Buoyant Convection Research Articles

Near-Field Optical Microscopy of Defects in Cholesteric Oligomeric Liquid Crystal Films

This paper describes formation of 2-D-hexagonal structures with a periodicity ∼0.5–0.8 μm in the defects of thin films of cholesteric oligomeric liquid crystals prepared by the evaporation of the solvent from the oligomer solution on the substrate. These regular arrays were observed by scanning near-field optical and concurrent atomic force microscopy. The mechanisms considered are both Bénard-Marangoni and buoyancy convections induced by solvent evaporation and air-bubble creation around the condensed water droplets from the air during evaporative cooling. Hexagonal structures prepared by this method can be used in photonic devices for emission enhancement, for instance, in liquid crystal lasers and single photon sources with oligomeric liquid crystal hosts.

The effect of shear convection on diffusion measurements in liquid metals using the foton shear cell

The shear convection in the Foton shear cell was investigated quantitatively and interpreted as an additional diffusion-like mixing. Diffusion experiments were done under 1g and µg (Foton-M2 mission June 2005). Since the measured mean squarediffusiondepth (MSDD) is a linear function of time, the offset represents the additional mass transport (and the averaging effect due to the analysis by Atom Absorption Spectroscopy, AAS). The offset is 1–3% of the MSDD and can be used to eliminate this systematic error. The influence of the liquid’s viscosity on the shear convection is discussed, using a simple fluid dynamical model. The absence of buoyancy convection in 1g-experiments was shown by comparison with the µg-result.

Diffusion measurements on a liquid monotectic alloy PbGa using the shear cell technique under µg in the foton-M2 mission and under 1G

Diffusion experiments of a liquid monotectic alloy PbGa were performed under 1g-conditions at 623, 773 and 903K, and under µg-conditions at 903K. As a measurement tool the shear cell specially designed for Russian satellite Foton missions within the AGAT-furnace was used to have a homogenization time before the diffusion and to avoid the influence of decomposition into two liquid phases during cooling-down. The experiment type was diffusion from a thick layer of PbGa5at% into pure Pb. The liquid sample in the capillary was pressurized using a reservoir system in order to minimize Marangoni convection. In 1g-experiments the diffusion axis was arranged vertically and the sample was set such that the density increases monotonously parallel to the gravity vector in order to suppress buoyancy convection. Four experiments were performed simultaneously for each set-up. The µg-experiment was performed in the AGAT facility during the Foton-M2 mission (June 2005) where one capillary was assigned for the PbGa-Pb experiment (PbGa was containing an enriched Pb-isotope tracer). The concentration profiles were obtained by AAS (1g) and by ICP-MS (µg). The diffusion coefficients were evaluated by fitting with the thick layer solution. For the evaluation a correction method was used for the shear convection and the averaging effect inside each cell. As a result, the obtained concentration curves agreed well with the fitting function. The reproducibility of the diffusion coefficients among four parallel 1g-experiments was good with a standard deviation among four capillaries smaller than 5.5% including the standard temperature deviation. The diffusion coefficients agreed well between 1g- and µg-experiments. The temperature dependence of the diffusion coefficients could be fitted well to a power law with an exponent about 2.4. From these results we conclude that the 1g-experimental method in this study for diffusion measurement is effective also for monotectic systems.

Three-dimensional modelling of melt flow and segregation during Czochralski growth of Ge xSi 1− x single crystals

A series of unsteady three-dimensional (3-D) numerical simulations were carried out to examine the flow field and the radial segregation of silicon (Si) in a Ge x Si 1− x melt during Czochralski (Cz) process. In addition to the gravity driven natural convection (buoyant convection), the effect of convection driven by surface tension on the free surface of the melt was included in the model, by considering thermal, as well as solutal Marangoni convection. The concentration and flow fields during crystal growth are presented for several temperature differences ( Δ T ) , driving buoyant and Marangoni convection. It was found that the maximum silicon concentration difference at the growth interface decreases as temperature difference increases due to higher flow velocities in the vicinity of the interface. However, temporal fluctuations of Si concentration at the interface increase at higher temperature differences. The effects of aspect ratio ( A r ) were also considered in the model. It was found that the radial segregation of Si at the crystal-melt interface improves as the aspect ratio of the melt in the crucible decreases.

Buoyancy convection in cylindrical conducting melt with low Grashof number under uniform static magnetic field

Damping of convection is key in the precise measurement of a diffusion coefficient in melt, and applying a static magnetic field to the melt is a promising method of realizing damping in electrically conducting melt such as a semiconductor and metal. Convection behavior in a melt with a low Grashoff number under a uniform static magnetic field was calculated on the basis of the finite element method. Using the results, the specimen geometry and the direction of the applied magnetic field in diffusion experiments with a diffusion-couple method were evaluated by the numerical simulation.

The effect of crystal rotation direction on the thermal and velocity fields of a Czochralski system with a low Prandtl number melt

The purpose of this study is to understand the effect of crystal co- and counter-rotation on the thermal and velocity fields of a Czochralski (Cz) melt in a large crucible. The physical modeling of the Cz system was performed using Wood's metal, which has a similar Prandtl ( Pr) number (=0.019) with Si melt and a low melting temperature (70 °C). The velocities and temperatures in a large crucible with 800 mm diameter were measured using an incorporated magnetic probe and thermocouples, respectively. The rate of crystal rotation affects the temperature and velocity fields. Without crystal rotation, the maximum thermal fluctuation region is located under the crystal due to buoyancy convection. With increasing crystal rotations rate, however, the maximum thermal fluctuation region migrates toward the crucible sidewall. When the rate of crystal counter-rotation is increased, the azimuthal velocities decrease and the thermal fluctuations are reduced at the edge of the crystal. With increasing crystal co-rotation rate, however, the azimuthal velocities increase considerably and the temperature fluctuations remain strongly at the edge of the crystal. The results of 3-D numerical simulations using the k– ε turbulent model are well in agreement with the experimental results.

Influences of pressure on reduced-gravity combustion of 1-propanol droplets

Reduced-gravity experiments on combustion of individual 1-propanol droplets with initial diameters of about 1 mm were conducted in air at standard temperature and with pressures ranging from 0.1 MPa to 1.0 MPa. Flames at 0.1 MPa were non-sooting with blue coloring during most of the combustion process. At higher pressures, flames exhibited significant amounts of soot during most of the combustion history. Flames were also non-spherical at elevated pressure, which is likely a result of the increased importance of buoyant convection at elevated pressure. Droplet burning rates increased as the ambient pressure was increased. Empirical correlations indicate that buoyant convection did not significantly influence droplet burning rates. Calculations indicate, however, that increasing the ambient pressure increased the liquid temperature, which decreased the liquid density and enthalpy of vaporization, leading to burning rate increases that are consistent with experimental results. Calculations also indicate that absorption of water into droplets was not significant in the experiments.

Transient buoyant convection in a 45°‐inclined enclosure heated and cooled on adjacent walls

PurposeTo conduct a numerical study on two‐dimensional, transient, buoyant flow inside an air‐filled 45°‐inclined enclosure, heated and cooled on adjacent walls.Design/methodology/approachThe governing equations obtained through the stream function‐vorticity formulation are solved using finite differences. Flow characteristics have been investigated for an aspect ratio of 1. Calculations are carried out for the Rayleigh numbers in the range of 103≤Ra≤5×107.FindingsWith the increasing Rayleigh number, four distinct flow regimes were identified based on the time variations of the mid‐point stream function and the mean Nusselt number at the heated wall as well as those of flow and temperature fields: steady flow with symmetric two cells at low Ra; steady flow with asymmetric two cells at lower moderate Ra; oscillatory flow with the periodic nature at upper moderate Ra; and oscillatory flow in chaotic nature at higher Ra range.Originality/valueThe distinct flow regimes are observed only at ϕ=45°; a small deviation of the tilting angle from ϕ=45° results in the disappearance of the distinction.

Critical phenomena in atmospheric precipitation

Critical phenomena near continuous phase transitions are typically observed on the scale of wavelengths of visible light[1]. Here we report similar phenomena for atmospheric precipitation on scales of tens of kilometers. Our observations have important implications not only for meteorology but also for the interpretation of self-organized criticality (SOC) in terms of absorbing-state phase transitions, where feedback mechanisms between order- and tuning-parameter lead to criticality.[2] While numerically the corresponding phase transitions have been studied,[3, 4] we characterise for the first time a physical system believed to display SOC[5] in terms of its underlying phase transition. In meteorology the term quasi-equilibrium (QE)[6] refers to a state towards which the atmosphere is driven by slow large-scale processes and rapid convective buoyancy release. We present evidence here that QE, postulated two decades earlier than SOC[7], is associated with the critical point of a continuous phase transition and is thus an instance of SOC.

Bridgman-Stockbarger Growth of Binary Alloyed Semiconductor Crystals with Steady Magnetic Fields

Single crystals of alloyed compound semiconductor crystals such as gallium‐aluminum‐antimonide are needed for optoelectronic devices. These crystals are solidified from a solution of molten gallium‐antimonide and aluminum‐antimonide in a Bridgman‐Stockbarger furnace. During the growth of alloyed semiconductor crystals, the solute’s concentration is not small so that the density differences in the melt are very large. These compositional variations drive compositionally driven buoyant convection, or solutal convection, in addition to thermally driven buoyant convection. These buoyant convections drive convective species transport, which produce nonuniformities in the concentration in both the melt and the crystal. A numerical model is presented for the unsteady transport for the growth of alloyed semiconductor crystals during the vertical Bridgman‐Stockbarger process with a steady axial magnetic field. Predictions of alloy concentration in the crystal and in the melt at several different stages during crystal growth are presented.

Two-dimensional numerical simulations of Marangoni–Bénard instabilities during liquid–liquid mass transfer in a vertical gap

Two-dimensional (2D) simulations of isothermal liquid–liquid mass transfer subject to surface tension- and buoyancy-driven hydrodynamic instabilities have been carried out. Simulation is based on the numerical solution of 2D equations of momentum and mass transport, using a combination of finite difference and finite volume methods. Two different cases have been considered: (1) buoyancy stable mass transfer, only surface tension-driven convection occurs; (2) surface tension-driven instability superseeded by buoyant convection. The faster attenuation of mass transfer coefficients in buoyancy stable situations is attributed to the merging of convection cells leading to a reduction in the number of renewal zones along the interface. Concentration profiles next to the interface reveal the diffusional nature of the mass transfer in the immediate interfacial neighbourhood.

Convective damping of buoyancy anomalies and its effect on lapse rates in the tropical lower troposphere

Abstract. In regions of the tropics undergoing active deep convection, the variation of lower tropospheric lapse rates (2.0 km to 5.2 km) with height is inconsistent with both reversible moist adiabatic and pseudoadiabatic assumptions. It is argued that this anomalous behavior arises from the tendency for the divergence of a convective buoyancy anomaly to be primarily offset by the collective divergence of other updrafts and downdrafts within one Rossby radius of deformation. Ordinarily, convective mass flux divergences are at least partially offset by an induced radiative mass flux divergence in the background atmosphere. If mass flux divergences from lower tropospheric convection are balanced mainly by those of neighboring updrafts/downdrafts, it would force the vertical clear sky radiative mass flux of the background atmosphere to be weakly dependent on height. This is observed at several radiosonde locations in the Western Tropical Pacific between 2.0 and the 5.2 km melting level. At tropical locations where SST's exceed 27°C over a region whose horizontal extent exceeds the local Rossby radius, this condition on the vertical variation of the background radiative mass flux partially constrains the range of physically allowed mean temperature and moisture profiles in the lower troposphere.

Simulation of transport processes during Czochralski growth of YAG crystals

Numerical simulation of transport phenomena in the solid, liquid and gaseous phases of a Czochralski process is reported. The Czochralski domain comprises a YAG melt, crystal and gas within the enclosure. The mathematical model is axisymmetric in space and unsteady in time. The governing equations are those of conservation of mass, momentum and energy. The simulation includes a bulk radiation model to account for the semi-transparency of the YAG melt and the growing crystal. Results have been obtained for thermal boundary conditions that do not change with time, a constant diameter growing crystal for which the pull velocity changes with time. Buoyant convection in the melt is seen to produce a melt–crystal interface that is convex into the melt. When the crystal is given rotation, centrifugal forces drive a clockwise roll that counteracts the thermally driven motion. At a specific rotation rate, the interface shape changes from convex to concave. The critical rotation rate for interface inversion has been obtained in the study as a function of the radius ratio and the aspect ratio. Marangoni convection has an effect of strengthening buoyancy-driven flow. Unsteadiness in the YAG melt is observed at high Grashof numbers. The introduction of crystal rotation at high Grashof numbers is found to change the periodic oscillations to aperiodic high amplitude fluctuations. Simulation that includes the crystal and the gas phases along with the melt reveals the possibility of superheating of the crystal beyond its melting point. Similarly, the possibility of subcooling of the melt near the crystal edge below the melting point of YAG is indicated for a certain range of parameters. The internal absorption of radiation in the crystal increases thermal losses from the melt, steepens temperature gradients and is found to create deeply convex melt–crystal interface towards the melt. Additionally, the bulk of the melt is found to become cooler. Scattering is found to have an opposite, though minor influence on the melt–crystal interface, strength of natural convection and pull velocity.

Transport and chemical transformations influenced by shallow cumulus over land

Abstract. The distribution and evolution of reactive species in a boundary layer characterized by the presence of shallow cumulus over land is studied by means of two large-eddy simulation models: the NCAR and WUR codes. The study focuses on two physical processes that can influence the chemistry: the enhancement of the vertical transport by the buoyant convection associated with cloud formation and the perturbation of the photolysis rates below, in and above the clouds. It is shown that the dilution of the reactant mixing ratio caused by the deepening of the atmospheric boundary layer is an important process and that it can decrease reactant mixing ratios by 10 to 50 percent compared to very similar conditions but with no cloud formation. Additionally, clouds transport chemical species to higher elevations in the boundary layer compared to the case with no clouds which influences the reactant mixing ratios of the nocturnal residual layers following the collapse of the daytime boundary layer. Estimates of the rate of reactant transport based on the calculation of the integrated flux divergence range from to −0.2 ppb hr-1 to −1 ppb hr-1, indicating a net loss of sub-cloud layer air transported into the cloud layer. A comparison of this flux to a parameterized mass flux shows good agreement in mid-cloud, but at cloud base the parameterization underestimates the mass flux. Scattering of radiation by cloud drops perturbs photolysis rates. It is found that these perturbed photolysis rates substantially (10–40%) affect mixing ratios locally (spatially and temporally), but have little effect on mixing ratios averaged over space and time. We find that the ultraviolet radiance perturbation becomes more important for chemical transformations that react with a similar order time scale as the turbulent transport in clouds. Finally, the detailed intercomparison of the LES results shows very good agreement between the two codes when considering the evolution of the reactant mean, flux and (co-)variance vertical profiles.

A Cloud-Base Quasi-Balance Constraint for Parameterized Convection: Application to the Kain–Fritsch Cumulus Scheme

Abstract A quasi balance with respect to parcel buoyancy at cloud base between destabilizing processes and convection is imposed as a constraint on convective cloud-base mass flux in a modified version of the Kain–Fritsch cumulus parameterization. Supporting evidence is presented for this treatment, showing a cloud-base quasi balance (CBQ) on a time scale of approximately 1–3 h in explicit simulations of deep convection over the U.S. Great Plains and over the tropical Pacific Ocean with the Naval Research Laboratory’s Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS).1 With the exception of the smaller of two convective events in the Great Plains simulation, a CBQ is still observed upon restriction of the data analysis to instances where the available buoyant energy (ABE) exceeds a threshold value of 1000 J kg−1. This observation is consistent with the view that feedbacks between convection and cloud-base parcel buoyancy can control the rate of convection on shorter time scales than those associated with the elimination of buoyant energy and supports the addition of a CBQ constraint to the Kain–Fritsch mass-flux closure. Tests of the modified Kain–Fritsch scheme in single-column-model simulations based on the explicit three-dimensional simulations show a significant improvement in the representation of the main convective episodes, with a greater amount of convective rainfall. The performance of the scheme in COAMPS precipitation forecast experiments over the continental United States is also investigated. Improvements are obtained with the modified scheme in skill scores for middle to high rainfall rates.

Development of new and validation of existing convection correlations for rooms with displacement ventilation systems

Building airflow, thermal, and contaminant simulation programs need accurate models for the surface convective boundary conditions. This is, especially, the case for displacement ventilation (DV) systems, where convective buoyancy forces at room surfaces significantly affect the airflow pattern and temperature and contaminant distributions. Nevertheless, for DV, as a relatively new ventilation system, the convective correlations are adopted from more traditional mixing ventilation correlations, or non-existent. In this study, the existing recommended correlations are validated in a full-scale experimental facility representing an office space. In addition, new correlations are developed for floor surfaces because the current literature does not provide necessary correlations, even though, the floor surface is responsible for >50% of the total convective heat transfer at the envelope. The convective correlations are typically functions of a surface-air temperature difference, airflow parameters, and characteristic room dimensions. Validation results show that the floor convection correlations expressed as a function of volume flow rate are much stronger than the correlations expressed as a function of a temperature difference between the surface and local air. Consequently, the new convection correlation for floor surfaces is a function of the number of hourly room air changes (ACH). This correlation also takes into account buoyant effects from local floor heat patches. Experimental data show that the existing correlation can be successfully applied to vertical and ceiling surfaces in spaces with DV diffuser(s). Overall, the new and the existing convection correlations are tabulated for use in building simulation programs, such as annual energy analyses or computational fluid dynamics.

Numerical Model for Bridgman-Stockbarger Crystal Growth with a Magnetic Field

This paper presents a model for the unsteady species transport for the growth of doped semiconductor crystals during the vertical Bridgman‐Stockbarger process with a steady axial magnetic field. This dilute species transport depends on the convective and diffusive species transport of the dopant. This convective species transport is driven by buoyant convection in the melt, which produces compositional nonuniformities in both the melt and the crystal. This transient model predicts the distribution of species in the entire crystal grown in a steady axial magnetic field. The present study presents results of concentration in the crystal and in the melt at several different stages during crystal growth. I. Introduction D URING crystal growth without a magnetic field or with a weak magnetic field, turbulent or oscillatory melt motions can produce undesirable spatial oscillations of the concentration, or microsegregation, in the crystal. 1 Turbulent or oscillatory melt motions lead to fluctuations in the heat transfer across the growth interface from the melt to the crystal. Because the local rate of crystallization depends on the balance between the local heat fluxes in the melt and the crystal, fluctuations in the heat flux from the melt create fluctuations in the local growth rate, which create microsegregation. A moderate magnetic field can be used to create a body force that provides an electromagnetic (EM) damping of the melt motion can to eliminate oscillations in the melt motion and thus in the concentration of the crystal. Unfortunately, the elimination of mixing and a moderate or strong EM damping of the residual melt motion can lead to a large variation of the crystal’s composition in the direction perpendicular to the growth direction (radial macrosegregation). On the other hand, if the magnetic field strength is so strong that the melt motion is reduced sufficiently so that it has no effect on the composition in the crystal, then this diffusion-controlled species transport can produce a radially and axially uniform composition in the crystal grown. 2 To achieve diffusion-controlled species trans�

Two-dimensional density currents in a confined basin

We present new experimental results on the mechanisms through which steady two-dimensional density currents lead to the formation of a stratification in a closed basin. A motivation for this work is to test the underlying assumptions in a diffusive “filling box” model that describes the oceanic thermohaline circulation (Hughes, G.O. and Griffiths, R.W., A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions, Ocean Modeling, 2005, submitted.). In particular, they hypothesized that a non-uniform upwelling velocity is due to weak along-slope entrainment in density currents associated with a large horizontal entrainment ratio of E eq ∼ 0.1. We experimentally measure the relationship between the along-slope entrainment ratio, E, of a density current to the horizontal entrainment ratio, E eq, of an equivalent vertical plume. The along-slope entrainment ratios show the same quantitative decrease with slope as observed by Ellison and Turner (Ellison, T.H. and Turner, J.S., Turbulent entrainment in stratified flows, J. Fluid Mech., 1959, 6, 423–448.), whereas the horizontal entrainment ratio E eq appears to asymptote to a value of E eq = 0.08 at low slopes. Using the measured values of E eq we show that two-dimensional density currents drive circulations that are in good agreement with the two-dimensional filling box model of Baines and Turner (Baines, W.D. and Turner, J.S., Turbulent buoyant convection from a source in a confined region, J. Fluid. Mech., 1969, 37, 51–80.). We find that the vertical velocities of density fronts collapse onto their theoretical prediction that U =-2−2/3 B 1/3 E eq 2/3 (H/R) ζ, where U is the velocity, H the depth, B the buoyancy flux, R the basin width, E eq the horizontal entrainment ratio and ζ = z/H the dimensionless depth. The density profiles are well fitted with Δ = 2−1/3 B 2/3 E eq −2/3 H -1 [ln(ζ ) + τ ], where τ is the dimensionless time. Finally, we provide a simple example of a diffusive filling box model, where we show how the density stratification of the deep Caribbean waters (below 1850 m depth) can be described by a balance between a steady two-dimensional entraining density current and vertical diffusion in a triangular basin.

Capture of particles of dust by convective flow

Interaction of particles of dust with vortex convective flows is under theoretical consideration. It is assumed that the volume fraction of solid phase is small, variations of density due to nonuniform distribution of particles and those caused by temperature nonisothermality of medium are comparable. Equations for the description of thermal buoyancy convection of a dusty medium are developed in the framework of the generalized Boussinesq approximation taking into account finite velocity of particle sedimentation. The capture of a cloud of dust particles by a vortex convective flow is considered, general criterion for the formation of such a cloud is obtained. The peculiarities of a steady state in the form of a dust cloud and backward influence of the solid phase on the carrier flow are studied in detail for a vertical layer heated from the sidewalls. It is shown that in the case, when this backward influence is essential, a hysteresis behavior is possible. The stability analysis of the steady state is performed. It turns out that there is a narrow range of governing parameters, in which such a steady state is stable.

Thermal convection in liquid bridges with curved free surfaces: Benchmark of numerical solutions

Numerical solutions of thermocapillary and buoyant convection in liquid bridges with curved free interfaces are benchmarked. The results were presented in the Second International Marangoni Association, IMA-2 Congress, Brussels, 2004. Only small Prandtl number fluids ( Pr ≈ 10 - 2 ) are considered. The study consists of two parts: (1) investigation of axisymmetric steady states in curved liquid bridges in a wide range of contact angles and different gravity conditions; (2) calculation of critical Reynolds numbers for the first stationary bifurcation with straight and concave interfaces. The numerical simulations were performed for two aspect ratios Γ = 1 and 1.2. Nine research groups participated in this effort and are thus considered co-authors of the present manuscript. Because all the groups employed body-fitted curvilinear coordinates for solving the Navier–Stokes and energy equations a brief description of this method is presented.