Three-dimensional natural convective states in a narrow-gap horizontal annulus

Buoyancy-driven flow in a narrow-gap annulus formed by two concentric horiz ontal cylinders is investigated numerically. The three-dimensional transien t equations of fluid motion and heat transfer are solved to study multiple supercritical states occurring within annuli having impermeable endwalls, w hich are encountered in various applications. For the first time, three-dim ensional supercritical states are shown to occur in a narrow-gap annulus an d the existence of four such states is established. These four states are c haracterized by the orientations and directions of rotation of counter-rota ting rolls that form in the upper part of the annulus owing to thermal inst ability, and exhibit (i) transverse rolls, (ii) transverse rolls with rever sed directions of rotation, (iii) longitudinal rolls in combination with tr ansverse rolls, and (iv) longitudinal rolls with reversed directions of rot ation in combination with transverse rolls, respectively. Simulations are p erformed at Rayleigh numbers approaching and exceeding the critical value t o gain insight into the physical processes influencing development of the s econdary flow structures. The evolution of the supercritical flow fields an d temperature distributions with increasing Rayleigh number and the interac tion between the secondary and primary flows are thoroughly investigated. F actors influencing the number of rolls are studied for each supercritical s tate. Heat transfer results are presented in the form of local Nusselt numb er distributions and overall annulus Nusselt numbers. Two-dimensional natur al convection occurring early in the transient evolution of the flow field is also examined. Results obtained for a wide range of annulus radius ratio s and Rayleigh numbers are shown to be in excellent agreement with results from previous experimental and numerical studies, thereby validating the pr esent numerical scheme.