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Register a new userHeat transfer enhancement in Rayleigh-Benard convection using a single passive barrier
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In this numerical study on Rayleigh-Benard convection we seek to improve the heat transfer by passive means. To this end we introduce a single tilted conductive barrier centered in an aspect ratio one cell, breaking the symmetry of the geometry and to channel the ascending hot and descending cold plumes. We study the global and local heat transfer and the flow organization for Rayleigh numbers $10^5 leq Ra leq 10^9$ for a fixed Prandtl number of $Pr=4.3$. We find that the global heat transfer can be enhanced up to $18%$, and locally around $800%$. The averaged Reynolds number is always decreased when a barrier is introduced, even for those cases where the global heat transfer is increased. We map the entire parameter space spanned by the orientation and the size of a single barrier for $Ra=10^8$.
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Steady flows that optimize heat transport are obtained for two-dimensional Rayleigh-Benard convection with no-slip horizontal walls for a variety of Prandtl numbers $Pr$ and Rayleigh number up to $Rasim 10^9$. Power law scalings of $Nusim Ra^{gamma}$ are observed with $gammaapprox 0.31$, where the Nusselt number $Nu$ is a non-dimensional measure of the vertical heat transport. Any dependence of the scaling exponent on $Pr$ is found to be extremely weak. On the other hand, the presence of two local maxima of $Nu$ with different horizontal wavenumbers at the same $Ra$ leads to the emergence of two different flow structures as candidates for optimizing the heat transport. For $Pr lesssim 7$, optimal transport is achieved at the smaller maximal wavenumber. In these fluids, the optimal structure is a plume of warm rising fluid which spawns left/right horizontal arms near the top of the channel, leading to downdrafts adjacent to the central updraft. For $Pr > 7$ at high-enough Ra, the optimal structure is a single updraft absent significant horizontal structure, and characterized by the larger maximal wavenumber.
We numerically investigate turbulent Rayleigh-Benard convection within two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number $Nu$) in two-layer systems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number $Ra=10^8$, Prandtl number $Pr=4.38$, and Weber number $We=5$. We vary the relative thickness of the upper layer between $0.01 le alpha le 0.99$ and the thermal conductivity coefficient ratio of the two liquids between $0.1 le lambda_k le 10$. Two flow regimes are observed: In the first regime at $0.04lealphale0.96$, convective flows appear in both layers and $Nu$ is not sensitive to $alpha$. In the second regime at $alphale0.02$ or $alphage0.98$, convective flow only exists in the thicker layer, while the thinner one is dominated by pure conduction. In this regime, $Nu$ is sensitive to $alpha$. To predict $Nu$ in the system in which the two layers are separated by a unique interface, we apply the Grossmann-Lohse theory for both individual layers and impose heat flux conservation at the interface. Without introducing any free parameter, the predictions for $Nu$ and for the temperature at the interface well agree with our numerical results and previous experimental data.
To understand how internal flow structures manifest themselves in the global heat transfer, we study the correlation between different flow modes and the instantaneous Nusselt number ($Nu$) in a two-dimensional square Rayleigh-Benard convection cell. High-resolution and long-time direct numerical simulations are carried out for Rayleigh numbers between $10^{7}$ and $10^{9}$ and a Prandtl number of 5.3. The investigated Nusselt numbers include the volume-averaged $Nu_{text{vol}}$, the wall-averaged $Nu_{text{wall}}$, the kinetic energy dissipation based $Nu_{text{kinetic}}$, and the thermal energy dissipation based $Nu_{text{thermal}}$. The Fourier mode decomposition and proper orthogonal decomposition are adopted to extract the coherent flow structure. Our results show that the single-roll mode, the horizontally stacked double-roll mode, and the quadrupolar flow mode are more efficient for heat transfer on average. In contrast, the vertically stacked double-roll mode is inefficient for heat transfer on average. The volume-averaged $Nu_{text{vol}}$ and the kinetic energy dissipation based $Nu_{text{kinetic}}$ can better reproduce the correlation of internal flow structures with heat transfer efficiency than that of the wall-averaged $Nu_{text{wall}}$ and the thermal energy dissipation based $Nu_{text{thermal}}$, even though these four Nusselt numbers give consistent time-averaged mean values. The ensemble-averaged time trace of $Nu$ during flow reversal shows that only the volume-averaged $Nu_{text{vol}}$ can reproduce the overshoot phenomena that is observed in the previous experimental study. Our results reveal that the proper choice of $Nu$ is critical to obtain a meaningful interpretation.
We study, using direct numerical simulations, the effect of geometrical confinement on heat transport and flow structure in Rayleigh-Benard convection in fluids with different Prandtl numbers. Our simulations span over two decades of Prandtl number $Pr$, $0.1 leq Pr leq 40$, with the Rayleigh number $Ra$ fixed at $10^8$. The width-to-height aspect ratio $Gamma$ spans between $0.025$ and $0.25$ while the length-to-height aspect ratio is fixed at one. We first find that for $Pr geq 0.5$, geometrical confinement can lead to a significant enhancement in heat transport as characterized by the Nusselt number $Nu$. For those cases, $Nu$ is maximal at a certain $Gamma = Gamma_{opt}$. It is found that $Gamma_{opt}$ exhibits a power-law relation with $Pr$ as $Gamma_{opt}=0.11Pr^{-0.06}$, and the maximal relative enhancement generally increases with $Pr$ over the explored parameter range. As opposed to the situation of $Pr geq 0.5$, confinement-induced enhancement in $Nu$ is not realized for smaller values of $Pr$, such as $0.1$ and $0.2$. The $Pr$ dependence of the heat transport enhancement can be understood in its relation to the coverage area of the thermal plumes over the thermal boundary layer (BL) where larger coverage is observed for larger $Pr$ due to a smaller thermal diffusivity. We further show that $Gamma_{opt}$ is closely related to the crossing of thermal and momentum BLs, and find that $Nu$ declines sharply when the thickness ratio of the thermal and momentum BLs exceeds a certain value of about one. In addition, through examining the temporally averaged flow fields and 2D mode decomposition, it is found that for smaller $Pr$ the large-scale circulation is robust against the geometrical confinement of the convection cell.
We have developed a small, neutrally buoyant, wireless temperature sensor. Using a camera for optical tracking, we obtain simultaneous measurements of position and temperature of the sensor as it is carried along by the flow in Rayleigh-Benard convection, at $Ra sim 10^{10}$. We report on statistics of temperature, velocity, and heat transport in turbulent thermal convection. The motion of the sensor particle exhibits dynamics close to that of Lagrangian tracers in hydrodynamic turbulence. We also quantify heat transport in plumes, revealing self-similarity and extreme variations from plume to plume.
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