Natural Convection In Horizontal Annulus Research Articles

SPH modeling of natural convection in horizontal annuli

SPH modeling of natural convection in horizontal annuli

Bifurcation phenomena of natural convection in horizontal annulus under self-induced circular magnetic fields

PurposeIn general, the bifurcation phenomenon of the natural convection has largely been studied. But the bifurcation of natural convection under magnetic conditions has not been studied as per the authors’ knowledge. This paper aims to investigate the changes in bifurcation phenomenon by the self-induced circular magnetic field.Design/methodology/approachThe authors numerically solved the natural convection in an annulus. The SIMPLE algorithm was adopted for pressure-momenturm coupling. The Boussinesq approximation was used for numerical modeling of natural convection. Finally, the Lorentz force effect by the magnetic field was considered through the source terms in the momentum conservation equation.FindingsIt was determined that the heat-transfer rate changes by 17% owing to the applied magnetic effect, and the range of the Rayleigh number for flow bifurcation is changed by the magnetic effect. Moreover, under the strong magnetic condition, the flow bifurcation continues even at very high Ra. Previously, flow bifurcation has been understood as a flow instability phenomena, and the Lorentz force was regarded as a flow-damping effect; however, in this study, it was found that the magnetic field can boost the flow instability and induce flow bifurcation even in the Rayleigh number region where the bifurcation does not appear.Originality/valueThis paper is dealing with the bifurcation phenomenon in MHD natural convection problems. In the past, the electromagnetic forces were regarded as always acting to damp out the existing flows; herewith, the authors first investigated that the magnetic effect can boost the bifurcation of a kind of flow instability phenomenon.

Evolution to chaotic natural convection in a horizontal annulus with an internally slotted circle

The characteristics of transition from laminar to chaotic natural convection in a two-dimensional horizontal annulus with an internally slotted circle is analyzed using Lattice Boltzmann method (LBM). The aim of this paper is to identify the route(s) to chaos, and to illustrate the dynamical response of the flow with the change of the control parameter (Ra). The results obtained for a range of the Rayleigh number, Ra, from 5 × 103 to 2 × 106 at Pr = 0.71, and the slot degree, Sf, from 0.1 to 0.4. The numerical results show that slot ratio, slot configuration, and Rayleigh number are influential to oscillation phenomenon in this model; the flow inside the annulus may be: (1) a stable base-two-cells regime, (2) a multi-cellular flow with four-stable-symmetrical-secondary cells regime, (3) a multi-cellular flow with four-oscillatory-secondary cells regime, and (4) an asymmetrical oscillation regime. The results also show that the oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow after the first bifurcation. In addition, certain features of nonlinear dynamical systems like bifurcation, self-sustained oscillations are also observed. The simulation results also show that slot degree Sf is relevant to oscillations. Furthermore, with the larger slotted ratio, the flow is more unstable, and the configuration with top and bottom slot seems to be the most unstable among the given four models.

A numerical study on the non-Boussinesq effect in the natural convection in horizontal annulus

In the present study, the non-Boussinesq effect in the thermal convection in an air-filled horizontal concentric annulus is studied numerically by using the variable property-based lattice Boltzmann flux solver (VPLBFS), with the radial temperature difference ratio of 1.0, the radius ratio of 2.0, and the Rayleigh number in the range 104 ≤ Ra ≤ 106. Several solutions are obtained by using the standard form or simplified versions of the VPLBFS, including the real solution with the total variation in fluid properties considered, named as the variable property solution (VPS), the constant property solution (CPS) based on the Boussinesq approximation, the solution with variable dynamic viscosity (VVS), the solution based on the partial Boussinesq approximation (PBAS), the solution with variable thermal conductivity (VCS) and the solution with variable fluid density (VDS). The discrepancy between these solutions is analyzed to illuminate the influence of the non-Boussinesq effects induced by partial or total variation in fluid properties on flow instability behaviors and heat transfer characteristics. The present study reveals the complicated flow instability behavior under non-Boussinesq conditions and its tight association with heat transfer characteristics. Also, it demonstrates the necessity of considering the integral effect of the total variation in fluid properties and highlights the essential role of the fluid density variation.

Natural convection in horizontal annuli: evaluation of the error for two approximations

We consider convection inside annuli, driven by a uniform temperature gap on the boundaries and gravitation as outer force. It takes place for any Rayleigh number while steady convective motions are observed only for small ones (but any Prandtl number and gap width). We provide estimates for the relative error of two popular approximations to the full Navier–Stokes–Fourier equations. For this we propose a new method. In particular we have to derive a lower bound for the norm of the velocity and the temperature both for steady nonlinear coupled and decoupled approximations in two space dimensions.

Flow and Heat Transfer of Natural Convection in Horizontal Annulus With a Heating Element on Inner Cylinder

Experiments have been performed to study natural convection flow and heat transfer in a horizontal annulus when a square heating element is positioned at different locations on the inner insulated cylinder. The annulus is filled with water and has cylinder to cylinder diameter ratio of 3. The square heating element is small and has the width to annulus gap width ratio of 1/6. The range of Rayleigh number studied is approximately from 1.9×106 to 3.3×107. It has been found that the flow pattern, the temperature distribution around the inner cylinder wall, and the local heat transfer rate around the outer cylinder are very sensitive to the location of the heating element. The heating element Nusselt numbers at various locations on the inner cylinder are obtained and well correlated against the Rayleigh number to the 1/3 powers. A maximum in the correlation parameter C is obtained when the heating element is placed 90 deg from the bottom.

Natural convection in horizontal annuli: a lower bound for the energy

Natural convection in the gap between two infinitely long horizontal coaxial cylindrical surfaces, each of which is maintained at constant temperature, is studied. If the inverse relative gap width A is large, relevant steady convective flow and considerable heat transfer are observed, even for extremely small Rayleigh numbers Ra. A lower bound for the norm of the velocity and of the temperature is rigorously found by studying an approximation problem, which is a good model in the parameter range where steady stable flow occurs. The lower bound depends on A only, and is an increasing function of A. This means that the bound can be arbitrarily increased via the geometry only, no matter how small the temperature difference is, and independently of the Prandtl number Pr.

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

Natural convection in horizontal differentially heated annuli is numerically investigated both by linear stability analysis and by solving the three-dimensional flow equations for a radius ratio R = 1.7. The governing equations were solved numerically by using a finite volume method. The stability of the basic crescent-shaped flows to three-dimensional disturbances is investigated. The existence of a stability region corresponding to a reversal from 3D- to 2D-flows is predicted for the first time. Three-dimensional computations show that multiple solutions are possible in the new stability region according to the initial conditions. Computations performed at supercritical Rayleigh numbers for the oscillatory régime elucidated the influence of the annulus length. Conflicting results reported in the archival literature are clarified.

Numerical simulation of laminar natural convection in horizontal annuli with radial fins

Natural convection heat transfer in the annular region between two concentric cylinders with radial fins is studied numerically. The basic conservation equations are discretized using the finite volume approach together with the SIMPLER algorithm. Computations are performed for laminar flow with Rayleigh numbers up to 106. The velocity and temperature fields are presented for various Rayleigh numbers and fin heights by streamline and isothermal plots. The local and mean Nusselt number predictions show that the fin height has an optimum value for which the heat transfer rate is increased. Long fins have a blocking effect on flow recirculation.

Natural convection in horizontal annulus filled with an anisotropic porous medium

The natural two‐dimensional convection taking place between horizontal concentric cylinders filled with a satured anisotropic porous medium is studied numerically. The anisotropy concerns exclusively the permeability. Isothermal boundary conditions are applied on both inner and outer boundaries, with the outer boundary being warmer. The effects of the anisotropic permeability ratio K*, of the orientation angle of the principal axes defined by γ, and of the Rayleigh number Ra* on the flow and heat transfer are investigated. Results indicate that a net circulating flow around the annulus is generated, except for values of γ that preserve the symmetry of flow conditions with respect to the vertical diameter. It is also shown that the anisotropic part of the resistivity tensor is equivalent to a magnetic resistivity tensor.

Study of natural convection in horizontal annuli

Natural convection of gases in a horizontal annulus, where the inner cylinder is heated by the application of a constant heat flux and the outer cylinder is isothermally cooled, is studied numerically. Detailed results of temperature, velocity and heat transfer are presented for a wide range of Rayleigh numbers extending from conduction to the convection-dominated steady flow regime, and diameter ratios of 1.2–10. A crescent-shaped eddy dominates for the small diameter ratio and a kidney-shaped flow pattern appears for the large diameter ratio as observed by previous investigators in their flow visualization studies. The inner wall temperature is a function of diameter ratio and Rayleigh number. An increase in Rayleigh number based on the same temperature difference for the inner wall boundary condition of constant heat flux or constant temperature increases the heat transfer rate; however, the increase is larger for the constant heat flux case. At large diameter ratios ( κ ≥ 10), the heat transfer rates are the same for both types of heating, and a single cylinder in an infinite atmosphere gives nearly the same results.

Flow patterns of natural convection in horizontal cylindrical annuli

Instabilities in the flow of natural convection in a horizontal annulus of radius ratio 2 filled with fluid of Prandtl number 0.1 are investigated numerically. The investigation largely focuses on the very small range of Rayleigh numbers between 3,500 and 5,000 in which the equivalent thermal conductivity increases suddenly. Since this instability is quite uncommon and only occurs in a narrow range of Rayleigh numbers, previous studies have not concentrated on the mechanism behind it. However, the present numerical simulation with very fine increments in Rayleigh number reveals that the jump in equivalent conductivity is caused by a transition into chaos, and this transition is akin to the typical Ruelle-Takens-Newhouse and Pomeau-Manneville scenarios. As well, it is more interesting that the flow escapes out of chaos and re-stabilizes at around the Rayleigh number of 4,800; it follows a reverse Pomeau-Manneville route. The progressions in the oscillatory pattern, power spectral density, and trajectories of equivalent conductivity in 2D and 3D phase spaces are plotted against the Rayleigh number in detail.