Turbulent Rayleigh-Benard convection in a closed cylindrical cell is studied in the Lagrangian frame of reference with the help of three-dimensional direct numerical simulations. The aspect ratio of the cell Gamma is varied between 1 and 12, and the Rayleigh number Ra between 10^7 and 10^9. The Prandtl number Pr is fixed at 0.7. It is found that both the pair dispersion of the Lagrangian tracer particles and the statistics of the acceleration components measured along the particle trajectories depend on the aspect ratio for a fixed Rayleigh number for the parameter range covered in our studies. This suggests that large-scale circulations present in the convection cell affect the Lagrangian dynamics. Our findings are in qualitative agreement with existing Lagrangian laboratory experiments on turbulent convection.
The Boussinesq equations for Rayleigh-Benard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25,000, the axisymmetric flow becomes unstable to standing or travelling azimuthal waves. The standing waves are slightly unstable to travelling waves. This scenario is identified as a Hopf bifurcation in a system with O(2) symmetry.
Rayleigh-Benard convection in a cylindrical container can take on many different spatial forms. Motivated by the results of Hof, Lucas and Mullin [Phys. Fluids 11, 2815 (1999)], who observed coexistence of several stable states at a single set of parameter values, we have carried out simulations at the same Prandtl number, that of water, and radius-to-height aspect ratio of two. We have used two kinds of thermal boundary conditions: perfectly insulating sidewalls and perfectly conducting sidewalls. In both cases we obtain a wide variety of coexisting steady and time-dependent flows.
Zonal flows are often found in rotating convective systems. Not only are these jet-flows driven by the convection, they can also have a profound effect on the nature of the convection. In this work the cylindrical annulus geometry is exploited in order to perform nonlinear simulations seeking to produce strong zonal flows and multiple jets. The parameter regime is extended to Prandtl numbers that are not unity. Multiple jets are found to be spaced according to a Rhines scaling based on the zonal flow speed, not the convective velocity speed. Under certain conditions the nonlinear convection ap…
We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average di…
We study the fractionation of two components between a well-mixed gas and a saturated convecting porous layer. Motivated by geological carbon dioxide (CO$_2$) storage we assume that convection is driven only by the dissolved concentration of the first component, while the second acts as a tracer with increased diffusivity. Direct numerical simulations for convection at high Rayleigh numbers reveal that the partitioning of the components, in general, does not follow a Rayleigh fractionation trend, as commonly assumed. Initially, increases in tracer diffusivity also increase its flux, because th…
We have developed novel instrumentation for making Lagrangian measurements of temperature in diverse fluid flows. A small neutrally buoyant capsule is equipped with on-board electronics which measure temperature and transmit the data via a wireless radio frequency link to a desktop computer. The device has 80 dB dynamic range, resolving milli-Kelvin changes in temperature with up to 100 ms sampling time. The capabilities of these "smart particles" are demonstrated in turbulent thermal convection in water. We measure temperature variations as the particle is advected by the convective motion, a…
Natural convection is of great importance in many engineering applications. This paper presents a smoothed particle hydrodynamics (SPH) method for natural convection. The conservation equations of mass, momentum and energy of fluid are discretized into SPH equations. The body force due to the change of density in a temperature field is considered by the Boussinesq approximation. The numerical method is validated by comparing numerical results with experimental results from literature. The numerical and experimental results reach a good agreement. Then the SPH method is applied to study the nat…
We present simulations of cumulus convection over land with shortwave radiation computed by a Monte Carlo ray tracer coupled to the flow solver. Ray tracing delivers very realistic in-cloud heating rates and global horizontal irradiance fields. The necessary performance of the ray tracer has been enabled by the raw power of GPU computing and from techniques for accelerating data lookup and ray tracer convergence. We used a case study over a grassland in the Netherlands to compare simulations with a coupled ray tracer to those with a conventional two-stream solver, and to test ray tracer conver…
Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating cylindrical annulus with conical caps is considered with the aim to establish whether a small fraction of compositional buoyancy added to the thermal buoyancy (or vice versa) can significantly reduce the critical Rayleigh number and amplify convection in planetary cores. It is shown that the neutral surface describing the onset of convection in the double-buoyancy case is essentially different from that of the well-studied purely thermal case, and does indeed allow the possibility of low-Rayleigh number…
We report measurements of properties of turbulent thermal convection of a fluid with a Prandtl number $\Pra=4.38$ in a cylindrical cell with an aspect ratio $Γ=0.50$. The rotational symmetry was broken by a small tilt of the sample axis relative to gravity. Measurements of the heat transport (as expressed by the Nusselt number \Nu), as well as of large-scale-circulation (LSC) properties by means of temperature measurements along the sidewall, are presented. In contradistinction to similar experiments using containers of aspect ratio $Γ=1.00$ \cite[]{ABN06} and $Γ=0.50$ \cite[]{CRCC04,SXX05,RGK…
Approximate empirical models of thermal convection can allow us to identify the essential properties of the flow in simplified form, and to produce empirical estimates using only a few parameters. Such "low-dimensional" empirical models can be constructed systematically by writing numerical or experimental measurements as superpositions of a set of appropriate basis modes, a process known as Galerkin projection. For three-dimensional convection in a cylinder, those basis modes should be vector-valued, mutually orthogonal, and defined in cylindrical coordinates. Here we construct such a basis s…
We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-Bénard flow in a cylindrical sample at Rayleigh numbers Ra=10^8 to Ra=2\times10^{12} and Prandtl numbers Pr=6.4 and Pr=0.7 with the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010)] thus extending previous results for quasi-2-dimensional systems to 3D systems for the first time. The dynamical frame method shows that the measured temperature profiles in the spatially and temporally local frame are much closer to the temperatu…
The axisymmetric flow in an aspect-ratio-one cylinder whose upper and lower bounding disks are maintained at different temperatures and rotate at equal and opposite velocities is investigated. In this combined Rayleigh-Benard/von Karman problem, the imposed temperature gradient is measured by the Rayleigh number Ra and the angular velocity by the Reynolds number Re. Although fluid motion is present as soon as Re is non-zero, a symmetry-breaking transition analogous to the onset of convection takes place at a finite Rayleigh number higher than that for Re=0. For Re<95, the transition is a pitch…
We consider two common heat transfer processes and perform a through sensitivity study of the variables involved. We derive and discuss analytical formulas for the heat transfer coefficient in function of film velocity, air temperature and pipe diameter. The according plots relate to a qualitative analysis of the multi-variable function $h$, according to functional optimization. For each process, we provide with graphs and tables of the parameters of interest, such as the Reynolds number. This method of study and the specific values can constitute a useful reference for didactic purposes.
A large number of flows with distinctive patterns have been observed in experiments and simulations of Rayleigh-Benard convection in a water-filled cylinder whose radius is twice the height. We have adapted a time-dependent pseudospectral code, first, to carry out Newton's method and branch continuation and, second, to carry out the exponential power method and Arnoldi iteration to calculate leading eigenpairs and determine the stability of the steady states. The resulting bifurcation diagram represents a compromise between the tendency in the bulk towards parallel rolls, and the requirement i…
The analysis of vibration effect on non-isothermal fluid in closed cavity is important for planning technological experiments in space. Control and optimization of these processes critically depend on the understanding of liquid response to the vibrations. With this aim the theoretical investigation for infinite plane and cylindrical fluid layers are performed. We investigated simple case of the fluid response-thermal vibrational convection in a cylindrical fluid layer with rigid conducting boundaries. It is found that steady modes of thermal vibrational convection are subjected to various bif…
Direct numerical simulations are performed to study turbulent Rayleigh-Bénard convection in a vertical cylindrical cavity with uniform axial magnetic field. Flows at high Hartmann and Rayleigh numbers are considered. The calculations reveal that, similarly to the behavior observed in Rayleigh-Bénard convection with strong rotation, flows at strong magnetic field develop a central vortex, while the heat transfer is suppressed.
We report an experimental study of the properties of the velocity boundary layer in turbulent Rayleigh-Bénard convection in a cylindrical cell. The measurements were made at Rayleigh numbers $Ra$ in the range $2.8\times10^{8}<Ra<5.6\times10^{9}$ and were conducted with the convection cell tilted with an angle $θ$ relative to gravity, at $θ=0.5^{o}$, $1.0^{o}$, $2.0^{o}$, and $3.4^{o}$, respectively. The fluid was water with Prandtl number $Pr=5.3$. It is found that at small tilt angles ($θ\le 1^{o}$), the measured viscous boundary layer thickness $δ_{v}$ scales with the Reynolds number $Re$ wi…
We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of water (Prandtl number sigma = 4.38) with diameters D = 49.7, 24.8, and 9.2 cm, all with aspect ratio Gamma = D/L = 1 (L is the sample height). In addition, we present data for D = 49.7 and Gamma = 1.5, 2, 3, and 6. For each sample the data cover a range of a little over a decade of R. For Gamma = 1 they jointly span the range 10^7 < R < 10^11. Where needed, the data were corrected for the influence of the finite conductivity of the top and bottom plates and of the si…
We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of water (Prandtl number sigma = 4.4) with a diameter D of 49.7 cm and heights L = 116.3, 74.6, and 50.6 cm, as well as for D = 24.8 cm and L = 90.2 cm. For each aspect ratio Gamma = D/L = 0.28, 0.43, 0.67, and 0.98 the data cover a range of a little over a decade of R. The maximum R ~= 10^12 and Nusselt number N ~= 600 were reached for Gamma = 0.43 and D = 49.7. The data were corrected for the influence of the finite conductivity of the top and bottom plates on the hea…
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 the 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. However, experiments never operate in unbounded domains and it is important to understand how confinement might alter the approach to this ultima…
Recent studies of rotating Rayleigh-Bénard convection at high rotation rates and strong thermal forcing have shown a significant discrepancy in total heat transport between experiments on a confined cylindrical domain on the one hand and simulations on a laterally unconfined periodic domain on the other. This paper addresses this discrepancy using direct numerical simulations on a cylindrical domain. An analysis of the flow field reveals a region of enhanced convection near the wall, the sidewall circulation. The sidewall circulation rotates slowly within the cylinder in anticyclonic direction…
Non-isothermal particles suspended in a fluid lead to complex interactions -- the particles respond to changes in the fluid flow, which in turn is modified by their temperature anomaly. Here, we perform a novel proof-of-concept numerical study based on tracer particles that are thermally coupled to the fluid. We imagine that particles can adjust their internal temperature reacting to some local fluid properties and follow simple, hard-wired active control protocols. We study the case where instabilities are induced by switching the particle temperature from hot to cold depending on whether it …
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-Bénard 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 t…
We report an experimental study of the three-dimensional spatial structure of the low frequency temperature oscillations in a cylindrical Rayleigh-Bénard convection cell. It is found that thermal plumes are not emitted periodically, but randomly and continuously, from the top and bottom plates. We further found that the oscillation of the temperature field does not originate from the boundary layers, but rather is a result of the horizontal motion of the hot ascending and cold descending fluids being modulated by the twisting and sloshing motion of the bulk flow field.
We study turbulent Rayleigh-Bénard convection over four decades of Rayleigh numbers 4E8 < Ra < 2E12, while harmonically modulating the temperatures of the plates of our cylindrical cell. We probe the flow by temperature sensors placed in the cell interior and embedded in the highly conducting copper plates and detect thermal waves propagating at modulation frequency in the bulk of the convective flow. We confirm the recent numerical prediction [PRL 125, 154502 (2020)] of the significant enhancement of Nusselt number and report its dependence on the frequency and amplitude of the temperature mo…
Rayleigh--Bénard convection, which is the buoyancy-induced motion of a fluid enclosed between two horizontal plates, is an idealised setup to study thermal convection. We analyse the modes that transport the most heat between the plates by computing the proper orthogonal decomposition (POD) of numerical data. Instead of the usual POD ansatz of finding modes that describe the energy best, we propose a method that is optimal in describing the heat transport. Thereby, we can determine the modes with the major influence on the heat transport and the coherent structures in the convection cell. We a…
We present observations of oscillations in the shape of the temperature profile of the large-scale circulation (LSC) of turbulent Rayleigh-B{é}nard convection. Temperature measurements are broken down into Fourier moments as a function of $θ-θ_0$, where $θ$ is the azimuthal angle in a horizontal plane at mid-height, and $θ_0$ is the LSC orientation. The oscillation structure is dominated by a 3rd order sine moment and 3rd order cosine moment in a cubic cell. In contrast, these moments are not found to oscillate in a cylindrical cell. This geometry-dependent behavior can be explained by a model…
Spatial regions that do not mix effectively with their surroundings and thus contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-Bénard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CS) which we investigate here in direct numerical simulations in convection cells with square cross section of aspect ratio $Γ= 16$, Rayleigh number $Ra = 10^{5}$, and Prandtl numbers $Pr = 0.1, 0.7$ and $7$. The analysis is based on $N=524,288$ Lagrangian tracer particles which are advected in…
The spontaneous convective patterns induced by evaporation of a pure liquid layer are studied experimentally. A volatile liquid layer placed in a cylindrical container is left free to evaporate into air at rest under ambient conditions. The liquid/gas interface of the evaporating liquid layer is visualized using an infrared (IR) camera. The phenomenology of the observed convective patterns is qualitatively analysed, showing in particular that the latter can be quite complex especially at moderate liquid thicknesses. Attention is also paid to the influence of the container diameter on the obser…
Turbulent Rayleigh-Bénard convection in slender cylindrical cells exhibits rich dynamics of the large-scale circulation (LSC), with several rolls stacked on top of each other. We propose that the elliptical instability is the mechanism which causes the twisting and breaking of the LSC into multiple rolls and that the volume-averaged heat and momentum transport, represented by the Nusselt number and Reynolds number, is generally weaker for larger number $n$ of the LSC rolls. This is supported by direct numerical simulations for $Ra=5\times10^5$, $Pr=0.1$, $H=5D$ and $1\leq~n\leq4$.
We present measurements of the orientation theta_0(t) of the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection in cylindrical cells of aspect ratio 1. theta_0(t) undergoes irregular reorientations. It contains reorientation events by rotation through angles Delta theta with a monotonically decreasing probability distribution p(Delta theta), and by cessations (where the LSC stops temporarily) with a uniform p(Delta theta). Reorientations have Poissonian statistics in time. The amplitude of the LSC and the magnitude of the azimuthal rotation rate have a negative correlation.
Using direct numerical simulations, we study rotating Rayleigh-Bénard convection in a cylindrical cell for a broad range of Rayleigh, Ekman, and Prandtl numbers from the onset of wall modes to the geostrophic regime, an extremely important one in geophysical and astrophysical contexts. We connect linear wall-mode states that occur prior to the onset of bulk convection with the boundary zonal flow that coexists with turbulent bulk convection in the geostrophic regime through the continuity of length and time scales and of convective heat transport. We quantitatively collapse drift frequency, bo…
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…
We report experimental measurements of heat transport in rotating Rayleigh-B{é}nard convection in a cylindrical convection cell with aspect ratio $Γ= 1/2$. The fluid was helium gas with Prandtl number Pr = 0.7. The range of control parameters was Rayleigh number $4 \times 10^9 < {\rm Ra} < 4 \times 10^{11}$ and Ekman number $2 \times 10^{-7} < {\rm Ek} < 3 \times 10^{-5}$(corresponding to Taylor number $4 \times 10^9 < {\rm Ta} < 1 \times 10^{14}$ and convective Rossby number $0.07 < {\rm Ro} < 5$). We determine the crossover from weakly rotating turbulent convection to rotation dominated geos…
Measurements of the Nusselt number $Nu$ and of temperature variations $ΔT_b$ in the bulk fluid are reported for turbulent Rayleigh-Bénard convection of a cylindrical sample. They cover the Rayleigh-number range $10^{9} \alt Ra \alt 3\times 10^{14}$ using He (Prandtl number $Pr = 0.67$), N$_2$ ($Pr = 0.72$) and SF$_6$ ($Pr = 0.79$ to 0.84) at pressures up to 15 bars and near-ambient temperatures. The sample had a height $L=2.24$m and diameter $D = 1.12$m and was located in a new High-Pressure Convection Facility (HPCF) at the Max Planck Institute for Dynamics and Self-Organization in Göttingen,…
Large-scale patterns, which are well-known from the spiral defect chaos regime of thermal convection at Rayleigh numbers $Ra < 10^4$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh-Bénard convection in extended cylindrical cells with an aspect ratio $Γ=50$ and $Ra>10^5$. They are uncovered when the turbulent fields are averaged in time and turbulent fluctuations are thus removed. We apply the Boussinesq closure to estimate turbulent viscosities and diffusivities, respectively. The resulting turbulent Rayleigh number $Ra_{\ast}$, that describes the convection…
A fully non-dimensional correlation for the Nusselt number associated to cooling processes in vertical storage tanks under laminar natural convection is presented. The derived correlation depends on the average temperature and can be used for the improvement of temperature profiles found from global methods. A Finite Volume method is employed using a transient bi-dimensional model in cylindrical coordinates and is experimentally validated. Forty cases of cooling with four aspect ratios, five overall heat transfer coefficients and two different volumes are considered. Thermal losses for the env…
We measured Reynolds numbers R_e of turbulent Rayleigh-Benard convection over the Rayleigh-number range 2 times 10^8 < R < 10^11 and Prandtl-number range 3.3 < sigma < 29 for cylindrical samples of aspect ratio Gamma = 1. For R < R_c = 3 times 10^9 we found R_e ~ R^beta_eff with beta_eff = 0.46 < 1/2. Here both the sigma- and R-dependences are quantitatively consistent with the Grossmann-Lohse (GL) prediction. For R > R_c we found R_e = 0.106 sigma^-3/4 R^1/2, which differs from the GL prediction. The relatively sharp transition at R_c to the large-R regime suggests a qualitative and sudden ch…
Temperature and velocity oscillations have been found in a rectangular Rayleigh-Bénard convection cell, in which one large scale convection roll exists. At $Ra=8.9 \times 10^{11}$ and $Pr=4$, temperature oscillation can be observed in most part of the system and the oscillation period remains almost constant, $t_T = 74 \pm 2$ seconds. Velocity oscillation can only be found in its horizontal component, $v_y$ (perpendicular to large scale circulation plane), near the cell sidewall, its oscillation period is also constant, $t_T = 65 \pm 2$ seconds, at these positions. Temperature and velocity osc…
A removable holder carrying a set of miniature temperature sensors inside our Rayleigh-Bénard convection cylindrical cell has been developed. The sensors should not disturb the temperature and velocity fields of the buoyancy-driven turbulent flow of our working fluid - cryogenic helium gas (~ 5 K). The cell, 300 mm both in diameter and height, must withstand the overpressure up to 2.5 bar, which is why all its parts are welded together. The holder consists of a pair of identical feedthroughs (each with 6 glass-sealed pins), constantan wires (0.1 mm), Be bronze springs and insulating elements a…
High-Rayleigh number convective turbulence is ubiquitous in many natural phenomena and in industries, such as atmospheric circulations, oceanic flows, flows in the fluid core of planets, and energy generations. In this work, we present a novel approach to boost the Rayleigh number in thermal convection by exploiting centrifugal acceleration and rapidly rotating a cylindrical annulus to reach an effective gravity of 60 times Earth's gravity. We show that in the regime where the Coriolis effect is strong, the scaling exponent of Nusselt number versus Rayleigh number exceeds one-third once the Ra…
We report an experimental study aiming to clarify the role of boundary conditions (BC) in high Rayleigh number $10^8 < {\rm{Ra}} < 3 \times 10^{12}$ turbulent thermal convection of cryogenic helium gas. We switch between BC closer to constant heat flux (CF) and constant temperature (CT) applied to the highly conducting bottom plate of the aspect ratio one cylindrical cell 30 cm in size, leading to dramatic changes in the temperature probability density function and in power spectral density of the temperature fluctuations measured at the bottom plate, while the dynamic thermal behaviour of the…
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…
The heat transfer and flow structure in rotating Rayleigh-Bénard convection are strongly influenced by the Rayleigh ($Ra$), Prandtl ($Pr$), and Rossby ($Ro$) number. For $Pr\gtrsim 1$ and intermediate rotation rates, the heat transfer is increased compared to the non-rotating case. We find that the regime of increased heat transfer is subdivided into a low and a high $Ra$ number regime. For $Ra\lesssim 5\times10^8$ the heat transfer at a given $Ra$ and $Pr$ is highest at an optimal rotation rate, at which the thickness of the viscous and thermal boundary layer is about equal. From the scaling …
Direct numerical simulations are carried out to study flow structure and transport properties in turbulent Rayleigh-Bénard convection in a cylindrical cell of aspect ratio one with an imposed axial magnetic field. Flows at the Prandtl number 0.025 and the Rayleigh and Hartmann numbers up to $10^9$ and 1400 are considered. The results are consistent with those of earlier experimental and numerical data. As anticipated, the heat transfer rate and kinetic energy are suppressed by strong magnetic field. At the same time, their growth with the Rayleigh number is found to be faster in flows at high …
In RB convection for fluids with Prandtl number $Pr\gtrsim 1$, rotation beyond a critical (small) rotation rate is known to cause a sudden enhancement of heat transfer which can be explained by a change in the character of the BL dynamics near the top and bottom plates of the convection cell. Namely, with increasing rotation rate, the BL signature suddenly changes from Prandtl--Blasius type to Ekman type. The transition from a constant heat transfer to an almost linearly increasing heat transfer with increasing rotation rate is known to be sharp and the critical Rossby number $Ro_{c}$ occurs t…
Rayleigh-Bénard convection, i.e. the flow of a fluid between two parallel plates that is driven by a temperature gradient, is an idealised setup to study thermal convection. Of special interest are the statistics of the turbulent temperature field, which we are investigating and comparing for three different geometries, namely convection with periodic horizontal boundary conditions in three and two dimensions as well as convection in a cylindrical vessel, in order to work out similarities and differences. To this end, we derive an exact evolution equation for the temperature probability densit…
We present high-resolution numerical investigations of heat transport by two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection over the Rayleigh number range $10^8 \leqslant Ra\leqslant 10^{10}$ and the Prandtl number range $0.7\leqslant Pr \leqslant10$. We find that there exist strong counter-gradient local heat flux with magnitude much larger than the global Nusselt number $Nu$ of the system. Two mechanisms for generating counter-gradient heat transport are identified: one is due to the bulk dynamics and the other is due to the competitions between the corner-flow rolls and the larg…
Influence of Aspect ratio in the Convection in Rotating Annulus In the Presence of Localized Heating
School of Artificial Intelligence, Amrita Vishwa Vidyapeetham（阿迈塔维迪亚佩塔姆大学人工智能学院）；Department of Mechanical Engineering, Indian Institute of Technology（印度理工学院机械工程系）
In turbulent thermal convection in cylindrical samples of aspect ratio Γ= D/L (D is the diameter and L the height) the Nusselt number Nu is enhanced when the sample is rotated about its vertical axis, because of the formation of Ekman vortices that extract additional fluid out of thermal boundary layers at the top and bottom. We show from experiments and direct numerical simulations that the enhancement occurs only above a bifurcation point at a critical inverse Rossby number $1/\Ro_c$, with $1/\Ro_c \propto 1/Γ$. We present a Ginzburg-Landau like model that explains the existence of a bifurca…
We report results for the temperature profiles of turbulent Rayleigh-Bénard convection (RBC) in the interior of a cylindrical sample of aspect ratio $Γ\equiv D/L = 0.50$ ($D$ and $L$ are the diameter and height respectively). Results from experiment over the Rayleigh number range $4\times 10^{12} \alt Ra \alt 10^{15}$ for a Prandtl number $\Pra \simeq 0.8$ and from direct numerical simulation (DNS) at $Ra = 2 \times 10^{12}$ for $\Pra = 0.7$ are presented. We find that the temperature varies as $A*ln(z/L) + B$ where $z$ is the distance from the bottom or top plate. This is the case in the clas…
Results from direct numerical simulations for three dimensional Rayleigh-Benard convection in a cylindrical cell of aspect ratio 1/2 and Pr=0.7 are presented. They span five decades of Ra from $2\times 10^6$ to $2 \times10^{11}$. Good numerical resolution with grid spacing $\sim$ Kolmogorov scale turns out to be crucial to accurately calculate the Nusselt number, which is in good agreement with the experimental data by Niemela et al., Nature, 404, 837 (2000). In underresolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the fully resolved case, because t…
This work focuses on the dissolution of a train of unconfined bubbles in cylindrical microchannels. We investigate how the mass transfer is affected by the channel and bubble sizes, distance between bubbles, diffusivity, superficial velocity, deformation of the bubble, the presence of surfactants in the limit of rigid interface and off-centred positions of the bubbles. We analyse the influence of the dimensionless numbers and especially the distance between bubbles and the Péclet number, Pe, which we vary among eight decades and identify five different dissolution regimes. We show different co…
