求单自由度非线性振动数值解的Taylor展开法

本文针对具体单自由度非线性振动系统建立了便于计算机实现的形式，求数值解Ｔａｙｌｏｒ展开法，给出实例与Ｒｕｎｇｅ－Ｋｕｔｔａ法进行比较，并应用于混沌解的计算．     

溶质在微极流体中的弥散——考虑无偶应力边界条件

本文研究溶质在作圆管和渠道层流的微极流体中的弥散规律，考虑了化学反应效应。利用Ｅｒｉｎｙｅｎ的微极流体理论，无偶应力边界条件和Ｔａｙｌｏｒ简化假定，导出相对浓度分布Ｃ和等效扩散系数Ｄ＊的解析式，并作数值计算，分析了微极参数λ．ｋ０和化学反应率参数β对上述量的影响。     

计算流体选讲(一)

计算流体是对描述流体运动的偏微分方程(或方程组)给出数值解的一门科学.目的在于进一步理解物理现象从而改进工程设计,实用性十分明确.计算流体的内容十分丰富并涉及多种学科:流体力学,偏微分方程,数值分析,计算几何,计算机科学等等.它需要书本文献中的理论和技巧,也需要实际工作中的经验和见解.在多年工作中我们深刻体会到从一般偏微分方程数值解的基本课程到从事计算流体的研究工作还有相     

计算流体选讲(一)

<正> 计算流体是对描述流体运动的偏微分方程(或方程组)给出数值解的一门科学.目的在于进一步理解物理现象从而改进工程设计,实用性十分明确.计算流体的内容十分丰富并涉及多种学科:流体力学,偏微分方程,数值分析,计算几何,计算机科学等等.它需要书本文献中的理论和技巧,也需要实际工作中的经验和见解.在多年工作中我们深刻体会到从一般偏微分方程数值解的基本课程到从事计算流体的研究工作还有相     

单自由度线性系统自由振动的Taylor级数法

本文从单自由度线性系统的运动方程及初始条件出发，用递推的方式导出初始时刻解的各阶导数，并由Ｔａｙｌｏｒ级数直接得到系统自由振动的通解表达式．     

三维非均匀不稳定渗流方程的二维不均匀粗化算法

在无源汇条件下,根据流过某一个横截面的流体流量等于流过这一横截面内所有精细网格的流体流量之和这一特点提出了粗化网格等效渗透率的计算方法。在粗化区内,利用直接解法求解二维渗流方程,再用这些解合成粗化网格的三维合成解,并由合成解计算粗化网格的等效渗透率。根据精度的要求采用了不均匀网格粗化,在流体流速大的区域采用精细网格。利用所得等效渗透率计算了粗化网格的某三维非均匀不稳定渗流场的压降解,结果表明三维非均匀不稳定渗流方程的二维不均匀粗化解非常逼近采用精细网格的解,但计算的速度比采用精细网格提高了80倍。     

二维拉氏辐射流体力学人为解构造方法

人为构造解方法是复杂多物理过程耦合程序正确性验证的重要方法之一，适用于二维拉氏大变形网格的流体、辐射耦合人为解模型较为少见。针对拉氏辐射流体力学程序正确性验证的需要，从二维拉氏辐射流体力学方程组出发，基于坐标变换技术，给出了拉氏空间到欧氏空间的物理变量导数关系式，开展了辐射流体耦合的人为解构造方法研究，构造了一类质量方程无源项的二维人为解模型，并应用于非结构拉氏程序LAD2D辐射流体力学计算的正确性考核，为流体运动网格上的辐射扩散计算提供了一种有效手段。数值结果显示观测到的数值模拟收敛阶与理论分析一致。     

SPH方法的运动边界条件研究Research on the moving boundary condition in SPH method

提出一种设置运动边界条件的方法,研究边界附近流体粒子积分截断和非物理穿透边界的问题。边界外的虚粒子在每个时间步由边界附近流体粒子对称生成,赋予相应的物理量,并在虚粒子中引入排斥力,利用拉格朗日形式的N‐S方程自编SPH程序,参考一维激波管的精确解验证边界方法的适用性,研究运动边界条件在计算模型中应用。激波管的模拟结果与精确解基本一致,且在运动边界模型中也计算获得合理的结果。文中提出的运动边界条件,避免了边界附近流体粒子积分截断问题,阻止流体粒子在边界处发生非物理穿透的现象。     

Oldroyd粘弹性流体缝隙流问题的解析解

本文得到了满足Oldroyd 四参数模型的粘弹性流体的平板Poiseuille 流问题的解析解.利用所得结果计算了共挤出问题--一种新的聚合物加工过程,并得到了解析解.     

局部采用标志质点的流体网格法

本文提出了一个解具有大形变的二维非定常的多物质流体力学问题的数值方法,在采用流体网格法思想的同时采用了标志质点,在不同的物质的界面附近,借助于标志质点计算流量;对连续流的区域,用流体网格法计算流量。计算检验表明,与质点网格法相比,减少了数值波动。     

On Stabilization of Multi-Layer Hele-Shaw and Porous Media Flows in the Presence of Gravity

Stabilization of multi-layer Hele-Shaw flows is studied here by including the influence of Rayleigh?CTaylor instability in our earlier work (Daripa, J. Stat. Mech. 12:28, 2008a) on stabilization of multi-layer Saffman?CTaylor instability. Furthermore, this article goes beyond our previous work with few extensions, improvements, new interpretations, and clarifications on the use of some terminologies. Results of two complete studies have been presented: the first investigates the effect of individually unstable interfaces on the overall stability of the flow, and the second studies the cumulative effect of unstable interfaces as well as unstable internal viscous layers. In each case, modal and absolute upper bounds on the growth rate are reported. Next, these bounds are used to investigate (i) stabilization of long waves on various interfaces; (ii) stabilization of all waves on all interfaces in comparison to pure Taylor instability; (iii) stabilization of disturbances on interior interfaces instead of exterior interfaces. In the first study, notions of partial and total stabilization with respect to the pure Taylor growth rate are introduced. Then necessary and sufficient conditions for partial and total stabilizations are found. Proof of stabilization of long waves on one of the two external interfaces in multi-layer flows is also proved. In the second study, an absolute upper bound is obtained in the presence of stabilizing density stratification across each internal interface even though all interfaces and layers have unstable viscous profiles. Exact results on the upper bounds, and necessary and sufficient conditions for control of instabilities driven by stable/unstable density stratification, unstable viscous layers and unstable interfaces are new and may be relevant to explain observed phenomena in many complex flows generating these kinds of viscous profiles and density stratification as they evolve. The present work builds upon and goes much further in details and new results than our previous work. The gravity effect included here brings with it restrictions which have not been addressed before in this multi-layer context.     

Turbulent Taylor-Couette vortex flow between large radius ratio concentric cylinders

Turbulent Taylor vortices between two concentric cylinders have been studied at a very high radius ratio of 0.985, equivalent to that found in relatively small underwater thruster units (typically with gaps of 2 mm). In order to study the flow at this radius ratio, a 1.42-m diameter experimental apparatus (with a rotating inner cylinder and a stationary outer cylinder) was constructed possessing a gap of 10 mm. Consequently, air bubbles could be visualised translating in water. A method was developed for identifying Taylor vortex properties from filtered digital images of the air bubbles and summing intensities to produce bubble density distributions. Whereas individual instantaneous images can be misleading, averaged bubble density distributions make it possible to identify vortex separation sizes and the positions of vortex outflow boundaries.     

Gravitational instability of thin gas layer between two thick liquid layers

We consider the problem of gravitational instability (Rayleigh–Taylor instability) of a horizontal thin gas layer between two liquid half-spaces (or thick layers), where the light liquid overlies the heavy one. This study is motivated by the phenomenon of boiling at the surface of direct contact between two immiscible liquids, where the rate of the “break-away” of the vapor layer growing at the contact interface due to development of the Rayleigh–Taylor instability on the upper liquid–gas interface is of interest. The problem is solved analytically under the assumptions of inviscid liquids and viscous weightless vapor. These assumptions correspond well to the processes in real systems, e.g., they are relevant for the case of interfacial boiling in the system water-n-heptane. In order to verify the results, the limiting cases of infinitely thin and infinitely thick gas layers were considered, for which the results can be obviously deduced from the classical problem of the Rayleigh–Taylor instability. These limiting cases are completely identical to the well-studied cases of gravity waves at the liquidliquid and liquid–gas interfaces. When the horizontal extent of the system is long enough, the wavenumber of perturbations is not limited from below, and the system is always unstable. The wavelength of the most dangerous perturbations and the rate of their exponential growth are derived as a function of the layer thickness. The dependence of the exponential growth rate on the gas layer thickness is cubic.     

Particle motion in a Taylor vortex

Here we present a study on the behavior of individual particles in the Taylor vortex. Two particle-fluid systems were tested: a cube with the edge length of 2 mm and the density of 0.13 g/cm³ (‘light particle’) in a working fluid of mineral oil (density of 0.86 g/cm³ and viscosity of 0.066 Pa.s); and a sphere with the diameter of 1.6 mm and the density of 2.2 g/cm³ (‘heavy particle’) in 90% glycerin/water (density of 1.23 g/cm³ and viscosity of 0.128 Pa.s). The Taylor–Couette device used for this study was featured with a short column (aspect ratio ≤ 6) and a wide gap (radius ratio ≤ 0.67). The interaction between the floating particle and Taylor vortices was investigated using a high speed camera and a particle image velocimetry (PIV) system. Moreover, computational fluid dynamics simulation was performed to calculate the liquid flow pattern and analyze the particle motion. Our results show that the particle behavior in the Taylor–Couette device is strongly dependent on the particle density and Reynolds number. With the increasing Reynolds number, four types of particle trajectories were sequentially identified from the light particle, including a circular trajectory on the surface of the inner cylinder, random shifting between the circular trajectory and oval orbit, a stable oval orbit in the annulus, and a circle along the vortex center. On the other hand, the heavy particle moves along a circular orbit and an oval orbit at low and high Reynolds numbers, respectively. Several unreported particle behaviors were also observed, such as the self-rotation of the particle when it moves along the above trajectories, the shifting axis of the oval orbit, etc. In addition, the PIV measurements show that the trapped particle can only influence the flow pattern locally around the particle. The study can help understand the particle behavior in a Taylor vortex better and therefore benefit applications of particle-laden Taylor vortex devices.     

初期Taylor弥散实验观察

本文利用激波管所能产生的瞬时定常流场,观察了一种具有间断初始密度分布的物质在这个流场中 Taylor 弥散过程.实验中所测量的物质,是空气中的 CO_2成份;测量手段是红外光谱吸收法;所观察到的过程发生在无量纲时间<0.07的范围内.实验数据与理论结果的比较表明:湍流 Taylor 弥散在初始阶段具有一定的对称性质.     

Stability of stratified shear flows in channels with variable cross sections

For the instability problem of density stratified shear flows in sea straits with variable cross sections, a new semielliptical instability region is found. Furthermore, the instability of the bounded shear layer is studied in two cases: (i) the density which takes two different constant values in two layers and (ii) the density which takes three different constant values in three layers. In both cases, the dispersion relation is found to be a quartic equation in the complex phase velocity. It is found that there are two unstable modes in a range of the wave numbers in the first case, whereas there is only one unstable mode in the second case.     

On the Taylor hypothesis in forced unsteady wall flows

Experiments on the modulation characteristics of the wall shear stress τ′-longitudinal velocity u′ and u′−u′ space–time correlations are reported in a forced turbulent channel flow in a wide range of imposed frequencies. The resulting integral and Taylor scale properties are discussed in detail in the low buffer layer under steady and unsteady flow conditions. It is shown that the small-scale turbulence is sensitive to the imposed unsteadiness since the amplitude and phase of the Taylor length scale vary considerably in the imposed frequency range investigated here. The Taylor hypothesis is acceptably valid in steady and unsteady wall layers just above the low buffer layer. Production and instantaneous pressure gradients are mostly responsible for the deviation of the frozen turbulence-state in the viscous and low buffer sublayers.     

The Compressible Viscous Surface-Internal Wave Problem: Nonlinear Rayleigh–Taylor Instability

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and t he upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The fluids are acted on by gravity in the bulk, and at the free interfaces we consider both the case of surface tension and the case of no surface forces.We are concerned with the Rayleigh–Taylor instability when the upper fluid is heavier than the lower fluid along the equilibrium interface. When the surface tension at the free internal interface is below the critical value, we prove that the problem is nonlinear unstable.     

Mechanism-based strain gradient crystal plasticity—I. Theory

We have been developing the theory of mechanism-based strain gradient plasticity (MSG) to model size-dependent plastic deformation at micron and submicron length scales. The core idea has been to incorporate the concept of geometrically necessary dislocations into the continuum plastic constitutive laws via the Taylor hardening relation. Here we extend this effort to develop a mechanism-based strain gradient theory of crystal plasticity. In this theory, an effective density of geometrically necessary dislocations for a specific slip plane is introduced via a continuum analog of the Peach-Koehler force in dislocation theory and is incorporated into the plastic constitutive laws via the Taylor relation.     

Prediction of growth rate and density of frost layer developing under forced convection

An experimental study was carried out on heat and mass transfer rates, growth rates and the density of frost layers on a flat plate in forced convection conditions. The density and thickness of the frost layers were correlated by the dimensionless parameters introduced in the authors' previous paper [6]. Measured density and thickness of the frost layers are compared with those in natural convection conditions and with those measured by other investigators. It is shown that these parameters can also be used to generalize the density and growth rates of frost layers developed under forced convection conditions.