Study on the Route to Chaos of Natural Convection in Cylindrical Envelope With an Internal Concentric Cylinder With Slots

Natural convection heat transfer was investigated numerically in a cylindrical envelope with an internal concentric cylinder with slots. Governing equations are discretized using finite volume method and solved using SIMPLE algorithm with QUICK scheme. Calculations were performed on certain parameters with a Rayleigh number varying from 700 to 20000. The effect of the Rayleigh number on the route to the chaos of the system was analyzed by the phase space of velocity at the sample point. The results show that the system can reach to steady state and symmetric when the Rayleigh number is below 700, and to steady state and asymmetric when the Rayleigh number is equal to 1000. For a Rayleigh number ranged between 1500 and 3000, an asymmetric periodical solution is obtained although the initial field and boundary conditions were symmetric. As the Rayleigh numbers increase further, a quasi-periodic solution of the system is achieved at Ra = 2000. There is one more bifurcation and period doubling at successive critical values of Rayleigh numbers from to. It is ascertained that periodicity is lost at Ra = 20000. The results show that the oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow.