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

Weiss, Stephan; He, Xiaozhou; Ahlers, Guenter; Bodenschatz, Eberhard; Shishkina, Olga

doi:10.1017/jfm.2018.507

Cited by 31 publications

(28 citation statements)

References 49 publications

(78 reference statements)

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“…The experiments used pressurized sulfur hexafluoride (SF 6 ) and were performed over a large parameter space in the High Pressure Convection Facility (HPCF, 2.24 m high) at the Max Planck Institute for Dynamics and Self-Organization in Göttingen [30]. In the studied parameter range, the Oberbeck-Boussinesq approximation is valid [31][32][33], and the centrifugal force is negligible [8,34,35].…”

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Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

et al. 2020

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For rapidly rotating turbulent Rayleigh-Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like Ra 1/4 Ek 2/3 where the Ekman number Ek decreases with increasing rotation rate.Turbulent fluid motion driven by buoyancy and influenced by rotation is a common phenomenon in nature and is important in many industrial applications. In the widely studied laboratory realization of turbulent convection, Rayleigh-Bénard convection (RBC) [1, 2], a fluid is confined in a convection cell with a heated bottom, cooled top, and adiabatic vertical walls. For these conditions, a large scale circulation (LSC) arises from cooperative plume motion and is an important feature of turbulent RBC [1]. The addition of rotation about a vertical axis produces a different type of convection as thermal plumes are transformed into thermal vortices, over some regions of parameter space heat transport is enhanced by Ekman pumping [3][4][5][6][7][8][9][10], and statistical measures of vorticity and temperature fluctuations in the bulk are strongly influenced [11][12][13][14][15][16][17]. A crucial aspect of rotation is to suppress, for sufficiently rapid rotation rates, the LSC of non-rotating convection [12,13,18,19], although the diameter-to-height aspect ratio Γ = D/H appears to play some role in the nature of the suppression [20].In RBC geometries with 1/2 ≤ Γ ≤ 2, the LSC usually spans the cell in a roll-like circulation of size H. For rotating convection, the intrinsic linear scale of separation of vortices is reduced with increasing rotation rate [21,22], suggesting that one might reduce the geometric aspect ratio, i.e., Γ < 1 while maintaining a large ratio of lateral cell size to linear scale [5]; such convection cells are being implemented in numerous new experiments [23]. Thus, an important question about rotating convection in slender cylindrical cells is whether there is a global circulation that substantially influences the internal state of the system and carries appreciable global heat transport. Direct numerical simulations (DNS) of rotat-ing convection [24] in cylindrical geometry with Γ = 1, inverse Rossby number 1/Ro = 2.78, Rayleigh number Ra = 10 9 and Prandtl number Pr = 6.4 (Ro, Ra and Pr defined below) revealed a cyclonic azimuthal velocity boundary-layer flow surrounding a core region of anticyclonic circulation and localized near the cylinder sidewall. The results were interpreted in the context of sidewall Stewartson layers driven by active Ekman layers at the top and bottom of the cell [25,26].Here we show through DNS and experimental measurements for a...

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Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

et al. 2020

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“…There is a considerable analytical and numerical effort to solve Boussinesq approximations or similar forms both for waves [29][30][31][32][33][34][35][36][37][38] and for dissipative dynamics with possible density variations [39][40][41][42][43]. Experiments for certain parameter values are also realized [44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Self-similar analysis of a viscous heated Oberbeck–Boussinesq flow system

Barna¹,

Mátyás²,

Pocsai³

2020

Fluid Dyn. Res.

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The simplest model to couple the heat conduction and Navier-Stokes equations together is the Oberbeck-Boussinesq(OB) system which were investigated by E.N. Lorenz and opened the paradigm of chaos. In our former studies -Chaos Solitons and Fractals 78, 249 (2015), ibid, 103, 336 (2017) -we derived analytic solutions for the velocity, pressure and temperature fields. Additionally, we gave a possible explanation of the Rayleigh-Bènard convection cells with the help of the self-similar Ansatz. Now we generalize the OB hydrodynamical system, including a viscous source term in the heat conduction equation. Our results may attract the interest of various fields like micro or nanofluidics or climate studies.

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“…In general, the variations of fluid parameters between the warm bottom and the cold top destroy the up-down symmetry of the system, resulting in T c = T m , with T m being the average temperature T m = (T t + T b )/2. For liquids, T c > T m was observed [11][12][13][14][15][16][17], while T c < T m was found for gases as the working fluid [14,[18][19][20][21]. Various models predicting T c as a function of , T m , and fluid parameters have been proposed and predict T c more or less accurately.…”

Section: Introductionmentioning

confidence: 99%

“…Ahlers et al [14,19] assumed laminar boundary layers at the bottom and top and solved numerically the momentum and heat equation assuming temperature-dependent fluid properties, while neglecting buoyancy. There is also the virtual cell model [20] that predicts T c by assuming that the top part and the bottom part of the convection system can be described as two separate OB systems that both follow the same Nu(Ra) relation.…”

Section: Introductionmentioning

confidence: 99%

“…While there are a handful of models developed to predict T c in NOB fluids [11,12,[18][19][20], there is a wide research gap in modeling the global heat flux theoretically. For example, the extended mixing zone model by Wu and Libchaber [18] is based on the same assumption that led to a Nu ∝ Ra 2/7 scaling in the OB case, which is experimentally observed only in a rather narrow range of Ra and Pr.…”

Section: Introductionmentioning

confidence: 99%

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Turbulent Rayleigh-Bénard convection under strong non-Oberbeck-Boussinesq conditions

2020

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We report on Rayleigh-Bénard convection with strongly varying fluid properties experimentally and theoretically. Using pressurized sulfur-hexafluoride (SF 6) above its critical point, we are able to make measurements at mean temperatures (T m) and pressures (P m) along Prandtl-number isolines in the (T, P) parameter space. This allows us to keep the mean Rayleigh-(Ra m) and Prandtl number (Pr m) constant while changing the temperature dependences of the fluid properties independently, e.g., probing the liquidlike or gaslike region that are left and right of the supercritical isochore. Hence, non-Oberbeck-Boussinesq (NOB) effects can be measured and analyzed cleanly. We measure the temperature at midheight (T c) as well as the global vertical heat flux. We observe a significant heat transport enhancement of up to 112% under strong NOB conditions. Furthermore, we develop a theoretical model for the global vertical heat flux based on ideas of Grossmann and Lohse (GL) in OB systems, adjusted for nonconstant fluid properties. In this model, the NOB effects influence the boundary layer and hence T c , but the change of the heat flux is predominantly due to a change of the fluid properties in the bulk, in particular the heat capacity c p and density ρ. Predictions from our model are consistent with our experimental results as well as with previous measurements carried out in pressurized ethane and cryogenic helium.

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

Cited by 31 publications

References 49 publications

Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

Self-similar analysis of a viscous heated Oberbeck–Boussinesq flow system

Turbulent Rayleigh-Bénard convection under strong non-Oberbeck-Boussinesq conditions

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