Transitions of natural convection flows in a square enclosure with a heated circular cylinder

Numerical investigations are carried out for natural convection within domains with curved geometry by using an immersed-boundary method. Influence of the Prandtl number (0.71-0.07) on the flow structure are investigated through the flow structure map in the Ra-Pr plane. By reducing the Prandtl number, the flow experiences transition from steady single thermal-plume state, steady double thermal-plume state and then to unsteady state for Ra ≤ 2 × 106. However at elevated Rayleigh number (Ra > 2 × 106), the transition is directly from steady single-plume state to unsteady state without going through double-plume regime. The variations of the threshold Pr during transition from single-plume to double-plume or to unsteady regime at different Rayleigh numbers are also addressed.