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## Numerical Studies of a Fluidized Bed as long as IFE Target Layering Presented by Kurt J

Strength, Don, Morning Show Host has reference to this Academic Journal, PHwiki organized this Journal Numerical Studies of a Fluidized Bed as long as IFE Target Layering Presented by Kurt J. Boehm1,2 N.B. Alex in addition to er2, D.T. Goodin2 , D.T. Frey2, R. Raffray1, et alt. 1- University of Cali as long as nia, San Diego 2- General Atomics, San Diego HAPL Project Review Santa Fe, NM April 8-9, 2008 Overview Cryogenic fluidized bed is under investigation as long as 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 in addition to verification of the proposed model Computing the heat in addition to mass transfer Future Plans Research Path A Fluidized Bed is being Investigated as long as 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 as long as m uni as long as m layer LAYERING Fluidized Bed Gas Flow Frit SPIN CIRCULATION

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Unknowns in Bed Behavior call as long as Numerical Analysis RT – Experimental observations (presented at last meeting by N. Alex in addition to er) 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 as long as 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 Model Part I: Granular Model Discrete Particle Method (DPM) Motion of individual particles is tracked by computing the as long as ces acting on the particles at each time step Apply Newtons second law of motion Traditionally a spring dashpot in addition to /or friction slider model is applied as long as particle collisions Limitations: Not developed as long as unbalanced spheres Forces are computed based on relative velocity at contact point Cundall in addition to Struck, Geotechnique, Vol.29, No.1, 1979

When Modeling Unbalanced Spheres the Forces depend on Particles Orientation Contact as long as ces 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 Torque around center of mass Equations as long as the as long as ce computation need to be adjusted to account as long as the different contact geometry Overview Fluidized Bed Model Particles need to be spaced apart Initialize position, velocity in addition to quaternion vectors Start time stepping Predictor step Compute as long as ces based on predicted positions Correct positions, velocities in addition to accelerations based on the updated as long as ces Create time averaged statistics Write Output every 1000 time steps Particle wall collisions Compute as long as ce due to particle particle collisions Loop over all particles Add gravitational Force Fluidized Bed Model Part II: Fluid- Particle Interaction 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 = 0.42 Particle void fraction = 0.00 Common Approach as long as Numerical Fluidized Bed Model: Control Volume Method Void Fraction is determined from number of grains in each fluid cell MFIX Multiphase Flow with Interphase eXchanges Developed by National Energy Technology Laboratory – http://mfix.org

The Traditional Approach as long as the Fluid Model Fails in this Case Problem with fluid cell sizes: Minimum of seven pellets per fluid cell as long as cell average to work in control volume method Not useful to solve fluid equation as long as 3x3x4 grid The Traditional Approach as long as 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 as long as cell average to work in Control Volume Method Not useful to solve fluid equation as long as 3×4 grid The Traditional Approach as long as 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 as long as cell average to work in Control Volume Method Not useful to solve fluid equation as long as 3×4 grid

The most important in as long as mation we are trying to get is the particle spin in addition to circulation rate Experimental observations indicate, that the spin of the particles is dominantly induced by collisions, not by fluid interaction The most important in as long as mation we are trying to get is the particle spin in addition to circulation rate Application of 1-D Lagrangian Model to Determine Void Fraction Compute the void fraction as long as each slice of the fluidized bed, bounded by one radius in each direction of the center of each sphere. Experimental observations indicate, that the spin of the particles is dominantly induced by collisions, not by fluid interaction The most important in as long as mation we are trying to get is the particle spin in addition to circulation rate

Application of 1-D Lagrangian Model to Determine Void Fraction Compute the void fraction as long as 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 Experimental observations indicate, that the spin of the particles is dominantly induced by collisions, not by fluid interaction The most important in as long as mation we are trying to get is the particle spin in addition to circulation rate Application of 1-D Lagrangian Model to Determine Void Fraction Compute the void fraction as long as 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 as long as ce can be computed Experimental observations indicate, that the spin of the particles is dominantly induced by collisions, not by fluid interaction The most important in as long as mation we are trying to get is the particle spin in addition to circulation rate Knowing Void Fraction, Richardson-Zaki Drag model is applied Void Fraction is known based on 1-D Lagrangian Model Richardson-Zaki Drag Force as long as homogeneous fluidized beds: Terminal Free Fall Velocity is a constant system parameter: Dellavalle Drag Model: Archimedes Number: Drag as long as ce is added to the total as long as ce on the particle at each time step

Overview Fluidized Bed Model Particles need to be spaced apart Initialize position, velocity in addition to quaternion vectors Start time stepping Predictor step Compute as long as ces based on predicted positions Compute the resulting pressure drop Determine bed expansion Correct positions, velocities in addition to accelerations based on the updated as long as ces Create time averaged statistics Write Output every 1000 time steps Particle wall collisions Compute void fraction Compute drag as long as ce Compute effective weight Compute as long as ce due to particle particle collisions Loop over all particles Preliminary Results from Fluidized Bed Model indicate Models Validity quantitatively Exact System parameters need to be determined Bubbling behavior can be predicted theoretically, seen in the experiment, in addition to are modeled numerically Visualization of the output: Merrit in addition to Bacon, Meth. Enzymol. 277, pp 505-524, 1997 Stability in addition to convergence can be shown modeling granular collapse (Kinetic Eng) Total Kinetic Energy in System during Granular Collapse as long as 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 s^2

Stability in addition to convergence can be shown modeling granular collapse (Rotational Eng) 0.1 Time (s) Total Rotational Energy in System during Granular Collapse as long as decreasing time step size 0.2 1e-06 2e-06 4e-06 3e-06 (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 s^2 Validation of the Flow Model in Packed Beds Compare the numerical output against experiment in addition to theory as long as 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 as long as ces as long as overall pressure drop Model, theory in addition to experiment have good agreement Homogeneous Fluidization as long as Validation Purposes

The Model Prediction Compare with Theory in addition to Experiments Experiment: room temperature setup using two different sets of shells Theory: Apply Richardson Zaki Relation Model: Use the parameters describing the system System Parameters as long as PAMS shells are found by analyzing simple Cases Normal contact of shell with table at 10,000 frames per second Angled contact of shell with table at 1,000 frames per second The Model Prediction Compare with Theory in addition to 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

Validation of the Unbalanced Contact is considered crucial!!! However, has not been done yet. Validation of the model as long as 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 in addition to preferential position, we can compute the average temperature/ temperature difference between the thick in addition to the thin side of the shell 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 in as long as mation Numerical model is proposed Existing fluidized bed models Development of new model Validation through theory in addition to experiments Experimental surrogate layering Validate layering model Show proof of principle Find optimized parameters as long as D2 Layering prior to experiment STARTING POINT: A fluidized bed is under investigation as long as mass production layering of IFE targets Guidelines as long as Successful Target Layering

Equations to Compute Contact Forces Distance between two sphere centers Distance between two mass centers Convert spin into space fixed coordinates Compute contact point velocity Normal in addition to Tangential Force Component Apply Forces to:

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