Evolution to chaotic natural convection in a horizontal annulus with an internally slotted circle

The characteristics of transition from laminar to chaotic natural convection in a two-dimensional horizontal annulus with an internally slotted circle is analyzed using Lattice Boltzmann method (LBM). The aim of this paper is to identify the route(s) to chaos, and to illustrate the dynamical response of the flow with the change of the control parameter (Ra). The results obtained for a range of the Rayleigh number, Ra, from 5 × 10³ to 2 × 10⁶ at Pr = 0.71, and the slot degree, S_f, from 0.1 to 0.4. The numerical results show that slot ratio, slot configuration, and Rayleigh number are influential to oscillation phenomenon in this model; the flow inside the annulus may be: (1) a stable base-two-cells regime, (2) a multi-cellular flow with four-stable-symmetrical-secondary cells regime, (3) a multi-cellular flow with four-oscillatory-secondary cells regime, and (4) an asymmetrical oscillation regime. The results also show that the oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow after the first bifurcation. In addition, certain features of nonlinear dynamical systems like bifurcation, self-sustained oscillations are also observed. The simulation results also show that slot degree S_f is relevant to oscillations. Furthermore, with the larger slotted ratio, the flow is more unstable, and the configuration with top and bottom slot seems to be the most unstable among the given four models.