| EPSRC Reference: |
GR/M79288/01 |
| Title: |
DYNAMIC EVOLUTION OF A MUSH-LIQUID INTERFACE |
| Principal Investigator: |
Worster, Professor MG |
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| Department: |
Applied Maths and Theoretical Physics |
| Organisation: |
University of Cambridge |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 June 1999 |
Ends: |
31 July 1999 |
Value (£): |
3,265
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The study concerns a current, fundamental problem in the mathematical modelling of solidifying alloys. Typically, when an alloy in solidified from its melt, a mushy layer forms that is a reactive porous medium comprising a matrix of solid crystals bathed in residual melt. Natural, buoyancy-driven convection can cause dissolution of the solid matrix, by redistributing solute, to the point that a channel (called a chimney) is formed. The mathematical determination of the interfaces between a mushy layer and the melt, particularly the interface forming the boundary of a chimney, is a challenging free-boundary problem. Dr Schulze and I have recently made numerical calculations of convection in a mushy layer and have shown that a chimney can be initiated as a liquid inclusion internal to the layer. We plan to extend this work to study the subsequent evolution of an inclusion, as it bursts out of the mushy layer to form a chimney. In order to capture this change of topology, we propose to develop and apply the new computational method of level sets. As part of our previous work, we have shown that the boundary conditions usually applied at a mush-liquid interface are not independent along the lower boundary of an inclusion. To over come this, we have derived rigorously the new, independent condition that must be applied there. During Dr Schulze's visit, we propose to apply this new condition in a numerical computation of strongly non-linear convection in a mushy layer.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.cam.ac.uk |