2. Materials Process Design and Control Laboratory COMBINED EXPERIMENTAL AND COMPUTATIONAL APPROACH FOR THE DESIGN OF MOLD SURFACE TOPOGRAPHY IN ALUMINUM CASTING DATE OF PRESENTATION : 4 OCTOBER 2005 PRINCIPAL INVESTIGATOR : PROF. NICHOLAS ZABARAS PERFORMING ORGANIZATION : MATERIALS PROCESS DESIGN AND CONTROL LABORATORY, CORNELL UNIVERSITY PROJECT START DATE : 31 AUGUST 2002 PROJECT END DATE : 30 AUGUST 2005

3. Materials Process Design and Control Laboratory Industrial Partners Alcoa Technical Center, Alcoa Center, PA Ingot and Solidification Platform (Dr. Alvaro Giron, Coordinator) Provide experimental data Validate important results obtained through simulations Perform pilot experiments to demonstrate and validate key modifications and technologies developed

4. Materials Process Design and Control Laboratory A design methodology will be developed with which casting mold surface topologies can be tuned to produce required surface features and microstructural features of Aluminum ingots. Both static and continuous casting processes will be examined with instrumental molds. Mold surface topographies, which consist of unidirectional and bidirectional groove textures, will be generated using contact and non-contact techniques to elicit a radiator like effect at the mold casting interface. Project Objectives

5. Materials Process Design and Control Laboratory Surface defects in casting (a) (b) (c) (a) Sub-surface liquation and crack formation on top surface of a cast (b) Ripple formation (c) Non-uniform front and undesirable growth with non-uniform thickness Project Objectives

6. Materials Process Design and Control Laboratory Cracks CAST SURFACE DEFECTS Subsurface segregation and non-uniform microstructure Liquation TCG Duplex micro. Cavities Surface irregularities Surface porosity Gas porosity Blisters Surface tears Pre-solidification cracks Post-solidification cracks Cold shuts Ripples/Laps Folds Sweats Oxide patches Classification of direct cast surface defects in direct chill cast ingots Blebs Bleed bands Project Objectives

7. Materials Process Design and Control Laboratory This project is developing methodologies to reduce surface defects in castings by designing appropriate mold surface topologies. These techniques can help reduce material, energy and monetary losses during post-scalping operations. Project Innovations

8. Materials Process Design and Control Laboratory Some mold surface topographies used in Alcoa Profound effects on the morphology of final cast surfaces Project Innovations

9. Materials Process Design and Control Laboratory Data collected from Aluminum Association’s Aluminum Statistical Review 2000 and Aluminum Association’s LCI report for North American Aluminum industry. Net shipments of sheet and plate (made from rectangular ingots) = 10800 million lb. With average semi-fabricating recovery of 60%, 18000 million lb of rectangular ingot cast in 2000. Approximately 5% of each rectangular ingot lost in ingot scalping process. Success of research and subsequent implementations assumed to give a reduction of 50% reduction in ingot scalping. Project Energy Savings

10. Materials Process Design and Control Laboratory Amount of scalper chips would decrease from 900 million lb to 450 million lb. Total energy required for secondary ingot casting. = 115 kWh of electricity + 126 m3 of natural gas per 1000 kg of cast ingot = 2240 BTU/lb of cracked ingot that is re-melted and re-cast The potential manufacturing energy savings from successful implementation of these technologies estimated around 1.01 TRILLION BTU/year. Project Energy Savings

11. Materials Process Design and Control Laboratory Project Baseline and Critical metrics Baseline Metrics: Current Aluminum casting techniques result in the formation of scalp depth and ingot scalping consumes approximately 5% of each rectangular ingot scalped. Therefore, the volume of scalped chips is 900 million lb/year with the total amount of Aluminum cast taken as 18000 lb per year approximately. The total energy required for secondary ingot casting is 115 kWh of electricity plus 126 cubic meters of natural gas per 1000 kg of cast ingot, or 2240 BTU/lb of cracked ingot that is re-melted and re-cast. The principal emissions from the secondary casting are 0.066 lb of CO 2, 0.023 lb of CO and 0.080 lb of solid waste per lb of cast ingot.

12. Materials Process Design and Control Laboratory Project Baseline and Critical metrics Project Metrics: Success in research efforts could achieve around 2.5% reduction in ingot scalping and the volume of scalp chips would come down to 450 million lb/yr. The potential for manufacturing energy savings in the domestic Aluminum industry is estimated to be around 1.01 trillion BTU/yr. A potential reduction of up to 29 million lb/yr of CO 2, 10 million lb/yr of CO and 36 million lb/yr of solid waste can be accomplished.

13. Materials Process Design and Control Laboratory Technical Decision Points Mold topography: Use of distorted or grooved molds to arrest or suppress gap nucleation Modify heat transfer/solidification rate, thermal contact resistance, wettability by using grooved molds Effect of varying mold topographies on fluid flow solidification and macrosegregation Aluminum and Aluminum alloys. Uneven growth Plain mold plate Mold plate with grooves Even growth

14. Materials Process Design and Control Laboratory Cast Surface defects Bleed bands Blobs Liquation Presolidification cracks Shell formation Shell distortion & mold movement Reduction in heat transfer Air gap formation Re-melting of shell Crack initiation Flow of interdendritic residual melt Air gap related events and resulting defects Ref: Anyalebechi, P. N., ALCOA (2000) Technical Decision Points

15. Materials Process Design and Control Laboratory Technical Decision Points Mold materials: May improve or retard heat transfer between metal and mold Affect gap nucleation time (very important during the initial stages of solidification) Degree of superheat: Increases thermal load Improves wettability and metal-mold contact Increases heat flux Finer microstructure Smooth solid-shell interface Fluid flow: Improve heat transfer rate due to convection Changes in solid-liquid front morphology because of convection Affects macro-segregation and inverse segregation in alloys

16. Materials Process Design and Control Laboratory Project Accomplishments Development of a robust, dimension independent stabilized finite element simulator to model solidification of alloys under various process conditions. Investigating the effects of varying mold surface topography, in the form of sinusoids, on fluid flow and macrosegregation in solidifying Aluminum alloys. Development of a simulator for modeling coupled deformation, air-gap formation, thermal and inelastic stresses in solidifying Aluminum metal and alloys. Investigations of uneven cooling and non-uniform contact, due to air gap formation, uneven surface topography and liquid pressure on thermal stresses in solidifying Aluminum. Parametric analysis of air-gap formation, equivalent stresses and segregation in Aluminum alloys under varying process conditions.

17. Materials Process Design and Control Laboratory Project Accomplishments Microstructure evolution during solidification of metals in two and three dimensions using energy conserving level set methods. Evolution of droplet surfaces and early stage solidification using surface evolver and level set methods.

18. Materials Process Design and Control Laboratory x y Solidification of Aluminum-Copper alloy on uneven surfaces v x = v y = 0 q = h (T – T amb ) v x = v y = 0 q = 0 q = h (T – T amb ) q = 0 v x = v y = 0 Surfaces from where heat is removed modeled as sinusoids with fixed amplitude A and wavelength λ. Varying surface topography by changing A and λ leads to changes in heat transfer, fluid flow and macrosegregation. The reference case consists of a perfectly rectangular cavity. L s 0.08 m 0.13 m

19. Materials Process Design and Control Laboratory Vertical solidification from uneven surfaces (a)Isotherms (b) liquid mass fraction (c) liquid solute concentrations A = 1 mm, λ = 10 mm t = 66 sec t = 121 sec

20. Materials Process Design and Control Laboratory Vertical solidification from uneven surfaces (a)Isotherms (b) liquid mass fraction (c) liquid solute concentrations A = 0.5 mm, λ = 10 mm t = 66 sec t = 121 sec

21. Materials Process Design and Control Laboratory Vertical solidification from uneven surfaces (a)Isotherms (b) liquid mass fraction (c) liquid solute concentrations A = 0.5 mm, λ = 5 mm t = 66 sec t = 121 sec

22. Materials Process Design and Control Laboratory Vertical solidification from uneven surfaces Extent of inverse segregation found to increase with increase in amplitude or decrease in wavelength. For both cases, inverse segregation is lowest when surface is even. Midplane solute (Cu) concentrations for varying mold topography

23. Materials Process Design and Control Laboratory Vertical solidification from uneven surfaces Midplane vertical velocities (v y ) for varying mold topography Vertical velocity magnitudes increase with increase in amplitude or decrease in wavelength. For both cases, the magnitude is lowest when the surface is even.

24. Materials Process Design and Control Laboratory Horizontal solidification from uneven surfaces Evolution of solid/mushy zones and velocity for varying mold topography A = 0.5 mm, λ = 10 mmA = 1mm, λ = 10 mm A = 0.5 mm, λ = 5 mmA = 0 mm, λ = mm Fluid flow primarily driven by thermal and solutal convection for all cases here. Fluid flow much stronger here compared to the vertical solidification cases. Magnitudes of velocity vary with amplitude and wavelength of the surface.

25. Materials Process Design and Control Laboratory Horizontal solidification from uneven surfaces Overall macrosegregation evolution for varying mold topography A = 0.5 mm, λ = 10 mmA = 1mm, λ = 10 mm A = 0.5 mm, λ = 5 mmA = 0 mm, λ = mm Macrosegregation driven by thermosolutal convection occurs throughout the cavity. Solute depletion occurs at the top and solute enrichment at the bottom. Degree and extent of macrosegregation vary with amplitude and wavelength.

26. Materials Process Design and Control Laboratory Main observations and conclusions from this study In vertical solidification, increase in unevenness either by increasing the amplitude or decreasing the wavelength leads to increase in inverse segregation. This is because, the increase in contact surface area accelerates the phase change rate and increases the intensity of shrinkage driven flow, which is the main factor behind inverse segregation. Maximum velocity magnitudes and differences in maximum and minimum solute concentrations also highlight this fact. In horizontal solidification, increase in unevenness leads to increase in the overall extent of segregation highlighted by the GES values, but differences in the maximum and minimum solute concentrations first increase and then decrease. Maximum velocity magnitudes first increase and then decrease when either the amplitude is increased or wavelength decreased. Thermosolutal convection, which is the dominating factor affecting macrosegregation in horizontal solidification, is suppressed when surface unevenness increases leading to higher rate of phase change.

27. Materials Process Design and Control Laboratory Solidification of Al on Uneven Surfaces Hypoelastic model without plastic deformation (Hector et al. 2000) Heat transfer in the mold, solid shell and melt. Heat transfer causes deformation (thermal stress). Gaps or contact pressure affect heat transfer. Solidification after air-gap nucleation not modeled.

28. Materials Process Design and Control Laboratory Thermal resistance at mold/shell interface Contact resistance: At the very early stages, the solid shell is in contact with the mold and the thermal resistance between the shell and the mold affected by the contact conditions Uneven contact pressure generates an uneven thermal stress development and accelerates distortion or warping of the shell. Example: Aluminum-Ceramic Contact Before gap nucleation, the thermal resistance is determined by pressure After gap nucleation, the thermal resistance is determined by the size of the gap Heat transfer retarded due to gap formation

29. Materials Process Design and Control Laboratory Mold – Metal Boundary Conditions The actual air – gap sizes or contact pressure are determined from the contact sub problem. This modeling of heat transfer mechanism due to imperfect contact very crucial for studying the non-uniform growth at early stages of solidification. Consequently, heat flux at the mold – metal interface is a function of air gap size or contact pressure: = Air-gap size at the interface = Contact pressure at the interface

30. Materials Process Design and Control Laboratory Gap nucleation time: effects of wavelength At the very early stages of aluminum solidification, contact pressure between mold and solid shell will drop at the trough due to thermal stress development. When this contact pressure drops to zero, gap nucleation is assumed to take place. For rigid mold (with an topography amplitude=1 µm, wavelength=1-5 mm), under liquid pressure 8000 Pa, the gap nucleation time is in the order of seconds. Physical Conditions: Liquid pressure P=8000 Pa Thermal resistance at mold-shell interface R=10 -5 m 2 o C sec J -1

31. Materials Process Design and Control Laboratory Gap nucleation time: effects of mold conductivity Mold conductivity affects gap nucleation time The higher the conductivity, the quicker the gaps nucleate from the mold surface In this calculations, the deformation of the mold is neglected to illustrate the effects of mold conductivity. Physical conditions: Liquid pressure P=10000 Pa Mold thickness h=0.5 mm Thermal resistance at mold-shell interface R=10 -5 m 2 o C sec J -1 Wavelength=2 mm

32. Materials Process Design and Control Laboratory When the wavelength is relatively small, the evolution of the contact pressure at the trough is mainly affected by the conductivity of the mold, i.e. the deformation of the mold does not play a crucial role. Gap nucleation time: effects of mold material ( deformable mold ) Physical Conditions: Liquid pressure P=10000 Pa Mold thickness h=0.5 mm Thermal resistance at mold-shell interface R=10 -5 m 2 o C sec J -1 Wavelength=10 mm, (20 mm, 30 mm in the next two slides)

33. Materials Process Design and Control Laboratory When the wavelength increases, the Ptr-t line is about to show a turn-around pattern when pressure reaches zero. This is defined as the `critical wavelength’ in the analytical studies of L. Hector. From this figure, we can say that the critical wavelength is slightly above 20 mm. In Hector’s analytical study, the critical wavelength is 16.60 mm, for iron mold and 14.03 mm for lead mold under the same conditions. Gap nucleation time: effects of mold material ( deformable mold )

34. Materials Process Design and Control Laboratory When the wavelength is greater than the critical value, the Ptr-t curve shows a turn- around pattern before the contact pressure reaches zero. Gap nucleation time: effects of mold material ( deformable mold ) The pressure won’t decrease to 0 for an iron or lead mold, so a large wavelength is preferred. But in practice, we can never get a such a smooth mold topography with amplitude 1 µm and wavelength 30 mm.

35. Materials Process Design and Control Laboratory Shell thickness at gap nucleation time ( rigid mold ) The shell thickness at gap nucleation time plays an important role in deformation. The thicker the shell, the more its ability to prevent distortion or warping. From calculations, high pressure is the preferred option to achieve larger shell thickness at gap nucleation time.

36. Materials Process Design and Control Laboratory Liquid or low solid fraction mush - any deformation induced by thermal expansion is permanent. (Without any strength) Solid or high solid fraction mush - plastic deformation is developed only gradually. The parameter w is defined as: Low solid fractions usually accompanied by melt feeding and no deformation due to weak or non – existent dendrites  leads to zero thermal strain. With increase in solid fraction, there is an increase in strength and bonding ability of dendrites  to non – zero thermal strain. The presence of a critical solid volume fraction is observed in experiment and varies for different alloys. Modeling Deformation In Mushy Zone

37. Materials Process Design and Control Laboratory For deformation, we assume the total strain can be decomposed into three parts: elastic strain, thermal strain and plastic strain. Elastic strain rate is related with stress rate through an hypo-elastic constitutive law Plastic strain evolution satisfy this creep law with its parameters determined from experiments (Strangeland et al. (2004)). The thermal strain evolution is determined from temperature decrease and shrinkage. Strain measure : Elastic strain Thermal strain Plastic strain Modeling Deformation In Mushy Zone

38. Materials Process Design and Control Laboratory Parameters for simulation of deformation in mushy zone Volumetric thermal expansion coefficient Volumetric shrinkage coefficient Strain-rate scaling factor Stress scaling factor Activation energy Creep law exponent Mushy zone softening parameter Creep law for plastic deformation Ref. Strangeland et al. (2004) Critical solid fraction for different copper concentrations in aluminum-copper alloy Ref: Mo et al.(2004)

39. Materials Process Design and Control Laboratory Schematic of the Problem Definition An Aluminum-copper alloy is solidified on an sinusoidal uneven surface. With growth of solid shell, air – gaps form between the solid shell and mold due to imperfect contact – which further leads to variation in boundary conditions. The solid shell undergoes plastic deformation and development of thermal and plastic strain occurs in the mushy zone also. Inverse segregation caused by shrinkage driven flow causes variation in air – gap sizes, front unevenness and stresses developing in the casting.

40. Materials Process Design and Control Laboratory Solidification Coupled with Deformation and Air-gap Formation Because of plastic deformation, the gap formed initially will gradually decrease. As shown in the movies, a 1mm wavelength mold would lead to more uniform growth and less fluid flow. Important parameters 1) Mold material - Cu 2) C Cu = 8 wt.% 3) ΔT melt = 0 o C Air gap is magnified 200 times. Preferential formation of solid occurs at the crests and air gap formation occurs at the trough, which in turn causes re-melting.

41. Materials Process Design and Control Laboratory Deformation problem Heat Transfer (Mold is rigid and non- deformable) Solidification problem We carried out a parametric analysis by change these four parameters 1) Wavelength of surfaces (λ) 2) Solute concentration (C Cu ) 3) Melt superheat (ΔT melt ) 4) Mold material (Cu, Fe and Pb) Both the domain sizes are on the mm scale Combined thermal, solutal and momentum transport in casting. Assume the mold is rigid. Imperfect contact and air gap formation at metal – mold interface Solidification of Al-cu Alloy on Uneven Surfaces

42. Materials Process Design and Control Laboratory Transient Evolution of Important Fields (λ = 5 mm) (a)Temperature (b)Solute concentration (c)Equivalent stress (d) Liquid mass fraction (d) (c) (b) (a) Important parameters 1) Mold material - Cu 2) C Cu = 5 wt.% 3) ΔT melt = 0 o C We take into account solute transport and the densities of solid and liquid phases are assumed to be different. Inverse segregation, caused by shrinkage driven flow, occurs at the casting bottom.This is observed in (b).

43. Materials Process Design and Control Laboratory Transient Evolution of Important Fields (λ = 3 mm) (d) (c) (b) (a) (a)Temperature (b)Solute concentration (c)Equivalent stress (d) Liquid mass fraction For smaller wavelengths, similar result is observed: (1) preferential formation of solid occurs at the crests (2) remelting at the trough due to the formation of air gap. For wavelength 3mm, the solid shell unevenness decreases faster than the case of 5mm wavelength.

44. Materials Process Design and Control Laboratory Variation of Air-gap Sizes and Max. Equivalent Stress Air-gap sizes increase with time Increasing melt superheat leads to some suppression of air gaps Initially, stresses higher for lower superheat At later times, the difference is small λ = 5 mm, C Cu = 5 wt.%, mold material = Cu Increasing melt superheat leads to some suppression of air gaps and a smaller stress at beginning stages. At later times, the difference of equivalent stresses is however small.

45. Materials Process Design and Control Laboratory Effect of Wavelength on Air-gap Sizes and Max Equivalent Stress Max. equivalent stress σ eq variation with λ σ eq first increases and then decreases Initially, σ eq is higher for greater λ Later (t=100 ms), stress is lowest for 5 mm wavelength. Air-gap size variation with wavelength λ Initially, air-gap sizes nearly same for different λ At later times, air-gap sizes increase with increasing λ ΔT melt = 0 o C, C Cu = 5 wt.%, mold material = Cu

46. Materials Process Design and Control Laboratory Variation of Air-gap Sizes and Maximum Equivalent Stress σ eq first increases and then decreases Variation of σ eq with Cu concentration is negligible after initial times Air-gap sizes increase with time Increasing Cu concentration leads to increase in air-gap sizes ΔT melt = 0 o C, λ = 5 mm, mold material = Cu Increase of solute concentration leads to increase in air-gap sizes, but its effect on stresses are small.

47. Materials Process Design and Control Laboratory Variation of Air-gap Sizes and Max. Equivalent Stress Equivalent stress far lower for Cu molds than Fe or Pb molds Air gap sizes higher for Cu molds than Fe or Pb molds ΔT melt = 0 o C, λ = 5 mm, C Cu = 5 wt.% Gap nucleation and stress development are prominent for a mold of higher thermal conductivity like Cu. For Fe or Pb molds, heat removal is inhibited due to their lower thermal conductivity. This in turn inhibits air-gap formation and development of stresses..

48. Materials Process Design and Control Laboratory Effect of Inverse Segregation – Air Gap Sizes Differences in air-gap sizes for different solute concentrations are more pronounced in the presence of inverse segregation. (a) With inverse segregation(b) Without inverse segregation By comparing the result with modeling inverse segregation and without modeling inverse segregation, we can find that inverse segregation actually plays an important role in air- gap evolution.

49. Materials Process Design and Control Laboratory Value of front unevenness and maximum equivalent stress for various wavelengths one cannot simultaneously reduce both stress and front unevenness when the wavelength greater than 5mm, both unevenness and stress increase-> implies wavelength less than 5 mm is optimum Equivalent stress at dendrite roots The highest stress observed for 1.8% copper alloy suggest that aluminum copper alloy with 1.8% copper is most susceptible to hot tearing Phenomenon is also observed experi- mentally Rappaz(99), Strangehold(04) Variation of Equivalent Stresses and Front Unevenness Time t = 100 ms

50. Materials Process Design and Control Laboratory Effect of Mold Coatings on Solidification of Al-cu Alloy Deformation problem Heat Transfer (Mold is rigid and non- deformable) Solidification problem - Thickness of coating assumed to be of the order of mm. - Thermal conditions assumed to be similar as before. - Coefficient of friction μ varied for different mold coatings. Both the domain sizes are on the mm scale Combined thermal, solutal and momentum transport in casting. Assumption of a rigid mold. Imperfect contact and air gap formation at metal – mold interface Mold coating

51. Materials Process Design and Control Laboratory Variation Of Air-gap Sizes And Max. Equivalent Stress Magnitude of equivalent stresses unaffected. Transient behavior same as before. Magnitude of air-gap sizes unaffected. Transient behavior same as before. ΔT melt = 0 o C, λ = 5 mm, mold material = Cu Effect of change in the coefficient of friction ( μ ) on air gap sizes and equivalent stresses is negligible.

52. Materials Process Design and Control Laboratory CONCLUSIONS Early stage solidification of Al-Cu alloys significantly affected by non – uniform boundary conditions at the metal mold interface. Variation in surface topography leads to variation in transport phenomena, air-gap sizes and equivalent stresses in the solidifying alloy. Air-gap nucleation and growth significantly affects heat transfer between metal and mold. Distribution of solute primarily caused by shrinkage driven flows and leads to inverse segregation at the casting bottom. Presence of inverse segregation leads to an increase in gap sizes and front unevenness. Effect of melt pressure on solidification beyond gap nucleation was found to be negligible. Effects of surface topography more pronounced for a mold with higher thermal conductivity Computation results suggests that aluminum copper alloy with 1.8% copper is most susceptible for hot tearing defects.. The optimum mold wavelength should be less than 5mm to reduce growth front uneveness and equivalent stresses in the solidifying alloy.

53. Materials Process Design and Control Laboratory Effects of surface tension The initial contact between molten aluminum and mold plays an important role in the early solidification process. Initial contact between mold and liquid The size of micro-gap Heat flux at early stages of solidification Surface quality of aluminum casting Mold topographySurface energyLiquid pressure/Gravity We studied the effects of mold topography, surface energy and liquid pressure on the initial contact.

54. Materials Process Design and Control Laboratory Typical contact condition

55. Materials Process Design and Control Laboratory Energy under consideration We use software Surface Evolver to calculate the state with minimum energy. The energy considered includes surface energy(free liquid surface and contact surface), prescribed pressure energy and gravitational potential energy. In calculation of all these energies, volume integral is transformed into surface integral according to the Green’s Theorem.

56. Materials Process Design and Control Laboratory Effects of surface tension The surface energy between molten metal and mold surface can be decreased by coating.

57. Materials Process Design and Control Laboratory Effects of liquid pressure

58. Materials Process Design and Control Laboratory Effects of mold topography

59. Materials Process Design and Control Laboratory Effects of Surface tension on macro-gap In all of the above examples studying effects of surface tension, the geometry of surface topography is in the micro-scale (um). Using surface evolver, we found that when the geometry is in the macro-scale (mm), molten Aluminum always fills the entire cavity under a liquid pressure of about 10 3 ~10 4 Pa. When a droplet is in contact with a v-shaped mold surface, the liquid pressure exerted by the droplet causes the molten Aluminum droplet to contact the bottom of the cavity.

60. Materials Process Design and Control Laboratory Simulation procedure First use Surface Evolver to calculate the state with minimum energy. Then generate the mesh with required density.

61. Materials Process Design and Control Laboratory Effect of surface tension A change of surface tension could drastically change the solidification speed at very early stages of solidification.

62. Materials Process Design and Control Laboratory Dynamic coupling of surface tension In the previous case, the pressure of the air gap is assumed to be the atmosphere pressure, which is valid for sand casting. For metal molds, the air is trapped and its pressure could change with time. Initially, pressure of the trapped air increases due to temperature increase. The gas phase would push back the liquid and escape when it is above the crest. Four phases involved: liquid, gas, mold and solid. Surface Evolver is designed for single phase motion and requires specific inputs that restricts us from dynamic coupling the surface tension effects with solidification. We use level set method to handle multi-phase motion.

63. Materials Process Design and Control Laboratory Level set method  Individual signed distance functions for each phases.  Adaptive mesh is used to achieve fine mesh density on interface.  Example to make a conforming adaptive mesh.

64. Materials Process Design and Control Laboratory Example of adaptive meshing Finer mesh density at the phase boundary of wall and collapsing liquid column is achieved.

65. Materials Process Design and Control Laboratory Minimize energy using level set method We assume at each time step, the liquid is at its equilibrium shape with minimum energy. In the context of level sets, the system energy can be written in the following form

66. Materials Process Design and Control Laboratory Minimize energy using level set method The problem becomes: minimize energy Subject to constraints (No overlap or gap between phases) : Difficult to solve the above problem because of the infinite number of constraints (one constraint at each point). Relax the constraints to Subject to one constraint (No overlap or gap between phases) :

67. Materials Process Design and Control Laboratory Gradient projection method Minimize Subject to constraints Problem can be solved using the gradient projection method: Our problem further becomes:

68. Materials Process Design and Control Laboratory Validation problem Problem (Droplet hanging on the floor): Minimize Subjects to constraints (No gap & volume conservation) Surface tension with unwetted wall =0.5, air =1, and gravity =100

69. Materials Process Design and Control Laboratory Dynamic coupling of surface tension 4 stages: (1)Initially the gas pressure increases due to increase in temperature, which pushes the liquid back. We assume the gas escapes when it is above the crest. (2)The gas pressure decreases due to decrease in temperature. Liquid begins to contact with mold again. (3)Solidification starts accompanied with liquid surface shape change due to surface tension. (4)The bottom side of liquid becomes fully solidified. We assume that the pressure inside the gas phase satisfies the ideal gas equation:

70. Materials Process Design and Control Laboratory Commercialization Plan The technology developed within this project is being made available through journal publications and conference presentations.

71. Materials Process Design and Control Laboratory Awards/Recognition N. Zabaras and D. Samanta, “A stabilized volume-averaging finite element method for flow in porous binary alloy solidification processes”, International Journal for numerical methods in Engineering, (2004) Vol. 60(6) 1103-1138. D. Samanta and N. Zabaras, “Modeling melt convection in solidification processes with stabilized finite element techniques”, International Journal for Numerical Methods in Engineering in press, 2005. N. Zabaras and D. Samanta, “A stabilized finite element method for flow in porous media and solidification systems”, presented at the Symposium on ‘Stabilized and Multi-length scale methods’, in the Seventh U.S. National Congress on Computational Mechanics, Albuquerque, New Mexico, July 2003. D. Samanta and N. Zabaras, “Macrosegregation in the solidification of Aluminum alloys on uneven surfaces”, International Journal of Heat and Mass Transfer (2005), Vol. 48, 4541-4556. Lijian Tan and Nicholas Zabaras, “Modeling the effects of mold topography on aluminum cast surfaces”, presented in the symposium on ‘Solidification of Aluminum alloys : Gas – porosity/Micro-Macro Segregation’, 2004 TMS Annual Meeting & Exhibition, Charlotte, North Carolina.

72. Materials Process Design and Control Laboratory Awards/Recognition D. Samanta and N. Zabaras, “Solidification and macrosegregation of Aluminum alloys on uneven surfaces”, presented in the symposium on ‘CFD Modeling and Simulation of Engineering Processes : Advanced Casting and Solidification Processes’, 2004 TMS Annual Meeting and Exhibition, Charlotte, North Carolina. Lijian Tan and Nicholas Zabaras, “A thermomechanical study of the effects of mold topography on the solidification of Aluminum alloys”, Materials Science and Engineering: A, (2005), Vol. 404, 197-207. Lijian Tan and Nicholas Zabaras, “A level set simulation of dendritic solidification with combined features of front tracking and fixed domain methods”, Journal of Computational Physics, (2006), Vol. 211, 36-63. D. Samanta and N. Zabaras, “A coupled thermomechanical, thermal transport and segregation analysis of solidification of Aluminum alloys on molds of uneven topographies”, Materials Science and Engineering: A, in press. L. Tan, D. Samanta and N. Zabaras, “A coupled thermomechanical, thermal transport and segregation analysis of the solidification of aluminum alloys on molds of uneven surface topographies ”, presented at the symposium on ‘Multiphysics Coupling in Materials Processing’ in the Third M.I.T. Conference on Computational Fluid and Solid Mechanics, M.I.T., Cambridge, Massachusets, June 2005.

73. Materials Process Design and Control Laboratory Number of students supported = 2 Deep Samanta Lijian Tan Awards/Recognition D. Samanta and N. Zabaras, “Freckle suppression in directional solidification of binary and multicomponent alloys using magnetic fields”, presented in the symposium on ‘Multiphysics Coupling in Materials Processing’, in the Third M.I.T. Conference on Computational Fluid and Solid Mechanics, M.I.T., Cambridge, Massachusets, June 2005. L. Tan and N. Zabaras, “Level set method for simulating multi-phase multi-component dendritic solidification”, presented in the symposium on ‘Multiscale, Multiphysics Computational Fluid Dynamics’ in the Third M.I.T. Conference on Computational Fluid and Solid Mechanics, M.I.T., Cambridge, Massachusets, June 2005. L. Tan and N. Zabaras, “An energy conserving level set simulation of dendritic solidification including the effects of melt convection”, presented at the symposium on ‘Advances in Flow Simulation and Modeling: I) Fundamental and Enabling Technologies, II) Moving Boundaries and Interfaces’ in the Eight U.S. National Conference on Computational Mechanics, University of Texas Austin, Texas, July 2005.