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"Convection"
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Combined particle image velocimetry and thermometry of turbulent superstructures in thermal convection
Turbulent superstructures in horizontally extended three-dimensional Rayleigh–Bénard convection flows are investigated in controlled laboratory experiments in water at Prandtl number ${Pr}=7$. A Rayleigh–Bénard cell with square cross-section, aspect ratio $\\varGamma =l/h=25$, side length $l$ and height $h$ is used. Three different Rayleigh numbers in the range $10^{5} < {Ra} < 10^{6}$ are considered. The cell is accessible optically, such that thermochromic liquid crystals can be seeded as tracer particles to monitor simultaneously temperature and velocity fields in a large section of the horizontal mid-plane for long time periods of up to 6 h, corresponding to approximately $10^{4}$ convective free-fall time units. The joint application of stereoscopic particle image velocimetry and thermometry opens the possibility to assess the local convective heat flux fields in the bulk of the convection cell and thus to analyse the characteristic large-scale transport patterns in the flow. A direct comparison with existing direct numerical simulation data in the same parameter range of $Pr$, ${Ra}$ and $\\varGamma$ reveals the same superstructure patterns and global turbulent heat transfer scaling ${Nu}({Ra})$. Slight quantitative differences can be traced back to violations of the isothermal boundary condition at the extended water-cooled glass plate at the top. The characteristic scales of the patterns fall into the same size range, but are systematically larger. It is confirmed experimentally that the superstructure patterns are an important backbone of the heat transfer. The present experiments enable, furthermore, the study of the gradual evolution of the large-scale patterns in time, which is challenging in simulations of large-aspect-ratio turbulent convection.
Journal Article
The influence of the cell inclination on the heat transport and large-scale circulation in liquid metal convection
Inclined turbulent thermal convection in liquid sodium is studied at large Rayleigh numbers$Ra\\gtrsim 10^{7}$based on the results of both experimental measurements and high-resolution numerical simulations. For a direct comparison, the considered system parameters are set to be similar:$Ra=1.67\\times 10^{7}$in the direct numerical simulations (DNS),$Ra=1.5\\times 10^{7}$in the large-eddy simulations and$Ra=1.42\\times 10^{7}$in the experiments, while the Prandtl number of liquid sodium is very small ($Pr\\approx 0.009$). The cylindrical convection cell has an aspect ratio of one; one circular surface is heated, while the other one is cooled. Additionally, the cylinder is inclined with respect to gravity and the inclination angle varies from$\\unicode[STIX]{x1D6FD}=0^{\\circ }$, which corresponds to Rayleigh–Bénard convection (RBC), to$\\unicode[STIX]{x1D6FD}=90^{\\circ }$, as in a vertical convection (VC) set-up. Our study demonstrates quantitative agreement of the experimental and numerical results, in particular with respect to the global heat and momentum transport, temperature and velocity profiles, as well as the dynamics of the large-scale circulation (LSC). The DNS reveal that the twisting and sloshing of the LSC at small inclination angles periodically affects the instantaneous heat transport (up to$\\pm 44\\,\\%$of the mean heat transport). The twisted LSC is associated with a weak heat transport, while the sloshing mode that brings together the hot and cold streams of the LSC is associated with a strong heat transport. The experiments show that the heat transport scales as$Nu\\sim Ra^{0.22}$in both limiting cases (RBC and VC) for Rayleigh numbers around$Ra\\approx 10^{7}$, while any inclination of the cell,$0<\\unicode[STIX]{x1D6FD}\\leqslant 90^{\\circ }$, leads to an increase of $Nu$.
Journal Article
Enhanced heat transfer and reduced flow reversals in turbulent thermal convection with an obstructed centre
We report an experimental study about the effect of an obstructed centre on heat transport and flow reversal by inserting an adiabatic cylinder at the centre of a quasi-two-dimensional Rayleigh–Bénard convection cell. The experiments are carried out in a Rayleigh number ($Ra$) range of $2\\times 10^7 \\leq Ra \\leq 2\\times 10^9$ and at a Prandtl number ($Pr$) of $5.7$. It is found that for low $Ra$, the obstructed centre leads to a heat transfer enhancement of up to 21 $\\%$, while as $Ra$ increases, the magnitude of the heat transfer enhancement decreases and the heat transfer efficiency ($Nu$) eventually converges to that of the unobstructed normal cell. Particle image velocimetry measurements show that the heat transfer enhancement originates from the change in flow topology due to the presence of the cylindrical obstruction. In the low-$Ra$ regime the presence of the obstruction promotes the transition of the flow topology from the four-roll state to the abnormal single-roll state then to the normal single-roll state with increasing obstruction size. While in the high-$Ra$ regime, the flow is always in the single-roll state regardless of the obstruction size, although the flow becomes more coherent with the size of the obstruction. We also found that in the presence of the cylindrical obstruction, the stability of the corner vortices is significantly reduced, leading to a large reduction in the frequency of flow reversals.
Journal Article
No sustained mean velocity in the boundary region of plane thermal convection
We study the dynamics of thermal and momentum boundary regions in three-dimensional direct numerical simulations of Rayleigh–Bénard convection for the Rayleigh-number range $10^5\\leq Ra \\leq 10^{11}$ and $Pr=0.7$. Using a Cartesian slab with horizontal periodic boundary conditions and an aspect ratio of 4, we obtain statistical homogeneity in the horizontal $x$- and $y$-directions, thus approximating best an extended convection layer relevant for most geo- and astrophysical flow applications. We observe upon canonical use of combined long-time and area averages, with averaging periods of at least 100 free-fall times, that a global coherent mean flow is practically absent and that the magnitude of the velocity fluctuations is larger than the mean by up to 2 orders of magnitude. The velocity field close to the wall is a collection of differently oriented local shear-dominated flow patches interspersed by extensive shear-free incoherent regions which can be as large as the whole cross-section, unlike for a closed cylindrical convection cell of aspect ratio of the order 1. The incoherent regions occupy a 60 % area fraction for all Rayleigh numbers investigated here. Rather than resulting in a pronounced mean flow with small fluctuations about such a mean, as found in small-aspect-ratio convection, the velocity field is dominated by strong fluctuations of all three components around a non-existent or weak mean. We discuss the consequences of these observations for convection layers with larger aspect ratios, including boundary layer instabilities and the resulting turbulent heat transport.
Journal Article
Confined inclined thermal convection in low-Prandtl-number fluids
Any tilt of a Rayleigh–Bénard convection cell against gravity changes the global flow structure inside the cell, which leads to a change of the heat and momentum transport. Especially sensitive to the inclination angle is the heat transport in low-Prandtl-number fluids and confined geometries. The purpose of the present work is to investigate the global flow structure and its influence on the global heat transport in inclined convection in a cylindrical container of diameter-to-height aspect ratio
$\\unicode[STIX]{x1D6E4}=1/5$
. The study is based on direct numerical simulations where two different Prandtl numbers
$Pr=0.1$
and 1.0 are considered, while the Rayleigh number,
$Ra$
, ranges from
$10^{6}$
to
$10^{9}$
. For each combination of
$Ra$
and
$Pr$
, the inclination angle is varied between 0 and
$\\unicode[STIX]{x03C0}/2$
. An optimal inclination angle of the convection cell, which provides the maximal global heat transport, is determined. For inclined convection we observe the formation of two system-sized plume columns, a hot and a cold one, that impinge on the opposite boundary layers. These are related to a strong increase in the heat transport.
Journal Article
Side-heated Rayleigh–Bénard convection
Unlike in solids, heat transfer in fluids can be greatly enhanced due to the presence of convection. Under gravity, an unevenly distributed temperature field results in differences in buoyancy, driving fluid motion that is seen in Rayleigh–Bénard convection (RBC). In RBC, the overall heat flux is found to have a power-law dependence on the imposed temperature difference, with enhanced heat transfer much beyond thermal conduction. In a bounded domain of fluid such as a cube, how RBC responds to thermal perturbations from the vertical sidewall is not clear. Will sidewall heating or cooling modify flow circulation and heat transfer? We address these questions experimentally by adding heat to one side of the RBC. Through careful flow, temperature and heat flux measurements, the effects of adding side heating to RBC are examined and analysed, where a further enhancement of flow circulation and heat transfer is observed. Our results also point to a direct and simple control of the classical RBC system, allowing further manipulation and control of thermal convection through sidewall conditions.
Journal Article
Localized Convection in Sputnik Planitia, Pluto
The cellular plains on Sputnik Planitia (SP) are thought to originate from convection in the nitrogen ice layer that fills the basin. Whereas the cells toward the center of SP's cellular plains are wider and interconnected—features explained by vigorous convection—the cells near the margins are smaller and less contiguous, with some appearing completely isolated. We propose that these isolated cells are surface expressions of localized convection—a rare planform in which stable thermal plumes can form in isolation from one another. Numerical simulations of convection using experimentally determined flow laws for power‐law creep in nitrogen ice show that for typical parameters of SP, the viscosity contrasts across the layer are sufficiently high for localization to occur. The diameter of the isolated cells provides constraints on the thickness of the nitrogen ice layer, the surface topographic anomaly, surface heat flow, and surface velocities associated with the localized cells.
Journal Article
Scaling regimes in rapidly rotating thermal convection at extreme Rayleigh numbers
The geostrophic turbulence in rapidly rotating thermal convection exhibits characteristics shared by many highly turbulent geophysical and astrophysical flows. In this regime, the convective length and velocity scales and heat flux are all diffusion-free, i.e. independent of the viscosity and thermal diffusivity. Our direct numerical simulations (DNS) of rotating Rayleigh–Bénard convection in domains with no-slip top and bottom and periodic lateral boundary conditions for a fluid with the Prandtl number $Pr=1$ and extreme buoyancy and rotation parameters (the Rayleigh number up to $Ra=3\\times 10^{13}$ and the Ekman number down to $Ek=5\\times 10^{-9}$) indeed demonstrate all these diffusion-free scaling relations, in particular, that the dimensionless convective heat transport scales with the supercriticality parameter $\\widetilde {Ra}\\equiv Ra\\, Ek^{4/3}$ as $Nu-1\\propto \\widetilde {Ra}^{3/2}$, where $Nu$ is the Nusselt number. We further derive and verify in the DNS that with the decreasing $\\widetilde {Ra}$, the geostrophic turbulence regime undergoes a transition into another geostrophic regime, the convective heat transport in this regime is characterized by a very steep $\\widetilde {Ra}$-dependence, $Nu-1\\propto \\widetilde {Ra}^{3}$.
Journal Article