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Solidification of a two-dimensional high-Reynolds-number flow and its application to laser percussion drilling

Published online by Cambridge University Press:  01 February 2007

W. R. SMITH  and
R. M. M. MATTHEIJ
W. R. SMITH
Affiliation:
School of Mathematics, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK email: smithwar@maths.bham.ac.uk
R. M. M. MATTHEIJ
Affiliation:
Department of Mathematics and Computing Science, Technische Universiteit Eindhoven, PO Box 513, 5600 MB Eindhoven, The Netherlands
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Abstract

The competition between inertia and solidification for the high-Reynolds-number flow of molten aluminium across a cool solid aluminium surface is investigated. A two-dimensional molten aluminium droplet is of finite extent and is surrounded by a passive gas. The droplet initially freezes due to rapid thermal conduction into the solid. Depending on the initial velocity of the molten aluminium, one of two situations may develop: (i) If the molten aluminium has a non-decreasing initial velocity profile, solidification continues until the passing of the trailing edge of the liquid/gas interface or the flow is engulfed; (ii) If the molten aluminium has a decreasing initial velocity profile, the droplet narrows and thickens resulting in a reduction in the heat flux and in the rate of solidification; this will eventually lead to fluid clumping and shock formation. The rate of solidification may also be reduced by increasing the ambient temperature. The results are interpreted in terms of the recast observed during the solidification phase of laser percussion drilling.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 1 , February 2007 , pp. 1 - 19
Copyright
Copyright © Cambridge University Press 2007

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