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.

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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

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- 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

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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.

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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

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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

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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.