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Linear spatio-temporal instability analysis of ice growth under a falling water film

Published online by Cambridge University Press:  13 April 2010

JUN HU ,
BING-HONG ZHOU ,
YI-HONG HANG ,
QIU-SHENG LIU  and
SHU-DAO ZHANG
JUN HU*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
BING-HONG ZHOU
Affiliation:
Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190, China
YI-HONG HANG
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
QIU-SHENG LIU
Affiliation:
Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China
SHU-DAO ZHANG
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
*
†Email address for correspondence: hu_jun@iapcm.ac.cn
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Abstract

A linear spatio-temporal stability analysis is conducted for the ice growth under a falling water film along an inclined ice plane. The full system of linear stability equations is solved by using the Chebyshev collocation method. By plotting the boundary curve between the linear absolute and convective instabilities (AI/CI) of the ice mode in the parameter plane of the Reynolds number and incline angle, it is found that the linear absolute instability exists and occurs above a minimum Reynolds number and below a maximum inclined angle. Furthermore, by plotting the critical Reynolds number curves with respect to the inclined angle for the downstream and upstream branches, the convectively unstable region is determined and divided into three parts, one of which has both downstream and upstream convectively unstable wavepackets and the other two have only downstream or upstream convectively unstable wavepacket. Finally, the effect of the Stefan number and the thickness of the ice layer on the AI/CI boundary curve is investigated.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 649 , 25 April 2010 , pp. 453 - 466
Copyright
Copyright © Cambridge University Press 2010

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