Large Eddy Simulations of Rayleigh-Bénard Convection in a Cubic Cavity

This paper conducts a Large Eddy Simulation (LES) of Rayleigh Bénard convection in a cubic cavity based on the WMLES S-Omega subgrid-scale model. For a cubic cavity with a vertical temperature difference of 6.7°C and 20°C, the velocity pulsation profiles and the mean velocity profiles of the vertical section in the middle of the cubic cavity were simulated, respectively. And they are consistent with the experiment results. Furthermore, the mean velocity field of the vertical cross-section in the middle of the cavity was calculated. Structures of the mean velocity field in the two cases are similar. A counterclockwise large vortex is found to occupy the cavity, and there are two small clockwise vortices in the lower left and upper right corners, and the mean velocity fields at two different temperature differences are consistent with the experimental results. The two-dimensional instantaneous temperature field and mean temperature field with different cross-sections in the z-direction, as well as the three-dimensional instantaneous isothermal surface structure, indicate that the large-scale circulation motion within the cubic cavity is moving diagonally. In addition, the structure of the mean streamline also illustrates this viewpoint. For the reverse vortex formed at two corners in the mean streamline structure, we used the Q criterion to identify and obtain two vortex structures similar to boomerangs. The basic turbulent structure in RB thermal convection includes the rising and falling plumes generated by buoyancy effects.

Simulation of the Rayleigh–Benard Convection in a T-Shaped Cavity

Rayleigh-Benard convection driven by the temperature difference between top and bottom surfaces of a T-shaped cavity with two different boundary conditions is studied numerically. Steady or unsteady cellular flow structures and temperature patterns are illustrated along with the evolution of heat transfer rates (Nusselt number, Nu). The cavity is filled with fluids of various Pr (Prandtl number), including 0.024, 0.71, 6, and 450. The effect of Pr and Ra (Rayleigh number) on the flow regime and heat transfer is established, while comparing the results also with those of the square cavity.

Laminar-Turbulent Bifurcation Scenario in 3D Rayleigh-Benard Convection Problem

We are considering two initial-boundary value problems for Rayleigh-Benard convection in Oberbeck-Boussinesq approximation for incompressible fluid in 3D-rectangular domain with 4:4:1 geometric ratio with periodicity in two directions and cubic domain with 1:1:1 ratio and zero velocity and temperature gradient boundary conditions. For this purpose, we use two numerical method: one is a Pseudo-Spectral-Galerkin method with trigonometric-Chebyshev polynomials and the other is finite element/volume method with WENO interpolation for advection term. Numerical methods are presented shortly and are benchmarked against known DNS data and against one another (for quasi-periodic domain problem). Then we perform stability analysis using analytical expression for main stationary solutions and eigenvalue numerical analysis by applying Implicitly Restarted Arnoldi (IRA) method. The IRA is used to perform linear stability analysis, find bifurcations of stationary points and analyze eigenvalues of monodromy matrices. Thus characteristic exponents of the system for time periodic solutions (limited cycles of various periods and resonance invariant tori) are computed. We show, numerically, the existence of multistable rotes to chaos through chaotic fractal attractors, full Feigenbaum-Sharkovski cascades and multidimensional torus attractors (Landau-Hopf scenario). The existence of these attractors is shown through analysis of phase subspaces projections, Poincare sections and eigenvalue analysis of numerically computed DNS data. These attractors burst into chaos with the increase of Rayleigh number either through resonance and phase-locking or through emergence of singular chaotic attractors.

Characterization of Rayleigh Convection in Interfacial Mass Transfer by Lattice Boltzmann Simulation and Experimental Verification

Concentration gradient induced Rayleigh convection can influence effectively interracial mass transfer processes, but the convection phenomena are known as mesoscopic and complex. In order to investigate this phenomenon, a two-equation Lattice Boltzmann Method （LBM） is proposed to simulate the velocity and the concentra-tion distributions of Rayleigh convection generated in the CO2 absorptlon into ethanol liquid.The simulated results on velocity distributions are experimentally verified by PIV （particle image velocimetry technique） measurements. In order to simplify the analysis, the convection in the simulation as well as in the experiment, the Rayleigh convection was manipulated into a single down flow pattern, The simulated results show that the concentration contours agree qualitatively with the schlieren images in the literature. The experimental and simulated results show that theRayleigh convection under investigation is dominated by the flow in the downward direction and impels exchange of the liquid between the interfacial vicinity and the liquid bulk promoting the renewal of interfacial liquid, and hence enhances mass transfer. The comparison between the simulated and experimental results demonstrated that the proposed LBM is a promising alternative for simulating mass transfer induced Rayleigh convection.

CO_(2)吸收过程中气相分压对Rayleigh对流传质特性的影响

界面浓度梯度导致的Rayleigh对流现象能够显著提高CO_(2)吸收过程的传质速率,然而目前该过程的传质强化机制尚未清晰。为探究Rayleigh对流传质过程的强化机制,本文以水吸收CO_(2)过程为研究对象,基于粒子图像测速技术(PIV)和激光诱导荧光技术(LIF)实现了不同气相CO_(2)分压条件下界面对流的可视化与定量测量。实验发现,界面平均浓度在对流发生的临界时刻会瞬间下降并在有序的自组织结构形成后上升,最终的界面平均浓度会随着气相CO_(2)分压减小而减小;对流发生后,系统传质能力的提高分为两个阶段,涡量场在有序的自组织结构形成前起主导作用,有序的自组织结构形成后,系统传质能力的提高则是由涡量场与界面浓度共同作用的结果;有序的自组织结构形成后,不同系统的平均瞬时传质系数与平均涡量具有很强的相关性,表明浓度场与速度场相互作用形成的涡量场在对流传质强化过程中发挥着重要作用。

Numerical study of heat-transfer in two-and quasi-two-dimensional Rayleigh–Bénard convection

A detailed comparative numerical study between the two-dimensional（2 D） and quasi-two-dimensional（quasi-2 D）turbulent Rayleigh–B＇enard（RB） convection on flow state, heat transfer, and thermal dissipation rate（TDR） is made. The Rayleigh number（Ra） in our simulations ranges up to 5×10^10 and Prandtl number（Pr） is fixed to be 0.7. Our simulations are conducted on the Tianhe-2 supercomputer. We use an in-house code with high parallelization efficiency, based on the extended PDM–DNS scheme. The comparison shows that after a certain Ra, plumes with round shape, which is called the ＂temperature islands＂, develop and gradually dominate the flow field in the 2 D case. On the other hand, in quasi-2 D cases, plumes remain mushroom-like. This difference in morphology becomes more significant as Ra increases, as with the motion of plumes near the top and bottom plates. The exponents of the power-law relation between the Nusselt number（Nu） and Ra are 0.3 for both two cases, and the fitting pre-factors are 0.099 and 0.133 for 2 D and quasi-2 D respectively,indicating a clear difference in magnitude of the heat transfer rate between two cases. To understand this difference in the magnitude of Nu, we compare the vertical profile of the horizontally averaged TDR for both two cases. It is found that the profiles of both cases are nearly the same in the bulk, but they vary near boundaries. Comparing the bifurcation height zb with the thermal boundary layer thickness dq, it shows that zb 〈 δθ（3 D） 〈 δθ（2 D） and all three heights obey a universal power-law relation z ~Ra^-0.30. In order to quantify the difference further, we separate the domain by zb, i.e., define the area between two zb（near top and bottom plates respectively） as the ＂mid region＂ and the rest as the ＂side region＂, and integrate TDR in corresponding regions. By comparing the integral it is found that most of the difference in TDR between two cases, which is connected to the heat transfer rate, occurs within the thermal boundary layers. We also compare the ratio of contributions to total heat transfer in BL–bulk separation and side–mid separation.

Space-time correlations in turbulent Rayleigh–Bnard convection

The recent development of the elliptic model （He, et al. Phy. Rev. E, 2006）, which predicts that the space-time correlation function Cu（r, r） in a turbulent flow has a scaling form Cu（rE, 0） with re being a combined space-time separa- tion involving spatial separation r and time delay T, has stimulated considerable experimental efforts aimed at testing the model in various turbulent flows. In this paper, we review some recent experimental investigations of the space-time correlation function in turbulent Rayleigh-Benard convection. The experiments conducted at different representative locations in the convection cell confirmed the predictions of the elliptic model for the velocity field and passive scalar field, such as local temperature and shadowgraph images. The understanding of the functional form of Cu（r, v） has a wide variety of applications in the analysis of experimental and numerical data and in the study of the statistical properties of small-scale turbulence. A few examples are discussed in the review.

PIV Measurement for Rayleigh Convection and Its Effect on Mass Transfer

The velocity distribution in Rayleigh convection caused by acetone volatilization in acetone-ethyl acetate binary system was observed in a vertical cross section of an initially quiescent liquid layer by utilizing particle image velocimetry. Obvious turbulent vortexes that were induced by Rayleigh convection appeared in the bulk liquid,and its statistic features indicated that Rayleigh convection became more intense with the increase of Ra number and ReGnumber. Mass transfer coefficient was measured and the computed enhancement factor indicated that Rayleigh convection could promote the surface renewal of the liquid phase and intensify the interfacial mass transfer significantly. A method was proposed for the prediction of mass transfer coefficient based on the measured velocity vector, and the predicted mass transfer coefficients are in reasonable agreement with the experimental results.

Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh-Bénard Electro Convection in a Micropolar Fluid

The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Bénard convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations and for isothermal and/or adiabatic temperature boundaries. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters and electric Rayleigh number on the onset of convection has been analyzed. One linear and five non-uniform temperature profiles are considered and their comparative influence on onset is discussed.

Investigation of mass transfer model of CO_(2) absorption with Rayleigh convection using multi-relaxation time lattice Boltzmann method

CO_(2) absorption into absorbents is a widely used method to reduce carbon emissions,in which the concentration gradient near the gas-liquid interface may induce Rayleigh convection(RC).Once RC occurs,the mass transfer rate will be significantly enhanced.Therefore,it is necessary to explore the mass transfer enhancement mechanism further and develop a penetration/surface divergence hybrid mass transfer model.In this study,we conduct research on the process of CO_(2) absorption into ethanol with RC.Firstly,we use a multi-relaxation time lattice Boltzmann method to simulate the absorption process and obtain the flow and concentration fields.And we also verify the reliability of the numerical simulation results by comparing with the experimental results.Then,we analyze the characteristics of non-uniform flow and concentration fields in RC.Moreover,we divide the near-interface region into diffusion-dominated and convection-dominated mass transfer zones by checking whether the horizontal average velocity is greater than 1.0×10^(-4) m·s^(-1).Furthermore,based on the differences in mass transfer mechanisms of the aforementioned two zones,we propose a penetration/surface divergence hybrid model to predict the instantaneous mass transfer coefficient.The prediction results demonstrate that the hybrid model can precisely predict the instantaneous mass transfer coefficient of the entire CO_(2) absorption process.Our proposed hybrid model provides a promising way to deal with the complex mass transfer problems with non-uniform flow and concentration fields.

Enhancement of Photocatalytic Water Splitting Rate via Rayleigh Convection

In order to enhance photocatalytic water splitting rates with Pt/TiO2 powder, sufficient agitation of the biphasic medium is required to switch surficial reactions to volumetric reactions. Additionally, agitation is conducive to higher diffusion rates of the generated hydrogen and co-produced oxygen, hindering their ability to re-couple to water on Pt loaded to TiO2 powder. In order to create agitation without consuming any electricity, a novel technique utilizing Rayleigh convection was applied, and its ability to enhance photocatalytic water splitting rates was evaluated. Higher Rayleigh convective flow rates resulted in higher photocatalytic water splitting rates. Utilization of Rayleigh convection approximately doubled the photocatalytic water splitting rates, despite relatively low convective flow velocities (obtained through simple thermo-hydrodynamic simulations). The rate enhancement achieved through Rayleigh convection is a result of its ability to disperse the ultrafine Pt/TiO2 particles throughout the whole medium, leading to volumetric reactions.

The limit of the Boussinesq system of Rayleigh-Bénard convection as the Prandtl number approaches infinity

Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.

POD Analysis and Low-Dimensional Model Based on POD-Galerkin for Two-Dimensional Rayleigh-Bénard Convection

Direct numerical simulation based on OpenFOAM is carried out for two-dimensional RayleighBénard( RB) convection in a square domain at high Rayleigh number of 107 and Pr = 0.71. Proper orthogonal decomposition( POD) is used to analyze the flow and temperature characteristics from POD energy spectrum and eigenmodes. The results show that the energy spectrum converges fast and the scale of vortex structures captured by eigenmodes becomes smaller as the eigenmode order increases. Meanwhile,a low-dimensional model( LDM) for RB convection is derived based on POD eigenmodes used as a basis of Galerkin project of Navier-Stokes-Boussinesq equations. LDM is built based on different number of eigenmodes and through the analysis of phase portraits,streamline and isothermal predicted by LDM,it is suggested that the error between LDM and DNS is still large.

EXTENDED SELF SIM ILARITY OF PASSIVE SCALAR IN RAYLEIGH-BNARD CONVECTION FLOW BASED ON WAVELET TRANSFORM

Wavelet transform is used to analyze the scaling rule of temperature data (passive scalar) in Rayleigh Bénard convection flow from two aspects. By utilizing the method of extended self similarity (ESS), one can find the obtained scaling exponent agrees well with the one obtained from the temperature data in a experiment of wind tunnel. And then we propose a newly defined formula based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data. The obtained results demonstrate that we can correctly extract ξ(q) by using the method which is named as wavelet transform maximum modulus (WTMM).

EXTENDED SELF SIMILARITY OF PASSIVE SCALAR IN RAYLEIGH-BNARD CONVECTION FLOW BASED ON WAVELET TRANSFORM

Wavetet transform was used to analyze the scaling law of temperature data (passive scalar) in Rayleigh-Bénard convection flow from two aspects. The first one was to utilize the method of extended self similarity, presented first by Benzi et al., to study the scaling exponent of temperature data. The obtained results show that the inertial range is much wider than that one determined directly from the conventional structure function, and find the obtained scaling exponent agrees well with the one obtained from the temperature data in an experiment of wind tunnel. The second one was that, by extending the formula which was proposed by A. Arneodo et al. for extracting the scaling exponent ζ(q) of velocity data to temperature data, a newly defined formula which is also based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data was proposed. The obtained results demonstrate that by using the method which is named as WTMM (wavelet transform maximum modulus) ξ(q) correctly can be extracted.

Study of Rayleigh-Bénard Magneto Convection in a Micropolar Fluid with Maxwell-Cattaneo Law

The effects of result from the substitution of the classical Fourier law by the non-classical Maxwell-Cattaneo law on the Rayleigh-Bénard Magneto-convection in an electrically conducting micropolar fluid is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal or adiabatic temperature on the spin-vanishing boundaries. The influences of various micropolar fluid parameters are analyzed on the onset of convection. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigenvalues are less than the classical ones.

Experimental and Numerical Investigation of a Rayleigh-Bénard Convection Affected by Coriolis Force

In this paper the influence of an impressed Coriolis force field on the configuration of a turbulent Rayleigh-Bénard convection problem is investigated in an experimental and numerical study. The main purpose of both studies lie on the analysis of a possible stabilising effect of a Coriolis acceleration on the turbulent unsteady structures inside the fluid. The relative Coriolis acceleration which is caused in the atmosphere by the earth rotation is realised in the experimental study by a uniform-rotational movement of the setup in a large-scale centrifuge under hyper-gravity. The same conditions as in the atmosphere in the beginning of a twister or hurricane should be realised in the experiment. The investigated Rayleigh numbers lie between 2.33 × 106 ≤ Ra ≤ 4.32 × 107.

轴向通流旋转盘腔内类Rayleigh-Benard对流稳定性研究

利用数值模拟的方法对冷气轴向通流旋转盘腔的流动过程进行了研究。研究发现 ,对应一进口冷气的雷诺数 ,存在一临界瑞利数 ( Rac) ,高于该瑞利数 ( Ra) ,流动出现不稳定现象 ,且 Ra越大 ,不稳定行为越严重。对于特例 ,盘腔内的流动可以看成是由类 Rayleigh-Benard对流和强迫对流两个区域构成 ,两个区域通过能量和质量交换相互影响 ,流动随着 Ra的增加从稳态发展为非稳态 ;采用频谱图分析的方法对数值解的不稳定性进行定性分析 ,结果显示随着 Ra的增大 ,数值解经历了从稳定解到分贫的周期性不稳定和准周期不稳定的发展过程。离心浮升力引起的类 Rayleigh-Benard对流是造成流动从稳定到不稳定发展的重要原因 。

矩形腔体中Rayleigh-Benard对流结构的分析

通过对二维流体力学基本方程的数值摸拟,讨论了在二维矩形腔体中,不同条件与Rayleigh-Benard(RB)对流耦合作用的结构图案和特性。在分析了RB对流结构的基础上,分别对比分析了水平流及脉冲流与RB对流耦合作用的结构,并得出了其规律。RB对流系统为定常流动,对流轨道具有空间周期性。当RB对流与水平来流耦合作用时,系统为非定常流动,对流结构既表现空间周期性,同时也表现时间周期性。当外加来流的大小呈周期性变化时,此时系统流动的形式与外加来流的周期密切相关。

双流体Rayleigh-Benard对流中的局部行波

Rayleigh-Benard对流是研究非平衡对流的斑图(Pattern)及非线性动力学特性的典型模型之一。据此,通过流体力学基本方程组的数值模拟,探讨了分离比ψ=-0.4时双流体局部行波的形成过程;讨论了双流体局部行波流速场、温度场、浓度场、平均浓度流的结构和特性,分析了局部行波被局部化的原因。研究结果表明:局部行波始终在背离端壁方向传播并被限定在此端,它存在于腔体左端还是右端取决于经过过渡后对传波中最终控制腔体的一支行波的传播方向;在局部行波的存在范围内(1.519≤r≤1.604),随相对瑞利数增加,衡量对流振幅的最大垂直流速、特征通过流体层的垂直热流量的努塞尔数、局部行波宽度等都在增加,但反映浓度特性的混合参数减小。