Flow instability and cellular vortex formation in natural convection from a heated horizontal cylinder under an adiabatic wall

Laminar flow instability between a heated horizontal cylinder and an adiabatic ceiling was investigated computationally and experimentally for relatively small cylinder-to-ceiling distances h (h ≤ D; D is the cylinder diameter) and for Rayleigh numbers Ra_D in the range from 1.4×10⁴ to 3.5×10⁷. Computations for a uniformly heated cylinder wall and for h=0.2D show that, in the range 3×10⁶ ≤ Ra_D ≤ 5×10⁶, two pairs of steady roller-type vortices appear in the gap region. For Ra_D >1×10⁷, however, the rollers break down to well defined, toroidal convection cells, which are arranged quasi-periodically along the cylinder axis direction. These cells are relatively stable in time, although they occasionally break down and, following some time, they get reconnected. A physical model describing the formation of these cells is proposed. The presence of quasi-periodic convection cells is confirmed experimentally for a larger range of conditions, i.e., for 0.1D ≤ h ≤ 0.5D. The h = 0.1D, 0.3D and 0.5D configurations were found to be stable for all Rayleigh numbers investigated, for both uniform temperature and uniform heat flux conditions on the cylinder wall.