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 = 100 to 108 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 × 103 and 7.6 × 103 and the Hopf bifurcation occurs between Ra = 1.5 × 107 and 1.6 × 107. Additionally, a further bifurcation from periodic to chaotic state occurs between Ra = 5 × 107 and 6 × 107. 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.