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Rayleigh–Bénard convection in viscoelastic liquid bridges

Published online by Cambridge University Press:  05 October 2020

Marcello Lappa Open the ORCID record for Marcello Lappa [Opens in a new window]  and
Alessio Boaro
Marcello Lappa*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Strathclyde, James Weir Building, 75 Montrose Street, GlasgowG1 1XJ, UK
Alessio Boaro
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Strathclyde, James Weir Building, 75 Montrose Street, GlasgowG1 1XJ, UK
*
†Email address for correspondence: [email protected]
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Abstract

Rayleigh–Bénard convection in a floating zone held by the surface tension between two supporting disks at different temperatures is considered. Through direct numerical solution of the mixed parabolic–elliptic–hyperbolic set of governing equations in complete time-dependent and nonlinear form, we investigate the still unknown patterns and spatio-temporal states that are produced when the fluid has viscoelastic properties. The following conditions are examined: Prandtl number Pr = 8, aspect ratio (A = length/diameter) in the range 0.17 ≤ A ≤ 1 and different values of the elasticity number (0 ≤ θ ≤ 0.2). It is shown that, in addition to elastic overstability, an important ingredient of the considered dynamics is the existence of multiple solutions i.e. ‘attractors’ coexisting in the space of phases and differing with respect to the basin of attraction. We categorize the emerging states as modes with dominant vertical or horizontal vorticity and analyse the related waveforms, generally consisting of standing waves with central symmetry or oscillatory modes featuring almost parallel rolls, which periodically break and reform in time with a new orientation in space. In order to characterize the peculiar features of these flows, the notions of disturbance node and the topological concept of ‘knot’ are used. Azimuthally travelling waves are also possible in certain regions of the space of parameters, though they are generally taken over by convective modes with dominant pulsating nature as the elasticity parameter is increased. The case of an infinite horizontal layer is finally considered as an idealized model to study the asymptotic fluid-dynamic behaviour of the liquid bridge in the limit as its aspect ratio tends to zero.

JFM classification

Convection: Buoyancy-driven instability Non-Newtonian Flows: Viscoelasticity Nonlinear Dynamical Systems: Pattern formation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A2
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© The Author(s), 2020. Published by Cambridge University Press

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