Numerical research on the sudden change characteristic of the first bifurcation for natural convection of air enclosed in 2D rectangular cavity

Based on grid independence analysis, a second order Euler-Taylor-Galerkin finite element method of fractional steps was used to numerically investigate the first bifurcation of natural convection of air enclosed in a 2D rectangular cavity. The characteristics of the first bifurcation of natural convection in 2D cavities were numerically studied with different height-to-width ratios. The corresponding critical Rayleigh number for each case was estimated using the flow topologies varied with Ra and L/B, and the bisection method. It can be concluded that the first bifurcation depends on the values of Ra and L/B. Flow topologies and the first bifurcation experienced a sudden change as L/B varied between 2.5 (from 1 core to 2 cores) and 2.6 (from 2 cores to 3 cores). For each interval of L/B adjacent to the interval of sudden change, the critiacl Ra decreased with the increase in L/B. Furthermore, there is a step increase for Ra_Cr for the sudden change interval. It can then be concluded that natural convection of air enclosed in a rectangular cavity experiences local instability more easily with higher value of L/B. According to the given results, it can also be deduced that the variation of the characteristic of the first bifurcation should be more complex with higher L/B.