Session F33: Convection and Buoyancy Driven Flows: Free Convection

Direct numerical simulations of Couette flow with unstable stratifications

A series of direct numerical simulations of Couette flow with unstable stratification have been performed with a second-order finite difference code, optimized for a GPU cluster (AFiD GPU). Defining $ h $ as the channel height, shear Reynolds numbers up to $ Re_\tau=hu_\tau /\nu \approx 370$ have been achieved. Looking at the different mean temperatures and velocities of the datasets, it can be seen that, as expected, the convection and shear regimes compete with each other. For low $ Ra $, the statistics show a shear dominated flow field, whereas it becomes more difficult for the shear to dominate in the higher $ Ra $ regime. Studying the the Nusselt number ($ Nu $) as function of the $ Re $ number for different $ Ra $ numbers shows that for higher $ Ra $ the heat transfer first decreases with increasing shear before it increases strongly for higher mechanical driving. This unexpected non-monotonic change of $ Nu $ as a function of $ Re $ is due to a breakup of the large scale convection rolls formed by the buoyancy forces when moderate shear is applied. The large scale dynamics of pure thermal and pure mechanical driving can be observed in the extreme cases.   

Thermal convection in dielectric liquids in a cylindrical annulus

Thermal convection is investigated in a dielectric liquid of thermal expansion coefficient $\alpha $, kinematic viscosity $\nu $, thermal diffusivity $\kappa $ and electric permittivity $\varepsilon $ in a cylindrical annulus of inner radius $a$ and outer radius $b $with a radial temperature gradient and a high-frequency electric tension. The coupling between the electric field and the gradient of the permittivity yields the dielectrophoretic force. The control parameters are $\eta =$ a/b, Pr $=$ $\nu $/$\kappa $, the classic Rayleigh number Ra $= \quad \alpha \Delta $T gd$^{\mathrm{3}}$/$\nu \kappa $, and the electric Rayleigh number L $=$ $\alpha \Delta $T g$_{\mathrm{e}}$d$^{\mathrm{3}}$/$\nu \kappa $ The electric gravity g$_{\mathrm{e}}$ is the gradient of the electric energy in the condenser. Linear stability analysis shows that for infinite annulus, depending on values of $\eta $, Ra and L, critical modes are either hydrodynamic or thermal modes, helical electric modes or columnar vortices. Experiments in an annulus of aspect ratio $\Gamma =$19.6 during parabolic flight campaigns indicate the existence of columns. Columnar vortices result from the competition between Archimedean buoyancy and dielectrophoretic force. Direct numerical simulations in the annulus of $\Gamma =$20 show that the columnar vortices occupy the central part of the annulus, while near the end-zones the flow is laminar and dominated by an azimuthal vorticity.   

Thermal convection in a co-rotating cylindrical annulus

We investigate thermal convection in a fluid of thermal expansion coefficient $\alpha $, kinematic viscosity $\nu $, thermal diffusivity $\kappa $ in a cylindrical annulus of inner radius $a$ and outer radius $b $with a solid body rotation of angular frequency $\Omega $ and an inward heating with a temperature difference $\Delta $T. The control parameters are $\eta =$ a/b, Pr $= \quad \nu $/$\kappa $ and the Rayleigh number Ra $= \quad \alpha \Delta $T gd$^{\mathrm{3}}$/$\nu \kappa $ where the centrifugal gravity g$_{\mathrm{c}} \quad = \quad \Omega^{\mathrm{2}}$(a$+$b)/2. We adopt the generalized Boussinesq approximation. Linear stability analysis shows that for infinite annulus, the threshold Ra$_{\mathrm{c}}$ decreases with $\eta $ and tends to the value Ra$_{\mathrm{c}}=$1708 when $\eta \to $1 and that critical modes are columnar vortices. Direct numerical simulations using periodic boundary conditions in the axial direction, show that the columnar vortices appear via a supercritical bifurcation. Higher modes of columnar vortices have been determined using the frequency spectra and the Nusselt number for Pr$=$1 and $\eta \quad =$ 0.5: drifting vortices, vacillation modes and chaotic modes have been identified from Ra$=$1700 to Ra$=$10$^{\mathrm{7}}$ The contribution of the centrifugal buoyancy to the variation of the kinetic energy in the flow is analysed.   

Penetrative Convection at High Rayleigh Numbers

We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is $Ra = \left[10^6, 10^8 \right]$ and the Prandtl numbers are $Pr = 1$ and $11.6$. An evolution equation for the growth of the convecting region is obtained through an integral energy balance. We identify a new non-dimensional parameter, $\Lambda$, which is the ratio of temperature differences in the stable and unstable regions of the flow, and show that the characteristics of the flow depend sensitively upon it. We study the effects of $\Lambda$ on the flow field using well-resolved lattice Boltzmann simulations. The Nusselt number is found to scale with $Ra$ as $Nu = A\left(\Lambda\right) \times Ra^{1/4}$, where $A\left(\Lambda\right)$ is a function of $\Lambda$, for $\Lambda = 0.25$ and $2$, showing that the presence of the stable layer can be modelled as a geometric effect for the values of $\Lambda$ considered.   

Simulations of thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model

Operating a liquid-metal battery produces Ohmic losses in the electrolyte layer that separates both metal electrodes. As a consequence, temperature gradients establish which potentially cause thermal convection since density and interfacial tension depend on the local temperature. In our numerical investigations, we considered three plane, immiscible layers governed by the Navier-Stokes-Boussinesq equations held at a constant temperature of 500°C at the bottom and top. A homogeneous current is applied that leads to a preferential heating of the mid electrolyte layer. We chose a typical material combination of Li separated by LiCl-KCl (a molten salt) from Pb-Bi for which we analyzed the linear stability of pure thermal conduction and performed three-dimensional direct-numerical simulations by a pseudospectral method probing different: electrolyte layer heights, overall heights, and current densities. Four instability mechanisms are identified, which are partly coupled to each other: buoyant convection in the upper electrode, buoyant convection in the molten salt layer, and Marangoni convection at both interfaces between molten salt and electrode. The global turbulent heat transfer follows scaling predictions for internally heated buoyant convection.   

Direct numerical simulation of vacillation in convection induced by centrifugal buoyancy

Flows induced by centrifugal buoyancy occur in industrial systems, such as in the compressor cavities of gas turbines, as well as in flows of geophysical interest. In this numerical study we use direct numerical simulation (DNS) to investigate the transition between the steady waves regime, which is characterized by great regularity, to the vacillation regime, which is critical to understand transition to the fully turbulent regime. From previous work it is known that the onset of convection occurs in the form of pairs of nearly-circular rolls which span the entire axial length of the cavity, with small deviations near the parallel, no-slip end walls. When non-linearity sets in triadic interactions occur and, depending on the value of the centrifugal Rayleigh number, the flow is dominated by either a single mode and its harmonics or by broadband effects if turbulence develops. In this study we increase the centrifugal Rayleigh number progressively and investigate mode interactions during the vacillation regime which eventually lead to chaotic motion.   

Experimental evidence of a new regime in horizontal convection at high Rayleigh and Schmidt numbers

Horizontal convection is a flow driven by differential buoyancy forcing across a horizontal surface. It has been considered as a simple model to study the influence of heating, cooling and freshwater fluxes at the ocean surface on the Meridional Overturning Circulation. We investigate the flow properties of horizontal convection by mean of scaling analysis at high Rayleigh and Schmidt numbers. The present experiment is driven by the diffusion of salt in water across membranes localized at the surface. Salt diffusion is controlled across porous dialysis membranes. The resulting experiments are performed for Schmidt numbers $\rm{Sc}\approx 610$ and Rayleigh numbers in the range $10^{12} < Ra=\Delta b L^3/(\nu\kappa) < 10^{17}$, where $\nu$ is the kinematic viscosity of water, $\kappa$ is the diffusion coefficient of salt, $L=[.5,2,5]$m is the length of the different tanks and $\Delta b=g(\rho_{salt}-\rho_{fresh}/\rho_{fresh}$ is the reduced gravity difference. We show that the scaling follows a $Nu\sim Ra^{1/4}$ type scaling, which was recently theorized by Shishkina $et\; al.$ (2016), and was also observed recently for another distribution of the buoyancy forcing at the surface (Griffiths \& Gayen, 2015).   

Combined Lorentz force and ultrasound Doppler velocimetry in a vertical convection liquid metal flow

We report experimental studies on turbulent vertical convection flow in the liquid metal alloy gallium-indium-tin. Flow measurements were conducted by a combined use of local Lorentz force velocimetry (LLFV) and ultrasound Doppler velocimetry (UDV). It is known that the forced convection flow in a duct generates a force on the LLFV magnet system, that grows proportional to the flow velocity. We show that for the slower flow of natural convection LLFV retains this linear dependence in the range of micronewtons. Furthermore experimental results on the scaling of heat and momentum transport with the thermal driving are presented. The results cover a range of Rayleigh numbers $3\times10^5 < Ra < 3\times10^7$ at a Prandtl number $Pr \sim 0.032$. The Nusselt number $Nu$ is found to scale as $Nu\propto Ra^{0.31}$. A Reynolds number $Re_z$ based on the vertical velocities close the heated and cooled side walls scales with $Re_z \propto Ra^{0.45}$. Additionally a Reynolds number based on the horizontal flow component is scaling as $Re_x \propto Ra^{0.67}$. These results agree well with numerical simulations and theoretical predictions.   

Passively Enhancing Convection Heat Transfer Around Cylinder Using Shrouds.

Natural convection heat transfer around a horizontal cylinder has received~considerable attention through decades since it has been used in several~viable applications. However, investigations into passively enhancement of the free convective cooling using external walls and chimney effect are lacking. In this work, a numerical simulation to study natural convection~from a horizontal cylinder configured with semicircular shrouds with an~expended chimney is employed. The fluid flow and convective heat transfer~around the cylinder are modeled. The bare cylinder is also simulated for~comparison. The present study are aimed at improving our understanding of~the parameters advancing the free convective cooling of the cylinder~implemented with the shrouds configuration. For validation, the present~results for the bare tube are compared with data reported in the literature.~The numerical simulations indicate that applying the shrouds configuration~with extended chimney to a tube promotes the convection heat transfer from~the cylinder. Such a method is less expensive and simpler in design than~other configurations (e.g. utilizing extended surfaces, fins), making the~technology more practical for industrial productions, especially for cooling~systems.