Rayleigh-Benard Cell Research Articles

Darcy–Benard convection through a uniformly permeable porous slab

In this article, we study the onset of convection in porous media with through flow based on Darcy formulation. Unlike the impermeable porous medium problems between horizontal two parallel plates frequently accessed in the literature, the thermal instability of convective cells under the influence of a uniform vertical flow is of the prime concern here in an aim to control the thermal instability onset. Three devised thermal boundary constraints representing external heat transfer with isothermal or isoflux lines across the walls are investigated fully taking into account the linear stability equations with small flow/heat wave disturbances with respect to the normal modes. In each case, the neutral stability response of the saturated porous layer separating the stable and unstable perturbation regimes are identified affected by a Peclet number manifesting itself as the through flow strength. The pre-analysis of the analytical solutions of thermal fields proves that the thermal layer thickness is lowered by the opposing through flow, otherwise an assisting through flow enhances the thickness. The critical Darcy–Rayleigh numbers and Benard cell wavenumbers of lateral fluctuating perturbations initiating the convective Darcy–Benard thermal rolls within the porous media for a prescribed Peclet number are ultimately worked out numerically, except an analytical expression is elaborated where the heating is supplied from the walls via varying heat fluxes. The well-documented thresholds of Rayleigh numbers 39.47, 27.09 and 12 with vanishing Peclet number (Barletta, 2019) corresponding to the three studied thermal cases are reproduced successfully. Further results clarified that both opposing and assisting through flows are sources of stabilization when the walls are thermally isothermal. On the other hand, the other thermally conducting porous walls lead to a more unstable convection with the assisting through flow having a thermal layer growth, otherwise stable convection occurs with the opposing through flow.

Suppression of Wall Modes in Rapidly Rotating Rayleigh-Bénard Convection by Narrow Horizontal Fins.

The heat transport by rapidly rotating Rayleigh-Bénard convection is of fundamental importance to many geophysical flows. Laboratory measurements are impeded by robust wall modes that develop along vertical walls, significantly perturbing the heat flux. We show that narrow horizontal fins along the vertical walls efficiently suppress wall modes ensuring that their contribution to the global heat flux is negligible compared with bulk convection in the geostrophic regime, thereby paving the way for new experimental studies of geophysically relevant regimes of rotating convection.

Tristable flow states and reversal of the large-scale circulation in two-dimensional circular convection cells

Abstract

Reduced-order modelling of radiative transfer effects on Rayleigh–Bénard convection in a cubic cell

This paper presents a reduced-order modelling strategy for Rayleigh-Benard convection of a radiating gas, based on the proper orthogonal decomposition (POD). Direct numerical simulation (DNS) of coupled natural convection and radiative transfer in a cubic Rayleigh-Benard cell is performed for an air/H 2 O/CO 2 mixture at room temperature and at a Rayleigh number of 10 7. It is shown that radiative transfer between the isothermal walls and the gas triggers a convection growth outside the boundary-layers. Mean and turbulent kinetic energy increase with radiation, as well as temperature fluctuations to a lesser extent. As in the uncoupled case, the large-scale circulation (LSC) settles in one of the two diagonal planes of the cube with a clockwise or anticlockwise motion, and experiences occasional brief reorientations which are rotations of π/2 of the LSC in the horizontal plane. A POD analysis is conducted and reveals that the dominant POD eigenfunctions are preserved with radiation while POD eigenvalues are increased. Two POD-based reduced-order models including radiative transfer effects are then derived: the first one is based on coupled DNS data while the second one is an a priori model based on uncoupled DNS data. Owing to the weak temperature differences, radiation effects on mode amplitudes are linear in the models. Both models capture the increase in energy with radiation and are able to reproduce the low-frequency dynamics of reorientations and the high-frequency dynamics associated with the LSC velocity observed in the coupled DNS.

Experimental and numerical shadowgraph in turbulent Rayleigh–Bénard convection with a rough boundary: investigation of plumes

We show that, in the case of turbulent Rayleigh-Benard convection, shadowgraph can be used to have quantitative results on the plumes statistics and their velocity. For this purpose, we compare the experimental shadowgraph of a Rayleigh-Benard cell with the synthetic shadowgraph obtained by calculating the integrated 2D Laplacian of the temperature field from a numerical simulation very similar to the experiment. We use image processing tools to enhance the quality of the shadowgraph image, and obtain quantitative statistics for the thermal plumes, such as plume density, and plume velocity distribution. To highlight the efficiency of this new process of plume counting, we use, both in the experiment and in the numerical simulation, a turbulent Rayleigh-Benard convection cell with a rough bottom surface, and a smooth top surface, where the statistics of the plumes can be influenced (or not) by the roughness. In addition, the distribution of velocity obtained from processing the synthetic shadowgraph images of the DNS or the experimental shadowgraph images, are compared to the velocity fluid at mid plane of the DNS or PIV measurement in the experiment, respectively. It will be shown that the mean velocity profile measured using the advection of the plumes is different from the average eulerian velocity profile.

Flux and storage of energy in nonequilibrium stationary states.

Systems kept out of equilibrium in stationary states by an external source of energy store an energy ΔU=U-U_{0}. U_{0} is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine ΔU for two model systems: ideal gas and a Lennard-Jones fluid. ΔU depends not only on the total energy flux, J_{U}, but also on the mode of energy transfer into the system. We use three different modes of energy transfer where the energy flux per unit volume is (i) constant, (ii) proportional to the local temperature, and (iii) proportional to the local density. We show that ΔU/J_{U}=τ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. τ is the characteristic timescale of energy outflow from the system immediately after the shutdown of energy flux. We prove that τ is minimized in stable states of the Rayleigh-Benard cell.

Effect of thermophoresis on natural convection in a Rayleigh–Benard cell filled with a nanofluid

Abstract The objective of this paper is to clarify the role of thermophoresis in laminar natural convection in a Rayleigh–Benard cell filled with a water-based nanofluid and to study its relative importance compared to other effects, in an attempt to correct the present confusing interpretation of the magnitude of the thermophoresis coefficient in nanofluids. The major forces are introduced and the transport equations are solved using a two-phase lattice Boltzmann method (LBM) for a laminar flow with Ra numbers up to 106 with various particle loadings (particle volume fractions). The results indicate an increase in the average Nu number with an increase in the Ra number and particle loading. An increase in the Nu number for a 10% particle loading at Ra = 106 is less than 20%. When thermophoresis effect is taken into consideration, an increase in the Nu number is predicted, which is about 10%. Therefore, it is concluded that using a nanofluid in bottom-heated laminar natural convection results in a considerable increase in heat transfer rate and thermophoresis force is a significant contributor to heat transfer augmentation, particularly for high Ra numbers (Ra ∼ 106 and higher). It is observed that at low Ra numbers (weak convective flows), the nanofluid behaves homogenously, but at higher Ra numbers, it starts to behave heterogeneously.

Visual and dynamical measurement of Rayleigh-Benard convection by using fiber-based digital holographic interferometry

We present a method for visual and dynamical measurement of the Rayleigh-Benard convection by using fiber-based digital holographic interferometry. A SM600 fiber with 4 μm core diameter is used instead of conventional pinhole, which has better performance to filter out the noises, effectively modify the structure of the optical path and relax the requirement of the laser performance (e.g., coherence length and beam uniformity). The experimental results show the development process of Rayleigh-Benard cell in the container. The corresponding Rayleigh number is 3.6. In the process, the temperature at the top and bottom plates is controlled at 295 K and 300 K, respectively. The measured temperature distribution and the number of Rayleigh-Benard cell are verified by using simulation and are in good agreement.

Time Scaling in the Convection Onset of Supercritical 3He

A review is presented of the laboratory experiments and simulations of the convection onset of a supercritical fluid, 3He, in a Rayleigh-Benard cell after the start of a steady heat flow q from the bottom wall at the time t=0. The experiments were conducted at several temperatures along the critical isochore and over a wide range of q and measured the temperature drop ΔT(t) across the fluid layer. It was empirically found that the various characteristic times t i observed in the profile of ΔT(t), and also in the convection growth determined by numerical simulations, could each be expressed by t i /τ D as function of the Rayleigh number, where τ D is the diffusive relaxation time. This scaled representation is to be expected, as has been shown in a general demonstration by Michael Cross (unpublished) and its implications are discussed. A comparison of the profiles ΔT(t) from experiments and simulations are presented and various unresolved discrepancies will be discussed.

Rough horizontal plates: heat transfer and hysteresis

To investigate the influence of a rough-wall boundary layer on turbulent heat transport, an experiment of high-Rayleigh convection in water is carried out in a Rayleigh-Benard cell with a rough lower plate and a smooth upper plate. A transition in the heat transport is observed when the thermal boundary layer thickness becomes comparable to or smaller than the roughness height. Besides, at larger Rayleigh numbers than the threshold value, heat transport is found to be increased up to 60 %. This enhancement cannot be explained simply by an increase in the contact area of the rough surface since the contact area is increased only by a factor of 40 %. Finally, a simple model is proposed to explain the enhanced heat transport.

The effect of the temperature distribution along the perimeter of the boundary on the the flow in the convective Rayleigh-Benard cell

This paper is devoted to the study of the natural convection of a viscous incompressible fluid in a two-dimensional cell with combined vertical and horizontal heating in symmetrical and asymmetrical cases; investigation of the dependence of the maximum speed and intensity of heat exchange on different heating regimes.

Numerical Modeling of Polymerase Chain Reaction in the Convection Cell

A polymerase chain reaction occurring under convection conditions is studied in a simplified Rayleigh-Benard cell. During the reaction, copies of the original DNA templates are created due to circulation of the flow between the cold and hot regions. The process of creating the DNA templates copies (DNA amplification) is described by evolution equations that determine concentrations for each of the components of the mixture.

Long relaxation times and tilt sensitivity in Rayleigh Bénard turbulence

We study the influence of a small tilt angle (\(0 < \theta < 3 \times 10^{-2}\)rd) on the Nusselt number in a 1/2 aspect ratio Rayleigh-Benard cell, at high Rayleigh number (5 x 1011 < Ra < 4 x 1012). The small decrease observed is interpreted as revealing a two rolls structure of the flow. Transitions between different global flows are also observed, on very long times, comparable to the diffusion time on the whole cell. The consequence is that the Nusselt number observed in most high Ra experiments should significantly depend on initial conditions.

Growth of Nonlinear Patterns in Binary-Fluid Convection, Analysis of Models

A recently proposed “minimal model” of the convection of binary mixtures in a Rayleigh–Benard cell of aspect ratio 2 with realistic boundary conditions is invoked to study the transient dynamics from the entirely diffusive ground state to the convection state. The model was designed to reproduce the subcritical Hopf bifurcation found for negative Soret coupling in finite-difference simulations and experiments, but also performs well for the growth transients, including the competition between two counter-propagating waves. We prepared an initial state with only one wave, thus avoiding complicated wave competition. This allows us to elucidate the interaction of the concentration field with the pure-fluid fields, i.e., temperature and velocity, by means of modulus and phase equations. We explain the linear and nonlinear transient dynamics responsible for the strong decrease in frequency and concentration, and the feed-back loop responsible for propagation.

On the Heat Transfer in Rayleigh–Bénard Systems

In this paper we discuss some theoretical aspects concerning the scaling laws of the Nusselt number versus the Rayleigh number in a Rayleigh–Benard cell. We present a new set of numerical simulations and compare our findings against the predictions of existing models. We then propose a new theory which relies on the hypothesis of Bolgiano scaling. Our approach generalizes the one proposed by Kadanoff, Libchaber, and coworkers and solves some of the inconsistencies raised in the recent literature.

Effects of external noise on the Swift-Hohenberg equation.

The Swift-Hohenberg equation is studied in the presence of a multiplicative noise. This stochastic equation could describe a situation in which a noise has been superimposed on the temperature gradient between the two plates of a Rayleigh-Benard cell. A linear stability analysis and numerical simulations show that, in constrast to the additive-noise case, convective structures appear in a regime in which a deterministic analysis predicts a homogeneous solution

Correlation of subsystems for the transition to a convective pattern

The authors implement an evolutionary model of spatially coupled subsystems to clarify the cooperative effect causing the transition to a convective roll pattern in a Rayleigh-Benard cell. This cell is swept through its threshold by means of a step in the heat input from the lower plate. The correlation of subsystems accounts for the amplification of fluctuations. The experimental transients for the onset of the convective pattern are shown to be theoretically reproducible.

The effects of thermal noise in a Rayleigh-Benard cell near its first convective instability

Recent experiments by Meyeret al. on the onset of convection in a Rayleigh-Benard cell near the first convective instability can be described as being caused by random noise terms in the currents of heat and momentum, but the amplitude of these terms turns out to be about 105 times as large as would follow from standard fluctuating hydrodynamics.

Constraints on the time-reversible Liouville equation in order to derive a stochastic order-parameter equations at the onset of a convective roll pattern

It is shown that an adequate Fokker-Planck equation for the transition to a convective roll pattern in a Rayleigh-Benard cell can be derived by projecting the time-reversible Liouville equation onto the centre manifold for the onset and introducing the source of irreversibility on the initial conditions. Thus the author elucidates the microscopic origin of the random source in the order-parameter evolution.

Transition to Chaotic Behavior via a Reproducible Sequence of Period-Doubling Bifurcations

We present the results of measurements of the vertical and horizontal temperature gradients in a Rayleigh-Benard cell. By an appropriate preparation of the initial state, the system can be brought into a single-frequency oscillatory regime. Further stepwise increase in the imposed temperature gradient makes the system go through a reproducible sequence of period-doubling bifurcations up to $\frac{{f}_{1}}{16}$. The Feigenbaum $\ensuremath{\delta}$ and $\ensuremath{\mu}$ universal numbers are determined.