Mixing in a stably stratified medium by horizontal shear near vertical walls

Stratified environmental flows near boundaries can have a horizontal mean shear component, orthogonal to the vertical mean density gradient. Vertical transport, against the stabilizing force of gravity, is possible in such situations if three-dimensional turbulence is sustained by the mean shear. A model problem, water with a constant mean density gradient flowing in a channel between parallel vertical walls, is examined here using the technique of large eddy simulation (LES). It is found that, although the mean shear is horizontal, the fluctuating velocity field has significant vertical shear and horizontal vorticity, thereby causing small-scale vertical mixing of the density field. The vertical stirring is especially effective near the boundaries where the mean shear is large and, consequently, the gradient Richardson number is small. The mean stratification is systematically increased between cases in our study and, as expected, the buoyancy flux correspondingly decreases. Even so, horizontal mean shear is found to be more effective than the well-studied case of mean vertical shear in inducing vertical buoyancy transport as indicated by generally larger values of vertical eddy diffusivity and mixing efficiency.     

Layered structure of turbulent plane wall jet

This paper investigates the layered structure of a turbulent plane wall jet at a distance from the nozzle exit. Based on the force balances in the mean momentum equation, the turbulent plane wall jet is divided into three regions: a boundary layer-like region (BLR) adjacent to the wall, a half free jet-like region (HJR) away from the wall, and a plug flow-like region (PFR) in between. In the PFR, the mean streamwise velocity is essentially the maximum velocity, and the simplified mean continuity and mean momentum equations result in a linear variation of the mean wall-normal velocity and Reynolds shear stress. In the HJR, as in a turbulent free jet, a proper scale for the mean wall-normal flow is the mean wall-normal velocity far from the wall and a proper scale for the Reynolds shear stress is the product of the maximum mean streamwise velocity and the velocity scale for the mean wall-normal flow. The BLR region can be divided into four sub-layers, similar to those in a canonical pressure-driven turbulent channel flow or shear-driven turbulent boundary layer flow. Building on the log-law for the mean streamwise velocity in the BLR, a new skin friction law is proposed for a turbulent wall jet. The new prediction agrees well with the correlation of Bradshaw and Gee (1960) over moderate Reynolds numbers, but gives larger skin frictions at higher Reynolds numbers.     

随机结构分析中的均值参数反应与反应均值

在结构分析中考虑力学参数的随机性时，均值参数系统反应往往不能反映结构反应均值。本文通过静力与动力典型例证的分析说明，对于具有随机参数的结构，在静力情况下，仅对于极为特殊的概率分布，结构均值参数系统反应才等于结构反应均值，但在一般情况下，随着结构力学参数变异性的增大，均值参数系统反应与结构反应均值的差异显著增大。而在动力情况下二者的相对误差则远比静力情况为大，并且对激励的频谱和结构固有频率的相对关系相当敏感。因此，以结构均值参数为标的确定性结构分析，其结果可能与现实工程结构的反应均值相去甚远，故而采用随机结构模型是必要的。     

Bifurcations in the Mean Angle of a Horizontally Shaken Pendulum: Analysis and Experiment

A pendulum excited by high-frequency horizontal displacement of its pivot point will vibrate with small amplitude about a mean position. The mean value is zero for small excitation amplitudes, but if the excitation is large enough the mean angle can take on non-zero values. This behavior is analyzed using the method of multiple time scales. The change in the mean angle is shown to be the result of a pitchfork bifurcation, or a saddle-node bifurcation if the system is imperfect. Analytical predictions of the mean angle as a function of frequency and amplitude are confirmed by physical experiment and numerical simulation.     

随机振动离散分析方法

本文提出了随机振动的离散分析方法,给出了一种可以求瞬态乃至稳态均值和均方响应的递推公式,并证明了它的无条件稳定性。应用该公式可以求出线性和等价线性化的非线性振动系统的精确稳态均值和均方响应。     

Equicontinuity and Sensitivity in Mean Forms

In this paper two mean forms of equicontinuity and sensitivity are mainly studied. For the equicontinuity side, it is shown that any topological dynamical system can be embedded into some almost equicontinuous in the mean system. For the sensitivity side, it turns out that the notions of sensitivity in the mean and mean sensitivity are identical in the measure-theoretical setting, though they are different in the topological setting. Moreover, levels of mean multi-variant versions of sensitivity in topological or measure-theoretical sense are completely classified.

     

The Mean Value Theorem and Converse Theorem of One Class the Fourth-Order Partial Differential Equations

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循环软化45碳钢和循环硬化304不锈钢的棘轮行为实验研究

对循环软化45碳钢的单轴应力循环下的平均应力、应力幅值以及先前应变循环对棘轮效应的影响进行了实验研究;并对循环硬化的304不锈钢进行了多种非比例循环加载路径下路径形状、路径等效应力幅值、平均应变与平均应力对材料棘轮变形行为的影响实验．发现平均应力和应力幅值及其历史对于材料的棘轮行为都有很大的影响．     

A MULTIAXIAL HIGH CYCLE FATIGUE LIFE PREDICTION MODEL CONSIDERING THE EFFECT OF MEAN STRESS FOR TENSION-TORSION LOADINGS WITH SAME FREQUENCY 1)

目前基于临界平面理论的高周疲劳寿命预测模型, 大都充分考虑了法向平均应力对材料疲劳寿命的影响, 但是没有有效反映剪切平均应力对疲劳寿命的影响. 通过分析7075-T651铝合金的试验数据发现, 与法向拉平均应力类似, 剪切平均应力同样对材料的疲劳寿命产生不利影响. 因此, 如果寿命预测模型中忽略剪切平均应力的影响, 存在明显剪切平均应力加载工况下, 预测寿命可能偏于危险. 由此, 本文定义具有较大法向应力的最大剪应力范围平面为临界平面, 建立了一个能够同时反映法向和剪切平均应力影响的高周疲劳寿命预测模型, 并给出了模型中材料常数的确定方法. 新模型首先将基于应变的Fatemi-Socie准则, 推广到材料的高周疲劳寿命预测, 给出了Fatemi-Socie准则的应力表述形式. 然后, 引入剪切和法向Walker因子, 反映剪切和法向平均应力对材料疲劳寿命的影响. 剪切和法向Walker因子的取值都介于0和1之间, 不同取值反映了材料对剪切和法向平均应力敏感程度的不同. 新模型适用于范围内的金属塑性材料. 利用5种材料在12种存在平均应力加载工况下的试验数据, 对所建模型进行了试验验证, 结果表明预测结果与试验结果吻合良好, 绝大多数寿命预测结果分布在3倍误差带以内.     

Mean Green operators and Eshelby tensors for hemispherical inclusions and hemisphere interactions in spheres. Application to bi-material spherical inclusions in isotropic spaces

This paper mainly presents an exact expression for the mean shape function of a hemispherical inclusion, from which are obtained analytical forms for the mean Green operator (GO) and Eshelby tensor of this hemi-sphere as well as for the related mean pair interaction Green operator (IGO) between the two hemi-spheres of a sphere, in media with isotropic (elastic or dielectric) properties. We secondly address the problem of bi-material inclusions, in the sense of a two-phase compact set of two or a few elementary domains, a particular inclusion pattern case for which we give an estimate of the mean stress and strain in each phase accounting for interactions. This estimate results from knowing the mean GO (or Eshelby tensor) for each pattern element plus the mean IGO between element pairs, what is rarely fulfilled analytically. The here solved case for bi-material spherical inclusions made of two different hemispherical elements adds to the recently made available solution for bi-material cylindrical inclusions made of piled coaxial finite cylinders. The obtained mean stress estimates are exemplified able to satisfactorily match with FEM calculations up to highly contrasted bi-material inclusions. Other types of bi-material spherical inclusions are mentioned for which the mean GOs for the sub-domains and their pair IGO can be obtained without calculation, owing to particular symmetries of the phase arrangement. Mean GOs and IGOs are also useful in certain homogenization frameworks yielding overall property estimates for inclusion-reinforced matrices. Further discussions and specific applications will be presented in forthcoming papers.     

The mean free path of dislocations in nanoparticle and nanorod reinforced metal composites and implication for strengthening mechanisms

The mean free path length of dislocations plays an important role in the plastic behavior of metals, which may be significantly enhanced by the addition of nanoparticles. The effects of particle distribution pattern, particle size, shape and volume fraction on the dislocation mean free path length and average obstacle distance are analyzed in two- and three-dimensional models. As the particle volume fraction increases, the dislocation mean free path length and average distance between dislocations obstacles can be significantly reduced, implying enhancement of strength. The random particle distribution exhibits the best combination of dislocation mean free path length and average obstacle distance. In addition, both dislocation mean free path and average obstacle distance can be significantly reduced by changing the particle shape from nanosphere to nanorod. The present analysis may provide useful information for designing the particle enforced composite materials.     

On simulations investigating droplet diameter–charge distributions in electrostatically atomized dielectric liquid sprays

A general procedure has been developed for the simulation of charged liquid and electrostatically atomized sprays. The procedure follows a Lagrangian approach for simulation of spray droplets and a Eulerian approach for gas‐phase variables, including the electric field generated by the charge presence on droplets. Validation of the procedure was examined through simulations of previously published charged spray experiments. Results showed that for the specification of initial droplet charge, modelling the droplet charge–diameter relationship through a scaling law is as reliable a method as using a directly obtained charge–diameter relationship from experimental measurements. The normalized root‐mean‐square errors for sprays using the two methods were shown to be within 12% of one another, for the prediction of spatially averaged profiles of mean droplet diameters, mean axial velocities and mean radial droplet velocities. Results showed that the general spatial characteristics and dynamics of a charged liquid spray can successfully be reproduced, including the axial and radial dispersal pattern of droplets and the distribution of mean droplet diameters throughout the spray plume. For all sprays with droplet charges defined through a scaling law relationship, the normalized root‐mean‐square errors range from 9.0% to 31.6% for mean droplet diameters, 10.4% to 67.9% for mean axial droplet velocities and 16.8% to 38.6% for mean radial droplet velocities. Lastly, we present a brief set of general recommendations for simulating electrostatically atomized dielectric liquid sprays.Copyright © 2013 John Wiley & Sons, Ltd.     

PDF of distance function for level‐set flamelet library modelling

The difference between a presumed distribution of flamelet position and a numerically simulated distribution of distance function (a signed distance to flamelet) is investigated. It is shown that even if the distribution of flamelet position is symmetrical and close to Gaussian, the distribution of distance function away from the mean flame position is skewed towards the mean position and the mean of the distance function is also different from the distance to the mean position. The difference depends on the distance to the mean flame and the flame wrinkling amplitude. An extension method for the variance of the distance function and an upwind scheme for solving the re‐initialization equation are presented. A numerical simulation of a premixed turbulent flame is compared to experimental data. Copyright © 2003 John Wiley & Sons, Ltd.     

单向加载,平均应力下的疲劳短裂纹生长

本文报道单向加载下平均应力和交变应力对疲劳短裂纹生长的影响。采用一种1.99%NiCrMo钢,在平均应力和交变应力不同组合的应力控制条件下进行室温疲劳试验,将疲劳过程划分为3个阶段:塑性局部化,微观组织短裂纹(MSC)生长和物理短裂纹(PSC)生长,研究了平均应力对上述3个阶段的影响并得到一组关系式,这些关系式可预测多种平均应力和交变应力组合条件下短裂纹的初始阶段和生长行为。获得了不同平均应力下疲劳承载曲线的满意的预测结果。本研究为仍依赖于传统的Goodman疲劳图的设计人员提供了一种以疲劳过程物理机制为基础的方法。     

考虑平均应力的同频拉扭多轴高周疲劳寿命评价方法

目前基于临界平面理论的高周疲劳寿命预测模型, 大都充分考虑了法向平均应力对材料疲劳寿命的影响, 但是没有有效反映剪切平均应力对疲劳寿命的影响. 通过分析7075-T651铝合金的试验数据发现, 与法向拉平均应力类似, 剪切平均应力同样对材料的疲劳寿命产生不利影响. 因此, 如果寿命预测模型中忽略剪切平均应力的影响, 存在明显剪切平均应力加载工况下, 预测寿命可能偏于危险. 由此, 本文定义具有较大法向应力的最大剪应力范围平面为临界平面, 建立了一个能够同时反映法向和剪切平均应力影响的高周疲劳寿命预测模型, 并给出了模型中材料常数的确定方法. 新模型首先将基于应变的Fatemi-Socie准则, 推广到材料的高周疲劳寿命预测, 给出了Fatemi-Socie准则的应力表述形式. 然后, 引入剪切和法向Walker因子, 反映剪切和法向平均应力对材料疲劳寿命的影响. 剪切和法向Walker因子的取值都介于0和1之间, 不同取值反映了材料对剪切和法向平均应力敏感程度的不同. 新模型适用于范围内的金属塑性材料. 利用5种材料在12种存在平均应力加载工况下的试验数据, 对所建模型进行了试验验证, 结果表明预测结果与试验结果吻合良好, 绝大多数寿命预测结果分布在3倍误差带以内.      

体育场环状悬挑屋盖脉动风压数值模拟

本文提出了预测悬挑屋盖上脉动风压的实用方法,用数值模拟中稳态计算得到的平均压力、平均速度和湍动能的分布计算大跨屋盖的脉动风压。以昆山体育场为例,通过数值模拟的平均压力系数、湍动能分布及脉动风压与风洞实验结果的比较,验证了用数值模拟方法预测环状悬挑屋盖脉动风压的有效性,并建议了需选用的合适湍流模型和参考点的风速。     

Inelastic deformations of mild-steel beams under symmetrical and unsymmetrical cyclic bending

The behavior of cantilever beams under the constraint of symmetrical and unsymmetrical cyclic deflections is investigated. An analytical technique developed predicts the behavior from cyclic moment-curvature relations derived from cyclic-strain control tests. Twenty tests were conducted on rectangular structural-steel sections under pure bending to establish these relations which couple the moment range and mean moment to curvature range. Models are proposed which fit the moment range and mean moment; these models are capable of accommodating, in discrete form, the phenomena of hardening and softening of a structural section as well as relaxation of the mean moment. Nine tests were conducted on cantilever beams under completely and partially reversed tip deflections. The load range changed little with changes in mean deflection. The mean load, in general, relaxed with increased cycling. The theory presented modelled the experimental behavior fairly accurately. It also suggested that the behavior may comprise:

1. an elastic case, where mean load is proportional to load range;
2. an intermediate range where the effects of mean deflection cannot be ignored; and
3. large inelastic cyclic deformation where the effects of mean deflection can be completely ignored except for associated changes in structural geometry and its secondary membrane effect.

     

圆柱尾流雷诺应力与平均运动变形率的空间弛豫效应

针对圆柱尾流中沿流向存在的Karman涡街周期性涡旋结构,对湍流雷诺应力与平均运动变形率之间的空间弛豫效应进行了实验研究.在回流式水槽中,放入不同直径的圆柱模型,获得不同雷诺数下的圆柱尾流,利用二维高时间分辨率粒子图像测速(TRPIV)技术测量圆柱尾流二维瞬时速度空间分布图像的时间序列.经过数字图像处理,获得二维雷诺应...     

双参数基础上弹性薄板的中值定理

本文提出了双参数基础上弹性薄板的中值定理并给出了证明。作为一种特殊情况,当地基特征参数 G_p 和 k 趋于零时,获得了 Winkler 基础上弹性薄板的中值定理和二维双调和函数的中值定理。     

Turbulent field helicity fluctuations and mean helicity appearance

There are many experiments where nonzero mean turbulent helicity is measured either directly or indirectly. Despite the study of mechanisms of its occurrence, the question of mean helicity generation remains open. In our paper, we explore the emergence of the mean helicity in the turbulent field created by an external random force with zero helicity under a simultaneous external large-scale impact (rotation or homogeneous magnetic field). It is shown that anisotropy (even weak one) results in the appearance of mean helicity and in the emergence of an analog of the diamagnetic effect in the vortex field.