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Rollover instability due to double diffusion in a stably stratified cylindrical tank

Zimmerman, W.B. and Rees, J.M. (2007) Rollover instability due to double diffusion in a stably stratified cylindrical tank. Physics of Fluids, 19 (12). Art. No. 123604. ISSN 1070-6631

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Double diffusion of a viscous fluid is simulated for heat leakage driven by buoyant convection under cryogenic storage conditions in a cylindrical tank with laminar flow. If the tank is stably stratified, there is a potential instability due to the inability of the fluid in the lower layer to release heat to the top vapor space, whereas the upper liquid layer can exchange heat and mass through sensible heat transfer and evaporation with the vapor space. Eventually, the lower layer becomes less dense due to thermal expansion and is no longer constrained in the stratification. The rapid rise and overturning of the fluid is termed rollover, and can be accompanied by a potentially explosive release of vapor. In this paper, hydrodynamics and heat and mass transport are used to study the stability characteristics of rollover. The transient state is used as a base state for a linear stability analysis which shows the transition from a “corner eddy” mode spinning down to spinning up is the driver for the rollover instability. Four different vapor-liquid interfacial boundary conditions are tested, with similar results for the time to rollover. Surprisingly, the long time prerollover state is dominated in the laminar flow regime by heat conduction and diffusion, as the expected double roll structure is suppressed and advection plays a small roll in the majority of the prerollover period. Scalings are suggested for controlling dimensionless groups on this prerollover basis that can be used as a guideline to determine the regime of double diffusion—a single roll or a double roll stratification, as well as the severity of the eventual rollover event. An energy analysis demonstrates the switch from practically advection free to free convection regimes.

Item Type: Article
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Chemical and Biological Engineering (Sheffield)
The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Mrs Megan Hobbs
Date Deposited: 17 Mar 2010 12:57
Last Modified: 16 Dec 2015 10:45
Published Version: http://dx.doi.org/10.1063/1.2827488
Status: Published
Publisher: American Institute of Physics
Identification Number: 10.1063/1.2827488
URI: http://eprints.whiterose.ac.uk/id/eprint/10546

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