Natural Convection in a Narrow Horizontal Annulus: The Effects of Thermal and Hydrodynamic Instabilities

Abstract

Multicellular natural convective flows in narrow horizontal air-filled concentric annuli are considered numerically in this paper. The results show that the multiplicity of the multicellular upper flows reported in the literature can be credited to the existence of an imperfect bifurcation with two stable branches. The emergence and extinction of the buoyancy-driven cells have been proved to be identical on both branches. The appearance of another secondary flow, the origin of which is purely hydrodynamic and located within the crescent base flow at the vertical portions of the annulus, has also been evidenced at moderate values of the Rayleigh number. As Ra is increased a reverse transition from a multicellular structure to a unicellular pattern occurs through a gradual decrease in the number of cells. In addition, it is shown that shear-driven instabilities cannot develop for radius ratios larger than a value close to R = 1.15.