Numerical Analysis of Natural Convection in a Cylindrical Envelope with an Internal Concentric Cylinder with Slots

Abstract

Detailed numerical analysis is presented for natural convection heat transfer in a cylindrical envelope with an internal concentric cylinder with slots. Governing equations are discretized using the finite volume method, and solved using SIMPLE algorithm with QUICK scheme. The results show that the system can reach steady state and be symmetric when the Rayleigh number is below 4 × 10⁵. When the Rayleigh number is greater than 6 × 10⁵, 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 = 2 × 10⁶, and the periodicity is lost at Ra = 6 × 10⁶. It is ascertained that the oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow.

Acknowledgments

Financial support from the Chinese National Natural Science Foundation under grants nos. 50876067 and 50828601, Project of Shanghai Education Committee 10ZZ91, and Shanghai Leading Academic Discipline Project J50501 are gratefully acknowledged.