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Detlef Lohse - One of the best experts on this subject based on the ideXlab platform.
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mixed insulating and conducting thermal boundary conditions in rayleigh benard Convection
Journal of Fluid Mechanics, 2018Co-Authors: Dennis Bakhuis, Rodolfo Ostillamonico, Roberto Verzicco, Erwin P Van Der Poel, Detlef LohseAbstract:A series of direct numerical simulations of Rayleigh–Benard 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.
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effect of velocity boundary conditions on the heat transfer and flow topology in two dimensional rayleigh benard Convection
Physical Review E, 2014Co-Authors: Erwin P Van Der Poel, Roberto Verzicco, Rodolfo Ostillamonico, Detlef LohseAbstract:The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-Benard Convection. Combinations of no-slip, stress-free, and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers Ra between 10 8 and 10 11 the heat transport is lower for Γ=0.33 than for Γ=1 in case of no-slip sidewalls. This is, surprisingly, the opposite for stress-free sidewalls, where the heat transport increases for a lower aspect ratio. In wider cells the aspect-ratio dependence is observed to disappear for Ra≥10 10 . Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll like. In two-dimensional Rayleigh-Benard Convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.
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logarithmic temperature profiles in turbulent rayleigh benard Convection
Physical Review Letters, 2012Co-Authors: Guenter Ahlers, Eberhard Bodenschatz, Denis Funfschilling, Siegfried Grossmann, Detlef Lohse, Richard J A M Stevens, Roberto VerziccoAbstract:We report results for the temperature profiles of turbulent Rayleigh-Benard Convection (RBC) in the interior of a cylindrical sample of aspect ratio ??D/L=0.50 (D and L are the diameter and height, respectively). Both in the classical and in the ultimate state of RBC we find that the temperature varies as A×ln?(z/L)+B, where z is the distance from the bottom or top plate. In the classical state, the coefficient A decreases in the radial direction as the distance from the side wall increases. For the ultimate state, the radial dependence of A has not yet been determined. These findings are based on experimental measurements over the Rayleigh-number range 4×1012?Ra?1015 for a Prandtl number Pr?0.8 and on direct numerical simulation at Ra=2×1012, 2×1011, and 2×1010, all for Pr=0.7.
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flow states in two dimensional rayleigh benard Convection as a function of aspect ratio and rayleigh number
Physics of Fluids, 2012Co-Authors: Erwin P Van Der Poel, Richard J A M Stevens, K Sugiyama, Detlef LohseAbstract:In this numerical study on two-dimensional Rayleigh-Benard Convection we consider 107 ⩽ Ra ⩽ 1012 in aspect-ratio 0.23 ⩽ Γ ⩽ 13 samples. We focus on several cases. First, we consider small aspect-ratio cells, where at high Ra number we find a sharp transition from a low Ra number branch towards a high Ra number branch, due to changes in the flow structure. Subsequently, we show that the influence of the aspect-ratio on the heat transport decreases with increasing aspect-ratio, although even at very large aspect-ratio of Γ ≈ 10 variations up to 2.5% in the heat transport as a function of Γ are observed. Finally, we observe long-lived transients up to at least Ra = 109, as in certain aspect-ratio cells we observe different flow states that are stable for thousands of turnover times.
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axially homogeneous rayleigh benard Convection in a cylindrical cell
Journal of Fluid Mechanics, 2012Co-Authors: Laura E Schmidt, Detlef Lohse, Enrico Calzavarini, Federico Toschi, Roberto VerziccoAbstract:Previous numerical studies have shown that the ‘ultimate regime of thermal Convection’ can be attained in a Rayleigh–Benard cell when the kinetic and thermal boundary layers are eliminated by replacing both lateral and horizontal walls with periodic boundary conditions (homogeneous Rayleigh–Benard Convection). Then, the heat transfer scales like Nu~Ra$_{1/2}$ and turbulence intensity as Re~Ra$_{1/2}$, where the Rayleigh number Ra indicates the strength of the driving force (for fixed values of Pr, which is the ratio between kinematic viscosity and thermal diffusivity). However, experiments never operate in unbounded domains and it is important to understand how confinement might alter the approach to this ultimate regime. Here we consider homogeneous Rayleigh–Benard Convection in a laterally confined geometry – a small-aspect-ratio vertical cylindrical cell – and show evidence of the ultimate regime as Ra is increased: in spite of the lateral confinement and the resulting kinetic boundary layers, we still find Nu~Re~Ra$_{1/2}$ at . Further, it is shown that the system supports solutions composed of modes of exponentially growing vertical velocity and temperature fields, with Ra as the critical parameter determining the properties of these modes. Counter-intuitively, in the low-Ra regime, or for very narrow cylinders, the numerical simulations are susceptible to these solutions, which can dominate the dynamics and lead to very high and unsteady heat transfer. As Ra is increased, interaction between modes stabilizes the system, evidenced by the increasing homogeneity and reduced fluctuations in the root-mean-square velocity and temperature fields. We also test that physical results become independent of the periodicity length of the cylinder, a purely numerical parameter, as the aspect ratio is increased.
Roberto Verzicco - One of the best experts on this subject based on the ideXlab platform.
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mixed insulating and conducting thermal boundary conditions in rayleigh benard Convection
Journal of Fluid Mechanics, 2018Co-Authors: Dennis Bakhuis, Rodolfo Ostillamonico, Roberto Verzicco, Erwin P Van Der Poel, Detlef LohseAbstract:A series of direct numerical simulations of Rayleigh–Benard 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.
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effect of velocity boundary conditions on the heat transfer and flow topology in two dimensional rayleigh benard Convection
Physical Review E, 2014Co-Authors: Erwin P Van Der Poel, Roberto Verzicco, Rodolfo Ostillamonico, Detlef LohseAbstract:The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-Benard Convection. Combinations of no-slip, stress-free, and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers Ra between 10 8 and 10 11 the heat transport is lower for Γ=0.33 than for Γ=1 in case of no-slip sidewalls. This is, surprisingly, the opposite for stress-free sidewalls, where the heat transport increases for a lower aspect ratio. In wider cells the aspect-ratio dependence is observed to disappear for Ra≥10 10 . Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll like. In two-dimensional Rayleigh-Benard Convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.
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logarithmic temperature profiles in turbulent rayleigh benard Convection
Physical Review Letters, 2012Co-Authors: Guenter Ahlers, Eberhard Bodenschatz, Denis Funfschilling, Siegfried Grossmann, Detlef Lohse, Richard J A M Stevens, Roberto VerziccoAbstract:We report results for the temperature profiles of turbulent Rayleigh-Benard Convection (RBC) in the interior of a cylindrical sample of aspect ratio ??D/L=0.50 (D and L are the diameter and height, respectively). Both in the classical and in the ultimate state of RBC we find that the temperature varies as A×ln?(z/L)+B, where z is the distance from the bottom or top plate. In the classical state, the coefficient A decreases in the radial direction as the distance from the side wall increases. For the ultimate state, the radial dependence of A has not yet been determined. These findings are based on experimental measurements over the Rayleigh-number range 4×1012?Ra?1015 for a Prandtl number Pr?0.8 and on direct numerical simulation at Ra=2×1012, 2×1011, and 2×1010, all for Pr=0.7.
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axially homogeneous rayleigh benard Convection in a cylindrical cell
Journal of Fluid Mechanics, 2012Co-Authors: Laura E Schmidt, Detlef Lohse, Enrico Calzavarini, Federico Toschi, Roberto VerziccoAbstract:Previous numerical studies have shown that the ‘ultimate regime of thermal Convection’ can be attained in a Rayleigh–Benard cell when the kinetic and thermal boundary layers are eliminated by replacing both lateral and horizontal walls with periodic boundary conditions (homogeneous Rayleigh–Benard Convection). Then, the heat transfer scales like Nu~Ra$_{1/2}$ and turbulence intensity as Re~Ra$_{1/2}$, where the Rayleigh number Ra indicates the strength of the driving force (for fixed values of Pr, which is the ratio between kinematic viscosity and thermal diffusivity). However, experiments never operate in unbounded domains and it is important to understand how confinement might alter the approach to this ultimate regime. Here we consider homogeneous Rayleigh–Benard Convection in a laterally confined geometry – a small-aspect-ratio vertical cylindrical cell – and show evidence of the ultimate regime as Ra is increased: in spite of the lateral confinement and the resulting kinetic boundary layers, we still find Nu~Re~Ra$_{1/2}$ at . Further, it is shown that the system supports solutions composed of modes of exponentially growing vertical velocity and temperature fields, with Ra as the critical parameter determining the properties of these modes. Counter-intuitively, in the low-Ra regime, or for very narrow cylinders, the numerical simulations are susceptible to these solutions, which can dominate the dynamics and lead to very high and unsteady heat transfer. As Ra is increased, interaction between modes stabilizes the system, evidenced by the increasing homogeneity and reduced fluctuations in the root-mean-square velocity and temperature fields. We also test that physical results become independent of the periodicity length of the cylinder, a purely numerical parameter, as the aspect ratio is increased.
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effect of vapor bubbles on velocity fluctuations and dissipation rates in bubbly rayleigh benard Convection
Physical Review E, 2011Co-Authors: Rajaram Lakkaraju, Detlef Lohse, Roberto Verzicco, Laura E Schmidt, Federico Toschi, Paolo Oresta, Andrea ProsperettiAbstract:Numerical results for kinetic and thermal energy dissipation rates in bubbly Rayleigh-Benard Convection are reported. Bubbles have a twofold effect on the flow: on the one hand, they absorb or release heat to the surrounding liquid phase, thus tending to decrease the temperature differences responsible for the convective motion; but on the other hand, the absorbed heat causes the bubbles to grow, thus increasing their buoyancy and enhancing turbulence (or, more properly, pseudoturbulence) by generating velocity fluctuations. This enhancement depends on the ratio of the sensible heat to the latent heat of the phase change, given by the Jakob number, which determines the dynamics of the bubble growth.
Guenter Ahlers - One of the best experts on this subject based on the ideXlab platform.
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logarithmic temperature profiles of turbulent rayleigh benard Convection in the classical and ultimate state for a prandtl number of 0 8
Journal of Fluid Mechanics, 2014Co-Authors: Guenter Ahlers, Eberhard BodenschatzAbstract:We report on experimental determinations of the temperature field in the interior (bulk) of turbulent Rayleigh-Benard Convection for a cylindrical sample with aspect ratio (diameter over height) of 0.50, both in the classical and in the ultimate state. The Prandtl number was close to 0.8. We find a "logarithmic layer" in which the temperature varies as A*ln(z/L) + B with the distance z from the bottom plate of the sample. The amplitude A varies with radial position r. In the classical state these results are in good agreement with direct numerical simulations (DNS); in the ultimate state there are as yet no DNS. A close analogy between the temperature field in the classical state and the "Law of the Wall" for the time-averaged down-stream velocity in shear flow is discussed.
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logarithmic temperature profiles in turbulent rayleigh benard Convection
Physical Review Letters, 2012Co-Authors: Guenter Ahlers, Eberhard Bodenschatz, Denis Funfschilling, Siegfried Grossmann, Detlef Lohse, Richard J A M Stevens, Roberto VerziccoAbstract:We report results for the temperature profiles of turbulent Rayleigh-Benard Convection (RBC) in the interior of a cylindrical sample of aspect ratio ??D/L=0.50 (D and L are the diameter and height, respectively). Both in the classical and in the ultimate state of RBC we find that the temperature varies as A×ln?(z/L)+B, where z is the distance from the bottom or top plate. In the classical state, the coefficient A decreases in the radial direction as the distance from the side wall increases. For the ultimate state, the radial dependence of A has not yet been determined. These findings are based on experimental measurements over the Rayleigh-number range 4×1012?Ra?1015 for a Prandtl number Pr?0.8 and on direct numerical simulation at Ra=2×1012, 2×1011, and 2×1010, all for Pr=0.7.
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prandtl rayleigh and rossby number dependence of heat transport in turbulent rotating rayleigh benard Convection
Physical Review Letters, 2009Co-Authors: Jinqiang Zhong, Detlef Lohse, Richard J A M Stevens, Roberto Verzicco, Herman Clercx, Guenter AhlersAbstract:For given aspect ratio and given geometry, the nature of Rayleigh Benard Convection (RBC) is determined by the Rayleigh number Ra = bg DL3 / (kn)Ra=gL3() and by the Prandtl number Pr = n/ kPr= is the thermal expansion coefficient, g the gravitational acceleration D = Tb - Tt=Tb−Tt the difference between the imposed temperatures Tb and Tt at the bottom and the top of the sample, respectively, and v and k the kinematic viscosity and the thermal diffusivity, respectively. The rotation rate Ω (given in rad/s) is used in the form of the Rossby number Ro = O{bg D/ L / (2 W)}Ro=gL(2)
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anomalous reynolds number scaling in turbulent rayleigh benard Convection
Journal of Statistical Mechanics: Theory and Experiment, 2007Co-Authors: Eric Brown, Denis Funfschilling, Guenter AhlersAbstract:This paper reports measurements of Reynolds numbers Rep corresponding to the turnover time of thermal excitations ('plumes') and Reω corresponding to the twisting-oscillation period of the large-scale circulation (LSC) of turbulent Rayleigh–Benard Convection over the Rayleigh-number range and Prandtl-number range for cylindrical samples of aspect ratio Γ = 1. For both periods, and hence both Reynolds numbers, were the same and scaled as Re~Rγeff with . Here both the σ- and R-dependences were quantitatively consistent with the Grossmann–Lohse (GL) prediction. For R>R* the results could be represented by Rep = 0.138 σ−0.82R0.493 for the plume turnover time and Reω = 0.17 σ−0.81R0.480 for the twisting oscillation, both of which differ significantly from the GL prediction as well as from each other. A relatively sharp transition at R* to the large-R regime and the separation of the two Reynolds numbers from each other suggest a qualitative and sudden change that renders the measured quantities inapplicable to the GL prediction. Combining Rep and previously reported measurements of the Nusselt number yielded the kinetic energy-dissipation as a function of Rep. For these results were in excellent agreement with the corresponding GL prediction, and both approached closely to the (Re)3-dependence that is expected at large Re where the bulk contribution to u dominates. For R>R* the data were consistent with . This differs from the expected large-Re behavior and suggests that Rep no longer is the Reynolds number relevant to u.
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effect of the earth s coriolis force on the large scale circulation of turbulent rayleigh benard Convection
Physics of Fluids, 2006Co-Authors: Eric Brown, Guenter AhlersAbstract:We present measurements of the large-scale circulation (LSC) of turbulent Rayleigh-Benard Convection in water-filled cylindrical samples of heights equal to their diameters. The orientation of the LSC had an irregular time dependence, but revealed a net azimuthal rotation with an average period of about 3days for Rayleigh numbers R≳1010. On average there was also a tendency for the LSC to be aligned with upflow to the west and downflow to the east, even after physically rotating the apparatus in the laboratory through various angles. Both of these phenomena could be explained as a result of the coupling of the Earth’s Coriolis force to the LSC. The rate of azimuthal rotation could be calculated from a model of diffusive LSC orientation meandering with a potential barrier due to the Coriolis force. The model and the data revealed an additional contribution to the potential barrier that could be attributed to the cooling system of the sample top that dominated the preferred orientation of the LSC at high R....
Quan Zhou - One of the best experts on this subject based on the ideXlab platform.
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the dependence of the critical roughness height in two dimensional turbulent rayleigh benard Convection
Journal of Fluid Mechanics, 2021Co-Authors: Jianlin Yang, Bofu Wang, Yizhao Zhang, Tiancheng Jin, Yuhong Dong, Quan ZhouAbstract:We carry out direct numerical simulations of turbulent Rayleigh–Benard Convection in a square box with rough conducting plates over the Rayleigh number range .
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experimental investigation of turbulent rayleigh benard Convection of water in a cylindrical cell the prandtl number effects for pr 1
Physics of Fluids, 2020Co-Authors: Yinghui Yang, Bofu Wang, Yulu Liu, Xu Zhu, Quan ZhouAbstract:We report an experimental study of turbulent Rayleigh-Benard Convection in a cylindrical cell of aspect ratio unity, focusing on the effects of the Prandtl number (Pr). Purified water was used as the convecting fluid. Five different Pr between 3.58 and 9.40 were achieved by changing the mean temperature of water, and the measurements were carried out over the Rayleigh number range 2.63 × 108 ≤ Ra ≤ 3.89 × 1010. Over the present parameter range, the measured Nusselt number Nu is found to scale as Nu ∼ Raβ with β = 0.30 and to be independent of Pr. Based on the oscillation period of the measured temperature, the Reynolds number Re scales as Re ∼ Ra0.47Pr−0.72. The local temperature fluctuations at the cell center and near the cell’s sidewall were measured, and their relations with Ra and Pr were studied. Our results further reveal that the non-Oberbeck-Boussinesq effects of water have a relatively small influence on the measured scaling relation Nu ∼ Raβ.
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scaling of maximum probability density function of velocity increments in turbulent rayleigh benard Convection
Journal of Hydrodynamics, 2014Co-Authors: Yongxiang Huang, Quan ZhouAbstract:In this paper, we apply a scaling analysis of the maximum of the probability density function (pdf) of velocity increments, i.e., pmax(τ)=maxΔuτp(Δuτ)−τ−αpmax(τ)=maxΔuτp(Δuτ)−τ−α, for a velocity field of turbulent Rayleigh-Benard Convection obtained at the Taylor-microscale Reynolds number Re λ≈60. The scaling exponent is comparable with that of the first-order velocity structure function, ζ(1), in which the large-scale effect might be constrained, showing the background fluctuations of the velocity field. It is found that the integral time T (x/D ) scales as T (x/D )-(x/D )-β, with a scaling exponent β=0.25±0.01, suggesting the large-scale inhomogeneity of the flow. Moreover, the pdf scaling exponent α(x,z ) is strongly inhomogeneous in the x (horizontal) direction. The vertical-direction-averaged pdf scaling exponent α˜(x,z) obeys a logarithm law with respect to x , the distance from the cell sidewall, with a scaling exponent ξ≈0.22 within the velocity boundary layer and ξ≈0.28 near the cell sidewall. In the cell's central region, α(x,z ) fluctuates around 0.37, which agrees well with ζ(1) obtained in high-Reynolds-number turbulent flows, implying the same intermittent correction. Moreover, the length of the inertial range represented in decade T˜I(x) is found to be linearly increasing with the wall distance with an exponent 0.65±0.05.
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aspect ratio dependence of heat transport by turbulent rayleigh benard Convection in rectangular cells
Journal of Fluid Mechanics, 2012Co-Authors: Quan Zhou, Bofang Liu, Baochang ZhongAbstract:We report high-precision measurements of the Nusselt number as a function of the Rayleigh number in water-filled rectangular Rayleigh–Benard Convection cells. The horizontal length and width of the cells are 50.0 and 15.0 cm, respectively, and the heights , 25.0, 12.5, 6.9, 3.5, and 2.4 cm, corresponding to the aspect ratios , , , , , and . The measurements were carried out over the Rayleigh number range and the Prandtl number range . 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 is found to be in general a decreasing function of , at least for 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 for plates with perfect conductivity. The local scaling exponents of are calculated and found to increase from 0.243 at to 0.327 at .
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horizontal structures of velocity and temperature boundary layers in two dimensional numerical turbulent rayleigh benard Convection
Physics of Fluids, 2011Co-Authors: Quan Zhou, Siegfried Grossmann, Kazuyasu Sugiyama, Keqing XiaAbstract:We investigate the structures of the near-plate velocity and temperature profiles at different horizontal positions along the conducting bottom (and top) plate of a Rayleigh-Benard Convection cell, using two-dimensional (2D) numerical data obtained at the Rayleigh number Ra = 108 and the Prandtl number Pr = 4.4 of an Oberbeck-Boussinesq flow with constant material parameters. The results show that most of the time, and for both velocity and temperature, the instantaneous profiles scaled by the dynamical frame method [Q. Zhou and K.-Q. Xia, “Measured instantaneous viscous boundary layer in turbulent Rayleigh-Benard Convection,” Phys. Rev. Lett. 104, 104301 (2010)] agree well with the classical Prandtl-Blasius laminar boundary layer (BL) profiles. Therefore, when averaging in the dynamical reference frames, which fluctuate with the respective instantaneous kinematic and thermal BL thicknesses, the obtained mean velocity and temperature profiles are also of Prandtl-Blasius type for nearly all horizontal positions. We further show that in certain situations the traditional definitions based on the time-averaged profiles can lead to unphysical BL thicknesses, while the dynamical method also in such cases can provide a well-defined BL thickness for both the kinematic and the thermal BLs
Richard J A M Stevens - One of the best experts on this subject based on the ideXlab platform.
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logarithmic temperature profiles in turbulent rayleigh benard Convection
Physical Review Letters, 2012Co-Authors: Guenter Ahlers, Eberhard Bodenschatz, Denis Funfschilling, Siegfried Grossmann, Detlef Lohse, Richard J A M Stevens, Roberto VerziccoAbstract:We report results for the temperature profiles of turbulent Rayleigh-Benard Convection (RBC) in the interior of a cylindrical sample of aspect ratio ??D/L=0.50 (D and L are the diameter and height, respectively). Both in the classical and in the ultimate state of RBC we find that the temperature varies as A×ln?(z/L)+B, where z is the distance from the bottom or top plate. In the classical state, the coefficient A decreases in the radial direction as the distance from the side wall increases. For the ultimate state, the radial dependence of A has not yet been determined. These findings are based on experimental measurements over the Rayleigh-number range 4×1012?Ra?1015 for a Prandtl number Pr?0.8 and on direct numerical simulation at Ra=2×1012, 2×1011, and 2×1010, all for Pr=0.7.
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flow states in two dimensional rayleigh benard Convection as a function of aspect ratio and rayleigh number
Physics of Fluids, 2012Co-Authors: Erwin P Van Der Poel, Richard J A M Stevens, K Sugiyama, Detlef LohseAbstract:In this numerical study on two-dimensional Rayleigh-Benard Convection we consider 107 ⩽ Ra ⩽ 1012 in aspect-ratio 0.23 ⩽ Γ ⩽ 13 samples. We focus on several cases. First, we consider small aspect-ratio cells, where at high Ra number we find a sharp transition from a low Ra number branch towards a high Ra number branch, due to changes in the flow structure. Subsequently, we show that the influence of the aspect-ratio on the heat transport decreases with increasing aspect-ratio, although even at very large aspect-ratio of Γ ≈ 10 variations up to 2.5% in the heat transport as a function of Γ are observed. Finally, we observe long-lived transients up to at least Ra = 109, as in certain aspect-ratio cells we observe different flow states that are stable for thousands of turnover times.
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prandtl blasius temperature and velocity boundary layer profiles in turbulent rayleigh benard Convection
Journal of Fluid Mechanics, 2010Co-Authors: Quan Zhou, Siegfried Grossmann, Richard J A M Stevens, Kazuyasu Sugiyama, Detlef LohseAbstract:The shapes of the velocity and temperature profiles near the horizontal conducting plates' centre regions in turbulent Rayleigh–Benard 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
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optimal prandtl number for heat transfer in rotating rayleigh benard Convection
New Journal of Physics, 2010Co-Authors: Richard J A M Stevens, Herman Clercx, Detlef LohseAbstract:Numerical data for the heat transfer as a function of the Prandtl (Pr) and Rossby (Ro) numbers in turbulent rotating Rayleigh–Benard Convection are presented for Rayleigh number Ra=108. When Ro is fixed, the heat transfer enhancement with respect to the non-rotating value shows a maximum as a function of Pr. This maximum is due to the reduced effect of Ekman pumping when Pr becomes too small or too large. When Pr becomes small, i.e. for large thermal diffusivity, the heat that is carried by the vertical vortices spreads out in the middle of the cell and Ekman pumping thus becomes less effective. For higher Pr the thermal boundary layers (BLs) are thinner than the kinetic BLs and therefore the Ekman vortices do not reach the thermal BL. This means that the fluid that is sucked into the vertical vortices is colder than that for lower Pr, which limits the upwards heat transfer.
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radial boundary layer structure and nusselt number in rayleigh benard Convection
Journal of Fluid Mechanics, 2010Co-Authors: Richard J A M Stevens, Roberto Verzicco, Detlef LohseAbstract:Results from direct numerical simulation (DNS) for three-dimensional Rayleigh–Benard Convection in a cylindrical cell of aspect ratio 1/2 and Prandtl number Pr=0.7 are presented. They span five decades of Rayleigh number Ra from 2 × 106 to 2 × 1011. The results are in good agreement with the experimental data of Niemela et al. (Nature, vol. 404, 2000, p. 837). Previous DNS results from Amati et al. (Phys. Fluids, vol. 17, 2005, paper no. 121701) showed a heat transfer that was up to 30% higher than the experimental values. The simulations presented in this paper are performed with a much higher resolution to properly resolve the plume dynamics. We find that in under-resolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the better-resolved ones, because of insufficient thermal dissipation mainly close to the sidewall (where the grid cells are largest), and therefore the Nusselt number in under-resolved simulations is overestimated. Furthermore, we compare the best resolved thermal boundary layer profile with the Prandtl–Blasius profile. We find that the boundary layer profile is closer to the Prandtl–Blasius profile at the cylinder axis than close to the sidewall, because of rising plumes close to the sidewall
