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.

A model for universal spatial variations of temperature fluctuations inturbulent Rayleigh-Bénard convection

We propose a theoretical model for spatial variations of the temperature varianceσ2(z,r)(z is the dis-tance from the sample bottom and r the radial coordinate)in turbulent Rayleigh-Bénard convection(RBC).Adapting the“attached-eddy”modelofshearflowtothe plumesofRBC,wederivedanequationforσ2 which is based on the universal scaling of the normalized RBC temperature spectra.This equation in-cludes both logarithmic and power-law dependences on z/λth,whereλth is the thermal boundary layer thickness.The equation parameters depend on r and the Prandtl number Pr,but have only an extremelyweak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for thetemperature variance profile in turbulent RBC.

Hybrid LES/URANS Simulation of Rayleigh-Bénard Convection Using BEM

In this paper,we develop and test a unified hybrid LES/URANS turbulence model with two different Large Eddy Simulation(LES)turbulence models.The numerical algorithm is based on the Boundary Element Method.In the existing hybrid LES/URANS turbulence model we implemented a new Smagorinsky LES turbulence model.The hybrid LES/URANS turbulence model is unified,which means that the LES/URANS interface is changed dynamically during simulation using a physical quantity.In order to define the interface between LES and unsteady Reynolds Averaged Navier Stokes(URANS)zones during the simulation,we use the Reynolds number based on turbulent kinetic energy as a switching criterion.This means that the flow characteristics define where the sub-grid scale or URANS effective viscosity and thermal conductivity are used in the governing equations in the next time step.In unified hybrid turbulence models,only one set of governing equations is used for LES and URANS regions.The developed hybrid LES/URANS model was tested on non-isothermal,unsteady and turbulent Rayleigh-Bénard Convection and compared with an existing model,where LES is based on turbulent kinetic energy.The hybrid turbulence model was implemented within a numerical algorithm based on the Boundary-Domain Integral Method,where a single domain and sub-domain approaches were used.The numerical algorithm uses governing equations written in a velocity-vorticity form.The false transient time scheme is used for the kinematics equation.

Heat transport in horizontally periodic and confined Rayleigh-Bénard convection with no-slip and free-slip plates

We report the results of the direct numerical simulations of two-dimensional Rayleigh-Bénard convection(RBC)in order to study the influence of the periodic(PD)and confined(CF)samples on the heat transport Nu.The numerical study is conducted with the Rayleigh number(Ra)varied in the range 10^(6)≤Ra≤10^(9) at a fixed Prandtl number Pr=4.3 and aspect ratio Γ=2 with the no-slip(NS)and freeslip(FS)plates.There exists a zonal flow for Ra≥3×10^(6) with the free-slip plates in the periodic sample.In all the other cases,the flow is the closed large-scale circulation(closed LSC).The striking features are that the heat transport Nu is influenced and the temperature profiles do not be influenced when the flow pattern is zonal flow.

Boundary layer structure in turbulent rayleigh-bénard convection in a slim box

Logarithmic boundary layers have been observed in different regions in turbulence. However, how thermal plumes correlate to the log law of temperature and how the velocity profile changes with pressure gradient are not fully understood. Here, we perform three-dimensional simulations of turbulence in a slim-box without the front and back walls with aspect ratio, width:depth:height=L:D:H=1:1/6:1width:depth:height=L:D:H=1:1/6:1 (respectively corresponding to xx, yy and zz coordinates), in the Rayleigh number Ra=[1×10^8,1×10^10]Ra=[1×10^8,1×10^10] for Prandtl number Pr=0.7Pr=0.7. To investigate the structures of the viscous and thermal boundary layers, we examine the velocity profiles in the streamwise and vertical directions (i.e. UU and WW) along with the mean temperature profile throughout the plume-impacting, plume-ejecting, and wind-shearing regions. The velocity profile is successfully quantified by a two-layer function of a stress length, e^+u=e^+0(z^+)3/2[1+(z^+/z^+sub)4]^1/4eu+=e^+0(z+)3/2[1+(z+/zsub+)4]1/4, as proposed by She et al.(J Fluid Mech, 2017), though it is neither \pb type nor logarithmic. In contrast, the temperature profile in the plume-ejecting region is logarithmic for all simulated cases, being attributed to the emission of thermal plumes. The coefficient of the temperature log-law, AA, can be described by composition of the thermal stress length ■■θ0■θ0■ and the thicknesses of thermal boundary layer z■subzsub■ and z?bufzbuf■, i.e. A■z?sub/(■■θ0z■buf3/2)A■zsub?/(■θ0■zbuf^3/2). The adverse pressure gradient responsible for turning the wind direction contributes to intensively emitting plumes and the logarithmic temperature profile at the plume-ejecting region. The Nusselt number scaling and the local heat flux in the slim box are consistent with previous results of the confined cells. Therefore, the slim-box RBC is a preferable system for investigating in-box kinetic and thermal structures of turbulent convection with the large-scale circulation in a fixed plane.

Scaling of maximum probability density function of velocity increments in turbulent Rayleigh-Bénard convection

In this paper, we apply a scaling analysis of the maximum of the probability density function（pdf） of velocity increments, i.e., max（） = max（）up p u, for a velocity field of turbulent Rayleigh-Bénard convection obtained at the Taylor-microscale Reynolds number Re60. The scaling exponent is comparable with that of the first-order velocity structure function, （1）, in which the large-scale effect might be constrained, showing the background fluctuations of the velocity field. It is found that the integral time T（x/ D） scales as T（x/ D）（x/ D）, with a scaling exponent =0.25 0.01, suggesting the large-scale inhomogeneity of the flow. Moreover, the pdf scaling exponent （x, z） is strongly inhomogeneous in the x（horizontal） direction. The vertical-direction-averaged pdf scaling exponent （x） obeys a logarithm law with respect to x, the distance from the cell sidewall, with a scaling exponent 0.22 within the velocity boundary layer and 0.28 near the cell sidewall. In the cell＇s central region, （x, z） fluctuates around 0.37, which agrees well with （1） obtained in high-Reynolds-number turbulent flows, implying the same intermittent correction. Moreover, the length of the inertial range represented in decade（）IT x is found to be linearly increasing with the wall distance x with an exponent 0.65 0.05.

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.

Lagrangian coherent structures and their heat-transport mechanism in the turbulent Rayleigh-Bénard convection

In this paper,we investigate the Lagrangian coherent structures(LCSs)and their heat-transport mechanism in turbulent Rayleigh-Bénard(RB)convection.Direct numerical simulations(DNS)are performed in a closed square cell with Rayleigh numbers(Ra)ranging from 10^(6) to 10^(9) and Prandtl(Pr)number fixed at Pr=0.7.First,our results show the power-law relationship between Nusselt number(Nu)and Ra,Nu=0.99Ra^(0.30±0.02),confirming the results from previous studies.To gain insights into the material transport,LCSs are extracted using the finite-time Lyapunov exponent(FTLE)method.Interestingly,lobe structures are widely present,and we elucidate their role in transporting heat from the corner rolls to large-scale circulation.Next,the relationships between LCSs and thermal plumes are examined,and we identify two behaviors of thermal plumes:first,most plumes transport along the LCSs;second,few plumes are exposed to the bulk and subsequently mix with the turbulent background.Furthermore,we quantify the heat flux along the LCSs,which contributes to about 85%of the total flux regardless of Ra.This suggests that LCSs play a significant role in heat transport.Finally,the viscous(thermal)dissipation rate along the LCSs is quantified,which is larger than 80%(60%)of the total value,suggesting that LCSs are responsible for the large viscous and thermal dissipations.

Pattern formation in Rayleigh-Bénard convection: Numerical simulation with a coupled-map-lattice model

The various patterns formed in Rayleigh-Bé- nard convection under different conditions are numerically simulated with a coupled-map-lattice model. In the case of a lower aspect ratio (L/d=5), the simulations vividly depicted the main features of the transition process from a laminar state to a soft turbulence and then to a hard turbulence. In this case, the cellular structure in a horizontal section is also reproduced. In the case of a larger aspect ratio (L/d=30), the simulations successfully reproduced the spiral-defect chaos and target chaos in the initial stage of the pattern evolution which were recently found in experiments. In this case, for a fluid of Pr=1, it is verified in simulations that both the ideal straight rolls and spiral-defect chaos are stable attractors in the same parameter regime, and that the initial condition is a decisive factor for which one of the two is formed. In the same case, for a fluid of Pr=4, the target patterns are dominant instead of the spirals, the sizes and distributions of the target are also notably dependent on the initial condition.

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).

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.

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.

The Perturbed Problem on the Boussinesq System of Rayleigh-Bénard Convection

In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞（0,t;H2（G）） is rigorously justified by analysis of asymptotic expansions.

二氧化碳超临界相变过程中Rayleigh-Bénard对流的实验研究

超临界流体是一种极端条件下(温度与压力均处于临界点以上)的非常态流体。浮力驱动的超临界流体Rayleigh-Bénard(RB)对流则是一种新的非线性热对流体系,其浮力作用不符合Boussinesq近似,且在温差的作用下物性在临界点附近出现剧烈畸变并伴随着丰富的流动与相变耦合过程。本实验设计了可承载超临界二氧化碳(SCO_(2))的透明蓝宝石压力容器,建立竖直温度梯度作用下的超临界流体RB对流,观测不同温差作用下的流动结构和超临界相变过程并通过图像互相关算法计算“雾化”液滴的速度场。实验采用铂电阻测温,并精确控制容器上下端的温差,研究SCO_(2)在线性降温过程中多种流态与速度场的演化。在线性降温过程中,SCO_(2)经历超临界流动、跨临界流动和气液两相流动3个典型过程。跨临界流动是相变与浮力热对流的强耦合过程,导致超临界二氧化碳RB对流具有多态的非稳态流动。实验结果表明:超临界RB对流对温差极为敏感,温差越大则超临界域内的对流越剧烈;随着温度的降低,雾化的液滴不断凝聚,形成丰富的多层流动结构,并最终向气液两相流动演化。

Rayleigh-Bénard湍流热对流研究的进展、现状及展望

对流现象广泛存在于恒星和行星里.在地球上,对流现象在诸如大气、海洋、地核和地幔等众多动力学系统中起着重要作用.Rayleigh-Bénard(RB)湍流热对流系统是从这些复杂的自然现象中抽象出来的研究对流问题的经典流体力学模型.本文主要从湍流传热、羽流、大尺度流动结构、速度和温度脉动的小尺度统计和非传统RB对流等几个方面着重评述近年来RB对流的若干研究新进展,并对今后的研究做出展望.

纳米流体Rayleigh-Bénard细胞流的格子-Boltzmann模拟

采用热格子-Boltzmann方法,对两平行平板间纳米流体的Rayleigh-Bénard细胞流现象及其影响因素进行数值模拟研究,模型计算结果与方腔内纳米流体的自然对流实验结果吻合较好。讨论了纳米颗粒种类(Al2O3、Cu和SiO2)、体积分数(1%～4%)等因素对细胞流流动和传热的影响。研究发现平板间纳米流体的Rayleigh-Bénard细胞流的流动和传热行为明显异于纯流体,同时发现纳米流体的热导率、黏度和颗粒的热运动共同决定细胞流的流场和温度场分布的规律:热导率越大、布朗运动的越强,会减小流体温度的非均匀性,削弱对流作用,使其细胞流对涡个数减小;黏度增大也会抑制细胞流的发展。

具有水平流动的Rayleigh-Bénard对流进口段特性分析

采用SIMPLE算法对二维流体力学基本方程组进行了数值模拟,对普朗特数Pr=0.0272的具有水平流动的Rayleigh-Bénard对流进口段特性进行了研究。结果表明,在某些流体参数下具有水平流动的Rayleigh-Bénard对流由进口段和行波对流段组成,进口段长度取决于雷诺数和相对瑞利数。对于雷诺数Re=150的情况,当相对瑞利数r≤4时腔体内是水平流动;当r≥12时腔体内是行波对流;在4<r<12范围内,存在进口段,并提出了进口段长度X0随着相对瑞利数变化的表达式。对于相对瑞利数r=3的情况,当雷诺数Re≤37.5时腔体中是行波对流;当雷诺数Re≥110时腔体中是水平流动;在37.5≤Re≤110范围内,存在进口段,并获得了进口段长度X0随着雷诺数变化的表达式。进口段长度随相对瑞利数的增大而减小,随着雷诺数的增大而增大。行波对流区的对流波数随着雷诺数的增大而减小。

含相变颗粒流体的Rayleigh-Bénard对流热启动

The onset of Rayleigh-Bnard convection in a fluid layer dispersed with phase-change-material particles was studied numerically by using the linear stability theory.The dimensionless fluctuation of specific heat Q with dimensionless temperature T was given as a form of sine-function Q =1+ b sin( ψT ).Two kinds of numerical methods were used separately in the calculation of critical Rayleigh number Ra _ cr and wave number k _ cr .One was the numerical integration method using Simpson 1/3 rule,and the other was the numerical difference method of Runge-Kutta with Newton-Raphson iteration. Both methods showed the same calculation results that the critical Rayleigh number Ra _ cr decreased monotonically with increase in the amplitude b of the sine-function,however,the critical wave number k _ cr did not show much difference with the amplitude b of the sine-function while ψ =π/2,but exponentially increased while ψ =π.

Rayleigh-Bénard对流中的熵产特征

通过建立Rayleigh-Bénard对流模型,数值模拟得到具有不同涡数的Bénard花胞的稳定流场,并以不同Ra下的2涡Bénard稳定流动为对象来研究系统的熵产特征。研究发现:在可以形成稳定Bénard流动的Ra范围内,采用线性理论和经典热力学理论分别计算出的系统熵产基本上一致;并且,在稳定的Bénard流场中,系统的熵产随着Ra的增加而增加。

双流体混合Rayleigh-Bénard对流

Rayleigh-Benard(RB)对流是研究非平衡对流的稳定性、非线性动力学特性及湍流形成机理的典型模型之一.本文论述了有无通过流动的双流体混合RB对流的研究价值、历史和现状,介绍了该问题的主要研究方法,提出了有待进一步研究和探讨的问题.