Dynamic vertical forces working on a large object floating in gas-fluidized bed
Hyun-sang Lim
2019. 01. 31
Computer Graphics @ Korea University
Kyohei Higashida et al.(Osaka University, Japan)Chemical Engineering Science 2016
Copyright of figures and other materials in the paper belongs to original authors.
Hyun-sang Lim | 2018. 01. 31 | # 2Computer Graphics @ Korea University
Index
1. Introduction– Motivation
– Related Work
– Contribution of this paper
– Why I select this paper
2. Fictitious Particle Method
– What is FPM method?
– The algorithm for calculating the motions
– Why is FPM method used?
3. Lagrangian sensor system
– Lagrangian sensor
– The algorithm for calculating dynamic force
4. Experiment
– Experimental conditions
– Result
5. Conclusion
Hyun-sang Lim | 2018. 01. 31 | # 3Computer Graphics @ Korea University
1. Introduction
Motivation: What is fluidized bed.
- A fluidized bed reactor (FBR) is a type of reactor device that can be used to carry out a variety of multiphase chemical reactions. In this type of reactor, a fluid is passed through a solid granular material at high enough velocities to suspend the solid and cause it to behave as though it were a fluid. This process, known as fludization.
Fig1. Basic diagram of a fluidized bed reactor
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1. Introduction
Motivation: Why is analysis of fluidized bed important?
- Motions of the fuel particles in fluidized bed like floating and sinking in addition to the residence time give significant influences on the system efficiency while it is not fully understood due to its complexity.
Hyun-sang Lim | 2018. 01. 31 | # 5Computer Graphics @ Korea University
1. Introduction
Related work : Nguyen and Grace(1978)
- Nguyen and Grace(1978) showed that the net buoyant force acting on floating objects in a fluidized bed can be estimated from the bulk density of the bed at fluidization while splashing particles on to the top of the objects cause periodic sinking.
Low buoyancy!
High buoyancy! + Bulk motion of air
Fig2. Concept of periodic sinking
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- Oshitani etal.(2004) investigated the floating and sinking motions of large spherical objects changing gas velocity, bed height, size of bed material sand objects.
- Soria-Verdugoetal. (2011) performed similar investigations in that the influence of object density, size and gas velocity on large cylindrical object motions in a two-dimensional bubbling fluidized bed were discussed.
- Cai etal.(2014) focused on the residence time of large spherical objects in a fluidized bed and investigated the influence of density, size of objects and gas velocity.
1. Introduction
Related work : Other empirical works
Hyun-sang Lim | 2018. 01. 31 | # 7Computer Graphics @ Korea University
- He etal.(2009) simulated flows in a bubbling fluidized bed with immersed fixed tubes by using a body-fitted mesh.
- Farzanehetal. (2015) and Hernández-Jiménez etal.(2015) simulated the motion of large fuel particles in a bubbling fluidized bed by combining Eulerian–Lagrangianmodel with Eulerian–Eulerian model where large fuel particles are treated as a discrete phase.
However, there are few studies focusing on the motion of large objects in a fluidized bed by Eulerian–Lagrangian approach
1. Introduction
Related work : Numerical simulations
Hyun-sang Lim | 2018. 01. 31 | # 8Computer Graphics @ Korea University
1. Introduction
Related work : Tsugi et al(2014)
- Tsugi investigated motion of large objects in a fluidized bed by applying new numerical method called Fictitious particle method.
Fig 3. Modeling based on small fictitious particles. (a) Particles and sphere. (b) Particles and fictitious particle.
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1. Introduction
Contribution of this paper
(1) Applying FPM to simulation of large object in fluidized bed.
(2) Designing experiment for measuring dynamic force in fluidized bed.
(3) Confirming the validation of FPM method for a large object simulation in
fluidized bed.
Hyun-sang Lim | 2018. 01. 31 | # 10Computer Graphics @ Korea University
1. Introduction
Why I select this paper
This work is very similar to my current work. The only difference is the
subject of simulation.
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2. Fictitious Particle Method
What is FPM Method : Euler – Lagrangian method
FPM Method is a kind of “Euler – Lagrangian method”
(𝑥𝑖 , 𝑦𝑖)
(𝑥𝑖−1 , 𝑦𝑖)(𝑥𝑖+1 , 𝑦𝑖)
7
2
4
3
65
1
Step1. Particles are scattered in space
Step2. Calculate average properties(like density, velocity, pressure) at grid location
7
2
4
3
65
1
Step3. Update particles properties(like position, velocity)
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2. Fictitious Particle Method
What is FPM Method : Cell size
Conditions for size of the cell
(1) Cell size should be small enough for
simulating mesoscopic phenomena like
bubbles.
(2) At the same time, cell size must be larger
than object size
However, in the case of which size of particles are various like
figure 3, it is difficult to select the appropriate size of cell.
Fig 4. Uneven size of particles
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2. Fictitious Particle Method
What is FPM Method : Solution for cell size problem
Replace the large particle to the group of small particles.
And Calculate the properties at the inner grid of the sphere.
Fig 5. Concept of the Fictitious particle method
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2. Fictitious Particle Method
Calculating the motions
ε is the void fraction in a computational cell.
U is the locally phase-averaged fluid velocity.
p is the pressure
ρf are the density of the fluid.
The momentum exchange between fluid and solids including particles and spheres is expressed by f, which will be calculated later.
(In particle based system, Actually continuity equation doesn’t have to be considered.)
(In particle based system, Navier stokes equation goes to be equal to Newton’s second Law F=ma)
- Governing equations
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2. Fictitious Particle Method
Calculating the motions
Step1. Calculate 𝜀 at the grid.
- Calculate epsilon based on position of particles in cell 1, 2, 3, 4.
- Calculate average value of epsilons at cell 1, 2, 3, 4 and save the value at grid ( i , j ).
Cell1 Cell2
Cell3 Cell4
Grid ( i , j )
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2. Fictitious Particle Method
Calculating the motions
Mp and Ip are the mass and moment of inertia of a particle
Upi and ωpi are velocity and angular velocity ofaparticle I
g is the gravitationalacceleration,
fCpi is the net contact force working on a particle i from the other particles, spheres, and walls.
fDpi is the fluid force working on a particle i, and Mpi is the net torque working on a particle i due to the contacts with other particles, spheres and walls.
Step2. Solve the equations of motion
Hyun-sang Lim | 2018. 01. 31 | # 17Computer Graphics @ Korea University
2. Fictitious Particle Method
Calculatin the motions: Contact force
Step3. Find 𝑓𝐶𝑃𝑖 𝑎𝑛𝑑 𝑓𝐶𝑆 which is calculated by spring damper model between particles
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2. Fictitious Particle Method
Calculating the motions
Step4. Fine 𝑓𝐷𝑃𝑖 𝑎𝑛𝑑 𝑓𝐷𝑆 is calculated by empirical equations
Hyun-sang Lim | 2018. 01. 31 | # 19Computer Graphics @ Korea University
2. Fictitious Particle Method
Calculating the motions
Step5. Update 𝜀 again with calculated velocities of particles and save the value at location.
Equations are same with step 1.
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3. Lagrangian sensor system
Lagrangian Sensor
- Lagrangian senor is a kind of acceleration sensor;
- The sensor is inserted in the sphere in this study.
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3. Lagrangian sensor system
The algorithm for calculating dynamic force
- Magnetic sensor can find the direction of gravitation.
- Acceleration sensor output is calculated by substracing gravitational acceleration.
Unit vector of gravity
Subtractgravitationalacceleration
Extract vertical component
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4. Experiment
Experimental condition
- Experiment setting is like below
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4. Experiment
Results: Snapshots
- Snapshot of the experimental result, and that simulation.
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4. Experiment
Results : Data comparison
- Time domain comparison and frequency domain comparison.
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5. Conclusion & Opinion
- Conclusion
(1) Results of the FPM simulation and experiment showed good agreement.
(2) It can be said that FPM Method is proper for simulation of fluidized bed.
- Opinion
(1) There are many user defined value. So other cases should be tested for proving validation of this method.
(2) I will apply Euler lagrangian approach to my work for stability.