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

Example: Macro-Segregation

Scheil vs lever

DistributionOf solute at scale of process

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

= 0.05, T0 = -0.65

time = 6000

= 0.25, = 0.75, x =4d0

FAST-CPUThis

On This

In 60 seconds !

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

Have Presented Two examples of multi-scale multi-physics framework

In The mean time theFramework of

Process-Grid-Sub-grid

Is an adequate bridge

Can produce insightful results

And in some ways may provide more insight in to the process as opposed toa direct simulation!