Convective State Research Articles

Low-frequency oscillations in narrow vibrated granular systems

We present simulations and a theoretical treatment of vertically vibrated granular media. The systems considered are confined in narrow quasi-two-dimensional and quasi-one-dimensional (column) geometries, where the vertical extension of the container is much larger than both horizontal lengths. The additional geometric constraint present in the column setup frustrates the convection state that is normally observed in wider geometries. This makes it possible to study collective oscillations of the grains with a characteristic frequency that is much lower than the frequency of energy injection. The frequency and amplitude of these oscillations are studied as a function of the energy input parameters and the size of the container. We observe that, in the quasi-two-dimensional setup, low-frequency oscillations are present even in the convective regime. This suggests that they may play a significant role in the transition from a density inverted state to convection. Two models are also presented; the first one, based on Cauchy's equations, is able to predict with high accuracy the frequency of the particles' collective motion. This first principles model requires a single input parameter, i.e. the centre of mass of the system. The model shows that a sufficient condition for the existence of the low-frequency mode is an inverted density profile with distinct low and high density regions, a condition that may apply to other systems too. The second, simpler model just assumes an harmonic oscillator like behaviour and, using thermodynamic arguments, is also able to reproduce the observed frequencies with high accuracy.

Relationships between the large‐scale atmosphere and the small‐scale convective state for Darwin, Australia

A persistent problem for numerical weather and climate models is the representation of tropical convective precipitation which for the most part occurs on spatial and temporal scales too small and too short to be explicitly resolved. Given that model parameterizations represent this subgrid convection as a function of the large‐scale atmospheric state, an understanding of the strongest relationships between the two scales is needed. This study introduces a method to create two concurrent long‐term data sets that describe both the large‐scale atmosphere and the characteristics of the small‐scale convection. Important relationships between these two scales are then investigated. It is found that convective precipitation, through convective precipitation area, has the strongest relationship with dynamical variables such as moisture convergence and vertical velocity at midlevels. The magnitude of the fluctuations of convective strength about the mean is found to be anticorrelated with the strength of the large‐scale variables, indicating a more stochastic behavior of tropical convection in weakly than strongly forced regimes, respectively. Atmospheric stability related variables are not found to be positively related to either convective precipitation area or convective precipitation intensity, which is often an assumption made in convective parameterization. On the contrary, in a more unstable atmosphere, there is lower convective precipitation.

Combined Spectral-Perturbation Approach for Systematic Mode Selection in Thermal Convection

A nonlinear spectral approach is proposed to simulate the post critical convective state for thermogravitational instability in a Newtonian fluid layer heated from below. The spectral methodology consists of expanding the flow and temperature fields periodically along the layer, and using orthonormal shape functions in the transverse direction. The Galerkin projection is then implemented to generate the equations for the expansion coefficients. Since most of the interesting bifurcation picture is close to criticality, a perturbation approach is developed to solve the nonlinear spectral system in the weakly post critical range. To leading order, the Lorenz model is recovered. The problem is also solved using amplitude equations for comparison. The similarity and difference among the three models are emphasized.

A bound on the vertical transport of heat in the ‘ultimate’ state of slippery convection at large Prandtl numbers

AbstractAn upper bound on the rate of vertical heat transport is established in three dimensions for stress-free velocity boundary conditions on horizontally periodic plates. A variation of the background method is implemented that allows negative values of the quadratic form to yield ‘small’ ($O\left(1/ \mathit{Pr}\right)$) corrections to the subsequent bound. For large (but finite) Prandtl numbers this bound is an improvement over the ‘ultimate’$R{a}^{1/ 2} $scaling and, in the limit of infinite$Pr$, agrees with the bound of$R{a}^{5/ 12} $recently derived in that limit for stress-free boundaries.

FULLY CONVECTIVE MAGNETOROTATIONAL TURBULENCE IN STRATIFIED SHEARING BOXES

We present a numerical study of turbulence and dynamo action in stratified shearing boxes with zero magnetic flux. We assume that the fluid obeys the perfect gas law and has finite (constant) thermal diffusivity. We choose radiative boundary conditions at the vertical boundaries in which the heat flux is propor- tional to the fourth power of the temperature. We compare the results with the corresponding cases in which fixed temperature boundary conditions are applied. The most notable result is that the formation of a fully convective state in which the density is nearly constant as a function of height and the heat is transported to the upper and lower boundaries by overturning motions is robust and persists even in cases with radiative boundary conditions. Interestingly, in the convective regime, although the diffusive transport is negligible the mean stratification does not relax to an adiabatic state.

Mixed convection and role of multiple solutions in lid-driven trapezoidal enclosures

This paper analyzes probable steady state flow structures and temperature patterns that may evolve during mixed convection within a lid-driven trapezoidal enclosure with cold top wall and hot bottom wall as the speed of moving lid varies with respect to the intensity of imposed temperature gradients. In this regard, a Grashof (Gr)–Reynolds (Re)–Prandtl (Pr) number formulation has been used to induce varying contributions from moving lid compared to that from imposed thermal gradients, where Grashof number has been varied from 103 to 105 at Re=1 and 100 for three different fluids of Pr=0.015, 0.7 and 10. Simulations have been performed for two different scenarios of isothermal (case 1) and non-isothermal (case 2) bottom wall with inclination angle of the side wall being kept at 45o. It has been found that non-isothermal bottom wall (case 2) leads to multiple steady states in either natural convection dominated regime (Gr/Re2≫1) or mixed convection regime (Gr/Re2∼O(1)) in convection dominated heat transport regime (Pr×Re≳1). Number of steady states are observed to be more in natural convection dominated regime at Re=1. The flow structures of various steady states are found to be crucial to achieve higher heat transfer rates for non-isothermal bottom wall.

Three-dimensional convective interactions in an inclined longitudinal air layer

The results of a three-dimensional numerical simulation of thermal-gravitational convection for an arbitrary direction of the gravity force are presented. The calculations were carried out for a rectangular domain with the solid-wall aspect ratio 4:0.5:1. The cavity filled with air was heated from below. The convection regime was laminar with Rayleigh numbers Ra = 103–105. The cavity was gradually turned about the short side in different directions in the range 0–90° to study how the initial conditions affect the convection. The average heat transfer characteristics and the spatial flow patterns are presented. A comparison with two-dimensional calculations is given. The conditions of the occurrence of a hysteresis in the steady state of convection are found, a regime map is constructed, and the specific features of the interaction of heat fluxes are described.

A three‐hourly data set of the state of tropical convection based on cloud regimes

Tropical convection is a key driver in the climate system and is often identified using infrared satellite information or precipitation. Satellite‐derived cloud regimes offer an alternative with potentially more informative distinctions between different types of convection. However, current ISCCP cloud regime data sets require visible satellite information and are therefore only available during daytime. We develop a convective regime data set for all three‐hour intervals of the day using ISCCP infrared‐only retrievals. We show that regimes derived in this way capture the essential properties of the original regimes, in particular, when identifying the state of tropical convection. We give examples for potential applications by illustrating the well‐known Madden‐Julian Oscillation and the diurnal cycle of convection in the framework of the newly derived regimes. The high temporal resolution, long record and global coverage of the regimes makes them a suitable tool for large‐scale studies of tropical convection.

Nonlinear mushy-layer convection with chimneys: stability and optimal solute fluxes

AbstractWe model buoyancy-driven convection with chimneys – channels of zero solid fraction – in a mushy layer formed during directional solidification of a binary alloy in two dimensions. A large suite of numerical simulations is combined with scaling analysis in order to study the parametric dependence of the flow. Stability boundaries are calculated for states of finite-amplitude convection with chimneys, which for a narrow domain can be interpreted in terms of a modified Rayleigh number criterion based on the domain width and mushy-layer permeability. For solidification in a wide domain with multiple chimneys, it has previously been hypothesized that the chimney spacing will adjust to optimize the rate of removal of potential energy from the system. For a wide variety of initial liquid concentration conditions, we consider the detailed flow structure in this optimal state and derive scaling laws for how the flow evolves as the strength of convection increases. For moderate mushy-layer Rayleigh numbers these flow properties support a solute flux that increases linearly with Rayleigh number. This behaviour does not persist indefinitely, however, with porosity-dependent flow saturation resulting in sublinear growth of the solute flux for sufficiently large Rayleigh numbers. Finally, we consider the influence of the porosity dependence of permeability, with a cubic function and a Carman–Kozeny permeability yielding qualitatively similar system dynamics and flow profiles for the optimal states.

Detailed Measurements of End-Wall Heat Transfer Coefficients of Square Pin-Fin Heat Sink for LED Lamp at Forced Convective State

The device made of fan and pin-fin heat sink should be a powerful heat sink for LED lamp. This study used transient liquid crystal experimentation to measure the end-wall heat transfer coefficient of linearly arrayed square pin array in the rectangular channel, and discussed the influence of axial spacing on heat transfer. The air was used as operating fluid, and the square pin size was 8 mm (d) × 8 mm (d) × 64 mm (Hf), arrayed in a 240 mm (L) × 120 mm (W) × 64 mm (H) rectangular channel. The relative lateral spacing (XT=ST/d) was set as 3, and the relative axial spacing (XL=SL/d=1.88~5) and the Reynolds number (Re=11047~17937) were changed. Considering the end-wall area, the average Nusselt number with square pin was 1.46~2.58 times of that without square pin, and the square pin array of XL= 3.75 had the maximum end-wall heat transfer gain.

Combined study of evaporation from liquid surface by background oriented schlieren, infrared thermal imaging and numerical simulation

Temperature fields in evaporating liquids are measured by simultaneous use of Background Oriented Schlieren (BOS) technique for the side view and IR thermal imaging for the surface distribution. Good agreement between the two methods is obtained with typical measurement error less than 0.1 K. Two configurations of surface layer are observed: thermocapillary convection state with moving liquid surface and small thermal cells, associated with Marangoni convection, and “cool skin” with negligible velocity at the surface, larger cells and dramatic increase of velocity within 0.1 mm layer beneath the surface. These configurations are shown to be formed in various liquids (water with various degrees of purification, ethanol, butanol, decane, kerosene, glycerine) depending rather on initial conditions and ambient parameters than on the liquid. Water, which has been considered as the liquid without observable Marangoni convection, actually can exhibit both kinds of behavior during the same experimental run. Evaporation is also studied by means of numerical simulations. Separate problemsin air and liquid are considered, with thermal imaging data of surface temperature making the separation possible. It is shown that evaporation rate can be predicted by numerical simulation of the air side with appropriate boundary conditions. Comparison is made with known empirical correlations for Sherwood-Rayleigh relationship. Numerical simulations of water-side problem reveal the issue of velocity boundary conditions at the free surface, determining the structure of surface layer. Flow field similar to observed in the experiments is obtained with special boundary conditions of third kind, presenting a combination of no-slip and surface tension boundary conditions.

Experimental Investigation on Thermo-Magnetic Convection Inside Cavities

This paper presents experimental results on thermo-magnetic convection inside cavities. We examine the flow induced by convective currents inside a cavity with aspect ratio near the unity and the heat transfer rates measurements inside a thin cavity with aspect ratio equal to twelve. The convective unstable currents are formed when a magnetic suspension is subjected to a temperature gradient combined with a gradient of an externally imposed magnetic field. Under these conditions, stratifications in the suspension density and susceptibility are both important effects to the convective motion. We show a comparison between flow patterns of magnetic and gravitational convections. The impact of the presence of a magnetic field on the amount of heat extracted from the system when magnetic and gravitational effects are combined inside the test cell is evaluated. The convection state is largely affected by new instability modes produced by stratification in susceptibility. The experiments reveal that magnetic field enhances the instability in the convective flow leading to a more effective mixing and consequently to a more statistically homogenous temperature distribution inside the test cell. The experimental results allow the validation of the scaling law proposed in a previous theoretical work that has predicted that the Nusselt number scales with the magnetic Rayleigh number to the power of 1/3, in the limit in which magnetic force balances viscous force in the convective flow.

Heat transport by turbulent Rayleigh–Bénard convection for Pr ≃ 0.8 and 3 × 1012 ≲ Ra ≲ 1015: aspect ratio Γ = 0.50

We report on the experimental results for heat-transport measurements, in the form of the Nusselt number Nu, by turbulent Rayleigh–Bénard convection (RBC) in a cylindrical sample of aspect ratio Γ ≡ D/L = 0.50 (D = 1.12 m is the diameter and L = 2.24 m the height). The measurements were made using sulfur hexafluoride at pressures up to 19 bar as the fluid. They are for the Rayleigh-number range 3 × 1012 ≲ Ra ≲ 1015 and for Prandtl numbers Pr between 0.79 and 0.86. For Ra < Ra*1 ≃ 1.4 × 1013 we find Nu = N0 Raγeff with γeff = 0.312 ± 0.002, which is consistent with classical turbulent RBC in a system with laminar boundary layers below the top and above the bottom plate. For Ra*1 < Ra < Ra*2 (with Ra*2 ≃ 5 × 1014) γeff gradually increases up to 0.37 ± 0.01. We argue that above Ra*2 the system is in the ultimate state of convection where the boundary layers, both thermal and kinetic, are also turbulent. Several previous measurements for Γ = 0.50 are re-examined and compared with our results. Some of them show a transition to a state with γeff in the range from 0.37 to 0.40, albeit at values of Ra in the range from 9 × 1010 to 7 × 1011 which is much lower than the present Ra*1 or Ra*2. The nature of the transition found by them is relatively sharp and does not reveal the wide transition range observed in this work. In addition to the results for the genuine Rayleigh–Bénard system, we present measurements for a sample which was not completely sealed; the small openings permitted external currents, imposed by density differences and gravity, to pass through the sample. That system should no longer be regarded as genuine RBC because the externally imposed currents modified the heat transport in a major way. It showed a sudden decrease of γeff from 0.308 for Ra < Rat ≃ 4 × 1013 to 0.25 for larger Ra. A number of possible experimental effects are examined in a sequence of appendices; none of these effects is found to have a significant influence on the measurements.

Convection and reaction in a diffusive boundary layer in a porous medium: Nonlinear dynamics

We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

Dual steady transports of heat and moisture in a vent enclosure with all round states of ambient air

Combined natural convective heat and moisture transports in a moist-air-filled enclosure with four free vent ports are numerically investigated. Four situations of ambient air states, hot and humid (I), hot and arid (II), cold and arid (III), and cold and humid (IV), are taken into consideration. Convective transports of semi-enclosed air, heat and moisture are respectively analyzed using the contours of streamfunction, heatfunction and massfunction, in addition to the isotherms and iso-concentrations. Overall convective heat transfer rate (Nu) and moisture transfer rate (Sh) of the internal concentrated heat and moisture source have been correlated with the thermal Rayleigh number respectively within the domain of the heat transfer driven flows and that of moisture transfer driven flows. When different initial convective flow conditions were imposed in the cases (I) and (IV), dual steady flow states of semi-enclosed heat and moisture convection are observed, and heat and moisture transport potentials can be enhanced or inhibited depending on the flow solution branches. These results can be adopted to guide the design of natural ventilation in the humid regions.

Finite-sample-size effects on convection in mushy layers

AbstractWe report theoretical and experimental investigations of the flow instability responsible for mushy-layer convection with chimneys, drainage channels devoid of solid, during steady-state solidification of aqueous ammonium chloride. Under certain growth conditions a state of steady mushy-layer growth with no flow is unstable to the onset of convection, resulting in the formation of chimneys. We present regime diagrams to quantify the state of the flow as a function of the initial liquid concentration, the porous-medium Rayleigh number, and the sample width. For a given liquid concentration, increasing both the porous-medium Rayleigh number and the sample width drove a transition from a weakly convecting chimney free state to a state of mushy-layer convection with fully developed chimneys. Increasing the concentration ratio stabilized the system and suppressed the formation of chimneys. As the initial liquid concentration increased, onset of convection and formation of chimneys occurred at larger values of the porous-medium Rayleigh number, but the critical cell widths for chimney formation are far less sensitive to the liquid concentration. At the highest liquid concentration, the mushy-layer mode of convection did not occur in the experiment. The formation of multiple chimneys and the morphological transitions between these states are discussed. The experimental results are interpreted in terms of a previous theoretical analysis of finite amplitude convection with chimneys, with a single value of the mushy-layer permeability consistent with the liquid concentrations considered in this study.

Pattern formation in anticonvective systems

Two-layer systems heated from above with buoyancy as the driving force may show a rather paradoxical instability mechanism called anticonvection. This transition from a conductive to a convective state is determined by the interface as well as bulk properties (buoyancy forces) of the two fluids. In this paper, we derive the equations for perturbated fields from the basic hydrodynamic equations. An analytical expression for the control parameter at threshold is presented for a vertically infinitely extended system. Further on, we perform a linear stability analysis of a vertically bounded mercury–water system and compare these results with the vertically infinitely extended system. Finally, we show some three-dimensional simulations of the fully nonlinear equations and the resulting patterns for an anticonvective mercury–water system.

BIFURCATION ANALYSIS OF THE FLOW PATTERNS IN TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION

We investigate the origin of various convective patterns for Prandtl number P = 6.8 (for water at room temperature) using bifurcation diagrams that are constructed using direct numerical simulations (DNS) of Rayleigh–Bénard convection (RBC). Several complex flow patterns resulting from normal bifurcations as well as various instances of "crises" have been observed in the DNS. "Crises" play vital roles in determining various convective flow patterns. After a transition of conduction state to convective roll states, we observe time-periodic and quasiperiodic rolls through Hopf and Neimark–Sacker bifurcations at r ≃ 80 and r ≃ 500 respectively (where r is the normalized Rayleigh number). The system becomes chaotic at r ≃ 750, and the size of the chaotic attractor increases at r ≃ 840 through an "attractor-merging crisis" which results in traveling chaotic rolls. For 846 ≤ r ≤ 849, stable fixed points and a chaotic attractor coexist as a result of an inverse subcritical Hopf bifurcation. Subsequently the chaotic attractor disappears through a "boundary crisis" and only stable fixed points remain. These fixed points later become periodic and chaotic through another set of bifurcations which ultimately leads to turbulence. As a function of Rayleigh number, |W101| ~ (r - 1)0.62 and |θ101| ~ (r - 1)-0.34 (velocity and temperature Fourier coefficient for (1, 0, 1) mode). However the Nusselt number scales as (r - 1)0.33.

Oscillatory states in thermal convection of a paramagnetic fluid in a cubical enclosure subjected to a magnetic field gradient

We report experimental and numerical studies of combined natural and magnetic convection of a paramagnetic fluid inside a cubical enclosure heated from below and cooled from above and subjected to a magnetic field gradient. Values of the magnetic field gradient are in the range 9≤|grad|b(0)|(2)|≤900 T(2)/m for imposed magnetic field strengths in the center of the superconducting magnet bore of 1≤|b(0)|(max)≤10 T. Very good agreement between experiments and simulation is obtained in predicting the integral heat transfer over the entire range of working parameters (i.e., thermal Rayleigh number 1.15×10(5)≤Ra(T)≤8×10(6), Prandtl number 5≤Pr≤700, and magnetization number 0≤γ≤58.5). We present a stability diagram containing three characteristic states: steady, oscillatory (periodic), and turbulent regimes. The oscillatory states are identified for intermediate values of Pr (40≤Pr≤70) and low magnetic field (|b(0)|(max)≤2 T). Turbulent states are generated from initially stable flow and heat transfer regimes in the range of 70≤Pr≤500 for sufficiently strong magnetic field (|b(0)|(max)≥4 T).

811 片面に凹凸を有する鉛直流路内の伝熱流動特性 : 住宅壁に適用した場合の解析結果(G01-2 熱伝達II,G01 熱流体部門)

In order to know the heat transfer and fluid flow characteristics of a vertical channel having grooved pattern in one side, we have carried out a numerical analysis using the commercial CFD code. This system may be used as a wall of house to reduce the electricity consumption of an air conditioner. The side wall is heated by radiation of solar energy and is cooled by natural convection of air. This paper describes fluid flow characteristics of inside channel having grooved pattern which are exposed to radiation heat and are cooled by air. We have analyzed the steady state of natural convection in the vertical channel by using Phoenics code (CHAM Limited). From the results obtained in the numerical analysis, it is found that air inside the channel heated by solar energy. This system have a potential to warm the air in a room, however, it is difficult to establish the flow of warmed air from the vertical channel to the room.