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
$\unicodeSTIX{x1D6FD}=0^{\circ }$
, which corresponds to Rayleigh–Bénard convection (RBC), to
$\unicodeSTIX{x1D6FD}=90^{\circ }$
, 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,
$0<\unicodeSTIX{x1D6FD}\leqslant 90^{\circ }$
, leads to an increase of
$Nu$
.
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
$\unicodeSTIX{x1D6E4}=1/5$
. 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
$\unicodeSTIX{x03C0}/2$
. 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.
Citation: Kantorovich S, Astary GW, King MA, Mareci TH, Sarntinoranont M, Carney PR (2013) Correction: Influence of Neuropathology on Convection-Enhanced Delivery in the Rat Hippocampus. PLoS ONE ...8(12): 10.1371/annotation/803a76cf-2d5c-4ac0-9f48-c826cc09a4b3. https://doi.org/10.1371/annotation/803a76cf-2d5c-4ac0-9f48-c826cc09a4b3
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
In this paper, we report on a direct numerical simulation (DNS) study of turbulent thermal convection in mixed porous–pure fluid domains. The computational domain consists of a cavity that contains a ...porous medium placed right above the bottom wall. The solid matrix is internally heated which, in turn, induces the convective motions of the fluid. The Rayleigh number of the flow in the pure fluid region above the porous medium is of the order of $10^7$. In our study, we consider cases of different sizes of the porous medium, as well as cases with both uniform and non-uniform heat loading of the solid matrix. For each case, we analyse the convective structures in both the porous and the pure fluid domains and investigate the effect of the porous medium on the emerging flow patterns above it. Results for the flow statistics, as well as for the Nusselt number and each of its components, are also presented herein. Further, we make comparisons of the flow properties in this pure fluid region with those in Rayleigh–Bénard convection. Our simulations predict that, depending on the area coverage, the large-scale circulation above the porous medium can be in a single-roll, dual-roll or intermediate state. Also, when the area coverage increases, the temperatures inside it increase due to reduced fluid circulation. Accordingly, when the area coverage increases, then the Nusselt number becomes smaller whereas the Rayleigh number is increased.
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.
Abstract
We carry out direct numerical simulations of turbulent Rayleigh–Bénard convection in a square box with rough conducting plates over the Rayleigh number range
$10^7\leqslant Ra\leqslant 10^9$
...and the Prandtl number range
$0.01\leqslant Pr\leqslant 100$
. In Zhang
et al.
(
J. Fluid Mech.
, vol. 836, 2018, R2), it was reported that while the measured Nusselt number
$Nu$
is enhanced at large roughness height
$h$
, the global heat transport is reduced at small
$h$
. The division between the two regimes yields a critical roughness height
$h_c$
, and we now focus on the effects of the Prandtl number (
$Pr$
) on
$h_c$
. Based on the variations of
$h_c$
, we identify three regimes for
$h_c(Pr)$
. For low
$Pr$
, thermal boundary layers become thinner with increasing
$Pr$
. This makes the boundary layers easier to be disrupted by rough elements, leading to the decrease of
$h_c$
with increasing
$Pr$
. For moderate
$Pr$
, the corner-flow rolls become much more pronounced and suppress the global heat transport via the competition between the corner-flow rolls and the large-scale circulation (LSC). As a consequence,
$h_c$
increases with increasing
$Pr$
due to the intensification of the corner–LSC competition. For high
$Pr$
, the convective flow transitions to the plume-controlled regime. As the rough elements trigger much stronger and more frequent plume emissions,
$h_c$
again decreases with increasing
$Pr$
.
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, $Nu-1\propto \widetilde {Ra}^{3}$.
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