Free Two-Dimensional Convective Bifurcation in a Horizontal Annulus

Abstract

Natural convection is investigated numerically and experimentally in a cylindrical annulus. The governing equations based on primitive variables are solved using Chorin’s method. In addition to the unicellular flows reported in the literature, depending on initial conditions, bicellular flows are observed for high Rayleigh numbers. The bifurcation point is determined numerically. The velocity field for unicellular flows is measured by laser-Doppler anemometry in an air-filled annulus. A perturbation solution is also presented. The experimental results are in good agreement with numerical predictions and the perturbation solution.

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

“…The authors showed that two different regimes could coexist for a wide range of Ra H , namely, the basic crescent-shaped unicellular flow, and a bicellular flow with a pair of thermally-driven counterrotating rolls in the top part of the annulus. A similar result, showing fair agreement with the analyses of Cheddadi et al [31] was generated later by Cadiou et al [32], who analyzed the 2D flow in very narrow annuli ðR > 1:24Þ. They were the first to postulate the dual solutions to be originated by the existence of an imperfect bifurcation, i.e.…”

“…Focusing on air flows, Pr ¼ 0:7, the occurrence of multiple solutions was detected experimentally and numerically by Cheddadi et al [31] for moderately narrow annuli, under the two-dimensional assumption but without imposing vertical symmetry. The authors showed that two different regimes could coexist for a wide range of Ra H , namely, the basic crescent-shaped unicellular flow, and a bicellular flow with a pair of thermally-driven counterrotating rolls in the top part of the annulus.…”

A numerical and experimental investigation of stability of natural convective flows within a horizontal annulus

“…For other than very small Prandtl numbers, only a few numerical studies of posttransitional flow in a horizontal annulus have been published. In nearly all of these studies, a two-dimensional model was employed (Powe, Carley & Carruth 1971 ;Fant, Rothmayer & Prusa 1991 ;Cheddadi et al 1992 ;Yoo 1996) and therefore neither the spiral secondary flows which are observed experimentally in annuli of moderate R nor the influence of solid endwalls which bound a finite-length annulus could be analysed. Rao et al (1985) carried out steady three-dimensional calculations for a case of moderate R. However, only a fluid with Prandtl number of 5000 was studied which limits the range of practical applicability of their results.…”

Solutions multiples et bifurcations des écoulements bidimensionnels de convection naturelle dans une cavité annulaire horizontaleMultiple solutions and bifurcations of two-dimensional natural convection flows in a horizontal annulus

“…Ces résultats furent complétés par les études numériques bidimensionnelles de Powe et al [2], Rao et al [3], Fant et al [4] et Kim et Ro [5] dans lesquelles la multiplicité de solutions pour un ensemble donné de valeurs des paramètres η, Ra et Pr fut mise en évidence. Ainsi, des solutions unicellulaires ou bi-cellulaires furent trouvées par Cheddadi et al [6] qui ont présenté un diagramme de bifurcation pour l'air. L'existence de solutions stationnaires duales fut ensuite confirmée par Yoo [7] et la multiplicité d'écoulements multicellulaires par Chung et al [8].…”