Volume 135, Number 5, September 2021
|Number of page(s)||7|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||02 November 2021|
Equilibrium states of the ice-water front in a differentially heated rectangular cell(a)
1 Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education Department of Energy and Power Engineering, Tsinghua University - Beijing 100084, China
2 Univ. Lille, Unité de Mécanique de Lille J. Boussinesq, UML, ULR 7512 - F-59000 Lille, France
3 Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University Beijing 100084, China
Received: 14 June 2021
Accepted: 19 October 2021
We study the conductive and convective states of phase change of pure water in a rectangular container where two opposite walls are kept respectively at temperatures below and above the freezing point and all the other boundaries are thermally insulating. The global ice content at the equilibrium and the corresponding shape of the ice-water interface are examined, extending the available experimental measurements and numerical simulations. We first address the effect of the initial condition, either fully liquid or fully frozen, on the system evolution. Secondly, we explore the influence of the aspect ratio of the cell, both in the configurations where the background thermal gradient is parallel to the gravity, namely the Rayleigh-Bénard (RB) setting, and when they are perpendicular, i.e., vertical convection (VC). We find that for a set of well-identified conditions the system in the RB configuration displays multiple equilibrium states, either conductive rather than convective, or convective but with different ice front patterns. The shape of the ice front appears to be always determined by the large scale circulation in the system. In RB, the precise shape depends on the degree of lateral confinement. In the VC case the ice front morphology is more robust, due to the presence of two vertically stacked counter-rotating convective rolls for all the studied cell aspect ratios.
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