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Natural convection along a heated vertical plate immersed in a nonlinearly stratified medium: application to liquefied gas storage

Published online by Cambridge University Press:  24 September 2007

M. FORESTIER  and
P. HALDENWANG
M. FORESTIER
Affiliation:
Modélisation et Simulation Numérique en Mécanique et Génie des Procédés (MSNM-GP), UMR-CNRS 6181, Universités d'Aix-Marseille, EGIM/ECM IMT/La Jetée, Technopôle de Château Gombert, 38, rue Frédéric Joliot-Curie, 13451 Marseille Cedex 20, France
P. HALDENWANG
Affiliation:
Modélisation et Simulation Numérique en Mécanique et Génie des Procédés (MSNM-GP), UMR-CNRS 6181, Universités d'Aix-Marseille, EGIM/ECM IMT/La Jetée, Technopôle de Château Gombert, 38, rue Frédéric Joliot-Curie, 13451 Marseille Cedex 20, France
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Abstract

We consider free convection driven by a heated vertical plate immersed in a nonlinearly stratified medium. The plate supplies a uniform horizontal heat flux to a fluid, the bulk of which has a stable stratification, characterized by a non-uniform vertical temperature gradient. This gradient is assumed to have a typical length scale of variation, denoted Z0, while Ψ0 is the order of magnitude of the related heat flux that crosses the medium vertically.

We derive an analytic solution to the Boussinesq equations that extends the classical solution of Prandtl to the case of nonlinearly stratified media. This novel solution is asymptotically valid in the regime RaS ≫ 1, where RaS denotes the Rayleigh number of nonlinear stratification, based on Z0, Ψ0, and the physical properties of the medium.

We then apply the new theory to the natural convection affecting the vapour phase in a liquefied pure gas tank (e.g. the cryogenic storage of hydrogen). It is assumed that the cylindrical storage tank is subject to a constant uniform heat flux on its lateral and top walls. We are interested in the vapour motion above a residual layer of liquid in equilibrium with the vapour. High-precision axisymmetric numerical computations show that the flow remains steady for a large range of parameters, and that a bulk stratification characterized by a quadratic temperature profile is undoubtedly present. The application of the theory permits a comparison of the numerical and analytic results, showing that the theory satisfactorily predicts the primary dynamical and thermal properties of the storage tank.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 588 , 10 October 2007 , pp. 217 - 241
Copyright
Copyright © Cambridge University Press 2007

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