Large-scale flow properties of turbulent thermal convection

Journal of Fluid Mechanics, 2008

We numerically investigate turbulent thermal convection driven by a horizontal surface of constant heat flux and compare the results with those of constant temperature. Below Ra ≈ 109, where Ra is the Rayleigh number, when the flow is smooth and regular, the heat transport in the two cases is essentially the same. For Ra > 109 the heat transport for imposed heat flux is smaller than that for constant temperature, and is close to experimental data. We provide a simple dimensional argument to indicate that the unsteady emission of thermal plumes renders typical experimental conditions closer to the constant heat flux case.

Physical Review Letters, 2013

We report an experimental and numerical study of the effect of spatial confinement in turbulent thermal convection. It is found that when the width of the convection cell is narrowed, the heat-transfer efficiency increases significantly despite the fact that the overall flow is slowed down by the increased drag force from the sidewalls. Detailed experimental and numerical studies show that this enhancement is brought about by the changes in the dynamics and morphology of the thermal plumes in the boundary layers and in the large-scale flow structures in the bulk. It is found that the confined geometry produces more coherent and energetic hot and cold plume clusters that go up and down in random locations, resulting in more uniform and thinner thermal boundary layers. The study demonstrates how changes in turbulent bulk flow can influence the boundary layer dynamics and shows that the prevalent mode of heat transfer existing in larger aspect ratio convection cells, in which hot and cold thermal plumes are carried by the large-scale circulation along opposite sides of the sidewall, is not the most efficient way for heat transport.

Journal of Fluid Mechanics

We investigate the counter-intuitive initial decrease and subsequent increase in the Nusselt number $Nu$ with increasing wall Reynolds number $Re_w$ in the sheared Rayleigh–Bénard (RB) system by studying the energy spectra of convective flux and turbulent kinetic energy for Rayleigh number $Ra = 10^{7}$ , Prandtl number $Pr=1.0$ and inverse Richardson numbers $0 \leq 1/Ri \leq 10$ . These energy spectra show two distinct high-energy regions corresponding to the large-scale superstructures in the bulk and small-scale structures in the boundary layer (BL) regions. A greater separation between these scales at the thermal BL height correlates to a higher $Nu$ and indicates that the BLs are more turbulent. The minimum $Nu$ , which occurs at $1/Ri=1.0$ , is accompanied by the smallest separation between the large- and small-scale structures at the thermal BL height. At $1/Ri=1.0$ , we also observe the lowest value of turbulent kinetic energy normalized with the square of friction velocity...

Physical Review Letters, 2011

The local kinetic energy dissipation rate u;c in Rayleigh-Bénard convection cell was measured experimentally using the particle tracking velocimetry method, with varying Rayleigh number Ra, Prandtl number Pr, and cell height H. It is found that u;c =ð 3 H À4 Þ ¼ 1:05 Â 10 À4 Ra 1:55AE0:02 Pr 1:15AE0:38 . The Ra and H dependencies of the measured results are found to be consistent with the assumption made for the bulk energy dissipation rate u;bulk in the Grossmann-Lohse model. A remarkable finding of the study is that u;c balances the directly measured local Nusselt number Nu c in the cell center, not only scalingwise but also in magnitude.

2006

The large scale "wind of turbulence" of thermally driven flow is analyzed for very large Rayleigh numbers between 4 • 10 11 and 7 • 10 11 and Prandtl number of 0.71 ͑air at 40°C͒ and aspect ratios order of one. The wind direction near the upper plate is found to horizontally oscillate with a typical time scale very similar to the large eddy turnover time. The temporal autocorrelation of the wind direction reveals an extremely long memory of the system for the direction. We then apply and extend the dynamical model of Gledzer, Dolzhansky, and Obukhov to the flow, which is based on the Boussinesq equations in the bulk and which can be solved analytically in the inviscid and unforced limit, but which completely ignores the boundary layer and plume dynamics. Nevertheless, the model correctly reproduces both the oscillations of the horizontal wind direction and its very long memory. It is therefore concluded that the boundary layers and the plumes are not necessary to account for the oscillations of the wind direction. The oscillations rather occur as intrinsic precession of the bulk flow.

Physics of Fluids, 2019

We derive scaling relations for the thermal dissipation rate in the bulk and in the boundary layers for moderate and large Prandtl number (Pr) convection. Using direct numerical simulations of Rayleigh-Bénard convection, we show that the thermal dissipation in the bulk is suppressed compared to passive scalar dissipation. The suppression is stronger for large Pr. We further show that the dissipation in the boundary layers dominates that in the bulk for both moderate and large Pr. The probability distribution functions of thermal dissipation rate, both in the bulk and in the boundary layers, are stretched exponential, similar to passive scalar dissipation.

2008

We report an experimental investigation of the spatial structure of the large-scale circulation in turbulent Rayleigh-Bénard convection for different aspect ratios. It was found that the number of the convection rolls depends systematically on the aspect ratio of the system. For aspect ratio 1 and 2 cells, it was found that one convection roll spans the whole convection system. In this case, hot thermal plumes and cold plumes are moving at opposite sidewalls. For aspect ratio larger than or equal to 4, the LSC breaks into multi-roll structure. Our results provide for the first time the number of convection rolls in turbulent thermal convection system with large aspect ratios. Our result also indicates that the transition aspect ratio from single-roll to multi-roll structure is around Γ = 4.

Physical Review Letters, 1997

We present an experimental study of turbulent convection in a cell with staggered fingers on its sidewall using water as the convecting fluid. Our measurements reveal that Nu ϳ Ra 20.27 , and that the temperature probability density function (PDF) at the cell center is a double-peaked function which can be fitted by the superposition of two Gaussians. Moreover, it is found that the size of the local temperature fluctuations scales with Ra and that the scaled PDFs for different Ra have an invariant form. Visualization studies show that the mean flow pattern in the cell is a twisted asymmetric fourroll circulation, which helped to explain the observed PDF. [S0031-9007 04841-2] PACS numbers: 47.27.Te, 44.25. + f 5006 0031-9007͞97͞79(25)͞5006(4)$10.00

Journal of Fluid Mechanics

We perform direct numerical simulations of wall sheared Rayleigh-Bénard convection for Rayleigh numbers up to Ra = 10 8 , Prandtl number unity and wall shear Reynolds numbers up to Re w = 10 000. Using the Monin-Obukhov length L MO we observe the presence of three different flow states, a buoyancy dominated regime (L MO λ θ ; with λ θ the thermal boundary layer thickness), a transitional regime (0.5H L MO λ θ ; with H the height of the domain) and a shear dominated regime (L MO 0.5H). In the buoyancy dominated regime, the flow dynamics is similar to that of turbulent thermal convection. The transitional regime is characterized by rolls that are increasingly elongated with increasing shear. The flow in the shear dominated regime consists of very large-scale meandering rolls, similar to the ones found in conventional Couette flow. As a consequence of these different flow regimes, for fixed Ra and with increasing shear, the heat transfer first decreases, due to the breakup of the thermal rolls, and then increases at the beginning of the shear dominated regime. In the shear dominated regime the Nusselt number Nu effectively scales as Nu ∼ Ra α with α 1/3, while we find α 0.30 in the buoyancy dominated regime. In the transitional regime, the effective scaling exponent is α > 1/3, but the temperature and velocity profiles in this regime are not logarithmic yet, thus indicating transient dynamics and not the ultimate regime of thermal convection.

Journal of Fluid Mechanics, 2014

A 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}$and decays exponentially to the LSC turnover time with increasing$\Gamm...

Proceedings of the Sixth International Symposium On Turbulence, Heat and Mass Transfer, 2009

Low frequency oscillations in the heat transfer of mixed convection in a rectangular cavity with an aspect ratio of Γ xz = 1 and Γ yz = 5 have been observed. Mixed convective flow at Ra = 2.4 × 10 8 , Re = 1.0 × 10 4 , Ar = 3.3 and P r ≈ 0.7 was studied to determine the nature of these oscillations. Therefore Particle Image Velocimetry (PIV) and temperature measurements have been performed under ambient and heigh pressure conditions. The PIV results have been analysed using Proper Orthogonal Decomposion (POD) to identify the characteristic frequencies of the coherent largescale structures dynamics and compared their dynamics with the low frequency oscillations found in the heat transfer.

The European Physical Journal B - Condensed Matter, 2003

In this paper the effects of viscous boundary layers and mean flow structures on the heat transfer of a flow in a slender cylindrical cell are analysed using the direct numerical simulation of the Navier-Stokes equations with the Boussinesq approximation. Ideal flows are produced by suppressing the viscous boundary layers and by artificially enforcing the flow axisymmetry with the aim of checking some proposed explanations for the Nusselt number dependence on the Rayleigh number. The emerging picture suggests that, in this slender geometry,the presence of the viscous boundary layers does not have appreciable impact on the slope of the Nu vs. Ra relation while a transition of the mean flow is most likely the reason for the slope increase observed around Ra = 2 × 10 9 .

Springer Proceedings Physics, 2007

EPL (Europhysics Letters), 2009

PACS 47.27.te-Turbulent convective heat transfer PACS 44.25.+f-Heat transfer: Natural convection PACS 47.80.-v-Instrumentation and measurement methods in fluid dynamics Abstract.-A new regime of turbulent convection has been reported nearly one decade ago, based on global heat transfer measurements at very high Rayleigh numbers. We examine the signature of this "Ultimate Regime" from within the flow itself. A systematic study of probe-size corrections shows that the earlier temperature measurements within the flow were altered by an excessive size of thermometer, but not according to a theoretical model proposed in the literature. Using a probe one order of magnitude smaller than the one used previously, we find evidence that the transition to the Ultimate Regime is indeed accompanied with a clear change in the statistics of temperature fluctuations in the flow.

2008

The mechanisms governing the transition to turbulence in natural convection boundary layers along strongly heated vertical walls remain neither very clear nor well understood, because of the lack of experiments and the difficulties of physical modelling. Our measurements bring experimental data focusing on this transition, in quiescent air along radiating and conducting plates, in the whole range of 2000 to 8000 W.m-2 heating rate. The analysis of the time series obtained by sliding window cross-correlation thermoanemometry leads us to point out coherent turbulent structures on short heights throughout the thin boundary layer, which seem to be governed by heat transfer and time microscales of turbulence through the inner sublayer. Physical interpretations are given to relate the observed heat transfer correlation and these turbulence transition structures along with radiation and conduction.