A MODELLING S FILTRATION MECHANISMS FOR MICRON … Kong Thesis.pdf · applied. A coupled lattice Boltzmann method (LBM) and discrete element method (DEM) is implemented to investigate

A MODELLING STUDY OF FILTRATION

MECHANISMS FOR MICRON-PARTICLES

FILTRATION IN FIBROUS DIESEL

PARTICULATE FILTERS

Deyi Kong

IF80 Master of Philosophy

Submitted in fulfilment of the requirements for the degree of Master of Philosophy (Research)

School of Chemistry, Physics and Mechanical Engineering Science and Engineering Faculty

Queensland University of Technology

2019

A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate Filters i

Keywords

smog, diesel particulate matter, fibrous filter, lattice Boltzmann method,

discrete element method, porosity, particle deposition, pressure drop

ii A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate

Filters

Abstract

This thesis aims to discover the filtration mechanism inside a fibrous

diesel particulate filter (DPF), as the mechanism of small particles’ filtration is

still not fully understood. A diesel exhaust has a particle size less than 10 µm;

for the visualisation of micron-particles’ motion, the numerical method is

applied. A coupled lattice Boltzmann method (LBM) and discrete element

method (DEM) is implemented to investigate the mechanism that governs

particle-gas flows and particle fouling in idealised 2D fibrous DPFs. The open-

source library, Mechsys, is validated and then implemented for idealised filter

configurations. The initial parameters of simulations are filter configurations,

initial velocities of fluid, density of the particles, porosity of the filters, with the

particle diameter being 10 µm. These results consider the numbers of particle

deposition, filtration time, pressure drop, and location of particle deposition.

The results have shown that the different filter configurations have different

filtration performances for different velocities or densities. The filters of 75%

porosity have better than 90% porosity filtration performance for 10 µm

particles. This study has demonstrated the capabilities of a coupled LBM-DEM

model for filtration. The development of the numerical methods of this research

will thus allow for optimisation in fibrous DPFs. Furthermore, the proposed

model can be extended to smaller particles. This will ultimately contribute to

reducing the emission of toxic particles in the atmosphere, thus improves the

quality of human life.

A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate Filters iii

Table of Contents

Keywords ................................................................................................................... i

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

Table of Contents .................................................................................................... iii

List of Figures ........................................................................................................... v

List of Tables .......................................................................................................... vii

List of Abbreviations .............................................................................................. viii

List of Symbols ......................................................................................................... x

Statement of Original Authorship ........................................................................... xiii

Acknowledgements ................................................................................................ xiv

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

1.1 Objectives ........................................................................................................... 5

Chapter 2: Literature Review ........................................................................ 7

2.1 Engines and Emissions ....................................................................................... 7 2.1.1 Different Types of Engines ...................................................................... 7 2.1.2 Diesel Engines ........................................................................................ 9 2.1.3 Diesel Particulate Matter (DPM) ............................................................ 10 2.1.4 Other Emission of Diesel Engines (CO2, H2O, NOx, SO2, CO, HCs) ...... 12

2.2 Diesel Particulate Filter (DPF) ........................................................................... 13 2.2.1 Commercial DPF .................................................................................. 13 2.2.2 Disposable Filters ................................................................................. 14

2.3 Theory of Gas-particle Flow and Filtration ......................................................... 14 2.3.1 Filtration Mechanisms ........................................................................... 14 2.3.2 Particle Adhesion in Filters.................................................................... 17

2.4 Numerical Modelling ......................................................................................... 18 2.4.1 Conventional CFD Method .................................................................... 19 2.4.2 LBM Approach ...................................................................................... 21 2.4.3 Discrete Element Method (DEM)........................................................... 24 2.4.4 Coupling of DEM and LBM.................................................................... 25

2.5 Research Gaps ................................................................................................. 28

Chapter 3: Research Methodology ............................................................. 29

3.1 Research Steps ................................................................................................ 29

3.2 Rational of LBM-DEM in Mechsys ..................................................................... 31 3.2.1 Theory of LBM Model in Mechsys ......................................................... 32 3.2.2 Theory of DEM Model in Mechsys ........................................................ 34 3.2.3 Theory of Coupling LBM-DEM Model in Mechsys ................................. 35

3.3 Configuration Set-up in Mechsys ...................................................................... 37

3.4 Post-processing ................................................................................................ 38

Chapter 4: Validation of LBM-DEM model ................................................. 41

4.1 Validation of LBM, Flow Around a Cylinder ....................................................... 41

iv A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate

Filters

4.2 Validation of DEM Code of Mechsys ................................................................ 46 4.2.1 Two-sphere Collision of DEM Simulation .............................................. 46 4.2.2 Sphere Rebounding of DEM Simulation ............................................... 48

4.3 LBM-DEM Validation ........................................................................................ 51

4.4 Particle-laden Air Flow in a Clear Channel ....................................................... 57

4.5 Compare FVM-DEM and LBM-DEM results for Air Flow over 6 circular Obstacles ............................................................................................................... 61

4.6 Summary of Mechsys Validation ....................................................................... 63

Chapter 5: Results and Discussion ............................................................ 65

5.1 Computational Domains for Different Filter Designs ......................................... 65

5.2 Catalogue & Design of Simulation Groups, for Comparison .............................. 67

5.3 Filtration Effect of 10 µm Particles Flow Through Filters of 90% Porosity ......... 68 5.3.1 Simulation of Group 1, Comparison and Selection of 6 Designs ........... 68 5.3.2 Investigation and Comparison of Filtering with Same Density but

Different Velocities ............................................................................... 72 5.3.3 Investigation and Comparison of Filtering with Same Velocity but

Different Densities ................................................................................ 74 5.3.4 Comparison of Filtering for Different Filter Configurations (A, D, E)

with Different Initial Parameters ............................................................ 76

5.4 Summarise and Analyse the Simulation Results of the Filter with 90% Porosity 79

5.5 Filtration Effect of 10 µm Particles Flow Through Filters of 75% Porosity ......... 80

5.6 Compare the Simulation Results between Φ=75% & Φ=90% ........................... 80

Chapter 6: Conclusions .............................................................................. 83

Bibliography ................................................................................................ 85

A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate Filters v

List of Figures

Figure 1: Diesel Particulate Size Distribution .............................................. 11

Figure 2: Four basic processes of filtration ................................................. 16

Figure 3: Filtration mechanism of electrostatic attraction ............................ 16

Figure 4: 2D case (D2Q9) ........................................................................... 22

Figure 5: Illustrations of Particle-solid relationship of Hertzian model ......... 24

Figure 6: The coupling procedure of DEM-LBM .......................................... 26

Figure 7: DEM-LBM coupling system .......................................................... 27

Figure 8: LB discretisation and D2Q9 model of Mechsys ........................... 33

Figure 9: Geometry of the computed domain .............................................. 41

Figure 10: Measurements of Geometry of Vortex street when Re<40 ........ 42

Figure 11: Visualisation of LBM for Low Reynolds Number vortex, a. Re=20, b. Re=40 ...................................................................... 42

Figure 12: Results of Strouhal number of Reynolds number from 100 to 1000, experiment: Coutanceau (1977); PISOFoam: Manueco et al., (2016); IB: Manueco et al., (2016) .................. 45

Figure 13: Free fall of a single particle ........................................................ 49

Figure 14: HSD-A, en=0.7, Particle Centre PSosition .................................. 49

Figure 15: HSD-A Model, en=0.7, Compare Mechsys Result with Caserta et al. (2016) Results of Particle Centre Position h, .............................................................................................. 51

Figure 16: 6 mm Teflon sphere bouncing motion in the air, h-t function, for the experiment, at the first impact Re=210, St=7.8×104, and 𝒆=0.8 ............................................................. 53

Figure 17: 6 mm Teflon sphere bouncing motion in the air, u-t function, for the experiment, at the first impact Re=210, St=7.8×104, and 𝒆=0.8 ............................................................. 54

Figure 18: 3 mm steel sphere bouncing motion in silicon oil RV10, h-t function, for the experiment, at the first impact Re=82, St=152, and 𝒆=0.78 .................................................................. 55

Figure 19: 3 mm steel sphere bouncing motion in silicon oil RV, 10 u-t function, for the experiment, at the first impact Re=82, St=152, and 𝒆=0.78 .................................................................. 56

Figure 20: Particle deposition and velocity flow field of 350 µm particles, a. FVM-DEM, b. LBM-DEM ....................................... 59

Figure 21: Deposition of 500 µm particles and velocity flow field, a. FVM-DEM, b. LBM-DEM .......................................................... 60

vi A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate

Filters

Figure 22: Deposition of 50 µm particles, a. FVM-DEM, b. LBM-DEM, c. LBM-DEM (current study) ..................................................... 63

Figure 23: 90% porosity of 6 different configuration of filters and 75% porosity of 3 different configurations of filters ........................... 66

Figure 24: Comparison for endings of simulations in 6 configurations, Φ=90%, v=0.1 m/s, ρ=2500 kg/m3 ........................................... 69

Figure 25: Summary of simulations group 1, number of particle filtration at different time, Φ=90%, 10 µm particles, v=0.1 m/s, ρ=2500 kg/m3 ................................................................... 71

Figure 26: Relationship between pressure drop and filtration fraction, Φ=90%, 10 µm particles, v=0.1 m/s, ρ=2500 kg/m3 ................. 72

Figure 27: Relationship between pressure drop and filtration fraction, Φ=90%, 10 µm particles, ρ=2500 kg/m3 (heavy), v=0.1 m/s (fast) or v=0.05 m/s (slow) ................................................. 73

Figure 28: Relationship between pressure drop and filtration fraction, Φ=90%, 10 µm particles, ρ=800 kg/m3 (light), v=0.1 m/s (fast) or v=0.05 m/s (slow) ....................................................... 74

Figure 29: Relationship between pressure drop and filtration fraction, Φ=90%, 10 µm particles, v=0.1 m/s (fast), ρ=800 kg/m3 (light) or ρ=2500 kg/m3 (heavy) ................................................ 75

Figure 30: Relationship between pressure drop and filtration fraction, Φ=90%, 10 µm particles, v=0.1 m/s (fast), ρ=800 kg/m3 (light) or ρ=2500 kg/m3 (heavy) ................................................ 76

Figure 31: Comparing the simulation results in each configuration, Φ=90%, 10 µm particles, v=0.1 m/s (fast) or v=0.05 m/s (slow), ρ=800 kg/m3 (light) or ρ=2500 kg/m3 (heavy) ............... 78

Figure 32: Simulation results of Φ=75% configurations, v=0.05 m/s, ρ=800 kg/m3, a, configuration A, b, configuration D, c, configuration E ......................................................................... 80

A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate Filters vii

List of Tables

Table 1: AQI pollutant gases and particulate matter & key emissions of diesel engines ........................................................................2

Table 2: LBM simulation results .................................................................. 42

Table 3: To compare simulation results of dimensions’ ratio ...................... 43

Table 4: Strouhal number analysis .............................................................. 44

Table 5: Mechsys simulation results of particle-collisions ........................... 47

Table 6: Particle Collision studies with different velocity and particle size ........................................................................................... 48

Table 7: Mechsys Results of The Real Time and Particle Centre Position (h) ............................................................................... 50

Table 8: Compare FVM-DEM and LBM-DEM results for 350 µm particles .................................................................................... 58

Table 9: Compare FVM-DEM and LBM-DEM results for 500 µm particles .................................................................................... 60

Table 10: Summary of results for 50 µm particles ....................................... 62

Table 11: Catalogue & design of simulation groups, for comparison of filtration effect by using different initial parameters ................... 67

Table 12: Results of 75% porosity simulations ........................................... 81

viii A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate

Filters

List of Abbreviations

AQI: air quality index

BGK: Bhatnagar-Gross-Krook

CE: combustion engine

CFD: computational fluid dynamics

CI: compression ignition

D2Q9: 2-dimension, 9 potential moves

DEM: discrete element method

DPF: diesel particulate filters

DPM: diesel particulate matter

ECE: external combustion engine

EGR: exhaust gas recirculation

EU: European Union

FVM: finite-volume method

HPCR: high-pressure common-rail

IARC: International Agency for Research on Cancer

ICE: internal combustion engine

LBM: lattice Boltzmann method

LBM-DEM: lattice Boltzmann method and discrete element method

NS: Navier-Stokes

PM: particulate matter

PM0.1: paticulate matter diameter less than 0.1 µm

PM10: particulate matter diameter less than 10 µm

PM2.5: particulate matter diameter less than 2.5 µm

PN: particulate number

A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate Filters ix

Re: Reynolds number

SI: spark ignition

St: Strouhal number

x A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate

Filters

List of Symbols

English Symbols:

𝐴: contact area

𝐴𝑣: van der Waals energy of ashesion

𝐵: weight function

𝐶𝑑: drag coefficient

𝐶𝑖: lattice velocity

𝐶𝑠: speed of sound

𝐶𝑣𝑖𝑟: virtual mass factor

𝐷: diameter of the cylinder

𝑑𝑝: particle diameter

𝑑𝑡: dimensionless time step

𝑑𝑥: dimensionless lattice size

𝐸𝑑: dissipated energy

𝐸𝑒: elastic energy

𝐸𝑘1: kinetic energy

𝐸𝑘2: rebounds energy

𝑒𝑖: real velocity

��: additional force term

𝐹𝑖,𝑏: summarised other body force

𝐹𝑖,𝑓: force that the surrounding fluid phase may exert on the particles

𝐹𝑖,𝑛: normal particle-particle contact force

𝐹𝑖,𝑡: tangential particle-particle contact force

𝐹𝑛𝑐𝑜ℎ𝑒: normal cohesive force

𝐹𝑛𝑐𝑜𝑛𝑡: normal contact force

𝐹𝑡𝑐𝑜ℎ𝑒: tangent cohesive force

𝐹𝑡𝑐𝑜𝑛𝑡: tangent contact force

𝑓: represents body accelerations acting on the continuum

𝑓𝑖𝑒𝑞

: equilibrium distribution

𝐼𝑖𝑑𝜔𝑖

𝑑𝑡: moment of particles

A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate Filters xi

𝐾𝑛: normal stiffness constant

𝐾𝑡: tangent stiffness constant

𝑘: collision parameter

𝑀𝑛𝑐𝑜ℎ𝑒: normal elastic modulus

𝑀𝑡𝑐𝑜ℎ𝑒: tangent elastic modulus

𝑚𝑖: mass of particles

𝑛: unit vector of normal direction

P: pressure

𝑝: momentum

𝑅: length between particle and surface

𝑟𝑖,𝑐: radius of particles

𝑇𝑖,𝑟: additional torque on the particle

t: time

𝑡: unit vector of tangent direction

𝑇: torque of particles

𝑢𝑝 : particle velocity

��: flow velocity

𝑈: velocity of fluid flows through the cylinder

𝑣𝑐: critical velocity for rebound

𝑣𝑝: solid velocity at position x

��𝑖: linear acceleration of particles

𝑥𝑐𝑚: the mass centre of the DEM particle

𝑥𝑛: the position of cell

𝑍: length of surface

Greek Symbols:

𝛾: coefficient of bounce-back

∆𝑙𝑛: normal overlapping lengths

∆𝑙𝑡: tangent overlapping lengths

∆𝑡: time step

∆𝑥: lattice size

𝜀𝑛: normal strains

𝜀𝑡: tangent strains

xii A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate

Filters

𝜇: dynamic viscosity of fluid

𝜇f: friction coefficient

𝜗: kinematic viscosity

𝜌𝑎: density of air

𝜌𝑝: particle density

𝜏𝑟: particle relaxation time

Φ: porosity

𝜔𝑖: lattice weights

Ω𝑖𝑠: fluid-solid interaction term

Subscript:

𝑎: air

𝑏: body

𝑓: fluid phase

f: friction

𝑖: direction of movement

𝑛: normal

𝑝: particle

𝑡: tangential

Superscript:

𝑒𝑞: equilibrium

𝑐𝑜ℎ𝑒: cohesive

𝑐𝑜𝑛𝑡: contact

Other Symbols:

∇: divergence

𝜕��

𝜕𝑡: convective derivative

A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate Filters xiii

Statement of Original Authorship

The work contained in this thesis has not been previously submitted to

meet requirements for an award at this or any other higher education

institution. To the best of my knowledge and belief, the thesis contains no

material previously published or written by another person except where due

reference is made.

Signature:

Date: April 2019

QUT Verified Signature

xiv A Modelling Study of Filtration Mechanisms for Micron-particles Filtration in Fibrous Diesel Particulate

Filters

Acknowledgements

I want to acknowledge the continuous support and encouragement from

my supervisory team, Emilie Sauret, Willem Dekkers, and Thomas Rainey,

during the period of this research; to Sahan Kuruneru and Christopher Soriano

From for their advice on theory and technical support; to Sergio Galindo-Torres

and Pei Zhang for their development of numerical tools and shearing the

templates; to Chun Huei Fan and Pei Wang for their advice on installation of

Linux software and C++ programming; and to Wei Li for his advice on how to

analyse the flow field and particle movement.

I would like to acknowledge the following groups, group members or

staff: LAMSES group, QUT library, the School of Chemistry, Physics and

Mechanical Engineering, and Queensland University of Technology. I also

acknowledge the services of professional editor, Diane Kolomeitz, who

provided copyediting and proofreading services, according to the guidelines

laid out in the university-endorsed national ‘Guidelines for Editing Research

Theses’.

Last but not least, I thank my family, as I would not have been able to

complete this research without their financial and emotional support.

Chapter 1: Introduction 1

Chapter 1: Introduction

Environmental problems resulting from human activity are a worldwide issue.

In particular, air pollution is a major environmental problem in the 21st century.

Rapid industrialisation in developing countries, such as mainland China, has

resulted in increases in the severity of air pollution to such an extent that it is

now of worldwide concern (Shi, Wang, Chen, & Huisingh, 2016). For example,

from October 2016 to January 2017, heavy smog was recorded over Beijing

and other major cities in China, and the air quality index (AQI) was at Level 5

or 6 (primary pollutant is PM2.5, (particulate matter less than 2.5 µm)), (Data

centre, MEP of PRC, 2017). An air quality of Level 5 is defined as an AQI

between 201 and 300, where the health implications are that “healthy people

will be noticeably affected; people with breathing or heart problems will

experience reduced endurance in activities; these individuals and elders

should remain indoors and restrict activities”; Level 6 is defined as an AQI

higher than 300, where the health implications are that “healthy people will

experience reduced endurance in activities; there may be strong irritations and

symptoms that may trigger other illnesses; elders and the sick should remain

indoors and avoid exercise; healthy individuals should avoid outdoor activities”

(MEP of PRC, 2012).

There are several different methods for evaluating AQI, such as the pollutant

standards index (Singapore) or air pollution banding (United Kingdom).

Although there are several different standards to evaluate AQI, most are based

on measuring the concentration of pollutants, shown in Table 1 (Jassim, &

Coskuner, 2017; & Perlmutt, & Cromar, 2015).

The primary sources of pollutants are industrial and motor vehicle exhausts,

where the pollutants are generated as a by-product of burning fossil fuels to

generate energy (Lei, Zhang, Nielsen, & He, 2011). Modern economies are

sustained by significant energy consumption and still require increased energy

consumption in order to grow. Currently, the energy consumed is primarily

generated by burning fossil fuels (IEA, 2015). Historically, world energy

2 Chapter 1: Introduction

demand has increased with time; for example, from 1971 to 2013, energy

demand has kept increasing and the majority of energy has been produced

from fossil fuels (IEA, 2015). Crude oil is the most important fossil fuel,

producing various liquid fuels such as petroleum, diesel and heavy fuel oil.

Diesel plays a significant role in economic development where it is used in

transportation (most heavy-duty vehicles use diesel engines) and some types

of marine engines as well as diesel generators.

Generally, the emissions of diesel engines include similar components to other

industrial sources contributing to air pollution. For diesel engines, key

emissions are shown in Table 1. Diesel engine exhausts thus contribute to AQI

measurements of CO, SO2, NOX (NO and NO2), and PM pollutants, where

incomplete combustion of the fuel results in the emission of CO and HCs as

unburnt fuel. Furthermore, hazardous emission of SO2 depends on the quality

of diesel, where low sulphur diesel will produce lower SO2.

Table 1: AQI pollutant gases and particulate matter & key emissions of

diesel engines (Jassim, & Coskuner, 2017; Perlmutt, & Cromar, 2015;

Plaia, & Ruggieri, 2011 & 2010; Jarauta-Bragulat, Hervada-Sala, &

Egozcue, 2016 &2015; Kurnia et al., 2014; Beatty et al., 2011)

AQI measuring (Pollutant gases & Particulate matter)

Pollutants gases CO, SO2, NO2, O3

Particulate matters PM10, PM2.5,

Key emissions of diesel engines

Greenhouse gas CO2

Hazardous gases CO, HCs, SO2, NOx,

Particulate matter PM10 to PM0.1

Diesel engine exhaust contains particles of different sizes, and these particles

vary in their physico-chemical composition. If these physico-chemical

compositions cannot be cleaned by the environment itself, this will cause

serious environmental impacts, such as heavy smog, photochemical smog or

acid rain. These environmental impacts would, in turn, cause various health


problems. There are many scientific studies that have mentioned that soot or

PM has serious health effects, for example, higher risk of asthma, higher risk

of respiratory system diseases, decreased lung function in children, and a

higher risk of lung cancer (WHO, 2013). According to the International Agency

for Research on Cancer’s (IARC) research in 2012, diesel exhaust is a group

1 carcinogen. It appears that PM is causing smog and smog in turn is causing

health problems. Nanoparticles are very small, so they can pass almost

unheeded into the lungs and thence even into the circulatory system (Twigg,

2007). The health issues related to diesel exhaust are of worldwide concern,

particularly issues related to the emission of nanoparticles (Bensaid,

Marchisio, Russo, & Fino, 2009).

Current research aims to reduce the environmental impact of vehicles and

industry by controlling emissions. Optimisation of diesel engines, especially

the exhaust filtration system used to remove diesel particulate matter (DPM),

is imperative. Currently, most diesel particulate filters (DPF) used in modern

diesel engines have a very high filtration efficiency of removal PM10, and good

efficiency of removal PM2.5, but limited efficiency of removal PM0.1 (WHO,

2013). While PM10 and PM2.5 have high particulate mass concentration, PM0.1

has a high particulate number (PN), representing a small mass made up of a

very large number of very small particles. Further technical development is

needed to solve the problem of how to remove PM0.1 from exhaust emissions.

Current applications and experiments are able to measure particle

concentration, but the study of filtration mechanisms is limited because the

observation of particle movement inside the DPF is very difficult.

Regulations such as the emission standard Euro 5 (EU Emission Standards,

2007) provide a requirement that auto manufacturers control both PM and PN.

PM2.5 and PM0.1 are the most hazardous PM. It is known that diesel emissions

have DPM from PM10 to PM0.1 (Ristovski et al., 2012, & Rahimi Kord Sofla,

2015). Current DPFs must meet the emission standards which can remove

most of PM, but to reduce PN, further research is needed to develop a method

that can control PM10 to PM0.1 as well as PN. Usually, the commercial DPFs

can remove more than 85% PM by measuring total mass of particles, in some

4 Chapter 1: Introduction

condition the efficiency of removal is around 99% (Park, Nguyen, Kim, & Lee,

2014). Removal of these tiny particles, especially PM0.1 is important to meet

the requirements of new emission standards such as Euro 6, and thus to avoid

negative health impacts from diesel emissions. However, the smaller particles

are difficult to remove.

Another PhD student from QUT, Rahimi Kord Sofla (2015), conducted

experimental research in this area. There are limitations to experimental

studies of diesel exhaust filtration to date, and none observe the filtration

mechanism of the filter materials.

• It is very time-consuming to produce filters with a wide-range of

geometries and pore structures.

• Due to the small size of the particles, it is impractical to observe their

motion and entrapment within a filter medium.

• Experimental research does not elucidate mechanisms for

agglomeration and entrapment.

• Most engine facilities are limited in the duration of experiments and so

it is impractical to measure how the filter blocks over time (loading) and

pressure drop (i.e. backpressure) increases.

There are some numerical treatments of particle transport, for example, using

the finite-volume method (FVM) solving Navier-Stokes (NS) equations,

coupled with the discrete element method (DEM). FVM-DEM is a conventional

method to study the particle transport in fluid flows. Another option is using

Lattice Boltzmann methods (LBM), which can simulate gas flow but does not

use the conventional method. The Boltzmann equation is a mesoscopic

description to simulate the fluid with streaming and collision (Suzuki & Senba,

2010). It is suitable to simulate the fluid flows through the porous media. For

the particle movement, DEM can compute a large number of small particles’

movement (Bicanic & Ninad, 2004). Coupling LBM and DEM is another option

to study the particle-fluid flows.

This project will use one method or couple these two methods to model the

filtration process of DPM inside the filter. A computational fluid dynamics (CFD)


simulation will be used to study the flow field and particle movement as well as

agglomeration and entrapment mechanisms. The findings will assist in

improving the efficiency of DPFs in removing micron and nanoparticles.

This project studies the filtration process in detail, using numerical methods to

study the mechanism of DPFs and exhaust particles at micrometer and

nanometer scales. Coupled numerical methods will be used to develop

mathematical models, which are suitable for micron or nano-particles.

1.1 Objectives

This research aims to identify the mechanisms of micro-particles filtration in

idealised 2D fibrous filters for diesel engine exhausts through the development

and application of an LBM-DEM model. To achieve this aim, the objectives

are:

▪ To characterise key pore-scale filtration mechanism of micro-particles

by using LBM-DEM model

▪ To apply the model to characterise the effects of particle properties

(diameter, density, velocity) on the filtration process

▪ To elucidate the effect of filter geometry and porosity on the filtration

mechanisms and efficiency

▪ To investigate how the numerical simulations can contribute to the

micron particle filtration process

Chapter 2: Literature Review 7

Chapter 2: Literature Review

This project proposes to use numerical methods to simulate the filtration

progress. This section will study the current literature to discover research

gaps, which highlight the need for appropriate diesel particulate treatments

and numerical simulations. Firstly, the research will provide the detail of diesel

emission, which is required for developing the modeling of emission gasses.

Secondly, it will study the literature on current diesel emission treatments,

especially the exhaust system for reducing particles. Thirdly, it will study

mathematics model which is related to the particle filtration. Lastly, this section

will focus on CFD modeling, which can help researchers solve filtration

problems. When the literature review section is complete, the research gap will

be highlighted. This will help researchers in their future studies.

2.1 Engines and Emissions

2.1.1 Different Types of Engines

There are many types of engine. Heat engines are one category of engine

that is widely used (Cengel, Boles, & Kanoglu, 2011). Combustion engines

are a kind of heat engine, typically used to create motion or convert thermo-

energy to kinetic energy (Cengel et al., 2011). Combustion engines (CE) can

be categorised as three types: internal combustion engines (ICE), external

combustion engines (ECE), and air-breathing combustion engines (ACE)

(Chattopadhyay, 2015; Cengel & Boles, 2015; Jacobs, 2013). CE can convert

heat energy, which is produced by a chemical reaction (combustion), to kinetic

energy (Cengel & Boles, 2015). Currently, most vehicles use gasoline and

diesel engines, which are the typical ICE.

The operation of ICEs has a negative impact on air quality. The combustion

process will produce exhaust (Sher, 1998). ICEs are used widely on vehicles

for controlling the air quality, as most of researchers and governments have

suggested controlling vehicle exhausts (Wang et al., 2016; Perlmutt & Cromar,

8 Chapter 2: Literature Review

2015; Kurnia et al., 2014; Beatty et al., 2011; Sher, 1998). Some studies have

shown that the emissions of ICE include some different physico-chemical

compositions, for example greenhouse gases such as carbon dioxide (CO2),

and hazardous gases such as carbon monoxide (CO), hydrocarbon (HC),

nitrogen oxides (NOx), and particulate matter (PM) (Kurnia et al., 2014; Beatty

et al., 2011; Sher, 1998). To control the emissions of vehicles, governments

have laid down some regulations and standards, because some of the

emissions are harmful to human health; some them are harmful to the

environment, causing global warming and acid rain. It is known, for reduction

of air pollution, the European Union (EU) has enacted Euro1 to Euro6 emission

standards which have many followers. Australia and China are also following

these standards. Based on the Kyoto Protocol, for reduction of greenhouse

gasses, the EU has established a regulation of No 443/2009 (2009) to control

the CO2 emission from vehicles, so exhaust control is an emerging wide

research area.

This research will concentrate on ICE exhaust. ICEs have two major types:

four stroke gasoline engines and diesel engines (Cengel et al., 2011). The

engines may be categorised by considering the different fuels: one is the

gasoline engine, using petrol and the other is the diesel engine, using diesel.

ICE may also be classified in terms of how the fuel is ignited: gasoline engines,

using spark plugs to ignite the fuel which is also called spark-ignition (SI)

engine; diesel engines, using high temperature of compressed air to burn the

fuel, so they are also called compression-ignition (CI) engines. Also, these two

types of engines may be categorised by different thermos-cycles: gasoline

engine powered Otto cycle, diesel engine powered diesel cycle. These two

types of engines also have other differences, such as compression ratio.

Normally, gasoline engines have a compression ratio between 7:1 and 13:1,

but diesel engines have a compression ratio between 15:1 and 24:1 (Cengel

et al., 2011).

Gasoline engines’ exhaust have the following components: nitrogen 70% to

75%, water vapor 10% to 12%, carbon dioxide 10 to 13.5%, hydrogen 0.5 to

2%, oxygen 0.2 to 2%, carbon monoxide: 0.1 to 6%, unburnt hydrocarbons


and partial oxidation products (e.g. aldehydes) 0.5 to 1%, nitrogen monoxide

0.01 to 0.4%, nitrous oxide <100 ppm, sulphur dioxide 15 to 60 ppm, traces of

other compounds such as fuel additives and lubricants, also halogen and

metallic compounds, and other particles (Courtois, Molinier, Pasquereau,

Degobert, & Festy, 1993).

2.1.2 Diesel Engines

Diesel engines are widely used, including in some passenger cars, many

methods of public transportation, most commercial vehicles, most heavy-duty

vehicles, some types of marine engines, and some industrial engines. These

wide applications have shown that diesel engines provide important

development for the economy and society. To date, modern diesel engines are

the most cost-effective internal combustion engine for vehicles and other non-

road engine applications. However, the exhaust of diesel engines also has

some negative impact on human health and the environment.

Most of the current technologies in diesel engines are the emission-controlling

technologies, for compliance with the emission standards as well as protecting

the environment. The idealised combustion of engines can only produce CO2

and H2O, but the real combustion exhausts are complex organic and inorganic

compounds, including gasses, semi-volatile oil, and particulate phases. The

components of diesel emissions are: CO (100-10000 ppm), HC (50-500 ppm),

NOx (30-1000 ppm), SO2 (proportional to fuel sulphur content), DPM (20-200

mg/m3), CO2 (2-12 vol%), ammonia (1.24 mg/km), cyanides (0.62 mg/km),

benzene (3.73 mg/km), toluene (1.24 mg/km), polycyclic aromatic hydrocarbon

(PAH) (0.19 mg/km), aldehydes (0.0 mg/km) (Jelles, 1999 & Tschöke et al.,

2010).

Modern technologies of diesel engines can catalyse or oxidise most of the toxic

and unburnt components. These technologies can be categorised as in-

cylinder control technologies and exhaust after treatment controls.


In-cylinder controls have some implementations, such as turbocharger with

intercooler, exhaust gas recirculation (EGR), high-pressure common-rail

(HPCR) fuel delivery systems. Turbocharger with intercooler can compress

more air into the cylinders, so it could generate more power and decrease the

unburnt components, but the NOx would be increased. EGR is a combustion

control technology for reducing the NOx, but it will reduce the power output and

cause increase in HC, CO, and DPM formation. HPCR can reduce the unburnt

components and the formation of DPM (Bennett, 2015 & Mollenhauer, &

Tschöke, 2010).

There are applications of exhaust gas after treatment controls, such as to use

the catalytic or non-catalytic method to reduce the exhausts or catalyse the

gasses to be vapour and CO2.

2.1.3 Diesel Particulate Matter (DPM)

Many governments and environmental organisations strongly recommend

controlling the particulate matter emissions. It is known that if the particulate

size is smaller than fine particles (PM2.5), these would be very dangerous for

human beings, because they can penetrate the respiratory system (Hamra,

2016 & Ristovski et al., 2003, Morawska et al., 2006). Another effect is when

PM is suspended in the air, it can create smog, acid rain, and a photochemical

environment.

Diesel emission produces PM to the air, and it becomes one of the sources to

produce PM (Ristovski et al., 2012 & Barrios et al., 2014). The literature is full

of references dealing with the distribution of diesel particulate matter. The PM

of diesel exhaust has aerodynamic diameters that can be classified as coarse

particles (PM10) that have an aerodynamic diameter of less than 10 µm, fine

particles (PM2.5), for which the aerodynamic diameter is less than 2.5 µm,

ultrafine particles (PM0.1), for which aerodynamic diameter is less than 0.1 µm

and nanoparticles with aerodynamic diameter less than 50 nm (Ristovski et al.,

2012 & Barrios et al., 2014). Figure 1 shows the distribution size of diesel


particulate matter. From this graph, it is clear that more than 90% of the

number distribution of diesel particulates have sizes of significantly lower than

1000 nm (i.e. 1 µm). For the number distribution, there is only one peak around

0.01 µm, but for the mass distribution, 0.1 µm to 1 µm is the first peak, and

lower than 10 µm (PM10) is the second peak.

Figure 1: Diesel Particulate Size Distribution (Ristovski et al., 2012, &

Rahimi Kord Sofla, 2015)

When analysing the ingredients of DPM, it contains some different chemical

and physical compositions. Some chemical compositions such as sulphate or

HC can be catalysed by convertor or have a chemical reaction with some

emission additives (diesel exhaust fluid) (Twigg, 2007). The other particles,

such as solid carbon or inorganic ash, must be removed by physical filters. For

controlling the particle exhaust, there are two things that have to be

considered: one is the mass of particles, another is the number of particles.

Currently, to control the particle emission by measuring the mass is distinct;

for further studies, to control the number distribution of DPM is required in the

new emission standards, such as Euro 6, CARB and Japanese Emission

Control Standards.


2.1.4 Other Emission of Diesel Engines (CO2, H2O, NOx, SO2, CO,

HCs)

Except for DPM, diesel emissions still have some other gas phase

components. Some of them are toxic; some of them are non-toxic but have

another environmental impact.

CO2 is a major greenhouse gas, which would bring global-warming. Although

it is not a toxic gas, for vehicle emission standards, most of them do not restrict

CO2. Most of the United Nations members have signed the Kyoto Protocol

(1992) for controlling the CO2 emissions.

Vapour (H2O), it is a non-toxic gas which is an idealised output for a chemical

reaction. ICEs burn fuels; the ideal reaction is that O2 totally consumes fuel

and produces H2O and CO2. Vapour could be the only safety emission of fossil

fuels as diesel or petroleum.

NOX is the major emission gas of diesel engines. There are two components

of NOX, NO, and NO2. Air contains 78% of Nitrogen; combustion inside the

cylinder forms NOX. Diesel engines’ combustion needs more air than gasoline

engines, so the concentration of nitrogen and oxygen will be higher than in a

gasoline engine (Bennett, 2015 & Tschöke, 2010). Some researchers have

found out that diesel engines produce around 20 times more NOX than

gasoline engines (Fuller, 2012).

SO2 and other sulphates will cause acid rain and most of these sulphates are

harmful. For several years, the petroleum industry has tried to produce a high

quality and low sulphur content in diesel fuels. To meet the fuel and emission

standards, some developed countries have fully applied low-sulphur diesel

fuels, but there are still some developing countries using substandard diesel

fuels.


CO and HCs are the typical emissions of ICEs, because of the not fully

combusted air and fuels (Tschöke, 2010). These two compounds are toxic and

in the measurement list of AQI. Some of the HCs could be solid phase

(Bennett, 2015).

2.2 Diesel Particulate Filter (DPF)

2.2.1 Commercial DPF

In order to meet increases in emission standards for diesel engines, particulate

filters have become common devices to decrease the discharge of DPM into

the environment. There are several categories of DPFs. The filters may be

categorised by considering different designs: common types are wall-flow

filters and flow-through filters. Filters may also be classified in terms of how

the deposited particulate matter is removed: the removal process is referred to

as regeneration of the filter and may be described as either active regeneration

or passive regeneration. In some types of filtration, the filter material is

disposable, and filter replacement is used instead of a cleaning or regeneration

process.

Currently, most of the commercial DPFs have high filtration efficiency to

remove PM10 and PM2.5, but they have low efficiency in removing PM0.1, Figure

1 shows that, in diesel emission, PM10 and PM2.5 have major mass distribution

but low number distribution. On the other hand, PM0.1, as well as 50 nm and

10 nm particles, has the highest number distribution. One piece of research

shows, removal of 10 µm to 0.7 µm particles the filtration efficiency of PN is

more than 95% in both real road test and laboratory test (Yu et al., 2017).

Based on the Euro 6 emission standard, it requires removing PM0.1, because

it has a very high risk of causing respiratory diseases, such as lung cancer

(Ristovski et al., 2012 & Barrios et al., 2014 & Casati et al., 2007 & WHO,

2013). Current experiments’ commercial applications can measure the

transient difference before and after the DPF, and also the total mass of the

DPF can be measured to investigate the performance of filtration.


2.2.2 Disposable Filters

From Rahimi Kord Sofla’s research (2015), it is shown that disposable filters

(such as filter paper) have a good result for removing DPMs. The filter has

cellulose media, which is a kind of fibrous structure; this fibre and fibrous

structure has the ability to adhere or obstruct the DPMs and the fluid can pass

through the cellulose media. This kind of filter materials is not widely used for

DPFs, but it has some advantages, which are valuable for more intensive

research. For example, the costs of filter paper are obviously lower than

current commercial DPFs; filter paper is disposable, and the replacement of

filter paper is easier than for the other DPFs.

Experimental investigations of filtration processes have some limitations

because the tiny particles are not easy to observe. The deposition processes

that occur inside the filter material are difficult for direct observation by the

human eye. To study the flow through the filter material, and the particulate

deposition processes, CFD modeling can be used to extend the current

understanding of the filtration process beyond what can be achieved by

experimental investigations.

2.3 Theory of Gas-particle Flow and Filtration

2.3.1 Filtration Mechanisms

There are four basic ways filtration media captures particles:

1. Inertial impaction

Inertia works on large (d>1 µm), heavy particles suspended in the flow

stream. These particles are heavier than the fluid surrounding them. As the

fluid changes direction to enter the media space, the particle continues in

a straight line and collides with the media, where it is trapped and held

(Baker, 2011).


2. Diffusion

Diffusion works on the smallest particles (d<0.1 µm). Small particles are

not held in place by the viscous fluid and diffuse within the flow stream. As

the particles traverse the flow stream, they collide with, and are collected

by, filtration media (Baker, 2011).

3. Interception

Direct interception works on particles in the mid-range (d<0.1 µm) size that

are not quite large enough to have inertia and not small enough to diffuse

within the flow stream. These mid-sized particles follow the flow stream as

it bends through the filtration media spaces. Particles are intercepted or

captured when they touch a filtration media (Baker, 2011).

4. Sieving

Sieving, the most common mechanism in filtration, occurs when the particle

is too large to fit on the filtration media. Normally, porous media is the

typical filtration media having a sieving process (Baker, 2011).

All the filtration process is shown in Figure 2.


Figure 2: Four basic processes of filtration (Baker, 2011)

There is another filtration mechanism that can present the relationship

between low mass particles and filter fibre; it is an electrostatic attraction. This

capture process does not favour a certain particle size. When the fiber and

particles have oppositely charged, the fiber can capture the particles. shown

in Figure 3 (Baker, 2011).

Figure 3: Filtration mechanism of electrostatic attraction (Baker, 2011)

Due to the diesel exhaust that included different sizes of particulates, it is

difficult to define the filtration mechanism of different sizes of particulates and

filter materials by experiments. The numerical simulation could be the solution

to study these filtration effects.


2.3.2 Particle Adhesion in Filters

Scientists try to explain filtration mechanisms in physics and mathematics, for

which particle adhesion in filters is one of the basic filtration concepts. This

concept can be explained in a physics and mathematics way, which is relevant

to the energy and forces transform between particles and the filtration media.

Solid particles are held in contact with the filtering surface, be it either fibrous

or porous material, by van der Waals forces (Davies, 1973). Van der Waals

forces can explain the relationship between the tiny objects in a microcosmic

view, such as attraction and repulsions between atoms, molecules, surfaces,

and intermolecular forces (Davies, 1973). Furthermore, some researchers

have found out the capture process between particles and surfaces has the

electrostatic force of adhesion (Davies, 1973). There are many experiments

that have studied adhesion of particles. To summarise those experiments and

literature, the particle capture can be explained in terms of conservation of

energy.

For example, if the particle strikes the surface with kinetic energy, 𝐸𝑘1 and

rebounds with 𝐸𝑘2 then

𝐸𝑘1 + 𝐴𝑣1 = 𝐸𝑒 + 𝐸𝑑 Impact

𝐸𝑒 = 𝐸𝑘2 + 𝐴𝑣2 Rebound

(1)

Where Av is the van der Waals energy of adhesion, Ee is the elastic energy

stored on deformation and Ed is dissipated. The conditions for adhesion are

𝐸𝑘2 = 0

𝑘2𝐸𝑘1 < 𝐴𝑣1 − 𝐴𝑣2 = ∆𝐴𝑣

𝑘2 = (𝐸𝑘1 − 𝐸𝑑)/ 𝐸𝑘1

(2)

and k is the collision parameter.

Other values of force between a particle and a surface are ordinary force and

retarded force: 𝑟 is the radius of particle, 𝑍 is length of surface, 𝑅 is the length

between particle and surface (Davies, 1973).

Ordinary force=1.8×10−13𝑟

𝑍2 (3)


Retarded force=1.7×10−19𝑟

𝑍3

Hence

∆𝐴𝑣 = ∫ (0 + 𝑅)𝑑𝑍∞

𝑍0

(4)

where 𝑍0, the separation at contact, is taken as the thickness of a monolayer

of adsorbed air, it gives

∆𝐴𝑣 = 5.76 × 10−5𝑟𝑘2 × 10−7 𝐽𝑜𝑢𝑙𝑒𝑠 (5)

The critical impact energy between adhesion and rebound is thus

𝐸𝑘1 = 5.76 × 10−12𝑟𝑘−2 =2

3𝜋𝑎3𝜌𝑎𝑣𝑐

2 (6)

which gives

𝑣𝑐 =5.24 × 10−3

𝑘𝑎√𝜌𝑎

(7)

The value of k must depend on the material, a is the particle radius, and vc is

the critical velocity for rebound. Equation 6 shows a smaller particle radius will

create smaller critical impact energy. 𝐸𝑑, dissipated energy is the constant of

the material, so equation 2 will be

𝐸𝑘1 − 𝐸𝑑 < ∆𝐴𝑣 (8)

The particles will have lower rebound effects. As Davies (1973) said, when the

particle diameter is smaller than 0.3 µm, the particles will have more adhesion.

These mathematical models are based on conservation of energy theory. It

implies collisions, bound and rebound of particles, and adhesion of particles

and filters. This is an important theory of filtration. For further research, it would

supplement this project to study the particle movement and establish a logical

CFD model. This will consider the reaction between particles, particle and

surface, particle and filtration materials.

2.4 Numerical Modelling

To study the filtration mechanism, the tiny particles (micron-scale & nanoscale)

are not easy to observe from the experiments, so the numerical method and


CFD simulation could be the solution. All the simulations are based on physics

theory and mathematics approach, so the basic theory has to be prepared

before the modeling process. For example, particle-gas flows of fluid

dynamics, filtration theory and numerical methods are all the preparatory

theory. Then, to study the filtration process, CFD simulation can help people

to study the fluid and particles flowing through the filter. For some conditions

such as inlet and outlet, researchers can study the results from experiments

or theoretical calculation. If people want to study the relationship between

particles and filter in microcosmic view, it is very difficult to observe. This study

must consider the fluid flows, particle movements, and the particle-particle

interaction, particle-wall interaction, as well as particle-filter interaction. Then,

the researcher could select a suitable numerical method and select the

suitable software.

2.4.1 Conventional CFD Method

In terms of conventional CFD method, the most popular one is implementation

of the Navier-Stokes (N-S) equations, which is a typical Eulerian method

(Vasquez, Walters & Walters, 2015). N-S equations are widely used for solving

CFD problems, especially in the commercial software. This method can

compute the fluid motion of viscous fluid substances. The N-S equation of

Eulerian method is a continuous method for the fluid simulation (Liu, van

Wachem, Mudde, Chen, van Ommen, 2016 & Vasquez et al., 2015 & Pilou,

Tsangaris, Neofytou, Housiadas, Drossinos, 2011). Although the conventional

CFD method does not have the ability to solve particle flows, it can be the

governing equation to simulate the carrier fluid (Liu et al., 2016 & Pilou et al.,

2011). There are some pieces of commercial software and open source

software that can be selected for running the simulation.

ANSYS Fluent is a powerful commercial software, which is a piece of

conventional CFD software. To study the fluid flow, the N-S equation is written

as (Andersson, 2015):


𝜌𝜕��

𝜕t+ 𝜌(�� ∙ ∇��) = −𝑝 + 𝜇 ∙ ∇2�� + 𝜌 ∙ 𝑓

(9)

ANSYS Fluent has included multiphase modelling approaches, which are the

Euler-Euler approach and the Euler-Lagrange approach. It shows that the

Euler-Lagrange approach with a discrete phase model (DPM) can achieve

particle tracking, but the DPM has a limitation on particle-particle interaction,

in which the collisions and breakup are indirect (ANSYS Fluent User’s Guide,

2015). Between the continuum and discrete phases, there is an exchange of

momentum, mass and energy (Brikmukhametov, 2016). After 2016, ANSYS

Fluent has the discrete element method (DEM) add-in to enhance the particle

collision. The particle tracking is considered in a Lagrangian reference frame

of ANSYS Fluent. This can integrate the force balance on each particle to

predict the particle movement.

Also, the conventional CFD method must consider mesh sizes for the ANSYS

Fluent, when the particle size smaller than 1 µm would cause a stability issue;

because the mesh size must be much smaller than particle size it is difficult to

generate the small mesh size using Fluent. Another consideration is the

computational domain size, because of the limitation of solving the N-S

equation.

As alternative software, CFDEM could be another option, but it has limited

compatibility in the mesh process (Kuruneru, Sauret, Saha, & Gu, 2016).

OpenFOAM could be another option; it is open source software, and can adjust

the mesh size manually, but the limitation of a conventional CFD method

should be considered as well.

The multiphase flow of the Euler-Lagrange approach is a continuum model, so

the size of computational domain and size of particle are the important

consideration for the selection of a conventional CFD method and software.

Some researchers have coupled a conventional CFD method with DEM to

study particle filtration or deposition (Qian, Huang, Lu, Han, 2014 & Kuruneru


et al., 2016). Qian et al. (2014) have studied a complex mimic structure of

particle filtration; the particle size is 2 µm to 3 µm and the computational

domain is 200 µm × 100 µm × 100 µm. It is a 3D simulation; the results have

only shown the large number of particles’ filtration of a complex fibrous media.

Kuruneru, Sauret, Saha, & Gu., (2017) have studied the particle deposition;

the particle size is 50 µm and the computational domain is 4 mm × 0.6 mm.

This research has studied an idealised structure, but the particle size and

computational domain are too large to compare with DPM filtration.

2.4.2 LBM Approach

The Lattice Boltzmann method (LBM) is a class of CFD method. A brief

summary of some of the relevant concepts in LBM is presented in some

textbooks, in which LBM is the numerical method for the random motion of

particles as a kinetic model. The LBM is a mesoscopic description of the

motion of gas particles using the atomic probability of entropy (Suzuki &

Senba, 2010). For further studies in two phases, fluid and particles, LBM is an

alternative method to solve the multi-phase flow simulation. The further

proposed study is a filtration flow simulation, which will consider small particles

in different sizes as well the gas flow. The LBM-CFD studies offer more

detailed results, including fluid flow, particle transport, particle deposition, and

heat transfer (Wagner, 2008). This is because of the development of LBM,

which is a tool for use instead of the Navier-Stokes equation and simulating

complex fluid with collision models such as Bhatnagar-Gross-Krook (BGK)

flows. The BGK model shows that LBM can be considered as a special

discretised form of the continuous Boltzmann equation (Latt, 2008). The fluid

can be considered as a Newtonian fluid.

Firstly, studying the 2D square case can make clear an understanding for

LBM:

• Streaming steps

Generally, the model can be divided into a nine-square structure. In fact,

each arrow corresponds to a whole set of particles, the so-called particle


populations or particle distribution functions. In the current sketch, the

motion of particles is restricted to nine potential moves. Either a particle

moves to respective neighbouring cells or rests in the current cell,

shown in Figure 4. The following denotes the nine directions that the

particles can move in: C0, C1, and so on, as shown in Figure 4. In C0 to

C8 the scale is such that for a given time in ∆𝑡 the particles

simultaneously move from one cell to a neighboring one. To keep it

simple, it is assumed that the mesh size ∆𝑥 and the time interval ∆𝑡 are

equal to 1. The vectors C0 to C8 are called lattice velocities.

Figure 4: 2D case (D2Q9)

The transport of particle distributions to neighbouring cells is called streaming

step LBM. Basically, this models the convective transport in the fluid flow,

where all distributions are copied to the neighbouring cells. This also fills the

current cell in a new set of distributions.

Let the particles collide locally inside each grid cell so the particle populations

are redistributed. Both mass and momentum need to be concerned during a

collision. If each particle population is denoted with 𝑓0, 𝑓1 as forces up to 𝑓8, it

can compute the mass per grade as rho from the sum of the distributions,

equation 10. There is momentum that arises from the sum of the terms of 𝑓𝑖

times 𝑐𝑖 , equation 11. To model the collision process, the most common

collision model is given by the BGK model. First, it can compute mass and

momentum inside the single grid cell from the distributions that have just

entered. Then, the equilibrium distribution 𝑓𝑒𝑞 is computed. The vector product


used, for example for 𝑐𝑖 and 𝑢 in this formula, corresponds to well-known in a

product. Computing mass and momentum from the equilibrium distributions

returns the same values for O and u, s if we use 𝑓0 to 𝑓8 (equation 12), this is

basically due to a clipper choice of the lattice weights wi. It may just do the

computation by hand to understand what is basically happening and check out

the isotropic structure of the lattice velocities and weights, 𝑤0,2,6,8 = 1/36 ,

𝑤1,3,5,7,=1/9, 𝑤4=4/9, 𝐶𝑠=1/√3,

𝜌 = ∑ 𝑓𝑖𝑖 (10)

𝜌�� = ∑ 𝑓𝑖𝑐𝑖𝑖 (11)

𝑓𝑖𝑒𝑞 = 𝑤𝑖𝜌(1 +

𝑐𝑖 ∙��

𝑐𝑠2 +

(𝑐𝑖 ∙��)2

2𝑐𝑠4 −

��∙��

2𝑐𝑠2) (12)

𝑓𝑖 ∶= 𝑓𝑖 −1

𝜏(𝑓𝑖 − 𝑓𝑖

𝑒𝑞) (𝜏 ∈ (0.5,2)) (13)

where a 𝑢0 is the initial velocity for 𝑢, Re= (inertial force)/ (viscosity force) is the

Reynolds number. The inertial force is computed from 𝑓0, 𝑓0 is computed from

𝑢0. The expression of the equilibrium function can basically derive from LBM

distribution in the low-velocity limit, that means for flow velocities in which 𝑢

are much smaller than the speed of sound (‖��‖ ≪ 𝑐𝑠). Finally, the distribution

𝑓𝑖 towards the equilibrium distribution at a given collision frequency 1/ 𝜏. 𝜏 is

chosen, such that the correct viscosity of the considered fluid is obtained. For

𝜏 =1, the relaxation process is that the distributions 𝑓𝑖 exactly to the

corresponding counterparts 𝑓𝑒𝑞 of the equilibrium distribution (equation 13).

That means the BGK model basically pushes all distributions 𝑓𝑖 towards to the

equilibrium state. Due to the numerical stability 𝜏 needs to be in the range 0.5

to 2.0.

It shows LBM has the better viscosity performance than N-S equations, so it

can be the carrier fluid for particles. LBM is a grid-based method, and the

model of LB equations is totally suitable for energy conservation and

momentum conservation; it can simulate the microscopic flows and complex

porous media to make sure simulations of the microscopic view are united with

the whole domain. All the equations are based on kinetic theory. LBM has


some limitations. It is not suitable for high-Mach-number flows, nor is it suitable

for highly compressible fluid.

2.4.3 Discrete Element Method (DEM)

DEM is a numerical method to compute the motion and effect of a large

number of small particles, and it is a well-established method for particle-

particle systems (Leonardi, Wittel, Mendoza, & Herrmann, 2014). Also, DEM

is a finite size particle method, so the characteristics of each particle, such as

shape and size, have to be considered. The relationship of particles is based

on Newton’s second law, as shown in Figure 5.

Figure 5: Illustrations of Particle-solid relationship of Hertzian model (Qian

et al., 2014)

Between the particles, each two particles have interactions in tangential

direction and normal direction; this is based on the Hertzian model, shown in

Figure 5. The DEM can be applied for granular and discontinuous flows. The

DEM approach can only simulate the particles’ motion, so selecting the DEM

code must consider coupling with a fluid flow code.

The limitations of DEM are that it is difficult to develop a suitable carrier bed;

particles conditions have to be considered clearly. For these reasons,

sometimes coupling DEM and a conventional CFD method (NS) together is a


choice in solving the particle-fluid flows, because DEM is an efficient tool in

modelling and tracking the particle phase.

2.4.4 Coupling of DEM and LBM

It is known that to simulate both the gas and particle dynamics of the transport

and filtration process, it is necessary to employ some methods in coupling

strategy. Both DEM and LBM have limitations that are the complement of

relation. Many researchers used this method to simulate particle-gas flows.

Coupling of DEM and LBM will be proved to be a powerful numerical tool in

both qualitative description and qualitative analysis in particle-fluid flows (Han

& Cundall, 2016 & 2013). The wide implementation of DEM is particle flow

code (PFC). Some researchers coupled PFC and LBM to run the simulation

(Han & Cundall, 2016 & 2013). Coupling these two methods is going to

simulate the cases that are close to the real phenomenon. Comparing this

research topic with others’ research, coupling DEM and LBM is suitable for this

research.

The coupling procedure is as follows: at each time step, the equations of

motion for DEM particles are first solved by obtaining the particle positions and

velocities; this enables the state of each LBM cell to be determined; the LBM

calculation is then carried out to yield the fluid velocity and pressure fields,

from which the drag forces acting on particles can then be computed (Figure

6); the forces acting on particles and each fluid cell are used to update the

positions and velocities of particles at the next time step. This procedure is

repeated until a specified time step is reached (Xue et al., 2015). The current

study of this implementation is to simulate the interaction between particles

and fluid.


Figure 6: The coupling procedure of DEM-LBM (Xue et al., 2015)

Furthermore, another coupling concept is present by Han and Cundall (2016),

when in the equation of motion, Fi is the sum of all the external forces, which

is acting on the particle, so it is a vector of resultant force; m is total mass of

the particle; 𝑥�� is the vector of acceleration; g is gravity. Mi is the resultant

moment acting on the particle; 𝐼 is the inertial moment of the particle; 𝜃�� is the

rotation acceleration. In the force-displacement equation, 𝐹 𝑖𝑛 is the normal

component vector of the contact force; Kn is the secant normal stiffness; Un is

the normal component vector of the displacement; ∆𝐹𝑖𝑠 is the incremental

shear component vector of the contact force; Ks is the tangential shear

stiffness; ∆𝑈𝑖𝑠 is the incremental shear component vector of the displacement.

Note stiffness properties (i.e., Ks and Kn) are not necessarily constants, e.g.,

in the Hertz-Mindlin model, they are dependent of particle radii, contact force

and other material properties (Itasca Consulting Group, 2008). In each

computational loop, Newton’s second law is solved at all the contacts. Then,

the additional forces need to be applied on this step. The additional forces are

the fluid forces. The two methods coupled with fluid forces are applied on

particles and then modifiy the collision, which is based on the time steps,

shown in Figure 7 (Han & Cundall, 2016). This implementation of LBM-DEM is

prepared for the particle flow through a complex porous media.


Figure 7: DEM-LBM coupling system (Han & Cundall, 2016)

Another option is an open-source programming library, Mechsys (Galindo-

Torres, 2013). The coupling method is based on the immersed boundary (IB)

method introduced by Owen and Feng (2007), which uses LBM to solve the

Navier-Stoke equation and the IB method to couple the DEM particles and

carrier fluid. Owen’s method has only considered the spherical particles;

Galindo-Torres has extended Owen’s method by using the sphero-polyhedron

technique. Mechsys is able to simulate complex particles and complex porous

media. For these reasons, the complex structure and carrier fluid can be

simulated by using Mechsys. It seems that Mechsys could be the powerful tool

to study the filtration effect.

Han & Cundall, (2013 & 2016) have used the LBM-DEM method to study the

interaction of particles and porous media; the particle size is 1 mm, so it is not

a filtration study. Zhou et al. (2018) have studied the micron particle flow

through a complex porous media, the concentration is on particle suspension

flow and permeability impairment, the model being close to the filtration

studies. Mino, Sakai, & Matsuyama (2018) have studied a filtration case, which

is the particle flows passing through a single pore of membrane. In all the

studies shown, coupling of LBM and DEM is able to simulate DPM filtrations,

in which the conditions include micron particle motions, particle-fluid

interactions, complex porous media, and particle filtration.


For studing the particle filtration phenomenon, the software should have the

ability to simulate the large number of particles, complex porous media and

carrier fluid. LBM can study the fluid flow through the micron scale, and DEM

can study the large number of particles’ movement. Mechsys coupled these

two methods and gives a solution to simulate complex porous media, so

Mechsys should be the option.

2.5 Research Gaps

There are some research gaps relevant to this study that remain uncovered by

the literature review.

1. For micron scale particle motion there are a limited number of previous

studies investigating the coupling of LBM-DEM methods, particularly

studies focused on filtration of diesel particulate emissions.

2. Experiments are not capable of capturing the mechanism of particle

deposition inside a filter medium.

3. There are considerable uncertainties about the effects of particle

properties (e.g. size and density), fluid velocities and filter geometry (e.g.

fibre size, orientation and porosity) on the filtration effectiveness.

4. Number of filtered particles, location of particle gathering, pressure drop,

and filtration time are considered to quantify the filtration ability.

Chapter 3: Research Methodology 29

Chapter 3: Research Methodology

The increase of diesel engine applications makes the public and researchers

consider the way to control and limit the emissions from those applications, in

particular particulate matters that are responsible for cancer. From the

research gaps and objectives, this project is going to use an advanced

numerical method to study the relationship between microparticles and fibrous

filters. This research will use Mechsys open source code (Galindo-Torres,

2015; Galindo-Torres, 2013), which has already coupled LBM and DEM

methods, then analyse particle-laden flows through different configurations of

fibrous filters. This methodology will support the characterisation of the effects

of particle properties (diameter, density, velocity) on the filtration process and

understanding and identifying the key characteristics of the filters (geometry,

porosity) that affect the filtration mechanisms and efficiency of idealised 2D

fibrous filters. The research will only focus on two-dimensional (2D) cases as

it can accurately simulate the cross section of fibrous filters and, more

importantly, significantly reduce the computational cost of each simulation.

3.1 Research Steps

Based on the literature review, the assumption of this research is that the

fibrous filters (disposable DPFs) can assist current diesel exhaust systems to

control and limit the emission of particulate matters and thus reduce negative

environmental and health problems (Ristovski et al., 2012, & Rahimi Kord

Sofla, 2015). An effective way to assess the validity and performance of such

filters is to use advanced numerical modelling to study the gas and

microparticles flow. In this research, an LBM-DEM approach is deployed to

study micron particles filtration. The innovation of this research lies in the

simulation results obtained. In particular, some researchers applied LBM-DEM

to study particles’ transport or particles’ movement through a porous media,

also the studies of particles or porous media were larger than micron scale, no

one has ever used LBM-DEM to study micron particles filtration. Due to the

30 Chapter 3: Research Methodology

limited research time and computational costs, this research will focus on 10

µm particles only, for developing and validating the model.

The following steps are required to conduct this research:

1. To identify a robust numerical model that is appropriate for microscale

particles and fluid simulations. An appropriate numerical model was

selected for simulating the movement of microparticles and investigating

the influence of a carrier fluid. Mechsys was chosen as a solver for

coupling LBM and DEM methods. To validate the numerical methods of

gas-particle flow. The LBM-DEM method uses the LB method to solve

the N-S equations to study fluid flows and uses DEM to study particle

movement (Galindo-Torres, 2013). This step is to initialize all the

research, which is to develop and setup the model or configuration of

the simulation.

2. To implement and validate the LBM-DEM approach on 2D clear channel,

which is based on particle-laden laminar flows. Also, to compare the

simulation results with FVM-DEM, and ascertain what the necessity is

for further study. These 2D clear channel cases are going to study the

ability of fluid flows, pressure drop, and deposition fraction (Kuruneru et

al., 2016). The 2D clear channel studies can help the candidate to

optimise LBM-DEM solver in Mechsys, and also optimise the boundary

conditions for the 2D modelling studies, then, to implement the LBM-

DEM approach on a simple idealised 2D model, in which the obstacles

are parallel. The 2D pattern of obstacles is going to follow modelling of

the real structure of a fibrous filter in micro structure. Compare the 2D

obstacles cases with FVM-DEM cases and other LBM-DEM cases which

have the similar configuration. The 2D simulations are close to real

structures, so this can assist the candidate to study the particle capture

process by obstacles or pattern of obstacles. This step corresponds to

the validation for first objective and is used to prepare for the second

objective.


3. To establish some 2D geometries that have the porosity of 90%. The

pattern or structure is close to real fibrous filter but is more complex than

the idealised model in step 2. It will be a porous media or a fibrous media.

The input parameters will follow step 2, validation cases. The results of

simulations can be compared with each other. Pressure drop, and the

ability of filtration, will be the most important findings, from which the

most effect configurations can be discovered. This step is to prepare the

second and third objectives.

4. To investigate particle properties, such as size, density, etc. Use the

select configurations keeping 90% porosity, particle velocity and other

boundary conditions that will have different settings, to perform

numerical investigations based on an idealised and real 2D fibrous filter

structure. This step is to investigate the filtration process and mechanism,

which corresponds to the second and third objectives.

5. Based on step 4, use the selected configurations with 75% porosity then

run the simulations. The results of simulations will be validated against

results from the 90% porosity cases, and analytical models available in

the literature. To analyse the simulation results, this step responds to the

third and fourth objectives.

3.2 Rational of LBM-DEM in Mechsys

In order to satisfy the objectives of this research, an appropriate method must

be selected. The approach of such clear and detailed methods in the resulting

area depends on the research objectives and the strengths and limitations of

the various numerical and experimental methods, which are used by other

researchers as highlighted broadly in the literature review section.

As the literature review mentioned, the particle filtration process includes

particle-particle interaction, particle-fluid interaction and particle-obstacle


interaction. The consideration is that the structure of the filter would be

complex, and the gaps between the filter obstacles would be close to the

particle diameter. Also, for studies of filtration mechanics and particle tracking,

the computational domain would be very small. LBM can simulate the air flow

for the small domain and complex structure, and the input parameter is easier

to set up so that the input parameters only consider the input velocity and

direction. DEM can simulate the particle movements, the property of particles

and the interaction between particle-particle and particle-obstacle so they are

all included. The conventional CFD methods, which are FVM solvers to solve

the NS equations, have been coupled with the DEM method such as in

Kuruneru’s research (2016 & 2017). These methods or solvers have good

performance for large-scale simulations, but for small scale or pore scale they

have some limitations (Galindo-Torres, 2013). This research will study the

particle filtration progress, in which the maximum size of a particle is 10 µm

and the filter materials create small pores. It is due to the LBM having good

effect such as locality of the dynamic steps, and solving the porous media

problems, that LBM and DEM can be coupled to be the solver (Galindo-Torres,

2013).

3.2.1 Theory of LBM Model in Mechsys

The development of LBM is implemented in Mechsys to solve the fluid

dynamics problem, including 2D model (D2Q9) and 3D model (D3Q15). The

LBM approach of Mechsys can be selected D2Q9 model, which is a robust 2D

LB discretisation scheme. The idealised model shows that the domain can be

divided into square lattice, with spacing h in the length and width of the lattice,

as shown in Figure 8. Each node can move to its eight immediate neighbours.


Figure 8: LB discretisation and D2Q9 model of Mechsys

The centre node has the velocity 𝑒0=0 and moving to the other nodes the

velocities are ei (i=1, …8). The nine discrete velocities can be defined as:

𝑒0 = (0, 0)

𝑒𝑖 = 𝐶 (cos𝜋(𝑖 − 1)

2, sin

𝜋(𝑖 − 1)

2) (𝑖 = 1, 2, 3, 4)

𝑒𝑖 = 𝐶 (cos𝜋(2𝑖 − 9)

4, sin

𝜋(2𝑖 − 9)

4) (𝑖 = 5, 6, 7, 8).

(14)

In equation 14, C is the lattice speed, which is given as =ℎ

∆𝑡 , ∆𝑡 is the discrete

time step.

For Mechsys, the Boltzmann equation is solved in the discrete lattices. The

governing equations, N-S equations, are described by the Chapman-Enskog

expansion. The collision operator is the BGK model, which is simplified as a

linearised function. The developed equation is:

𝑓𝑖(𝑥 + 𝑒𝑖∆t + ∆t) = 𝑓𝑖(𝑥, t) −1

𝜏(𝑓𝑖(𝑥, t) − 𝑓𝑖

𝑒𝑞(𝑥, t)) , (𝑖 = 0, … ,8). (15)

In this equation, x is the position vector, 𝑓𝑖 defines the discrete velocity

direction of 𝑒𝑖 in the lattice, 𝑓𝑖𝑒𝑞

is the corresponding equilibrium distribution.

Another consideration is the fluid kinematic viscosity (𝜗). It is written as


𝜗 =(𝜏 − 0.5)∆𝑥2

3∆t .

(16)

It is shown that ∆𝑥 is the lattice size, which is same as h in Figure 8, 𝜏 is a

dimensionless parameter, relaxation time. It is known that 𝐶 is the lattice

speed, so the equilibrium distribution for the D2Q9 model is given as

𝑓0𝑒𝑞 = 𝜔0𝜌(1 −

3𝑢2

2𝐶2)

𝑓𝑖𝑒𝑞(𝜌, 𝑢) = 𝜌𝜔𝑖 (1 +

3𝑒𝑖𝑢

𝑐2+

9(𝑒𝑖𝑢)2

2𝑐4−

3𝑢2

2𝑐2) (𝑖 = 1, … 8).

(17)

In this equation 𝜔 are the weighting factors, which 𝜔0 =4

9, 𝜔1,2,3,4 =

1

9, 𝜔5,6,7,8 =

1

36.

The fluid density (𝜌) and velocity (u), which are the macroscopic fluid variables,

can be defined from the moments of the distribution functions given as

𝜌 = ∑ 𝑓𝑖

8

𝑖=0

, 𝜌𝑢 = ∑ 𝑓𝑖𝑒𝑖

8

𝑖=1

. (18)

Based on the LBM approach, there is a limitation for the compressive flow. The

Fluid pressure P has a relationship with speed of sound and fluid density 𝜌,

which is:

P = 𝑐𝑠2𝜌 (19)

3.2.2 Theory of DEM Model in Mechsys

For the modelling of moving or fixed particles, a DEM approach is selected.

Mechsys has implemented DEM modelling of the particles’ cohesive force and

contact force to study the particle movements. The relationship of particles is

based on Newton’s second law.

𝑚𝑖��𝑖 = 𝐹𝑖,𝑛 + 𝐹𝑖,𝑡 + 𝐹𝑖,𝑓 + 𝐹𝑖,𝑏 (20)

𝐼𝑖

𝑑𝜔𝑖

𝑑𝑡= 𝑟𝑖,𝑐 × 𝐹𝑖,𝑡 + 𝑇𝑖,𝑟

(21)

Equation 20 and 21 show, where 𝐹𝑖,𝑛 is the normal particle-particle contact

force, 𝐹𝑖,𝑡 is the tangential particle-particle contact force. 𝐹𝑖,𝑓 is the force that


the surrounding fluid phase may exert on the particles. 𝐹𝑖,𝑏 has summarised

other body force, including gravity, electrostatic and magnetic forces. 𝑇𝑖,𝑟 is an

additional torque on the particle.

The cohesive forces are given by

𝐹𝑛𝑐𝑜ℎ𝑒 = 𝑀𝑛

𝑐𝑜ℎ𝑒𝐴𝜀𝑛𝑛

𝐹𝑡𝑐𝑜ℎ𝑒 = 𝑀𝑡

𝑐𝑜ℎ𝑒𝐴𝜀𝑡𝑡,

(22)

the forces having both normal and tangential directions. 𝑀𝑛𝑐𝑜ℎ𝑒 and 𝑀𝑡

𝑐𝑜ℎ𝑒 are

the elastic modulus for both directions modelling the material, 𝜀𝑛 and 𝜀𝑡 are the

strains of two adjacent particle faces, 𝑛 and 𝑡 are the unit vectors for both

directions. When 𝜀𝑛 > 𝜀𝑡, the particles have the broken bonds which are shear

failure, and when 𝜀𝑛 < 𝜀𝑡, the particles have tensile failure. For the particle

collisions, the contact forces are given by

𝐹𝑛𝑐𝑜𝑛𝑡 = 𝐾𝑛∆𝑙𝑛𝑛

𝐹𝑡𝑐𝑜𝑛𝑡 = 𝐾𝑡∆𝑙𝑡𝑡,

(23)

where 𝐾𝑛 and 𝐾𝑡 are the stiffness constant for both normal and tangential

directions. ∆𝑙𝑛 and ∆𝑙𝑡 are the overlapping lengths of both normal and

tangential directions. The relationship of 𝐹𝑛𝑐𝑜𝑛𝑡 and 𝐹𝑡

𝑐𝑜𝑛𝑡 is given by

𝐹𝑡𝑐𝑜𝑛𝑡 > 𝜇𝑓𝐹𝑛

𝑐𝑜𝑛𝑡

𝐹𝑡𝑐𝑜𝑛𝑡 = 𝜇𝑓𝐹𝑛

𝑐𝑜𝑛𝑡𝑡,

(24)

𝜇𝑓 is the friction coefficient.

Using DEM, mechanism for diesel filters can be numerically obtained for the

first aim.

3.2.3 Theory of Coupling LBM-DEM Model in Mechsys

This research will employ Mechsys, which uses LBM modelling for the carrier

fluid and DEM modelling for the particles’ movement. As the literature review

shows, LBM has a better viscosity effect than the conventional CFD method,

so coupled LBM-DEM would be the better numerical method to simulate the

particle and fluid interaction, for the smaller and lighter particles.


Mechsys has coupled LBM and DEM. The coupling of LBM and DEM is on the

immersed boundary method (Galindo-Torres, 2013; Sauret et al., 2017). In

Mechsys, the NS equations are solved by LBM. The NS solver module of LBM

solves a set of density functions 𝑓𝑖 for each node in the square lattice.

Some studies have used MechSys to run the simulations. The coupling of

LBM-DEM in MechSys shows:

𝑓𝑖(𝑥 + 𝑒𝑖∆t, t + ∆t) = 𝑓𝑖(𝑥, t) − (1 − 𝐵)1

𝜏(𝑓𝑖(𝑥, t) −

𝑓𝑖𝑒𝑞(𝑥, t)) + 𝐵Ω𝑖

𝑠 .

(25)

The fluid-solid interaction term Ω𝑖𝑠 is derived by the bounce-back for the non-

equilibrium part:

Ω𝑖𝑠 = [𝑓−𝑖(𝑥, 𝑡) − 𝑓−𝑖

𝑒𝑞(𝜌, 𝑣𝑝)] − [𝑓𝑖(𝑥, t) − 𝑓𝑖𝑒𝑞(𝜌, 𝑣𝑝)]. (26)

𝐵 =𝛾(𝜏 − 0.5)

(1 − 𝛾) + (𝜏 − 0.5)

(27)

In equation 26, 𝑣𝑝 is the solid velocity at position x. In equation 25 and 27, B is

a weight function depending on 𝛾 in each cell, when 𝛾 = 0, 𝐵 = 0; and 𝛾 =

1, 𝐵 = 1 (Chen, & Wang, 2017 & Zhang, 2016). The coupling equation 26 can

recover the standard lattice Boltzmann equation and bounce-back rule for 𝛾 =

1 and 0. The relationship between DEM particle and hydrodynamic force is

calculated by the change of momentum in all cells covered by the particle,

which means particles must be larger than the LBM cells; n is the number of

cells covered by the DEM particle, shown in equation 28 (Chen & Wang, 2017).

𝐹 =∆𝑥3

∆t∑ 𝐵𝑛(∑ Ω𝑖

𝑠𝑒𝑖)

𝑖𝑛

(28)

The torque is shown in equation 30, where 𝑥𝑛 is the position of cell, 𝑥𝑐𝑚 is the

mass centre of the DEM particle.

𝑇 =∆𝑥3

∆t∑ [(𝑥𝑛 − 𝑥𝑐𝑚)𝐵𝑛(∑ Ω𝑖

𝑠𝑒𝑖)

𝑖

]

𝑛

(29)


3.3 Configuration Set-up in Mechsys

Mechsys is based on C++ language for the implementation of simulation tools

in mechanics. The solver of Mechsys including LBM, DEM and coupled LBM-

DEM, the LBM-DEM solver, can simulate the fluid solid interaction. This can

be applied to solve the filtration problems for this research. This research will

select the D2Q9 scheme, as the core solver of LBM, which is a two-

dimensional simulation scheme.

The customisation of Mechsys is to rebuild the template of the simulation case.

Initially, the parameters, which are required by Mechsys to run the cases, need

to be found out. Secondly, the basic Mechsys templates are C++ code, which

is dimensionless value. For the real application, the dimensionless value must

be converted to the dimensional value. Thirdly, rebuild the filter configuration

and computational domain.

Firstly, for the fluid, the Mechsys cases require building of an LBM domain

which is divided by nodes (nx, ny) to make the small lattices. For the 2D cases,

both X and Y axis must be more than 150 nodes; these nodes are

dimensionless value. Then, set a lattice size (dx) as a real dimensional value

and the nx × dx, ny × dx are the real size of the domain. The other parameter

that is required by Mechsys is kinematic viscosity ( 𝜈 ). This value is a

dimensional value, so it can directly use the real value of the fluid. This value

is related to the lattice size (dx), lattice time (dt) and relaxation time (𝜏), shown

in equation 30.

𝑑𝑡 = 𝐶𝑠2(𝜏 − 0.5)

𝑑𝑥2

𝜗 (30)

Then, another required value is dt, this is the lattice time and it will be the same

as the simulation time step; it is also converted to the dimensional value by

using dx. The relaxation time (𝜏) is another important parameter for LBM. The

value of 𝜏 is 0.5 < 𝜏 < 2, due to the numerical stability. 𝜏 is related to the dx, dt

and kinematic viscosity (𝜈). Furthermore, to set the boundary conditions of the

fluid, the density of the fluid can directly use the real value when the lattice


value has been converted to the dimensional value. The other boundary

conditions, such as gravity and fluid velocity, can use the real value.

Secondly, the DEM particles are based on the LBM domain, so the DEM

particles must comply the LBM parameters. To make sure the particle size

complies with the LBM domain, the particle diameter (dp) must be 10 times

larger than lattice size, which is dp>10dx. To limit computational cost the

particle size is restricted to 10 µm for developing the filtration model. Once

developed and validated this model will be able to use for smaller particles.

This can make the simulation stable and give a clearer visualisation. The other

parameters are particle density, particle velocity, initial positions of particles,

and stiffness constant. The stiffness constant affects the particle-particle

interaction and particle-wall/obstacles interaction. The value of stiffness

constant is related to the particle shape and particle size.

3.4 Post-processing

The simulation results focus on particle deposition, filtration time, filtration

fraction, number of filtered particles, pressure drop between inlet and outlet,

and location of particles’ accumulation. These are key parameters to

characterise the effectiveness of the filters. For example, any increase of

pressure drop is an indication of particle accumulation in the filter, blocking the

flow and building up pressure, while the filtration fraction is a direct measure

of the particles trapped in the filter and will be used to compare the performace

of different filters.

The filtration fraction is defined as the percentage of filtered particles over

injected particles during the filtration time, shown in equation 31.

𝒇𝒊𝒍𝒕𝒓𝒂𝒕𝒊𝒐𝒏 𝒇𝒓𝒂𝒄𝒕𝒊𝒐𝒏 =𝒇𝒊𝒍𝒕𝒆𝒓𝒆𝒅 𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆𝒔

𝒊𝒏𝒋𝒆𝒄𝒕𝒆𝒅 𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆𝒔× 𝟏𝟎𝟎% (31)

LBM-DEM has some limitation to present the pressure conditions (Junk &

Yang, 2009; Sauret et al., 2017). The pressure is related to the lattice speed

and fluid density and can be calculated using equation 19 in which 𝐶𝑠 is the


sound speed of the lattice and is a dimensionless value. However, the lattice

velocity 𝐶 can be a dimensional value or a dimensionless value.

In the case where the lattice values are considered as dimensionless, the

lattice velocity and sound speed of the lattice are defined as:

𝐶 =𝑑𝑥

𝑑𝑡= 1, 𝐶𝑠 =

1

√3

(32)

If the lattice size and time steps are calculated based on the dimensional

values, the sound speed of the lattice is obtained from equation 33 (Feng, Han,

& Owen, 2007).

𝐶 =ℎ

∆𝑡, 𝐶𝑠 =

𝐶

√3 (33)

In Mechsys, when dimensional parameters are used to control the LBM

stability, the lattice sound of speed is set by equation (33) and thus the

pressure can be calculated as p=𝜌𝐶2

3. In the case where the computational

domain and/or the lattice size are too small, the lattice velocity is set to unity

to ensure the stability of the LBM method. In that case, the lattice speed of

sound becomes 1

√3 and the pressure is defined as p=

𝜌

3. This approach is

applied in all the results presented in Chapter 5.

Chapter 4: Validation of LBM-DEM model 41

Chapter 4: Validation of LBM-DEM model

4.1 Validation of LBM, Flow Around a Cylinder

This simulation is going to use Mechsys code and make a validation of the

Lattice Boltzmann (LBM) case, which is fluid flow around a cylinder. Mechsys

is an open source programming library for mechanical systems, which is

written in C++. The author is Sergio Galindo-Torres. Mechsys has an LBM

case, which is a D2Q9 simulation for the studies of fluid flow around a cylinder

(2D simulation).

Firstly, set up the computational domain. Set the diameter of the obstacle as

D. Then, from inlet to the centre of the obstacle is 20 times diameter, from the

outlet to the centre of the obstacle is 40 times diameter, and the boundary

walls to the centre of the obstacle is 20 times diameter, as shown in Figure 9.

Figure 9: Geometry of the computed domain

Secondly, to quantify the output of the simulation, Re=20 and Re=40 is the first

validation part. This part has compared the geometry of vortex street (Figure

10) with others’ research. Then, Re=100 to Re=1000 is the second validation

part. This part has compared the Strouhal number with others’ research.

42 Chapter 4: Validation of LBM-DEM model

Figure 10: Measurements of Geometry of Vortex street when Re<40

For Mechsys simulation, most important to note is that it can set the Reynolds

number as a constant for each simulation. The result of the LBM simulation is

shown in Table 2 and Figure 11.

Table 2: LBM simulation results

Mechsys

LBM

L a B θ

Re=20 18 7.1 8.4 43.63

Re=40 42 15 12 53.13

a b

Figure 11: Visualisation of LBM for Low Reynolds Number vortex, a.

Re=20, b. Re=40


Regenerate the geometry measurements, as L/a, L/b, a/b, and θ. The results

are shown in Table 3. These results show, for the low Reynolds number

(Re<40) simulation, Mechsys LBM code has a similar output to others’ results.

Table 3: To compare simulation results of dimensions’ ratio

L/a L/b a/b θ

Re 20 40 20 40 20 40 20 40

Experiment

(Coutanceau,

1977)

2.81 2.80 2.02 3.6 0.72 1.28 45 53.8

Immersed

interface

method (Xu,

2008)

2.58 3.11 2.16 3.73 0.84 1.2 44 53.8

IB solver

(Manueco et

al., 2016)

2.67 2.84 2.13 3.65 0.8 1.28 44 51

PISOFoam

(Manueco et

al., 2016)

2.76 2.99 2.14 3.85 0.77 1.29 44 52

Mechsys

LBM

2.54 2.8 2.14 3.5 0.85 1.25 43.63 53.13

The next step is to make the validation of Reynolds number between 100 to

1000. Then, to modify the code again and check suitable validation cases, for

which Manueco et al., (2016) have a validation paper. Furthermore, for

100<Re<1000 cases, the curve of Strouhal number and Reynolds number can

be plotted to show the relationship.

When the Reynolds number is larger than 40, the fluid flows will start to create

a Von Kaman Vortex street, which is asymmetric vortices undergoing periodic


oscillations by constantly interchanging their position with respect to the circle

(Lienhard, 1966). The Reynolds number is defined in equation 34, where 𝜐 is

kinematic viscosity of the fluid (m2/s), D is the diameter of cylinder (m), U is the

velocity of the fluid with respect to the object (m/s), 𝜌 is density of the fluid

(kg/m3), 𝜇 is the dynamic viscosity of the fluid (Pa.s). Also, Strouhal number is

given as equation 35, f is the frequency of the vortex shedding.

𝑅𝑒 =𝑈𝐷

𝜐=

𝜌𝑈𝐷

𝜇𝑓 (34)

𝑆𝑡 =𝑓𝐷

𝑈 (35)

Time analysis of the velocity can find the frequency, then calculate the Strouhal

number, shown in Table 4. It shows the Reynolds number increase from 100

to 1000, the maximum velocity and frequency have the increased tendency.

Table 4: Strouhal number analysis

Re Exp(St) Piso(St) IB(St) LBM(St)

vmax

(m/s) f (Hz) T (s)

100 0.165 0.165 0.165 0.17

0.141 0.12 525

200 0.191 0.193 0.192 0.1906

0.171 0.163 504

500 0.208 0.209 0.21 0.2011

0.179 0.18 498

550 0.209 0.21 0.212 0.2063

0.188 0.194 488

600 0.209 0.212 0.214 0.208

0.2 0.208 460

700 0.21 0.214 0.218 0.212

0.227 0.241 461

800 0.21 0.219 0.222 0.212

0.272 0.288 446

1000 0.21 0.22 0.232 0.228

0.288 0.332 408

The relationship between Reynolds number and Strouhal number can be

plotted in a line chart, shown in Figure 12. The LBM results compare with IB

simulation, pisoFoam simulation, and experimental results. When the Re=100,

LBM result is higher than others, St=0.17 and the other results are the same,

St=0.165. When the Re=200, all the results are very close, and LBM result is

the closest to the experimental result. When the Re ranges from 600 to 800,

the LBM results are also the closest to experimental results. Indeed, the

tendency of LBM results is increased from Re=100 to Re=1000, but compared


with others’ curve, this LBM curve is not smooth. The experiment curve is flat,

after Re=500. The IBM curve appears to have a linear increase. PISOFoam

results also presented a non-smooth line, and it is between the IB curve and

the experiment curve, when it is after Re=500. For the Mechsys LBM curve,

after Re=600, it is between the IB curve and the experiment curve. The further

studies will be micron scale simulations. As it is difficult to have Re>100, this

step of validation is to confirm the LBM code has the similar effects as others’

methods.

Figure 12: Results of Strouhal number of Reynolds number from 100 to

1000, experiment: Coutanceau (1977); PISOFoam: Manueco et al.,

(2016); IB: Manueco et al., (2016)

This validation section has studied the LBM simulations, which are fluid flows

around a cylinder 2D case. For Re=20 and Re=40, which created two

symmetric eddies behind the circle, LBM simulations gave very acceptable

results. When 100<Re<1000, LBM simulations gave the results in the suitable

range and correct tendency. When the Re=200, Re=600, Re=700, and

Re=800, at these points LBM simulations have the closest result to the

experimental results. Due to these simulation results, the Mechsys LBM code

has been validated. For further studies, the micron particles and domain will

0.16

0.17

0.18

0.19

0.2

0.21

0.22

0.23

0.24

50 150 250 350 450 550 650 750 850 950 1050

St

Exp

Piso

IB

LBM


be used; the Renolds number could be very small and the simulations should

be laminar flows. This LBM code can be used for further simulations.

4.2 Validation of DEM Code of Mechsys

Further research will use the LBM-DEM coupling method. Mechsys LBM code

has been validated, which is a considerable simulation tool for fluid flow.

Mechsys have DEM simulation capabilities for particle movement studies and

LBM-DEM coupling. It is considered, the validated DEM code can provide the

modelling of particles, for both validated codes (LBM and DEM) are going to

support the validation of coupled LBM-DEM code. If all the validations have

been done, Mechsys code can be the choice for use in further research.

DEM can compute the motion and effect of a large number of small particles.

Also, DEM can study the relationship between particle and particle, or particle

and wall in a practical manner. There are two steps of validation. First

validation is particle-particle collisions. Second validation is particle-wall

rebound.

4.2.1 Two-sphere Collision of DEM Simulation

First of all, a particle-collision case, which can study the relationship between

two particles, must be developed. The Mechsys tutorial case of two particles’

collision studies the dynamics of two non-spherical particles: a tetrahedron and

a cube. This case can be modified as a two-sphere collision simulation.

For this two-sphere collision, the validation can use the theory of conservation

of momentum, shown in equation 36, equation 37 and equation 38: p is the

momentum of particle, m is mass of particle, v is the velocity of particle. The

momentum conservation means, in a closed system, the total momentum is

constant. As for Scenario 1, when the initial condition is m1=m2, v1=1 m/s, v2=-

1 m/s, after the collision the velocities of m1 and m2 have been exchanged. The


second scenario shows that the initial condition is m2=0.5m1 and the velocity

is the same as Scenario 1. This scenario will use equation 39. The calculation

result is v’1=-0.333 m/s and v’2=1.665 m/s, and the two spheres change their

moving direction after collision. Scenario 3 is a case of moving sphere colliding

with a stop sphere. After the collision, the two spheres change velocities.

Scenario 4 is to calculate a two-spheres-collision in which m1=m2, v1=2 m/s,

v2=-1 m/s. After the collision, the two spheres have the same moving direction,

and the velocities are the same, which is 0.5 m/s. By using this theory,

comparing the manual calculation results and simulation results, the results

are the same; the simulation results are shown in Table 5. These four

scenarios are the typical physics studies of conservation of momentum.

𝑝 = 𝑚𝑣 𝑎𝑛𝑑 𝑝 = 𝑝’ (36)

𝑚1𝑣1 + 𝑚2𝑣2 = 𝑚1𝑣1’ + 𝑚2𝑣2’ (37)

𝑚1𝑣1’ − 𝑚1𝑣1 = −(𝑚2𝑣2’ − 𝑚2𝑣2) (38)

Velocity for head-on collisions: 𝑣′1 =𝑚1−𝑚2

𝑚1+𝑚2𝑣1 (39)

Table 5: Mechsys simulation results of particle-collisions

m1 (g) v1 (m/s) m2 (kg) v2 (m/s)

Scenario 1 Initial 8.76×10-3 1 8.76×10-3 -1

Final 8.76×10-3 -1 8.76×10-3 1


Final 8.76×10-3 -0.333 4.38×10-3 1.665

Scenario 3 Initial 8.76×10-3 1 8.76×10-3 0

Final 8.76×10-3 0 8.76×10-3 1


Final 8.76×10-3 0.5 8.76×10-3 0.5

These four scenarios are the spheres that have the diameter of 1 mm. Due to

the results of typical studies being the same, the validation could try the other

cases, which have smaller diameter, lower mass, and higher velocities. The

next studies will use the smaller particles with different diameter and initial

velocities, with the results shown in Table 6.


Table 6: Particle Collision studies with different velocity and particle size

Cases v’1 (m/s) v’2 (m/s)

d1=0.1 mm,

ρ=0.004 g/mm3,

m1=2.1×10-6 g,

v1=5 m/s

d2=0.02 mm,

ρ=0.004 g/mm3,

m2=1.676×10-8 g,

v2=1 m/s

Calculation

results:

4.90499 10.90499

Simulation

results:

4.8776 10.901

d1=0.1 mm,

ρ=0.004 g/mm3,

m1=2.1×10-6 g,

v1=10 m/s

d2=0.02 mm,

ρ=0.004 g/mm3,

m2=1.676×10-8 g,

v2=-10 m/s

Calculation

results:

9.6833 29.6833

Simulation

results:

9.0253 29.0452

To compare the calculations and simulations of these two cases, the result is

very close: the maximum error is 6.8%, the minimum error is 0.04%. The very

small difference of the calculations and simulations could be considered as

two technical reasons. Firstly, the time steps can be set smaller, for more

accurate value. Secondly, the visualisation software can only read four

decimals. The simulation results are close to the calculation results by using

the theory of conservation of momentum, so the particle-particle collision for

Mechsys DEM code can be used.

4.2.2 Sphere Rebounding of DEM Simulation

The next simulation is to study the particle and surface relationship. This

validation is going to compare a free-fall-particle bumping a flat solid surface.


The configuration of this validation is shown in Figure 13. This simulation will

study a particle from an initial position drop on the fixed surface and bump

back, because of the gravity (g=9.81 m/s2). Caserta, Navarro, and Cabeza-

Gomez (2016) have studied some parameters of a DEM-approach, such as

damping coefficient (η) and restitution coefficient (e).

Figure 13: Free fall of a single particle

Caserta's (2016) work studied three kinds of model, which are a Linear Spring-

Dashpot (LSD), and two non-linear models, HSD-A and HSD-B (Hertzian

Spring-Dashpot). HSD-A and HSD-B have a difference in computing the

damping force.

For the free fall studies, Caserta’s (2016) group has done four scenarios, which

each have two models with en=0.9 and en=0.7 (en is the normal restitution

coefficient). The example is shown in Figure 14 and redraws the curve.

Figure 14: HSD-A, en=0.7, Particle Centre PSosition (Caserta, et al.,

2016)


The Mechsys simulation results are shown in Figure 15 and Table 7. The

dashed curve shows the simulation result of Mechsys. It presents the particle

drop from the initial position, which is 5 m high measured from the top of the

particle. The first part of the curve shows the particle’s first time touching the

surface from the initial position. This curve has a high coincidence rate with

Caserta’s (2016) work. The first bouncing compares the top point of

simulations with Caserta’s (2016) work, with the simulation result having

1.87% difference. Then, in the second bouncing, the top point has 7.43%

difference, and the third bouncing has 17.52% difference. To calculate the

difference equation 40 can be used. For the case of the HSD-A model, en=0.7,

the Mechsys simulation result is acceptable.

ε=𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑙𝑢𝑒−𝑒𝑥𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑙𝑢𝑒

𝑒𝑥𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑙𝑢𝑒× 100% (40)

Table 7: Mechsys Results of The Real Time and Particle Centre Position

(h)

t (s) h (m)

0 0.5

0.1 0.45

0.2 0.3038

0.3 0.06

0.4 0.245

0.532 0.264

0.764 0.06

0.943 0.158

1.123 0.06

1.262 0.095

1.4 0.06


Figure 15: HSD-A Model, en=0.7, Compare Mechsys Result with Caserta

et al. (2016) Results of Particle Centre Position h,

It is shown in Figure 15, that the sphere drop from the initial state to the

surface has a similar curve, the second rebounding has a small difference,

then in the third and the fourth rebounding, the errors have been increased. It

could be considered this simulation and case study have different time steps,

so the measurement could have this small error.

4.3 LBM-DEM Validation

The validation of pure LBM and DEM codes of Mechsys has produced

acceptable results. From the LBM validation, it is shown when the Reynolds

number is less than 800, the output of Mechsys is close to the experimental

results. Furthermore, the pure DEM code also produced good results for

particle-particle collision and particle-wall bouncing motion. This validation is

going to use or modify the coupling code of LBM-DEM in Mechsys to find out

the suitability for the application of Mechsys.

One experimental work has been selected (Gondret, Lance & Petit, 2002),

which has studied the bouncing motion of spherical particles in fluids. The

material of spheres in this experiment has some physical properties: for steel,

density ρs (7.8×103 kg/m3), Young’s modulus E (240×109 Pa), Poisson’s ratio ν


(0.30),and maximal coefficient of restitution emax (0.97); and for Teflon, density

ρs (2.15×103 kg/m3), Young’s modulus E (0.4×109 Pa), Poisson’s ratio ν (0.46),

and maximal coefficient of restitution emax (0.80) . The physical properties of

the fluid are: for air, ρ (1.2 kg/m3) and dynamic viscosity μ (1.85×10-5 Pa∙s);

and for silicone oil (RV10), ρ (0.935×103 kg/m3) and dynamic viscosity μ (10-2

Pa∙s). Two cases have been selected, one is a Teflon ball in the air, another

is a steel ball in silicone oil (RV10).

Firstly, the simulation results will compare the height of the bouncing motion of

spheres at different times. Another is comparing the velocity of spheres at

different times. The first experiment has set the Re, St, and e, at the first impact

between Teflon sphere (d=6 mm) and fluid (air), which are Re=210,

St=7.8×104, and 𝑒=0.80. From these values, it is possible to control the initial

position or velocity of the sphere. The Mechsys simulation for the first case will

use the initial position of sphere as 0.038 m, measured from the bottom of the

sphere to the surface. The simulation results compared with experimental

results have been shown in Fig 16. The purple curve is the particle from the

initial position drop to the surface. The purple curve shows the bouncing motion

of the sphere. The first bouncing of the sphere did not reach the maximum

height of the experiment, the second bouncing is higher than the experimental

data, and the third bouncing height is almost the same as the experiment. The

top of first bouncing is clear, the difference is 10.97%. For the second top, the

difference is 0.32%. For the third bouncing, the difference is 1.43%. From

fourth bouncing to sixth bouncing, the difference is 4.86%, 6.73%, and 11.89%.

From this validation, although it is not totally the same, the bouncing motion of

simulation is close to the experiment, with the difference being less than 20%.

Next is to compare the velocity u as a function of time t.


Figure 16: 6 mm Teflon sphere bouncing motion in the air, h-t function, for

the experiment, at the first impact Re=210, St=7.8×104, and 𝒆=0.8

(Gondret, Lance & Petit, 2002)

The velocity versus time graph is shown in Fig 17. The movement of first

bouncing shows the u-t function is close to a straight line and similar to the

experiment results. Comparing the second and third bouncing, the u-t function

is still close to a straight line. Then, in the fourth and fifth bouncing, the u-t

function of simulation becomes curves, but the results are still in the suitable

range of experiment’s value.


Figure 17: 6 mm Teflon sphere bouncing motion in the air, u-t function, for

the experiment, at the first impact Re=210, St=7.8×104, and 𝒆=0.8

(Gondret, Lance & Petit, 2002)

Next, it uses the same method, to run a simulation of 3 mm steel sphere in

silicon oil (RV10). The initial position of the steel sphere is 0.009 m, from

sphere bottom to the surface. The first impact of sphere and fluid is Re=82,

St=152, and 𝑒=0.78. The simulation results are shown in Fig 18. The bouncing

motion of the steel sphere in the silicon oil (RV10) is similar to the experiment

value. The maximum point and the minimum point for this simulation result is

almost the same as the experimental result; for the first two motions, the

difference of the top point is 0.17% and 0.23%.


Figure 18: 3 mm steel sphere bouncing motion in silicon oil RV10, h-t

function, for the experiment, at the first impact Re=82, St=152, and

𝒆=0.78 (Gondret, Lance & Petit, 2002)

Then, comparing the velocity at different times, the results are close to the

experiment’s result for the first two motions, shown in Figure 19. Comparing

Figure 18 and Figure 19, when the particle is at the top of the bouncing motion,

velocity equals to 0. The velocity at this point is coincident with the experiment.


Figure 19: 3 mm steel sphere bouncing motion in silicon oil RV, 10 u-t

function, for the experiment, at the first impact Re=82, St=152, and

𝒆=0.78 (Gondret, Lance & Petit, 2002)

Comparing the 6 mm Teflon ball bouncing case and 3 mm steel ball bouncing

case, it has been shown that LBM has the better performance for small

Reynolds number simulation and dynamic viscosity. The maximum difference

of the Teflon ball case is 11.89%, and the density ratio of Teflon and air is

1791.667; the sphere motion has lower influence from fluid than the steel ball

case. The 3 mm steel sphere has the smaller Reynolds number at the first

impact with fluid, than does the 6 mm Teflon sphere. Also, the silicon oil has

larger dynamic viscosity than the air. The maximum difference is 0.23%, and

the density ration of steel and silicon oil is 8.342, showing that the sphere

motion has larger influence from the fluid. Due to these reasons, the second

simulation results are more reasonable than the first simulation results.


For the validation of LBM-DEM simulation, the code of Mechsys is validated,

and can be used for further research. This validation still has some

weaknesses, and further research could avoid these situations for more

accurate results. The first is the time steps, which can be set smaller, to make

more reading and more accurate. Secondly, some physical parameters, such

as dimensions and material, can use more accurate values.

From the pure LBM and pure DEM simulations, both LBM and DEM are

validated. Then, from this simulation, the coupling LBM-DEM code is also a

useful code and validated. Mechsys code can be applied for further LBM-DEM

research.

4.4 Particle-laden Air Flow in a Clear Channel

Clear channel simulation is a flow domain which has top and bottom parallel

walls as well as left and right inlet and outlet, also inside the flow domain, there

is no obstacle. The validation of the basic theories for each method has been

achieved, and it shows that Mechsys results have very small differences with

others’ experiments and simulations, so Mechsys is found suitable to do further

research. This simulation will use Mechsys to run an LBM-DEM case, which is

a clear-channel study. The results will be compared with Kuruneru et al.’s

(2016) result, which used an FVM-DEM approach.

Kuruneru et al. (2016) have created a clear channel, which is 5 mm high and

25 mm long. The simulation will study two different diameters of particles, one

is 350 µm, the other is 500 µm. Also, the parameters are kept the same as

Kuruneru et al.’s (2016) simulation, with particle density of 2500 kg/m3, input

velocity of 0.5 m/s from left to right, and the particles randomly injected along

the inlet section. The simulation results will be analysed, including maximum

fluid velocity, deposition fraction, numerical pressure drop, and particle

deposition plots. The analytical pressure drop from Kuruneru et al.’s (2016)

work used the Ergun analytical equation. Based on Kuruneru et al.’s (2016)

journal, the Mechsys simulation has similar settings for both cases, with 160


particle injected from 0.2 s to 1 s, top and bottom walls being solid wall, and

the fluid being air.

Table 8 and Figure 20 show the simulation results of 350 µm particles. It is

shown in Table 9, all the simulation results of LBM-DEM are larger than the

results of FVM-DEM. For the pressure drop, FVM-DEM result is closer to the

analytical pressure drop than LBM-DEM. Figure 20a shows that particle

deposition of FVM-DEM is around the middle of the channel, some particles

are deposited at the left of the midsection, with more particles deposited at the

right of the midsection. For LBM-DEM, all the particles deposited at the right

of the midsection and close to the outlet of the domain, where the deposition

location starts from 13.25 mm to the end. Comparing these two numerical

approaches, the difference is very minimal for this case. The percentage of

difference for the results are 7.59% of velocity, 14.77 of deposition fraction,

and 28% of numerical pressure drop.

Table 8: Compare FVM-DEM and LBM-DEM results for 350 µm particles

Max Fluid

velocity

(m/s)

Deposition

Fraction (%)

Numerical

Pressure

Drop (Pa)

Analytical

Pressure

Drop (Pa)

FVM-DEM,

Kuruneru et

al. (2016)

0.8500 44.00 0.321 0.319

LBM-DEM 0.9145 50.50 0.411 0.319


a

b

Figure 20: Particle deposition and velocity flow field of 350 µm particles,

a. FVM-DEM (Kuruneru et al. 2016), b. LBM-DEM

Table 9 and Figure 21 shown the simulation of 500 µm particles. Comparing

these two approaches, LBM-DEM has only the maximum fluid velocity larger

than FVM-DEM, and the deposition fraction and pressure drop; FVM-DEM is

larger, as shown in Table 9. From Figure 21, it is shown that FVM-DEM has

the average distribution of particle deposition around the midsection, and the

distribution range is larger. For LBM-DEM, the distribution range of particle

deposition is smaller than FVM-DEM results, and the distribution section is

from the middle to the right side. Figure 21b shows, at the midsection, the

particle deposition is slightly more than in the right section. The percentage of

difference for the results are 15% of velocity, 14.29% of deposition fraction,

and 41% of numerical pressure drop. The pressure drop for both methods in

this case has an obvious difference.


Table 9: Compare FVM-DEM and LBM-DEM results for 500 µm particles

Max Fluid

velocity

(m/s)

Deposition

Fraction (%)

Numerical

Pressure

Drop (Pa)

Analytical

Pressure

Drop (Pa)

FVM-DEM,

Kuruneru’s et

al. (2016)

1.0 63.00 0.746 0.698

LBM-DEM 1.150 54.00 0.440 0.698

a

b

Figure 21: Deposition of 500 µm particles and velocity flow field, a. FVM-

DEM (Kuruneru et al. 2016), b. LBM-DEM

Using the same method, when the particle size changes from 350 µm to 500

µm, all the results (maximum fluid velocity, deposition fraction, pressure drop)

are increased for both FVM-DEM and LBM-DEM approaches. For the FVM-

DEM approach, the particle deposition and pressure drop increased a lot,


when the particle size increased from 350 µm to 500 µm. For the LBM-DEM

approach, the particle deposition and pressure drop only increased a little,

when the particle size increased from 350 µm to 500 µm.

4.5 Compare FVM-DEM and LBM-DEM results for Air Flow over 6

circular Obstacles

The simulation will use Mechsys to run an LBM-DEM case, and will be

compared with Kuruneru et al.’s (2017) and Sauret et al.’s (2017) FVM-DEM

simulation results, in which Sauret et al. (2017) have compared Kuruneru et

al.’s (2017) results with Mechsys LBM-DEM results.

For the author’s simulations, the computational domain, geometry, and

boundary conditions are same as the Kuruneru et al. (2017) and Sauret et al.

(2017) simulations. The difference here from the Sauret et al. (2017) work is

the use of a smaller lattice unit (dx), in which the 0.6mm×4mm domain has

been divided into 160×1067 lattices, whereas the Sauret et al. (2017) work

uses 152×1000 lattices. The reasons for choosing the smaller lattice unit are

that the smaller could make the simulation more stable, minimising the

difference between computational domain and real geometry, and tending

toward better convergence. The other parameters are the same as Sauret et

al.’s (2017) paper: the particle density is 2400 kg/m3, particle diameter is 50

µm, particles and fluid input velocity is 0.1 m/s, and 160 particles will randomly

inject from 0.2 s to 1.0 s along the inlet of the domain.

It is shown in Figure 22 and Table 10 that the maximum fluid velocities for each

case are very close, the difference between both LBM-DEM being only 0.0013

m/s, which is 0.161% difference. Then, the difference of deposition fraction is

also in a small reasonable range; Sauret’s result has 2% higher than

Kuruneru’s result, Kuruneru’s result has 1% lower than the present results, and

Sauret’s result has 1% higher than the present results. For the pressure drop,

both LBM-DEM results are larger than the FVM-DEM result, due to the LBM

having better viscosity performance than FVM. For both LBM-DEM results,


between the particles, the maximum pressure is close to 15 Pa. Figure 22a

shows the particle deposition result of the FVM-DEM approach, where each

column of obstacles has the effect to stop some particles; the first column of

the obstacles which is close to the linlet is the most effective column. Figure

22b shows Sauret’s LBM-DEM simulation result, the particle deposition area

is different as is the FVM-DEM approach. It shows that the major particles have

been stopped by the first column of the obstacles, the second and third column

seem to have no effect in stopping the particles. Figure 22c shows the author’s

simulation results of LBM-DEM; although the particle deposition is lower than

Figure 22b, the deposition area is similar to Figure 22b, because these two

simulations use the same source code, with only the lattice unit being different.

Table 10: Summary of results for 50 µm particles

Max Fluid

velocity (m/s)

Deposition

Fraction (%)

Numerical

Pressure Drop

(Pa)

FVM-DEM,

Kuruneru et al.

(2016)

0.6 68.16 6.37

LBM-DEM,

(Mechsys

Code) Sauret

et al. (2017)

0.807 70.00 9.0

LBM-DEM,

(Mechsys

code) current

study

0.8057 69.18 7.81


a

b

c

Figure 22: Deposition of 50 µm particles, a. FVM-DEM (Kuruneru et al.,

2017), b. LBM-DEM (Sauret et al. (2017)), c. LBM-DEM (current study)

4.6 Summary of Mechsys Validation

In this chapter, the Mechsys code of LBM-DEM has been validated, which can

be applied for the particle filtration simulations. The LBM approach has good

simulation results for the low Reynolds number cases. The DEM approach has

been validated for the particle collisions of momentum studies, and particle

rebound studies. Then, the validation of coupled LBM-DEM has been

completed. For particles dropped in the fluid, LBM-DEM has presented similar

results as experimental data. The 3 mm steel sphere has presented a low error

result, which has maximum 0.23% difference to the experimental data. The

compared FVM-DEM approach and LBM-DEM approach, for the particles’

deposition in the clear channel has shown error of maximum velocity and


particle deposition fraction are less than 20%, but the pressure drop has

obvious errors. Lastly, the particle-laden air flow over six circular obstacles has

shown that the location of deposition is different between FVM-DEM and LBM-

DEM but using the same code of LBM-DEM, decreasing the lattice size, both

LBM-DEM results have similar particle deposition area. The small difference

is pressure drop.

The validation chapter has shown LBM of Mechsys code can present the

similar results as others’ validated simulations for fluid flows. Then, the DEM

of Mechsys code has been validated for both particle-particle reaction and

particle-wall reaction. Also, the coupled LBM-DEM of Mechsys code has been

validated which fluid and particle interaction is close to the others’ simulation

results. The validation has been done, so Mechsys code can be applied for

this research.

Chapter 5: Results and Discussion 65

Chapter 5: Results and Discussion

For the simulation of particle filtration, there were two major conditions of filter

that should be considered, which are the porosity of the filter and sizes of filter

material. This section has shown the simulation results and discuss the

filtration effects. The constant porosity and sizes of filter material have been

applied, then the different configurations of the filters compared to discuss the

filtration effects. These results were all the idealised 2D simulations. The

simulations used an LBM-DEM numerical approach from Mechsys code, which

is an open source code based on c++.

5.1 Computational Domains for Different Filter Designs

First of all, 90% porosity (Φ) filters have been designed as six configurations,

as shown in Figure 23, the filter materials considered two sizes of obstacles,

20 µm or 10 µm. The filters have 112 µm width and 140 µm length for A, B, C,

D; and 112 µm width and 168 µm length for E, F to keep the porosity of 90%.

The domain is 112 µm × 252 µm for A, B, C, D; and 112 µm × 280 µm for E,

F. The fluid flow and particle injection are from top (inlet) to bottom (outlet),

same as the gravity direction, and all the boundaries are solid-wall. Also, there

are some other important conditions: solid particles of 2500 kg/m3 or 800 kg/m3

density, fluid of 1.225 kg/m3 density, simulation time is 0.1 s, particles are

injected from 0.01 s to 0.1 s. The injected position is randomly along the inlet,

the total injected number of particles is 125, all the particles have 10 µm

diameter, and the inlet velocity of particles and fluid is 0.1 m/s or 0.05 m/s.

There are six different configurations of the filters that have been created.

Configuration A and configuration B are the regular pattern of obstacles,

configuration C and configuration D have a random pattern of obstacles,

configuration E and configuration F are the two layers of small obstacles

covering a middle layer of obstacles. The porosities have been calculated

between the filters’ bound. As the porosity is 90%, for each configuration, the

66 Chapter 5: Results and Discussion

minimum distance of obstacles to the filters’ bound is 2 µm, and the minimum

distance of obstacles to the boundary walls is 18 µm. Furthermore, the filter

area can be compressed to reduce the porosity to 75%. The filters A and D

have 112 µm width and 116 µm length to keep the porosity, and filter E has

112 µm × 122 µm. The total computational domain is kept the same, at 112

µm × 252 µm. The minimum distance from obstacles to the boundary wall is

18 µm as well. All the configurations are shown in Figure 23.

90

% p

oro

sity

75

% p

oro

sity

Con

fig

ura

tio

ns

A

B

C

D

E

F

Figure 23: 90% porosity of 6 different configuration of filters and 75%

porosity of 3 different configurations of filters


5.2 Catalogue & Design of Simulation Groups, for Comparison

Based on the filter configurations, the simulations have been catalogued as

five groups, shown in Table 11. Group 1 is following the validated parameters

to run the six configurations of 90% porosity, in which velocity is 0.1 m/s,

particle size is 10 µm, and density is 2500 kg/m3. The configurations of high

filtration have been selected, which are configuration A, D, and E. These three

configurations run the simulations of other initial parameters, such as group 2,

to group 5.

Table 11: Catalogue & design of simulation groups, for comparison of

filtration effect by using different initial parameters

Φ v (m/s) ρ (kg/m3) Geometry

Group 1 90% 0.1 2500 A, B, C, D, E,

F

Group 2 90% 0.05 2500 A, D, E

Group 3 90% 0.1 800 A, D, E

Group 4 90% 0.05 800 A, D, E

Group 5 75% 0.05 800 A, D, E

Due to the different configurations having different filtration effects, the

simulation results have been analysed based on the change of configuration,

variation of particle density, etc. … In the LBM-DEM approach, the pressure is

related to the mass flow, then the results gave the fluid density difference, so

to calculate the pressure, the formula P = C𝑠2 × ρ will be applied.


5.3 Filtration Effect of 10 µm Particles Flow Through Filters of 90%

Porosity

5.3.1 Simulation of Group 1, Comparison and Selection of 6 Designs

The first group of the simulations have run all the six cases of the filters, in

which the input velocity is 0.1 m/s, particle size is 10 µm in diameter, and the

particle density is 2500 kg/m3. From these six simulations, the results have

been compared between each case, shown in Figure 24. The comparisons

considered three parameters, which are filtration fraction, pressure drop, and

filtration time. The first group of simulations kept initial velocity of 0.1 m/s, for

continue the computational stability from the validation cases.


Configuration A:

t=0.1 s

Configuration B:

t=0.1 s

Configuration C:

t=0.1 s

Configuration D:

t=0.0832 s

Configuration E:

t=0.07 s

Configuration F:

t= 0.1 s

Figure 24: Comparison for endings of simulations in 6 configurations,

Φ=90%, v=0.1 m/s, ρ=2500 kg/m3

All the six simulations have shown that 1-A, 1-D, 1-E and 1-F have high

filtration efficiency to remove the 10 µm particles, which have the heavy density

of 2500 kg/m3, and the high initial velocity of 0.1 m/s. The reason can be

considered, for 1-A, that if each row of obstacle(s) can reduce the velocity of


particles, the slower particle velocity will make the particle gathering and

deposition inside the filter. For 1-D, 1-E and 1-F, with the same porosity, the

smaller obstacles create smaller gaps between each obstacle. It is not easy

for the particles to pass through the smaller gap together. The configuration of

1-C and 1-D are similar; the results of 1-D are better than 1-C, so this research

chooses configuration 1-D. The same as 1-E and 1-F, which 1-E has the better

filtration effect. The real filter has the majority of 20 µm fibre and some 10 µm

fibre, so the configurations 1-A, 1-D and 1-E were worth including in further

studies. Further studies have chosen these three configurations as the

computational domain, but they will reduce the velocity or density.

Summing up the first group of simulations, the results were shown in Figure

25. 1-A has a good filtration effect; at 0.1 s of total filtration time, 68 particles

have been blocked, and the pressure drop was 1.6 Pa. For 1-B, it has shown,

the filtration effect was low; at 0.1 s, only 37 particles remained in the domain,

but the particles were not deposited or blocked by the filter material, and the

pressure drop was 0.42 Pa. For 1-C, the filtration effect was good, at 0.1 s 82

particles have been blocked by the filter material, and the pressure drop was

0.80 Pa. For 1-D, the filtration effect is better than 1-C, the simulation has

stopped at 0.0823 s, there were 77 particles that have been blocked and the

pressure drop was 254.8 Pa. For 1-E, the filtration effect was good, because

the simulation stopped at 0.0715 s, there were 55 particles that have been

blocked and the pressure drop was 29.8 Pa. For 1-F, the filtration effect was

not better than 1-E; in total 68 particles have been blocked at 0.1 s and the

pressure drop was 31 Pa. As these results have shown, number of particles

remaining or deposited inside the domain was one of the parameters to explain

the filtration effect. Pressure drop was another parameter; when the particles

have been stopped by the filter, the fluid and particles cannot pass the filter,

so the pressure has increased around the inlet area. Furthermore, filtration

time can explain the filtration effect. When the filters have been totally blocked,

neither fluid and particles can pass the filter, so the simulation stopped at this

time, lower filtration time meaning a higher filtration effect. 1-B has shown

when the simulation stopped at 0.1 s, there was no clear pressure drop; that

meant the particles and fluid were still moving, so 1-B was not suitable for


further study. 1-C and 1-D were similar configurations, 1-D was better than 1-

C for the short filtration time, so 1-D has been selected for further studies. From

the similar configurations of 1-E and 1-F, 1-E have been selected.

Figure 25: Summary of simulations group 1, number of particle filtration at

different time, Φ=90%, 10 µm particles, v=0.1 m/s, ρ=2500 kg/m3

Another was to compare pressure drop and filtration fraction of all the

simulation results. Some of the simulations stopped at different filtration times,

due to the filters that have been totally blocked, so it is difficult to analyse the

filtration effect by using particle numbers. The particle injection rate is the

same, which is 1380 per second, so the filtration fraction can be calculated for

different filtration times. The filtration fraction for each simulation was: 1-A

54.4%, 1-B 29.6%, 1-C 65.6%, 1-D 74%, 1-E 61.5%, 1-F 54.4%. The

relationship between pressure drop and filtration fraction has been shown in

Figure 26. Configuration A has had good filtration fraction and low pressure

drop; it has had a good performance for a filter. D has had the best filtration

fraction for all the configurations when the injected particles had v=0.1 m/s,

ρ=2500 kg/m3. E has had good filtration fraction, and it has had the shortest

filtration time. The configurations A, D, and E have been selected to run the

other simulations.

0

10

20

30

40

50

60

70

80

90

A B C D E F

Nu

mb

er o

f p

arti

cles

0.02 s 0.04 s 0.06 s 0.08 s 0.1 s


Figure 26: Relationship between pressure drop and filtration fraction,

Φ=90%, 10 µm particles, v=0.1 m/s, ρ=2500 kg/m3

5.3.2 Investigation and Comparison of Filtering with Same Density but Different Velocities

For 90% porosity filters, comparison of the influence from different initial

velocities when particles had the same density, has shown in Figure 27. For

configuration A, when the heavy particles (ρ=2500 kg/m3) had 0.1 m/s initial

velocity, the filtration fraction is 54.4%, but when the particles had 0.05 m/s

initial velocity the particle filtration was low. It was only 22.4%. for configuration

D; when the heavy particles have had 0.1 m/s initial velocity the filtration

fraction was 74%, when the particles have had 0.05 m/s initial velocity the

filtration fraction was 62.4%. For configuration E, when the initial velocity was

0.1 m/s, the filtration fraction was 61.5%; when the particles have had 0.05 m/s

velocity the filtration fraction was 93.4%. These results have shown, for heavy

particles, configuration A has had the better filtration efficiency for faster

AB C

D

E

F

0

20

40

60

80

100

120

140

160

180

200

220

240

260

20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

pre

ssu

re d

rop

(P

a)

filtration fraction (%)

Compare all the configurations


particles, but very low efficiency for slow particles. Configuration D has had

good filtration efficiency for both fast and slow particles, but for fast particles

the pressure drop was very high, and it seemed the particles have totally

blocked the filter (Figure 27). Configuration E has had good results for fast

particles and the best results for slow particles.


Φ=90%, 10 µm particles, ρ=2500 kg/m3 (heavy), v=0.1 m/s (fast) or

v=0.05 m/s (slow)

For light particles, the influence of initial velocity was shown in Figure 28.

Configuration A had a good filtration fraction and pressure drops for fast

(53.6%) and slow (57.6%) particles, with the pressure drops low (0.45 Pa for

fast particles & 0.71 for slow particles). These results have shown, for light

particles that the initial velocities had small influence. Configuration D had

better filtration results than configuration A in these conditions, but for the slow

particles, the filtration fraction was high (66.5%) and the pressure drop was

A, fast

D, fast

E, fast

A, slow D, slow

E, slow

0

20

40

60

80

100

120

140

160

180

200

220

240

260

20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

pre

ssu

re d

rop

(P

a)


Heavy particle, different velocity


also high. The pressure drop was 562.3 Pa, which was the hightest pressure

drop for all the simulations. Configuration E had 80% filtration fraction for fast

particles, and 61.6% filtration fraction for slow particles. Also, the pressure drop

was 104.9 Pa for fast particles and 37.87 Pa for slow particles.


Φ=90%, 10 µm particles, ρ=800 kg/m3 (light), v=0.1 m/s (fast) or v=0.05

m/s (slow)

5.3.3 Investigation and Comparison of Filtering with Same Velocity but Different Densities

From the simulations, these results kept the velocity as a constant, and

analysed influence of particle densities.

For the fast particles, the influence of densities has been shown in Figure 29.

For heavy and light particles, configuration A had very low influence when the

initial velocity is fast (0.1 m/s). Configuration D had low influence on particle

filtration; it has had only 4.4% difference of filtration fractions, but it has had

high influence on pressure drop, which in the heavy particles’ case had 254.8

Pa, while the light particles’ case has only 0.423 Pa. Configuration E has had

A, fastD, fast

E, fast

A, slow

D, slow

E, slow

0

50

100

150

200

250

300

350

400

450

500

550

600

20 30 40 50 60 70 80 90 100

pre

ssu

re d

rop

(P

a)


Light particle, diferent velocity


low influence on pressure drop, which in the heavy particles’ case had 63 Pa,

and in the light particles’ case had 104.9 Pa. Furthermore, configuration E has

had better filtration effect for the light particles than heavy particles.


Φ=90%, 10 µm particles, v=0.1 m/s (fast), ρ=800 kg/m3 (light) or ρ=2500

kg/m3 (heavy)

For slow particles, the influence of densities has been shown in Figure 35.

Configuration A had very limited filtration effect for heavy particles. The

influence of density for configuration D has shown that light particles have

higher pressure drop (561.851 Pa difference) than heavy particles, but the

filtration fraction (4.1% difference) was close. The influence for configuration E

had high difference on filtration fraction (31.8% difference) but low difference

on pressure drop (31.87 Pa difference).

A, heavy

D, heavy

E, heavy

A, light

D, light

E, light

0

40

80

120

160

200

240

280

20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

pre

ssu

re d

rop

(P

a)


Fast particle, different density



Φ=90%, 10 µm particles, v=0.1 m/s (fast), ρ=800 kg/m3 (light) or ρ=2500

kg/m3 (heavy)

5.3.4 Comparison of Filtering for Different Filter Configurations (A, D, E) with Different Initial Parameters

Comparison of all the results of each configuration has been shown in Figure

31.

Configuration A had one case (slow, heavy particle) less than the 20% filtration

fraction. The other three simulations of configuration A were very close; the

maximum pressure drop was 1.6 Pa, the minimum pressure drop was 0.409

Pa; the maximum filtration fraction was 57.6%, the minimum filtration fraction

was 53.6%.

Configuration D has good filtration effect for all the conditions, as the filtration

fractions were all higher than 60%. Changing the input parameters, the

filtration fraction was not very heavy, the maximum filtration fraction is 74%,

A, heavyD, heavy

E, heavyA, light

D, light

E, light

0

50

100

150

200

250

300

350

400

450

500

550

600

20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

pre

ssu

re d

rop

(P

a)


Slow particle, different density


and the minimum was 62.4%. However, for slow and light particles’ simulation,

the pressure drop was very high (562.3 Pa).

Configuration E has had very good filtration effect, as all the filtration fractions

were higher than 60%. For the slow and heavy particles, it has had the best

filtration effect, which is 93.4%, and the pressure drop was low, 6 Pa.

Comparing all the simulations of configuration E, between each case, the

difference of pressure drop was not very high. The maximum pressure drop of

configuration E was fast and light particle simulation, with the pressure drop

being 104.9 Pa.


Figure 31: Comparing the simulation results in each configuration,

Φ=90%, 10 µm particles, v=0.1 m/s (fast) or v=0.05 m/s (slow), ρ=800

kg/m3 (light) or ρ=2500 kg/m3 (heavy)

fast, heavy

slow, heavy

fast, light

slow, light

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

20 30 40 50 60 70 80 90 100

pre

ssu

re d

rop

(P

a)


Configuration A

fast, heavy

slow, heavy fast, light

slow, light

050

100150200250300350400450500550600

20 30 40 50 60 70 80 90 100

pre

ssu

re d

rop

s (P

a)


Configuration D

fast, heavy

slow, heavy

fast, light

slow, light0

102030405060708090

100110120

20 30 40 50 60 70 80 90 100

pre

ssu

re d

rop

(P

a)


Configuration E


5.4 Summarise and Analyse the Simulation Results of the Filter with

90% Porosity

It has been shown that from the first group of simulations, configuration A, D

and E had the better filtration effect than the other configurations for the fast

and heavy particles, so configuration A, D and E with 90% porosity had been

selected. These three configurations can run the simulations with other

conditions, to analyse the filtration mechanism by implementing LBM-DEM

model. LBM approach had better performance for slow flows, so it can for fast

flows, it may work for slower flows. The initial or input parameters were particle

densities and velocities. Then, filtration time, filtration fraction, and pressure

drop were the three results to analyse the filtering efficiency.

All the simulation results have been compared in different conditions. The real

filters considered higher filtration fraction and lower pressure drop (Rahimi

Kord Sofla, 2015). These three results can analyse that the selected

configurations had good effect to remove PN of 10 µm particles for almost all

conditions. Only configuration A had limited filtration effect to remove slow and

heavy particles. Although configuration A had one condition with lower filtration

effect, the pressure drops were the lower than the other configurations, all the

pressure drops were lower than 1.6 Pa. Configuration D had good filtration

effect, but higher pressure drops for some conditions. Configuration E had the

better balance of pressure drop and filtration fraction for all conditions. In some

conditions the particles have blocked the filters, then the simulations would

stop earlier than 0.1 s, the short simulation time always followed higher

pressure drops. The filter design of durability, this would be an important

parameter. As some researchers gave some results of experiments, in some

conditions the removal of 10 µm particles are more than 95%, also the larger

particles are easier to remove (Yu et al., 2017 & Park et al., 2014). Thus, the

three results can be used for study filtering with other conditions.


5.5 Filtration Effect of 10 µm Particles Flow Through Filters of 75%

Porosity

The filter materials have been compressed to 75% porosity. The computational

domains were reduced, and the gap between each obstacle were smaller than

90% porosity filters. The particles were more difficult to smaller gaps, shown

in Figure 32. The filtration fraction of configuration A was 98.3% at 0.07 s, D

was 86.5% at 0.086 s, E was 87.5% at 0.0933 s. These were very high

percentage of particles’ removal. Due to the porosity has reduced to 75%, the

filtration effect has increased, so the filtration time were all stopped earlier than

0.1 s. Then, the pressure drop of D and E were small, but for A was high.

a,

t=0.07 s

b,

t=0.086 s

c,

t=0.0933 s

Figure 32: Simulation results of Φ=75% configurations, v=0.05 m/s,

ρ=800 kg/m3, a, configuration A, b, configuration D, c, configuration E

5.6 Compare the Simulation Results between Φ=75% & Φ=90%

Summing up the simulations, the 75% porosity has very good filtration effect

for these simulations. The three cases have similar particle deposition, as

shown in Figure 33. The particles are well-distributed on the filter. Due to the


filter change on the smaller porosity, the distance between obstacles is

smaller, so the particles cannot easily pass through the gap of obstacles. All

the cases are stopped earlier than 0.1 s. In comparing with similar cases of

90% porosity, the filtration effect is better than those cases, as shown in Table

12. All the results show that the smaller porosity has better filtration effect in

these simulations.

Table 12: Results of 75% porosity simulations

Configurations Number of

particles

Filtration time

(s)

Pressure

drops

(Pa)

Φ=75%,

v=0.05

m/s, ρ=800

kg/m3

A 86 0.07 508

D 98 0.086 6.4

E 102 0.0933 4.0

Φ=90%,

v=0.05

m/s, ρ=800

kg/m3

A 72 0.1 0.71

D 69 0.095 562.3

E 77 0.1 37.87


Figure 33: Comparison of 90% porosity and 75% porosity simulations, 10

µm particles, v=0.05 m/s (slow), ρ=800 kg/m3 (light)

A, 90%

D, 90%

E, 90%

A, 75%

D, 75% E, 75%0

50

100

150

200

250

300

350

400

450

500

550

600

20 30 40 50 60 70 80 90 100

pre

ssu

re d

rop

(P

a)


Φ=75% vs Φ=90%

Chapter 6: Conclusions 83

Chapter 6: Conclusions

To study the mechanism of DPM filtration, for reducing environmental impact,

this research has used the numerical method modelling the particle-fluid flows

through the idealised filter materials. The open source library, Mechsys, has

been applied, which has coupled LBM and DEM methods. The findings have

shown LBM-DEM can study micron particle filtrations.

This research presents the implementation of LBM-DEM for the modelling of

particle filtration. The method has been validated, and shown to be suitable for

this research. LBM-DEM has the advantages of micron scale fluid flow

simulation and complex porous media simulation. The cross section of fibrous

filters can be observed as porous media.

The idealised filters and particle-fluid mixture of diesel exaust have been

applied. This research has studied the filtration of 10 µm particles. The results

have shown the idealised filter configurations have different filtration effects.

Then, the configurations with better results have been selected, which are

configurations A, D, and E. These configurations of filter design can precede

further studies, as references. The input parameters have considered the

density of 10 µm particles, and particle initial velocity. The results have

concentrated on filtration fraction and pressure drops. The high filtration

fraction and low pressure drop are the aims of investigating the filtration effect.

The results of this research have shown the spherical particles of 10 µm

diameter can be filtered by some designs of filter when the filter has porosity

of 90% or 75%. The particle initial velocity and particle density are the only

conditions affecting the filtration process. Configuration A of 90% porosity has

better filtration effect for some conditions but not all conditions. Also,

Configuration A of 90% porosity created very low pressure drops for all

conditions, but for 75% porosity the pressure drop is higher than configurations

D and E of 75% porosity. Configuration D of 90% porosity has better filtration

effect than configuration A, but this created a high pressure drop for slow-light

84 Chapter 6: Conclusions

and fast-heavy conditions. The input parameter affects pressure drop

obviously. Configuration E of 90% porosity has good filtration effect and low

pressure drop. The fast particles created higher pressure drop than slow

particles obviously. The filters of 75% porosity have a better filtration effect

than the filters of 90% porosity for A, D, and E configurations when the particles

have small density and low initial velocity.

In conclusion, the LBM-DEM approach is able to study DPF filtration

processes. This research has illustrated LBM-DEM model make the filtration

of micro-particle number more clear, which is the weakness of real experiment.

The largest DPM with large or small initial velocities and densities have been

applied in this research, these parameters can influence the filtration

efficiency. Change of initial velocity and density, configuration E has lower

influence. Also, this research has studied similar filter configerations with

different porosities, the smaller porosity has better filtration efficiency than

larger porosity. It is shown that LBM-DEM model can help researches to design

and improve the DPF, and find out the filtration mechanism of the filter.

There are some limitations of this research, but further study to continue this

research would be worthy. This research has only studied the filtration of 10

µm particles, as this is the biggest particulate matter of diesel exaust. For

further study, the smaller particles can be applied, and then the concentration

of different particle sizes. Also, this research has only considered two different

velocities, whereas the further research can simulation different velocities. This

research is a 2D simulation, but for further studies, 3D simulations can be

applied.

Bibliography 85

Bibliography

Andersson, H. I. (2015). Lectures of the course TEP4112 “Turbulent Flows”.

Norwegian University of Science and Technology (NTNU), Energy and

Process, Trondheim, Norway.

ANSYS, Inc. (2015). ANSYS FLUENT user’s guide. ANSYS Release 16.2.

Baker, R. (2012) Membrane technology and applications. 3rd ed. Oxford: Wiley-

Blackwell.

Balevičius, R., Kačianauskas, R., Mróz, Z., & Sielamowicz, I. (2011). Analysis and

DEM simulation of granular material flow patterns in hopper models of different

shapes. Advanced Powder Technology, 22(2), 226-235.

Barrios, C. C., Martín, C., Domínguez-Sáez, A., Álvarez, P., Pujadas, M., &

Casanova, J. (2014). Effects of the addition of oxygenated fuels as additives

on combustion characteristics and particle number and size distribution

emissions of a TDI diesel engine. Fuel, 132, 93-100.

Beatty, T. K., & Shimshack, J. P. (2011). School buses, diesel emissions, and

respiratory health. J Health Econ, 30(5), 987-999.

Bennett, S. (2015). Modern Diesel Technology Diesel Engines 2nd edition. Gengage

Learning USA.

Bensaid, S. & Marchisio, D. & Russo, N. & Fino, D. (2009). Experimental investigation

of soot deposition in diesel particulate filters. Catalysis Today. 147, 295-300.

Bicanic, Ninad (2004). "Discrete Element Methods". In Stein, Erwin; De Borst;

Hughes, Thomas J.R. Encyclopedia of Computational Mechanics. 1. Wiley.

Bikmukhametov, T. (2016). CFD simulations of multiphase flows with particles.

Master’s Thesis.

Boon, J. P. (2003). The Lattice Boltzmann Equation for Fluid Dynamics and Beyond.

European Journal of Mechanics - B/Fluids, 22(1), 101.

Bright, I., Lin, G., & Kutz, J. N. (2016). Classification of Spatiotemporal Data via

Asynchronous Sparse Sampling: Application to Flow around a Cylinder.

Multiscale Modeling & Simulation, 14(2), 823-838.

Brumby, P. E., Sato, T., Nagao, J., Tenma, N., & Narita, H. (2015). Coupled LBM–

DEM Micro-scale Simulations of Cohesive Particle Erosion Due to Shear

Flows. Transport in Porous Media, 109(1), 43-60.

Bulling, J., John, V., & Knobloch, P. (2017). Isogeometric analysis for flows around a

cylinder. Applied Mathematics Letters, 63, 65-70.

86 Bibliography

Canuto, D., & Taira, K. (2015). Two-dimensional compressible viscous flow around a

circular cylinder. Journal of Fluid Mechanics, 785, 349-371.

Casati, R., Scheer, V., Vogt, R., & Benter, T. (2007). Measurement of nucleation and

soot mode particle emission from a diesel passenger car in real world and

laboratory in situ dilution. Atmospheric Environment, 41(10), 2125-2135.

Caserta, A., Navarro, H., & Cabezas-Gomez, L. (2016). Damping coefficient and

contact duration relations for continuous nonlinear spring-dashpot contact

model in DEM. Powder Technology, 302, 462-479.

Cengel, Y., Boles, M. (2015). Thermodynamics: an engineering approach (8th

edition in SI units). New York;: McGraw-Hill Education.

Cengel, Y., Boles, M., & Kanoglu. M. (2011). Thermodynamics: an engineering

approach (7th edition in SI units). Singapore;: McGraw-Hill.

Chagovets, T. V., & Van Sciver, S. W. (2015). Visualization of He II forced flow around

a cylinder. Physics of Fluids, 27(4), 045111.

Chattopadhyay, P. (2015). Engineering thermodynamics (Second edition.). New

Delhi: Oxford University Press.

Chen, W.L., Cao, Y., Li, H., & Hu, H. (2015). Numerical investigation of steady suction

control of flow around a circular cylinder. Journal of Fluids and Structures, 59,

22-36.

Chen, W.L., Gao, D.L., Yuan, W.Y., Li, H., & Hu, H. (2015). Passive jet control of flow

around a circular cylinder. Experiments in Fluids, 56(11).

Chen, Z., & Wang, M., (2017). Pore-scale modelling of hydro-mechanical coupling

mechanics in hydro-fracturing. Journal of Geophysical Research-Solid Earth,

122.

Chien, A., Balaji, P., Beckman, P., Dun, N., Fang, A., Fujita, H., Siegel, A. (2015).

Versioned Distributed Arrays for Resilience in Scientific Applications: Global

View Resilience. Procedia Computer Science, 51, 29-38.

Conserve Energy Future. (2017). 15 Major Current Environmental Problems.

Retrieved from http://www.conserve-energy-future.com/15-current-

environmental-problems.php.

Council of The European Union (EC). (2009). Regulation (EC) No 443/2009 of the

European Parliament and of the Council of 23 April 2009 setting emission

performance standards for new passenger cars as part of the Community's

integrated approach to reduce CO 2 emissions from light-duty vehicles.

retrieved from: http://eur-lex.europa.eu/legal-

content/EN/TXT/?uri=celex%3A32009R0443.

Bibliography 87

Courtois, Y., Molinier, B., Pasquereau, M., Degobert, P., & Festy, B. (1993). Influence

of the operating-conditions of a diesel-engine on the mutagenicity of its

emissions. Science of The Total Environment, 134(1-3), 61–70.

Coutanceau, R., Bouard, M. (1977) Experimental determination of main features of

the viscous flow in the wake of a circular cylinder in uniform translation, part 1

steady flow, Journal of Fluids Mechanics, 79, 4018-4037.

Cui, X. L., Li, J., Chan, A., & Chapman, D. (2014). Coupled DEM-LBM simulation of

internal fluidisation induced by a leaking pipe. Power Technology, 254, 299-

306.

Dalrymple, R. A., & Rogers, B. D. (2006). Numerical modeling of water waves with

the SPH method. Coastal Engineering, 53(2-3), 141-147.

Data Center of Ministry of Environmental Protection of the People's Republic of China

(DC of MEP of PRC). (2017). Data of Air Quality Index of 367 cities. retrieved

from: http://datacenter.mep.gov.cn/.

Davies, C. N. 1. (1973). Air filtration. New York; London; Acdemic Press.

Degobert, P. (1995). Society of Automotive Engineers. Automobiles and Pollution

Feng, Y. T., Han, K., & Owen, D R J., (2007). Coupled lattice Boltzmann method and

discrete element modelling of particle transport in fluid flows: Computational

issues. Int. J. Meth. Engng. 72, 1111-1134.

Feng, Y. T., Han, K., & Owen, D R J., (2009). Combined three-dimensional lattice

Boltzmann method and discrete element method for modelling fluid-particle

interactions with experimental assessment. Int. J. Meth. Engng. 81, 229-245.

Fino, D. (2016). Diesel emission control: Catalytic filters for particulate removal.

Science and Technology of Advanced Materials, 8(1-2), 93-100.

Fuller, C. (2012). Air pollution. Encyclopedia of Immigrant Health, 181-183.New York:

Springer-Verlag New York.

Galindo, J., Serrano, J. R., Piqueras, P., & García-Afonso, Ó. (2012). Heat transfer

modelling in honeycomb wall-flow diesel particulate filters. Energy, 43(1), 201-

213.

Galindo-Torres, S. A. (2015). MECHSYS multi-physics simulation library. Retrieved

from http:// http://mechsys.nongnu.org/

Galindo-Torres, S. A. (2013). A coupled discrete element lattice Boltzmann method

for the simulation of fluid-solid interaction with particles of general shapes.

Computer Methods in Applied Mechanics and Engineering, 265, 107-119.

Gan, N. (2017, January 16). Heavy smog back to haunt Beijing two days after acting

mayor Cai Qi vows air pollution crackdown. South China Morning Post.

88 Bibliography

Gill, S. S., Chatha, G. S., & Tsolakis, A. (2011). Analysis of reformed EGR on the

performance of a diesel particulate filter. International Journal of Hydrogen

Energy, 36(16), 10089-10099.

Gondret, p., Lance, M., & Petit, L., (2002). Bouncing motion of spherical particles in

fluids. Physics of Fluids, 14(2), 643-652.

Hamra, G., Guha, N., Cohen, A., Laden, F., Raaschou-Nielsen, O., Samet, J., …

Loomis, D. (2014). Outdoor particulate matter exposure and lung cancer: a

systematic review and meta-analysis. Environmental Health Perspectives,

122(9), 906–911.

Han, Y., & Cundall, P. (2013). LBM-DEM modelling of fluid -solid interaction in porous

media. International Journal for Numerical and Analytical Methods in

Geomechanics, 37(10), 1391-1407.

Han, Y., & Cundall, P. (2016). Verification of two-dimensional LBM-DEM coupling

approach and its application in modeling episodic sand production in borehole.

Petroleum. 3(2), 179-189.

International Agency for Research on Cancer (IARC). (2012). Diesel and gasoline

engine exhausts and some nitroarenes. IARC Monographs on the Evaluation

of Carcinogenic Risk to Humans, 5. Lyon, France.

International Energy Agency (IEA). (2015). World Energy Outlook 2015. OECD.

Itasca Consulting Group, Inc. (2008). Particle Flow Code, ver. 4.0. Itasca:

Minneapolis.

Jacobs, P. (2013). Thermodynamics. London, UK: Imperial College Press.

Jarauta-Bragulat, E., Hervada-Sala, C., & Egozcue, J. J. (2015, & 2016). Air Quality

Index Revisited from a Compositional Point of View. Mathematical

Geosciences, 48(5), 581-593.

Jassim, M. S., & Coskuner, G. (2017). Assessment of spatial variations of particulate

matter (PM10 and PM2.5) in Bahrain identified by air quality index (AQI).

Arabian Journal of Geosciences, 10(1), 1-14.

Jelles, S. J. (1999). Development of catalytic systems for diesel particulate oxidation,

Ph.D. Thesis, Delft University of Technology.

Junk, M., & Yang, Z., (2009). Pressure boundary condition for the lattice Boltzmann

method. Computers and Mathematics with Applications, 58(5), 922-929.

Kurnia, J. C., Sasmito, A. P., Wong, W. Y., & Mujumdar, A. S. (2014). Prediction and

innovative control strategies for oxygen and hazardous gases from diesel

emission in underground mines. Sci Total Environ, 481, 317-334.

Bibliography 89

Kuruneru, S, T, W., Sauret, E., Saha, S, C., & Gu, Y, T. (2016). Unresolved CFD-

DEM of sandstone-laden air flow in a clear channel. 20th Australian Fluid

Mechnics Conference. Perth Australia.

Kuruneru, S, T, W., Sauret, E., Saha, S, C., & Gu, Y, T. (2017). A coupled finite volume

& discrete element method to examine particulate foulant transport in metal

foam heat exchangers. International Journal of Heat and Mass Transfer, 115,

43-61.

Lei, Y., Zhang, Q., Nielsen, C., & He, K. (2011). An inventory of primary air pollutants

and CO2 emissions from cement production in China, 1990-2020.

Atmospheric Environment, 45(1), 147-154.

Leonardi, A., Wittel, F., Mendoza, M., & Herrmann, H. (2014). Coupled DEM-LBM

method for the free-surface simulation of heterogeneous suspensions.

Computational Particle Mechanics, 1(1), 3–13.

Li, J., Xiao, Z., Zhao, H.Q., Meng, Z.P., & Zhang, K. (2016). Visual analytics of smogs

in China. Journal of Visualization, 19(3), 461-474.

Li, Q., Raj, P., Husain, F. A., Varanasi, S., Rainey, T., Garnier, G., & Batchelor, W.

(2015). Engineering cellulose nanofibre suspensions to control filtration

resistance and sheet permeability. Cellulose, 23(1), 391-402.

Liu, D., van Wachem, B., Mudde, R., Chen, X., & van Ommen, J. (2016).

Characterization of fluidized nanoparticle agglomerates by using adhesive

CFD-DEM simulation. Powder Technology, 304(C), 198–207.

Manueco, L., Sarfati, T., Sauret, E., Angelo, Y. D., (2016). Flows in Metal Foams

Using Immersed Boundary Method. 20th Australian Fluid Mechnics

Conference. Perth Australia.

Mino, Y., Sakai, S., & Matsuyama, H. (2018). Simulations of particulate flow passing

through membrane pore under dead-end and constant-pressure filtration

condition. Chemical Engineering Science, 190, 68–76.

Mokhri, M. A., Abdullah, N. R., Abdullah, S. A., Kasalong, S., & Mamat, R. (2012).

Soot Filtration Recent Simulation Analysis in Diesel Particulate Filter (DPF).

Procedia Engineering, 41, 1750-1755.

Mollenhauer, K., & Tschöke, H. (2010). Handbook of Diesel Engines (1st ed.). Berlin,

Heidelberg: Springer Berlin Heidelberg.

Morawska, L., Johnson, G., He, C., Ayoko, G., Lim, M., Swanson, C., Moore, M.

(2006). Particle number emissions and source signatures of an industrial

facility. Environmental Science & Technology, 40(3), 803–814.

Nagamatsu, T., Honjo, K., Ebisawa, K., Ishimatsu, T., Saito, T., Mori, D., . . . Yagi, H.

(2016). Use of Non-conductive Film (NCF) with Nano-Sized Filler Particles for

90 Bibliography

Solder Interconnect: Research and Development on NCF Material and

Process Characterization. 923-928.

Owen, D. R. J., Leonardi, C. R., & Feng, Y. T., (2010). An efficient framework for fluid

structure interaction using the lattice Boltzmann method and immersed

moving boundaries. Int. J. Meth. Engng. 87, 66-95.

Park, J., Nguyen, T., Kim, C., & Lee, S. (2014). Simulation of flow in diesel particulate

filter system using metal fiber filter media. International Journal of Automotive

Technology, 15(3), 361–367.

Perlmutt, L., & Cromar, K. (2015). Construction of A us-based multi-pollutant air

quality index. American Journal of Respiratory and Critical Care Medicine, 191

Pilou, M., Tsangaris, S., Neofytou, P., Housiadas, C., & Drossinos, Y. (2011). Inertial

Particle Deposition in a 90° Laminar Flow Bend: An Eulerian Fluid Particle

Approach. Aerosol Science and Technology, 45(11), 1376–1387.

Plaia, A., & Ruggieri, M. (2010, & 2011). Air quality indices: a review. Reviews in

Environmental Science and Bio/Technology, 10(2), 165-179.

Qian, F., Huang, N., Lu, J., & Han, Y., (2014). CFD-DEM simulation of the filtration

performance for fibrous media based on the mimic structure, Computers and

Chemical Engineering, 71(C), 478-488.

Qiu, L.C. (2015). A coupling model of DEM and LBM for fluid flow through porous

media. Procedia Engineering, 102, 1520-1525.

Rahimi Kord Sofla, M., Rainey, T., & Brown, R. (2015). Improving the efficiency and

fire/water resistance of disposable diesel particulate filters using

nanocellulose. Confirmation of PhD. Candidature Report. Queensland

University of Technology Brisbane, Australia

Ramirez, J., Brown, R., & Rainey, T. (2015). A Review of Hydrothermal Liquefaction

Bio-Crude Properties and Prospects for Upgrading to Transportation Fuels.

Energies, 8(7), 6765-6794.

Ren, C., & Tong, S. (2006). Temperature modifies the health effects of particulate

matter in Brisbane, Australia. Int J Biometeorol, 51(2), 87-96.

Ristovski, Z. D., Miljevic, B., Surawski, N. C., Morawska, L., Fong, K. M., Goh, F., &

Yang, I. A. (2012). Respiratory health effects of diesel particulate matter.

Respirology, 17(2), 201-212.

Ristovski, Z., Morawska, L., Moore, M., Agranovski, V., Swanson, C., & Hughes, D.

(2003). The impact of sulphur content of diesel fuel on ultrafine particle

formation.

Sadeque, M. A. F., Rajaratnam, N., & Loewen, M. R. (2008). Flow around cylinders

in open channels. Jounal of Engineering Mechanics, 134(1), 60-71.

Bibliography 91

Sauret, E., Galindo-Torres, S. A., Kuruneru, S, T, W., Zhang, Pei., Saha, S, C., & Gu,

Y, T. (2017). Comparison between FVM-DEM & LBM-DEM of particle-laden

flows in idealised porous metal foam heat exchangers. 18th IAHR International

Conference on Cooling Tower and Cooled Heat Exchanger. Lyon, France.

Senba, T., & Suzuki, T. (2011). Applied analysis: Mathematical methods in natural

science (2nd ed.). Imperial College Press.

Sher, E., & Sher, E. (1998). Handbook of Air Pollution from Internal Combustion

Engines: Pollutant Formation and Control. San Diego: Elsevier Science &

Technology.

Shi, H. et. al. (2016). Preventing smog crises in China and globally. Journal of Cleaner

Production. 112 1261-1271.

Stringer, R. M., Zang, J, & Hillis, A. J, (2014). Unsteady RANS computations of flow

around a circular cylinder for a wide range of Reynolds numbers. Ocean

Engineering.

Tabor, D., & Winterton, R. (1969.). The Direct Measurement of Normal and Retarded

van der Waals Forces. Proceedings of the Royal Society of London. Series A,

Mathematical and Physical Sciences (1934-1990), 312(1511), 435–450.

Tschöke, H. (2010). Exhaust Heat Recovery. In Handbook of Diesel Engines (pp.

401–413). Berlin, Heidelberg: Springer Berlin Heidelberg.

Twigg, M. (2007). Progress and future challenges in controlling automotive exhaust

gas emissions. Applied Catalysis B, Environmental, 70(1), 2–15.

Vasquez, E., Walters, K., & Walters, D. (2015). Analysis of Particle Transport and

Deposition of Micron-Sized Particles in a 90° Bend Using a Two-Fluid

Eulerian-Eulerian Approach. Aerosol Science and Technology, 49(9).

Wang, Y. & Sun, M. & Yang, X. & Yuan, X. (2016) Public awareness and willingness

to pay for tackling smog pollution in China: a case study. Journal of Cleaner

Production. 112 1627-1634.

World Health Organization. (2013). World Health Statistics 2013. Geneva: World

Health Organization.

Xu, S., (2008). The immersed interface method for simulating pre-scribed motion of

rigid objects in an incompressible viscous flow, Journal of Computational

Physics, 227:5045-5071.

Yu, Q. Tan, J. Ge, Y. Hao, L. & Peng, Z. (2017). Application of diesel particulate filter

on in-use on-road vehicles, Energy Procedia, 105, 1730-1736.

Zhou, K., Hou, J., Sun, Q., Guo, L., Bing, S., Du, Q., & Yao, C. (2018). A Study on

Particle Suspension Flow and Permeability Impairment in Porous Media Using

92 Bibliography

LBM–DEM–IMB Simulation Method. Transport in Porous Media, 124(3), 681–

698.

Bibliography 93

Documents

A MODELLING S FILTRATION MECHANISMS FOR MICRON … Kong Thesis.pdf · applied. A coupled lattice Boltzmann method (LBM) and discrete element method (DEM) is implemented to investigate