numerical studies of a fluidized bed for ife target layering presented by kurt j. boehm 1,2 n.b....

Numerical Studies of a Fluidized Bed for IFE Target Layering

Presented by Kurt J. Boehm1,2

N.B. Alexander2, D.T. Goodin2 , D.T. Frey2, R. Raffray1, et alt.

1- University of California, San Diego2- General Atomics, San Diego

HAPL Project ReviewSanta Fe, NM April 8-9, 2008

Overview

• Cryogenic fluidized bed is under investigation for IFE target mass production

• Experimental setup is being built at General Atomics in San Diego

• Numerical model of fluidized bed is being developed under guidance of R. Raffray at UCSD– Improvements to the granular part– The gas – solid flow model– Stepwise validation and verification of the proposed model– Computing the heat and mass transfer

• Future Plans – Research Path

A Fluidized Bed is being Investigated for Mass Production of IFE Fuel Pellets

• Filled particles (targets) are levitated by a gas stream

• Target motion in the cryogenic fluidized bed provides a time-averaged isothermal environment

• Volumetric heating causes fuel redistribution to form uniform layer

LAYERING

Fluidized Bed

Gas Flow

Frit

SPIN

CIRCULATION

Unknowns in Bed Behavior call for Numerical Analysis

• RT - Experimental observations (presented at last meeting by N. Alexander) are restricted to the particles close to the wall

• The behavior of unlayered shells is unknown (unbalanced spheres)

• Tests on the cryogenic apparatus are time consuming

• Results might be hard to interpret

Optimize operating conditions: Define narrow window of operation for successful deuterium layering prior to completion of entire setup– gas pressure, flow speed, bed dimensions, additional heating, frit

design, …

Numerical Model consists of three Parts

• Fluidized Bed Model– Granular model– Fluid-Solid interaction

• Layering Model – Quantification of mass transfer

Fluidized Bed ModelPart I: Granular Model

• Discrete Particle Method (DPM)

• Motion of individual particles is tracked by computing the forces acting on the particles at each time step

• Apply Newton’s second law of motion

• Traditionally a spring – dashpot and/or friction slider model is applied for particle collisions

• Limitations: Not developed for unbalanced spheres

Forces are computed based on relative velocity at contact point

Cundall and Struck, Geotechnique, Vol.29, No.1, 1979

Contact forces are a function of relative velocity at contact point depends on the orientation of the particle

displacement

wall

Normal Force

Tangential Force

Orientation defined by Euler angles

Center of mass Geometrical Center

wall

When Modeling Unbalanced Spheres the Forces depend on Particle’s Orientation

Torque around center of mass

Equations for the force computation need to be adjusted to account for the different contact geometry

Particles need to be spaced apart

Initialize position, velocity and quaternion vectors

Start time stepping

Predictor step

Compute forces based on predicted positions

Correct positions, velocities and accelerations based on the updated forces

Create time averaged statistics

Write Output every 1000 time steps

Particle – wall collisions

Compute force due to particle – particle collisionsLoop over all particles

Overview Fluidized Bed Model

Add gravitational Force

Fluidized Bed ModelPart II: Fluid- Particle Interaction

0,

igggi

gg Uxt

igg

M

mgmi

j

ij

i

gg

jgigggj

iggg

gIxx

P

UUx

Ut

1

,,,

Granular Navier Stokes Equation:

Granular Continuity Equation:

Time:0.00 s

Time:0.04 s

Time:0.08 s

Time:0.12 s

Example:2-D numerical simulation using MFIX

Particle void fraction = 0.42Particle void fraction = 0.00

Common Approach for Numerical Fluidized Bed Model:

Control Volume MethodVoid Fraction is determined from number of grains in each fluid cell

*MFIX – Multiphase Flow with Interphase eXchangesDeveloped by National Energy Technology Laboratory -- http://mfix.org

The Traditional Approach for the Fluid Model Fails in this Case

Problem with fluid cell sizes:• Minimum of seven pellets per fluid cell

for cell average to work in control volume method

• Not useful to solve fluid equation for 3x3x4 grid


• DNS model to resolve flow around each sphere computationally VERY expensive


for cell average to work in Control Volume Method

• Not useful to solve fluid equation for 3x4 grid


• DNS model to resolve flow around each sphere computationally VERY expensive

• Choosing a grid size of the same order than the shells leads to complication determining the “average void fraction” around a sphere


for cell average to work in Control Volume Method

• Not useful to solve fluid equation for 3x4 grid

The most important information we are trying to get is the particle spin and circulation rate

Experimental observations indicate, that the spin of the particles is dominantly induced by collisions, not by fluid interaction


Application of 1-D Lagrangian Model to Determine Void Fraction

Compute the void fraction for each slice of the fluidized bed, bounded by one radius in each direction of the center of each sphere.





This “region of interest” moves with each particle from time step to time step





This “region of interest” moves with each particle from time step to time step

Once the void fraction is known, the drag force can be computed



Knowing Void Fraction, Richardson-Zaki Drag model is applied

8.3

8.4

6

n

tfp

pd u

Ug

df

Void Fraction is known based on 1-D Lagrangian Model

Richardson-Zaki Drag Force for homogeneous fluidized beds:

25.05.02 832.1809.3809.3Re Art 2

3

f

fpfpgdAr

tf

fpt u

d

ReTerminal Free Fall Velocity is a constant system parameter:

Dellavalle Drag Model:

Archimedes Number:

Drag force is added to the total force on the particle at each time step

Particles need to be spaced apart

Initialize position, velocity and quaternion vectors

Start time stepping

Predictor step

Compute forces based on predicted positions

Compute the resulting pressure drop

Determine bed expansionCorrect positions, velocities and accelerations based on the updated forces

Create time averaged statistics Write Output every 1000 time steps

Particle – wall collisions

Compute void fraction

Compute drag force

Compute effective weight

Compute force due to particle – particle collisionsLoop over all particles

Overview Fluidized Bed Model

Preliminary Results from Fluidized Bed Model indicate Model’s Validity quantitatively

Exact System parameters need to be determined

Bubbling behavior can be predicted theoretically, seen in the experiment, and are modeled numerically

Visualization of the output:Merrit and Bacon, Meth. Enzymol. 277, pp 505-524, 1997

Stability and convergence can be shown modeling granular collapse (Kinetic Eng)

6e-05

4e-05

3e-05

2e-05

1e-05

5e-05

0.1 0.2

Time (s)

k

mn 2

Total Kinetic Energy in System during Granular Collapse for decreasing time step size

(J)

Nt n

2

200 particlesM = 2E-6 KgDiameter = 4 mmK_eff = 1000 N/mC_eff = 0.004 N s/m = 0.0125 N s/m = 0.4I = 5E-12 Kg s^2

0.1Time (s)

Total Rotational Energy in System during Granular Collapse for decreasing time step size

Stability and convergence can be shown modeling granular collapse (Rotational Eng)

0.2

1e-06

2e-06

4e-06

3e-06

(J)

200 particlesM = 2E-6 KgDiameter = 4 mmK_eff = 1000 N/mC_eff = 0.004 N s/m = 0.0125 N s/m = 0.4I = 5E-12 Kg s^2

k

mn 2

Nt n

2

Validation of the Flow Model in Packed Beds

8.4

21

33.0Re

18

p

f

p d

ULP

• Compare the numerical output against experiment and theory for non-fluidizing conditions

• Experiment: room temperature loop with two different set of delrin spheres

• Established empirical relation: Ergun’s Equation

• Model: Use Richardson-Zaki drag relation, add drag forces for overall pressure drop

• Model, theory and experiment have good agreementConstant void fraction pressure drop

3.96875 mm diameter

00.20.40.60.8

11.21.41.61.8

0 0.2 0.4 0.6 0.8 1 1.2

Flow speed (m/s)

Pre

ssu

re d

rop

(in

ches

of

wat

er)

Experiment

Ergun

Numerical

Packed bed pressure drop3.175 mm diametervoid fraction ~ 0.40

00.20.40.60.8

11.21.41.61.8

0 0.2 0.4 0.6 0.8 1

Flow Speed (m/s)

Pres

sure

Dro

p (in

ches

of

wat

er)

Experiment

Ergun

Numerical

Homogeneous Fluidization for Validation Purposes

The Model Prediction Compare with Theory and Experiments

• Experiment: room temperature setup using two different sets of shells

• Theory: Apply Richardson Zaki Relation

• Model: Use the parameters describing the system

Homogenious Fluidization of 350 spheres in water

0.00

0.02

0.04

0.06

0.08

0.10

0.12

50.00% 60.00% 70.00% 80.00% 90.00%

Void Fraction

Flo

w s

pee

d (

m/s

)

Experiment

Numerical Solution

Richardson ZakiRelation

System Parameters for PAMS shells are found by analyzing simple Cases

Measurement Variable to be Determined Value Unit

Scale Mass 1.89 – 0.677 Kg

Volume of X spheres Radius 1.183 and 1.97 mm

Contact Timek-value

(Stiffness of collision contact)672-1865 N/m

Energy out vs. Energy inc-value

(Damping coefficient)0.01-0.001 (N*s) / m

Transfer from Kinetic to Rotational Energy

- value

(Coefficient of tangential friction)tbd -

From Model- value

(Coefficient of dynamic friction) 0.0125 - 0.025 (N*s) / m

Normal contact of shell with table at10,000 frames per second

Angled contact of shell with table at1,000 frames per second

610

Homogenious Fluidization of 350 spheres in water

0.00

0.02

0.04

0.06

0.08

0.10

0.12

50% 60% 70% 80% 90%

Void Fraction

Flo

w s

pee

d (

m/s

)

Experiment

Numerical Solution

Richardson ZakiRelation

The Model Prediction Compare with Theory and Experiments

• Experiment: room temperature setup using two different sets of shells

• Theory: Apply Richardson Zaki Relation

• Model: Use the parameters determined earlier as input

Bubbling fluidization 200 PAMS shells ~4mm diameter in N2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

30% 40% 50% 60% 70% 80% 90% 100%Void Fraction

Flo

w S

pe

ed

(m

/s) Experiment

Numerical Analysis• Large error bars due to the uncertainty in pellet radius

• Richardson Zaki is not applicable in bubbling beds as a whole

Validation of the Unbalanced Contact is considered crucial!!!

However, has not been done yet.

Validation of the model for off centered particle collisions is considered very important…

Layering Model

• Compute the redistribution of fuel based on the fluidized bed behavior• Solve 1-D equations simultaneously:

• This leads to a layering time constant of

• Time step: ~1E-5 s Fluidized Bed vs. ~30-60s Layering• Based on the time averaged motion and preferential position, we can

compute the average temperature/ temperature difference between the thick and the thin side of the shell

1

1

2

2

T

P

T

P

lR

C

ICE

diff

Mass Transfer Equation

fICEICE

ICE hqk

t

hTT

1221

Heat Transfer Equation

q

ht fe

Latent heat

Volumetic heating

Marin et alt., J.Vac.Sci.Technol.A. Vol.6, Issue 3, 1988

Summary

• Room temperature fluidized bed experiments(Presented at the past meeting)– Promising, but unable to deliver enough

information

• Numerical model is proposed– Existing fluidized bed models – Development of new model – Validation through theory and experiments

• Experimental surrogate layering– Validate layering model – Show proof of principle

• Find optimized parameters for D2 Layering prior to experiment

STARTING POINT:A fluidized bed is under investigation for mass production layering of IFE targets

Guidelines for Successful Target Layering

Equations to Compute Contact Forces

amF

i

ji

sj

sis

ji rss

sss

,

sji

sjiji

s

jicp vsv ,,,,

s

jcps

icps

cp vvv

effs

ncpeffjijisn cvkrrssF ,

s

tcp

stcps

tcpsn

st

v

vvFF

,

,,,min

st

sji

si Fs ,

Distance between two sphere centers

Compute contact point velocity

Normal and Tangential Force Component

Apply Forces to:

Iss

Orientation of the Particle cannot be determined

i

ji

sj

sis

ics rss

sss

bji

Tji

sji

s

jicg oAss ,,,,

bji

Tji

sji A ,,,

sji

s

jicgjis

jicp vsv ,,,,

s

jcps

icps

cp vvv

effs


s

tcp

stcps

tcpsn

st

v

vvFF

,

,,,min

stot

sicg

si Fs ,

sb A


by

bx

zz

yyxx

zz

bzb

z

bx

bz

yy

xxzz

yy

byb

y

bz

by

xx

zzyy

xx

bxb

x

I

II

I

I

II

I

I

II

I


Distance between two mass centers

Convert spin into space fixed coordinates



amF

Apply Forces to:

Quaternion Description allows Following Orientation of Particles

• Rotational equations require body fixed and the space fixed coordinate systems

• Matrix of rotation is applied to switch between the two

• Unlike the translational motion (keeping track of x-y-z coordinates) the rotational motion cannot be tracked simply recording pitch-yaw-roll angles

• This rotation matrix depends on the order by which the rotations are applied

• Solution: Quaternions

Quaternion representation describes the orientation of a body by a vector and a scalar

Simple description of rotational motion

i

ji

sj

sis

ics rss

sss

bji

Tji

sji

s

jicg oAss ,,,,

bji

Tji

sji A ,,,

sji

s

jicgjis

jicp vsv ,,,,

s

jcps

icps

cp vvv

effs


s

tcp

stcps

tcpsn

st

v

vvFF

,

,,,min

stot

sicg

si Fs ,

sb A


by

bx

zz

yyxx

zz

bzb

z

bx

bz

yy

xxzz

yy

byb

y

bz

by

xx

zzyy

xx

bxb

x

I

II

I

I

II

I

I

II

I

amF

bz

by

bx

qqqq

qqqq

qqqq

qqqq

q

q

q

q

0

2

1

0123

1032

2301

3210

3

2

1

0


Distance between two mass centers

Convert spin into space fixed coordinates



Apply Forces to:

amF

numerical studies of a fluidized bed for ife target layering presented by kurt j. boehm 1,2 n.b....

Documents

bed behavior

bed dimensions

time consumingresults

unbalanced spheres forces

particle collisionslimitations

time stepapply newtons

ife target layering

granular continuity