Onset of double-diffusive Rayleigh-Bénard convection of a moderate Prandtl number binary mixture in cylindrical enclosures

Abstract

A series of three-dimensional numerical simulations were conducted on double-diffusive Rayleigh-Bénard convection in cylindrical enclosures filled with an isopropanol/water mixture, with the aim of determining the critical threshold of Rayleigh-Bénard convection and the primary bifurcation flow patterns for different geometric dimensions. The Prandtl number of the fluid was 13.2, the aspect ratio of the cylindrical enclosure and the buoyancy ratio N varied from 0.5 to 4 and from −1 to 2, respectively. Results show that the critical Rayleigh number at the primary threshold for the onset of convection is influenced by both the aspect ratio and the buoyancy ratio. When 0<N<2, the solutal gradient has an accelerative effect to the flow destabilization and the critical Rayleigh number decreases with the increase of the buoyancy ratio. When −1<N<0, the fluid stability is enhanced, and the critical Rayleigh number increases with the increase of the absolute value of the buoyancy ratio. Furthermore, the buoyancy ratio has a direct effect on bifurcation sequences and flow pattern formations. When N=0, the system undergoes a supercritical pitchfork bifurcation and passes through various steady flow patterns. When 0<N<2, the flow bifurcates to a non-periodic oscillatory flow. However, when −1<N<0, the flow experiences a subcritical bifurcation and evolves into a periodic oscillatory flow pattern, consisting in an azimuthal rotation. Furthermore, the results have been compared with those obtained for a pure fluid to identify the effect of the buoyancy ratio.