A computational (DEM) study of fluidized beds with particle size distribution...Masayuki Horio
Numerical simulations based on three dimensional discrete element model (DEM) are conducted for the mono-disperse, binary and ternary system of particles in a fluidized bed. Fluid drag force acting on each particle depending on its size and relative velocity is assigned. An expression for the drag coefficient corresponding to Ergun’s correlation is developed and applied to the system of fluidized bed with particle size ratios of 1:1 for the mono-disperse system, 1:1.2, 1:1.4 and 1:2 for the binary system as well as 1:1.33:2 for the ternary system by keeping total volume and surface area of the particles constant. Results indicated that a reasonable estimation of modified drag force is achieved in the fluid cells. Total translational kinetic energy of particles is found to be increasing with the corresponding increase in the particle size ratio, emphasizing an enhanced momentum transfer between the particles with size distribution. Systems with wide size distribution indicated higher particle velocities around the bubble resulting in the faster bubble growth and its subsequent transition through the fluidized bed. Interesting yet promising nature of these results for the particle systems with size distribution reveals the important trends in determining mixing and segregation of particles in the fluidized bed.
How lively if space illumination is designed through collaboration of an art...Masayuki Horio
Two videos and some slides invites you to the wonderland of powder technology. We powder scientists & engineers, Dr Satoshi Kimura, Mr Rintaro Watanabe, Mr Shigeru Tanimoto and myself, have been keen to develop some novel applications of fluidization and particle technologies to amusement use. Bubbly lamps were some of our ideas. Please enjoy the video.
100520 fluidization past and future, plenary by horio at fluidization xiiiMasayuki Horio
The lecture consists of two parts:
1. Introduction of my recent activity at JST-RISTEX on community based activities against global warming
2. Historical perspective of fluidization science and engineering
In the latter a unique discussion was attempted on the structure of nature (existing things) and the 3 stage law in paradigm shift in scientific research. The history of fluidization research was then analysed in terms of the three stage law.
A computational (DEM) study of fluidized beds with particle size distribution...Masayuki Horio
Numerical simulations based on three dimensional discrete element model (DEM) are conducted for the mono-disperse, binary and ternary system of particles in a fluidized bed. Fluid drag force acting on each particle depending on its size and relative velocity is assigned. An expression for the drag coefficient corresponding to Ergun’s correlation is developed and applied to the system of fluidized bed with particle size ratios of 1:1 for the mono-disperse system, 1:1.2, 1:1.4 and 1:2 for the binary system as well as 1:1.33:2 for the ternary system by keeping total volume and surface area of the particles constant. Results indicated that a reasonable estimation of modified drag force is achieved in the fluid cells. Total translational kinetic energy of particles is found to be increasing with the corresponding increase in the particle size ratio, emphasizing an enhanced momentum transfer between the particles with size distribution. Systems with wide size distribution indicated higher particle velocities around the bubble resulting in the faster bubble growth and its subsequent transition through the fluidized bed. Interesting yet promising nature of these results for the particle systems with size distribution reveals the important trends in determining mixing and segregation of particles in the fluidized bed.
How lively if space illumination is designed through collaboration of an art...Masayuki Horio
Two videos and some slides invites you to the wonderland of powder technology. We powder scientists & engineers, Dr Satoshi Kimura, Mr Rintaro Watanabe, Mr Shigeru Tanimoto and myself, have been keen to develop some novel applications of fluidization and particle technologies to amusement use. Bubbly lamps were some of our ideas. Please enjoy the video.
100520 fluidization past and future, plenary by horio at fluidization xiiiMasayuki Horio
The lecture consists of two parts:
1. Introduction of my recent activity at JST-RISTEX on community based activities against global warming
2. Historical perspective of fluidization science and engineering
In the latter a unique discussion was attempted on the structure of nature (existing things) and the 3 stage law in paradigm shift in scientific research. The history of fluidization research was then analysed in terms of the three stage law.
An easily traceable scenario for GHG 80% reduction in Japan for local energy ...Masayuki Horio
To develop a scenario sure and easily traceable even for ordinary citizens toward the national challenge target of 80% CO2 reduction by 2050, we first developed a model to calculate the total CO2 emission corresponding to the final consumption and second developed an appropriate technology based scenario consisting of the following consumer oriented sub-scenarios: (1) energy saving through electrification of all transportation, (2) promotion of wood utilization for housing and household energy saving; (3) introduction of renewable energies; and (4) efficient energy utilization of wastes. Applying the scenario to Kyoto that has the similar strategies to our proposed scenarios, we found that about 80% CO2 emission reduction is possible just within the appropriate technology limit with the effect of population reduction and with the potential emission reduction from construction of private and public infrastructures, and that shifting our final consumption mode into low CO2 emission mode has a significant impact.
Keywords: CO2 emission reduction, appropriate technologies, local energy strategy, the final consumption
New Developments Through Microscopic Reconstruction of the Nature of Fluidize...Masayuki Horio
Presentation was made at AIChE Particle Technology Forum as an Award Lecture.
After a brief review of achievements of fluidization engineering over decades, a discussion is made on one of the latest issues for applications in material industries as well as for the improvements in reliability of many fluidization processes, i.e., granulation and defluidization issues.
2.1 Background
For a long period, phenomena associated with agglomerating fluidization have been treated with complete empiricism and scientific lights were shed seldom on them. It was, however, natural because the basic intention of fluidization has long been the better gas and solid contacting and, accordingly, agglomeration has been only one of unwanted side effects, which, once technically avoided, tend to be forgotten. At the same time, knowledge on elementary processes that should be relevant to agglomerating fluidization, e.g., bubble characteristics, forces acting among fluidized particles, surface characteristics of solids etc., was only gradually established during the last decades.
Defluidization/agglomeration issues are, however, quite significant in a majority of fluidization processes probably except for gas-to-gas catalytic processes. In polyolefin processes agglomeration due to softening of plastic particles in local hot spots should be avoided. In a polyolefin reactor it has been confirmed by a DEM simulation of Kaneko et al. (1998) that a stable solid circulation does not help removing the heat of polymerization. Instead, a solid motion induced by the always-fluctuating bubbling action is necessary as shown in Fig. 3.
Ash melting and agglomeration, which finally causes defluidization, limits the operating temperature and pressure of pressurized fluidized bed combustion (PFBC) or gasification (PFBG). Figure 4 shows the so-called "sinter eggs" formed in a FBC boiler that is close to those found in AEP Tidd PFBC. Sinter egg/grain formation is again experienced recently in a commercial scale PFBC in Japan.
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
Building better applications for business users with SAP Fiori.
• What is SAP Fiori and why it matters to you
• How a better user experience drives measurable business benefits
• How to get started with SAP Fiori today
• How SAP Fiori elements accelerates application development
• How SAP Build Code includes SAP Fiori tools and other generative artificial intelligence capabilities
• How SAP Fiori paves the way for using AI in SAP apps
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
- Reduction in onboarding time from 5 weeks to 1 day
- Improved developer experience and productivity through actionable findings and reduction of false positives
- Maintenance of superior security standards and inherent policy enforcement with Authorization to Operate (ATO)
Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
We will cover:
- How to remove silos in DevSecOps
- How to build efficient development pipeline roles and component templates
- How to deliver security artifacts that matter for ATO’s (SBOMs, vulnerability reports, and policy evidence)
- How to streamline operations with automated policy checks on container images
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
An easily traceable scenario for GHG 80% reduction in Japan for local energy ...Masayuki Horio
To develop a scenario sure and easily traceable even for ordinary citizens toward the national challenge target of 80% CO2 reduction by 2050, we first developed a model to calculate the total CO2 emission corresponding to the final consumption and second developed an appropriate technology based scenario consisting of the following consumer oriented sub-scenarios: (1) energy saving through electrification of all transportation, (2) promotion of wood utilization for housing and household energy saving; (3) introduction of renewable energies; and (4) efficient energy utilization of wastes. Applying the scenario to Kyoto that has the similar strategies to our proposed scenarios, we found that about 80% CO2 emission reduction is possible just within the appropriate technology limit with the effect of population reduction and with the potential emission reduction from construction of private and public infrastructures, and that shifting our final consumption mode into low CO2 emission mode has a significant impact.
Keywords: CO2 emission reduction, appropriate technologies, local energy strategy, the final consumption
New Developments Through Microscopic Reconstruction of the Nature of Fluidize...Masayuki Horio
Presentation was made at AIChE Particle Technology Forum as an Award Lecture.
After a brief review of achievements of fluidization engineering over decades, a discussion is made on one of the latest issues for applications in material industries as well as for the improvements in reliability of many fluidization processes, i.e., granulation and defluidization issues.
2.1 Background
For a long period, phenomena associated with agglomerating fluidization have been treated with complete empiricism and scientific lights were shed seldom on them. It was, however, natural because the basic intention of fluidization has long been the better gas and solid contacting and, accordingly, agglomeration has been only one of unwanted side effects, which, once technically avoided, tend to be forgotten. At the same time, knowledge on elementary processes that should be relevant to agglomerating fluidization, e.g., bubble characteristics, forces acting among fluidized particles, surface characteristics of solids etc., was only gradually established during the last decades.
Defluidization/agglomeration issues are, however, quite significant in a majority of fluidization processes probably except for gas-to-gas catalytic processes. In polyolefin processes agglomeration due to softening of plastic particles in local hot spots should be avoided. In a polyolefin reactor it has been confirmed by a DEM simulation of Kaneko et al. (1998) that a stable solid circulation does not help removing the heat of polymerization. Instead, a solid motion induced by the always-fluctuating bubbling action is necessary as shown in Fig. 3.
Ash melting and agglomeration, which finally causes defluidization, limits the operating temperature and pressure of pressurized fluidized bed combustion (PFBC) or gasification (PFBG). Figure 4 shows the so-called "sinter eggs" formed in a FBC boiler that is close to those found in AEP Tidd PFBC. Sinter egg/grain formation is again experienced recently in a commercial scale PFBC in Japan.
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
Building better applications for business users with SAP Fiori.
• What is SAP Fiori and why it matters to you
• How a better user experience drives measurable business benefits
• How to get started with SAP Fiori today
• How SAP Fiori elements accelerates application development
• How SAP Build Code includes SAP Fiori tools and other generative artificial intelligence capabilities
• How SAP Fiori paves the way for using AI in SAP apps
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
- Reduction in onboarding time from 5 weeks to 1 day
- Improved developer experience and productivity through actionable findings and reduction of false positives
- Maintenance of superior security standards and inherent policy enforcement with Authorization to Operate (ATO)
Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
We will cover:
- How to remove silos in DevSecOps
- How to build efficient development pipeline roles and component templates
- How to deliver security artifacts that matter for ATO’s (SBOMs, vulnerability reports, and policy evidence)
- How to streamline operations with automated policy checks on container images
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
UiPath Test Automation using UiPath Test Suite series, part 3
040603 Four topics for further development of dem to deal with industrial fluidization issues, ICMF plenary2004
1. Four Topics for Further
Development of DEM to
Deal with Industrial
Fluidization Issues
Masayuki Horio and Wenbin Zhang
Department of Chemical Engineering,
Tokyo University of Agriculture and
Technology,
Koganei Tokyo, 184-8588 Japan,
masa@cc.tuat.ac.jp
2. Come & Visit Tokyo Univ. A&T
at Koganei (25min from Shinjuku)
4. From Burton to Fluid Cat. Cracking
Chemical Engineers’ Unforgettable
Memory
The FCC Development (1940-50)
Capacity in world total [%]
5. product
Competition and Evolution product product
of Fluid Catalytic Plants in
1940-50
product
steam
steam
air
kerocene
kerocene & steam air
& steam product kerocene air
& steam
FCC Plant development
air in Catalytic Cracking of
kerocene
& steam
air
steam Kerocene(1940-50)
6. Post
cloud
mdern
Era:
Natural Science and
Engineering Science
The presence of
column wall makes
research much
easier
hail
artificial
plant volcanic plateau
AIChE Fluor Daniel Lectureship Award
Lecture (2001)
7. My background
-1974 Fixed/Moving Bed Reactors
and iron-making Processes
1974- Fluidization Engineering
75-99 Pressurized Fluidized Bed Combustion
Jets, Turbulent Transport in Freeboard
82-89 Scaling Law of Bubbling Fluidized Bed
89-92 Scaling Law of Clustering Suspensions
93- DEM Simulation
Waste Management, Material Processes
1997- Sustainability and Survival Issues
Biomass Utilization, Appropriate Technology
8. When Professor Tsuji et al. 1993 proposed an
excellent idea of applying the concept of
discrete/distinct element method of Cundall et al.
(1979) to fluidized beds borrowing the fluid phase
formulation from the two phase model,
I (Horio) almost immediately decided to join in the
simulation business of fluidized beds from
chemical engineers' view points.
This was because with his approach the real
industrial issues, such as agglomeration, gas
solid reactions and/or heat transfer, can be
directly incorporated into the model without the
tedious derivation of stochastic mechanics,
which is not only indirect but also sometimes
impossible from analytical reasons.
9. DEM, the last 10 years
DEM: Discrete Element Method
Fluid phase: local averaging
Particles: semi-rigorous treatment
User friendly compared to Two Fluid Model & Direct
Navier-Stokes Simulation
•A new pressure/tool to reconstruct particle
reaction engineering based on individual
particle behavior
•Potential for more realistic problem definition/
solution
Our code development: SAFIRE
Simulation of Agglomerating Fluidization for Industrial
Reaction Engineering
10. Normal and tangential component of Fcollision
and Fwall
Fn = k nD x n - h dx n
n
dt
Ft = m Fn x t Ft > m Fn
x t
Ft = k tD x - h dx t
m Fn
t t Ft
dt
h = 2g g = ( ln e ) 2
km
( ln e ) 2 + p 2
SAFIRE (Horio et al.,1998~)
Rupture joint h c
Attractive force Fc Surface/bridge force
(Non-linear spring)
kn Normal dumping h n w/wo Normal Lubrication
Normal elasticity
No tension joint Tangential dumping h t
Tangential elasticity k t
SAFIRE is an extended Tsuji-Tanaka model
developed by TUAT Horio group
Friction slider m
w/wo Tangential Lubrication
Soft Sphere Model with Cohesive Interactions
11. COMBUSTION Spray Agglomerating AGGLOMERATION
Granulation/Coating Fluidization
FB
w/ Immersed Ash
Tubes : Melting
FB of Particles w/
Pressure Effect I-H
Solid Bridging van der Waals
Rong-Horio 1998 Tangential
2000 FB w/ Interaction
Kuwagi-Horio Lubrication
Immersed Iwadate-Horio Effect
1999
Coal/Waste Tubes 1998
Kuwagi-Horio
Combustion Parmanently
Rong-Horio 2000
in FBC Wet FB
1999
Mikami,Kamiya,
Fluidized Bed DEM Horio
Started from 1998
Particle-Particle Dry-Noncohesive Bed
Single Char Heat Transfer
Tsuji et al. 1993
Combustion Rong-Horio Natural Phenomena
in FBC 1999
Rong-Horio
OTHER
1999 Lubrication
Force Effect
SAFIRE Olefine Scaling Law
Achievements Polymerization Noda-Horio for DEM Scaling Law
for DEM
PP, PE Structure of
2002 Computation
Computation
Kaneko et al. Emulsion Phase Kajikawa-Horio
2000~ Kuwagi-Horio
1999 2002~
Kajikawa-Horio
Catalytic Reactions
2001
CHEMICAL REACTIONS FUNDAMENTAL LARGE SCALE SIMULATION
12. AGGLOMERATION
Industrial Issues & DEM
■ Agglomerating Fluidization
by Liquid Bridging
by van der Waals Interaction
by Solid Bridging through surface diffusion
through viscous sintering
by solidified liquid bridge
Coulomb Interaction
■ Size Enlargement
by Spray Granulation (Spraying, Bridging, Drying)
by Binderless Granulation (PSG)
■ Sinter/Clinker Formation
in Combustors / Incinerators (Ash melting)
in Polyolefine Reactors (Plastic melting)
in Fluidized Bed of Particles (Sintering of Fe, Si, etc.)
in Fluidized Bed CVD (Fines deposition and Sintering)
13. CHEMICAL REACTORS
Industrial Issues & DEM
Heat and Mass Transfer gas-particle
particle-particle
Heterogeneous Reactions
Homogeneous Reactions
Polymerization
Catalytic Cracking (with a big gas volume increase)
Partial Combustion (high velocity jet)
COMBUSTION / INCINERATION
Boiler Tube Immersion Effect
Particle-to-Particle Heat Transfer
Char Combustion
Volatile Combustion (Gas Phase mixing / Reaction)
Combustor Simulation
14. 10m m
Sintering of
2xneck
2xneck
steel particles
neck diameter, 2
neck diameter
in Fluidized
Bed Reduction
(a) 923K (b) 1123K
Steel shot :dp=200m m, H2, 3600s SEM images of necks
30
Calculated from
after 3600s contact
25 surface diffusion model
20
Neck diameter 2x
15
10 d p=200 m m
d p=20 m m
5
0
700 800 900 1000 1100 1200 1300
Temperature [K]
Neck diameter determined from SEM images
after heat treatment in H2 atmosphere
Solid Bridging Particles (Mikami et al , 1996)
15. Model for Solid Bridging Particles
1. Spring constant: Hooke type (k=800N/m)
Duration of collision: Hertz type
2. Neck growth: Kuczynski’s surface diffusion model
1/ 7
4
56gd 3
x neck = DS rg t
kBT
Ds = D0,s exp (-Es /RT)
-2 5
D0,s =5.2x10 m/s, E =2.21x10 J/mol (T>1180K)
3. Neck breakage
Fnc = s neck Aneck
Ftc = t neck Aneck Kuwagi-Horio
Kuwagi-Horio 1999
19. Intermediate condition Weakest sintering Strongest sintering
condition condition
(a) Smooth surface
(b) 3 micro-contact (c) 9 micro-contact
points points
Kuwagi-Horio d p =200mm, T=1273K, u 0=0.26m/s
Agglomerates Sampled at t = 1.21s
Kuwagi-Horio 1999
20. Poly-Olefine Reactor Simulation,
Kaneko et al. (1999)
fluid cell
uy
Energy balance
Gas phase :
( ) ∂εu T )
∂ Tg
ε ( i g 1 particle
+ = Q
∂t ∂i
x ρcp,g g
g
ux
Particle : vy ε Tg
dTp
Vpcp,pρp
dt
H (
= Rp (- Δ r ) - hp Tp - Tg S ) Qg
vx
Tpn
6(1- ε )
Qg =
dp
(
hp Tp - Tg ) external gas film
E heat transfer hpn
Rp = k exp ( ) w cPr
RTp coefficient
1
(different for each particle)
1
Nu = 2.0 + 0.6 Pr Rep 3 2 (Ranz-Marshall equation)
Nu = hpdp / kg Pr = cp,gμ / kg
g Rep = u - v ρdp / μ
g g
21. Particle circulation Kaneko et al. 1999
(artificially generated by feeding gas nonuniformly from distributor nozzles)
t=9.1 sec t=6.0 sec t=8.2 sec
393
(120℃)
343
293
T [K] (20℃) 2.5umf 2.5umf
2umf 2umf
3umf 3umf 3umf
9.3umf
Ethylene polymerization 15.7umf
Number of particles=14000
Gas inlet temp.=293 K Hot spot
u0=3 umf
Tokyo University of Agriculture & Technology Idemitsu Petrochemical Co.,Ltd.
22. Uniform gas feeding Nonuniform gas feeding
particle temp. particle velocity particle temp. particle velocity
vector vector
t=9.1 sec t=8.2 sec
: Upward motion 2umf 2umf
3umf 3umf 3umf
: Downward motion 15.7umf
Stationary
circulation
Stationary solid revolution helps Petrochemical Co.,Ltd.
Tokyo University of Agriculture & Technology Idemitsu
the formation of hot spots.
23. A Rough Evaluation of
Heat Transfer Between Particles
radiation
A B
0.4 nm
contact point heat transfer
A B
convection
particle-thinned film-particle
Rong-Horio 1999 heat transfer
when l AB < 2r + d : particle-particle heat conduction
24. Four Topics for Further
Development of DEM
1. PSD
2. Large Scale Computation via
Similar Particle Assemblage Model
3. Surface Characterization and
Reactor Simulation
4. Lubrication Force and Effective
Restitution Coefficient
25. PSD Issue
Derivation of CD
corresponding to Ergun
Correlation and A Case Study
Master Thesis
by Nobuyuki Tagami
26. 1. PSD
What We need for moving
from Uniform Particle
Systems to Non-uniform Ones
○ 3D Computation
○ Contact Model with Particle Size Effect
Fookean to Herzean Spring
○ Fluid-Particle Interactions Today’s topic
1) not from Ergun (1952) Correlation
2) not indifferent to particle arrangement
27. 1. PSD
Apparent Drag Coefficient
that corresponds to Ergun
Correlation
(1) Bed Pressure Drop Correlation (Ergun(1952))
ΔP * /DL = ΔP/ΔL - ρ f g
=
(1 - ε ) 150 (1 - ε )μ f ( )
+ 1.75ρ f u - v u - v
d p : Particle diameter
ε : Void fraction
d p
d p
ρ f : Fluid density
(2) Equation of motion for fluid (1D) u : Fluid velocity
ΔP
( )
v : Particle velocity
-ε - nFpf + ερ f g = 0 n = (1 - ε )/ πd p 3 /6
ΔL
(3) Drag Coeff.
8 F pf → Apparent Drag Coeff.
CD 200(1 - ε )μ f
p d p ρf u - v
2 2
C D, Ergun = + 2.33
d pρ f ε u - v
28. 1. PSD
Extension of CD,Ergun
200(1 - ε )μ f
C D,Ergun = + 2.33
d pρ f ε u - v
200(1 - ε )μ f
C D,Ergun = + 2.33
d pρ f ε u - v
29. 1. PSD
The Sum of Drag Force Consistent
with Ergun Correlation ?
Error was within the Accuracy of
dp1/dp2 Number of Ergun Correlation ±25%. F
i,C D,Ergun
[mm/mm] particles Binary System
Fi,Ergun
1.00 30000
1.50 / 4444 /
0.750 35556 1.25
ρ p = 2650kg/m 3
1.00
ρ f = 1.204kg/m 3
μ f = 18 μ Pa s
0.75
u 0 = 0.811
1.122m/s (t 0.5s)
= 1.122m/s (t 0.5s)
30. 1. PSD
PSD Effect: A Case Study
Run1 Run2 Run3
Diameter [mm] 3.00 4.50/3.00/2.25 4.50/2.25
Number [#] 30000 2963/10000/23703 4444/35556
Vol. Fraction 1 0.333/0.333/0.333 0.500/0.500
Surface to Volume Mean Diameter:
dsv=Σ(Ndp3)/Σ(Ndp2) = 3.00 mm
Total solid volume = 4.24×10-4m3,
Total solid surface area = 8.48×10-1m2
Young’s modulus: 80GPa, Poisson ratio: 0.3, friction coefficient: 0.3
(Glass beads)
Contact Force Model Normal:Hertz’ Model
Tangential: ‘no-slip’ Solution of Mindlin,
and Deresiewicz (1953)
31. Comparison of the three cases
Run 1 Run 2 Run 3
3.00mm 4.50 / 3.00 / 2.25 4.50 / 2.25 mm
mm
u0 = 1.438→2.938m/s (t<1sec), u0 = 2.938m/s (t≧1sec)
32. 1. PSD
Run3
Large particles become more mobile
receiving forces from smaller ones
33. 2. SPA Fluidization XI, May 9-14, 2004,
Ischia (Naples), Italy
The Similar Particle Assembly (SPA)
Model,
An Approach to Large-Scale Discrete
Element (DEM) Simulation
Kuwagi K.a, Takeda H.b and Horio M.c,*
aDept. of Mech. Eng., Okayama University of Science,
Okayama 700-0005, Japan
bRflow Co., Ltd., Soka, Saitama 340-0015, Japan
cDept. of Chem. Eng., Tokyo University of Agri. and Technol.,
Koganei, Tokyo 184-8588, Japan
34. Development of Computer Pormance
1.0E+16
Fastest computer models
Nishikawa et al. (1995)
Performance [MFLOPS]
Seki (2000)
1.0E+13 Oyanagi(2002) 15 to 20 years
Single processor for PC
1.0E+10 Moore's Law
1.0E+7
1.0E+4
1.0E+1
1,940 1,960 1,980 2,000 2,020
Year
35. 2. SPA
How to deal with billions of particles?
TFM (Two-fluid model)
DSMC (Direct Simulation Monte Carlo)
Difficult to deal with realistic particle-particle and
particle-fluid interactions including cohesiveness
DEM (Discrete Element Method)
One million or less particles with PC in a practical
computation time
Hybrid model of DEM and TFM (Takeda & Horio, 2001)
Similarity condition for particle motion (Kazari et al., 1995)
Imaginary sphere model (Sakano et al., 2000)
36. 2. SPA
Similar Particle Assembly (SPA) Model
Assumptions
(0. Particles are spherical)
1. A bed consists of particles of different species
having different properties, i.e. particle size,
density and chemical composition, and it has
some local structure of their assembly.
2. Of each group (species) N particles are supposed
to be represented by one particle at the center of
them. This center particle is called a
representative particle for the group.
3. The representative particles for different groups
can conserve the local particle assembly similar.
37. m times larger system
(a) (b) of the same particles
as the smaller bed
A particle Represented volume
for N particles
Similar structure
(c) + (d)
+
+ + +
i
+x + +
x+Dx i’
x x+mDx
original system m times larger system
Particle Coordination Scaling
38. 2. SPA
Preparation
(1) All particles are numbered: i=1~NT.
(2) Subspace: (
Gk d p , p )
(3) Group number of particles: (( )
ki k d pi , pi Gk )
(4) Equation of motion for particle i:
p 3 dv i p 3
pi d pi = Ffi + Fpij + pi d pi g
6 dt j i 6
Ffi: particle-fluid interaction force
Fpij: particle-particle interaction force
39. 2. SPA
Governing Equations
Equation of motion for original particle:
p 3 dv i p 3
pi d pi = Ffi + Fpij + pi d pi g
6 dt j i 6
Equation of motion for m-times larger volume:
p 3 dv i ' p 3
pi ' d pi ' = Ffi ' + F pi ' j ' + pi ' d pi ' g
* *
6 dt j ' i ' 6
where d pi ' = md pi
p 3 dv i ' p 3
m pi ' d pi '
3
= Ffi ' + F pi ' j ' + m pi ' d pi ' g
* * 3
6 dt j ' i ' 6
If F +*
fi ' F *
pi ' j '
= m Ffi + F pij
3
, v i' = v i
j ' i ' j i
(1 - )2 m f (u - v) f (u - v) u - v
FPi = 150 + 1.75(1 - ) Ncell
2
d pi d pi
p
Fpi =
CD f 2 (u - v l ) u - v l d pi
2
8
40. Computation Conditions for Case 1
Particles Geldart Group: D
Particle diameter: dp [mm ] (a) 1.0 (b) 3.0 (c) 6.0
Particle density: p [ kg/m3 ] 2650
Number of Particles (a) 270,000 (b) 30,000 (c) 7,500
Restitution coefficient 0.9
Friction coefficient 0.3
Spring constant: k [ N/m ] 800 (Dt=2.58x10-5s)
Bed
Column size 0.5×1.5m
Distributor Porous medium
Gas Air
Viscosity: mf [Pa.s ] 1.75x10-5
Density: f [kg/m3 ] 1.15
41. 0.262s 0.528s 0.790s 1.05s 1.31s 1.58s 1.84s 2.10s 2.36s 2.62s
(a) Original bed (dp=1.0mm)
(b) SPA bed (representative particle, dp’=3.0mm)
(c) SPA bed (representative particle, dp’=6.0mm)
Snapshots of Dry Particles
42. p=2650kg/m3, Column : 0.5×1.5m, u0=1.2m/s
of lower half set particles [m] 0.4
d p =1.0mm (Original bed) Dry
(fluid cell: 134x333)
0.3
Average height
0.2 d p =1.0mm (Original bed)
d p' =3.0mm (SPA bed)
d p' =6.0mm (SPA bed)
0.1 (fluid cell: 22x56)
u0: increasing u0: decreasing0
decreasing U +
0
0 1 2 3 4 5
Time [s]
Average height of dry particles
initially located in the half lower region
43. 0.262s 0.528s 0.790s 1.05s 1.31s 1.58s 1.84s 2.10s 2.36s 2.62s
(a) Original bed (dp=1.0mm)
(b) SPA bed (representative particle, dp’=3.0mm)
(c) SPA bed (representative particles, dp’=6.0mm)
Snapshots of Wet Particles (V=1.0x10-2)
44. p=2650kg/m3, Column : 0.5×1.5m, u0=1.2m/s
of lower half set particles [m] 0.4
d p =1.0mm (Original bed) Wet
(fluid cell: 134x333)
0.3
Average height
0.2
d p' =6.0mm (SPA bed)
d p' =3.0mm (SPA bed)
0.1 d p =1.0mm (Original bed)
(fluid cell: 22x56)
u0: increasing decreasing U
u0: decreasing0 +
0
0 1 2 3 4 5
Time [s]
Average height of wet particles
initially located in the half lower region
45. 2. SPA
10,000 10,000
Umf = 0.72m/s dry wet (V=1.0x10-2)
8,000 8,000
Umf = 0.70m/s
DP [Pa]
DP [Pa]
6,000 6,000
4,000 d p =1.0mm 4,000 d p =1.0mm
d p'=3.0mm d p' =3.0mm
2,000 2,000
d p' =6.0mm d p' =6.0mm
0 0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4
U0 [m/s] U0 [m/s]
(a) Dry particles (b) Wet particles
Umf from Wen-Yu correlation = 0.57m/s
Comparisons of umf
46. 2. SPA
CPU time for real 1s on Pentium 4 2.66GHz
Dry [s] Wet [s]
Original bed 27,300 27,600
(dp=1mm) (7hrs 34min) (7hrs 39min)
SPA bed 1,760 1,870
(dp’=3mm) (29min)
1/15 (31min) 1/15
SPA bed 426 508
(dp’=6mm) (7min) 1/64 (8min) 1/55
47. Computation Conditions for Case 2
Single bubble fluidization of two-density mixed particles
Column 0.156x0.390m p=3000kg/m3
Nozzle width 4mm p=2000kg/m3
Particle (original)
dp 1.0mm
p 2000, 3000 kg/m3
Gas Air
f 1.15kg/m3 0.7m/s 0.7m/s
mf 1.75x10-5Pa.s 15m/s (0.482s)
Fig: Initial state
50. Z 0.14 SPA model 0.14
SPA model
[m]
0.12 0.12 0.12
0.10 0.1 0.1
0.08 0.08 0.08
Original bed
z [m]
Original bed
0.06 0.06 0.06
0.04 0.04 0.04
Bubble region
0.02 0.02 0.02 (No particles exist.)
0 0
0 0.5 1 1.5 2 2.5
0
0 0.05 0.1 0.15 0.2 0.25 0.3
(a) t=0.056s Gas velocity [m/s] Particle velocity averaged
in each fluid cell [m/s]
Z 0.14 0.14
[m] SPA model
0.12 0.12 0.12 Original bed
0.10 0.1 0.1
Original SPA
0.08 z [m] 0.08
bed 0.08
model
0.06 0.06 0.06
0.04 0.04 0.04
0.02 0.02 0.02
0 0
0 0.5 1 1.5 2 2.5 3
0
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Gas velocity [m/s] Particle velocity averaged
(b) t=0.111s in each fluid cell [m/s]
Vertical velocity distributions of particle
and gas phases along the center line
51. 2. SPA
SPA concept: promising.
Similar Particle Assembly (SPA) model
for large-scale DEM simulation
Validations (comparisons with the original)
Non-cohesive particles
>Slug flow occurred at the beginning of fluidization: similar
>Bubble diameter: almost the same
>Bubble shape: not clear with large representing volume
>Umf: fair agreement
Cohesive particles: the same tendency as the above
Binary (density) System:
>Bubble: similar
>Particle mixing: similar
52. 3. More Realistic Surface Characterization
Measurement
of
Stress-Deforemation Characteristics
for a Polypropylene Particle
of Fluidized Bed Polymerization
for DEM Simulation
M. Horio, N. Furukawa*, H. Kamiya and Y. Kaneko
*) Idemitsu Petrochemicals Co.
53. Computation conditions
Particles
Number of particles nt 14000
Particle diameter dp 1.0×10-3 m
Restitution coefficient e 0.9
Friction coefficient μ 0.3
Spring constant k 800 N/m
Bed
Bed size 0.153×0.383 m
Types of distributor perforated plate
Gas velocity 0.156 m/s (=3Umf)
Initial temperature 343 K
Pressure 3.0 MPa
Numerical parameters
Number of fluid cells 41×105
Time step 1.30×10-5 s
54. 0 7 15 ΔT [K]
Snapshots of temperature distribution in PP bed
(without van der Waals force)
55. Ha = 5×10-20 J
Ha = 5×10-19 J
0 7 15 ΔT [K]
Snapshots of temperature distribution in PP bed
(with van der Waals force)
57. 3. Surface Characterization
Catalyst TiCl3 0.35
Pressure 0.98 MPa 0.3
Diameter[mm]
Temperature 343 K 0.25
Reactor stage φ14 mm 0.2
0.15
0.1
0.05
0
0 10 20 30 40 50 60
Time [min]
PP growth with time
The micro reactor
0 min 1 min 2 min 5 min 10 min 15 min 20 min 30 min 60 min
Optical microscope images
Polymerization in a Micro Reactor
58. 3. Surface Characterization
1: material testing machine’s
10 stage
2: electric balance
9 3: table
7
8 4: polypropylene particle
5: aluminum rod
6 5 6: capacitance change
1
4 3 7: micro meter
2 8: nano-stage
9: x-y stage
1 10: cross-head of material
testing machine
Force-displacement meter
59. k ~100 N/m Fdp0.5x1.5 (Hertzean spring)
10 -3
10-3 10-3
dp = 597μm dp = 597μm dp = 597μm 3rd
10-4 10-4 10-4
Force [N]
Force [N]
Force [N]
2nd
3rd
10-5 10-5 10-5
2nd 2nd
2nd
1st 1st 1st
10-6 10-6 10-6
10 -8 10-7
10 -6
10 -5
10 -8 10-7
10 -6
10 -5
10 -8 10 -7 10-6 10-5
Displacement [m] Displacement [m] Displacement [m]
x
dp=597mm
FE-SEM images: whole grain and its surface
Repeated force-displacement characteristics
of a polypropylene particle
60. Fdp0.5x1.5 (Hertzean spring)
10 -3 10-3 10-3
dp = 487μm dp = 487μm dp = 487μm
10 -4 10-4 10-4 3rd
Force [N]
Force [N]
Force [N]
3rd
2nd
10 -5 1st 10-5 10-5 2nd
1st 1st
2nd 2nd
1st 1st 1st
10 -6 10-6 10-6
10-8 10 -7
10 -6
10 -5 10 -8 10-7 -6
10 10 -5
10-8 10-7 10-6 10 -5
Displacement [m] Displacement [m] Displacement [m]
x
dp=487mm
FE-SEM images: whole grain and its surface
Repeated force-displacement
characteristics of a polypropylene particle
(maximum load from first cycle)
62. 3. Surface Characterization
Particle surface morphology changes by
collisions
Plastic deformation in the case of PP
Hertz model stands OK
Experimental Determination of Cohesion
Force: Now on going
63. 4. Lubrication Force
Lubrication Force and
effective Restitution
Coefficient
W. Zhang, R. Noda and M. Horio
Submitted to Powder Technology
64. 4. Lubrication Force
Restitution
Spring constant
coefficient
? ? Heat transfer, agglomeration
Realistic collision process Fluidization behavior
‘Near Contact’ force:
Interparticle forces
Lubrication force
Field force: Contact force:
Electrostatic Van der Waals force
force Liquid and solid bridge force
Impact force
65. 4. Lubrication Force
Classical lubrication theory
For Liquid-Solid Systems; Tribology, filtration etc.
Why not in Gas-solid systems?
Lubrication force negligible ?
Introduction of “Stokes Paradox” ?
Two solid surfaces can never make contact in a finite
time in any viscous fluid due to the infinite lubrication
force when surface distance approaches zero
Can we avoid the paradox practically or essentially?
66. Davies’ development of lubrication theory to gas-solid systems
dh
= -v(t ) = -(v1 + v2 ) v1
dt
dv
m = -F (t ) = - FL
dt r
H(r,t) h(0,t)
p(r,t)
• identical and elastic
• head-on collision
v2
• rigid during approaching
Assumptions in classical lubrication theory
Initial gap size h0 is assumed to be much smaller than particle radius
Upper limit of integration of pressure for lubrication force is extended to infinity
Paraboloid approximation of undeformed surface
Fluid is treated as a continuum
3mRv 3
H (r , t ) = h(0, t ) + r / R
2
p(r , t ) = FL , = 2prp(r , t )dr = pmR 2v / h
2(h + r 2 / R) 2 0 2
67. Examination of the assumptions in gas-solid systems
R: particle
Ratio of lubrication force FL,R/FL,¡Þ
10
radius
Ratio of FL,0 to other forces
1.0
8 0.9
FL,0/Fd
6 0.8 h0: initial
4 0.7 separation
0.6
2 FL,0/G
0.5
0
0.4
0.01 0.1 1 0.0 0.2 0.4 0.6 0.8 1.0
h0/R Relative initial distance
Order-of-magnitude estimation
FL, = 2prp(r , t )dr
0
• FCC particles: 50mm, v0=ut, at 20C R
FL, R = 2prp(r , t )dr accurate
0
• Comparison of initial lubrication
force to other forces
more reasonable with large
• Particle radius as “near contact lubrication effect area
area” or “lubrication effect area”
68. Numerical solutions for pressure distribution
Pressure
h0=0.01R h0=0. 1R h0=R
Relative radial distance r/R numerical
analytical with paraboloid
approximation
• Pressure decays to zero much more slowly than that with paraboloid
approximation
• Contribution of pressure in the outer region to the lubrication force
may play an important role
• Numerical calculations for lubrication force are needed
69. Avoidance of “Stokes Paradox”
• Assume that minimum surface distance equals to surface roughness
• Whether the fluid remains as a continuum is determined by the relative magnitude
of surface distance to mean free path of fluid molecules
Case 1: hmin>l0 FL ,num h h
K1 (h) = = 1.041 - 0.281lg - 0.035 lg 2
FL ,ana R R
25
Ratio of lubrication force to
1 1
initial value FL,0 at h0
R 3
20 contact FL ,ana (h) = 2prpdr = pmR 2v -
0 2 h h+R
15
10
approaching Surface roughness of FCC is observed
5
to be one tenth of particle radius
detaching
0
0.0 0.2 0.4 0.6 0.8 1.0 Maximum lubrication force is reached
hmin/h0 Ratio of surface distance h/h when roughness make contact
0
• FCC particle: 50mm, v0=ut/5 To realistic particles, stokes paradox is
avoided
• Fluid: Continuum
70. Avoidance of “Stokes Paradox”
Case 2: hmin<l0 • Particles in this case have relatively smaller roughness
• Non-continuum fluid effect should be
considered in the last stage of approaching
• Maxwell slip theory (Hocking 1973) was adopted
v0=ut/2 FL ,num, slip h h
1E-6 K 2 ( h) = = 1.309 - 0.082 lg - 0.009 lg 2
Lubrication force FL (N)
Non-continuum fluid FL ,ana,slip R R
v0=ut/5
1E-7 Continuum fluid
pmR 2v h + 6l0 h + R + 6l0
1E-8 FL ,ana, slip = (h + 6l0 ) ln h - (h + R + 6l0 ) ln h + R
2
12l 0
1E-9 l0>>h
1E-10 pmR 2v 6l0
FL ,ana, slip = ln
2l0 h
1E-11
1E-8 1E-7 1E-6 1E-5 1E-4
Surface distance h (m) Increase of lubrication force is slowed
down in close approaching distance
• GB particle: 50mm, v0=ut/5
Treatment of fluid as a non-continuum
• Fluid: Non-continuum helps us avoid the infinite lubrication force
71. Avoidance of “Stokes Paradox”
Case 3: hmin is comparable to Z0
• When the surface distance can be approached to the dominant range
of van der Waals force, -----
-7 FL m
dv
= - F (t ) = -( FL - Fvw )
2.0x10
0.0 dt
-7 F
total AR
-2.0x10
F Fvw = -
Forces F(N)
A: Hamaker constant
Forces F (N)
-7
-4.0x10 vw 12h 2
-7
-6.0x10
-8.0x10
-7
Magnitude of van der Waals force
-6
-1.0x10 increases more rapidly when h -> 0
-6
-1.2x10 hvw
-1.4x10
-6 A characteristic distance hvw is
1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 defined to indicate the adhesive force
Surface distance h (m) dominant region (~10-9m)
• GB particle: 50mm, v0=ut/10 Consideration of adhesive force in
the last approaching stage saves us
• Fluid: Non-continuum again from Stokes Paradox
72. Effective Restitution Coefficient
• Lubrication effect is actually a kind of damping effect, causing kinetic energy
dissipation during both approaching and separating stage
• Restitution coefficient can be regarded as a criterion for evaluating the
lubrication effect on collision process
*
Ste mv0
e = 1- where St = Ratio of particle inertia to viscous force
St 6pmR 2
* *
mvc mve
Critical Stokes Number St =
*
Ste =
*
= 2Stc
*
c
6pmR 2
6pmR 2
• vc* is called “critical contact velocity” under which particles cannot make
contact due to the repulsive lubrication force in the approaching stage
• ve* is called “critical escape velocity” under which particles cannot escape
from the lubrication effect area and will cease during the separation stage
h 2 h 3 h
f1 (h) = 0.962 ln - 0.079 ln - 0.004 ln Case 1
St = f (h0 ) - f (hmin )
*
e
h+R h+R h+R
2 2
1 h 6l 1 h+R
ln 1 + 0 - ln 1 + -
6l R R
f(h): characteristic function f 2 (h) = 6 + ln 1 + 0 - 6 +
h+R Case 2,3
36 l0 h 36 l0 h 6l0
73. Examples and discussion
1.0 1.0
Restitution coefficient e
Restitution coefficient e
ut hmin/h0=1/5
0.8 0.8
ut/5
0.6 0.6
ut/2 ut/20 hmin/h0=1/10
ut/10
0.4 0.4
ut/50
0.2 umf 0.2 hmin/h0=1/20
0.0 0.0
20 30 40 50 60 70 80 90 100 110 0.1 1 10 100 1000
Diameter of FCC particles dp (mm) Stokes Number St
Case 1: FCC, hmin/h0=1/10 Case 1: FCC, different roughness
Under same approaching velocity, effect of the lubrication force on larger
particles is less significant than on smaller particles
The independent effects of particle size and approaching velocity on the
coefficient of restitution can be included in the consideration of Stokes numbers
Collisions with Stokes numbers less than Ste* result in a restitution coefficient
to be zero, consequently causing cluster and agglomeration to occur
74. Examples and discussion
Restitution coefficient e
Restitution coefficient e
1.0 1.0
0.8 0.8
0.6 0.6
0.4 ut 0.4
ut
0.2 ut /2 0.2 ut /5
ut /10
0.0 0.0 ut /20
ut /50
20 30 40 50 60 70 80 90 100 110 20 30 40 50 60 70 80 90 100 110
Diameter of GB d (mm) Diameter of smooth GB dp (mm)
Case 2: GB, solid line: with slip, dotted Case 3: GB, solid line: with slip and van der
line: without slip Waals force, dotted line: without slip
Consideration of non-continuum fluid weakens the lubrication effect and thus
increases the values of the restitution coefficient
The lubrication effect is more significant in case 3 since particles can approach
much more closely so that the effect of non-continuum fluid may be more
significant
75. 4. Lubrication Force
Remarks
By numerically extending classical lubrication
theory into gas-solid systems, semi-empirical
expressions for lubrication force are proposed.
Evaluation of lubrication effect on collision
process are made according to restitution
coefficient.
Stokes Paradox is avoided by considering
surface roughness, non-continuum fluid and van
der Waals force.
Further research should be aiming at
incorporating lubrication force and an effective
restitution coefficient into DEM simulation in the
near contact area.
76. Industrial Development and
Fundamental Knowledge
Development need each other
Wishing much frequent
Exchange and Collaboration
between Physical/Mechanical
Scientists and Chemical
Engineers
77. In Japanese very
old folk song
Ryojin-Hisho:
Asobi-wo sen-to-ya
Umare-kem.
(Were’nt we born
for doing fun?)