Presentation is loading. Please wait.

Presentation is loading. Please wait.

Key Issues in Solidification Modeling—

Published byAgnes Poole Modified over 9 years ago

Similar presentations

Presentation on theme: "Key Issues in Solidification Modeling—"— Presentation transcript:

1 Key Issues in Solidification Modeling—
Vaughan Voller, University of Minnesota, Aditya Birla Chair ~0.5 m Process Scales: ~10 mm Micro-strcture Validation and Verification: Do governing equations model the correct physics? Is approximate solution a solution of governing Equations ? Ferreira et al How can we deal with this problem Micro-macro models How feasible is Direct Modeling of Microstructure? What can it tell us about the process Scale? Prediction Of microstructure

2 solid crystals + liquid
Scales: An Example Problem: Macrosegregation—Ingot alloy solidification Csolid Cliquid In mushy region solute is partitioned at solid-liquid interface Result after full solidification is macro-scale areas with concentration above or Below the nominal concentration see Flemings (Solidification Processing) and Beckermann (Ency. Mat) solid crystals + liquid “mushy region” This solute is redistributed at process scale by fluid and solid motions shrinkage grain motion solid liquid alloy convection 1m

3 Computational grid size
Key Scales in Macro-segregation ~0.5 m Process ~5 mm REV ~ 50 mm solid representative ½ arm space sub-grid model g Computational grid size Solute value in liquid phase controlled by local diffusion in solid “microsegregation” Solute transport controlled by advection

4 Scales in General Solidification Processes
chill A Casting The REV Nucleation Sites columnar equi-axed The Grain Envelope The Secondary Arm Space The Tip Radius f = 1 f = -1 The Diffusive Interface ~ 0.1 m ~10 mm ~ mm ~100 mm ~1 nm Scales in General Solidification Processes 103 101 10-1 10-3 10-5 10-7 10-9 Length Scale (m) interface kinetics nucleation solute diffusion growth grain formation casting heat and mass tran. Time Scale (s) (after Dantzig) Question for later: Can we build a direct-simulation of a Casting Process that resolves to all scales?

5 Meso Solid-liquid interface NANO-Meter
A solidification model has three components: The Domain: The Grid: The sub-Grid: Examples Problem Domains The Grid Sub-grid --Constitutive -- Controlled by averaged Properties in REV Realizations--Of multi-phase regions Element in numerical Calculation ---REV State described by averaged mixture values Macro Process Effect of morphology on flow REV METER Meso Microstructure The Grain Envelope Solid-liquid interface A representative Arm spacing— Form of Constitutive model T=F(g) f = 1 f = -1 The Diffusive Interface, e.g. NANO-Meter

6 Computational grid size
Key Scales in Macro-segregation ~0.5 m Process ~5 mm REV ~ 50 mm solid representative ½ arm space sub-grid model g Computational grid size Solute value in liquid phase controlled by local diffusion in solid “microsegregation” Solute transport controlled by advection Develop a “Macro-Micro Model” (Rappaz) Solve transport equations at macroscopic scale (MACRO) Use sub-grid model to account for microsegregation (MICRO) a “constitutive model”

7 Macro (Process) Scale Equations
Equations of Motion (Flows) mm REV Heat: Solute Concentrations: Assumptions for shown Eq.s: -- No solid motion --U is inter-dendritic volume flow If a time explicit scheme is used to advance to the next time step we need find REV values for T temperature Cl liquid concentration gs solid fraction Cs(x) distribution of solid concentration

8 Computational grid size
The Micro-Macro Model MACRO: ~ 50 mm solid representative ½ arm space sub-grid model g microsegregation and solute diffusion in arm space MICRO: ~0.5 m ~5 mm Computational grid size Process REV from computation Of these Mixture values need to extract --

9 Primary Solidification Solver g
Transient mass balance g model of micro-segregation Iterative loop Cl T (will need under-relaxation) Gives Liquid Concentrations A C equilibrium

10 before solidification
Micro-segregation Model liquid concentration due to macro-segregation alone Solute Fourier No. ½ Arm space of length l takes tf seconds to solidify In a small time step new solid forms with lever rule of concentration transient mass balance gives liquid concentration Solute mass density before solidification of new solid (lever) after solidification Q -– back-diffusion Need an easy to use approximation For back-diffusion

11 The Ohnaka approximation
The parameter Model --- Clyne and Kurz, Ohnaka For special case Of Parabolic Solid Growth And ad-hoc fit sets the factor and In Most other cases The Ohnaka approximation Works very well

12 The Profile Model Wang and Beckermann Need to lag calculation one
time step and ensure Q >0 m is sometimes take as a constant ~ 2 BUT In the time step model a variable value can be use Due to steeper profile at low liquid fraction Propose

13 An Important wrinkle ---Coarsening
Due to dissolution processes some arms will melt and arm-space will coarsen Time 1 Time 2 > Time 1

14 Coarsening Arm-space will increase in dimension with time
This will dilute the concentration in the liquid fraction—can model be enhancing the back diffusion  A model by Voller and Beckermann suggests If we assume that solid growth is close to parabolic m =2.33 in Parameter model In profile model

15 Verification: of Micro Models:
Constant Cooling of Binary-Eutectic Alloy With Initial Concentration C0 = 1 and Eutectic Concentration Ceut = 5, No Macro segregation , k = 0.1 T Cl As solidification proceeds the concentration in liquid increases. When the eutectic composition is reached remaining liquid solidifies isothermally, Eutectic Fraction In model calculate the transient value of g from Use 200 time steps and equally increment 1 < Cl < 5 Parameter or Profile

16 Verification of Micro Models:
Verify approximate model for back-diffusion by comparing solution with FD solution of Fick’s equation in arm space. Parameter or Profile Remaining Liquid when C =5 is Eutectic Fraction

17 Validation of Micro Model:
Predictions of Eutectic Fraction With constant cooling Co = 4.9 Ceut = 33.2 k = 0.16 Al-4.9% Cu Comparison with Experiments Sarreal-Abbaschian Met Trans 1986 X-ray analysis determines average eutectic fraction

18 Macro-Micro Model of Solidification
Predict g predict Cl predict T Calculate Transient solute balance in arm space Macro-Micro Model of Solidification Two MICRO Models For Back Diffusion My Method of Choice Parameter Robust Easy to Use Poor Performance at very low liquid fraction— can be corrected Profile A little more difficult to use With this Ad-hoc correction Excellent performance at all ranges Account for coarsening

19 Modeling the fluid flow could require a
Two Phase model, that may need to account for: Both Solid and Liquid Velocities at low solid fractions A switch-off of the solid velocity in a columnar region A switch-off of velocity as solid fraction g  o. An EXAMPLE 2-D form of the momentum equations in terms of the interdentrtic fluid flow U, are: Extra Terms Magically vanish Buoyancy Friction between solid and liquid Accounts for mushy region morphology Can requires a solid-momentum equation

20 Verification: of Macro-Micro Model—Inverse Segregation in a Binary Alloy
chill solid mushy liquid riser y Shrinkage sucks solute rich fluid toward chill – results in a region of +ve segregation at chill 100 mm Flow by simple app. of continuity Fixed temp chill results in a similarity solution Parameter Current estimate empirical

21 Validation: Comparison with Experiments
chill solid mushy liquid riser y 100 mm Ferreira et al Met Trans 2004

22 Direct Microstructure Modeling
chill A Casting The REV Nucleation Sites columnar equi-axed The Grain Envelope The Secondary Arm Space The Tip Radius f = 1 f = -1 The Diffusive Interface ~ 0.1 m ~10 mm ~ mm ~100 mm ~1 nm Macro-Micro models at process scale grid sub-grid domain domain grid constitutive Micro-Nano model for micro-structure

23 Example: Growth of dendritic crystal in an under-cooled melt
(seminar on July 14) Solved in ¼ Domain with A 200x200 grid Growth of solid seed in a liquid melt Initial dimensionless undercooling T = -0.8 Resulting crystal has an 8 fold symmetry

24

25

26

27

28

29

30

31

32

33

34

35

36 Grid independent results with correct dynamics can be readily obtained
Tip Velocity Interacting grains grid anisotropy prediction of concentration field Scale of calculations shown 1 mm

37 Computational grid size
So can we use DMS to predict microstructure at the process level? ~0.5 m ~5 mm Computational grid size Process REV ~ 1 mm Sub grid scale For 2-D calc at this scale Will need 1018 grids

38 For 2-D calc at this scale
Will need 1018 grids Voller and Porte-Agel, JCP 179, (2002 Year “Moore’s Law” 2055

39 CONCLUSIONS Validated and Verified Models that
Conclusion: Can Currently Build Validated and Verified Models that Can successfully model across ~ 4 decades Of length scales chill A Casting The REV Nucleation Sites columnar equi-axed The Grain Envelope The Secondary Arm Space The Tip Radius f = 1 f = -1 The Diffusive Interface ~ 0.1 m ~10 mm ~ mm ~100 mm ~1 nm Able to use Macro-Micro Approach To model all scales of Heat and Mass Transport Able to build Local Microstructure models But a long way from DMS Direct microstructure simulation at the process scale In the meantime what Value Added can we get from Local microstructure models Use as generator for constitutive models Use in volume averaging approaches

Download ppt "Key Issues in Solidification Modeling—"

Similar presentations

Hongjie Zhang Purge gas flow impact on tritium permeation Integrated simulation on tritium permeation in the solid breeder unit FNST, August 18-20, 2009.

Hongjie Zhang Purge gas flow impact on tritium permeation Integrated simulation on tritium permeation in the solid breeder unit FNST, August 18-20, 2009.
Combined thermal, solutal and momentum transport. Assume a rigid mold. Imperfect contact and air gap formation at metal/mold interface Design of mold surface.

Combined thermal, solutal and momentum transport. Assume a rigid mold. Imperfect contact and air gap formation at metal/mold interface Design of mold surface.
Self-propelled motion of a fluid droplet under chemical reaction Shunsuke Yabunaka 1, Takao Ohta 1, Natsuhiko Yoshinaga 2 1)Department of physics, Kyoto.

Self-propelled motion of a fluid droplet under chemical reaction Shunsuke Yabunaka 1, Takao Ohta 1, Natsuhiko Yoshinaga 2 1)Department of physics, Kyoto.
L10B: Phases in equilibrium with one another: Composition and amount of each The temperature and pressure must be the same in each phase in equilibrium.

L10B: Phases in equilibrium with one another: Composition and amount of each The temperature and pressure must be the same in each phase in equilibrium.
2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003 CFD Modeling of Heat and Moisture Transfer on a 2-D Model of a Beef.

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003 CFD Modeling of Heat and Moisture Transfer on a 2-D Model of a Beef.
Alloy Solidification Def. Partition coefficient k

Alloy Solidification Def. Partition coefficient k
Application of the Enthalpy Method: From Crystal Growth to Sedimentary Basins Grain Growth in Metal Solidification From W.J. Boettinger  m  10km “growth”

Application of the Enthalpy Method: From Crystal Growth to Sedimentary Basins Grain Growth in Metal Solidification From W.J. Boettinger  m  10km “growth”
Solidification and Grain Size Strengthening

Solidification and Grain Size Strengthening
~0.5 m Computational grid size Process ~5 mm REV Modeling Microsegregation In Metal Alloys – Vaughan Voller, University of Minnesota 1 of 14 Can we build.

~0.5 m Computational grid size Process ~5 mm REV Modeling Microsegregation In Metal Alloys – Vaughan Voller, University of Minnesota 1 of 14 Can we build.
Modeling of Micro segregation in Metal Alloys Vaughan R. Voller University of Minnesota.

Modeling of Micro segregation in Metal Alloys Vaughan R. Voller University of Minnesota.
Voller, University of Minnesota Application of an Enthalpy Method for Dendritic Solidification Vaughan R. Voller and N. Murfield.

Voller, University of Minnesota Application of an Enthalpy Method for Dendritic Solidification Vaughan R. Voller and N. Murfield.
An Enthalpy—Level-set Method Vaughan R Voller, University of Minnesota + + speed def. Single Domain Enthalpy (1947) Heat source A Problem of Interest—

An Enthalpy—Level-set Method Vaughan R Voller, University of Minnesota + + speed def. Single Domain Enthalpy (1947) Heat source A Problem of Interest—
Computational grid size ~0.5 m Process ~5 mm REV Maco-Micro Modeling— Simple methods for incorporating small scale effects into large scale solidification.

Computational grid size ~0.5 m Process ~5 mm REV Maco-Micro Modeling— Simple methods for incorporating small scale effects into large scale solidification.
Session III: Computational Modelling of Solidification Processing Analytical Models of Solidification Phenomena V. Voller QUESTION: As models of solidification.

Session III: Computational Modelling of Solidification Processing Analytical Models of Solidification Phenomena V. Voller QUESTION: As models of solidification.
An Enthalpy Based Scheme for Simulating Dendritic Growth V.R. Voller 4d o (blue) 3.25d o (black) 2.5d o (red) Dendrite shape with 3 grid sizes shows reasonable.

An Enthalpy Based Scheme for Simulating Dendritic Growth V.R. Voller 4d o (blue) 3.25d o (black) 2.5d o (red) Dendrite shape with 3 grid sizes shows reasonable.
GROWING NUMERICAL CRYSTALS Vaughan Voller, and Man Liang, University of Minnesota We revisit an analytical solution in Carslaw and Jaeger for the solidification.

GROWING NUMERICAL CRYSTALS Vaughan Voller, and Man Liang, University of Minnesota We revisit an analytical solution in Carslaw and Jaeger for the solidification.
CENG151 Introduction to Materials Science and Selection

CENG151 Introduction to Materials Science and Selection
Oxygen Diffusion Model in LWR Fuel using Thermochimica in MOOSE/BISON Theodore M. Besmann.

Oxygen Diffusion Model in LWR Fuel using Thermochimica in MOOSE/BISON Theodore M. Besmann.
~0.5 m ~ 50  m solid ~5 mm Computational grid size ProcessREV representative ½ arm space sub-grid model g A Microsegregation Model – Vaughan Voller, University.

~0.5 m ~ 50  m solid ~5 mm Computational grid size ProcessREV representative ½ arm space sub-grid model g A Microsegregation Model – Vaughan Voller, University.
Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 1 Development of microstructure.

Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 1 Development of microstructure.

Similar presentations

Ads by Google