Rayleigh-Bénard convection with a melting boundary

Abstract

We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane layer geometry, this can be seen as classical Rayleigh-Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier-Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appears as the depth -- and therefore the effective Rayleigh number of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells.

36 pages, 16 figures

References in corpus (5)

• Inverse cascade and symmetry breaking in rapidly-rotating Boussinesq convection
• On the triggering of the Ultimate Regime of convection
• Dissolution instability and roughening transition
• Anelastic Versus Fully Compressible Turbulent Rayleigh-Bénard Convection
• Dynamics of Mixed Convective--Stably-Stratified Fluids

Cited by in corpus (11)

• Bistability in Rayleigh-Bénard convection with a melting boundary
• Sea Water Freezing Modes in a Natural Convection System
• Bistability in radiatively heated melt ponds
• Emergence of tip singularities in dissolution patterns
• Circular objects do not melt the slowest in water
• Buoyancy-driven flow regimes for a melting vertical ice cylinder in saline water
• Theoretical framework for designing phase change material systems
• Solid-liquid phase change in planetary cores
• Experimental study of the convection in a thin cylindrical gas layer with imposed bottom and top fluxes and imposed side temperature
• Collective effects of neighbouring melting ice objects
• Heat Transfer in Phase Change Materials with Multiple Fin Insertion