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

Abstract

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.

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

“…Powe et al 15 experimentally investigated the bifurcation of natural convection of air (Pr = 0.7) by visualizing flow patterns, and categorized the flow patterns obtained by their experiments and accumulated results by other researchers in a parameter space of (Ra, R) where R is radius ratio. This experiment was repeated and the classification was confirmed by Dyko et al 16 Busse 17 discussed the non-linear properties such as the dependence of the heat transport on Rayleigh and Prandtl numbers and the stability properties of thermal convection. Janssen et al 18 analyzed the instabilities in three dimensional differentially heated cavities with adiabatic horizontal walls.…”

Numerical investigation of the convective flow in the toroidal gap

“…28 (left) differs from the flow in the cylindrical gap in Fig. 1c with a further increase in the Grashof number because of the influence of the boundary conditions for the velocity field on the endwalls of the cylinders [6].…”

“…The flow patterns depend on the radius ratio, Prandtl number and Grashof or Rayleigh number ( Table 1). The numerical results of the natural convection in a cylindrical gap for different Rayleigh numbers [6] are presented in Fig. 1.…”

“…27, 28, 29 and 30 and show that the flow is highly dependent on this Stream function for = 0.5, η = 0.8, Gr = 2 × 10 Pr Stream function (left), temperature (middle) and pressure distribution −P eff (right) for = 0.8, η = 0.1, Gr = 2 × 10 5 , Stream function (left), temperature (middle) and pressure distribution −P eff (right) for = 0.8, η = 0.5, Gr = 2 × 10 5 , Pr = 1parameter. The chosen fluid and geometrical parameters in this section correspond to the parameters for which the numerical investigation in the cylindrical and spherical geometry has been performed.The numerical results performing for = 0.01 can be compared with the numerical investigation of the natural convection in the horizontal cylindrical gap[6], because the curvature effects have a small influence on the flow in this case. The calculations have been made for the Grashof number Gr = 15211, which correspond with to the Grashof number Gr Dyko = 1428.57[6], as well as Pr = 0.7.…”

“…The chosen fluid and geometrical parameters in this section correspond to the parameters for which the numerical investigation in the cylindrical and spherical geometry has been performed.The numerical results performing for = 0.01 can be compared with the numerical investigation of the natural convection in the horizontal cylindrical gap[6], because the curvature effects have a small influence on the flow in this case. The calculations have been made for the Grashof number Gr = 15211, which correspond with to the Grashof number Gr Dyko = 1428.57[6], as well as Pr = 0.7. The flow in the toroidal gap inFig.…”