computer simulation of ceramic processing using microwave...

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


Initialize Material Properties, ε, µ, a, cp, ρ





fs







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 ∇× • ∇× + • ∂

− • =∂

∫

∫

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

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

computer simulation of ceramic processing using microwave...

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