Flow patterns of Rayleigh‐Bénard convection in cold water at maximum density in vertical cylindrical containers under conducting sidewall conditions

Abstract

To understand the effects of aspect ratio and density inversion parameters on the critical conditions at the onset of convection in vertical cylindrical containers with perfectly-conducting side walls, a series of linear stability analyses (LSA) and three-dimensional numerical simulations were performed. The working fluid was cold water at maximum density and Prandtl number at ∼11.57. Results indicated that, with increased aspect ratio (A, ratio of radius to height), the critical Rayleigh number (Racri) was reduced and the number of convective rolls was more at a higher A than that at a lower one. The effects of A and density inversion (Θm=(Tm-Tc)/(Th-Tc)) were discussed in detail. The Θm had a dramatic influence on the Racri as well as flow structure at the primary threshold. With increased Θm, Racri sharply increased at higher values. Moreover, flow motion was only occurred near the bottom wall and a motionless fluid layer was found near the top wall, which were quite different from the fact that flow motion would occur in the whole container in a Boussinesq fluid. The depth of the convective fluid layer was thinner at a higher Θm. Notably, more convective rolls were found in the Z-direction at high Θm due to fluid viscosity. Racri obtained by LSA were satisfyingly consistent with those by three-dimensional numerical simulations.