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Vorticity transport in solidification boundary layers

Published online by Cambridge University Press:  12 January 2001

BARRY L. REED ,
AMIR H. HIRSA  and
PAUL H. STEEN
BARRY L. REED
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
AMIR H. HIRSA
Affiliation:
Department of Mechanical Engineering, Aeronautical Engineering & Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180 USA
PAUL H. STEEN
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA
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Abstract

A solidification boundary layer, where vorticity is concentrated, is shown to scale as δ ∼ (v/V) sin θ where θ is the angle that the solidification front makes with the oncoming flow, v is the kinematic viscosity of the melt, and V is the solidification rate. Key similarities with the suction boundary layer are outlined. Transport of vorticity, by diffusion and advection, in flows that solidify is discussed in the context of the planar-flow spin casting process, with special attention paid to how vorticity leaves the flow. Direct experimental evidence for a solidification layer in that application is reported.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 426 , 10 January 2001 , pp. 397 - 406
Copyright
© 2001 Cambridge University Press

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