Numerical Studies of a Fluidized Bed for IFE Target Layering

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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.
HAPL Project Review Santa Fe, NM April 8-9, 2008
1- University of California, San Diego 2- General
Atomics, San Diego
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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

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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
SPIN
Frit
Gas Flow
CIRCULATION
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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,

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Numerical Model consists of three Parts

• Fluidized Bed Model
• Granular model
• Fluid-Solid interaction
• Layering Model
• Quantification of mass transfer

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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 Newtons 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
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When Modeling Unbalanced Spheres the Forces
depend on Particles Orientation
Orientation defined by Euler angles
Contact forces are a function of relative
velocity at contact point ? depends on the
orientation of the particle
Center of mass
Geometrical Center
wall
Equations for the force computation need to be
adjusted to account for the different contact
geometry
Torque around center of mass
wall
Normal Force
displacement
Tangential Force
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Overview Fluidized Bed Model
Particles need to be spaced apart
Initialize position, velocity and quaternion
vectors
Start time stepping
Predictor step
Compute forces based on predicted positions
Particle wall collisions
Compute force due to particle particle
collisions
Loop over all particles
Add gravitational Force
Correct positions, velocities and accelerations
based on the updated forces
Write Output every 1000 time steps
Create time averaged statistics
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Fluidized Bed ModelPart II Fluid- Particle
Interaction
Example 2-D numerical simulation using MFIX
Common Approach for Numerical Fluidized Bed
Model Control Volume Method Void Fraction is
determined from number of grains in each fluid
cell
Time 0.00 s
Time 0.04 s
Time 0.12 s
Time 0.08 s
Granular Continuity Equation
Granular Navier Stokes Equation
Particle void fraction 0.42 Particle void
fraction 0.00
MFIX Multiphase Flow with Interphase
eXchanges Developed by National Energy Technology
Laboratory -- http//mfix.org
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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

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The Traditional Approach for the Fluid Model
Fails in this Case

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

• 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 3x4 grid

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The Traditional Approach for the Fluid Model
Fails in this Case

• 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

• 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 3x4 grid

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The most important information we are trying to
get is the particle spin and circulation rate
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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
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Application of 1-D Lagrangian Model to Determine
Void Fraction
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
Compute the void fraction for each slice of the
fluidized bed, bounded by one radius in each
direction of the center of each sphere.
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Application of 1-D Lagrangian Model to Determine
Void Fraction
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
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
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Application of 1-D Lagrangian Model to Determine
Void Fraction
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
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
Once the void fraction is known, the drag force
can be computed
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Knowing Void Fraction, Richardson-Zaki Drag model
is applied
Richardson-Zaki Drag Force for homogeneous
fluidized beds
Void Fraction is known based on 1-D Lagrangian
Model
Dellavalle Drag Model
Archimedes Number
Terminal Free Fall Velocity is a constant system
parameter
Drag force is added to the total force on the
particle at each time step
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Overview Fluidized Bed Model
Particles need to be spaced apart
Initialize position, velocity and quaternion
vectors
Start time stepping
Predictor step
Compute forces based on predicted positions
Particle wall collisions
Compute force due to particle particle
collisions
Loop over all particles
Compute void fraction
Compute the resulting pressure drop
Compute drag force
Compute effective weight
Determine bed expansion
Correct positions, velocities and accelerations
based on the updated forces
Write Output every 1000 time steps
Create time averaged statistics
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Preliminary Results from Fluidized Bed Model
indicate Models Validity quantitatively
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
Exact System parameters need to be determined
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Stability and convergence can be shown modeling
granular collapse (Kinetic Eng)
Total Kinetic Energy in System during Granular
Collapse for decreasing time step size
(J)
200 particles M 2E-6 Kg Diameter 4 mm K_eff
1000 N/m C_eff 0.004 N s/m g 0.0125 N s/m m
0.4 I 5E-12 Kg s2
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Stability and convergence can be shown modeling
granular collapse (Rotational Eng)
Total Rotational Energy in System during Granular
Collapse for decreasing time step size
(J)
4e-06
3e-06
200 particles M 2E-6 Kg Diameter 4 mm K_eff
1000 N/m C_eff 0.004 N s/m g 0.0125 N s/m m
0.4 I 5E-12 Kg s2
2e-06
1e-06
0.1
Time (s)
0.2
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Validation of the Flow Model in Packed Beds

• 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 Erguns Equation
• Model Use Richardson-Zaki drag relation, add
  drag forces for overall pressure drop
• Model, theory and experiment have good agreement

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Homogeneous Fluidization for Validation Purposes
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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

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System Parameters for PAMS shells are found by
analyzing simple Cases
Angled contact of shell with table at 1,000
frames per second
Normal contact of shell with table at 10,000
frames per second
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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

• Large error bars due to the uncertainty in pellet
  radius
• Richardson Zaki is not applicable in bubbling
  beds as a whole

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Validation of the Unbalanced Contact is
considered crucial!!!
Validation of the model for off centered particle
collisions is considered very important
However, has not been done yet.
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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

Marin et alt., J.Vac.Sci.Technol.A. Vol.6, Issue
3, 1988
Latent heat
Volumetic heating
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Summary
STARTING POINT A fluidized bed is under
investigation for mass production layering of IFE
targets

• 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

? Guidelines for Successful Target Layering
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Equations to Compute Contact Forces
Normal and Tangential Force Component
Distance between two sphere centers
Apply Forces to
Compute contact point velocity
Orientation of the Particle cannot be determined
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Equations to Compute Contact Forces
Normal and Tangential Force Component
Distance between two sphere centers
Distance between two mass centers
Convert spin into space fixed coordinates
Apply Forces to
Compute contact point velocity
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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

Simple description of rotational motion
Quaternion representation describes the
orientation of a body by a vector and a scalar
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Equations to Compute Contact Forces
Normal and Tangential Force Component
Distance between two sphere centers
Distance between two mass centers
Apply Forces to
Convert spin into space fixed coordinates
Compute contact point velocity