This is an author's version published in: http://oatao.univ-toulouse.fr/20645To cite this version: A numerical and experimental study of buoyancy-driven flow in the annulus between two horizontal coaxial cylinders at Rayleigh numbers approaching and exceeding the critical values is presented. The stability of the flow is investigated using linear theory and the energy method. Theoretical predictions of the critical Rayleigh number for onset of secondary flows are obtained for a wide range of radius ratio R and are verified by comparison with results of previous experimental studies. A subcritical Rayleigh number which provides a necessary condition for global flow stability is also determined. The three-dimensional transient equations of fluid flow and heat transfer are solved to study the manifestation of instabilities within annuli having impermeable endwalls, which are encountered in various applications. For the first time, a thorough examination of the development of spiral vortex secondary flow within a moderate gap annulus and its interaction with the primary flow is performed for air. Simulations are conducted to investigate factors influencing the size and number of post-transitional vortex cells. The evolution of stable three-dimensional flow and temperature fields with increasing Rayleigh number in a large gap annulus is also studied. The distinct flow structures which coexist in the large gap annulus at high Rayleigh numbers preceding transition to oscillatory flow, including transverse vortices at the end walls which have not been previously identified, are established numerically and experimentally. The solutions for the large-gap annulus are compared to those for the moderate-gap case to clarify fundamental differences in behaviour. Heat transfer results in the form of local Nusselt number distributions are presented for both the moderate-and large-gap cases. Results from a series of experiments performed with air to obtain data for validation of the numerical scheme and further information on the flow stability are presented. Additionally, the change from a crescent-shaped flow pattern to a unicellular pattern with centre of rotation at the top of the annulus is investigated numerically and experimentally for a Prandtl number of 100. Excellent agreement between the numerical and experimental results is shown for both Prandtl numbers studied. The present work provides, for the first time, quantitative three-dimensional descriptions of spiral convection within a moderate-gap annulus containing air, flow structures preceding oscillation in a large-gap annulus for air, and unicellular flow development in a large-gap annulus for large Prandtl number fluids.

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.

A numerical study of three-dimensional supercritical states of natural convection in a narrow-gap horizontal cylindrical annulus is presented. For the first time, an odd number of counter-rotating transverse rolls is shown to occur in a narrow-gap annulus. Flow and temperature fields associated with the odd roll state are compared to those of transverse roll states exhibiting even numbers of rolls, and factors influencing the occurrence and number of odd rolls are investigated.

Results from a combined experimental and numerical investigation of buoyancy driven flow and heat transfer in a narrow annular gap between co-axial, horizontal cylinders are presented in this work. The annulus is open at both ends through which the ambient fluid can interact with the fluid inside the gap. In the experimental study, a constant heat flux was utilized to simulate buoyancy induced convection in an open ended annular cavity with a low gap to inner cylinder radius ratio; local surface temperature measurements were made to determine heat transfer characteristics of the convective flow. The heat transfer results are correlated by Nu = 0.134(Ra*)0.264 for the range of Rayleigh numbers considered (7.09 ×108 ≤ Ra* ≤ 4.76 × 109) in the experiments. In the numerical investigation, solutions to the three-dimensional time-averaged (Reynolds) steady-state equations of fluid motion and heat transfer were obtained using a finite element analysis. Results of the conjugate study including the local temperature distributions, heat transfer coefficients, and the flow field showing the interactions between the ambient and cavity flow fields agree favorably with experimental results. An investigation was also carried out to study the effect of axial length and the gap width of the annulus. A correlation for the average Nusselt number as a function of Rayleigh number, axial length and gap width has been obtained. The present work provides, for the first time, an experimental and numerical study of turbulent buoyancy induced flows in a narrow open-ended annulus.

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