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.

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 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} $.

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.

Bulk temperature and heat transport in turbulent Rayleigh–Bénard convection of fluids with temperature-dependent properties

2018 ◽  
Vol 851 ◽  
pp. 374-390 ◽  
Author(s):  
Stephan Weiss ◽  
Xiaozhou He ◽  
Guenter Ahlers ◽  
Eberhard Bodenschatz ◽  
Olga Shishkina
Keyword(s):  
Heat Transport ◽  
Convection Cell ◽  
Bulk Temperature ◽  
Bénard Convection ◽  
Benard Convection ◽  
Theoretical Predictions ◽  
Fluid Properties ◽  
Temperature Dependent Properties ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We critically analyse the different ways to evaluate the dependence of the Nusselt number ($\mathit{Nu}$) on the Rayleigh number ($\mathit{Ra}$) in measurements of the heat transport in turbulent Rayleigh–Bénard convection under general non-Oberbeck–Boussinesq conditions and show the sensitivity of this dependence to the choice of the reference temperature at which the fluid properties are evaluated. For the case when the fluid properties depend significantly on the temperature and any pressure dependence is insignificant we propose a method to estimate the centre temperature. The theoretical predictions show very good agreement with the Göttingen measurements by He et al. (New J. Phys., vol. 14, 2012, 063030). We further show too the values of the normalized heat transport $\mathit{Nu}/\mathit{Ra}^{1/3}$ are independent of whether they are evaluated in the whole convection cell or in the lower or upper part of the cell if the correct reference temperatures are used.

Direct numerical simulations of Rayleigh–Bénard convection in water with non-Oberbeck–Boussinesq effects

2019 ◽  
Vol 881 ◽  
pp. 1073-1096 ◽  
Author(s):  
Andreas D. Demou ◽  
Dimokratis G. E. Grigoriadis
Keyword(s):  
Numerical Simulations ◽  
Two Dimensions ◽  
Direct Numerical Simulations ◽  
Wall Region ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Near Wall

Rayleigh–Bénard convection in water is studied by means of direct numerical simulations, taking into account the variation of properties. The simulations considered a three-dimensional (3-D) cavity with a square cross-section and its two-dimensional (2-D) equivalent, covering a Rayleigh number range of $10^{6}\leqslant Ra\leqslant 10^{9}$ and using temperature differences up to 60 K. The main objectives of this study are (i) to investigate and report differences obtained by 2-D and 3-D simulations and (ii) to provide a first appreciation of the non-Oberbeck–Boussinesq (NOB) effects on the near-wall time-averaged and root-mean-squared (r.m.s.) temperature fields. The Nusselt number and the thermal boundary layer thickness exhibit the most pronounced differences when calculated in two dimensions and three dimensions, even though the $Ra$ scaling exponents are similar. These differences are closely related to the modification of the large-scale circulation pattern and become less pronounced when the NOB values are normalised with the respective Oberbeck–Boussinesq (OB) values. It is also demonstrated that NOB effects modify the near-wall temperature statistics, promoting the breaking of the top–bottom symmetry which characterises the OB approximation. The most prominent NOB effect in the near-wall region is the modification of the maximum r.m.s. values of temperature, which are found to increase at the top and decrease at the bottom of the cavity.

The large-scale flow structure in turbulent rotating Rayleigh–Bénard convection

2011 ◽  
Vol 688 ◽  
pp. 461-492 ◽  
Author(s):  
Stephan Weiss ◽  
Guenter Ahlers
Keyword(s):  
Large Scale ◽  
Working Fluid ◽  
Flow Mode ◽  
Unexpected Result ◽  
Vertical Sidewall ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractWe report on the influence of rotation about a vertical axis on the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection in a cylindrical vessel with aspect ratio $\Gamma \equiv D/ L= 0. 50$ (where $D$ is the diameter and $L$ the height of the sample). The working fluid is water at an average temperature ${T}_{av} = 40{~}^{\ensuremath{\circ} } \mathrm{C} $ with a Prandtl number $\mathit{Pr}= 4. 38$. For rotation rates $\Omega \lesssim 1~\mathrm{rad} ~{\mathrm{s} }^{\ensuremath{-} 1} $, corresponding to inverse Rossby numbers $1/ \mathit{Ro}$ between 0 and 20, we investigated the temperature distribution at the sidewall and from it deduced properties of the LSC. The work covered the Rayleigh-number range $2. 3\ensuremath{\times} 1{0}^{9} \lesssim \mathit{Ra}\lesssim 7. 2\ensuremath{\times} 1{0}^{10} $. We measured the vertical sidewall temperature gradient, the dynamics of the LSC and flow-mode transitions from single-roll states (SRSs) to double-roll states (DRSs). We found that modest rotation stabilizes the SRSs. For modest $1/ \mathit{Ro}\lesssim 1$ we found the unexpected result that the vertical LSC plane rotated in the prograde direction (i.e. faster than the sample chamber), with the rotation at the horizontal midplane faster than near the top and bottom. This differential rotation led to disruptive events called half-turns, where the plane of the top or bottom section of the LSC underwent a rotation through an angle of $2\lrm{\pi} $ relative to the main portion of the LSC. The signature of the LSC persisted even for large $1/ \mathit{Ro}$ where Ekman vortices are expected. We consider the possibility that this signature actually is generated by a two-vortex state rather than by a LSC. Whenever possible, we compare our results with those for a $\Gamma = 1$ sample by Zhong & Ahlers (J. Fluid Mech., vol. 665, 2010, pp. 300–333).

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