Transition to a chaotic flow in a V-shaped triangular cavity heated from below

Natural convection in a V-shaped cavity heated from below and cooled from top is investigated owing to its extensive presence in industrial systems and in nature such as in a valley. Two dimensional numerical simulation is performed for natural convection in the cavity using a Finite Volume Method. A wide range of Rayleigh numbers of Ra = 10(0) to 10(8) for the aspect ratio of A = 0.5 and the Prandtl number of Pr = 0.71 is considered. A set of supercritical bifurcations in a transition to a chaotic flow are described, which include a Pitchfork bifurcation from symmetric to asymmetric state and a Hopf bifurcation from steady to unsteady state. It is found that the Pitchfork bifurcation occurs between Ra = 7.5 x 10(3) and 7.6 x 10(3) and the Hopf bifurcation occurs between Ra = 1.5 x 10(7) and 1.6 x 10(7). Additionally, a further bifurcation from periodic to chaotic state occurs between Ra = 5 x 10(7) and 6 x 10(7). The power spectral density, the phase space trajectory and the largest Lyapunov exponent of unsteady flows in the transition to a chaotic state have been described. Further, heat transfer in the cavity is calculated and the corresponding dependence on the Rayleigh number is discussed and quantified. (C) 2018 Elsevier Ltd. All rights reserved.