scholarly journals Effect of tilting on turbulent convection: cylindrical samples with aspect ratio

2013 ◽  
Vol 715 ◽  
pp. 314-334 ◽  
Author(s):  
Stephan Weiss ◽  
Guenter Ahlers
Keyword(s):  
Aspect Ratio ◽  
Heat Transport ◽  
Large Scale ◽  
Rotational Symmetry ◽  
Torsional Oscillation ◽  
Large Scale Circulation ◽  
Cylindrical Cell ◽  
Quantitative Measurements ◽  
Gravity Measurements ◽  
Cylindrical Samples

AbstractWe report measurements of the properties of turbulent thermal convection of a fluid with a Prandtl number $\mathit{Pr}= 4. 38$ in a cylindrical cell with an aspect ratio $\Gamma = 0. 50$. The rotational symmetry was broken by a small tilt of the sample axis relative to gravity. Measurements of the heat transport (as expressed by the Nusselt number Nu), as well as properties of the large-scale circulation (LSC) obtained from temperature measurements along the sidewall, are presented. In contradistinction to similar experiments using containers of aspect ratio $\Gamma = 1. 00$ (Ahlers et al., J. Fluid Mech., vol. 557, 2006b, pp. 347–367) and $\Gamma = 0. 50$ (Chillà et al., Eur. Phys. J. B, vol. 40, 2004, pp. 223–227; Sun, Xi & Xia, Phys. Rev. Lett., vol. 95, 2005, p. 074502; Roche et al., New J. Phys., vol. 12, 2010, p. 085014), we see a very small increase of the heat transport for tilt angles up to about 0.1 rad. Based on measurements of properties of the LSC we explain this increase by a stabilization of the single-roll state (SRS) of the LSC and a destabilization of the double-roll state (DRS) (it is known from previous work that the SRS has a slightly larger heat transport than the DRS). Quantitative measurements of the strength and the orientation of the LSC show that its azimuthal diffusion is suppressed with increasing tilt whereas the torsional oscillation becomes more pronounced and its frequency increases.

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.

Reversals of the large-scale circulation in quasi-2D Rayleigh–Bénard convection

2015 ◽  
Vol 778 ◽  
Author(s):  
Rui Ni ◽  
Shi-Di Huang ◽  
Ke-Qing Xia
Keyword(s):  
Aspect Ratio ◽  
Large Scale ◽  
Relative Weight ◽  
Tuning Parameter ◽  
Viscous Drag ◽  
Time Interval ◽  
Damping Force ◽  
Large Scale Circulation ◽  
2D System ◽  
The Difference

We report an experimental study of the large-scale circulation (LSC) reversal in quasi-2D turbulent thermal convection, in which the aspect ratio ${\it\Gamma}$ ($=\text{height}/\text{length}$ of a rectangular box) is used as a parameter to perturb the stability of the LSC. It is found that the mean time interval $\langle {\it\tau}\rangle$ between two successive reversals increases strongly with increasing ${\it\Gamma}$. A stochastic model is proposed to incorporate the effect of the corner rolls. In the model, the aspect ratio serves as a tuning parameter for the relative weight of the corner rolls that damp the LSC. The model predictions for the shape of the bistable states of the system and $\langle {\it\tau}\rangle$ agree excellently with the experimental results, with $\langle {\it\tau}\rangle$ having an unexpected stretched exponential Rayleigh number dependence, ${\sim}\!\exp (Ra^{{\it\alpha}})$. We further show quantitatively that the main damping force of the LSC in a quasi-2D system is from the corner rolls rather than the viscous drag from the sidewalls, which bridges the difference found in quasi-2D and 3D systems.

scholarly journals Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection

2010 ◽  
Vol 655 ◽  
pp. 152-173 ◽  
Author(s):  
J. BAILON-CUBA ◽  
M. S. EMRAN ◽  
J. SCHUMACHER
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Large Scale ◽  
Turbulent Convection ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Cylindrical Cell ◽  
Aspect Ratios ◽  
Pod Analysis

The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh–Bénard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio Γ of a closed cylindrical cell and the Rayleigh number Ra. The Prandtl number is Pr = 0.7 throughout the study. The aspect ratio Γ is varied between 0.5 and 12 for a Rayleigh number range between 107 and 109. The Nusselt number Nu is the dimensionless measure of the global turbulent heat transfer. For small and moderate aspect ratios, the global heat transfer law Nu = A × Raβ shows a power law dependence of both fit coefficients A and β on the aspect ratio. A minimum of Nu(Γ) is found at Γ ≈ 2.5 and Γ ≈ 2.25 for Ra = 107 and Ra = 108, respectively. This is the point where the LSC undergoes a transition from a single-roll to a double-roll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations in the convection cell. For larger aspect ratios Γ ≳ 8, our data indicate that the heat transfer becomes independent of the aspect ratio of the cylindrical cell. The aspect ratio dependence of the turbulent heat transfer for small and moderate Γ is in line with a varying amount of energy contained in the LSC, as quantified by the Karhunen–Loève or proper orthogonal decomposition (POD) analysis of the turbulent convection field. The POD analysis is conducted here by the snapshot method for at least 100 independent realizations of the turbulent fields. The primary POD mode, which replicates the time-averaged LSC patterns, transports about 50% of the global heat for Γ ≥ 1. The snapshot analysis enables a systematic disentanglement of the contributions of POD modes to the global turbulent heat transfer. Although the smallest scale – the Kolmogorov scale ηK – and the largest scale – the cell height H – are widely separated in a turbulent flow field, the LSC patterns in fully turbulent fields exhibit strikingly similar texture to those in the weakly nonlinear regime right above the onset of convection. Pentagonal or hexagonal circulation cells are observed preferentially if the aspect ratio is sufficiently large (Γ ≳ 8).

scholarly journals The influence of the cell inclination on the heat transport and large-scale circulation in liquid metal convection

2019 ◽  
Vol 884 ◽  
Author(s):  
Lukas Zwirner ◽  
Ruslan Khalilov ◽  
Ilya Kolesnichenko ◽  
Andrey Mamykin ◽  
Sergei Mandrykin ◽  
...  
Keyword(s):  
Liquid Metal ◽  
Heat Transport ◽  
Large Scale ◽  
Large Scale Circulation ◽  
Image Position

Turbulent thermal convection in a cell with ordered rough boundaries

2000 ◽  
Vol 407 ◽  
pp. 57-84 ◽  
Author(s):  
Y.-B. DU ◽  
P. TONG
Keyword(s):  
Secondary Flow ◽  
Heat Transport ◽  
Large Scale ◽  
Horizontal Shear ◽  
Large Scale Circulation ◽  
Thermal Plumes ◽  
A Cell ◽  
Efficient Heat Transfer ◽  
Rough Boundaries ◽  
Rough Cell

A novel convection experiment is conducted in a cell with rough upper and lower surfaces. The measured heat transport in the rough cell is found to be increased by more than 76%. Flow visualization and near-wall temperature measurements reveal new dynamics for the emission of thermal plumes. The experiment shows that the interaction between the horizontal shear flow due to the large-scale circulation and the ordered rough surface creates a secondary flow (eddies) in the groove region. The secondary flow together with the large-scale circulation enhance the detachment of the thermal boundary layer from the tip of the rough elements. These extra thermal plumes are responsible for the enhanced heat transport in the rough cell. The discovery of the enhanced heat transport has important applications in engineering for more efficient heat transfer.

Dynamics of large-scale circulation of turbulent thermal convection in a horizontal cylinder

2014 ◽  
Vol 740 ◽  
pp. 136-167 ◽  
Author(s):  
Hao Song ◽  
Eric Brown ◽  
Russell Hawkins ◽  
Penger Tong
Keyword(s):  
Aspect Ratio ◽  
Thermal Convection ◽  
Large Scale ◽  
Horizontal Cylinder ◽  
Turnover Time ◽  
Stochastic Motion ◽  
Large Scale Circulation ◽  
Aspect Ratios ◽  
Measured Probability ◽  
Horizontal Cylinders

AbstractA systematic study of the effects of cell geometry on the dynamics of large-scale flows in turbulent thermal convection is carried out in horizontal cylindrical cells of different lengths filled with water. Four different flow modes are identified with increasing aspect ratio $\Gamma $. For small aspect ratios ($\Gamma \leq 0.16$), the flow is highly confined in a thin disc-like cell with a quasi-two-dimensional (quasi-2D) large-scale circulation (LSC) in the circular plane of the cell. For larger aspect ratios ($\Gamma >0.16$), we observe periodic switching of the angular orientation $\theta $ of the rotation plane of LSC between the two longest diagonals of the cell. The sides of the container along which the LSC oscillates changes at a critical aspect ratio $\Gamma _{c}\simeq 0.82$. The measured switching period is equal to the LSC turnover time for $\Gamma \leq \Gamma _c$, shows a sharp increase at $\Gamma _{c}$ and decays exponentially to the LSC turnover time with increasing $\Gamma $. For $\Gamma \geq 1.3$, a periodic rocking of LSC along the long axis of the cylinder is also observed. The measured probability density function $P(\theta )$ of the LSC orientation $\theta $ peaks at the two diagonal positions, and its shape is described by a phenomenological model proposed by Brown & Ahlers (Phys. Fluids, vol. 20, 2008b, 075101; J. Fluid Mech., vol. 638, 2009, pp. 383–400). Using this model, we describe the dynamics of the LSC orientation $\theta $ by stochastic motion in a double-well potential. The potential is predicted from a model in which the sidewall shape produces an orientation-dependent pressure on the LSC. This model also captures key features of the four flow modes. The experiment reveals an interesting array of rich dynamics of LSC in the horizontal cylinders, which are very different from those observed in the upright cylindrical convection cells. The success of the model for both upright and horizontal cylinders suggests that it can be applied to different geometries.

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