A MULTI-SCALE/MULTI-PHYSICS MODELING FRAMEWORK FOR SOLIDIFICATION SYSTEMS
Vaughan R VollerSaint Anthony Falls LabUniversity of Minnesota
Acknowledgments
National Science Foundation who through have supported some of the multi-scale work
National Center For Earthsurface Dynamics
For the Aditya Birla visiting Chair in the department of Mechanical Engineering
CFD- Model
Experiment
Plant/fieldData
e.g. optimization of wheel castingCleary et al, Fluent
1. Process OptimizationBy blending models, plant/field and experiment Multi-physics –Multi-Scale
KEY AREA OF INTEREST IN CFD
3
Flow +
LIDAR (1mm) measurementOf bed topography
2. Dovetailing Modeling and High ResolutionDistributed Measurement Techniques
Multi-physics –Multi-Scale Framework
defines the domain of the problem
Three Scaleswhere nodal values of process variables are defined and stored
phenomena at scales below the grid resolution are incorporated into the analysis via the use of volume averaging and the development of constitutive relationships.
Solidification Phenomena (The Science)occur at the local scale of the SolidLiquid Interface (~ microns)
Solidification Process (The Engineering)occur at the global scale of a product (~meters)
To make progress in the “science” and “engineering” we need to bridge between these scales
Growth of Equiaxed CrystalIn under-cooled melt
A microstructure model
Phase change temperaturedepends on interfacecurvature, speed and concentration
Sub-grid modelsAccount for Crystal anisotropyand “smoothing” of interface jumps
In Detail
)4cos151()( Four fold symmetry
Sub grid constitutive
TtH 2
fTH fHT If f= 0 or f = 1 If 0 < f < 1
2/32y
2x
yy2xxyyxxx
2y
)ff(
fffff2ff
)ff
(tany
x1curvature
Local direction
)(dT o
Capillary length 10-9 m in Al alloys Easy and Direct
ENTHALPY
seed
Typical gridSize 200x200¼ geometry
At end of time step if solidificationCompletes in cell iForce solidification in ALL fullyliquid neighboring cells.
Physical domain ~ 2-10 microns
Initially insulated cavity contains liquid metal with bulk undercoolingT0 < 0. Solidification induced by placing solid seed at center.
Some Results
4do (blue)
3.25do (black)
2.5do (red)
Dendrite shape with 3 grid sizes shows reasonable independence
= 0.05, T0 = -0.65
Dimensionless time = 6000
= 0.25, = 0.75
0
0.02
0.04
0.06
0.08
0.1
0 5000 10000 15000 20000
Dim. Time
Dim
. Tip
Vel
.
at t =37,000, T0 = -0.55, = 0.05, = 2.5do ( ¼ box size 800x800)
Tip Velocity ApproachesTheoretical Limit
Verification 1 Looks Right!!
= 0.05, T0 = -0.65, x = 3.333d0
Enthalpy Calculation
Dimensionless time = 0 (1000) 60002
odtk
= 0.05, T0 = -0.55, x = d0
Level Set Kim, Goldenfeld and Dantzig
Dimensionless time = 37,600
do5.2x Red my calculation for these parameters With grid size
The Solid color is solved with a 45 deg twist on the anisotropy and then twisted back—the white line is with the normal anisotropy
,75.0)0(
,95.0)45(
,25.0
0
0
Note: Different “smear” parameters are used in 00 and 450 case
0
50
100
150
200
250
300
350
0 2000 4000 6000
Dim. Time
Tip
Po
s.
45 deg. twist in anisotropy
Tip position with time
Dimensionless time = 6000
= 0.05, T0 = -0.65
Not perfect: In 450 case the tip velocity at time 6000 (slope of line) is below the theoretical limit.
Low Grid Anisotropy
Playing Around
A Problem with Noise Multiple Grains-multiple orientations
Grains in A Flow Field
Thses calculations were performed by Andrew Kao, University of Greenwich, LondonUnder supervision of Prof Koulis Pericleous and Dr. Georgi Djambazov.
100 10-9
Together they cover a vast range of scales
Have Presented Two examples of multi-scale multi-physics framework
Model 1
Model 2
Can we Eliminate The middle ManAn model AcrossScales in One model?
“Direct Microscale modeling”
Do we really want to do it?
3 Largest grid sizes (nodes/elements) reported in 11 MCWASP proceedingsDating back to 1980 and ending in 2006
Update of Voller and Porte-AgelJCP 2003