Session P06: Turbulent Convection

Forced convective heat transfer by turbulent baroclinic acoustic streaming

Unusually strong acoustic streaming flows can be generated in gases subjected to an imposed cross-channel temperature gradient. In contrast with classic Rayleigh streaming, standing sound waves acquire vorticity owing to baroclinic torques acting throughout the domain rather than via viscous torques acting in Stokes boundary layers [Chini et al., J. Fluid Mech., Vol. 744 (2014); Michel & Chini, J. Fluid Mech., Vol. 858 (2019)]. Consequently, these baroclinically-driven streaming flows have an amplitude comparable to that of the acoustic waves, leading to fully two-way wave/mean-flow coupling. The present investigation extends our earlier studies by accessing a parameter regime in which the streaming flow is spatiotemporally chaotic. Although the flow is acoustically-driven and buoyancy forces are not included, the time-dependent streaming temperature field resembles that arising in turbulent Rayleigh--B\'{e}nard convection. The velocity field differs, however, being strongly confined to the periphery of the unsteady convection cells. We elucidate the physical origin of this flow pattern and quantify the forced convective heat transport accomplished by the turbulent baroclinic acoustic streaming.   

An Experimental Investigation of Turbulence-Enhanced Ice Melting

Melting in polar regions has been hypothesized to be heavily influenced by turbulence, as turbulence continually stirs away the meltwater surrounding the ice to replenish warmer ambient fluid adjacent to the ice, thus encouraging efficient melting. However, a quantification of how turbulence, when coupled with ambient salinity and temperature, increases melt rates has yet to be determined. To understand the fundamental physics by which turbulence, salinity, and temperature affect melting rates, we have designed an experimental study that explores melting of an ice sphere centered in homogeneous isotropic turbulence absent mean flow. Particle image velocimetry is used to measure the velocity field of the ambient water and meltwater; statistics including turbulent kinetic energy, dissipation rates, and integral scales are computed directly. By dyeing the ice sphere fluorescent, simultaneous laser-induced fluorescence measurements are used to instantaneously visualize and quantify melting in response to turbulent dynamics. Time-lapse photography is used to quantify ice loss in time. A full quantification of melting is presented across a wide parameter space exploring contributions from ambient turbulence, salinity, and temperature in a zero mean shear environment.   

Transition to the ultimate regime in a stochastic model of radiatively driven thermal convection

Measurements of convection in a fluid whose bottom layer is radiatively heated show a transition from classical to ultimate Nu dependence on Ra for order-one Pr, with ultimate-regime Ra exponent 0.55. This transition is reproduced with the same exponent value by stochastic simulations using a formulation of one-dimensional turbulence (ODT) akin to a formulation previously applied to Rayleigh convection with fixed wall temperatures. ODT simulates viscous and conductive thermal transport along a vertical line of sight, punctuated by eddy events that instantaneously modify the flow state within sub-intervals of the line. A local energy-based event-sampling criterion endows the formulation with key attributes of turbulence phenomenology. For the radiatively driven case, the classical-to-ultimate transition is accompanied by an abrupt reduction in occurrences of small near-wall eddy events, consistent with both the conceptual picture of the ultimate regime and empirical evidence. ODT results suggest a slight dependence of the ultimate exponent on the normalized thickness of the heated layer. No other available method or evidence presently allows a statistically significant test of this prediction.   

Heat transfer scaling in volumetrically heated and cooled convection

Adequately modelling of the amount of heat transferred in a thermally driven flow is crucial for understanding many processes in Nature and technology. For this purpose, many studies of thermal convection have been performed which historically focus on systems where heat is injected through the boundaries. However, systems where the heat is added partially or fully into the volume are common and the difference between both configurations has not been studied systematically. We set out to do so by conducting a series of simulations to determine how the heat transfer behaves when a system is volumetrically heated, while being cooled through a combination of boundary and volume. If the cooling happens exclusively through the boundary, we find that homogeneously heated flows are driven by falling plumes near the top plate, and that inhomogeneously heating from the bottom can trigger a more symmetric distribution that also includes upwards plumes. However, the effective heat transfer laws remain largely unaffected despite the increasing the level of turbulence in the system. By removing heat through volumetric sinks we can increase the effective heat transfer rate. When the heat is fully removed this way such there is no boundary heat transfer we achieve viscosity-independent scaling laws for the total heat transfer.   

Collective effect of thermal plumes on temperature fluctuations in a closed Rayleigh-Bénard convection cell

We report a systematic study of the collective effect of thermal plumes on the probability density function (PDF) P(δT) of temperature fluctuations δT in turbulent Rayleigh-Bénard convection. By decomposing δT into five basic fluctuation modes associated with single and multiple plumes and a turbulent background, we derive an analytic form of P(δT) based on convolutions of the five modes. To test our theory, we conduct temperature measurements in two convection cells: one is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. For a given normalized position in most regions of the convection cells, all the measured P(δT) for different Rayleigh number fall onto a single curve, once δT is normalized by its rms value σ_T. The P(δT) measured along the symmetric horizontal and vertical axes of the convection cells agrees excellently with our theoretical predictions. The fitting parameters are closely linked to the spatial distribution of thermal plumes and local dynamics of the large-scale circulation in a convection cell. Our work thus provides a unified theoretical approach for understanding scalar PDFs in a turbulent field, which is very useful not only for the present study but also for the study of many turbulent mixing problems of practical interest.   

Not Participating

Traditionally considered rotating Rayleigh-Bénard convection can be seen as a simple model for astrophysical and geophysical flows in polar regions. Comparatively, Rayleigh-Bénard convection with spanwise rotation corresponds to flows in equatorial regions. However, it is not very clear how the flows transition in between. In this study, we consider Rayleigh-Bénard convection with rotation axis at different angles, mimicking the transition from equatorial regions to polar regions, up to Rayleigh number 10¹⁰ and Ekman number 10⁶. It is found that distinct flow patterns exist for different rotation angles, resulting in also distinct heat transfer scaling regimes. With increasing Rayleigh number, for a given rotation rate, heat is mostly contributed from the equatorial regions for low Rayleigh number, whereas, heat is contributed more from the polar regions for high Rayleigh numbers   

Not Participating

Employing immediate analogies with phase transitions in equilibrium statistical mechanics, we explore the transitions between turbulent states from a 3D flow state towards a quasi-2D condensate known as the large-scale vortex (LSV). Using direct numerical simulations of rotating Rayleigh-Benard convection, we vary the Rayleigh number Ra as control parameter and study the system response (strength of the LSV) in terms of order parameters assessing the energetic content in the flow and the upscale energy flux. By sensitively probing the boundaries of the domain of existence of the LSV, we find discontinuous transitions and we identify the presence of a hysteresis loop as well as nucleation-and-growth type of dynamics, manifesting striking correspondence with first-order phase transitions in equilibrium statistical mechanics. We show furthermore that the creation of the condensate state coincides with a discontinuous transition of the energy transport into the largest mode of the system.   

Force balance in rapidly rotating turbulent Rayleigh-Bénard convection

We study the force balance of turbulent rotating Rayleigh–Bénard convection, a simple model for large-scale natural flows. Direct numerical simulations are carried out on a laterally periodic domain, vertically bounded by no-slip walls. We provide a comprehensive overview of the interplay between the governing forces. Flow transitions are identified as distinct changes in the dominant or subdominant force balance, leading to a natural identification of each flow regime. In the rapidly rotating geostrophic regime, where the principal balance is between Coriolis and pressure gradient forces, we observe various flow states: cells, convective Taylor columns, plumes, and large-scale vortices. These geostrophic flow features can be distinguished by the subdominant force balance, where inertia, buoyancy and viscous forces can contribute. Closer to the plates the contribution of inertia is larger, though still a dominant geostrophic balance is observed. Kinetic boundary layers are of Ekman type, as expected for rapidly rotating flows. By contrast, in rotation-affected convection inertial and pressure-gradient forces form the dominant balance, with a change in boundary layer structure.   

Flow measurements of turbulent rotating Rayleigh-Bénard convection in the geostrophic regime

The study of turbulent rotating convection is of paramount importance for the understanding of many features of geophysical and astrophysical flows. Our experimental setup TROCONVEX, through its huge dimensions (up to 4 m tall), allows the investigation of parameters closer than ever before to the ones of geo- and astrophysical flows. In this talk we present flow measurements from this unique experimental setup using stereoscopic particle image velocimetry. We can compute flow statistics and characteristic length scales from these measurements. For high buoyancy forcing, we find a remarkable quadrupolar organization of the flow instead of the large-scale vortex observed in horizontally periodic simulations. We describe the dynamics of this quadrupolar vortex and its interactions with the wall mode near the sidewall.   

Markov State Modelling of discrete flow states in turbulent Rayleigh-B\'enard convection in a cubic container

The turbulent convection flow in closed cells, which is driven by rising and falling thermal plumes, are known to form large scale circulations (LSC). The LSC structures depend on the aspect ratio and the geometrical shape of the cell. Studies of LSC are of relevance as they can significantly affect the heat transport in the system. We carried out our investigations in a closed cubic container with no-slip boundary conditions at all boundaries, using an open source code nek5000 based on the spectral-element method. The simulations were performed for a fixed value of Rayleigh number Ra = 10⁶ for incompressible fluids of three different Prandtl numbers Pr = 0.1, 0.7, and 10, which allowed us to vary the effective Reynolds numbers while maintaining the Nusselt number Nu nearly constant. In accordance with previous studies, we identified four stable LSC states (aligned along the diagonals) and an unstable LSC state (aligned parallel to the edges). Additionally, we also found a decoherent ``null state'', where the system does not have any well-defined LSC. A long-term single trajectory analysis for 10⁵ free-fall times confirmed that the LSC state re-orients from one stable to another state via the four possible unstable and the null states. We confirmed that all stable states have equal probability of occurrence. We then performed an alternative approach based on ensemble averaging of short-term simulations. The initial conditions for these short-term simulations were randomly chosen from the single long-term trajectory run. The ensemble averaging generated a transition probability matrix and thereafter we were able to probe if the Markov property of the transition between the different large-scale flow states is effective.   

Droplet-turbulence interaction in moist tube convection

The role of turbulence in the growth of droplet size and spectrum in cumulus clouds leading to precipitation has been a topic of intense research. However, due to the difficulty in simulating the turbulence in that of clouds in laboratory scale, there have been very few experimental studies in this area. To study some aspects of droplet behaviour in clouds, we have set up an experiment with turbulent moist tube convection in a vertical square tube connecting two reservoirs maintained at an unstable density difference (due to difference in both temperature and vapour concentration). While heated water at the bottom reservoir provides hot moist air, slow-moving cold air at the tube top in a closed-loop cold chamber acts as the cold reservoir. Due to the mixing of different air parcels of varying temperature and moisture, the vapour condenses to form droplets on the available aerosols and interact with the turbulence created in the tube. Preliminary experiments reveal a near-linear mean temperature gradient exist along the tube length. Imaging of the droplet field is done using laser and high-speed camera to quantify droplet velocity and inter-particle distance. The evolution of the droplet diameter and velocity spectra are studied to understand the behaviour of droplets in turbulence.   

On the transport properties of natural and mixed convective flow fields

Turbulence is present in many natural processes where plays a relevant role as in the spread of pollutants in the atmosphere and oceans. It is also present in industrial processes and is the main conductor in industrial mixers among others.

In many of these natural or industrial systems, not only turbulence but also a difference of temperatures can dominate their behavior. This fact provokes lots of research about the combination of both factors: turbulent flows with thermal convection.

Our aim is the experimental study of the transport of heat and momentum in natural thermal convective flows and mix convention where the thermal convection is enhanced by becoming the flow turbulent.

For that, we have built an octagonal convection cell of diameter $D$ = 325 mm and height $H$ = 430 mm filled by water. The temperature is controlled by two plates: the hot one below and the cold one on top. To create turbulence, two mesh grids inside the tank are operated from both plates.

The flow field is measured in 3D thanks to the implementation of a Lagrangian tracking of the tracers seeded in the fluid followed by 4 monochromatic cameras. In addition, the temperature field is measured in 2D seeding the fluid with TLCs that change their color with the temperature and are recorded by a color camera.