Turbulent temperature fluctuations in a closed Rayleigh–Bénard convection cell

2019 ◽  
Vol 874 ◽  
pp. 263-284 ◽  
Author(s):  
Yin Wang ◽  
Xiaozhou He ◽  
Penger Tong
Keyword(s):  
Temperature Fluctuations ◽  
Convection Cell ◽  
Thermal Plumes ◽  
Bénard Convection ◽  
Conducting Plate ◽  
Benard Convection ◽  
Analytic Expressions ◽  
Spatio Temporal ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We report a systematic study of spatial variations of the probability density function (PDF) $P(\unicode[STIX]{x1D6FF}T)$ for temperature fluctuations $\unicode[STIX]{x1D6FF}T$ in turbulent Rayleigh–Bénard convection along the central axis of two different convection cells. One of the convection cells is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. By changing the distance $z$ away from the bottom conducting plate, we find the functional form of the measured $P(\unicode[STIX]{x1D6FF}T)$ in both cells evolves continuously with distinct changes in four different flow regions, namely, the thermal boundary layer, mixing zone, turbulent bulk region and cell centre. By assuming temperature fluctuations in different flow regions are all made from two independent sources, namely, a homogeneous (turbulent) background which obeys Gaussian statistics and non-uniform thermal plumes with an exponential distribution, we obtain the analytic expressions of $P(\unicode[STIX]{x1D6FF}T)$ in four different flow regions, which are found to be in good agreement with the experimental results. Our work thus provides a unique theoretical framework with a common set of parameters to quantitatively describe the effect of turbulent background, thermal plumes and their spatio-temporal intermittency on the temperature PDF $P(\unicode[STIX]{x1D6FF}T)$.

Spatio-temporal regimes in Rayleigh–Bénard convection in a small rectangular cell

1989 ◽  
Vol 209 ◽  
pp. 309-334 ◽  
Author(s):  
M. A. Rubio ◽  
P. Bigazzi ◽  
L. Albavetti ◽  
S. Ciliberto
Keyword(s):  
Travelling Waves ◽  
Rectangular Cell ◽  
Complex Behaviour ◽  
Temporal Behaviour ◽  
Bénard Convection ◽  
Benard Convection ◽  
Spatio Temporal ◽  
Roll Axis ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

By means of an original optical technique we have studied the spatio-temporal behaviour in a Rayleigh–Bénard convection experiment of small rectangular geometry. The experimental technique allows complete reconstruction of the temperature field integrated along the roll axis. Two main spatiotemporal regimes have been found, corresponding to localized oscillations and travelling waves respectively. Several parameters are proposed for the quantitative characterization of this complex behaviour.

Exploring the severely confined regime in Rayleigh–Bénard convection

2016 ◽  
Vol 805 ◽  
Author(s):  
Kai Leong Chong ◽  
Ke-Qing Xia
Keyword(s):  
Rayleigh Number ◽  
Flow Topology ◽  
Thermal Plumes ◽  
Bénard Convection ◽  
Benard Convection ◽  
Wide Range ◽  
Classical Boundary ◽  
Global And Local ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We study the effect of severe geometrical confinement in Rayleigh–Bénard convection with a wide range of width-to-height aspect ratio $\unicode[STIX]{x1D6E4}$, $1/128\leqslant \unicode[STIX]{x1D6E4}\leqslant 1$, and Rayleigh number $Ra$, $3\times 10^{4}\leqslant Ra\leqslant 1\times 10^{11}$, at a fixed Prandtl number of $Pr=4.38$ by means of direct numerical simulations in Cartesian geometry with no-slip walls. For convection under geometrical confinement (decreasing $\unicode[STIX]{x1D6E4}$ from 1), three regimes can be recognized (Chong et al., Phys. Rev. Lett., vol. 115, 2015, 264503) based on the global and local properties in terms of heat transport, plume morphology and flow structures. These are Regime I: classical boundary-layer-controlled regime; Regime II: plume-controlled regime; and Regime III: severely confined regime. The study reveals that the transition into Regime III leads to totally different heat and momentum transport scalings and flow topology from the classical regime. The convective heat transfer scaling, in terms of the Nusselt number $Nu$, exhibits the scaling $Nu-1\sim Ra^{0.61}$ over three decades of $Ra$ at $\unicode[STIX]{x1D6E4}=1/128$, which contrasts sharply with the classical scaling $Nu-1\sim Ra^{0.31}$ found at $\unicode[STIX]{x1D6E4}=1$. The flow in Regime III is found to be dominated by finger-like, long-lived plume columns, again in sharp contrast with the mushroom-like, fragmented thermal plumes typically observed in the classical regime. Moreover, we identify a Rayleigh number for regime transition, $Ra^{\ast }=(29.37/\unicode[STIX]{x1D6E4})^{3.23}$, such that the scaling transition in $Nu$ and $Re$ can be clearly demonstrated when plotted against $Ra/Ra^{\ast }$.

scholarly journals Experimental investigation of longitudinal space–time correlations of the velocity field in turbulent Rayleigh–Bénard convection

2011 ◽  
Vol 683 ◽  
pp. 94-111 ◽  
Author(s):  
Quan Zhou ◽  
Chun-Mei Li ◽  
Zhi-Ming Lu ◽  
Yu-Lu Liu
Keyword(s):  
Experimental Investigation ◽  
Velocity Field ◽  
Space Time ◽  
Turbulent Shear ◽  
Convection Cell ◽  
Mean Velocity ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractWe report an experimental investigation of the longitudinal space–time cross-correlation function of the velocity field, $C(r, \tau )$, in a cylindrical turbulent Rayleigh–Bénard convection cell using the particle image velocimetry (PIV) technique. We show that while Taylor’s frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows (He & Zhang, Phys. Rev. E, vol. 73, 055303) is valid for the present velocity field for all over the cell, i.e. the isocorrelation contours of the measured $C(r, \tau )$ have an elliptical curve shape and hence $C(r, \tau )$ can be related to $C({r}_{E} , 0)$ via ${ r}_{E}^{2} = (r\ensuremath{-} U\tau )^{2} + {V}^{2} {\tau }^{2} $ with $U$ and $V$ being two characteristic velocities. We further show that the fitted $U$ is proportional to the mean velocity of the flow, but the values of $V$ are larger than the theoretical predictions. Specifically, we focus on two representative regions in the cell: the region near the cell sidewall and the cell’s central region. It is found that $U$ and $V$ are approximately the same near the sidewall, while $U\simeq 0$ at the cell centre.

Reynolds number scaling in cryogenic turbulent Rayleigh–Bénard convection in a cylindrical aspect ratio one cell

2017 ◽  
Vol 832 ◽  
pp. 721-744 ◽  
Author(s):  
Věra Musilová ◽  
Tomáš Králík ◽  
Marco La Mantia ◽  
Michal Macek ◽  
Pavel Urban ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Large Scale ◽  
Temperature Fluctuations ◽  
Reynolds Numbers ◽  
Distribution Functions ◽  
Bénard Convection ◽  
Benard Convection ◽  
Helium Gas ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We perform an experimental study of turbulent Rayleigh–Bénard convection up to very high Rayleigh number, $10^{8}<Ra<10^{14}$, in a cylindrical aspect ratio one cell, 30 cm in height, filled with cryogenic helium gas. We monitor temperature fluctuations in the convective flow with four small (0.2 mm) sensors positioned in pairs 1.5 cm from the sidewalls and 2.5 cm vertically apart and symmetrically around the mid-height of the cell. Based on one-point and two-point correlations of the temperature fluctuations, we determine different types of Reynolds numbers, $\mathit{Re}$, associated with the large-scale circulation (LSC). We observe a transition between two types of $\mathit{Re}(\mathit{Ra})$ scaling around $\mathit{Ra}=10^{10}{-}10^{11}$, which is accompanied by a scaling change of the skewness of the probability distribution functions (PDFs) of the temperature fluctuations. The $\mathit{Re}(\mathit{Ra})$ dependencies measured near the sidewall at Prandtl number $\mathit{Pr}\sim 1$ are consistent with the $\mathit{Ra}^{4/9}\mathit{Pr}^{-2/3}$ scaling above the transition, while for $\mathit{Ra}<10^{10}$, the $\mathit{Re}(\mathit{Ra})$ dependencies are steeper. It seems likely that this change in $\mathit{Re}(\mathit{Ra})$ scaling is linked to the previously reported change in the Nusselt number $\mathit{Nu}(\mathit{Ra})$ scaling. This behaviour is in agreement with independent cryogenic laboratory experiments with $\mathit{Pr}\sim 1$, but markedly different from the $\mathit{Re}$ scaling obtained in water experiments ($\mathit{Pr}\sim 3.3{-}5.6$). We discuss the results in comparison with different versions of the Grossmann–Lohse theory.

scholarly journals Rayleigh–Bénard convection with a melting boundary

2018 ◽  
Vol 858 ◽  
pp. 437-473 ◽  
Author(s):  
B. Favier ◽  
J. Purseed ◽  
L. Duchemin
Keyword(s):  
Heat Flux ◽  
Stokes Equations ◽  
Two Dimensions ◽  
Convection Cell ◽  
Solid Boundary ◽  
Melting Front ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane-layer geometry, this can be seen as classical Rayleigh–Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier–Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appear as the depth – and therefore the effective Rayleigh number – of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells.

Test of the anomalous scaling of passive temperature fluctuations in turbulent Rayleigh–Bénard convection with spatial inhomogeneity

2014 ◽  
Vol 753 ◽  
pp. 104-130 ◽  
Author(s):  
Xiaozhou He ◽  
Xiao-dong Shang ◽  
Penger Tong
Keyword(s):  
Structure Function ◽  
Temperature Fluctuations ◽  
Thermal Dissipation ◽  
Temperature Structure ◽  
Anomalous Scaling ◽  
Bénard Convection ◽  
Benard Convection ◽  
Turbulent Statistics ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractThe scaling properties of the temperature structure function (SF) and temperature–velocity cross-structure function (CSF) are investigated in turbulent Rayleigh–Bénard convection (RBC). The measured SFs and CSFs exhibit good scaling in space and time and the resulting SF and CSF exponents are obtained both at the centre of the convection cell and near the sidewall. A universal relationship between the CSF exponent and the thermal dissipation exponent is found, confirming that the anomalous scaling of passive temperature fluctuations in turbulent RBC is indeed caused by the spatial intermittency of the thermal dissipation field. It is also found that the difference in the functional form of the measured SF and CSF exponents at the two different locations in the cell is caused by the change of the geometry of the most dissipative structures in the (inhomogeneous) temperature field from being sheetlike at the cell centre to filament-like near the sidewall. The experiment thus provides direct evidence showing that the universality features of turbulent cascade are linked to the degree of anisotropy and inhomogeneity of turbulent statistics.

LBE SIMULATIONS OF RAYLEIGH-BÉNARD CONVECTION ON THE APE100 PARALLEL PROCESSOR

1993 ◽  
Vol 04 (05) ◽  
pp. 993-1006 ◽  
Author(s):  
A. BARTOLONI ◽  
C. BATTISTA ◽  
S. CABASINO ◽  
P. S. PAOLUCCI ◽  
J. PECH ◽  
...  
Keyword(s):  
Lattice Boltzmann ◽  
Parallel Computer ◽  
Convection Cell ◽  
Two Dimensional ◽  
Parallel Processor ◽  
Bénard Convection ◽  
Benard Convection ◽  
Dynamics Simulations ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In this paper we describe an implementation of the Lattice Boltzmann Equation method for fluid-dynamics simulations on the APE100 parallel computer. We have performed a simulation of a two-dimensional Rayleigh-Bénard convection cell. We have tested the theory proposed by Shraiman and Siggia for the scaling of the Nusselt number vs. Rayleigh number.

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