Convective State Research Articles

Influence of number of simulated particles on DSMC modeling of micro-scale Rayleigh–Bénard flows

Two-dimensional micro-scale Rayleigh–Bénard flows are investigated numerically using direct simulation Monte Carlo method. An enclosure of length-to-height aspect ratio of AS = 4 is taken to explore the influence of initial setting of simulated molecules. The simulation domain is divided into 81 × 21 sampling cells and the range of Rayleigh number from 3000 to 10 000 corresponds to the convection state. Cases of 8, 10, 12, 14, 16 and 24 simulated particles in each collision cell are examined. It is shown that flow patterns with three-, four- or five-roll modes may appear depending on the number of simulated particles.

A convective turbulent state that spatially orders upon increased drive

A nematic liquid crystal in a slot electrohydrodynamic convection geometry exhibits, with increasing drive, enhanced noisy high-dimensional flow fluctuations and weakened low-dimensional ordered flow, reaching a turbulent state with only short range velocity correlations in space and time for sufficiently high voltage. Upon additional voltage increase this disorganized turbulent state develops spatial order with extended temporal correlations, in the form of a one-dimensional periodic array of turbulent jet-like plumes along the slot. This array becomes more robust with reduced disorder and faster fluctuations as the drive is further increased. Remarkably this ordering depends sensitively on liquid crystal alignment conditions on the surface of the slot cell.

Experimental study of the onset of the 3D oscillatory thermocapillary convection around a single air or vapor bubble.: Influence on heat transfer

In a first section, Marangoni convection induced by a temperature gradient is studied around a single air bubble. The bubble is introduced under a downward facing heating element into a liquid layer heated from upper and cooled from below (silicone oils Pr = 16.7 and Pr = 228 or FC-72, Pr = 12.3). In this configuration stationary thermocapillary convection can be followed by the oscillatory convection. Firstly the 3D oscillatory thermocapillary convection is presented for a silicone oil ( Pr = 16.7). Then, the critical threshold between the stationary state and the first oscillatory mode is determined. The influence of the liquid kind on this threshold is presented for one layer height. Moreover, other parameters (horizontal wall temperature, layer height) are tested for one liquid. At least, we consider heat transfer induced by this convection, and we discuss the results versus the convection state. The second section of this paper concerns preliminary results on Marangoni convection with boiling around a single vapor bubble growing under a downward facing heating element into a subcooled liquid (FC-72). The oscillatory thermocapillary convection is observed. It occurs during the growth from a critical bubble radius. The influence of the subcooling level on its occurrence threshold is shown.

Gain-scheduled controller for the suppression of convection at high Rayleigh number

Recent studies in the feedback control of Rayleigh-Bénard convection indicate that one can sustain the no-motion state at a moderate supercritical Rayleigh number (Ra) using only proportional compensation. However, stabilization occurs at a much higher Rayleigh number using linear-quadratic-Gaussian (LQG) control synthesis. The restriction is that the convection model is linear. In this paper, we show that a comparable degree of stabilization is achievable for a fully nonlinear convection state. The process is demonstrated in two stages using a fully nonlinear, 3D Boussinseq model, compensated by a reduced-order LOQ controller and a gain-schedule table. In the first stage a fully-developed convective state is suppressed through the control action at a moderate supercritical Ra. After the residual convection decays to a sufficiently small amplitude, in the second stage, we increase the Ra by a large step and switch the compensator gains using the gain-schedule table. During this change the control action is in place. Our nonlinear simulation results suggest that the nonlinear system can be stabilized to the limit predicted by the linear analysis. The simulation shows that the large Ra jump induces a large transient temperature in the conductive component, which appears to have very small impact on the stabilization.

Axisymmetric convective states of pure and binary liquids enclosed in a vertical cylinder and boundary conditions’ influence thereupon

The high Rayleigh number (Ra) axisymmetric convection regimes of Pr=1 pure and (Le=0.1, Ψ=−0.2) binary liquids are numerically investigated and compared. The fluids are enclosed in a vertical cylinder of aspect ratio height∕radius=2 and heated from below, with either no-slip or free-slip kinematic lateral boundary conditions. Branches of solutions and transitions between states that occur as Ra is varied up to O(105) are given, along with a description of the encountered bifurcations. When a free-slip condition is imposed along the circumference of the cell, pure fluid and binary liquid stationary flows are found to become identical at high Ra, an often reported feature. When the lateral boundary condition is set to no-slip, the high Ra steady flows of pure and binary liquid, although very similar, undergo different bifurcations. This is related with a locally quasiquiescent region present in both cases, the stability of which controls the flow regime in the whole fluid layer. A branch of resulting oscillatory states thus does not appear in the bifurcation diagram of the binary liquid.

Magnetotail response to prolonged southward IMF Bz intervals: Loading, unloading, and continuous magnetospheric dissipation

The response of the Earth's magnetotail to prolonged southward interplanetary magnetic field (IMF) has been determined for the three Geotail magnetotail seasons from November to April, 1999–2002. We examine the total magnetotail pressure PT,tail = B2/2μ0 + NikTi because variations should be similar in this parameter in the lobes and in the plasma sheet. We found 13 events when IMF Bz remained southward for 8 hours or longer and Geotail was located within the magnetotail farther than 10 RE downstream. All 13 events were subdivided into separate intervals characterized as (1) loading, if the tail total pressure increased more than 100%; (2) unloading, if the total pressure decreased by more than 50%; and (3) what we term here continuous magnetospheric dissipation (CMD), if the tail total pressure increased by less than 100% and/or decreased less than 50% during the entire mode interval. In total, 37 loading, 37 unloading, and 28 CMD events were found. The plasma sheet magnetic flux transfer rate, ϕEarth ≈ vx · Bz, and plasma bulk velocity has been analyzed to determine the steadiness of the plasma sheet convection. Plasma sheet convection was found to be highly disturbed and intense plasma flows (BBFs and FBs) were observed during all convection states. However, the occurence rate and amplitude of plasma flows distinguish loading‐unloading and continuous dissipation periods from each other. BBFs seem to be more numerous (135) but weaker (about 500 km/s) during continuous dissipation intervals compared with BBFs existing during unloading mode (61 and 660 km/s). Finally, it was found that CMD‐type convection is more likely when the mean southward IMF Bz > −5 nT, while loading‐unloading is more likely when IMF Bz < −5 nT.

Effect of G-jitter on the thermocapillary convection experiment in ISS

Effects of g-jitter on the measurement of dynamic surface deformations (DSD) caused by the oscillatory thermocapillary convection in a liquid bridge have been studied experimentally. A vibration table driven by a piezoelectric actuator is constructed to generate g-jitters of realistic amplitude and frequency spectra. A microimaging displacement meter is used to measure DSD in the presence of g-jitter. It is shown that the natural DSD in the oscillatory state of thermocapillary convection is well separated in the frequency domain from that caused by harmonic and non-harmonic g-jitters. It is concluded that the DSD measurement in the future ISS experiment is feasible even in the presence of g-jitter there.

Application of Hierarchical Process Modelling Strategies to Fuel Cell Systems – Towards a Virtual Fuel Cell Laboratory

AbstractThere is an increasing need for adequate modelling and simulation tools for the design and analysis of fuel cell systems. In the present contribution, a modular modelling strategy is proposed, which is based on network theory for chemical engineering processes.According to this network theory, a fuel cell system is decomposed into elementary units on several hierarchical levels (process unit level, phase level, storage level). After decomposition, the model formulation starts on the storage level: electrochemical source terms were combined with the diffusive and convective transport phenomena and state equations, forming an elementary unit of the phase level. On the phase level several thermodynamic phases (e.g. fluid compartments, electrode backings, catalyst layers, and the membrane electrolyte) are aggregated to a single fuel cell unit. Finally on the top level, the process unit level, single cells or fuel cell stacks are combined with other process units to form a complete process model.This modelling procedure is demonstrated with a simple proton exchange membrane fuel cell system operated with hydrogen and oxygen.

Emergent Anisotropy and Flow Alignment in Viscous Rock

A novel class of nonlinear, visco-elastic rheologies has recently been developed by MUHLHAUS et al. (2002a, b). The theory was originally developed for the simulation of large deformation processes including folding and kinking in multi-layered visco-elastic rock. The orientation of the layer surfaces or slip planes in the context of crystallographic slip is determined by the normal vector the so-called director of these surfaces. Here the model (MUHLHAUS et al., 2002a, b) is generalized to include thermal effects; it is shown that in 2-D steady states the director is given by the gradient of the flow potential. The model is applied to anisotropic simple shear where the directors are initially parallel to the shear direction. The relative effects of textural hardening and thermal softening are demonstrated. We then turn to natural convection and compare the time evolution and approximately steady states of isotropic and anisotropic convection for a Rayleigh number Ra=5.64x10(5) for aspect ratios of the experimental domain of 1 and 2, respectively. The isotropic case has a simple steady-state solution, whereas in the orthotropic convection model patterns evolve continuously in the core of the convection cell, which makes only a near-steady condition possible. This near-steady state condition shows well aligned boundary layers, and the number of convection cells which develop appears to be reduced in the orthotropic case. At the moderate Rayleigh numbers explored here we found only minor influences in the change from aspect ratio one to two in the model domain.

The Influence of Ocean Convection Patterns on High-Latitude Climate Projections

Abstract The mean state and variability of deep convection in the ocean influence the North Atlantic climate. Using an ensemble experiment with a coupled atmosphere–ocean–sea ice model, it is shown that cooling and subdued warming areas can occur over the North Atlantic Ocean and adjacent landmasses under global warming. Different “present-day” convection patterns in the Greenland–Iceland–Norway (GIN) Sea result in different future surface-air temperature changes. At higher latitudes, the more effective positive sea ice feedback increases the likelihood of changes in convection causing a regional cooling that is larger than the warming brought about by the enhanced greenhouse effect. The modeled freshening of deep ocean layers in the North Atlantic in a time period preceding a reorganization of GIN Sea convection is consistent with recent observations. Low-frequency internal variability in the ocean model has relatively little impact on the response patterns.

Oscillatory convection in binary mixtures: Thermodiffusion, solutal buoyancy, and advection

The role of thermodiffusive generation of concentration fluctuations via the Soret effect, their contribution to the buoyancy forces that drive convection, the advective mixing effect of the latter, and the diffusive homogenisation are compared and elucidated for oscillatory convection. Numerically obtained solutions of the field equations in the form of spatially extended relaxed traveling waves, of standing waves, and of the transient growth of standing waves and their transition to traveling waves are discussed as well as spatially localized convective states of traveling waves that are surrounded by the quiescent fluid.

Convective Roll Dynamics in LiquidHe4near the Onset of Convection

We present results of experiments on Rayleigh-Bénard convection in liquid 4He at several temperatures. We show visually that with carefully defined boundary conditions the basic convection state consists of parallel rolls which are aligned in one of two directions, the angle thus defined as being temperature dependent and we attempt to explain this behavior. We also show directly the skew-varicose instability acting on the basic state and correlate it with fluctuations in the temperature difference across the fluid layer.

Wave-number selection by target patterns and sidewalls in Rayleigh-Bénard convection

We present experimental results for patterns of Rayleigh-Bénard convection in a cylindrical container with static sidewall forcing. The fluid used was methanol, with a Prandlt number sigma=7.17 , and the aspect ratio was Gamma identical withR/d approximately 19 ( R is the radius and d the thickness of the fluid layer). In the presence of a small heat input along the sidewall, a sudden jump of the temperature difference DeltaT from below to slightly above a critical value Delta T(c) produced a stable pattern of concentric rolls (a target pattern) with the central roll (the umbilicus) at the center of the cell. A quasistatic increase of epsilon identical withDeltaT/Delta T(c) -1 beyond epsilon(1,c) approximately 0.8 caused the umbilicus of the pattern to move off center. As observed by others, a further quasistatic increase of epsilon up to epsilon=15.6 caused a sequence of transitions at epsilon(i,b) ,i=1,...,8 , each associated with the loss of one convection roll at the umbilicus. Each loss of a roll was preceded by the displacement of the umbilicus away from the center of the cell. After each transition the umbilicus moved back toward but never quite reached the center. With decreasing epsilon new rolls formed at the umbilicus when epsilon was reduced below epsilon(i,a) < epsilon(i,b) . When decreasing epsilon , large umbilicus displacements did not occur. In addition to quantitative measurements of the umbilicus displacement, we determined and analyzed the entire wave-director field of each image. The wave numbers varied in the axial direction, with minima at the umbilicus and at the cell wall and a maximum at a radial position close to 2Gamma/3 . The wave numbers at the maximum showed hysteretic jumps at epsilon(i,b) and epsilon(i,a) , but on average agreed well with the theoretical predictions for the wave numbers selected in the far field of an infinitely extended target pattern. To our knowledge there is as yet no prediction for the wave number selected by the umbilicus itself, or by the cell wall of the finite experimental system.

Thermal convection in monodisperse and bidisperse granular gases: a simulation study.

We present results of a simulation study of inelastic hard disks vibrated in a vertical container. An event-driven molecular dynamics method is developed for studying the onset of convection. Varying the relevant parameters (inelasticity, number of layers at rest, intensity of the gravity) we are able to obtain a qualitative agreement of our results with recent hydrodynamical predictions. Increasing the inelasticity, a first continuous transition from the absence of convection to one convective roll is observed, followed by a discontinuous transition to two convective rolls, with hysteretic behavior. At fixed inelasticity and increasing gravity, a transition from no convection to one roll can be evidenced. If the gravity is further increased, the roll is eventually suppressed. Increasing the number of monolayers the system eventually localizes mostly at the bottom of the box: in this case multiple convective rolls as well as surface waves appear. We analyze the density and temperature fields and study the existence of symmetry breaking in these fields in the direction perpendicular to the injection of energy. We also study a binary mixture of grains with different properties (inelasticity or diameters). The effect of changing the properties of one of the components is analyzed, together with density, temperature, and temperature ratio fields. Finally, the presence of a low fraction of quasielastic impurities is shown to determine a sharp transition between convective and nonconvective steady states.

Multi-mode spatio-temporal instability in non-Boussinesq convection

It is shown that nonlinear (non-Boussinesq) fluid property variations caused by large temperature differences between the walls of a vertical channel are responsible for the appearance of physically distinct types of instability in mixed convection flows: the previously known shear and new buoyancy-induced instabilities. Shear instability dominates the forced convection regimes, while the buoyancy instability prevails in nearly natural convection states. The most challenging situation requiring elaborate theoretical analysis and numerical verification arises in a mixed convection regime where both instabilities compete, forming a wide variety of possible flow patterns. Each of the instabilities is found to undergo the transition from a convective state (when disturbances grow and propagate away from their source) to absolute (when disturbances grow and occupy the complete flow domain). A number of regions in a complete parameter space corresponding to qualitatively different flow scenarios are identified, and accurate boundaries separating them are computed. Various patterns are illustrated by the direct evaluation of the Fourier integrals representing disturbances.

The Convective Instability in a Microemulsion Phase-Change-Material Slurry Layer

In the present experimental study, the stability of Rayleigh-Benard convection has been investigated in rectangular enclosures filled with microemulsion Phase-Change-Material (PCM) slurry. The PCM slurry exhibited a pseudoplastic non-Newtonian fluid behavior. Hysteresis in convection was clearly observed while the PCM were in a solid phase and in phase changing. The critical Rayleigh number decreases with the PCM mass concentration while the PCM is in phase changing. The fluid temperature at the center of the enclosure showed a time-dependent oscillation during the transition from a heat conduction state to a convection state. The maximum Nusselt number has been observed for all of the slurries while the heating plate was controlled at a temperature that most of PCM was in phase changing.

Effect of Inclination on the Convection of Air in a Cubic Enclosure under Both Magnetic and Gravitational Fields with Flow Visualization

Recent development of super-conducting materials at high temperature has got enabled to use a super-conducting magnet of 5-10 Tesla and various new phenomena have been reported. In the present report, convection is considered for air containing oxygen whose magnetic susceptibility is exceptionally large among gases. Air is filled in a cubic enclosure whose one vertical wall is kept at a higher temperature and an opposing wall is cooled at a lower temperature and other four walls are thermally insulated in the presence of a gradient magnetic field produced by a one-turn coil located above the enclosure. A numerical model including the magnetizing force and the gravitational force was developed and numerical computations were carried out for the parameters, Pr = 0.71, Ra = 10 5 -10 6 , y= 0-10 to represent the strength of magnetic field versus the gravitational potential. For example, at Ra = 10 5 the average Nusselt number 4.476 at y= 0 (with no magnetic field) increased to 5.160 at γ= 10. This system was further studied on the effect of inclination with respect to a horizontal axis at the bottom of the hot wall. With an application of a magnetic field, the conduction state heated from above at an inclination angle of 1.5π radians was found to change to a convection state. Flow visualization experiments were further carried out for the same size of a cubic box attached at an outlet of a bore of a super-conducting magnet of 10T with 100 mm diameter. The magnetic field induced the convection for the system heated from above and cooled from below. The computed flow mode agreed well with the experimental one to support the computed results favorably.

A Vapotron Effect Application for Electronic Equipment Cooling

This research is aimed at investigating by experimental means a possible use of the Vapotron Effect for the cooling of electronic devices. The problem deals with a particular kind of subcooled boiling which is able to enhance heat exchange between a non-isothermal finned surface, simulating the packaging of an electronic component, and a refrigerant fluid (water in the case here presented) flowing on it. The experimental set up is first described in detail then employed to perform a number of tests aiming at a full characterization of the pulsatile nature of the phenomenon; the average heat transfer coefficient for the Vapotron Effect in a state of forced convection has been experimentally determined. The experimental tests have shown the existence of a relation that couples temperature trend of water in the cavities between the fins and cycle of events characterising the phenomenon. These results will be applied in the future to the study of more dynamic phenomena. A comparative analysis concerning the thermal performances of the Vapotron Effect concludes the paper.

The Fate of Nonradiative Magnetized Accretion Flows: Magnetically Frustrated Convection

We present a scenario for non-radiative accretion onto the supermassive black hole at the galactic center. Conducting MHD simulations with 1400^3 grid zones that break the axial and reflection symmetries of earlier investigations and extend inward from the Bondi radius, we find a quasi-hydrostatic radial density profile rho propto r^{-0.72} with superadiabatic gradient corresponding to an n~0.72 polytrope. Buoyancy generated by magnetic dissipation is resisted by the same fields so effectively that energy is advected inward: a state of magnetically-frustrated convection. This scenario is consistent with observational constraints on energetics andouter boundary conditions.

Stabilization of two-dimensional Rayleigh–Bénard convection by means of optimal feedback control

We consider the problem of suppressing the Rayleigh–Bénard convection in a finite domain by adjusting the heat flux profile at the bottom of the system while keeping the heat input the same. The appropriate profile of heat flux at the bottom is determined by the optimal feedback control. When most of the convection modes are taken into consideration in the construction of the feedback controller, the suppressed state is found to be stable for all range of Rayleigh number investigated. With the feedback controller constructed by employing only the dominant convection modes, however, there exists a threshold Rayleigh number beyond which a new convective state emerges due to the hydrodynamic instability. The threshold Rayleigh number is found to increase with the number of modes taken in the feedback controller.