Session M2: Convection and Buoyancy-Driven Flows VI: Turbulent Convection

Including APE in the energy budget of turbulent Rayleigh-B\'{e}nard convection

An expanded view of the mechanical energy budget for Rayleigh-B\'{e}nard convection is developed, recognising that the available part of potential energy (APE) is the energy source for convection. Energy conversion rates and the partitioning of energy pathways between large and small scales of motion are examined using three-dimensional numerical simulations. The relative magnitudes of different pathways change significantly over the range $Ra\sim10^7-10^{13}$. At $Ra<10^7$ small-scale turbulent motions are energized directly from APE while kinetic energy is dissipated by both the large- and small-scale motions at comparable rates. In contrast, at $Ra\ge 10^{10}$ most of the APE goes into kinetic energy of the large-scale flow, which then undergoes shear instabilities sustaining small-scale turbulence. At large $Ra$ one half of the total APE supply goes to viscous dissipation, the other half to mixing, giving a mixing efficiency of 50\% as predicted theoretically. While the viscous dissipation is largely in the interior, the irreversible mixing is largely confined to the unstable boundary layers. Thus inclusion of `the other half' of the energy in the budget provides new information on the mechanics of the interior and boundary layers, and the roles of different length scales.   

Turbulent plumes of unequal strength in a ventilated filling-box - thermal overshoots and bulk overturning

The activation of two non-interacting turbulent plumes of constant buoyancy fluxes $B_1$ and $B_2 > B_1$ in a ventilated box typically gives rise to a three-layer stratification comprised of two buoyant layers and a lower region at ambient density. A theoretical model is developed to predict the time evolution of this density stratification and the displacement flow driven by the two buoyant layers through openings, at the top and base, that connect the box to a quiescent stationary ambient of uniform density. When the top layer provides the dominant forcing, we show that the mean layer buoyancies evolve on two characteristically different timescales, thus inducing a time lag. As a result, the mean buoyancy of the intermediate (i.e. middle) layer exceeds its steady value for a significant duration, giving rise to a ``thermal overshoot.'' This phenomenon can have key practical implications in ventilated rooms as occupants would experience ``localised overheating.'' Furthermore, we find that the two plumes can induce a bulk overturning of the buoyant layers. We show that, for a given source strength ratio $\psi = B_1/B_2$, thermal overshoots are realised for dimensionless opening areas $A < A_{oh}$ and overturning for $A < A_{ot}$.   

Investigation of Transient, Turbulent Natural Convection in Vertical Tubes for Thermal Energy Storage in Supercritical CO$_{2}$

Heat transfer can be a limiting factor in the operation of thermal energy storage, including sensible heat and latent heat storage systems. Poor heat transfer between the energy storage medium and the container walls impairs the functionality of the thermal storage unit by requiring excessively long times to charge or discharge the system. In this study, the effect of turbulent, unsteady buoyancy-driven flow on heat transfer in vertical storage tubes containing supercritical CO$_{\mathrm{2}}$ as the storage medium is investigated computationally. The heat transfer from a constant-temperature wall to the storage fluid is studied during the charge cycle. The results of this study show that turbulent natural convection dominates the heat transfer mechanism and significantly reduces the required time for charging compared to pure conduction. Changing the L/D ratio of the storage tube has a major impact on the charge time. The charge time shows a decreasing trend with Ra$_{\mathrm{L}}$. The non-dimensional model of the problem shows that Nusselt number and non-dimensional mean temperature of the storage fluid in different configurations of the tube is a function Buoyancy-Fourier number defined as of Fo$_{\mathrm{L}}$ * Ra$_{\mathrm{L}}^{\mathrm{m}}$ * L/D.   

Small scale anisotropy in mixed convective turbulence

Turbulent convection is present in a variety of naturally occurring flows and engineering applications. Our concern is with mixed convection, where we study the transition from the Rayleigh-B\'enard (RB) convection to forced convection in a channel flow. We consider a fully developed turbulent RB cell and at a given time we apply a constant pressure gradient, orthogonal to gravity, to impose the channel flow. We will analyze some proper indicators of small scale anisotropy and focus on how they vary at changing from one regime (dominated by buoyancy) to the other (dominated by forced convection). The results are interpreted in relation to the turbulent structures present in the fluid, their timescale and size. The observations will be linked with recent experimental finding as well as previous numerical and experimental results.   

Nematic - isotropic phase transition in turbulent thermal convection

The nematic-isotropic transition of a liquid crystal (LC) at a temperature $T_{NI}$ is an example of a {\em soft} phase transition, where fluid properties, although discontinuous, change only very little and where the latent heat is small. Understanding thermal convection in the presence of such a phase change is relevant to convection in Earth's mantle where discontinuous changes of the crystalline structure occur. We report on turbulent Rayleigh-B\'enard convection of a nematic LC while it undergoes a transition from the nematic to the isotropic phase in a cylindrical convection cell with aspect ratio $\Gamma$ (height over diameter) of 0.50. The difference between the top- and the bottom-plate temperature $\Delta T =T_b-T_t$ was held constant, while the average temperature $T_{m} = (T_b+T_t) / 2$ was varied. There was a significant increase of heat transport when $T_{NI}$ was between $T_b$ and $T_t$. Measurements of the temperatures along the side wall as a function of $T_{m}$ showed several ranges with qualitatively different behavior of quantities such as the time-averaged side-wall temperature, temperature gradient, or temperature fluctuations. We interpret these different ranges in terms of processes in the thermal boundary layers close to the top and bottom plates.   

Increase of heat transfer efficiency and plume coherence induced by geometrical confinement in turbulent thermal convection

Using a classical convection model system, we show that a simple geometrical confinement can greatly increase the turbulent convective heat transfer efficiency, the Nusselt number $Nu$. It is found that when the aspect ratio (lateral dimension over height) of the system is decreased from 0.6 to 0.1, $Nu$ is increased by $17\%$ for the parameter range explored. Detailed experimental and numerical studies show that this enhancement is brought about by the changes in the dynamics and morphology of the thermal plumes in the boundary layers and in the large-scale flow structures in the bulk. It is found that the confined geometry produces more coherent and energetic hot and cold plume clusters that go up and down in random locations, resulting in more uniform and thinner thermal boundary layers. The study demonstrates how changes in turbulent bulk flow can influence the boundary layer dynamics and shows that the prevalent mode of heat transfer existing in larger aspect ratio convection cells, in which hot and cold thermal plumes are carried by the large-scale circulation along opposite sides of the sidewall, is not the most efficient way for heat transport.   

Test of the anomalous scaling of passive temperature fluctuations in turbulent thermal convection

The scaling properties of the temperature structure function (SF) and temperature-velocity cross-structure function (CSF) are investigated in turbulent Rayleigh-Benard convection. The measured SFs and CSFs are found to exhibit good scaling in space and time and a good agreement between the CSF exponents and the thermal dissipation exponents is observed, confirming that the anomalous scaling of passive temperature fluctuations in turbulent convection is indeed caused by the spatial intermittency of the dissipation field. Furthermore, the experiment demonstrates that the functional form of the SF and CSF exponents changes with the geometry of the most dissipative structures in the flow.   

Influence of thermal plumes on Lagrangian acceleration in thermally-driven turbulence

We report an experimental study of local acceleration measurement in turbulent Rayleigh-B\'enard (RB) convection. The experiment was conducted in a cylindrical cell of unity aspect ratio, spanning the range of Rayleigh number from $6.0 \times 10^8$ to $1.3 \times 10^{10}$ at Prandtl number 4.3 and 6.2 respectively. We focus on the regions that are close to the thermal boundary layer and sidewall where thermal plumes dominate. The measurements were made in two tracking regions that are located 1 cm away from the sidewall and 1.5 cm above the bottom plate, respectively, both with a volume of about 5 cm$^3$. We find that, near the bottom thermal boundary layer, the most probable acceleration deviates from zero. This may be understood as a result of the circular motion of large-scale circulation rather than the buoyancy. We also find that, at small $Ra$, the acceleration variances measured at both sidewall and bottom plate show a different power law scaling and are larger than those in the cell center. As $Ra$ increases, the variances gradually merge with those measured in the center. This result suggests that the influence of thermal plumes, or buoyancy, is significant under moderate levels of turbulent background fluctuations.   

Conditional temperature statistics in anisotropic turbulent thermal convection for Rayleigh numbers up to $10^{15}$

We present systematic measurements of conditional diffusion $r(x) = \langle \ddot{X} \vert X=x\rangle$ and dissipation $q(x) = \langle (\dot{X})^2 \vert X=x \rangle$ of the normalized temperature fluctuations $X=(T-\bar{T})/\sigma$ in turbulent Rayleigh-B\'enard convection (RBC) at several radial positions where the flow is anisotropic. The data cover the Rayleigh-number range $10^{13} \leq Ra \leq 10^{15}$ for a Prandtl number Pr $\simeq 0.80$. The sample was a right-circular cylinder with aspect ratio $\Gamma \equiv D/L = 0.50$ ($D= 1.12$ m is the diameter and $L = 2.24$ m is the height). We suggest analytic forms for the two conditional means and derived a general formula for the temperature probability-density function. Using $q(x)$ and $r(x)$, we calculated the normalized temperature dissipation $Q$.