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.