Two-dimensional buoyancy driven thermal mixing in a horizontally partitioned adiabatic enclosure

Abstract

The dynamics of the transient, two-dimensional buoyancy driven thermal mixing of two fluid masses at different temperatures, initially at rest and confined to separate portions of a horizontally partitioned adiabatic enclosure, is investigated numerically within the framework of the Boussinesq approximation. The fluids are allowed to mix through a centrally located opening or vent in the partition. Apart from the geometric parameters, the dynamics is governed by the Rayleigh ͑Ra͒ and Prandtl ͑Pr͒ numbers. Spanning the range 500ഛ Raഛ 10 4 at Pr= 0.71 and unity aspect ratios of the vent and the enclosures, the dominant spatial and temporal flow structures, in the asymptotic approach of the system towards a state of thermomechanical equilibrium, have been identified. These dominant modes have been utilized to classify the flow dynamics observed at different Ra into three distinct flow regimes. An approach utilizing new scalar norms to quantify the instantaneous state of mixing and to track the mixing process in time has been utilized to identify the flow modes favoring or opposing the mixing process. It is shown that the flow mode comprising of counterflowing streams in the vent yields the highest mixing rate. It is also shown that this flow mode results in a large build-up of enstrophy in the system. For Raഛ 5000, an increase in Ra brings about an increase in the overall mixing rate. However, for RaϾ 5000, there exists a vortex trapped in the vent for a significant length of time, preventing the two fluid masses to mix directly, thereby slowing down the overall mixing rate in comparison to the flows for Raഛ 5000.

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