Turbulent Thermal Convection Research Articles

The effect of tilt on turbulent thermal convection for a heated soap bubble

We use direct numerical simulation (DNS) to explore the effect of tilt on two-dimensional turbulent thermal convection on a half-soap bubble that is heated at its equator. In the DNS, the bubble is tilted by an angle δ∈[0°,90°], the Rayleigh number is varied between Ra∈[3×106,3×109], and the Prandlt number is fixed at Pr = 7. The DNS reveals two qualitatively different flow regimes: the dynamic plume regime (DPR) and the stable plume regime (SPR). In the DPR, small dynamic plumes constantly emerge from random locations on the equator and dissipate on the bubble. In the SPR, the flow is dominated by a single large and stable plume rising from the lower edge of the bubble. The scaling behavior of the Nusselt number Nu and Reynolds number Re is different in these two regimes, with Nu∝Ra0.3 for the DPR and Nu∝Ra0.24 for the SPR. Concerning Re, the scaling in the DPR lies between Re∝Ra0.48 and Re∝Ra0.53 depending on Ra and δ, while in the SPR, the scaling lies between Re∝Ra0.44 and Re∝Ra0.45 depending on δ. The turbulent thermal and kinetic energy dissipation rates (εT′ and εu′, respectively) are also very different in the DPR and SPR. The probability density functions (PDF) of the normalized log εT′ and log εu′ are close to a Gaussian PDF for small fluctuations but deviate considerably from a Gaussian at large fluctuations in the DPR. In the SPR, the PDFs of normalized log εT′ and log εu′ deviate considerably from a Gaussian PDF even for small values. The globally averaged thermal energy dissipation rate due to the mean temperature field was shown to exhibit the scaling ⟨ε⟨T⟩⟩B∝Ra−0.23 in the DPR and ⟨ε⟨T⟩⟩B∝Ra−0.28 in the SPR. The globally averaged kinetic energy dissipation rate due to the mean velocity field is shown to exhibit the scaling ⟨ε⟨u⟩⟩B∝Ra−0.47 in the DPR (the exponent reduces from 0.47 to 0.43 as δ is increased up to 30°). In the SPR, the behavior changes considerably to ⟨ε⟨u⟩⟩B∝Ra−0.27. For the turbulent dissipation rates, the results indicate the scaling ⟨εT′⟩B∝Ra−0.18 and ⟨εu′⟩B∝Ra−0.29 in the DPR. However, the dependencies of ⟨εT′⟩B and ⟨εu′⟩B on Ra cannot be described by power-laws in the SPR.

Enhancement of turbulent thermal convection in a circular tube with a slotted twisted tape

PurposeThe purpose of this paper, computational fluid dynamics (CFD) work, is to promote turbulent thermal convection in a heated circular tube using a passive scheme of a slotted twisted sheet.Design/methodology/approachThe inventive design uses square-cut and conjugate triangular perforations to diversify the twisted tape for better thermal convection. The current novel passive scheme methodology is accomplished by carving the same square cuts and slitting various sizes of equilateral triangle perforations (side length varies between 8 and 16 mm). The re-normalisation group turbulence model and the semi-implicit method for pressure-linked equation method examine the turbulent thermal convection aspects of all simulations at different Reynolds numbers (6,000, 10,000 and 14,000).FindingsThe analyses of simulations exhibit that the placement of a twisted tape with triangle perforations and equidistant square cuts can effectually promote thermal convection in a circular tube. A larger-sized triangle perforation can increase the thermal convection enhancement and thermal performance factor, but an enlarged perforation may decrease the thermal convection enhancement and thermal performance factor. As a result, compared with the smooth circular tube, the circular tube with the slotted twisted sheet slit by a 10 mm equilateral triangle brings about the maximum improvement ratio of the mean Nusselt number of about 2.8 at Re = 6,000. Under weighing the friction through the circular tube, the tube with the slotted twisted sheet slit by a 10 mm equilateral triangle gains the best thermal performance factor of about 1.36 at Re = 6,000.Research limitations/implicationsThe working fluid is water and its physical features are assumed to be constant. In addition, the fluid is considered a steady flow in this CFD work.Practical implicationsThese CFD predictions will benefit the development of heat exchanger tubes equipped with a slotted twisted sheet to acquire preferable thermal convection enhancement.Social implicationsHigher thermal performance achieved by placing a slotted twisted tape in a heated tube will benefit society in lower energy consumption, machinery maintenance costs and impact on the environment.Originality/valueThis study combined triangle perforations and square cuts on the twisted sheet. This combination can induce the fluid flow across the sheet to disturb the swirling flow and then promote the fluid mixing to increase thermal convection. Therefore, this modified tape can be a profitable passive device for designing a heat exchanger.

Transition between Boundary-Limited Scaling and Mixing-Length Scaling of Turbulent Transport in Internally Heated Convection.

Heat transport in turbulent thermal convection increases with thermal forcing, but in almost all studies the rate of this increase is slower than it would be if transport became independent of the molecular diffusivities-the heat transport scaling exponent is smaller than the mixing-length (or "ultimate") value of 1/2. This is due to thermal boundary layers that throttle heat transport in configurations driven either by thermal boundary conditions or by internal heating, giving a scaling exponent close to the boundary-limited (or "classical") value of 1/3. With net-zero internal heating and cooling in different regions, the larger mixing-length exponent can be attained because heat need not cross a boundary. We report numerical simulations in which heating and cooling are unequal. As heating and cooling rates are made closer, the scaling exponent of heat transport varies from its boundary-limited value to its mixing-length value.

Exploring the plume and shear effects in turbulent Rayleigh–Bénard convection with effective horizontal buoyancy under streamwise and spanwise geometrical confinements

We present an experimental and numerical study of turbulent thermal convection in the presence of an effective horizontal buoyancy that generates extra shear at the boundary. Geometrical confinements are also applied by varying the streamwise and spanwise aspect ratios of the convection cell to condense the plumes. With these, we systematically explore the effects of plume and shear on heat transfer. It is found that a streamwise confinement results in increased plume coverage but decreased shear compared with spanwise confinement. The fact that streamwise confinement leads to a higher vertical heat transfer efficiency than the spanwise confined case suggests that the increase of plume coverage is the dominant effect responsible for the enhanced heat transfer. Our results highlight the potential applications of coherent structure manipulation in efficient passive heat transfer control and thermal engineering. We also analyse the energetics of the present system and derive the expression of mixing efficiency accordingly. The mixing efficiency is found to increase with both the buoyancy ratio and streamwise dimension.

Thermal Waves and Heat Transfer Efficiency Enhancement in Harmonically Modulated Turbulent Thermal Convection

We study turbulent Rayleigh-Bénard convection over four decades of Rayleigh numbers 4×10^{8}<Ra<2×10^{12}, 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 [Yang etal., Phys. Rev. Lett. 125, 154502 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.154502] of the significant enhancement of the Nusselt number and report its dependence on the frequency and amplitude of the temperature modulation of plates.

Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models

In this paper, we develop a multivariate regression model and a neural network model to predict the Reynolds number (Re) and Nusselt number in turbulent thermal convection. We compare their predictions with those of earlier models of convection: Grossmann–Lohse [Phys. Rev. Lett. 86, 3316 (2001)], revised Grossmann–Lohse [Phys. Fluids 33, 015113 (2021)], and Pandey–Verma [Phys. Rev. E 94, 053106 (2016)] models. We observe that although the predictions of all the models are quite close to each other, the machine-learning models developed in this work provide the best match with the experimental and numerical results.

Counter-flow orbiting of the vortex centre in turbulent thermal convection

We present an experimental study of the large-scale vortex (or large-scale circulation, LSC) in turbulent Rayleigh–Bénard convection in a $\varGamma =\text {diameter}/\text {height}=2$ cylindrical cell. The working fluid is deionized water with Prandtl number ( $Pr$ ) around 5.7, and the Rayleigh number ( $Ra$ ) ranges from $7.64\times 10^7$ to $6.06\times 10^8$ . We measured the velocity field in various vertical cross-sectional planes by using the planar particle image velocimetry technique. The velocity measurement in the LSC central plane shows that the flow is in the single-roll form, and the centre of the single-roll (vortex) does not always stay at the centre of the cell; instead, it orbits periodically in the direction opposite to the flow direction of the LSC, with its trajectory in the shape of an ellipse. The velocity measurements in the three vertical planes in parallel to the LSC central plane indicate that the flow is in the vortex tube form horizontally filling almost the whole cell, and the centre line of the vortex tube is consistent with the so-called ‘jump rope’ form proposed by a previous study that combined numerical simulation and local velocity measurements in the low $Pr$ case (Vogt et al., Proc. Natl Acad. Sci. USA, vol. 115, 2018, pp. 12674–12679). In addition, we found that the oscillation of the local velocity in $\varGamma =2$ cells originates from the periodical orbiting of the vortex centre. Our velocity measurements further indicate that the vortex centre orbiting is absent in $\varGamma =1$ cells, at least in the $Ra$ range of our experiments.

Dynamics and length scales in vertical convection of liquid metals

Using complementary experiments and direct numerical simulations, we study turbulent thermal convection of a liquid metal (Prandtl number $\textit {Pr}\approx 0.03$ ) in a box-shaped container, where two opposite square sidewalls are heated/cooled. The global response characteristics like the Nusselt number ${\textit {Nu}}$ and the Reynolds number $\textit {Re}$ collapse if the side height $L$ is used as the length scale rather than the distance $H$ between heated and cooled vertical plates. These results are obtained for various Rayleigh numbers $5\times 10^3\leq {\textit {Ra}}_H\leq 10^8$ (based on $H$ ) and the aspect ratios $L/H=1, 2, 3$ and $5$ . Furthermore, we present a novel method to extract the wind-based Reynolds number, which works particularly well with the experimental Doppler-velocimetry measurements along vertical lines, regardless of their horizontal positions. The extraction method is based on the two-dimensional autocorrelation of the time–space data of the vertical velocity.

Heat transfer and plume statistics in turbulent thermal convection with sparse fractal roughness

Heat transfer and plume statistics in turbulent thermal convection with sparse fractal roughness

Turbulent transition in Rayleigh-Bénard convection with fluorocarbon (a) Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

We present measurements of the global heat transfer and the velocity field in two Rayleigh-Bénard cells (aspect ratios 1 and 2). We use Fluorinert FC770 as the working fluid, up to a Rayleigh number . The velocity field is inferred from sequences of shadowgraph pattern using a Correlation Image Velocimetry (CIV) algorithm. Indeed the large number of plumes, and their small characteristic scale, make it possible to use the shadowgraph pattern produced by the thermal plumes in the same manner as particles in Particle Image Velocimetry (PIV). The method is validated in water against PIV, and yields identical wind velocity estimates. The joint heat transfer and velocity measurements allow to compute the scaling of the kinetic dissipation rate which features a transition from a laminar scaling to a turbulent Re 3 scaling. We propose that the turbulent transition in Rayleigh-Bénard convection is controlled by a threshold Péclet number rather than a threshold Rayleigh number, which may explain the apparent discrepancy in the literature regarding the “ultimate” regime of convection.

Unravelling the large-scale circulation modes in turbulent Rayleigh-Bénard convection (a) Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

The large-scale circulation (LSC) is the most fundamental turbulent coherent flow structure in Rayleigh-Bénard convection. Further, LSCs provide the foundation upon which superstructures, the largest observable features in convective systems, are formed. In confined cylindrical geometries with diameter-to-height aspect ratios of , LSC dynamics are known to be governed by a quasi-two-dimensional, coupled horizontal sloshing and torsional (ST) oscillatory mode. In contrast, in cylinders, a three-dimensional jump rope vortex (JRV) motion dominates the LSC dynamics. Here, we use dynamic mode decomposition (DMD) on direct numerical simulation data of liquid metal to show that both types of modes co-exist in and cylinders but with opposite dynamical importance. Furthermore, with this analysis, we demonstrate that ST oscillations originate from a tilted elliptical mean flow superposed with a symmetric higher-order mode, which is connected to the four rolls in the plane perpendicular to the LSC in tanks.

Dynamics of flow reversals in the presence of a vertical magnetic field (a) (a)Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

We investigate the dynamics of flow reversals close to the onset of Rayleigh-Bénard convection (RBC) of electrically conducting low Prandtl number (Pr) Boussinesq fluids in the presence of an external vertical magnetic field. The investigation is carried out by performing three-dimensional (3D) direct numerical simulations (DNS) of the related mathematical model considering the quasi-static approximation. The numerical investigation reveals a rich dynamics of the flow reversals close to the onset of convection. Three qualitatively different kinds of flow reversals, namely chaotic, intermittent and periodic are identified and all are found to occur in the presence of weak magnetic field, measured in terms of the Chandrasekhar number (Q). Explored ranges of the Prandtl number (Pr), the Rayleigh number (Ra) and the Chandrasekhar number are , and , respectively. Out of the three different types of flow reversals, intermittent flow reversal is new and has not been reported so far in convective system to the best of our knowledge. The probability density function of the time interval of occurrences of chaotic flow reversals is found to decay exponentially. The heat transfer properties of the system are also numerically investigated and it is observed that magnetic field facilitates the heat transfer in the considered ranges of the parameter space.

Velocimetry in rapidly rotating convection: Spatial correlations, flow structures and length scales (a) (a)Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

Rotating Rayleigh-Bénard convection is an oft-employed model system to evaluate the interplay of buoyant forcing and Coriolis forces due to rotation, an eminently relevant interaction of dynamical effects found in many geophysical and astrophysical flows. These flows display extreme values of the governing parameters: large Rayleigh numbers Ra, quantifying the strength of thermal forcing, and small Ekman numbers E, a parameter inversely proportional to the rotation rate. This leads to the dominant geostrophic balance of forces in the flow between pressure gradient and Coriolis force. The so-called geostrophic regime of rotating convection is difficult to study with laboratory experiments and numerical simulations given the requirements to attain simultaneously large Ra values and small values of E. Here, we use flow measurements using stereoscopic particle image velocimetry in a large-scale rotating convection apparatus in a horizontal plane at mid-height to study the rich flow phenomenology of the geostrophic regime of rotating convection. We quantify the horizontal length scales of the flow using spatial correlations of vertical velocity and vertical vorticity, reproducing features of the convective Taylor columns and plumes flow states both part of the geostrophic regime. Additionally, we find in this horizontal plane an organisation into a quadrupolar vortex at higher Rayleigh numbers starting from the plumes state.

Equilibrium states of the ice-water front in a differentially heated rectangular cell (a) (a)Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

We study the conductive and convective states of phase change of pure water in a rectangular container where two opposite walls are kept respectively at temperatures below and above the freezing point and all the other boundaries are thermally insulating. The global ice content at the equilibrium and the corresponding shape of the ice-water interface are examined, extending the available experimental measurements and numerical simulations. We first address the effect of the initial condition, either fully liquid or fully frozen, on the system evolution. Secondly, we explore the influence of the aspect ratio of the cell, both in the configurations where the background thermal gradient is parallel to the gravity, namely the Rayleigh-Bénard (RB) setting, and when they are perpendicular, i.e., vertical convection (VC). We find that for a set of well-identified conditions the system in the RB configuration displays multiple equilibrium states, either conductive rather than convective, or convective but with different ice front patterns. The shape of the ice front appears to be always determined by the large scale circulation in the system. In RB, the precise shape depends on the degree of lateral confinement. In the VC case the ice front morphology is more robust, due to the presence of two vertically stacked counter-rotating convective rolls for all the studied cell aspect ratios.

Rotation suppresses giant-scale solar convection.

The observational absence of giant convection cells near the Sun's outer surface is a long-standing conundrum for solar modelers. We herein propose an explanation. Rotation strongly influences the internal dynamics, leading to suppressed convective velocities, enhanced thermal-transport efficiency, and (most significantly) relatively smaller dominant length scales. We specifically predict a characteristic convection length scale of roughly 30-Mm throughout much of the convection zone, implying weak flow amplitudes at 100- to 200-Mm giant cells scales, representative of the total envelope depth. Our reasoning is such that Coriolis forces primarily balance pressure gradients (geostrophy). Background vortex stretching balances baroclinic torques. Both together balance nonlinear advection. Turbulent fluxes convey the excess part of the solar luminosity that radiative diffusion cannot. We show that these four relations determine estimates for the dominant length scales and dynamical amplitudes strictly in terms of known physical quantities. We predict that the dynamical Rossby number for convection is less than unity below the near-surface shear layer, indicating rotational constraint.

A novel buoyancy-modified subgrid-scale model for large-eddy simulation of turbulent convection

PurposeThe purpose of this paper is to develop a subgrid-scale (SGS) model for large eddy simulation (LES) of buoyancy- and thermally driven transitional and turbulent flows and further examine its performance.Design/methodology/approachFavre-filtered, non-dimensional LES equations are solved using non-dissipative, fully implicit, kinetic energy conserving, finite-volume algorithm which uses an iterative predictor-corrector approach based on pressure correction. Also, to develop a new SGS model which accounts for buoyancy, turbulent generation term in SGS viscosity is properly modified and enhanced by buoyancy production.FindingsThe proposed model has been successfully applied to turbulent Rayleigh–Bénard convection. The results show that the model is able to reproduce the complex physics of turbulent thermal convection. In comparison with the original wall-adapting local eddy-viscosity (WALE) and buoyancy-modified (BM) Smagorinsky models, turbulent diagnostics predicted by the new model are in better agreement with direct numerical simulation.Originality/valueA BM variant of the WALE SGS model is newly developed and analyzed.

A comparative study of linear and step forcing temperature profiles in horizontal convection (a) (a)Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

We present a numerical study of horizontal convection using both step and linear forcing profiles as the imposed surface thermal driving, the former of which is commonly used in many studies but the latter is closer to the real ocean. Our investigation focuses on how forcing profiles can affect the theoretical and experimental results previously obtained based on the step forcing profile. We show that both types of forcing profiles exhibit similar behaviors in terms of global heat transfer (Nu), mean flow strength (Re), and boundary layer thickness. However, these two forcing profiles show significant differences for some other physical quantities, such as the generation rate of available potential energy G APE and global thermal dissipation rate, for which exact relationships with Nu can be derived for the step forcing profile but not for linear forcing. We show that a relationship between Nu and G APE can be developed for linear forcing by defining an effective forcing area, and such area is found to be approximately constant. We further derive an approximate relationship between Nu and the global thermal dissipation rate for linear forcing by assuming that the boundary heat flux is proportional to the local temperature deviation from the mean, which works best under the condition of moderate plume emissions. Differences are also found for the viscous dissipation rate; however, these differences diminish for sufficiently high Ra. Though step forcing is obviously less appropriate for modeling ocean circulations, we show that most differences arising from the forcing profile difference can be reconciled. Considering its convenience in experiment control and theoretical analysis, step forcing is a good configuration for most problems, but one should also be aware of the differences between step and other forcing types in quantities like the global thermal dissipation rate when extrapolating the results to more general situations.

Heat transport enhancement in confined Rayleigh-Bénard convection feels the shape of the container (a) (a)Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

Moderate spatial confinement enhances the heat transfer in turbulent Rayleigh-Bénard (RB) convection (Chong K. L. et al., Phys. Rev. Lett., 115 (2015) 264503). Here, by performing direct numerical simulations, we answer the question how the shape of the RB cell affects this enhancement. We compare three different geometries: a box with rectangular base (i.e., stronger confined in one horizontal direction), a box with square base (i.e., equally confined in both horizontal directions), and a cylinder (i.e., symmetrically confined in the radial direction). In all cases the confinement can be described by the same confinement parameter , given as height-over-width aspect ratio. The explored parameter range is , for the Rayleigh number, and a Prandtl number of . We find that both the optimal confinement parameter for maximal heat transfer and the actual heat transfer enhancement strongly depend on the cell geometry. The differences can be explained by the formation of different vertically coherent flow structures within the specific geometries. The enhancement is largest in the cylindrical cell, owing to the formation of a domain-spanning flow structure at the optimal confinement parameter .

Convective heat transport in slender cells is close to that in wider cells at high Rayleigh and Prandtl numbers (a) (a)Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

Direct numerical simulations of turbulent convection at high Rayleigh numbers in large aspect ratio cells are challenging because of the prohibitive computational resources required. One can achieve high Rayleigh numbers at affordable costs for low aspect ratios, but the effect of small aspect ratio remains to be understood fully. In this work, we explore integral quantities in convection in a cell with the small aspect ratio of 0.1 by varying both the Rayleigh and Prandtl numbers systematically. We find that the heat transport in this flow is within 10% of that in cells with large aspect ratios for high enough Rayleigh numbers and for Prandtl numbers larger than unity. For low Prandtl numbers, the increase of the heat transport is steeper for low aspect ratios, approaching that in large aspect ratios as the Prandtl number increases. Further, the global momentum transport, quantified by the Reynolds number, is reduced for all Prandtl numbers, presumably because of the larger volume of flow affected by the friction from sidewalls, compared to that in cells of larger aspect ratio.

Prandtl number dependence of the small-scale properties in turbulent Rayleigh-Bénard convection

We analyze the Prandtl number (Pr) dependence of spectra and fluxes of kinetic energy, as well as the energy injection rates and dissipation rates, of turbulent thermal convection using numerical data. As expected, for a flow with $ \mathrm{Pr} \lessapprox 1 $, the inertial-range kinetic energy flux is constant, and the kinetic energy spectrum is Kolmogorov-like ($ k^{-5/3} $). More importantly, we show that the amplitudes of the kinetic energy fluxes and spectra and those of structure functions increase with the decrease of Pr, thus exhibiting stronger nonlinearity for flows with small Prandtl numbers. Consistent with these observations, the kinetic energy injection rates and the dissipation rates too increase with the decrease of Pr. Our results are in agreement with earlier studies that report the Reynolds number to be a decreasing function of Prandtl number in turbulent convection. On the other hand, the tail of the probability distributions of the local heat flux grows with the increase of Pr, indicating increased fluctuations in the local heat flux with Pr.