How surface roughness reduces heat transport for small roughness heights in turbulent Rayleigh–Bénard convection

2017 ◽  
Vol 836 ◽  
Author(s):  
Yi-Zhao Zhang ◽  
Chao Sun ◽  
Yun Bao ◽  
Quan Zhou
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Heat Transport ◽  
Roughness Height ◽  
Physical Reason ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Rough surfaces have been widely used as an efficient way to enhance the heat-transfer efficiency in turbulent thermal convection. In this paper, however, we show that roughness does not always mean a heat-transfer enhancement, but in some cases it can also reduce the overall heat transport through the system. To reveal this, we carry out numerical investigations of turbulent Rayleigh–Bénard convection over rough conducting plates. Our study includes two-dimensional (2D) simulations over the Rayleigh number range $10^{7}\leqslant Ra\leqslant 10^{11}$ and three-dimensional (3D) simulations at $Ra=10^{8}$. The Prandtl number is fixed to $Pr=0.7$ for both the 2D and the 3D cases. At a fixed Rayleigh number $Ra$, reduction of the Nusselt number $Nu$ is observed for small roughness height $h$, whereas heat-transport enhancement occurs for large $h$. The crossover between the two regimes yields a critical roughness height $h_{c}$, which is found to decrease with increasing $Ra$ as $h_{c}\sim Ra^{-0.6}$. Through dimensional analysis, we provide a physical explanation for this dependence. The physical reason for the $Nu$ reduction is that the hot/cold fluid is trapped and accumulated inside the cavity regions between the rough elements, leading to a much thicker thermal boundary layer and thus impeding the overall heat flux through the system.

scholarly journals Aspect ratio dependence of heat transport by turbulent Rayleigh–Bénard convection in rectangular cells

2012 ◽  
Vol 710 ◽  
pp. 260-276 ◽  
Author(s):  
Quan Zhou ◽  
Bo-Fang Liu ◽  
Chun-Mei Li ◽  
Bao-Chang Zhong
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Finite Conductivity ◽  
Turbulent Heat ◽  
Number Range ◽  
Aspect Ratios ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractWe report high-precision measurements of the Nusselt number $Nu$ as a function of the Rayleigh number $Ra$ in water-filled rectangular Rayleigh–Bénard convection cells. The horizontal length $L$ and width $W$ of the cells are 50.0 and 15.0 cm, respectively, and the heights $H= 49. 9$, 25.0, 12.5, 6.9, 3.5, and 2.4 cm, corresponding to the aspect ratios $({\Gamma }_{x} \equiv L/ H, {\Gamma }_{y} \equiv W/ H)= (1, 0. 3)$, $(2, 0. 6)$, $(4, 1. 2)$, $(7. 3, 2. 2)$, $(14. 3, 4. 3)$, and $(20. 8, 6. 3)$. The measurements were carried out over the Rayleigh number range $6\ensuremath{\times} 1{0}^{5} \lesssim Ra\lesssim 1{0}^{11} $ and the Prandtl number range $5. 2\lesssim Pr\lesssim 7$. Our results show that for rectangular geometry turbulent heat transport is independent of the cells’ aspect ratios and hence is insensitive to the nature and structures of the large-scale mean flows of the system. This is slightly different from the observations in cylindrical cells where $Nu$ is found to be in general a decreasing function of $\Gamma $, at least for $\Gamma = 1$ and larger. Such a difference is probably a manifestation of the finite plate conductivity effect. Corrections for the influence of the finite conductivity of the top and bottom plates are made to obtain the estimates of $N{u}_{\infty } $ for plates with perfect conductivity. The local scaling exponents ${\ensuremath{\beta} }_{l} $ of $N{u}_{\infty } \ensuremath{\sim} R{a}^{{\ensuremath{\beta} }_{l} } $ are calculated and found to increase from 0.243 at $Ra\simeq 9\ensuremath{\times} 1{0}^{5} $ to 0.327 at $Ra\simeq 4\ensuremath{\times} 1{0}^{10} $.

scholarly journals Mixed insulating and conducting thermal boundary conditions in Rayleigh–Bénard convection

2017 ◽  
Vol 835 ◽  
pp. 491-511 ◽  
Author(s):  
Dennis Bakhuis ◽  
Rodolfo Ostilla-Mónico ◽  
Erwin P. van der Poel ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Heat Transport ◽  
Bottom Plate ◽  
Bulk Temperature ◽  
Stripe Pattern ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

A series of direct numerical simulations of Rayleigh–Bénard convection, the flow in a fluid layer heated from below and cooled from above, were conducted to investigate the effect of mixed insulating and conducting boundary conditions on convective flows. Rayleigh numbers between $Ra=10^{7}$ and $Ra=10^{9}$ were considered, for Prandtl numbers $\mathit{Pr}=1$ and $\mathit{Pr}=10$. The bottom plate was divided into patterns of conducting and insulating stripes. The size ratio between these stripes was fixed to unity and the total number of stripes was varied. Global quantities, such as the heat transport and average bulk temperature, and local quantities, such as the temperature just below the insulating boundary wall, were investigated. For the case with the top boundary divided into two halves, one conducting and one insulating, the heat transfer was found to be approximately two-thirds of that for the fully conducting case. Increasing the pattern frequency increased the heat transfer, which asymptotically approached the fully conducting case, even if only half of the surface is conducting. Fourier analysis of the temperature field revealed that the imprinted pattern of the plates is diffused in the thermal boundary layers, and cannot be detected in the bulk. With conducting–insulating patterns on both plates, the trends previously described were similar; however, the half-and-half division led to a heat transfer of about a half of that for the fully conducting case instead of two-thirds. The effect of the ratio of conducting and insulating areas was also analysed, and it was found that, even for systems with a top plate with only 25 % conducting surface, heat transport of 60 % of the fully conducting case can be seen. Changing the one-dimensional stripe pattern to a two-dimensional chequerboard tessellation does not result in a significantly different response of the system.

scholarly journals Prandtl–Blasius temperature and velocity boundary-layer profiles in turbulent Rayleigh–Bénard convection

2010 ◽  
Vol 664 ◽  
pp. 297-312 ◽  
Author(s):  
QUAN ZHOU ◽  
RICHARD J. A. M. STEVENS ◽  
KAZUYASU SUGIYAMA ◽  
SIEGFRIED GROSSMANN ◽  
DETLEF LOHSE ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Reference Frames ◽  
Temperature Profiles ◽  
Number Range ◽  
Velocity Boundary Layer ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The shapes of the velocity and temperature profiles near the horizontal conducting plates' centre regions in turbulent Rayleigh–Bénard convection are studied numerically and experimentally over the Rayleigh number range 108 ≲ Ra ≲ 3 × 1011 and the Prandtl number range 0.7 ≲ Pr ≲ 5.4. The results show that both the temperature and velocity profiles agree well with the classical Prandtl–Blasius (PB) laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses. The study further shows that the PB boundary layer in turbulent thermal convection not only holds in a time-averaged sense, but is most of the time also valid in an instantaneous sense.

scholarly journals Turbulent transition in Rayleigh-Bénard convection with fluorocarbon (a)

2021 ◽  
Vol 136 (1) ◽  
pp. 10003
Author(s):  
Lucas Méthivier ◽  
Romane Braun ◽  
Francesca Chillà ◽  
Julien Salort
Keyword(s):  
Heat Transfer ◽  
Velocity Field ◽  
Rayleigh Number ◽  
Working Fluid ◽  
Turbulent Transition ◽  
Bénard Convection ◽  
Benard Convection ◽  
Image Velocimetry ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract We present measurements of the global heat transfer and the velocity field in two Rayleigh-Bénard cells (aspect ratios 1 and 2). We use Fluorinert FC770 as the working fluid, up to a Rayleigh number . The velocity field is inferred from sequences of shadowgraph pattern using a Correlation Image Velocimetry (CIV) algorithm. Indeed the large number of plumes, and their small characteristic scale, make it possible to use the shadowgraph pattern produced by the thermal plumes in the same manner as particles in Particle Image Velocimetry (PIV). The method is validated in water against PIV, and yields identical wind velocity estimates. The joint heat transfer and velocity measurements allow to compute the scaling of the kinetic dissipation rate which features a transition from a laminar scaling to a turbulent Re 3 scaling. We propose that the turbulent transition in Rayleigh-Bénard convection is controlled by a threshold Péclet number rather than a threshold Rayleigh number, which may explain the apparent discrepancy in the literature regarding the “ultimate” regime of convection.

scholarly journals Effects of radius ratio on annular centrifugal Rayleigh–Bénard convection

2021 ◽  
Vol 930 ◽  
Author(s):  
Dongpu Wang ◽  
Hechuan Jiang ◽  
Shuang Liu ◽  
Xiaojue Zhu ◽  
Chao Sun
Keyword(s):  
Heat Transport ◽  
Zonal Flow ◽  
Radius Ratio ◽  
Bulk Temperature ◽  
Number Range ◽  
Mean Temperature ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We report on a three-dimensional direct numerical simulation study of flow structure and heat transport in the annular centrifugal Rayleigh–Bénard convection (ACRBC) system, with cold inner and hot outer cylinders corotating axially, for the Rayleigh number range $Ra \in [{10^6},{10^8}]$ and radius ratio range $\eta = {R_i}/{R_o} \in [0.3,0.9]$ ( $R_i$ and $R_o$ are the radius of the inner and outer cylinders, respectively). This study focuses on the dependence of flow dynamics, heat transport and asymmetric mean temperature fields on the radius ratio $\eta$ . For the inverse Rossby number $Ro^{-1} = 1$ , as the Coriolis force balances inertial force, the flow is in the inertial regime. The mechanisms of zonal flow revolving in the prograde direction in this regime are attributed to the asymmetric movements of plumes and the different curvatures of the cylinders. The number of roll pairs is smaller than the circular roll hypothesis as the convection rolls are probably elongated by zonal flow. The physical mechanism of zonal flow is verified by the dependence of the drift frequency of the large-scale circulation (LSC) rolls and the space- and time-averaged azimuthal velocity on $\eta$ . The larger $\eta$ is, the weaker the zonal flow becomes. We show that the heat transport efficiency increases with $\eta$ . It is also found that the bulk temperature deviates from the arithmetic mean temperature and the deviation increases as $\eta$ decreases. This effect can be explained by a simple model that accounts for the curvature effects and the radially dependent centrifugal force in ACRBC.

Torsional oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection

2008 ◽  
Vol 607 ◽  
pp. 119-139 ◽  
Author(s):  
DENIS FUNFSCHILLING ◽  
ERIC BROWN ◽  
GUENTER AHLERS
Keyword(s):  
Rayleigh Number ◽  
Aspect Ratio ◽  
Large Scale ◽  
Small Scale ◽  
Large Scale Circulation ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Measurements over the Rayleigh-number range 108 ≲ R ≲ 1011 and Prandtl-number range 4.4≲σ≲29 that determine the torsional nature and amplitude of the oscillatory mode of the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection are presented. For cylindrical samples of aspect ratio Γ=1 the mode consists of an azimuthal twist of the near-vertical LSC circulation plane, with the top and bottom halves of the plane oscillating out of phase by half a cycle. The data for Γ=1 and σ=4.4 showed that the oscillation amplitude varied irregularly in time, yielding a Gaussian probability distribution centred at zero for the displacement angle. This result can be described well by the equation of motion of a stochastically driven damped harmonic oscillator. It suggests that the existence of the oscillations is a consequence of the stochastic driving by the small-scale turbulent background fluctuations of the system, rather than a consequence of a Hopf bifurcation of the deterministic system. The power spectrum of the LSC orientation had a peak at finite frequency with a quality factor Q≃5, nearly independent of R. For samples with Γ≥2 we did not find this mode, but there remained a characteristic periodic signal that was detectable in the area density ρp of the plumes above the bottom-plate centre. Measurements of ρp revealed a strong dependence on the Rayleigh number R, and on the aspect ratio Γ that could be represented by ρp ~ Γ2.7±0.3. Movies are available with the online version of the paper.

Bounds on Rayleigh–Bénard convection with an imposed heat flux

2002 ◽  
Vol 473 ◽  
pp. 191-199 ◽  
Author(s):  
JESSE OTERO ◽  
RALF W. WITTENBERG ◽  
RODNEY A. WORTHING ◽  
CHARLES R. DOERING
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Heat Transport ◽  
Absolute Constant ◽  
Temperature Drop ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We formulate a bounding principle for the heat transport in Rayleigh–Bénard convection with fixed heat flux through the boundaries. The heat transport, as measured by a conventional Nusselt number, is inversely proportional to the temperature drop across the layer and is bounded above according to Nu [les ] cRˆ1/3, where c < 0.42 is an absolute constant and Rˆ = αγβh4/(νκ) is the ‘effective’ Rayleigh number, the non-dimensional forcing scale set by the imposed heat flux κβ. The relation among the parameter Rˆ, the Nusselt number, and the conventional Rayleigh number defined in terms of the temperature drop across the layer, is NuRa = Rˆ, yielding the bound Nu [les ] c3/2Ra1/2.

scholarly journals Bounds for Rayleigh–Bénard convection between free-slip boundaries with an imposed heat flux

2018 ◽  
Vol 837 ◽  
Author(s):  
Giovanni Fantuzzi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Temperature Drop ◽  
Three Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We prove the first rigorous bound on the heat transfer for three-dimensional Rayleigh–Bénard convection of finite-Prandtl-number fluids between free-slip boundaries with an imposed heat flux. Using the auxiliary functional method with a quadratic functional, which is equivalent to the background method, we prove that the Nusselt number $\mathit{Nu}$ is bounded by $\mathit{Nu}\leqslant 0.5999\mathit{R}^{1/3}$ uniformly in the Prandtl number, where $\mathit{R}$ is the Rayleigh number based on the imposed heat flux. In terms of the Rayleigh number based on the mean vertical temperature drop, $\mathit{Ra}$, we obtain $\mathit{Nu}\leqslant 0.4646\mathit{Ra}^{1/2}$. The scaling with Rayleigh number is the same as that of bounds obtained with no-slip isothermal, free-slip isothermal and no-slip fixed-flux boundaries, and numerical optimisation of the bound suggests that it cannot be improved within our bounding framework. Contrary to the two-dimensional case, therefore, the $\mathit{Ra}$-dependence of rigorous upper bounds on the heat transfer obtained with the background method for three-dimensional Rayleigh–Bénard convection is insensitive to both the thermal and the velocity boundary conditions.

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