Three-dimensional numerical simulation of natural convection of water near its density maximum in a horizontal annulus

A series of unsteady three-dimensional numerical simulations were conducted for natural convection of water near its density maximum in a horizontal annulus by using the finite volume method. The effects of Rayleigh number, density inversion parameter, gap aspect ratio and eccentricity on the flow pattern were analyzed in detail. The results show that the primary flow pattern at the cross section depends mainly on the density inversion parameters. At a small Rayleigh number, three basic primary flow patterns are presented, which are the same with those from two-dimensional simulation. With the increase of Rayleigh number, the secondary transverse rolls appear at the top or/and the bottom of the annulus, depending on the density inversion parameter and Rayleigh number. Afterward, the flow transits to unsteady three-dimensional flow. The number of the secondary transverse rolls increases with the increase of the gap aspect ratio. Variation law of the average Nusselt number on the inner wall of the annulus with Rayleigh number is almost independent on the secondary transverse rolls. Furthermore, the vertical or horizontal eccentricity has a significant effect on the flow pattern.