Transition from steady to chaotic flow of natural convection on a section-triangular roof

Abstract

Natural convection over a roof-shaped triangular surface is investigated using direct numerical simulations. The Rayleigh number (Ra) was varied from 1 to 5×106 with air as working fluid (Prandtl number of 0.71) at a fixed geometrical aspect ratio of 0.1, defined as the ratio of roof height to half-width. The transition route from a steady flow to a chaotic flow on the surface is characterized by the topological method with the increase of Ra. A weak flow, dominated by conduction, occurs when Ra was relatively small. As Ra increases, the convective flow becomes stronger and a sequence of bifurcations is found. Between Ra=102 and 103, a primary pitchfork bifurcation occurs. Secondary and tertiary pitchfork bifurcations are observed in the range Ra=[103,104] and [104,105], respectively. After another pitchfork bifurcation at Ra=[1.4,1.5]×106, which makes the plume tilt to either side of the roof top edge, a Hopf bifurcation is observed in Ra=[1.9,2]×106, after which both the slope flow and plume become periodic. This is followed by further bifurcations including a period doubling bifurcation at Ra≈3×106 and a quasiperiodic bifurcation firstly arising at Ra≈3.4×106. Finally, the flow becomes chaotic for Ra>3.7×106. The state space, the maximum Lyapunov exponent, the fractal dimension, and the power spectral density are presented to analyze the flows in the transition to chaos. This work is a comprehensive description of the flow transition from steady state to chaos on surface of a section-triangular roof that is pertinent to various settings where fluid flow develops. © 2021 American Physical Society