Study on the stability and 3-dimensional character for natural convection in a rectangular cavity heated from below

Abstract

Natural convection of air is numerically simulated in a 3-dimensional rectangular cavity heated from below using SIMPLE algorithm with a QUICK scheme. The results suggest that when all lateral walls are adiabatic, the fluid rolls occur along the long axis. When the Rayleigh number is smaller, the flow is of 2-dimensional character, and the rolls shapes are similar. The average Nusselt numbers in the central part of the cavity are similar. The average Nusselt numbers in the part near by the cavity are different. According to the comparison of 3-dimensional results with 2-dimensional results, the flow patterns and heat transfer in the central part of the cavity can be assumed as a 2-dimensional flow, While those in the part near by the cavity can not. With increasing Rayleigh number, the flow is 3-dimensional characteristic. The 3-dimensional result accords with the experimental result. When all lateral walls are adiabatic, the ten rolls occur along the long axis. But when lateral walls are heated or cooled, the rolls disappear along the long axis and two rolls occur along the short axis. The rotation direction of the rolls is reversed. When Rayleigh number is over some critical value, flow and heat transfer will be asymmetry, indicating unsteady oscillation occurs. By nonlinear analyses, it is shown that with increasing Rayleigh number, flow and heat transfer will change from steady state to unsteady state through HOPF bifurcation, and transition to chaos will occur through multi-periodical oscillation. Critical Raleigh number, 3-dimensional character, lateral boundaries, nonlinear characteristic, bifurcation Citation:Zhan N Y, Xu P W, Sun S M, et al. Study on the stability and 3-dimensional character for natural convection in a rectangular cavity heated from below.

Numerical Research on Self-Sustained Oscillation and Chaos of Natural Convection in Horizontal Fluids Layer

“…The governing equations are solved in primitive variables and two-dimensionally staggered grid based on the control volume method [7] . The SIMPLE algorithm with a QUICK scheme is used to solve the coupled heat transfer and fluid flow problem [8] .…”

“…Every 10 point is analyzed. (a) The reconstructed phase space of time series The time series (7) is reconstructed a m-dimensional phase space by using time difference method. ,...... 2 , 1 ), , ,…”

“…The bifurcation appeared under the smaller heat flux, and disappeared under the larger heat flux. Zhan N Y [7] conducted a numerical investigation on the nonlinear phenomenon of natural air convection in a 3-D rectangular cavity which was heated underneath by SIMPLE algorithm with QUICK scheme.…”

Experimental research on nonlinear characteristics of natural convection in a 3-D shallow cavity

“…The bifurcation appeared under the smaller heat flux, and disappeared under the larger heat flux. Zhan [11] conducted a numerical investigation on the nonlinear phenomenon of natural air convection in a 3-D rectangular cavity which was heated underneath by SIMPLE algorithm with QUICK scheme. The results showed that the static and dynamic bifurcation appeared with different initial conditions.…”