Chaotic phenomena of natural convection for water in a V-shaped enclosure

Abstract

The changes from steady-state to chaotic natural convection in a V-shaped differentially heated enclosure have been studied numerically because of their importance in nature, such as in a river or lake. The finite volume method (FVM) is applied to simulate the Navier-Stokes and Energy equations with proper boundary conditions. The working fluid is considered water with the Prandtl number, Pr = 7.0 for various Rayleigh numbers ranging from Ra = 100 to 106 with a fixed aspect ratio, A = 0.5. A group of bifurcations in the transitional flow is investigated, including a Pitchfork and a Hopf bifurcations. The occurrence of Pitchfork bifurcation happens between Ra = 1.3 × 104 and 1.4 × 104 and of Hopf bifurcation happens between Ra = 1.6 × 105 and 1.7 × 105. Moreover, another bifurcation occurs between Ra = 2.6 × 105 and 2.7 × 105 for the changeover from intervallic state to chaotic state. Power spectral density of temperature time series, phase space trajectories, and the largest Lyapunov exponents of the unsteady chaotic flows are also investigated. Additionally, heat and mass transfer are measured and explained elaborately with physical significance.