Modelling binary alloy solidification with adaptive mesh refinement

Parkinson, James R. G.; Martin, Daniel F.; Wells, Andrew J.; Katz, Richard F.

doi:10.1016/j.jcpx.2019.100043

Title: Modelling binary alloy solidification with adaptive mesh refinement

Abstract

The solidification of a binary alloy results in the formation of a porous mushy layer, within which spontaneous localisation of fluid flow can lead to the emergence of features over a range of spatial scales. We describe a finite volume method for simulating binary alloy solidification in two dimensions with local mesh refinement in space and time. The coupled heat, solute, and mass transport is described using an enthalpy method with flow described by a Darcy-Brinkman equation for flow across porous and liquid regions. The resulting equations are solved on a hierarchy of block-structured adaptive grids. A projection method is used to compute the fluid velocity, whilst the viscous and nonlinear diffusive terms are calculated using a semi-implicit scheme. A series of synchronization steps ensure that the scheme is flux-conservative and correct for errors that arise at the boundaries between different levels of refinement. We also develop a corresponding method using Darcy's law for flow in a porous medium/narrow Hele-Shaw cell. We demonstrate the accuracy and efficiency of our method using established benchmarks for solidification without flow and convection in a fixed porous medium, along with convergence tests for the fully coupled code. Finally, we demonstrate the ability of ourmore »« less

Authors:

; Martin, Daniel F.; Wells, Andrew J.; Katz, Richard F.

Publication Date:: 2020-01-01

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1577402

Alternate Identifier(s):: OSTI ID: 1603566

Grant/Contract Number:: AC02-05CH11231; IE141071

Resource Type:: Published Article

Journal Name:: Journal of Computational Physics: X

Additional Journal Information:: Journal Name: Journal of Computational Physics: X Journal Volume: 5 Journal Issue: C; Journal ID: ISSN 2590-0552

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; binary alloy solidification; adaptive mesh refinement; mushy layer convection; finite volume

Citation Formats


                    Parkinson, James R. G., Martin, Daniel F., Wells, Andrew J., and Katz, Richard F. Modelling binary alloy solidification with adaptive mesh refinement.  United States: N. p., 2020. 
Web.  doi:10.1016/j.jcpx.2019.100043.

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                    Parkinson, James R. G., Martin, Daniel F., Wells, Andrew J., & Katz, Richard F. Modelling binary alloy solidification with adaptive mesh refinement.  United States.  https://doi.org/10.1016/j.jcpx.2019.100043

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                    Parkinson, James R. G., Martin, Daniel F., Wells, Andrew J., and Katz, Richard F. Wed .  
"Modelling binary alloy solidification with adaptive mesh refinement".  United States.  https://doi.org/10.1016/j.jcpx.2019.100043.

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@article{osti_1577402,

  title        = {Modelling binary alloy solidification with adaptive mesh refinement},

  author       = {Parkinson, James R. G. and Martin, Daniel F. and Wells, Andrew J. and Katz, Richard F.},

  abstractNote = {The solidification of a binary alloy results in the formation of a porous mushy layer, within which spontaneous localisation of fluid flow can lead to the emergence of features over a range of spatial scales. We describe a finite volume method for simulating binary alloy solidification in two dimensions with local mesh refinement in space and time. The coupled heat, solute, and mass transport is described using an enthalpy method with flow described by a Darcy-Brinkman equation for flow across porous and liquid regions. The resulting equations are solved on a hierarchy of block-structured adaptive grids. A projection method is used to compute the fluid velocity, whilst the viscous and nonlinear diffusive terms are calculated using a semi-implicit scheme. A series of synchronization steps ensure that the scheme is flux-conservative and correct for errors that arise at the boundaries between different levels of refinement. We also develop a corresponding method using Darcy's law for flow in a porous medium/narrow Hele-Shaw cell. We demonstrate the accuracy and efficiency of our method using established benchmarks for solidification without flow and convection in a fixed porous medium, along with convergence tests for the fully coupled code. Finally, we demonstrate the ability of our method to simulate transient mushy layer growth with narrow liquid channels which evolve over time.},

  doi          = {10.1016/j.jcpx.2019.100043},

  journal      = {Journal of Computational Physics: X},

  number       = C,

  volume       = 5,

  place        = {United States},

  year         = {2020},

  month        = {1}

}

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Title: Modelling binary alloy solidification with adaptive mesh refinement

Abstract

Citation Formats

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains journal, November 1998

Instabilities of the liquid and mushy regions during solidification of alloys journal, April 1992

The origin of freckles in unidirectionally solidified castings journal, August 1970

Adaptive mesh refinement for hyperbolic partial differential equations journal, March 1984

Modeling Melt Convection in Phase-Field Simulations of Solidification journal, September 1999

Nonlinear analysis of buoyant convection in binary solidification with application to channel formation journal, July 1993

Local adaptive mesh refinement for shock hydrodynamics journal, May 1989

The Formation of Freckles in Binary Alloys journal, January 1985

A Cell-Centered Adaptive Projection Method for the Incompressible Euler Equations journal, September 2000

Chimneys on the Earth's inner-outer core boundary? journal, March 1994

Efficient Computation of Dendritic Microstructures Using Adaptive Mesh Refinement journal, April 1998

Solidification of an alloy from a cooled boundary journal, June 1986

Seaweed to Dendrite Transition in Directional Solidification journal, October 2003

Natural convective heat transfer in a fluid saturated variable porosity medium journal, October 1997

Convection in Mushy Layers journal, January 1997

A cell-centered adaptive projection method for the incompressible Navier–Stokes equations in three dimensions journal, January 2008

Compositional convection in a reactive crystalline mush and melt differentiation journal, January 1992

Visualizing brine channel development and convective processes during artificial sea-ice growth using Schlieren optical methods journal, February 2016

Natural convection in a mushy layer journal, March 1991

Steady-state mushy layers: experiments and theory journal, January 2007

Measurements of the temperature field of mushy and liquid regions during solidification of aqueous ammonium chloride journal, March 1998

Finite element analysis of directional solidification of multicomponent alloys journal, January 1998

An Unsplit 3D Upwind Method for Hyperbolic Conservation Laws journal, November 1994

Modeling Freckle Segregation with Mesh Adaptation journal, September 2011

The convergence rate for difference approximations to mixed initial boundary value problems journal, May 1975

A Thermodynamically Consistent Model of a Mushy zone journal, January 1983

Simulation of directional solidification, thermochemical convection, and chimney formation in a Hele-Shaw cell journal, December 2008

Natural convection solid/liquid phase change in porous media journal, January 1988

Nonlinear mushy-layer convection with chimneys: stability and optimal solute fluxes journal, January 2013

Solidification of a binary alloy: Finite-element, single-domain simulation and new benchmark solutions journal, July 2006

Weak convection, liquid inclusions and the formation of chimneys in mushy layers journal, June 1999

the phase evolution of Young Sea Ice journal, May 1997

A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier–Stokes Equations journal, May 1998

Stability of a Planar Interface During Solidification of a Dilute Binary Alloy journal, February 1964

A numerical investigation of steady convection in mushy layers during the directional solidification of binary alloys journal, February 1998

An adaptive finite element scheme for transient problems in CFD journal, April 1987

Modelling of macrosegregation during solidification processes using an adaptive domain decomposition method journal, June 2003

Convective flow and heat transfer in a tall porous cavity side-cooled with temperature profile journal, December 2009

Weakly nonlinear analysis of convection in mushy layers during the solidification of binary alloys journal, November 1995

Conditions for defect-free solidification of aqueous ammonium chloride in a quasi two-dimensional directional solidification facility journal, July 2008

On weakly nonlinear convection in mushy layers during solidification of alloys journal, January 2008

2-Dimensional FEM modeling of macrosegregation in the directional solidification with mesh adaptation journal, June 2009

Multidimensional upwind methods for hyperbolic conservation laws journal, March 1990

Steady-state chimneys in a mushy layer journal, March 2002

Growth of and brine drainage from NaCl-H 2 O freezing: A simulation of young sea ice journal, January 2004

Experimental study of convection in a mushy layer during directional solidification journal, June 1995

Adaptive mesh refinement for coupled elliptic-hyperbolic systems journal, October 2006

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains
journal, November 1998

Instabilities of the liquid and mushy regions during solidification of alloys
journal, April 1992

The origin of freckles in unidirectionally solidified castings
journal, August 1970

Adaptive mesh refinement for hyperbolic partial differential equations
journal, March 1984

Modeling Melt Convection in Phase-Field Simulations of Solidification
journal, September 1999

Nonlinear analysis of buoyant convection in binary solidification with application to channel formation
journal, July 1993

Local adaptive mesh refinement for shock hydrodynamics
journal, May 1989

The Formation of Freckles in Binary Alloys
journal, January 1985

A Cell-Centered Adaptive Projection Method for the Incompressible Euler Equations
journal, September 2000

Chimneys on the Earth's inner-outer core boundary?
journal, March 1994

Efficient Computation of Dendritic Microstructures Using Adaptive Mesh Refinement
journal, April 1998

Solidification of an alloy from a cooled boundary
journal, June 1986

Seaweed to Dendrite Transition in Directional Solidification
journal, October 2003

Natural convective heat transfer in a fluid saturated variable porosity medium
journal, October 1997

Convection in Mushy Layers
journal, January 1997

A cell-centered adaptive projection method for the incompressible Navier–Stokes equations in three dimensions
journal, January 2008

Compositional convection in a reactive crystalline mush and melt differentiation
journal, January 1992

Visualizing brine channel development and convective processes during artificial sea-ice growth using Schlieren optical methods
journal, February 2016

Natural convection in a mushy layer
journal, March 1991

Steady-state mushy layers: experiments and theory
journal, January 2007

Measurements of the temperature field of mushy and liquid regions during solidification of aqueous ammonium chloride
journal, March 1998

Finite element analysis of directional solidification of multicomponent alloys
journal, January 1998

An Unsplit 3D Upwind Method for Hyperbolic Conservation Laws
journal, November 1994

Modeling Freckle Segregation with Mesh Adaptation
journal, September 2011

The convergence rate for difference approximations to mixed initial boundary value problems
journal, May 1975

A Thermodynamically Consistent Model of a Mushy zone
journal, January 1983

Simulation of directional solidification, thermochemical convection, and chimney formation in a Hele-Shaw cell
journal, December 2008

Natural convection solid/liquid phase change in porous media
journal, January 1988

Nonlinear mushy-layer convection with chimneys: stability and optimal solute fluxes
journal, January 2013

Solidification of a binary alloy: Finite-element, single-domain simulation and new benchmark solutions
journal, July 2006

Weak convection, liquid inclusions and the formation of chimneys in mushy layers
journal, June 1999

the phase evolution of Young Sea Ice
journal, May 1997

A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier–Stokes Equations
journal, May 1998

Stability of a Planar Interface During Solidification of a Dilute Binary Alloy
journal, February 1964

A numerical investigation of steady convection in mushy layers during the directional solidification of binary alloys
journal, February 1998

An adaptive finite element scheme for transient problems in CFD
journal, April 1987

Modelling of macrosegregation during solidification processes using an adaptive domain decomposition method
journal, June 2003

Convective flow and heat transfer in a tall porous cavity side-cooled with temperature profile
journal, December 2009

Weakly nonlinear analysis of convection in mushy layers during the solidification of binary alloys
journal, November 1995

Conditions for defect-free solidification of aqueous ammonium chloride in a quasi two-dimensional directional solidification facility
journal, July 2008

On weakly nonlinear convection in mushy layers during solidification of alloys
journal, January 2008

2-Dimensional FEM modeling of macrosegregation in the directional solidification with mesh adaptation
journal, June 2009

Multidimensional upwind methods for hyperbolic conservation laws
journal, March 1990

Steady-state chimneys in a mushy layer
journal, March 2002

Growth of and brine drainage from NaCl-H ₂ O freezing: A simulation of young sea ice
journal, January 2004

Experimental study of convection in a mushy layer during directional solidification
journal, June 1995

Adaptive mesh refinement for coupled elliptic-hyperbolic systems
journal, October 2006