILES AT DIFFERENT UAM STATIONS ARE

SHOWN FOR 60 L/MIN ........................................................................................................................ 89

FIGURE 5.11, IMPACT OF EXPIRATORY VELOCITY PROFILES: (LEFT AND MIDDLE PANEL) ARE NAMELY TOP-HAT AND PARABOLIC

WITHOUT CONNECTOR TUBING; (RIGHT PANEL) TOP-HAT WITH CONNECTOR TUBING. VELOCITY MAGNITUDE CONTOURS,

STREAMLINES IN THE CENTRAL SAGITTAL PLANE, AND PARTICLE DISTRIBUTION PROFILES AT DIFFERENT UAM STATIONS ARE

SHOWN FOR 60 L/MIN. ....................................................................................................................... 91

FIGURE 5.12, TOTAL DEPOSITION EFFICIENCY; (LEFT PANEL) INSPIRATION; (RIGHT PANEL) EXPIRATION FOR 60 L/MIN .......... 92

FIGURE 5.13, RELATIVE DEPOSITION EFFICIENCIES,(TOP) 8M, (LOWER) 10M; (LEFT) INSPIRATION, (RIGHT) EXPIRATION .. 94

xvii

FIGURE 5.14, DEPENDENCE OF HELICITY EIM ON THE TURBULENCE MODEL; (LEFT) INSPIRATION, (RIGHT) EXPIRATION FOR

60L/MIN ......................................................................................................................................... 94

FIGURE 6.1, (A) RESOLVED AND UNRESOLVED EDDIES IN TURBULENT FLOW FIELD. (B) TRANSLATIONAL VELOCITY AND ROTATION

RATE COMPONENTS IN X, Y AND Z DIRECTIONS.......................................................................................... 104

FIGURE 6.2, DIMENSIONS OF CHANNEL FLOW TEST CASE ..................................................................................... 109

FIGURE 6.3, (A) THE CALCULATED MEAN STREAMWISE VELOCITY PROFILE COMPARED WITH THE DYNAMIC SMAGORINSKY, AND

DNS. (B) THE RELATED ABSOLUTE ERROR FIELD. (C) THE MODEL COEFFICIENT PROFILES. .................................... 111

FIGURE 6.4, (A) THE CALCULATED XY-COMPONENT OF REYNOLDS STRESS TENSOR COMPARED WITH THE DYNAMIC

SMAGORINSKY, NO MODEL LES AND DNS. (B) THE RELATED ABSOLUTE ERROR FIELD....................................... 111

FIGURE 6.5, (LEFT) THE CALCULATED DEVIATORIC DIAGONAL REYNOLDS STRESSES COMPARED WITH THE DYNAMIC

SMAGORINSKY MODEL AND DNS. (RIGHT) THE RELATED ABSOLUTE ERROR FIELD ............................................. 112

FIGURE 6.6, SCHEMATIC OF THE DUCT GEOMETRY AND THE COORDINATE SYSTEM IS SHOWN ........................................ 113

FIGURE 6.7, THE CALCULATED MEAN STREAMWISE VELOCITY COMPARED WITH THE DYNAMIC SMAGORINSKY MODEL, NO

MODEL, AND DNS. .......................................................................................................................... 114

FIGURE 6.8, THE CALCULATED RMS VALUES OF THE DIAGONAL REYNOLDS STRESSES COMPARED WITH THE DYNAMIC

SMAGORINSKY, NO MODEL, LES OF MADABHUSHI AND VANKA AND DNS ................................................... 116

FIGURE 6.9, (A) THE CALCULATED XY-COMPONENT OF REYNOLDS STRESS TENSOR COMPARED WITH THE DYNAMIC SMAGORINSKY

MODEL, NO MODEL AND DNS. (B) THE MODEL COEFFICIENT PROFILES.......................................................... 116

FIGURE 6.10, GRID IN THE X, Y-PLANE ............................................................................................................ 117

FIGURE 6.11, THE CALCULATED MEAN STREAMWISE VELOCITY COMPARED THE DYNAMIC SMAGORINSKY, NO MODEL, LES DATA

[111], DNS [114] AND EXPERIMENTS [115]. (A) / 1.06x D , (B) / 1.54x D . ............................... 118 FIGURE 6.12, THE CALCULATED MEAN VERTICAL VELOCITY COMPARED WITH THE DYNAMIC SMAGORINSKY, NO MODEL, LES

DATA [111] DNS [114] AND EXPERIMENTS [115]. (A) / 1.06x D , (B) / 1.54x D .......................... 119 FIGURE 6.13, THE CALCULATED STREAMWISE TURBULENT INTENSITY COMPARED WITH THE DYNAMIC SMAGORINSKY MODEL,

NO MODEL, LES DATA [111], DNS [114] AND EXPERIMENTS [115]. (A) / 1.06x D , (B) / 1.54x D . 120 FIGURE 6.14, THE CALCULATED CROSSWISE TURBULENT INTENSITY COMPARED WITH THE DYNAMIC SMAGORINSKY MODEL, NO

MODEL, LES DATA [111], DNS [114] AND EXPERIMENTS [115]. (A) / 1.06x D , (B) / 1.54x D ....... 120 FIGURE 6.15, THE CALCULATED XY-COMPONENT OF THE REYNOLDS STRESS TENSOR COMPARED WITH THE DYNAMIC

SMAGORINSKY MODEL, NO MODEL, LES DATA [111], DNS [114] AND EXPERIMENTS [115]. (A) / 1.06x D , (B)

/ 1.54x D . ............................................................................................................................ 121 FIGURE 6.16, LOCATION OF SECTION LINES CORRESPONDING TO SAGITTAL PLANE...................................................... 124

xviii

FIGURE 6.17, NORMALIZED TWO COMPONENT ( xu AND zu ) VELOCITY MAGNITUDE CORRESPONDING TO CENTRAL SAGITTAL

PLANE, (A), (B), AND (C) ARE ONE, TWO AND THREE TRACHEAL DIAMETER DOWNSTREAM OF LARYNX, RESPECTIVELY; (D)

FIVE MM ABOVE EPIGLOTTIS. ............................................................................................................... 124

FIGURE 6.18, NORMALIZED TIME AVERAGED 2 COMPONENT VELOCITY MAGNITUDE; (A) PIV, (B) RANS; (C) ROSM; (D) DSM

................................................................................................................................................... 125

FIGURE 6.19, NORMALIZED TWO COMPONENT ( '2xu AND '2zu ) KINETIC ENERGY CORRESPONDING TO CENTRAL SAGITTAL

PLANE, (A), (B), AND (C) ARE ONE, TWO AND THREE TRACHEAL DIAMETER DOWNSTREAM OF LARYNX, RESPECTIVELY; (D)

FIVE MM ABOVE EPIGLOTTIS. ............................................................................................................... 126

FIGURE 7.1, SCHEMATIC OF PARTICLE CALCULATION PROCEDURE, A) DYNAMIC APPROACH, B) MULTIPLE LES FROZEN FIELD

APPROACH...................................................................................................................................... 132

FIGURE 7.2, UAM MODEL GEOMETRY SHOWING LOCATION OF PLANES WITH ONE SAGITTAL PLANE AND FIVE PERPENDICULAR

PLANES NUMBERED 1-5 ..................................................................................................................... 140

FIGURE 7.3, RELATIVE INFORMATION CONTENT (RIC) FOR VARIOUS SAMPLE SETS DETAILED IN TABLE 7.1; CONSIDERING (A)

CASE 1 SAGITTAL PLANE; (B) CASE 2 SAGITTAL AND FIVE PERPENDICULAR PLANES (SEE FIGURE 7.2)...................... 141

FIGURE 7.4, CONTOURS AND PROFILES OF AVERAGE VELOCITY MAGNITUDE AT SAGITTAL PLANE FOR SELECTED SETS OF TABLE 1,

(A) VELOCITY MAGNITUDE CONTOUR; (B), (C) AND (D) ARE THE VELOCITY PROFILES AT SECTION 1-1 ..................... 143

FIGURE 7.5, AUTO CORRELATION INDEX; (A, D) X-VELOCITY, (B, E) Y-VELOCITY, (C, F) Z-VELOCITY RESPECTIVELY; (TOP) CASE 1,

(BOTTOM) CASE 2 ............................................................................................................................ 145

FIGURE 7.6, CONTOURS AND PROFILES OF AVERAGE VELOCITY MAGNITUDE AT SAGITTAL PLANE FOR SETS DETAILED IN TABLE 3,

(A) VELOCITY MAGNITUDE CONTOUR; (B), (C) AND (D) ARE THE VELOCITY PROFILES AT SECTION 1-1, 2-2 AND 3-3

RESPECTIVELY. ................................................................................................................................. 146

FIGURE 7.7, PARTICLE DEPOSITION EFFICIENCIES FOR SET I, II AND III; (A)TOTAL DEPOSITION EFFICIENCY, (B)-(C) RELATIVE

DEPOSITION EFFICIENCY FOR 3M AND 6M ............................................................................................ 148

FIGURE 7.8, PARTICLE DEPOSITION EFFICIENCIES COMPARISON ; (A) TOTAL DEPOSITION EFFICIENCY, (B)-(C) RELATIVE

DEPOSITION EFFICIENCY FOR 3M AND 6M ............................................................................................ 149

FIGURE 7.9, CONTOURS AND PROFILES OF AVERAGE VELOCITY MAGNITUDE AT SAGITTAL PLANE, (A) VELOCITY MAGNITUDE

CONTOUR; (B), (C) AND (D) ARE THE VELOCITY PROFILES AT SECTION 1-1, 2-2 AND 3-3 RESPECTIVELY ............... 150

FIGURE 7.10, PARTICLE DEPOSITION EFFICIENCIES COMPARISON ; (A)-(B)TOTAL DEPOSITION EFFICIENCY, (C)-(D) RELATIVE

DEPOSITION EFFICIENCY FOR 3M, (E)-(F) RELATIVE DEPOSITION EFFICIENCY FOR 6M ....................................... 154

FIGURE 7.11, COMPARISON OF resk (AVERAGED KINETIC ENERGY OF THE RESOLVED FIELD), sgsk (AVERRAGED SGS

KINETIC ENERGY) AND rmsk (KINETIC ENERGY CONTAINED IN THE FLUCTUATION), CORRESPONDING TO REFERENCE DATA

SET; DENOTES ENSEMBLE AVERAGE AND RMS DENOTES ROOM MEAN SQUARE FLUCTUATION ......................... 154

xix

FIGURE 7.12, COMPARISON OF PARTICLE DEPOSITION BETWEEN RANS AND LES AT INSPIRATORY FLOW RATE OF 60 L/MIN; (A)

TOTAL DEPOSITION EFFICIENCY, (B)-(C) RELATIVE DEPOSITION EFFICIENCY CORRESPONDING TO 3M AND 6 M ........ 155

FIGURE 8.1, UPPER AIRWAY GEOMETRY RECONSTRUCTED BY FUSING SCALED UAM MODEL WITH CT-SCAN DATA OF A FEMALE

ADULT. .......................................................................................................................................... 161

FIGURE 8.2, SAGITTAL PLANE WITH SECTION PLANES USED FOR MESH CONVERGENCE STUDY ........................................ 163

FIGURE 8.3, NON DIMENSIONAL MEAN VELOCITY MAGNITUDE AT SECTIONS A-F ........................................................ 164

FIGURE 8.4, CONTOURS OF MEAN VELOCITY MAGNITUDE (A) AND MEAN TURBULENT KINETIC ENERGY (B) ....................... 165

FIGURE 8.5, CONTOURS OF MEAN VELOCITY MAGNITUDE AND TURBULENT KINETIC ENERGY AT CENTRAL PLANE ................. 166

FIGURE 8.6, COMPARISON OF FLOW DISTRIBUTION AT OUTLETS AGAINST EXPERIMENTALLY MEASURED DATA AT 30 L/MIN .. 167

FIGURE 8.7, RELATIVE INFORMATION CONTENT i k1 1

q m

i kRIC

, WHERE M=1201 AND Q DENOTES VARIOUS

REDUCED SETS. THE RED LINE CORRESPONDS TO Q=1041 AND THE BLUE LINE CORRESPONDS TO THE REFERENCE DATA

BASE OF Q=1201 ............................................................................................................................. 168

FIGURE 8.8, 95% 95%1201/q qN N FOR VARIOUS SETS ........................................................................................... 169

FIGURE 8.9, AUTO CORRELATION INDEX; (A) X-VELOCITY, (B) Y-VELOCITY, (C) Z-VELOCITY ........................................... 170

FIGURE 8.10, ORAL DEPOSITION EFFICIENCY .................................................................................................... 172

FIGURE 8.11, TOTAL DEPOSITION EFFICIENCY ................................................................................................... 173

FIGURE 8.12, DEPOSITION EFFICIENCY AT GENERATION G1 ................................................................................. 173

FIGURE 8.13, LOBAR DEPOSITION EFFICIENCY: (A) 2 M, (B) 10 M ...................................................................... 174

FIGURE 9.1, LOBAR PARTICLE DEPOSITION VERSUS LOBAR FLOW DISTRIBUTION AT 60 L/MIN, PRELIMINARY EXPERIMENTAL

RESULTS. ........................................................................................................................................ 181

iii

1

Chapter 1

Human respiratory system and its interaction with aerosols

Contents

1.1 Introduction.............................................................................................................................................1 1.2 Anatomy of human respiratory system.................................................................................................2

1.2.1 Extra-thoracic region........................................................................................................................3 1.2.2 Tracheobronchial region..................................................................................................................5 1.2.3 Alveolar region..................................................................................................................................6

1.3 Aerosols....................................................................................................................................................6 1.4 Aerosol particle dynamics......................................................................................................................7 1.5 Aerosol deposition mechanism...............................................................................................................9 1.6 Factors affecting deposition mechanism.............................................................................................12

Introduction 1.1

The respiratory system present in mammals and other life forms, is a vital organ whose

primary function is to supply oxygen to the blood (needed by cells to function) and

remove carbon monoxide (by product of cells). This is achieved through the act of

inhaling air (termed as Inhalation) and exhaling air (termed as Exhalation). The whole

act/process is termed as respiration. Some amazing facts regarding human respiratory

system are listed as follows:

2

Breathing rate is faster in newborn than compared to woman and comparatively

slower in men. A newborn up to 6 weeks can takes in 40-60 breaths per minute.

At rest an adult respire at a normal rate of 12-20 breaths per minute. This accounts

to approximately 10000 to 20000 liters of inhaled air per day.

The total lung capacity (maximum amount of air that someones lungs are capable

of holding) is between 4 and 6 liters of air in an adult. Males usually have higher

total lung capacities than females.

The total airways when stacked up will amount to about 2400 km.

This chapter briefly discusses lung physiology and discusses how aerosols are connected

to human respiratory system.

Anatomy of human respiratory system 1.2

Topologically, a human respiratory tract consists of a series of connecting pipes, with

pipes becoming progressively smaller and ending at alveoli where the exchange of

oxygen with blood takes place. Giving all the details of the respiratory tract is almost

beyond the scope of current work, therefore a brief schematic detailing important parts is

shown in Figure 1.1. The entire respiratory tract can be classified into three basic regions

(described briefly in below sections) namely, extrathoracic region, tracheo-bronchial

region and the alveolar region.

3

Figure 1.1, Human respiratory tract [1]

Figure 1.2, Schematic of extrathoracic region representing different regions

Extra-thoracic region 1.2.1

The extra-thoracic region represents those areas that start the beginning of respiratory

system. It consists of nasal cavity (or nose), oral (or mouth) cavity, pharynx, and larynx

(see Figure 1.2). The extra-thoracic region is sometimes also referred to as upper airway.

4

Nasal cavity

The nasal cavity forms the main entrance point for the outside air into the respiratory

tract. The nasal cavity represents a hollow space lined up with hairs and mucus. The

primary function is to condition the air before it is conducted deeper inside the respiratory

system. As the air passes through the nasal cavity it gets warm, moisturized and filtered

for the foreign particle. The hair and mucus helps to trap foreign contaminants present in

the air before it reaches deeper inside lungs. In addition, mucus also helps in moistening

the air.

Oral cavity

Oral cavity is the secondary opening to the respiratory tract. Normally breathing takes

place through nasal cavity, but the oral cavity can be used to supplement the breathing

such during cold or heavy exercises. The mouth however does not condition the air

because of the lack of hairs and mucus. Since the mouth passage is shorter than nasal and

also because of larger cross sectional area, more air reaches quickly in the lungs.

Pharynx

Pharynx also known as throat extends from the posterior end of the nasal cavity to the

superior end of the esophagus and larynx (see Figure 1.1). It consists of three regions,

namely nasopharynx, oropharynx, and laryngopharynx. It shapes like a funnel and

collects air coming from mouth and nose and passes it down towards trachea. The

epiglottis, which is a flap of elastic cartilage present at the opening of the trachea,

prevents swallowed material from getting entered into the trachea.

Larynx

Larynx known as the voice box is a small region in the respiratory tract that connects

laryngopharynx and trachea. It is composed of several cartilage structures. It consists of

special structures known as vocal chords which vibrate when one expires air. The vocal

folds are made up of mucous membrane that vibrates to produce vocal sounds. Humans

5

have the ability to control the tension and vibration speed of the vocal folds to make

sound.

Tracheobronchial region 1.2.2

Distal to extrathoracic region are the tracheobronchial airways. This is referred to as

lower airways. This region is consists of airways that are responsible for conducting air to

the oxygen exchange part of the lungs. The tracheobronchial region is formed of

components starting from trachea and ending with terminal bronchioles.

Trachea

Trachea so called as the wind pipe consists of many C-shaped cartilage rings. It measures

roughly 10-14 cm in length and 16-20 mm in diameter. It is passage which connects

larynx to the bronchi. Similar to nasal cavity its inner surface is covered with mucus to

further trap foreign particles for getting deeper inside lungs. The main function of the

trachea is to provide a clear airway for air to enter and exit the lungs.

Bronchi and Bronchioles

At the inferior side, trachea bifurcates into two cartilage-ringed airways known as main

bronchi. The left and right main bronchi run into each lung bifurcating further into

smaller secondary bronchi. The secondary bronchi carry air into the different lobes of the

lungs (2 in the left lung and 3 in the right lung). Within each lobe the secondary bronchi

further splits into smaller airways called as tertiary bronchi which inturn bifurcates into

even smaller airway tubes. These smaller airway tubes are called as bronchioles and

spread throughout the lungs. These bronchioles further splits into many smaller branches

less than a millimeter in diameter called terminal bronchioles. Finally, the millions of tiny

terminal bronchioles conduct air to the alveoli of the lungs. The main function of the

bronchi and bronchioles is to carry air from the trachea into the lungs.

6

Alveolar region 1.2.3

Distal to tracheobronchial region is the region whose primary function is to exchange

oxygen and carbon monoxide between blood and air. This region is known as alveolar

region and composed of cup like structures called as alveoli, attached at the end of

respiratory bronchioles (bifurcations of terminal bronchioles, Figure 1.1). A typical lung

contains approximately 30 million alveoli.

Aerosols 1.3

Suspension of fine solid particles or liquid droplets in a carrier fluid (liquid or gas) is

termed as Aerosols. Examples include, haze, dust, smoke, mist etc. In the context of

human respiratory system, the study on aerosols is required for, a) evaluating

toxicological impact of inhaling toxic matter on human lungs and b) making efficient

devices delivering therapeutic drugs to affected sites of the lungs.

I) Toxicological impact, Prolonged exposure to particulate matter present in air can have

severe ill effects on human health. It is now been well recognized that deposition of

particulate matter present in aerosol scan is linked to many lung related ailments such as

asthma, chronic obstructive pulmonary diseases (COPD) and lung cancer. The recent

report from World Health Organization (WHO) [2] concludes that indoor air pollution

resulted in nearly 2.5 million premature deaths. Urban outdoor air pollution is estimated

to have caused nearly 1.3 million deaths worldwide per year. The size of the particulate

matter present in the air is the determining factor where in lungs particles will deposit.

Particle sizes smaller than 2.5 m pose more threat than particles having size greater than

10 m, since former has the higher probability of getting much deeper inside the lungs.

II) Therapeutic consideration, Delivering therapeutic drug via respiratory tract is

considered the preferred method for treating COPD and asthma. The advantages include

delivery of medication directly to the site of action thereby resulting in faster onset of

action. Moreover, one dose of inhaled medication contains less medication than a tablet

7

yet delivers the same effect. This mode of treatment achieved by devices called as

inhalers. Based on the working mechanism, there are three principle types of inhalers

available in the market, i) pressurized metered dose inhalers (pMDI), ii) dry powder

inhalers (DPI), and iii) nebulizers (see Figure 1.3). Nebulizer systems are typically less

portable than pMDI and DPI and are used in case of acute asthma attacks and for patients

unable to use other inhalers. The development of these devices is not a trivial task and

includes many design considerations, importantly, particle properties (density, diameter,

shape, chemical composition etc.), aerosol particle properties (volume fraction loading of

particles (concentration), particle size range, flow rate etc.), respiratory tract properties

(geometry, presence of disease etc.).

Figure 1.3, Different types of inhalers

Aerosol particle dynamics 1.4

The motion of a particle inside human respiratory tract is governed by certain physical

laws and its useful to have a brief look into each of these.

I) Drag Force ( dF ), Drag force is the retarding force exerted by the fluid to the aerosol

particle and is caused because of the relative motion between particle and fluid. The drag

force in general terms is given as

8

21

2

dd

rel

Cu A

F

(1.1)

where dC represents the drag coefficient and depends upon the particle Reynolds number

Re p . The term is the fluid density, relu is the magnitude of relative velocity vector

pu u ( u is the fluid velocity vector and pu is the particle velocity) and A is the cross

sectional area. The direction of drag force acts in a direction parallel to vector pu u .

II) Gravitational force ( gF ), As with every object on earth, aerosol particle is pulled by

earths gravity

g pmF g (1.2)

where pm is the particle mass and g is the acceleration vector due to gravity.

III) Brownian diffusion force, Particles having size less than 1 m are subjected to

random movement as a result of collision with fluid molecules. The accounting Brownian

force becomes increasingly important with decreasing particle size.

IV) Electrostatic force, If an aerosol particle has a net charge, its motion is affected by the

electrostatic forces. The lung airways in general do not have any net charge but they are

electrically conducting. As a result, close to the airway wall, the tissue in the wall gets

oriented because of the charged aerosol particle and creates a net electric field. In this

work, since we are dealing with particles having zero net charge we neglect this force.

As will be discussed later in chapter 3, due to the fact that particle density is 1000 times

greater than carried fluid density, other forces such as Buoyancy force, Magnus force, lift

force, Basset force etc. are neglected.

9

Aerosol deposition mechanism 1.5

The human respiratory system essentially acts as a filter by removing particles present in

the inhaled air. As soon as the particle gets in contact with walls of the respiratory system

it gets trapped. The mucus lining present on the walls prevent the particle from getting re-

entrained. There are varying physical mechanism by virtue of which a particle can reach

the airway wall and get deposited. The most important deposition mechanisms are, i)

inertial impaction, ii) sedimentation, iii) brownian diffusion, and iv) interception.

Inertial impaction

Deposition due to inertial impaction is associated with the particle inertia. The deposition

occurs since the particle in transit is unable to follow the streamlines of air negotiating a

curve, bend or airway bifurcations (illustrated in Figure 1.4) i.e. the particle follows its

original trajectory. Inertial impaction becomes important for bigger sized particles or at

locations where high air velocity exists. In respiratory system this generally occurs at first

few airway generations, where the stream lines are highly curved and flow velocities are

high [3].

Figure 1.4, Deposition due to inertial impaction

10

The importance of deposition due to inertia is represented via dimensionless Stroke

number, and interpreted as the ratio of characteristic particle time and characteristic flow

time,

rUStkD

(1.3)

where r is particle characteristic time, U is the air velocity and D is the airway diameter.

For a particle 1Stk indicates that it will closely follow flow streamlines and will quickly adjust to any change in air flow path. Similarly, for a particle with 1Stk or

1Stk , will not follow any sudden change in air flow streamline.

Sedimentation

Deposition due to sedimentation or gravitational settling refers to particle deposition due

to gravity (illustrated in Figure 1.5). The probability of a particle being deposited due to

sedimentation depends upon particle density, size and the time spent by the particle in

airway segment (called as residence time). In the respiratory system this usually occurs at

distal airway segments (smaller bronchi and bronchioles, alveolar region), where the flow

velocity is very low [4].

Figure 1.5, Deposition due to sedimentation

11

Brownian diffusion

At smaller airway segments (such as bronchioles, alveoli), where the particle residence

time is relatively long, smaller diameter particles ( 1pd m ) can come into contact of

airway walls and hence deposit as a result of Brownian motion (as illustrated in Figure

1.6). Brownian motion is a microscopic three dimensional stochastic random walk of

particle and occurs due to the collision of particle with the air molecules. For times much

longer than the time between molecular collision, Einstein formulated the displacement

of particle due to brownian motion as

2d bx D t (1.4)

where bD is the particle diffusion coefficient given as

3

cb

p

kTCDd

(1.5)

where k is the Boltzmann constant, T is the temperature in kelvin and cC is the

Cunningham slip correction factor, pd is the particle diameter and is fluid viscosity.

Figure 1.6, Deposition due to Brownian motion

12

Interception

A particle following the air stream without any deviation can still deposit at the airway

wall because of its physical size greater than the airway. This is termed as interception.

Usually this type of deposition mechanism occurs for long fibers (long in one dimension)

and ignored for pharmaceutical aerosols which mainly consist of spherical particles.

Factors affecting aerosol particle deposition 1.6

As explained in the above section three main deposition mechanisms (Impaction,

Sedimentation and Brownian motion) are usually considered responsible for the

deposition of inhaled particles. However, the above deposition mechanisms inturn

requires a priori knowledge of three important parameters,

I) Respiratory airway geometry, In order to evaluate the deposition characteristic of

aerosol particles, the first and foremost requirement is to have a geometrical model

representing lung. Unfortunately, there is not a single unique geometrical model which

can be said to represent the human population. In literature there exist simplified

mathematical models based on the classical symmetric model of Weibel [5] or the

asymmetric model Horsfield [6]. But such models are based on simplifying assumptions

such as representing the airways as smooth circular cylinders, basing airway dimension

and branch connectivity. Although with the recent advancement in imaging capability

one can now have anatomically accurate physical model of respiratory tract but this is

still restricted to first few generations of the airway and are subject specific. Further, from

the effectiveness point of view of inhaled pharmaceuticals, the extrathoracic airway

possesses some serious barrier. The extrathoracic airway region with is bends and sudden

cross-sectional changes reduce the quantity of the drug reaching alveolar region, thereby

rendering it ineffective.

II) Aerosol particle properties, Apart from the chemical composition particle size is a

critical parameter determining the fate of particle being inhaled. Particles having size

13

between 0.5-5m has the ability to reach much deeper inside the lungs. Particles having

size greater than 5 m tend to deposit mainly in the extrathoracic region, while particles

smaller than 0.5 m exhaled out without depositing. Figure 1.7, illustrates a typical

deposition pattern in various regions of the lungs depending upon the particle size

diameter.

Figure 1.7, Deposition probability with respect to particle size, [7]

III) Inhalation flow rate: The mode of inhalation directly affects the particles deposition.

With increased inhalation flow rate, the probability of particle depositing due to inertial

impaction in the extra-thoracic region increases. Conversely, reducing inhalation flow

rate allows particles to negate sudden changes in flow path as such the probability of

particles being carried much deeper inside the lungs increases. In general, the inhalation

flow rates are broadly classified into slow breathing (15 l/min), tidal breathing (30 l/min)

and heavy breathing (60 l/min).

Outline of the thesis 1.7

While Chapter 1 introduces the reader to various aspects of Human respiratory system

and its interaction with Aerosols in general, Chapter 2 provides an overview of the

14

existing CFD literature on human airways. Chapter 3 gives detailed mathematical models

used to describe fluid and particle phase.

Chapter 4 till Chapter 8 presents results from various numerical experiments conducted in

the present research. In particular within the framework of RANS, Chapter 4 discusses

and compares simulated particle data using classical eddy interaction model and Wang &

James model and describes a new simpler helicity based eddy interaction model (HEIM).

Further Chapter 5 presents various numerical experiments to evaluate the performance of

HEIM.

The last part of the research focuses on Large Eddy simulation (LES) (Chapter 6 till

Chapter 8). In this part, first a new simpler rotational based subgrid scale model for LES

is proposed and evaluated in Chapter 6. In continuation the next Chapter 7 discusses and

evaluates an efficient multiple LES frozen field approach based on Proper Orthogonal

decomposition (POD). Finally, Chapter 8 presents the preliminary results in a 5

generation intrathoracic airway model using LES and the approach of Chapter 7.

15

Chapter 2

Literature survey

Contents

2.1 Airway modelisation...............................................................................................................................15 2.1.1 Extrathoracic airway geometry.......................................................................................................16 2.1.2 Tracheobronchial airway geometry................................................................................................19

2.2 Modeling methods for aerosol transport..............................................................................................24 2.2.1 Modeling fluid phase.......................................................................................................................24

2.2.2 Particle phase....................................................................................................................................26

The entire spectrum representing aerosol transport in human respiratory tract can be

broadly divided in two main fields, namely i) airway modelisation, and ii) predictive

methods for aerosol transport. While the former concerns with development of airway

geometries for numerical and experimental studies. Latter concerns mainly with the

numerical modeling of aerosol transport i.e. modeling fluid phase and particle phase.

Airway modelisation 2.1

The anatomical description of human respiratory tract given in Chapter 1, shows that the

entire human respiratory tract is composed of many bends, sudden cross-sectional

changes, dichotomous bifurcation (i.e. parent branch divides in two daughter braches)

making the process of airway modelisation complex. Add to this complexity we have in

total around 16,000,000 airway segments, making the morphometric description of

airway structure unfeasible.

In literature there exist two approaches of generating airway structure. The first approach

uses mathematical algorithms which contain inhaled volume based rules for establishing

16

relationships between parent and daughter airways (e.g. Kitaoka et al. [8], Tawhai et al.

[9]). The second approach consists of digitally reconstructing the airway structure based

on the data available from CT-scan or micro CT-scan of patients (e.g. Matida et al. [10],

van Ertbruggen et al. [11] and Nithiarasu et al. [12]).

This work uses the second approach, whereby the airway geometries are modelled based

on the available CT-scan. Traditionally, for computational and experimental studies the

respiratory tract is divided into extrathoracic region or tracheobronchial region (typically

till 5th generation) or alveolar region. In this work we have kept ourselves to the

extrathoracic (or upper airway) and tracheobronchial region.

Extrathoracic airway geometry 2.1.1

Katz and Martonen [13] carried out flow studies in a simplified three dimensional model

of larynx. The simplified larynx model (Figure 2.1) was constructed based on the

morphometric measurements of human casts and Weibel [5] morphology of the tracheal

dimension. The larynx was modeled as a 6 cm long cylinder with a circular entrance and

exit cross-sections. The apertures created by ventricular and vocal cords were modeled as

ellipse.

Figure 2.1, Simplified larynx geometry by Katz and Martonen [13]

Corcoran and Chigier [14] measured the axial velocity and turbulence intensity, using

Phase Doppler Interferometry (PDI) in a cadaver-based simplified larynx-trachea model

(Figure 2.2). The model consisted of a polyurethane casting of the human larynx,

connected to a glass tube with an inside diameter matching the tracheal diameter of the

cadaver.

17

Figure 2.2, Larynx geometry used by Corcoran and Chigier [14]

The preliminary flow results obtained in the above mentioned geometries (Figure 2.1 and

Figure 2.2) did provided some useful initial flow physics but these geometries are over

simplified. As a result authors that followed used more realistic geometries such as

Kleinstreuer and Zhang [15], Matida et al. [10], Farkas et al. [16], Jin et al. [17]; Xi and

Longest [18]. For example, Kleinstreuer and Zhang [15] modeled the extrathoracic region

as 1800 curved bend (see Figure 2.3). The diameter variations along the airway model

from oral cavity to trachea where based on the Cheng et al. [19] morphometric

measurements of a human oral cast. Similarly, Stapleton et al. [20] , DeHaan and Finlay

[21] and Grgic, Finlay, and Heenan [22] performed their studies in an average

geometrical model based on the morphometric information available in the literature.

Further the model was refined by separate measurements using computed tomography

(CT) scans of patients (n=10) having no visible airway abnormalities and by the

observation of living subjects.

18

Figure 2.3, extrathoracic airway developed by Kleinstreuer and Zhang [15]

Figure 2.4, extrathoracic airway developed by [20]

On similar lines, a simplified extrathoracic airway shown in Figure 2.5 was developed at

Vrije Universiteit Brussel (VUB). The simplified model was based on the work of Brouns

et al. [23] of VUB, and was based on the CT-scan of five otherwise healthy never-smoker

male subjects. The simplification of the geometry was done so as to facilitate the

comparison of numerical and experimental studies. The simplification is done by keeping

the critical features such as shape of mouth cavity, position of trachea and the epiglottis

(as shown in Figure 2.5). Due to the availability of experimental, the simplified model is

extensively used in the present work.

19

Figure 2.5, (left) Realistic geometry; (b) simplified extrathoracic geometry of VUB.

Tracheobronchial geometry 2.1.2

While there are numerous successful aerosol studies of the extrathoracic region, the

complexity of obtaining morphometric description of human tracheobronchial tree has

defied detailed aerosol studies in anything more than small sections. In order to

adequately understand the aerosol dynamics, modelisation of the distal airways is

essential.

One of the earliest and well known airway model used for the description of

tracheobronchial airways is the Weibel [5] symmetric model also known as Weibel A

model. The model assumes that each generation of the airway bifurcates symmetrically

20

into two daughter branches. Although this simplify analysis but is not accurate since in

actual human airway diameters and lengths of daughter airways can be quite different

from one another. It is stated that the absence of airway curvature and surface

irregularities make the flow fields in a Weibel based model very different from those in a

real lung. For example, Nowak et al. [24] , who were first to compare Weibel A model

with a CT-scan of a cadaver lung cast (till 4th generation). Unsteady and steady

calculations were compared. These authors concluded there is no consistent pattern of

similarity between symmetric model of Weibel and asymmetric model based on CT-scan.

They also stated that differences between steady and unsteady flow solutions make the

former unreliable. Although physiologically incorrect, Weibel A geometry has been used

in several studies (such as Shi et al. [25], Zhang and Kleinstreuer [26] , Longest and

Vinchurkar [27], Jin et al. [17] and more recently by Vasconceloset al. [28], etc.). Figure

2.6, illustrates the upper airway geometries based on Weibel A model. The left most

panels represent the airway geometry used by Zhang and Kleinstreuer [26]. As shown the

upper airway model consists of two parts, an oral airway model, including oral cavity,

pharynx, larynx and trachea, and a symmetric, planar, triple-bifurcation lung airway

model representing generations G0 (trachea) to G3 based on Weibel A model. The

authors used this geometry to study the differences between micron and nano particle

deposition characteristics. Further, Figure 2.6 (middle panel), illustrates the geometry

used by Jin et al. [17] for conducting large eddy simulation calculations. The geometry

was generated by fusing the mouththroat geometry developed at ARLA (Aerosol

Research Laboratory of Alberta) [7] with the triple bifurcation based on Weibel A model.

Similarly, the left most panel of Figure 2.6 consists of a 4 bifurcation Weibel A model.

This geometry was recently used by Vasconceloset et al. [28] for investigating their

proposed approach of determining micron particle deposition by estimating escape rate at

each airway segment. In most of these studies the simplified model was used with the

sole purpose of proposing or validating a numerical approach, effect of mesh styling,

inlet boundary conditions etc. These studies were not meant to draw any physiological

conclusion.

21

Figure 2.6, Tracheobronchial geometries based on Weibel A model, (left) Zhang and Kleinstreuer [26], (middle) Longest and vinchurkar [27], (left) Vasconceloset et al. [28]

In order to simulate aerosol deposition in physiologically more accurately, further to

Weibel A model, Horsfield and Cumming [6] in 1968 (subsequently refined in 1971)

made measurements of the tracheobronchial measurements as close as possible and

introduce an asymmetric model. Weibel A model differs from the Horsfield geometry in

terms of branching angles (or bifurcation angles). While the former gave no information

regarding the branching angles, later gave the branching angle down to segmental

bronchi. Unlike Weibel [5] geometry who made measurements till 5th generation and

incomplete till 10th generation, Horsfield [6] accurately measured values of length,

diameter, curvature ratio and branching angle till segmental bronchi. Several aerosol

studies have utilized this information given by Horsfield. For example, Van Ertbruggen et

al. [11] used the morphometric data of Horsfield [6] to construct a realistic 3D model (see

Figure 2.7) of bronchial tree in order to study the flow and particle dynamics. Similarly,

Holbrook et al. [29] recently studied localized aerosol deposition in a double bifurcation

geometry having generations 3 to 5 (see Figure 2.8). While these studies present a more

extensive estimation of airflow behavior in the lungs, they still rely on an idealized

smooth representation of the airway geometry.

22

Because of the advent of new imaging modalities (Magnetic resonance imaging (MRI

scan) and Computer tomography (CT)) and increase computing resources, it is now

possible to recreate digitally realistic human airway geometries. The only shortcoming

with these modalities is that the reconstruction of human geometry is restricted to the

resolution of the camera. Therefore, to date geometries till 5th generation has been

reported in literature. For instance, in a detailed study Lin et al. [30] conducted direct

numerical simulation on CT imaged derived upper airway (shown in Figure 2.9). The

geometry of the human upper respiratory tract is derived from volumetric scans of a

volunteer imaged via multi detector row computed tomography. In this study Lin et al.

[30] used to geometries one starting with mouth and ending at generation 5, while other

starting at trachea and ending at generation 5. The author reported that neglecting

extrathoracic part and using simple inlet boundary conditions do not adequately represent

the effect of the upper airway structures. This inturn affects the estimate of flow through

several generations of airway and the tracheal wall shear stress. Similar to Lin et al. [30]

few more studies have been reported using CT-scan derived upper airway geometry (such

as Ma and Luchten et al. [31], Ghalati et al. [32] etc).

Figure 2.7, Tracheobronchial geometry generated by Van Ertbruggen et al. [11]

23

Figure 2.8, Double bifurcation generation generated by Holbrook et al. [29]

Figure 2.9, CT-scan based upper respiratory airway geometry used by Lin et al. [30], (left) extrathoracic region depicting various regions, (right) tracheobronchial region

24

Modeling methods for aerosols transport 2.2

Modeling methods involved for simulating particle transport involve prediction of fluid

phase and particle phase. The fluid phase is represented by numerically solving Navier-

stokes equation (called as computational fluid dynamics (CFD)). There is large amount of

scientific papers describing the use of CFD for studying the flow behavior in the human

airways. The different numerical methods are classified based on the nature of the flow

i.e. laminar or turbulent.

In past, aerosol studies where predominantly simulated assuming laminar flow (for

example, Hofmann et al. [33], Comer et al. [34], Li et al. [35], Kleinstreuer et al. [36]).

The reason for representing flow as laminar is mainly to avoid the complexity associated

with turbulence modeling. For example, Martonen et al. [37] performed laminar

calculation in larynx, trachea and main bronchi to provide basic flow information.

However, as Stapleton et al. [20] reported that the flows in larynx and trachea are

normally turbulent or at least transitional. Therefore, particle results assuming laminar

flow should be interpreted carefully. Recent aerosol studies have now focused in

applying turbulence modeling for predicting fluid-particle dynamics in airways which is

also the scope of the present work.

Modeling fluid phase 2.2.1

As will be seen in latter chapters, predicting flow simulations accurately is the

prerequisite for analyzing particle deposition characteristics inside human airways. This

in turn depends on the approaches used for modeling turbulence. So far, in literature three

approaches have been generally applied, namely, i) Reynolds averaged Navier-stokes

equation, ii) Large eddy simulation and iii) Direct numerical simulation (DNS).

In the framework of RANS, mostly two equation turbulence models have been applied.

The flow rates that are mostly considered in human airways correspond to an inlet

Reynolds number that lies in the transitional regime (for e.g. the Reynolds number range

25

in the present work ranges from 2500 for 30 l/min and 5000 for 60 l/min). At this

Reynolds number range as reported by Wilcox [38], and Pope [39], the standard

turbulence models (for e.g. k-, RNG k etc.) fails to predict laminar to turbulence

transition. Therefore, under such conditions low-Reynolds-number (LRN) turbulence

models have to be considered. For example, Stapleton et al. [20] reported significant

deviations from experimentally observed pressure drop when comparing against standard

k- simulations. To further investigate this problem Zhang and Kleinstreuer [40],

compared the performance of LRN k- model against k-, RNG k-, LRN k- and found

comparatively good experimental agreement for velocity and kinetic energy levels across

the geometry. This model has also been successfully employed in various other airway

geometries [ [15], [41], [42], [43]].

Even though LRN based turbulence model predicted comparatively better mean flow

field, still there were deviations in particle deposition when compared against

experiments (for e.g. Jayaraju et al. [44], Verbanck et al. [45]). This mainly because in

RANS there is no information of velocity fluctuations and as such it needs to be modelled

from simulated turbulent kinetic energy. The modelling is not straightforward and

involves some adhoc assumptions (more discussed in Chapter 4). Owing to this

ambiguity and the importance of predicting the flow field accurately, authors such as

Matida et al. [46], Jayaraju et al. [44], Lambert et al. [47], Jin et al. [48] etc., have

employed large eddy simulation (LES). For example, Matida et al. [46], employed LES

using constant Smagorisnky model and reported improved particle results over RANS.

Similarly, Jayaraju et al. [44] employed LES using WALE and constant Smagorinsky as

subgrid scale (SGS) model and found good overall agreement of flow and particle results

when compared against experimental data.

However, RANS till date is still preferred over LES because of computational

requirements. In this view, the present work proposes a new SGS model which will be

shown to be computationally faster and gives accurate results (see chapter 6 and 7).

Besides RANS and LES, direct numerical solution (DNS) in human airways has also

been cited. Till date the most comprehensive work remains that of Lin et al. [30], who

26

systematically studied the importance of upper and intrathoracic airways on air flow

patterns and turbulence characteristics. They found that the regions of high turbulence

intensity are associated with TaylorGrtler like vortices.

Modeling particle phase 2.2.2

Invariably, when simulating particle deposition inside human airways, the common

practice is to assume particles as spherical, non-interacting, and monodisperse. These

assumptions allow decoupling of fluid calculation from particle calculation i.e. one-way

coupling is assumed. Above assumptions are reasonable for inhaled aerosols owing to the

particle to air density ratio, volume fraction loading (Finlay [49]), and these assumptions

also apply in the present work. When considering dilute suspension in general there are

two approaches reported in literature, namely Euler-Lagrange and Euler-Euler. While the

Euler-Euler approach has been applied to particles having size less than 1m, Euler-

Lagrange approach is mostly confined to simulating micron particle sizes i.e. particle size

greater than 1m. This work is related to the conducting fluid-particle simulations using

Euler-Lagrange methodology.

In the Euler-Lagrange methodology, the Eulerian or the fluid phase is solved using

aforementioned approaches, whereas the Lagrangian phase is simulated by numerically

integrating individual particle equation of motion. In case of RANS, stochastic modeling

of the particle phase involves direct simulation of particle motion through a random

turbulent flow field. There are several approaches in developing stochastic models. Few

examples in literature include models based on the Langevin dispersion equation [50],

random Fourier modes [51] and pdf models [52]. However, one of the most widely used

models is the Eddy Interaction Model (EIM) first introduced by Hutchinson et al. [53]

and further developed by Gosman and Ioannides [54]. Even though several variants of

EIM model have been proposed in the literature ( [55], [56], [57], [58], [59]), the

originally proposed EIM of Gosman and Ioannides [54] remains the most widely used,

mainly because of its simplicity. Although largely used, the classical EIM when used

have resulted in large deviations in particle deposition values compared to experimental

27

data. For example, Matida et al. [10] studied the deposition of monodisperse particles (1-

26 m) in human mouth-throat geometry, at inhalation flow rates of 30 and 90 l/min. For

the Eulerian phase they employ LRN k turbulence model, while the Lagrangian phase

is simulated based on EIM by Gosman and Ioannides [54]. Contrary to the good

performance of LRN k- model reported by Zhang et al. [60], the simulations of Matida

et al. [10] showed huge deviations in deposition percentages (>50%), even for the lowest

Stokes number particles. Similar observations were reported in Jayaraju et al [44],

Verbanck et al. [45] etc. The main reason according to these authors was the underlying

assumption of isotropy in the EIM model. To this Matida employed near wall correction

function based on Wang and James [61] and obtained better overall deposition prediction.

Similar correction function were used by [62], [63], [64] etc. Inspite of using such adhoc

correction function one can introduce the anisotropy retrieved from the flow itself. This

new methodology will be discussed in chapter 4. As a result of ambiguities present with

EIM several authors applied large eddy simulation (LES) methods for the study of

particle deposition in the human airway (e.g. Matida et al. [46], Jayaraju et al. [44],

Lambert et al. [47]). Still the number of such studies are few because of the involved

computational and memory requirement. To this Agnihotri et al. [65] used a systematic

procedure to reduce computational requirement discussed in detail in chapter 7.

28

29

Chapter 3

Governing equations

Contents

3.1 Introduction............................................................................................................................................29 3.2 Importance of turbulence.....................................................................................................................30 3.3 Incompressible Navier-Stokes equation..............................................................................................31 3.4 Modeling turbulence.............................................................................................................................32 3.4.1 Reynolds averaged Navier-Stokes equation................................................................................33

3.4.2 Two equation SST k- EVM.........................................................................................................35 3.4.3 Large eddy eimulation...................................................................................................................39

3.4.4 Smagorinsky model.........................................................................................................................41 3.5 Modeling particle phase........................................................................................................................45 3.5.1 Modeling assumption......................................................................................................................46 3.5.2 Eulerian approach..........................................................................................................................47 3.5.3 Lagrangian approach.....................................................................................................................49

3.5.4 Eddy interaction model...................................................................................................................52

Introduction 3.1

In this chapter, we first begin by describing fluid dynamics from a purely heuristic point

of view. We then give a brief overview on the mathematical equations used in this work

to describe the transport of the fluid phase and particle phase. Firstly, the Navier-Stokes

equations (N-S) which govern the transport of fluid phase will be presented. Followed by

the representation of Navier-Stokes equation in the frame work of Reynolds Averaged

Navier Stokes equation (RANS) and Large Eddy Simulation (LES) will be presented.

Finally, the chapter concludes with the description of equation of motion for the particle

phase.

30

Importance of turbulence 3.2

Understanding of turbulence in fluid flows is the most important and yet most complex of

the phenomena to be understood in all of the classical physics. It is a fact that turbulence

exists at all scales, spanning from interior of biological cells to geophysical and

astrophysical phenomena. The human respiratory system is not an exception to this.

According to Lumley [66], turbulence is recognized as a distinct fluid behavior,

characterized by randomness, increased diffusivity, three dimensionality, and

dissipativity.

O. Reynolds [67] systematically investigated the transition from laminar to turbulence

through experiments in a pipe flow. He discovered that the flow instability resulting in

transition from laminar to turbulent flow is dependent on a non-dimensional parameter

known as Reynolds number. This parameter denoted by Re is a ratio of inertial forces to

viscous forces, i.e.

Re UL

(3.1)

where is the dynamic viscosity, is the fluid density. The termsU and L are the

characteristic velocity and length scales, respectively. At large Reynolds numbers

(inertial forces much larger than viscous forces), flow instabilities grow rapidly resulting

into intense mixing, and the flow is then termed as turbulent. On the other hand, at

moderate or low Reynolds number viscous forces are able to suppress the flow

instabilities and the resulting fluctuations, this behavior is termed as laminar.

Turbulence is generally perceived as the spectrum of eddies having varied sizes, where an

eddy is conceived as a coherent flow structure over a specified region (see Figure 3.1).

The spectrum spans from the largest energy containing eddies known as integral scale to

intermediate Taylor scale down to smallest scales known as Kolmogorov