Instability of convection of an ethanol–water solution in a vertical tank

Abstract

An experimental and numerical investigation has been carried out into the instability characteristics of natural convection of an ethanol–water solution in a vertical tank with aspect ratio (height/width) of 15. The solution contains 39 wt% ethanol with Prandtl number ${\it Pr}\,{=}\,26$. The density anomaly due to the Soret effect may be safely ignored in the present test configuration. Onset of instability, in the form of multicellular convection located in the mid-height of the tank, occurs at Grashof number $\hbox{\it Gr}\,{\cong}\,13\,500$. These convection cells are unsteady even at low supercritical states, similar to earlier observations for higher Pr fluids. The cause of such unsteadiness of the flow has been determined by studying the streak images constructed by superposing individual frames of a digital movie sequence. New cells are generated in the upper and lower portions of the tank and then migrate toward the centre, causing the convection cells in the mid-section to merge. At higher Gr, even the tertiary cells, which rotate in the opposite direction of the secondary cells, participate in the merging process. Numerical simulations of the two-dimensional natural convection of a Boussinesq fluid with constant thermophysical properties, carried out at low supercritical Gr equivalent to the experimental value, show the same process of cell generation and merging as that observed in the experiments. By analysing the substantial time rate of change of the kinetic energy of the fluid using the mechanical energy equation, it is determined that the energy needed for the cell generation process is supplied by the work of the dynamic pressure. The subsequent migration of the cells toward the middle is caused by the pressure gradient in the tank. The total kinetic energy of the fluid attains a relative maximum right after a merging process due to the reduction of dissipation associated with the region of strong shear between the cells.