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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 » method to simulate transient mushy layer growth with narrow liquid channels which evolve over time.« less

Authors:
ORCiD logo; ; ;
Publication Date:
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.
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
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.
@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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