Onset and Nonlinear Regimes of Convection of a Binary Mixture in Rectangular Cavity Heated from Below
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ORIGINAL ARTICLE
Onset and Nonlinear Regimes of Convection of a Binary Mixture in Rectangular Cavity Heated from Below Tatyana Lyubimova1,2
· Kseniya Rushinskaya1 · Nadezhda Zubova1
Received: 8 June 2020 / Accepted: 27 July 2020 © Springer Nature B.V. 2020
Abstract The paper is devoted to numerical simulation of nonlinear regimes of a binary liquid mixture in rectangular cavities elongated in the horizontal direction. The boundaries of the cavity are considered to be rigid, impermeable to the substance. The vertical boundaries are thermally insulated; constant different temperatures corresponding to heating from below are maintained on the horizontal boundaries. The calculations are carried out in the framework of a non-stationary approach, using the Boussinesq approximation. An aqueous NaCl solution was chosen as the studied mixture. The calculations were carried out for cases of Earth and reduced gravity. The local and integral characteristics of nonlinear regimes are obtained, the structure of the arising flow and the concentration distribution are found. An analysis of the data shows that in the case of terrestrial gravity in a square cavity, the regime of stationary oscillations with the reconnection of vortices is realized. A multi-vortex flow occurs and its intensity oscillates in an irregular manner in a rectangular cavity under Earth gravity. A stationary flow is observed when gravity is reduced: a single-vortex and a multi-vortex occur for a square and a rectangular cavity, respectively. When an intensity of convective flow is low, a process of mixture separation close to purely diffusive is observed at the initial stage of convection development. It was found that a sharp increase in the intensity of motion at the initial stage of convection development affects the separation of the mixture, it becomes much stronger. The resulting flow mixes the mixture quite strongly: it remains homogeneous in the central part of the cavity, strong changes in concentration are observed near the boundaries. In the case of Earth gravity, the concentration gradients near the upper and lower boundaries are not equal; in the case of reduced gravity, they are the equal. Keywords Thermal diffusion · Convection · Binary mixture
Introduction Convective phenomena in multicomponent liquids often accompany technological or natural processes or become the cause of their occurrence. Theoretical and experimental studies of heat and mass transfer in multicomponent mixtures have various applications in the field of filtration (Maryshev et al. 2016; Soboleva 2018), the diffusion of pollution (Lyubimova et al. 2019) and crystal growth (Lyubimova and Parshakova 2014).
Tatyana Lyubimova
[email protected] 1
Institute of Continuous Media Mechanics UB RAS, Perm, Russia
2
Perm State University, Perm, Russia
A linear analysis of the Rayleigh-Benard problem for a single-component fluid in a plane horizontal layer heated from below with rigid and perfectly thermally conductive boundaries shows that the convection occurs in a threshol
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