Fluxes through steady chimneys in a mushy layer during binary alloy solidification
Abstract Solute transport within solidifying binary alloys occurs predominantly by convection from narrow liquid chimneys within a porous mushy layer. We develop a simple model that elucidates the dominant structure and driving forces of the flow, which could be applied to modelling brine fluxes fro...
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Online Access: | http://dx.doi.org/10.1017/jfm.2012.462 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112012004624 |
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crcambridgeupr:10.1017/jfm.2012.462 2024-03-03T08:48:45+00:00 Fluxes through steady chimneys in a mushy layer during binary alloy solidification Rees Jones, David W. Worster, M. Grae 2013 http://dx.doi.org/10.1017/jfm.2012.462 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112012004624 en eng Cambridge University Press (CUP) https://www.cambridge.org/core/terms Journal of Fluid Mechanics volume 714, page 127-151 ISSN 0022-1120 1469-7645 Mechanical Engineering Mechanics of Materials Condensed Matter Physics journal-article 2013 crcambridgeupr https://doi.org/10.1017/jfm.2012.462 2024-02-08T08:27:06Z Abstract Solute transport within solidifying binary alloys occurs predominantly by convection from narrow liquid chimneys within a porous mushy layer. We develop a simple model that elucidates the dominant structure and driving forces of the flow, which could be applied to modelling brine fluxes from sea ice, where a cheaply implementable approach is essential. A horizontal density gradient within the mushy layer in the vicinity of the chimneys leads to baroclinic torque which sustains the convective flow. In the bulk of the mushy layer, the isotherms are essentially horizontal. In this region, we impose a vertically linear temperature field and immediately find that the flow field is a simple corner flow. We determine the strength of this flow by finding a similarity solution to the governing mushy-layer equations in an active region near the chimney. We also determine the corresponding shape of the chimney, the vertical structure of the solid fraction and the interstitial flow field. We apply this model first to a periodic, planar array of chimneys and show analytically that the solute flux through the chimneys is proportional to a mush Rayleigh number. Secondly we extend the model to three dimensions and find that an array of chimneys can be characterized by the average drainage area alone. Therefore we solve the model in an axisymmetric geometry and find new, sometimes nonlinear, relationships between the solute flux, the Rayleigh number and the other dimensionless parameters of the system. Article in Journal/Newspaper Sea ice Cambridge University Press The Chimney ENVELOPE(-55.748,-55.748,52.617,52.617) Journal of Fluid Mechanics 714 127 151 |
institution |
Open Polar |
collection |
Cambridge University Press |
op_collection_id |
crcambridgeupr |
language |
English |
topic |
Mechanical Engineering Mechanics of Materials Condensed Matter Physics |
spellingShingle |
Mechanical Engineering Mechanics of Materials Condensed Matter Physics Rees Jones, David W. Worster, M. Grae Fluxes through steady chimneys in a mushy layer during binary alloy solidification |
topic_facet |
Mechanical Engineering Mechanics of Materials Condensed Matter Physics |
description |
Abstract Solute transport within solidifying binary alloys occurs predominantly by convection from narrow liquid chimneys within a porous mushy layer. We develop a simple model that elucidates the dominant structure and driving forces of the flow, which could be applied to modelling brine fluxes from sea ice, where a cheaply implementable approach is essential. A horizontal density gradient within the mushy layer in the vicinity of the chimneys leads to baroclinic torque which sustains the convective flow. In the bulk of the mushy layer, the isotherms are essentially horizontal. In this region, we impose a vertically linear temperature field and immediately find that the flow field is a simple corner flow. We determine the strength of this flow by finding a similarity solution to the governing mushy-layer equations in an active region near the chimney. We also determine the corresponding shape of the chimney, the vertical structure of the solid fraction and the interstitial flow field. We apply this model first to a periodic, planar array of chimneys and show analytically that the solute flux through the chimneys is proportional to a mush Rayleigh number. Secondly we extend the model to three dimensions and find that an array of chimneys can be characterized by the average drainage area alone. Therefore we solve the model in an axisymmetric geometry and find new, sometimes nonlinear, relationships between the solute flux, the Rayleigh number and the other dimensionless parameters of the system. |
format |
Article in Journal/Newspaper |
author |
Rees Jones, David W. Worster, M. Grae |
author_facet |
Rees Jones, David W. Worster, M. Grae |
author_sort |
Rees Jones, David W. |
title |
Fluxes through steady chimneys in a mushy layer during binary alloy solidification |
title_short |
Fluxes through steady chimneys in a mushy layer during binary alloy solidification |
title_full |
Fluxes through steady chimneys in a mushy layer during binary alloy solidification |
title_fullStr |
Fluxes through steady chimneys in a mushy layer during binary alloy solidification |
title_full_unstemmed |
Fluxes through steady chimneys in a mushy layer during binary alloy solidification |
title_sort |
fluxes through steady chimneys in a mushy layer during binary alloy solidification |
publisher |
Cambridge University Press (CUP) |
publishDate |
2013 |
url |
http://dx.doi.org/10.1017/jfm.2012.462 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112012004624 |
long_lat |
ENVELOPE(-55.748,-55.748,52.617,52.617) |
geographic |
The Chimney |
geographic_facet |
The Chimney |
genre |
Sea ice |
genre_facet |
Sea ice |
op_source |
Journal of Fluid Mechanics volume 714, page 127-151 ISSN 0022-1120 1469-7645 |
op_rights |
https://www.cambridge.org/core/terms |
op_doi |
https://doi.org/10.1017/jfm.2012.462 |
container_title |
Journal of Fluid Mechanics |
container_volume |
714 |
container_start_page |
127 |
op_container_end_page |
151 |
_version_ |
1792505751823974400 |