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40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。     

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.     

二维Rayleigh-Bénard对流问题稳定性的数值追踪

用分解算子法和延续算法对二维Ｒａｙｌｅｉｇｈ－Ｂｅｎａｒｄ对流问题的稳定性进行了数值追踪研究．画出了 Ｐｒ＝ １０时不同 Ｒａ所对应的流线，等涡线和等温线图；并求出了对于不同Ｐｒ数所对应的临界Ｒａ数，其值大约为２７４０，计算结果与物理分析相一致，与三维实验结果比较也合理．     

压力梯度对湍流逆梯度输运的影响

研究Birkhoff系统的一般Lie对称性导致的非Noether守恒量. 得到非Noether守恒 量的存在定理，举例说明结果的应用.     

腔体高度对Rayleigh-Bénard对流的影响的二维数值分析

腔体高度的改变会对Rayleigh-Bénard对流产生影响.本文利用二维流体力学基本方程组进行数值模拟,在相对瑞利数r(28)5,腔体高度0 0 0 0 0d(28)1d,1.4d,1.8d,2d,3d(cm10d(28))时,研究了对流运动的动力学特性,发现随着腔体高度d的增加,稳定对流的对流圈数与之呈线性反比例关系,而对流波数k随之基本保持恒定;对流稳定后,对流振幅和努塞尔数随腔体高度d增大而减小,且得出对流振幅和努塞尔数随着相对腔体高度0/dd变化的函数关系式.在腔体高度0 0 0d(28)1d,1.4d,1.8d情况下,对流振幅和努塞尔数都随相对瑞利数r的增大而增大;且腔体高度d越大,其增长率反而越小.     

基于LBM的壁湍流跨尺度能量传递结构统计

壁湍流不同尺度间能量传输特性存在着明显的各向异性,了解能量不同尺度间传递的空间分布是进一步构造高保真各向异性大涡模拟亚格子模式的前提.基于格子Boltzmann数值(lattice Boltzmann method,LBM)模拟方法对雷诺数Reτ=180的槽道湍流进行直接数值模拟.结果与公开的槽道湍流数据库进行对比,平...     

Conditions of Rayleigh-Bénard convection onset and heat transfer in a near-critical medium

Thermal gravity convection in a horizontal layer of compressible perfect gas heated from below and a van der Waals gas near the critical state is investigated. The characteristics of the isentropic equilibrium of a compressible medium with a van der Waals equation of state are considered. The known conditions of convection onset in the perfect and van der Waals gases are checked on the basis of a solution of the complete and linearized equations. The restrictions imposed in deriving the known formulas for the adiabatic temperature gradients used in the conditions of absence and onset of convection are discussed. The characteristics of the convective heat transfer are examined, including the causes of the heat-transfer deterioration in the near-critical medium above the hydrostatic equilibrium threshold.     

The Prandtl number effect near the onset of Bénard convection in a porous medium

This note focuses on Kladias and Prasad's claim that the critical Rayleigh number for the onset of Bénard convection in an infinite horizontal porous layer increases as the Prandtl number decreases, and argues that the critical Rayleigh number (Ra_c) depends only on the Darcy number (Da), as linear stability analysis indicates. The two-dimensional steady-convection problem is then solved numerically to document the convection heat transfer effect of the Rayleigh number, Darcy number, Prandtl number, and porosity. The note concludes with an empirical correlation for the overall Nusselt number, which shows the effect of Prandtl number at above-critical Rayleigh numbers. The correlation is consistent with the corresponding correlation known for Bénard convection in a pure fluid.     

Active control and a simple estimation method for the onset of Rayleigh-Bénard convection in temperature-dependent-viscosity liquids

Active feedback control for the onset of Rayleigh-Bénard Convection in temperature-dependent-viscosity liquids is investigated. In this paper, three major problems are addressed: (1) The results of Tang-Bau control are improved by considering the effects of temperature-dependent viscosity; (2) A more efficient two-plate control strategy is presented. A phenomenon of coalescence of the unstable modes is observed as the controller gain is large enough; (3) A simple way to estimate the critical Rayleigh number under the effects of temperature-dependent viscosity is described. Numerical results show that the effects of temperature-dependent viscosity on the critical Rayleigh number should be taken into account in some cases and the onset of Rayleigh-Bénard convection can be effectively delayed or advanced by the active feedback control strategies studied here.     

Relations Between Energy and Enstrophy on the Global Attractor of the 2-D Navier-Stokes Equations

We examine how the global attractor of the 2-D periodic Navier–Stokes equations projects in the normalized, dimensionless energy–enstrophy plane (e, E). We treat time independent forces, with the view of understanding how the attractor depends on the nature of the force. First we show that for any force, is bounded by the parabola E = e^1/2 and the line E=e. We then show that for to have points near enough to the parabola, the force must be close to an eigenvector of the Stokes operator A; it can intersect the parabola only when the force is precisely such an eigenvector, and does so at a steady state parallel to this force. We construct a thin region along the parabola, pinched at such steady states, that the attractor can never enter. We show that 0 cannot be on the attractor unless the force is in H^m for all m. Different lower bound estimates on the energy and enstrophy on are derived for both smooth and nonsmooth forces, as are bounds on invariant sets away from 0 and near the line E = e. Motivation for the particular attention to the regions near the parabola and near 0 comes from turbulence theory, as explained in the introduction. Mathematics Subject Classification (2000): 35Q30, 76F02.     

A comparative study on low‐order,amplitude‐equation and perturbation approaches in thermal convection

A comparison among three weakly nonlinear approaches for thermo‐gravitational instability in a Newtonian fluid layer heated from below is presented. First, the dynamical systems describing the time evolution of the problem from different weakly nonlinear approaches, namely, the Lorenz model, the amplitude equations and the perturbation expansion approaches are obtained. Next, the steady states and their stability, as well as the transient behaviour are obtained from each dynamical system. The similarity and difference among the three models are emphasized. The role of each of the nondimensional groups, the Rayleigh number and the Prandtl number is compared for the three models. The different approaches lead to similar behaviours when the Rayleigh number is just above its critical value and Prandtl number is high. However, only the dynamical system obtained from the amplitude equations is able to reflect the role of the Prandtl number. On the other hand, the amplitude equations and perturbation expansion techniques are not suitable for predicting the uniform oscillatory behaviour observed frequently in Rayleigh–Bénard convection. The novelty of the current work lies in studying the critical differences in the findings of the three popular approaches to investigate weakly nonlinear thermal convection for the first time. Copyright © 2011 John Wiley & Sons, Ltd.     

二元翼型风洞的侧壁干扰与抽气研究

在二元翼型风洞实验段中的侧壁边界层将引起模型展向流动的不均匀性，使预想的二元流动受到三元扭曲，引起实验数据的误差，目前消除或减少侧壁干扰的有效方法之一是采用侧壁抽吸技术。本文就抽吸的有效性，抽吸区域和阻尼材料等问题进行了讨论和分析，并对抽吸技术中的问题提出了一些看法。     

Role of the inclination of an inverted‐V upper plate on the heat and flow behavior of trapped gases in a modified Rayleigh–Bénard cavity

Thermal buoyant air inside a modified Rayleigh–Bénard (RB) cavity bounded by a lower flat plate and an inverted‐V upper plate has been investigated numerically using the finite‐volume method. The second‐order‐accurate QUICK and SIMPLE schemes were used for the discretization of the convective terms and the pressure–velocity coupling in the set of conservation equations, respectively. The problem under study is controlled by two parameters: (1) the Rayleigh number ranging from 10³ to 10⁶ and (2) the relative height of the vertical sidewalls d. In reference to the latter, it varies from one limiting case corresponding to the standard RB cavity (a rectangle with d = 1) to another limiting case represented by an isosceles triangular cavity where d = 0. The numerical results for the velocity and temperature fields are presented in terms of streamlines, isotherms, local and mean heat fluxes. An additional effort was devoted to determine the critical Ra values characterizing the transition from symmetrical to asymmetrical buoyant airflow responsive to incremental changes in Ra. For purposes of engineering design, a general correlation equation for the Nusselt number in terms of the pertinent Ra and d was constructed using nonlinear multiple regression theory. Copyright © 2007 John Wiley & Sons, Ltd.     

Notes on Convection in a Porous Medium: (i) an Effctive Rayleigh Number for an Anisotropic Layer, (ii) the Malkus Hypothesis and Wavenumber Selection

Studies of convection in a layer of a saturated anisotropic porous medium uniformly heated from below are reviewed. Emphasis is placed on the usefulness of an effective Rayleigh number, defined (for certain boundary conditions) as the square harmonic-mean square root of horizontally-based and vertically-based Rayleigh numbers. The status of the Malkus hypothesis, together with its relationship with observed cell size, is also discussed. A possible explanation is provided for the observed phenomenon that in a porous medium the cell size decreases as the amplitude of convection increases, whereas in a clear fluid the cell size increases.     

Analysis and Modeling of the Turbulent Diffusion of Turbulent Kinetic Energy in Natural Convection

Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation, are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Bénard convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion. The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Bénard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable and unstable stratification and that it allows for the required counter gradient energy flux.     

Effects of Viscous Dissipation and Flow Work on Forced Convection in a Channel Filled by a Saturated Porous Medium

Fully developed forced convection in a parallel plate channel filled by a saturated porous medium, with walls held either at uniform temperature or at uniform heat flux, with the effects of viscous dissipation and flow work included, is treated analytically. The Brinkman model is employed. The analysis leads to expressions for the Nusselt number, as a function of the Darcy number and Brinkman number.