computer simulation of ceramic processing using microwave...
TRANSCRIPT
Computer Simulation of Ceramic Processing using Microwave Assist Technology
Shawn Allan* Morgana Fall, Dr. Holly Shulman, Ceralink Inc
Dr. Jeff Braunstein, Dr. Sheppard Salon, Rensselaer Polytechnic Institute
Ceralink Inc. Rensselaer Technology Park
Troy, New York
Rensselaer Polytechnic Institute Center for Automation Technologies & Systems Seminar
Troy, New York April 25, 2008
Outline
Ceramic Processing
Microwave Assist Technology
Computational Model
Summary
Ceralink 1700 °C MAT Lab Kiln 2.45 GHz
Ceramic Processing Metals oxide, nitride, carbide, boride
Parts are formed from powders
Casting, Pressing, Extrusion
Nearly all ceramic processing uses heat Drying 50-200 °C Binder Burnout 200-600 °C Calcining 300-1200 °C Sintering 600-2400 °C
Reactions, phase changes, mass loss, densification, property shifts
Temperature, time, heating rate dependent
Ceramic Thermal Processing: Calcining Heating to force a reaction in ceramic powders Degassing; remove physically adsorbed gas (water, CO2)
Dehydration; Al(OH)3 α-Al2O3 + H2O
Dissociation; CaCO3 CaO + CO2
Doping; 2% Eu + BaTiO3 Eu2+:BaTiO3
Reaction; BaCO3 + TiO2 BaTiO3 + CO2
Ceramic Thermal Processing: Sintering High temperature diffusion process Discrete particles become grains in microstructure Densification, shrinkage Grains, Grain Boundaries, & Porosity Small grains higher strength
As Formed As Sintered
Sintering: Temperature and Time Dependence
Zirconia, ZrO2, Ceramic Filters
Ceramic Processing: Simple Dimensional Changes
Zinc Oxide, ZnO
Thermal Expansion
Densification
Ceramic Processing: Complex Dimensional Changes
Kaolin Clay, Al4Si4O10(OH)8
Quartz Inversion
Metakaolin Transition
Isothermal Densification
Drying
Cooling
Ceramic Processing: Electrical Properties Change
Kaolin Clay
Quartz Inversion
Metakaolin Transition
Drying
Conventional Sintering Heat transfer by conduction in porous structure
Low thermal conductivity
Slow heating to prevent cracking
Long sintering times grain growth limited properties
Tem
p
Temperature profile
Microwave Assist Technology (MAT)
Combines radiant heat (gas or electric) with microwave energy Balance microwave heat with radiant heat Simultaneously apply both microwave and radiant Patented Technology
Ceralink has exclusive license in North America
Tem
p
Conventional Microwave MAT
Temperature profile across part thickness
MAT Process Benefits
Process time reduction
Energy savings
Nanograin ceramics
Lower temperature reactions
Drying, calcining, sintering
Scale-up and Production MAT Equipment
Build TEAMS, get funding support
Demonstration Cost Benefit & Manufacturability Analysis
Use model to replicate process in lab kiln scale to production
Use model for materials selection and design
C-Tech MAT Gas Shuttle Kiln
Ceralink MAT Electric Elevator Kiln
MAT Firing Data Refractories
Tem
pera
ture
(ºC
) En
ergy
use
d (th
erm
s)
MAT Gas Only
Time (hrs)
Gas input MW input
MAT Conventional
MAT: 22 hrs total
Conventional: 45 hrs total
Energy consumption
E = P*t MAT: 60 mil BTU
Conventional: 110 mil BTU
Total Firing Time
MAT Process Development
Dielectric Properties
Material
Kiln Specifications
Testing
Analysis
Explorative and Designed Experiments
MAT Process Development with Numerical Modeling
Dielectric Properties
Material
Insulation
Kiln Specifications
Model Output Testing
Analysis
Energy Gain and Loss
radconvcondElectricMWincs WWWWW −−−= + )(
o
o
cE
tT
ρεωε 2"
21
=∂∂
Electric Heating Radiation to surfaces Conduction through ceramic
Microwave Heating Internal loss mechanisms resistive heating losses dielectric polarization losses ε” represents combination of loss mechanisms temperature gain due to energy absorption is:
Algorithm for Numerical Simulations
Initialize Material Properties, ε, µ, a, cp, ρ, f, Eo
Diffusion Time Step, Based on Mesh Density
Frequency Domain Solutions of the Wave Equation
Time Domain Solution, Heat Equation
Adjust Temperature Dependent Properties
Set Materials & System Inputs System: Build Model of MAT Electric kiln
Lab scale kiln with MoSi2 elements and high T insulation Solid model Meshing
Materials: Introduce dielectric and thermal properties
ε, µ, a, cp, ρ as functions of T Product load Refractory insulation Assume constant, low permeability
Power: Determine level of microwave and electric power
Forward microwave power Microwave field intensity, Eo Radiant heat source
Microwave Heating
Tan δ 20 °C 2.45 GHz
Penetration Depth (m)
Alumina 0.0010 12.8 Zirconia 0.015 1.0 Silicon Carbide
0.08-1.05 0.004-0.047
Aluminum - 0.000001
Transparent to microwaves Very Low
Dielectric loss Tan δ < 0.01
Reflects microwaves Electrical conductor
Tan δ > 10
Absorb microwave (heats) Dielectric loss
Tan δ ~ 0.01 - 2
Conductivity increasing
Tan δ = ε”/ε’
Dielectric Property Testing Zirconia and Refractory Insulation Measured at 2.45 GHz
Predicts microwave heating behavior Higher Tan Delta Better absorption Want product to preferentially absorb Need radiant heat at low temp Avoid thermal runaway at high temp
Algorithm for Numerical Simulations
Initialize Material Properties, ε, µ, a, cp, ρ
Diffusion Time Step, Based on Mesh Density
Frequency Domain Solutions of the Wave Equation
Time Domain Solution, Heat Equation
Adjust Temperature Dependent Properties
fs
Algorithm for Numerical Simulations
Initialize Material Properties, ε, µ, a, cp, ρ, f, Eo
Diffusion Time Step, Based on Mesh Density
Frequency Domain Solutions of the Wave Equation
Time Domain Solution, Heat Equation
Adjust Temperature Dependent Properties
o
o
cE
tT
ρεωε 2"
21
=∂∂
Computer Simulations – Numerical Methods
Wave Equation - The Finite Element Method (FEM) to determine E-field distributon inside the furnace Power absorption in the lossy materials
Edge elements are implemented First order six sided elements are implemented (bricks)
Heat Equation - Integral and differential methods are investigated for
determining time domain solutions Volumetric integration over the finite element polygons Finite difference mesh applied to the domain with a boundary integral
approximation for radiation Finite Difference Method faster solutions and simpler implementation Finite Element Method greater modeling flexibility and accuracy
Maxwell’s Equations
tETtrB
tBE
∂∂
=×∇
∂∂
−=×∇
)),((
εµ
•Two first order differential equations represent the time dependent relationship between magnetic fields and electric fields
•Magnetic permeability and electric permittivity are important physical parameters in the relationship. In these simulations,
•Permeability, µ, is assumed constant
•Permittivity, ε, is a function of time and position. The time dependence reflects the temperature change as the material is heated
FEM Wave Equation
• Artificial planar source (forward power ≈ Eo) exists in the feed
• Perfect conductors applied to cavity walls
• Linear basis functions over brick elements
• A piecewise constant distribution is assumed for the permittivity in each element
• The permittivity can be assumed constant in time for tn< t < tn+1 where Δt is the time step between solutions of the wave equation
( ) ( )nttrTr =≈ | εε
( ) ( ) ( , )
0
E E r T E E dV
E dSn
ωµε ∇× • ∇× + • ∂
− • =∂
∫
∫
Algorithm for Numerical Simulations
Initialize Material Properties, ε, µ, a, cp, ρ, f, Eo
Diffusion Time Step, Based on Mesh Density
Frequency Domain Solutions of the Wave Equation
Time Domain Solution, Heat Equation
Adjust Temperature Dependent Properties
Heat Equation so fuk
tuc +∇=
∂∂ 2ρ
Integrating over the volume and applying the divergence theorem, the FETD diffusion equation is:
( )( ) dVfdSnua
dVuut
c
s
nno
∫∫∫
+•∇
=−∆
+
ˆ
1 1ρ
• Heat equation material properties assumed constant
• Linear approximation of heat distribution
• Change in temperature in a cell is dependent on the flow across the boundary and the power absorbed
fs is a source term for microwave power absorption.
Boundary Losses Convective losses due to fluid/gas circulation take the form:
)( oTThnT
−=∂∂
Radiation losses/gains are represented by:
))(( 44oTTAf
nT
−=∂∂ σ
•Typically very difficult to accurately characterize
•Motion of free molecules very sensitive to many factors
•Convective term, h, assumed constant for all temperature ranges
•Very significant contribution at high temperatures
•Dependent on distance between objects & geometric orientation
•Simple spherical radiation onto exposed surfaces applied
Algorithm for Numerical Simulations
Initialize Material Properties, ε, µ, a, cp, ρ, f, Eo
Diffusion Time Step, Based on Mesh Density
Frequency Domain Solutions of the Wave Equation
Time Domain Solution, Heat Equation
Adjust Temperature Dependent Properties
Electric Field Distribution in MAT Kiln
Empty cavity 25 °C
fs
Length, cm
E
fs
Length, cm
E 5 cm ZrO2 cube,
tan d ~ 0.01 Centered
25 °C
Model of Material Heating Profile
Radiant heat source T = Max T in sample at any time At high T, radiation significant surface slightly hotter
Field/Temperature Evolution in Material
Electric Field Magnitude [(V/m)2]
Temperature Differential [°C]
fs
fs
fs
Temperature [°C]
5 cm ZrO2 Cube
Putting the Model to Work
Tailor the radiant heating source to real processes
Adjust parameters in model Introduce shrinkage Heating rates and temperature dwells Energy efficiency Temperature uniformity
Test model against experiments
Surface, core, and ambient temperature
Model various furnace materials Products Kiln insulation & furniture
Technology Direction Integrate MAT modeling with sintering models
Develop prediction tools for microstructures and properties
Understand materials changes in microwave (MAT) heating
Better control mechanisms for MAT kilns
Similar efforts underway at Y-12 National Security Complex – Dr. Ed Ripley San Diego State University – Dr. Eugene Olevsky
Summary Access and ability to interpret dielectric data
Development of tool for MAT process development
Optimization of energy efficiency & process time
Applicability from lab-scale to production MAT systems
Tool for materials selection for MAT kilns
Groundwork for Computational Mat. Sci. of MAT processes
(sintering, phase changes, reactions)
Acknowledgments
Dr. Ron Hutcheon Microwave Properties North
Dr. Ken Connor
ESCE, RPI