The route to chaos for plumes from a top-open cylinder heated from underneath

Abstract

Natural convection in a top-open cylindrical cavity heated from the cavity bottom was simulated and analysed for a range of Rayleigh numbers, Ra = 100–106. A succession of bifurcations from steady to chaotic plumes, with increasing Rayleigh numbers, was observed in the three-dimensional simulation results. At Ra = 3.6 × 103, a symmetrical steady plume switched to becoming an asymmetric steady plume with a pitchfork bifurcation, owing to the symmetry break. When the Rayleigh number increased to 8.6 × 104, a periodic puffing flow appeared after a Hopf bifurcation. It was found that the Hopf bifurcation was followed by a cascade of period-doubling bifurcations, then a quasi-periodicity bifurcation, and a bifurcation to chaos for plumes from an open cylinder heated from underneath. The unsteady flow was further analysed using power spectral densities, attractors, and the largest Lyapunov exponents. In addition, the different scaling relationships within different regimes were attained, based on the Rayleigh number.