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

Abstract

Buoyancy-driven flow in a narrow-gap annulus formed by two concentric horizontal cylinders is investigated numerically. The three-dimensional transient equations of fluid motion and heat transfer are solved to study multiple supercritical states occurring within annuli having impermeable endwalls, which are encountered in various applications. For the first time, three-dimensional supercritical states are shown to occur in a narrow-gap annulus and the existence of four such states is established. These four states are characterized by the orientations and directions of rotation of counter-rotating rolls that form in the upper part of the annulus owing to thermal instability, and exhibit (i) transverse rolls, (ii) transverse rolls with reversed directions of rotation, (iii) longitudinal rolls in combination with transverse rolls, and (iv) longitudinal rolls with reversed directions of rotation in combination with transverse rolls, respectively. Simulations are performed at Rayleigh numbers approaching and exceeding the critical value to gain insight into the physical processes influencing development of the secondary flow structures. The evolution of the supercritical flow fields and temperature distributions with increasing Rayleigh number and the interaction between the secondary and primary flows are thoroughly investigated. Factors influencing the number of rolls are studied for each supercritical state. Heat transfer results are presented in the form of local Nusselt number distributions and overall annulus Nusselt numbers. Two-dimensional natural convection occurring early in the transient evolution of the flow field is also examined. Results obtained for a wide range of annulus radius ratios and Rayleigh numbers are shown to be in excellent agreement with results from previous experimental and numerical studies, thereby validating the present numerical scheme.

Three-dimensional study of multiple transitions for natural convection in horizontal annuli

“…In this latter case, the viscous shear forces produce transverse cells near each of the end walls. For narrow-gap annuli (R 6 1.2), Dyko and Vafai [8,9] found complex flow patterns produced by the combination of upper transverse rolls with two-dimensional multi-cellular flows. These flow patterns are similar to those discussed in Petrone et al [1].…”

Temperature distribution in an oscillatory flow with a sinusoidal wall temperature

“…Natural convection in two dimensions has been incorporated into many heat transfer studies (see for instance [16]) and its inclusion in the oscillatory boundary layer flow is a topic of future work. Furthermore, three-dimensional effects can have a large influence on heat transfer rates [17] but a corresponding analysis incorporating oscillatory flows would require more sophisticated numerical and analytical models than those presented here.…”

A critical review of buoyancy-induced flow transitions in horizontal annuli

“…Subsequently, Dyko and Vafai [43] analyzed air-filled narrowgap annuli ðR 1:15Þ by means of full 3D numerical simulations, detecting that the possible flow structures consisted either in transverse rolls or in a combination of longitudinal counterrotating cells (as observed for 2D flows, [40]) and transverse rolls.…”