Two-dimensional Turbulent 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.

Effects of Prandtl number in two-dimensional turbulent convection* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11961160719, 11702128, 91752201, and 11772362), the Shenzhen Fundamental Research Program (Grant No. JCYJ20190807160413162), the Fundamental Research Funds for the Central Universities (Sun Yat-sen University under Grant No. 19lgzd15), and the Department of Science and Technology of Guangdong Province, China (Grant

We report a numerical study of the Prandtl-number (Pr) effects in two-dimensional turbulent Rayleigh–Bénard convection. The simulations were conducted in a square box over the Pr range from 0.25 to 100 and over the Rayleigh number (Ra) range from 107 to 1010. We find that both the strength and the stability of the large-scale flow decrease with the increasing of Pr, and the flow pattern becomes plume-dominated at high Pr. The evolution in flow pattern is quantified by the Reynolds number (Re), with the Ra and the Pr scaling exponents varying from 0.54 to 0.67 and –0.87 to –0.93, respectively. It is further found that the non-dimensional heat flux at small Ra diverges strongly for different Pr, but their difference becomes marginal as Ra increases. For the thermal boundary layer, the spatially averaged thicknesses for all the Pr numbers can be described by δθ ∼ Ra −0.30 approximately, but the local values vary a lot for different Pr, which become more uniform with Pr increasing.

Reservoir computing model of two-dimensional turbulent convection

Reservoir computing is applied to model the large-scale evolution and the resulting low-order turbulence statistics of a two-dimensional turbulent Rayleigh-B\'{e}nard convection flow at a Rayleigh number ${\rm Ra}=10^7$ and a Prandtl number ${\rm Pr}=7$ in an extended domain with an aspect ratio of 6. Our data-driven approach which is based on a long-term direct numerical simulation of the convection flow comprises a two-step procedure. (1) Reduction of the original simulation data by a Proper Orthogonal Decomposition (POD) snapshot analysis and subsequent truncation to the first 150 POD modes which are associated with the largest total energy amplitudes. (2) Setup and optimization of a reservoir computing model to describe the dynamical evolution of these 150 degrees of freedom and thus the large-scale evolution of the convection flow. The quality of the prediction of the reservoir computing model is comprehensively tested. At the core of the model is the reservoir, a very large sparse random network charcterized by the spectral radius of the corresponding adjacency matrix and a few further hyperparameters which are varied to investigate the quality of the prediction. Our work demonstrates that the reservoir computing model is capable to model the large-scale structure and low-order statistics of turbulent convection which can open new avenues for modeling mesoscale convection processes in larger circulation models.

Numerical Study of Rotating Thermal Convection on a Hemisphere

Numerical simulations of rotating two-dimensional turbulent thermal convection on a hemisphere are presented in this paper. Previous experiments on a half soap bubble located on a heated plate have been used for studying thermal convection as well as the effects of rotation on a curved surface. Here, two different methods have been used to produce the rotation of the hemisphere: the classical rotation term added to the velocity equation, and a non-zero azimuthal velocity boundary condition. This latter method is more adapted to the soap bubble experiments. These two methods of forcing the rotation of the hemisphere induce different fluid dynamics. While the first method is classically used for describing rotating Rayleigh–Bénard convection experiments, the second method seems to be more adapted for describing rotating flows where a shear layer may be dominant. This is particularly the case where the fluid is not contained in a closed container and the rotation is imposed on only one side of it. Four different diagnostics have been used to compare the two methods: the Nusselt number, the effective computation of the convective heat flux, the velocity and temperature fluctuations root mean square (RMS) generation of vertically aligned vortex tubes (to evaluate the boundary layers) and the energy/enstrophy/temperature spectra/fluxes. We observe that the dynamics of the convective heat flux is strongly inhibited by high rotations for the two different forcing methods. Also, and contrary to classical three-dimensional rotating Rayleigh–Bénard convection experiments, almost no significant improvement of the convective heat flux has been observed when adding a rotation term in the velocity equation. However, moderate rotations induced by non-zero velocity boundary conditions induce a significant enhancement of the convective heat flux. This enhancement is closely related to the presence of a shear layer and to the thermal boundary layer just above the equator.

Numerical simulation of turbulent thermal convection based on LBM

The two-dimensional (2D) turbulent thermal convection is numerically investigated by using Lattice Boltzmann Method. The 2D turbulence is considered as 2D channel flow where the flow is forced by the arrays of adiabatic cylinders placed in the inlet and wall boundary of 2D channel, which is heated uniformly from the inlet as to inspire the paradigmatic motion of thermal convection. It is found that the spacing vortex number density distribution in the large-scale range [Formula: see text], based on the Liutex vortex definition criterion, which is in fair agreement with the Benzi prediction. The energy spectrum of the Liutex field [Formula: see text]. The scaling behavior of full-field energy spectrum in the large scale is [Formula: see text]. The temperature spectrum in the large-scale range is found to be approximate to [Formula: see text], which is according with the Bolgiano theory of 2D buoyancy driven turbulence. The energy flux cascades to the large scale, the enstrophy cascades to small scale. The moments of the energy dissipation field [Formula: see text] coarse grained at the scale [Formula: see text] have the power-law behaviors with the scale [Formula: see text]. The velocity intermittency measured by PDF exists in large-scale range of 2D turbulent thermal convection. The measured scaling exponents [Formula: see text] are determined by a lognormal formula. The measured intermittency parameter is [Formula: see text], which denotes the strong intermittency in the large-scale range of 2D turbulent thermal convection.

Turbulent natural convection combined with entropy generation in a nanofluid cavity with non-uniformly heated side walls

The two-dimensional turbulent natural convection and entropy generation within an alumina-water nanoliquid chamber in the presence of sinusoidal temperature profiles at vertical walls is calculated. The considered process has been modelled using the RANS (Reynoldsaveraged Navier–Stokes) approach for turbulent regime and Boussinesq approximation for the buoyancy force. The control equations written using the non-dimensional stream function, vorticity and temperature variables combined with parameters of standard κ-ε turbulence model have been solved by the finite difference method with non-uniform computational mesh. The special algebraic transformation has been used for an introduction of the non-uniform mesh in physical domain. The influence of the nano-sized particles concentration and Rayleigh number on the nanofluid circulation and energy transport patterns has been examined.

Effect of plume motion path on heat transfer characteristics in two-dimensional turbulent thermal convection

The Grossman and Lohse (GL) theory is an important theory for studying the heat transfer characteristics of the turbulent convection. Previous computational studies have found that when the Ra number is higher than a certain value, the change of the heat transfer Nu number with Ra number in two-dimensional turbulent thermal convection is different from that in the three-dimensional thermal convection, deviating from the multiples line of the GL theory prediction. Therefore, the value of studying the two-dimensional numerical calculation of turbulent thermal convection with high Ra number is questioned. The numerical calculations of a series of two-dimensional turbulent thermal convection events with high and very high Ra number(specifically, maximum Ra = 10<sup>13</sup> with Pr = 0.7 and 4.3) are carried out in this paper. The results show that there exists a good correlation between the heat transfer Nu number and the variation of large scale circulation path length(that reflects the plume motion) with Ra number in the two-dimensional turbulent convection, and they have two Ra number transition points. The first transition point appears in the large scale circulation from the ellipse to the circle, when its circumference C<sub>LSC</sub> of the large scale circulation suddenly decreases with Ra number increasing. The second transition point appears at the minimum circumference C<sub>LSC</sub>, and then the plume rheology becomes vortex group and the circumference C<sub>LSC</sub> increases with Ra number increasing. The Ra number at transition point for a smaller Pr number is lower. The variation of the heat transfer Nu number after Ra<sup>0.3</sup> compensation shows that the local scale law of Nu number decreases as the circumference C<sub>LSC</sub> of the large scale circulation becomes small, and a phenomenon of deviating from the multiples line of GL theory prediction appears. When Ra number is higher than the second transition point, the local scale law of the Nu number varying with Ra number is in good agreement with the multiples line of GL theory prediction again in 2D turbulent thermal convection. It means that the numerical results of two-dimensional turbulent thermal convection can correctly reflect the heat transfer characteristics of turbulent thermal convection under the condition of very high Ra number.

Numerical simulations of thermal convection on a hemisphere

In this paper we present numerical simulations of two-dimensional turbulent convection on a hemisphere. Recent experiments on a half soap bubble located on a heated plate have shown that such a configuration is ideal for studying thermal convection on a curved surface. Thermal convection and fluid flows on curved surfaces are relevant to a variety of situations, notably for simulating atmospheric and geophysical flows. As in experiments, our simulations show that the gradient of temperature between the base and the top of the hemisphere generates thermal plumes at the base that move up from near the equator to the pole. The movement of these plumes gives rise to a two-dimensional turbulent thermal convective flow. Our simulations turn out to be in qualitative and quantitative agreement with experiments and show strong similarities with Rayleigh-Benard convection in classical cells where a fluid is heated from below and cooled from above. To compare to results obtained in classical Rayleigh-Benard convection in standard three-dimensional cells (rectangular or cylindrical), a Nusselt number adapted to our geometry and a Reynolds number are calculated as a function of the Rayleigh number. We find that the Nusselt and Reynolds numbers verify scaling laws consistent with turbulent Rayleigh-Benard convection: Nu ∝ Ra 0.31 and Re ∝ Ra 1/2. Further, a Bolgiano regime is found with the Bolgiano scale scaling as Ra −1/4. All these elements show that despite the significant differences in geometry between our simulations and classical 3D cells, the scaling laws of thermal convection are robust.

Numerical study of Prandtl number effects in turbulent thermal convection

The high-resolution numerical simulations of two-dimensional (2D) turbulent Rayleigh-Bnard convection are conducted by using the Parallel direct method of DNS (PDM-DNS) with Ra=1010 and Pr in a range from 0.05 to 20. Using the flow visualization technique, the effects of Pr on the structure of plumes and large scale circulation (LSC) are investigated. With Pr decreasing, plumes become more active and the flow turns more turbulent. When Pr4.3, pronounced LSC and corner vortex exist. The thickness of thermal boundary layer varies slightly with the value of Pr changing, which obeys a scaling law. Nusselt number (Nu) increases with Pr value increasing when Pr value is low and becomes independent when Pr value is high. Furthermore, two definitions of Reynolds number (Re) are given. The Re〈u〉 angle is calculated from the fluctuation of horizontal velocity near the center of bottom plate, and the ReUmax is calculated from maximal horizontal velocity in the mean field. Both of them follow the same scaling Re~Pr0.81.

Temporal Evolution and Scaling of Mixing in Turbulent Thermal Convection for Inhomogeneous Boundary Conditions

AbstractNumerical simulations of two-dimensional (2D) turbulent thermal convection for inhomogeneous boundary condition are investigated using the lattice Boltzmann method (LBM). This study mainly appraises the temporal evolution and the scaling behavior of global quantities and of small-scale turbulence properties. The research results show that the flow is dominated by large-scale structures in the turbulence regime. Mushroom plumes emerge at both ends of each heat source, and smaller plumes increasingly rise. It is found that the gradient of root mean-square (rms) vertical velocities and the gradient of the rms temperature in the bottom boundary layer decreases with time evolution. It is further observed that the temporal evolution of the Kolmogorov scale, the kinetic-energy dissipation rates and thermal dissipation rates agree well with the theoretical predictions. It is also observed that there is a range of linear scaling in the 2nd-order structure functions of the velocity and temperature fluctuations and mixed velocity-temperature structure function.

Two-dimensional turbulent convection

We present an overview of the most relevant, and sometimes contrasting, theoretical approaches to Rayleigh–Taylor and mean-gradient-forced Rayleigh–Bénard two-dimensional turbulence together with numerical and experimental evidences for their support. The main aim of this overview is to emphasize that, despite the different character of these two systems, especially in relation to their steadiness/unsteadiness, turbulent fluctuations are well described by the same scaling relationships originated from the Bolgiano balance. The latter states that inertial terms and buoyancy terms balance at small scales giving rise to an inverse kinetic energy cascade. The main difference with respect to the inverse energy cascade in hydrodynamic turbulence [R. H. Kraichnan, “Inertial ranges in two-dimensional turbulence,” Phys. Fluids 10, 1417 (1967)] is that the rate of cascade of kinetic energy here is not constant along the inertial range of scales. Thanks to the absence of physical boundaries, the two systems here investigated turned out to be a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive “ultimate state of thermal convection” [R. H. Kraichnan, “Turbulent thermal convection at arbitrary Prandtl number,” Phys. Fluids 5, 1374–1389 (1962)].

Optimal and Experimental Analysis of Electrohydrodynamic Enhancement of Water Evaporation

The paper investigates the EHD effect on the evaporating rate of the water surfaces by numerical and experimental methods. Two-dimensional turbulent forced convection channel flow is theoretically analyzed. Parametric evaluation including the applied voltage, electrode location is executed in details. The related optimization of the electrode pitch and height for specified input voltage is investigated numerically along with a simplified conjugated-gradient method (SCGM). The results show the EHD effect on the evaporating rate is increased with increase of voltage and electrode pitch and decrease of electrode height. In addition, based on the per unit power consumption, the best mass transfer performance is obtained at the optimal electrode location for each input voltage case. At last, the numerical results get a good consistency with the experiment within a discrepancy of 27%.

Counter-gradient heat transport by large-scale circulation in two-dimensional turbulent convection

We investigate numerically the counter-gradient heat transport in two-dimensional turbulent Rayleigh-Bénard convection, which derives its existence from the descending hot plumes and ascending cold plumes with the large-scale circulation. Both qualitative and quantitative evidence is presented for the Rayleigh numbers from 104 to 1011 and the Prandtl number 1.0 in a domain of aspect ratio 2 with periodic boundary conditions in the horizontal direction. The counter-gradient heat transport increases with Rayleigh numbers, and becomes comparable to the gradient heat transport. The gradient heat transport has a power law dependence on the Rayleigh number with scaling exponent 1/3, while a phase transition of the counter-gradient heat transport can be identified around the critical Rayleigh number . The Reynolds numbers of the gradient and counter-gradient heat transports exhibit identical power law dependence on the Rayleigh numbers with scaling exponent 1/2. The gradient heat transport is partially compensated by the counter-gradient heat transport with increasing Rayleigh numbers, which attenuates the effects of the large-scale circulation on the global heat transfer especially for high Rayleigh numbers. We emphasize that the counter-gradient heat transport also exists in the three-dimensional turbulent Rayleigh-Bénard convection, although the plume and flow structures therein are quite different.

Characteristics of flow and thermal boundary layer in turbulent Rayleigh-Bénard convection

The parallel direct method of direct numerical simulation (PDM-DNS) for Rayleigh-Bénard (RB) convection is used in this paper. The differences and similarities in flow characteristic between two-dimensional (2D) and three-dimensional (3D) turbulent RB convection are studied using mean field for Ra=109, 1010, 5×1010, and Pr=4.3. Each of 2D and 3D cases has a large-scale circulation and corner rolls. The shape of large-scale circulation becomes round and the size of corner roll turns small as Ra increases. In 2D RB convection, there are four corner vortices at the corner of the square cavity and a stable large-scale circulation which is elliptical. For spanwise averaged 3D RB convection with two corner vortices, large-scale circulation reveals spindle shape. Due to the characteristic of the corner roll, the region plume dominating is wider in 2D RB convection than in the spanwise-averaged 3D case. Further, the Ra-dependence of thermal boundary layer properties is also studied. The thermal boundary layer thickness is scaled with Ra and the scaling exponents of λθ with Ra in the 2D and 3D cases are very similar.

Two-dimensional turbulent convection in a toroidal duct of a liquid metal blanket of a fusion reactor

Convection in a horizontal duct aligned with a uniform magnetic field is analysed computationally. The motivation of the study is the concept of a liquid metal blanket for a tokamak fusion reactor, in which ducts are oriented toroidally, i.e. parallel to the main component of the magnetic field. Computations of two-dimensional (streamwise-uniform) flows appearing at very strong magnetic fields and of three-dimensional flows in long domains are conducted. Non-uniform volumetric internal heating is applied, while the walls are maintained at a constant temperature. Two-dimensional or nearly two-dimensional turbulent convection is found at high Grashof and Hartmann numbers typical for fusion reactor conditions. The turbulence results in stronger mixing and more uniform distribution of wall heat flux, indicating promising potential of this concept of the blanket.

Mixed convective nanofluid flow in a channel having backward-facing step with a baffle

Two-dimensional laminar and turbulent mixed convection flows using nanofluids over backward facing step in a heated rectangular duct having a baffle mounted on its wall are numerically simulated. The continuity, momentum and energy equations are solved using Finite Volume Method (FVM) and the SIMPLE algorithm scheme is applied to examine the effects of the baffle on flow and heat transfer characteristics. The bottom wall of the duct is being heated with a constant heat flux, while other walls are being thermally insulated. In this study, several parameters such as different types of the nanoparticles (Al2O3, CuO, SiO2 and ZnO), different volume fractions in the range of 1% to 4%, and different nanoparticle diameters in the range of 25 to 80nm were used. The Reynolds number of laminar flow was in the range of 100≤Re≤400, while for turbulent flow it was in the range of 7500≤Re≤15,000. The effects of baffle distances in the range of ∞≤D≤4, baffle widths in the range of 0.01≤wb≤0.04, and baffle heights in the range of 0.005≤hb≤0.015 were studied. Baffle locations at the top wall and at bottom wall of the duct, and the number of baffles from 1 to 3 were also examined. The numerical results indicate that the nanofluid with SiO2 has the highest Nusselt number compared with other nanofluid types. The Nusselt number increases as the volume fraction of the nanoparticles and the Reynolds number increase, while it decreases as the nanoparticle diameter increases. The effects of baffle distance heights, and baffle locations on fluid flow and heat transfer characteristics are significant, while the effects of baffle widths and baffle numbers are slightly insignificant.

Polymer-induced change in scaling behavior in two-dimensional homogeneous turbulent thermal convection.

We study the effects of polymers in two-dimensional turbulent thermal convection using a shell model. In the absence of polymers, the inverse energy cascade in two dimensions leads to the observed Bolgiano-Obukhov scaling. When polymers are added, energy is extracted from the flow by the polymers, and as a result, the thermal balance between buoyancy and inertia in Bolgiano-Obukhov scaling is destroyed around the scales at which polymers interact strongly with the flow. This results in an increase in the Bolgiano scale and leads to a change in the scaling behavior of the velocity and temperature fluctuations for scales below the modified Bolgiano scale. We make theoretical estimates of the dependence of the mean rate of energy extracted by the polymers and the mean energy dissipation rate on the polymer relaxation time. Our theoretical analysis further leads to the prediction that the heat transport is not altered much by the polymers in two dimensions. We show that our theoretical estimates and prediction are in good agreement with the numerical results.

Flow reversals in turbulent convection via vortex reconnections.

We employ detailed numerical simulations to probe the mechanism of flow reversals in two-dimensional turbulent convection. We show that the reversals occur via a vortex reconnection of two attracting corner rolls having the same sign of vorticity, thus leading to major restructuring of the flow. Large fluctuations in heat transport are observed during the reversal due to the flow reconfiguration. The flow configurations during the reversals have been analyzed quantitatively using large-scale modes. Using these tools, we also show why flow reversals occur for a restricted range of Rayleigh and Prandtl numbers.

Nonlinear Cascades in Two-Dimensional Turbulent Magnetoconvection

The dynamics of spectral transport in two-dimensional turbulent convection of electrically conducting fluids is studied by means of direct numerical simulations in the frame of the magnetohydrodynamic Boussinesq approximation. The system performs quasioscillations between two different regimes of small-scale turbulence: one dominated by nonlinear magnetohydrodynamic interactions; the other governed by buoyancy forces. The self-excited change of turbulent states is reported here for the first time. The process is controlled by the ideal invariant cross helicity, H;{C}=integral_{S}dSv.b. The observations are explained by the interplay of convective driving with the nonlinear spectral transfer of total magnetohydrodynamic energy and cross helicity.

Turbulent Forced Convection in a Plane Asymmetric Diffuser: Effect of Diffuser Angle

A simulation of two-dimensional turbulent forced convection in a plane asymmetric diffuser with an expansion ratio of 4.7 is performed, and the effect of the diffuser angle on the flow and heat transfer is reported. This geometry is common in many heat exchanging devices, and the turbulent convective heat transfer in it has not been examined. The momentum transport in this geometry, however, has received significant attention already, and the studies show that the results from the υ2¯‐f type turbulence models provide better agreement with measured velocity distributions than that from the k‐ε or k‐ω turbulence models. In addition, the υ2¯‐f type turbulence models have been shown to provide good heat transfer results for separated and reattached flows. The k‐ε‐ζ (υ2¯‐f type) turbulence model is used in this study due to its improved numerical robustness, and the FLUENT-CFD code is used as the simulation platform. User defined functions for the k‐ε‐ζ turbulence model were developed and incorporated into the FLUENT-CFD code, and that process is validated by simulating the flow and the heat transfer in typical benchmark problems and comparing these results with available measurements. This new capability is used to study the effect of the diffuser angle on forced convection in an asymmetric diffuser, and the results show that the angle influences significantly both the flow and the thermal field. The increase in that angle increases the size of the recirculation flow region and enhances the rate of the heat transfer.