Emergence of substructures inside the large-scale circulation induces transition in flow reversals in turbulent thermal convection

2019 ◽  
Vol 877 ◽  
Author(s):  
Xin Chen ◽  
Shi-Di Huang ◽  
Ke-Qing Xia ◽  
Heng-Dong Xi
Keyword(s):  
Energy Barrier ◽  
Large Scale ◽  
Turnover Time ◽  
Reversal Rate ◽  
Flow Topology ◽  
Large Scale Circulation ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Flow Reversals ◽  
Rayleigh Benard

We present an experimental study of the reversal of the large-scale circulation (LSC) in quasi-two-dimensional turbulent Rayleigh–Bénard convection. It is found that there exists a transition in the Rayleigh number ($Ra$) dependence of the reversal rate $f$ with two distinct scalings: for $Ra$ less than a transitional value $Ra_{t}$, the non-dimensionalized reversal rate $ft_{E}\sim Ra^{-1.09}$; however, for higher $Ra$ the scaling changes to $ft_{E}\sim Ra^{-3.06}$, where $t_{E}$ is the turnover time of the LSC. Flow visualization shows that this regime transition originates from a change in flow topology from a single-roll state to a new, less stable, abnormal single-roll state with substructures inside the single roll. The emergence of the substructures inside the LSC lowers the energy barrier for the flow reversals to occur and leads to a slower decay of $f$ with $Ra$. Detailed analysis reveals that, although it is the corner rolls that trigger the reversal event, the probability for the occurrence of reversals mainly depends on the stability of the LSC. This is supported by a model we proposed to predict the critical condition for the transition, which agrees well with the experimental results.

Flow reversals in Rayleigh–Bénard convection with non-Oberbeck–Boussinesq effects

2016 ◽  
Vol 798 ◽  
pp. 628-642 ◽  
Author(s):  
Shu-Ning Xia ◽  
Zhen-Hua Wan ◽  
Shuang Liu ◽  
Qi Wang ◽  
De-Jun Sun
Keyword(s):  
Large Scale ◽  
Mass Conservation ◽  
Working Fluid ◽  
Large Temperature ◽  
Cold Wall ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Flow Reversals ◽  
Rayleigh Benard

Flow reversals in two-dimensional Rayleigh–Bénard convection led by non-Oberbeck–Boussinesq (NOB) effects due to large temperature differences are studied by direct numerical simulation. Perfect gas is chosen as the working fluid and the Prandtl number is 0.71 for the reference state. If NOB effects are included, the flow pattern $P_{11}$ with only one dominant roll often becomes unstable by the growth of the cold corner roll, which sometimes results in cession-led flow reversals. By exploiting the vorticity transport equation, it is found that the asymmetries of buoyancy and viscous forces are responsible for the growth of the cold corner roll because both such asymmetries cause an imbalance between the corner rolls and the large-scale circulation (LSC). The buoyancy force near the cold wall increases and decreases near the hot wall originating from the temperature-dependent isobaric thermal expansion coefficient ${\it\alpha}=1/T$ if NOB effects are included. Moreover, the decreased dissipation due to lower viscosity is favourable for the growth of the cold corner roll, while the increased viscosity further suppresses the growth of the hot corner roll. Finally, it is found that the boundary layer near the cold wall plays an important role in the mass transport from LSC to corner rolls subject to mass conservation.

scholarly journals Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition

2016 ◽  
Vol 791 ◽  
Author(s):  
Xiaozhou He ◽  
Eberhard Bodenschatz ◽  
Guenter Ahlers
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Cylindrical Sample ◽  
Ultimate State ◽  
Large Scale Circulation ◽  
Classical State ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We present measurements of the orientation ${\it\theta}_{0}$ and temperature amplitude ${\it\delta}$ of the large-scale circulation in a cylindrical sample of turbulent Rayleigh–Bénard convection (RBC) with aspect ratio ${\it\Gamma}\equiv D/L=1.00$ ($D$ and $L$ are the diameter and height respectively) and for the Prandtl number $Pr\simeq 0.8$. The results for ${\it\theta}_{0}$ revealed a preferred orientation with up-flow in the west, consistent with a broken azimuthal invariance due to the Earth’s Coriolis force (see Brown & Ahlers (Phys. Fluids, vol. 18, 2006, 125108)). They yielded the azimuthal diffusivity $D_{{\it\theta}}$ and a corresponding Reynolds number $Re_{{\it\theta}}$ for Rayleigh numbers over the range $2\times 10^{12}\lesssim Ra\lesssim 1.5\times 10^{14}$. In the classical state ($Ra\lesssim 2\times 10^{13}$) the results were consistent with the measurements by Brown & Ahlers (J. Fluid Mech., vol. 568, 2006, pp. 351–386) for $Ra\lesssim 10^{11}$ and $Pr=4.38$, which gave $Re_{{\it\theta}}\propto Ra^{0.28}$, and with the Prandtl-number dependence $Re_{{\it\theta}}\propto Pr^{-1.2}$ as found previously also for the velocity-fluctuation Reynolds number $Re_{V}$ (He et al., New J. Phys., vol. 17, 2015, 063028). At larger $Ra$ the data for $Re_{{\it\theta}}(Ra)$ revealed a transition to a new state, known as the ‘ultimate’ state, which was first seen in the Nusselt number $Nu(Ra)$ and in $Re_{V}(Ra)$ at $Ra_{1}^{\ast }\simeq 2\times 10^{13}$ and $Ra_{2}^{\ast }\simeq 8\times 10^{13}$. In the ultimate state we found $Re_{{\it\theta}}\propto Ra^{0.40\pm 0.03}$. Recently, Skrbek & Urban (J. Fluid Mech., vol. 785, 2015, pp. 270–282) claimed that non-Oberbeck–Boussinesq effects on the Nusselt and Reynolds numbers of turbulent RBC may have been interpreted erroneously as a transition to a new state. We demonstrate that their reasoning is incorrect and that the transition observed in the Göttingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as ‘ultimate’.

scholarly journals The origin of oscillations of the large-scale circulation of turbulent Rayleigh–Bénard convection

2009 ◽  
Vol 638 ◽  
pp. 383-400 ◽  
Author(s):  
ERIC BROWN ◽  
GUENTER AHLERS
Keyword(s):  
Large Scale ◽  
Lateral Displacement ◽  
Torsional Oscillation ◽  
Restoring Force ◽  
Large Scale Circulation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Sloshing Mode ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In agreement with a recent experimental discovery by Xi et al. (Phys. Rev. Lett., vol. 102, 2009, paper no. 044503), we also find a sloshing mode in experiments on the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection in a cylindrical sample of aspect ratio one. The sloshing mode has the same frequency as the torsional oscillation discovered by Funfschilling & Ahlers (Phys. Rev. Lett., vol. 92, 2004, paper no. 1945022004). We show that both modes can be described by an extension of a model developed previously Brown & Ahlers (Phys. Fluids, vol. 20, 2008, pp. 105105-1–105105-15; Phys. Fluids, vol. 20, 2008, pp. 075101-1–075101-16). The extension consists of permitting a lateral displacement of the LSC circulation plane away from the vertical centreline of the sample as well as a variation of the displacement with height (such displacements had been excluded in the original model). Pressure gradients produced by the sidewall of the container on average centre the plane of the LSC so that it prefers to reach its longest diameter. If the LSC is displaced away from this diameter, the walls provide a restoring force. Turbulent fluctuations drive the LSC away from the central alignment, and combined with the restoring force they lead to oscillations. These oscillations are advected along with the LSC. This model yields the correct wavenumber and phase of the oscillations, as well as estimates of the frequency, amplitude and probability distributions of the displacements.

Thermal convection in inclined cylindrical containers

2016 ◽  
Vol 790 ◽  
Author(s):  
Olga Shishkina ◽  
Susanne Horn
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Large Scale ◽  
Direct Numerical Simulations ◽  
Large Scale Circulation ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard ◽  
Small Inclination

By means of direct numerical simulations (DNS) we investigate the effect of a tilt angle ${\it\beta}$, $0\leqslant {\it\beta}\leqslant {\rm\pi}/2$, of a Rayleigh–Bénard convection (RBC) cell of aspect ratio 1, on the Nusselt number $\mathit{Nu}$ and Reynolds number $\mathit{Re}$. The considered Rayleigh numbers $\mathit{Ra}$ range from $10^{6}$ to $10^{8}$, the Prandtl numbers range from 0.1 to 100 and the total number of the studied cases is 108. We show that the $\mathit{Nu}\,({\it\beta})/\mathit{Nu}(0)$ dependence is not universal and is strongly influenced by a combination of $\mathit{Ra}$ and $\mathit{Pr}$. Thus, with a small inclination ${\it\beta}$ of the RBC cell, the Nusselt number can decrease or increase, compared to that in the RBC case, for large and small $\mathit{Pr}$, respectively. A slight cell tilt may not only stabilize the plane of the large-scale circulation (LSC) but can also enforce an LSC for cases when the preferred state in the perfect RBC case is not an LSC but a more complicated multiple-roll state. Close to ${\it\beta}={\rm\pi}/2$, $\mathit{Nu}$ and $\mathit{Re}$ decrease with increasing ${\it\beta}$ in all considered cases. Generally, the $\mathit{Nu}({\it\beta})/\mathit{Nu}(0)$ dependence is a complicated, non-monotonic function of ${\it\beta}$.

Dynamics of the large-scale circulation in turbulent Rayleigh–Bénard convection with modulated rotation

2015 ◽  
Vol 778 ◽  
Author(s):  
Jin-Qiang Zhong ◽  
Sebastian Sterl ◽  
Hui-Min Li
Keyword(s):  
Large Scale ◽  
Modulation Frequency ◽  
Rotation Velocity ◽  
Viscous Drag ◽  
Phase Lag ◽  
Large Scale Circulation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We present measurements of the azimuthal rotation velocity $\dot{{\it\theta}}(t)$ and thermal amplitude ${\it\delta}(t)$ of the large-scale circulation in turbulent Rayleigh–Bénard convection with modulated rotation. Both $\dot{{\it\theta}}(t)$ and ${\it\delta}(t)$ exhibit clear oscillations at the modulation frequency ${\it\omega}$. Fluid acceleration driven by oscillating Coriolis force causes an increasing phase lag in $\dot{{\it\theta}}(t)$ when ${\it\omega}$ increases. The applied modulation produces oscillatory boundary layers and the resulting time-varying viscous drag modifies ${\it\delta}(t)$ periodically. Oscillation of $\dot{{\it\theta}}(t)$ with maximum amplitude occurs at a finite modulation frequency ${\it\omega}^{\ast }$. Such a resonance-like phenomenon is interpreted as a result of optimal coupling of ${\it\delta}(t)$ to the modulated rotation velocity. We show that an extended large-scale circulation model with a relaxation time for ${\it\delta}(t)$ in response to the modulated rotation provides predictions in close agreement with the experimental results.

scholarly journals The effect of surfactant solutions on flow structures in turbulent Rayleigh-Benard convection

2018 ◽  
Vol 22 (Suppl. 2) ◽  
pp. 507-515 ◽  
Author(s):  
Tongzhou Wei ◽  
Weihua Cai ◽  
Changye Huang ◽  
Hongna Zhang ◽  
Wentao Su ◽  
...  
Keyword(s):  
Experimental Study ◽  
Large Scale ◽  
Particle Image ◽  
Surfactant Solution ◽  
Flow Structures ◽  
Large Scale Circulation ◽  
Surfactant Solutions ◽  
Image Velocimetry ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper presents an experimental study on the flow structures in turbulent Rayleigh-B?nard convection with surfactant solutions. The shadowgraph visualization was used to obtain the plumes and the velocity field was measured using particle image velocimetry. The results show that the size of plumes in surfactant solution case is larger than that in Newtonian fluid case and it needs more time for surfactant solution case to start convection. The large-scale circulation fails to form in surfactant solution case and the convection velocity is smaller. A decrease of the measured Nusselt number is observed in surfactant solution case. The above phenomena are caused by the shear-shinning and elastic chara cteristics of surfactant solution.

The wind in confined thermal convection

2001 ◽  
Vol 449 ◽  
pp. 169-178 ◽  
Author(s):  
J. J. NIEMELA ◽  
L. SKRBEK ◽  
K. R. SREENIVASAN ◽  
R. J. DONNELLY
Keyword(s):  
Rayleigh Number ◽  
Large Scale ◽  
Turnover Time ◽  
Turbulent Convection ◽  
Physical Explanation ◽  
Dynamical Parameter ◽  
Large Scale Circulation ◽  
Wide Range ◽  
Circulation Velocity ◽  
Rayleigh Benard

A large-scale circulation velocity, often called the ‘wind’, has been observed in turbulent convection in the Rayleigh–Bénard apparatus, which is a closed box with a heated bottom wall. The wind survives even when the dynamical parameter, namely the Rayleigh number, is very large. Over a wide range of time scales greater than its characteristic turnover time, the wind velocity exhibits occasional and irregular reversals without a change in magnitude. We study this feature experimentally in an apparatus of aspect ratio unity, in which the highest attainable Rayleigh number is about 1016. A possible physical explanation is attempted.

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