Driving Temperature Gradients Research Articles

The entire lifetime of a distinct double-diffusive staircase in crater Lake Nyos, Cameroon

Lake Nyos, a deep crater lake, located in the north-west of Cameroon, was permanently stratified below 50 m depth due to subaquatic sources supplying warm, salty and CO2-enriched water into the deepest reaches. The high CO2 content in these source waters caused the 1986 limnic eruption. The deep inflowing water is denser than the hypolimnetic water and maintains the stability of the water column, which is double-diffusively stratified. During the dry season in Feb 2002, cooling triggered the formation of a double-diffusive (DD) staircase, a sequence of homogeneously mixed layers separated by distinct stable interfaces. The initiation of the staircase was slightly below the permanent chemocline at ~ 50 m depth, from where the staircase expanded vertically in a diffusion-type manner for ~ 750 days to a maximal vertical extension of ~ 37 m. The staircase pattern caused the upward heat fluxes to increase which depleted the driving temperature gradient. Subsequently, the density ratio increased and reduced the upward heat flux divergence until DD progressively weakened and finally the staircase structure eroded. Based on 39 CTD profiles, we describe the DD phenomenon, explain the three distinct phases of this unique DD event, which lasted for ~ 850 days, and discuss the vertical extension of the DD zone in relation to the rates of new layer formation and layer decay. To our knowledge, this is the only observation over the entire lifespan—“from birth to death”—of a DD event in a natural water body.

A graph-theory based directed network feature for thermal anisotropy

The effective thermal conductivity of a granular material varies with the predominant heat transfers direction. The anisotropic effective thermal conductivity is known to be dominated by the microstructure in a dry material. However, no microstructural parameters that are well related to thermal anisotropy have been proposed. After analysing the heat transfer mechanisms at the particle scale, this work constructs new directed weighted thermal networks for both lattice and randomly distributed sphere packings, by considering particles as nodes and local heat transfer paths with thermal resistance as directed edges. With the implementation of graph theory to the directed weighted thermal networks, the shortest preferential heat transfer paths between nodes paired at opposite faces of a sample across the driving temperature gradient direction are identified. Based on the shortest heat transfer paths, a new sample-scale feature named “directed network thermal resistance” is computed for each sample. This new parameter accounts for particle connectivity, interparticle contact orientation and contact quality simultaneously. After computing the effective thermal conductivity of each sample in different directions using a weighted thermal network model, it is found that directed network thermal resistance is inversely proportional to anisotropic effective thermal conductivity.

Experimental Investigation of non‐periodic oscillations in a surface tension driven flow around a bubble

AbstractThermocapillary convection around an air bubble under a heated wall is experimentally investigated under gravitational conditions. The flow is basically studied through temperature fluctuation plots near the bubble periphery, which is subjected to an upward flow driving temperature gradient. This study illuminates the thermocapillary‐buoyancy convective flow behaviour within the regime of non‐periodic oscillations. Moreover, the fluid flow is qualitatively categorized according to the transient behaviour of the thermocapillary vortex boundary line around the bubble using the shadowgraph technique. A low viscous silicone oil as test fluid restricts reaching higher temperature gradients to avoid the formation of undesired vapour bubbles. However, pursuing the experiments under high pressures allowed reaching higher temperature gradients in order to achieve the non‐periodic flow regime. Both periodic and chaotic oscillations of the liquid flow around the bubble were recorded. They were distinguished from each other through the periodicity of the visualized thermocapillary vortex boundary line movements. The recording of temperature fluctuations at positions near the bubble during a time period Δt demonstrated the thermocapillary fluid flow behaviour at different Marangoni‐numbers Mg.

Early-Stage Temperature Gradients in Glazed Spandrels Due to Aesthetical Features to Support Design for Thermal Shock

Investigating thermal breakage of glass panes requires careful analysis of the environmental boundary conditions to determine the expected thermal gradient between the sunlit and shaded parts of the glass. This is particularly critical for glazed spandrels, where an opaque posterior insulation layer normally increases the system’s temperatures. The choice of the spandrel system should also be evaluated against the aesthetical impression that it conveys. The aim of this study is to understand how early design factors, such as aesthetical features like color, are driving temperature gradients in the glazed pane to design for thermal shock. Multiple finite-differences analyses in a quasi-static regime for non-ventilated, single glazed spandrels were conducted in three locations (London, New York and Mumbai). Results were then analyzed via a general linear model in SAS 9.4 and Tuckey post hoc analysis. It was shown that a low absorptance of the back insulation (e.g., light color) can lead to a wide range of possible temperature gradients depending on the glass transparency, with higher values of the thermally induced temperature gradients for more opaque glasses. Conversely, a high absorptance of the insulation layer leads to moderate values of glass temperature gradients, which are not substantially sensitive to the effect of the glass transparency.

Simple advecting structures and the edge of chaos in subcritical tokamak plasmas

In tokamak plasmas, sheared flows perpendicular to the driving temperature gradients can strongly stabilise linear modes. While the system is linearly stable, regimes with persistent nonlinear turbulence may develop, i.e. the system is subcritical. A perturbation with small but finite amplitude may be sufficient to push the plasma into a regime where nonlinear effects are dominant and thus allow sustained turbulence. The minimum threshold for nonlinear instability to be triggered provides a criterion for assessing whether a tokamak is likely to stay in the quiescent (laminar) regime. At the critical amplitude, instead of transitioning to the turbulent regime or decaying to a laminar state, the trajectory will map out the edge of chaos. Surprisingly, a quasi-travelling-wave solution is found as an attractor on this edge manifold. This simple advecting solution is qualitatively similar to, but simpler than, the avalanche-like bursts seen in earlier turbulent simulations and provides an insight into how turbulence is sustained in subcritical plasma systems. For large flow shearing rate, the system is only convectively unstable, and given a localised initial perturbation, will eventually return to a laminar state at a fixed spatial location.

Intrinsic rotation driven by turbulent acceleration

Differential rotation is induced in tokamak plasmas when an underlying symmetry of the governing gyrokinetic-Maxwell system of equations is broken. One such symmetry-breaking mechanism is considered here: the turbulent acceleration of particles along the mean magnetic field. This effect, often referred to as the ‘parallel nonlinearity’, has been implemented in the δf gyrokinetic code stella and used to study the dependence of turbulent momentum transport on the plasma size and on the strength of the turbulence drive. For JET-like parameters with a wide range of driving temperature gradients, the momentum transport induced by the inclusion of turbulent acceleration is similar to or smaller than the ratio of the ion Larmor radius to the plasma minor radius. This low level of momentum transport is explained by demonstrating an additional symmetry that prohibits momentum transport when the turbulence is driven far above marginal stability.

A study of self organized criticality in ion temperature gradient mode driven gyrokinetic turbulence

An investigation on the characteristics of self organized criticality (Soc) in ITG mode driven turbulence is made, with the use of various statistical tools (histograms, power spectra, Hurst exponents estimated with the rescaled range analysis, and the structure function method). For this purpose, local non-linear gyrokinetic simulations of the cyclone base case scenario are performed with the GENE software package. Although most authors concentrate on global simulations, which seem to be a better choice for such an investigation, we use local simulations in an attempt to study the locally underlying mechanisms of Soc. We also study the structural properties of radially extended structures, with several tools (fractal dimension estimate, cluster analysis, and two dimensional autocorrelation function), in order to explore whether they can be characterized as avalanches. We find that, for large enough driving temperature gradients, the local simulations exhibit most of the features of Soc, with the exception of the probability distribution of observables, which show a tail, yet they are not of power-law form. The radial structures have the same radial extent at all temperature gradients examined; radial motion (transport) though appears only at large temperature gradients, in which case the radial structures can be interpreted as avalanches.

Impurity transport in temperature gradient driven turbulence

In the present paper, the transport of impurities driven by trapped electron (TE) mode turbulence is studied. Non-linear (NL) gyrokinetic simulations using the code GENE are compared with results from quasilinear (QL) gyrokinetic simulations and a computationally efficient fluid model. The main focus is on model comparisons for electron temperature gradient driven turbulence regarding the sign of the convective impurity velocity (pinch) and the impurity density gradient R/LnZ (peaking factor) for zero impurity flux. In particular, the scaling of the impurity peaking factors with impurity charge Z and with driving temperature gradient is investigated and compared with results for the more studied ion temperature gradient (ITG) driven turbulence. The question of helium ash removal in TE mode turbulence is also investigated. In addition, the impurity peaking is compared to the main ion peaking obtained by a self-consistent fluid calculation of the density gradients corresponding to zero particle fluxes. For the scaling of the peaking factor with impurity charge Z, a weak dependence is obtained from NL GENE and fluid simulations. The QL GENE results show a stronger dependence for low Z impurities and overestimates the peaking factor by up to a factor of two in this region. As in the case of ITG dominated turbulence, the peaking factors saturate as Z increases, at a level much below neoclassical predictions. The scaling with Z is, however, weak or reversed as compared to the ITG case. The results indicate that TE mode turbulence is as efficient as ITG turbulence at removing He ash, with DHe/χeff>1.0. The scaling of impurity peaking with the background temperature gradients is found to be weak in the NL GENE and fluid simulations. The QL results are also here found to significantly overestimate the peaking factor for low Z values. For the parameters considered, the background density gradient for zero particle flux is found to be slightly larger than the corresponding impurity zero flux gradient.

Manipulation of a droplet in a planar channel by periodic thermocapillary actuation

Thermocapillary manipulation of a droplet in a planar microchannel with periodic actuations has been demonstrated by both theoretical simulation and experimental characterization. The driving temperature gradients are provided by four micro heaters embedded in the boundaries of the planar channel. The temperature distributions corresponding to the periodic actuations are calculated, and are coupled to the droplet through the surface tensions which drive the droplet. The results show that the droplet will be driven to move along closed loops whose patterns can be designed and controlled by the periodic heating schemes and actuation frequencies. Qualitative agreement between the simulation and experimental observation, in terms of the temperature distributions and droplet moving tracks, has been obtained.

Modeling of subcooling and solidification of phase change materials

Phase change materials (PCM) are able to store thermal energy in small temperature intervals very efficiently due to their high latent heat. Particularly high storage capacity is found in salt hydrates. Salt hydrates however often show subcooling, thus inhibiting the release of the stored heat. In the state of the art simulations of PCM, the effect of subcooling is almost always neglected. This is a practicable approach for small subcooling, but it is problematic for subcooling in the order of the driving temperature gradient on unloading the storage. In this paper, we first present a new algorithm to simulate subcooling in a physically proper way. Then, we present a parametric study to demonstrate the main features of the algorithm and a comparison of computed and experimentally obtained data. The new algorithm should be particularly useful in simulating applications with low cooling rates, for example building applications.

Thermocapillary actuation of droplet in a planar microchannel

A study on thermocapillary actuation of liquid droplet in a planar microchannel has been carried out by both theoretical modeling and experimental characterization. The driving temperature gradients are provided by four heaters at the channel boundaries. In the modeling, the temperature distributions corresponding to transient actuation are calculated, and are coupled to the droplet through the surface tensions which drive the droplet to move inside the channel. The droplet trajectories and final positions are predicted, and are compared with the experimental observations, in which a silicon oil droplet was actuated inside a 10 mm × 10 mm planar channel with four heater fabricated on the substrate plate. The results show that the droplet can be positioned anywhere in the channel, determined by a heating code related to the heating strengths. Qualitative agreement between the modeling results and experimental data, in terms of temperature distributions, droplet trajectories and positions, has been obtained.

The influence of a uniform magnetic field on the Soret coefficient of magnetic nanoparticles

Investigations were made to determine the Soret coefficient of magnetic particles in a ferrofluid. Based on zero field measurements from which the Soret coefficient is quantitatively determined with a theoretical model, the influence of a magnetic field on this parameter will be shown. A clear dependence of the intensity of the thermodiffusive process on the magnetic field strength could be found. In addition it could be shown, that the direction of the field relative to the driving temperature gradient has a significant influence too. In particular a change of the sign of the Soret coefficient was observed if the magnetic field is orientated parallel to the temperature gradient.

Dependence of upper critical field and pairing strength on doping in cuprates.

We have determined the upper critical field Hc2 as a function of hole concentration in bismuth-based cuprates by measuring the voltage induced by vortex flow in a driving temperature gradient (the Nernst effect), in magnetic fields up to 45 tesla. We found that Hc2 decreased steeply as doping increased, in both single and bilayer cuprates. This relationship implies that the Cooper pairing potential displays a trend opposite to that of the superfluid density versus doping. The coherence length of the pairs xi(0) closely tracks the gap measured by photoemission. We discuss implications for understanding the doping dependence of the critical temperature Tc0.

Heat transport in McMurdo Sound first‐year fast ice

We have monitored the temperature field within first‐year sea ice in McMurdo Sound over two winter seasons, with sufficient resolution to determine the thermal conductivity from the thermal waves propagating down through the ice. Data reduction has been accomplished by direct reference to energy conservation, relating the rate of change of the internal energy density to the divergence of the heat current density. Use of this procedure, rather than the wave attenuation predicted by the thermal diffusion equation, avoids difficulties arising from a strongly temperature dependent thermal diffusivity. The thermal conductivity is an input parameter for ice growth and climate models, and the values commonly used in the models are predicted to depend on temperature, salinity, and the volume fraction of air. The present measurements were performed at depths in the ice where the air volume is small and the salinity is nearly constant, and they permit the determination of the absolute magnitude of the thermal conductivity and its temperature dependence. The weak temperature dependence is similar to that predicted by the models in the literature, but the magnitude is smaller by ∼10% than the predicted value most commonly used in climate and sea ice models. In the first season we find an additional scatter in the results at driving temperature gradients larger than ∼10–15 °C/m. We suggest that the scatter arises from a nonlinear contribution to the heat current, possibly associated with the onset of convective motion in brine inclusions. Episodic convective events are also observed. We have further determined the growth rate of the ice and compared it with the rate explained by the heat flux from the ice‐water interface. The data show a sudden rise of growth rate, without a rise in heat flux through the ice, which coincides in time and depth with the appearance of platelet ice. Finally, we discuss the observation of radiative solar heating at depth in the ice and demonstrate that the absorption exceeds that in the ice alone; dust or algae must contribute to the absorption.