NMR imaging of thermal convection patterns

Two special magnetic resonance imaging techniques were applied to the Rayleigh/Bénard problem of thermal convection for the first time. The methods were tested using a water cell with horizontal bottom and top covers kept at different temperatures with a downward gradient. Using Fourier encoding velocity imaging (FEVI) a five-dimensional image data set was recorded referring to two space dimensions of slice-selective images and all three components of the local velocity vector. On this basis, the fields of the velocity components or of the velocity magnitude were evaluated quantitatively and rendered as gray shade images. Furthermore the convection rolls were visualized with the aid of two- or three-dimensional multistripe/multiplane tagging imaging pulse sequences based on two or three DANTE combs for the space directions to be probed. Movies illustrating the fluid motions by convection in all three space dimensions were produced. It is demonstrated that the full spatial information of the convection rolls is accessible with microscopic resolution of typically 100 × 100 × 100 μm³. This resolution is effectively limited by flow displacements in the echo time, which should be well within the voxel dimension. The main perspective of this work is that the combined application of FEVI and multistripe/multiplane tagging imaging permits quantitative examinations of thermal convection for arbitrary boundary conditions and with imposed through-flow apart from the direct visualization of convective flow in the form of movies.     

Chaotic travelling rolls in Rayleigh-Bénard convection

In this paper we investigate two-dimensional (2D) Rayleigh-Bénard convection using direct numerical simulation in Boussinesq fluids with Prandtl number P = 6.8 confined between thermally conducting plates. We show through the simulation that in a small range of reduced Rayleigh number r (770 < r < 890) the 2D rolls move chaotically in a direction normal to the roll axis. The lateral shift of the rolls may lead to a global flow reversal of the convective motion. The chaotic travelling rolls are observed in simulations with free-slip as well as no-slip boundary conditions on the velocity field. We show that the travelling rolls and the flow reversal are due to an interplay between the real and imaginary parts of the critical modes.     

Wall-enhanced convection in vibrofluidized granular systems

An event-driven molecular dynamics simulation of inelastic hard spheres contained in a cylinder and subject to strong vibration reproduces accurately experimental results [R. D. Wildman et al., Phys. Rev. Lett. 86, 3304 (2001)] for a system of vibrofluidized glass beads. In particular, we are able to obtain the velocity field and the density and temperature profiles observed experimentally. In addition, we show that the appearance of convection rolls is strongly influenced by the value of the sidewall-particle restitution coefficient. Suggestions for observing more complex convection patterns are proposed.     

Linear stability analysis of the natural convection in inclined rotating parallel plates

The linear stability analysis of the natural convection in a rectangular tilted infinite cavity filled with a Boussinesq fluid subject to Coriolis force is presented. The bottom and top surfaces have fixed temperatures. Both unstable and stable thermal conditions are studied (heated from below and heated from above respectively). The rotation axis passes through the center and it is orthogonal to the hot and cold surfaces. The stability equations were solved using the Tau–Chebyshev spectral method. The critical Rayleigh number and critical wave number were obtained for several rotation rates and different orientation of convective oblique rolls in a range of inclination of the cavity from 0 to 120 degrees. The stability analysis show that rotation rate affects the basic velocity profile, onset of convection, wave number and critical orientation of convective rolls.     

Flow, diffusion, and thermal convection in percolation clusters: NMR experiments and numerical FEM/FVM simulations.

Percolation objects were fabricated based on computer-generated, two- or three-dimensional templates. Random-site, semi-continuous swiss cheese, and semi-continuous inverse swiss-cheese percolation models above the percolation threshold were considered. The water-filled pore space was investigated by NMR imaging and, in the presence of a pressure gradient, NMR velocity mapping. The fractal dimension, the correlation length, and the percolation probability were evaluated both from the computer-generated templates and the corresponding NMR spin density maps. Based on velocity maps, the percolation backbones were determined. The fractal dimension of the backbones turned out to be smaller than that of the complete cluster. As a further relation of interest, the volume-averaged velocity was calculated as a function of the probe volume radius. In a certain scaling window, the resulting dependence can be represented by a power law the exponent of which was not yet considered in the theoretical literature. The experimental results favorably compare to computer simulations based on the finite-element method (FEM) or the finite-volume method (FVM). Percolation theory suggests a relationship between the anomalous diffusion exponent and the fractal dimension of the cluster, i.e., between a dynamic and a structural parameter. We examined interdiffusion between two compartments initially filled with H2O and D2O, respectively, by proton imaging. The results confirm the theoretical expectation. As a third transport mechanism, thermal convection in percolation clusters of different porosities was studied with the aid of NMR velocity mapping. The velocity distribution is related to the convection roll size distribution. Corresponding histograms consist of a power law part representing localized rolls, and a high-velocity cut-off for cluster-spanning rolls. The maximum velocity as a function of the porosity clearly visualizes the percolation transition.     

Localized transverse bursts in inclined layer convection

We investigate a novel bursting state in inclined layer thermal convection in which convection rolls exhibit intermittent, localized, transverse bursts. With increasing temperature difference, the bursts increase in duration and number while exhibiting a characteristic wave number, magnitude, and size. We propose a mechanism which describes the duration of the observed bursting intervals and compare our results to bursting processes in other systems.     

Benard-Marangoni convection in two-layered liquids

We describe experiments on Benard-Marangoni convection in horizontal layers of two immiscible liquids. Unlike previous experiments, which used gases as the upper fluid, we find a square planform close to onset which undergoes a secondary bifurcation to rolls at higher temperature differences. The scale of the convection pattern is that of the thinner lower fluid layer for which buoyancy and surface tension forces are comparable. The wave number of the pattern near onset agrees with the linear stability prediction for the full two-layer problem. The square planform is in qualitative agreement with recent two-layer weakly nonlinear theories, which fail however to predict the transition to rolls.     

Localized waves without the existence of extended waves: oscillatory convection of binary mixtures with strong soret effect

Spatially confined solutions of traveling convection rolls are determined numerically for binary mixtures such as ethanol-water. The appropriate field equations are solved in a vertical cross section of the rolls perpendicular to their axes subject to realistic horizontal boundary conditions. The localized convective states are stably and robustly sustained by strongly nonlinear mixing and complex flow-induced concentration redistribution. We elucidate how this enables their existence for strongly negative separation ratios at small subcritical heating rates below the saddle node of extended traveling convection rolls where the quiescent fluid is strongly stable.     

Pattern formation in inclined layer convection

We report experiments on thermally driven convection in an inclined layer of large aspect ratio in a fluid of Prandtl number sigma approximately 1. We observed a number of new nonlinear, mostly spatiotemporally chaotic, states. At small angles of inclination we found longitudinal rolls, subharmonic oscillations, Busse oscillations, undulation chaos, and crawling rolls. At larger angles, in the vicinity of the transition from buoyancy- to shear-driven instability, we observed drifting transverse rolls, localized bursts, and drifting bimodals. For angles past vertical, when heated from above, we found drifting transverse rolls and switching diamond panes.     

Dynamics of zero-Prandtl number convection near onset

We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Be?nard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (2009)]. We also observed a set of periodic and chaotic wavy rolls in DNS and in the model similar to those observed in experiments and numerical simulations. The time period of the wavy rolls is closely related to the eigenvalues of the stability matrix of the Hopf bifurcation points at the onset of convection. This time period is in good agreement with the experimental results for low-Prandtl number fluids. The chaotic attractor of the wavy roll solutions is born through a quasiperiodic and phase-locking route to chaos.     

Transitions in convection driven by a horizontal temperature gradient

We report the first detailed experimental study of transitions in the convection of a low Prandtl number fluid driven by a horizontal temperature gradient. The observed states, from time independent to one frequency with noise, to pure noise, to two frequencies with noise, can be related to the two secondary flows predicted for a cavity with large lateral extent, transverse stationary and longitudinal oscillatory rolls. Measured wavelengths and frequencies for the longitudinal rolls are in agreement with theoretical values, while the critical Grashof number is much higher than expected. Our results call for a new theoretical approach which takes both instability mechanisms into account.     

Reentrant hexagons in non-Boussinesq Rayleigh-Bénard convection: effect of compressibility

We present experimental studies of a new pattern sequence observed in non-Boussinesq convection in a compressible fluid near its gas-liquid critical point (CP). Besides the known hysteretic transitions among conduction state, hexagons, and rolls, another hysteretic transition from rolls to hexagons at higher values of the control parameter is found. This reentrance phenomenon is observed in a rather narrow range of about 60- to 100-microm cell heights and is attributed to large compressibility of a fluid near the CP.     

Thermal-noise effect on the transition to Rayleigh-Bénard convection

We report measurements of fluctuation and roll patterns near the transition to Rayleigh-Bénard convection which are consistent with a fluctuation-induced first-order transition, as predicted by Swift and Hohenberg. Above onset, we find convection rolls with noise-induced fluctuations, time-dependent amplitude modulation and roll undulation, and homogeneous dislocation nucleation.     

The fate of self-aligned rolls in gravity modulated magnetoconvection

We explore the modifications brought about by gravity modulation in self-aligned two-dimensional (2D) stationary rolls and higher-order convective instabilities with horizontal magnetic field. The Chandrasekhar number plays no role in determining critical values of the forcing parameters for convection to begin. The onset is in the form of 2D rolls with periodically varying intensity. The external magnetic field is solely responsible for aligning the rolls while the induced magnetic field comes into play after three-dimensional convection sets in. Gravity modulation destabilizes the system and results in chaotic flow much earlier above onset.     

Active thermal convection in vibrofluidized granular systems

We present a granular-hydrodynamic model that captures the essence of convection in a fully vibrofluidized granular system. The steady temperature distribution is solved analytically. Numerical simulation shows that the convection always develops through a supercritical bifurcation, with its energy about of the random (heat) one. A comparison calculation is performed for a normal fluid. The convection roll, or an active roll as we call it, has an angular velocity gradient from its interior to exterior. We conclude that active rolls are universal.Received: 25 March 2004, Published online: 9 September 2004PACS: 45.70.Mg Granular flow: mixing, segregation and stratification - 47.20.Bp Buoyancy-driven instability - 47.27.Te Convection and heat transfer     

Oscillations, cessations, and circulation reversals of granular convection in a densely filled rotating container

We study spontaneously forming convection in a container that is almost completely filled with a bidisperse granular mixture. The container with an aspect ratio close to 1 rotates slowly about a horizontal axis. In this geometry, single vortex rolls are observed in the cell plane, after a spontaneous symmetry breaking. The circulation of grains produces nonuniform segregation patterns of the mixture that in turn interact with the convective flow. We describe oscillatory modulations of the convection velocity, cessations and spontaneous reversals of the circulation. All these features are absent in multiroll granular convection.     

Instabilities of thermocapillary-buoyancy convection in open rectangular liquid layers

This article presents the experimental investigation on instabilities of thermocapillary-buoyancy convection in the transition process in an open rectangular liquid layer subject to a horizontal temperature gradient. In the experimental run,an infrared thermal imaging system was constructed to observe and record the surface wave of the rectangular liquid layer. It was found that there are distinct convection longitudinal rolls in the flow field in the thermocapillary-buoyancy convection transition process. There are different wave characterizations for liquid layers with different thicknesses. For sufficiently thin layers, oblique hydrothermal waves are observed, which was predicted by the linear-stability analysis of Smith Davis in 1983. For thicker layers, the surface flow is distinct and intensified, which is because the buoyancy convection plays a dominant role and bulk fluid flow from hot wall to cold wall in the free surface of liquid layers. In addition, the spatiotemporal evolution analysis has been carried out to conclude the rule of the temperature field destabilization in the transition process.     

Elastic convection in vibrated viscoplastic fluids

We observe a new type of behavior in a shear-thinning yield stress fluid: freestanding convection rolls driven by vertical oscillation. The convection occurs without the constraint of container boundaries, yet the diameter of the rolls is spontaneously selected for a wide range of parameters. The transition to the convecting state occurs without hysteresis when the amplitude of the plate acceleration exceeds a critical value. We find that a nondimensional stress, the stress due to the inertia of the fluid normalized by the yield stress, governs the onset of the convective motion.     

竖壁传热对方腔内Benard对流的影响

本文采用具有QUICK差分格式的SIMPLE算法对边界竖壁传热的方腔内空气Benard对流进行了数值计算,根据计算结果探讨了竖壁传热对Benard对流的影响.计算表明,在所考虑的几何和物理条件下,所有竖壁绝热时,腔内流体形成平行与短轴的多个涡卷;竖壁存在传热时,腔内流体形成平行于长轴的两个涡卷,并且平行于长轴竖壁的传热热流方向相反时,涡卷的旋转方向也相反;垂直于长轴蛏壁的传热对近壁附近的流动有一定影响.     

Three-dimensional absolute and convective instabilities in mixed convection of a viscoelastic fluid through a porous medium

By using the mathematical formalism of absolute and convective instabilities we study the nature of unstable three-dimensional disturbances of viscoelastic flow convection in a porous medium with horizontal through-flow and vertical temperature gradient. Temporal stability analysis reveals that among three-dimensional (3D) modes the pure down-stream transverse rolls are favored for the onset of convection. In addition, by considering a spatiotemporal stability approach we found that all unstable 3D modes are convectively unstable except the transverse rolls which may experience a transition to absolute instability. The combined influence of through-flow and elastic parameters on the absolute instability threshold, wave number and frequency is then determined, and results are compared to those of a Newtonian fluid.