Oscillatory instabilities of the liquid and mushy layers during solidification of alloys under rotational constraint
type: Item
instance of: scholarly article
title: Oscillatory instabilities of the liquid and mushy layers during solidification of alloys under rotational constraint
zbMATH Open document ID: 0884.76026
DOI: 10.1007/BF01262528
author: T. L. Sayre
author: Daniel N. Riahi
published in: Acta Mechanica
publication date: 1998-04-01T00:00:00Z
review text: This paper considers the problem of linear flow instabilities due to oscillatory disturbances of the liquid and mushy regions during solidification of binary alloys, under a rotational constraint where the rotation axis is inclined to gravity vector. The governing partial differential equations and boundary conditions are treated numerically in both the liquid and mushy regions, using a novel method proposed by the authors. This method seems to work very efficiently for problems of the present type. The authors present the results of stability analysis and numerical computations for a preferred centrifugal mode of general oscillatory disturbances at zero and non-zero rotation rates. It is found that, at different Prandtl numbers, the spatial locations of the mushy layer tend to form a freckle change as the rotation rate changes. Additionally, it is shown that the preferred oscillatory solution remains unchanged with respect to the change in the sign of the frequency in the absence of rotation, although it changes, generally, in the presence of rotation.
Mathematics Subject Classification ID: 76E99
Mathematics Subject Classification ID: 76T99
Mathematics Subject Classification ID: 76U05
zbMATH DE Number: 1019277
zbMATH Keywords: linear stability
zbMATH Keywords: centrifugal mode
zbMATH Keywords: rotation rates
reviewed by: Ioan Pop
MaRDI profile type: Publication
cites work: Instabilities of the liquid and mushy regions during solidification of alloys
cites work: Q5518219
cites work: Weakly nonlinear oscillatory convection in a rotating fluid
description: scientific article; zbMATH DE number 1019277