非线性流动稳定性理论

<正> 流体的湍流运动普遍存在于大气、海洋、飞行器周围、推进装置和流体机械中,探讨湍流形成的条件和过程是流动稳定性理论的研究对象。 早在1843年,Stokes就预见到流体状态转捩的原因是失稳。整整100年前(1883年),Reynolds让液体流入不同口径的圆管,并在对称轴上注入一股纤细的颜色水,以便明显、敏感地观察到湍流的发生。他发现: (1)流速较低时,可以看到层次分明的层流,流速增加到一定程度后,就转变成高度无序的湍流状态;

一个推广Virial定理的数学方法和应用

本文在提出广义Gauss定理的思路下,提出了广义Stokes定理和一个推广Virial定理的新方法,后者应用于天体磁流体力学和引力平衡问题时得到的结果有:(1)气体具有运动时的平衡系统的判据,(2)磁场对气团形态的影响。应用于实验室等离子体平衡问题时,其结果有:(1)包围在气体中孤立磁场的特性,(2)发现内包无力场必须外包一有力场,(3)无力场的形态,应用于Tokmak等离子体环时的结果有:(1)环的胖瘦对环表面磁压的影响,(2)两个外加磁场分量分别和气压、环的胖瘦,截面形态、环电流分布和逆磁或顺磁的平衡关系,搞清楚了外加磁场约束等离子体总体平衡的物理机制。

探测气体平衡及非平衡态的相干反斯托克斯喇曼散射技术

<正> 一、引言 这篇综述的目的在于介绍最近发展起来的相干反斯托克斯喇曼散射(Coherent Anti-Stokes Raman Scattering(CARS))方法在诊断平衡及非平衡态气体中的应用,包括实验及理论两部分.文内还扼要介绍了我们正在筹备的测试系统的方案。 在气体中,特别在稀薄气体非平衡流动中,探测粒子数密度分布;混合含气中各组分,各能态的分布;平动、振动、转动温度;粒子的激发和弛豫过程,都是比较困难的,而这些

稀薄气流在麦克斯韦类型边界条件下对球的绕流

本文讨论低速稀薄气流(K_n《1)中圆球阻力问题,在Knudsen层中取分子在表面作Maxwell类型反射的壁面条件求解线性B-K-W方程,而以Stokes区的匹配渐近展开解为无穷远处的边界条件,在表面与均匀来流间温差为小量的假设下得到了小K_n数下圆球绕流的解。除稀薄气体效应外,还考虑了惯性效应和分子在表面的反射机制,所得的球阻表达为K_n、Re和热适应系数α的函数。

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wave-current field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does sx, by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best.

Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat-plate

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions : the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a seriesexpansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

Theory of local mode excitation in polyatomics by frequency-modulated lasers

that the Stokes-interaction relation is reasonable qualitatively but not correct

圆形域内串列双柱振动诱导的定常整流流动的数值模拟

在ε<<和Rs≥0(1)下采用贴体网格生成、数值求解NS方程研究圆形域内串列等直径双柱作同频同相小振幅振动在静止粘性不可压缩流体中诱导的Stokes层外的定常整流旋涡流动。数值结果表明，流场外边界的存在使大于临界雷诺数时外边界附近产生高阶分离旋涡，在很小的整流雷诺数变化范围内造成整流流谱改变。串列双柱柱间距的增加及圆域对振动柱柱径比的减小都使发生高阶分离的临界整流雷诺数之值下降。

双柱振动诱导定常整流旋涡流动的实验研究

用流动显示实验研究圆形静止不可压缩粘性流体域内以圆心对称布置的双柱作同频同相小振幅振动时诱导的Stokes层外的定常整流旋涡流动。实验表明，串列双柱当柱间距足够大时整流流谱呈八涡结构，当间距很小或为零时呈四涡结构。双柱的斜置有利于整流旋涡的合并。当柱间距接近至一定范围时，整流流动呈三维特征。振幅的减小和频率的降低使流动易出现三维现象。

Characteristics of flow fields induced by interfacial waves in two-layer fluid

When designing deep ocean structures, it is necessary to estimate the effects of internal waves on the platform and auxiliary parts such as tension leg, riser and mooring lines. Up to now, only a few studies are concerned with the internal wave velocity fields. By using the most representative two-layer model, we have analyzed the behavior of velocity field induced by interfacial wave in the present paper. We find that there may exist velocity shear of fluid particles in the upper and lower layers so that any structures in the ocean are subjected to shear force nearby the interface. In the meantime, the magnitude of velocity for long internal wave appears spatially uniform in the respective layer although they still decay exponentially. Finally, the temporal variation for Stokes and solitary waves are shown to be of periodical and pulse type.

Molecular dynamics simulation of adhesion forces in a dipalmitoylphosphatidylcholine membrane

Adhesion forces of Dipalmitoylphosphatidylcholine ( DPPC) membrane in the gel phase are investigated by molecular dynamics ( MD) simulation. In the simulations, individual DPPC molecules are pulled out of DPPC membranes with different rates and we get the maximum adhesion forces of DPPC membrane. We find that the maximum adhesion forces increase with pull rate, from about 400 to 700 pN when pull rates are from 0.001 to 0.03 nm/ps. We analyze the relationship between pull rate and adhesion forces of different origins using Brownian dynamics and notice that viscosity of solvent plays an important role in adhesion forces. Then we simulate the motion of a single DPPC molecule in solvent and it elucidates that the maximum drag force is almost linear with respect to the pull rate. We use Stokes' relation to describe the motion of a single DPPC molecule and deduce the effective length of a DPPC molecule. Conformational analyses indicate that the free energy variation of a DPPC molecule inside and outside of the DPPC membrane is an essential part of adhesion energy.

模拟MEMS中气体流动的工具——信息保存法

MEMS中气体流动因特征尺度小而是稀薄气体的领域,本文首先介绍处理低速稀薄气体流动的一些方法:线化Boltzmann方程,Lattice Boltzmann方法,加滑移边界的Navier-Stoks方程,以及DSMC方法,并讨论它们模拟MEMS中过渡领域低速流动所遇到的困难。信息保存法克服了流速低使得信息噪声比小引起统计模拟的困难,已成功模拟了一些一维和二维问题。MEMS中流速低和大的长宽比的特点还引起出入口边界条件相互影响需要协调的问题,通过微槽道流动的算例,在模拟中采用守恒形式的质量守恒方程和超松弛法成功地解决了这一问题。处理有温度变化的MEMS流动问题和跨越领域的混合算法是重要的问题,本文用信息保存法也进行了有益的尝试。

分岔管路内油水两相流动的研究

分岔管路大量存在于石油行业的输送管网中,油水两相流在分岔管路内的流动特性将对流程控制、动力匹配及下游处理设施产生显著的影响。对分岔管路内的油水两相流动进行了实验研究,采用不可压缩Nayier-Stokes方程结合双流体模型和混合k-ε模型对分岔管路内的油水两相流动进行了数值模拟,获得了初步的结果。计算表明,数值模拟能够较好地反映分岔管路内的油水两相流动,为工程设计提供参考。

理性力学基础

《理性力学基础》为《中国科学院研究生教学丛书》之一。
    《理性力学基础》系统地介绍了理性力学的主要科学体系和基本理论。《理性力学基础》由四部分，共十五章组成。第一部分综合介绍了理性力学的科学意义、方法和特点，从理性力学角度概括论述变形几何学与运动学、力学基本定律与场方程以及本构方程的一般原理。着重阐明张量和场方程的时空无差异原理，以及本构方程所应遵循的客观性原理。第二部分着重介绍简单物质的理论体系。作为典型范例进一步阐明弹性物质和简单流体的本构方程以及弹性体有限变形边值问题的分析方法。第三部分详细介绍黏弹性物质、弹塑性物质及晶体塑性的基本理论。第四部分主要介绍含缺陷物质的本构理论。
    《理性力学基础》可作为力学、应用数学、理论物理等专业的研究生教材，也可供力学工作者及高等院校力学专业教师参考。

目录 

第一章 绪论
1·1 理性力学目的和意义
1·2 理性力学的特点与体系
1·3 理性力学的方法
1·4 符号
第二章 变形几何学和运动学
2·1 直角坐标系的张量
2·2 物体的构形与运动
2·3 变形梯度
2·4 应变度量和面元、体元变形
2·5 应变率
第三章 基本定律与场方程
3·1 质量守恒定律
3·2 应力原理与动量守恒定律
3·3 能量守恒定律和熵定律
3·4 功共轭与应力度量
3·5 场方程
3·6 随体坐标系
第四章 本构方程的一般原理
4·1 时空系的变换
4·2 基本定律的客观性
4·3 本构方程的一般原理
第五章 简单物质
5·1 张量函数
5·2 张量函数表示定理
5·3 简单物质的本构方程
5·4 本构方程的简化形式
5·5 各向同性物质
5·6 简单固体
5·7 简单流体和流晶
5·8 内部约束
5·9 特殊类型物质
5·10 衰退记忆
第六章 弹性物质
6·1 弹性物质的本构方程
6·2 物质对称性
6·3 各向同性弹性固体
6·4 超弹性物质
6·5 各向同性超弹性物质
6·6 主轴表示
6·7 储能函数表示式
6·8 二次弹性
6·9 均匀变形场
6·10 储能函数的实验确定
第七章 弹性体有限变形边值问题
7·1 边值问题的提法
7·2 若干典型问题
7·3 平面应变问题
7·4 不可压缩各向同性弹性体
第八章 简单流体
8·1 直线流动
8·2 曲线流动
8·3 伸长历史恒定运动
8·4 定常测黏流动
8·5 Poiseuille流动
8·6 Couette流动
8·7 圆锥-平板流动
8·8 端部正应力效应
8·9 Stokes流体测黏流动
8·10 定常拉伸流动
第九章 黏弹性物质
9·1 线性黏弹性理论
9·2 非线性黏弹性固体
9·3 本构泛函展开
9·4 非线性黏弹性流体
第十章 弹塑性物质
10·1 微小变形塑性理论
10·2 张量的时间导数
10·3 有限塑性变形的本构方程
10·4 塑性大变形基本方程
10·5 Drucker公设与有限塑性变形
第十一章 晶体塑性理论
11·1 晶体塑性变形运动学
11·2 硬化规律
11·3 硬化系数表示式
11·4 晶体塑性本构关系
11·5 滑移剪切率γ(α)的存在性与惟一性
11·6 率相关流动规律
第十二章 缺陷连续统的线性理论
12·1 张量场的微分运算
12·2 协调条件
12·3 缺陷的几何意义
12·4 位错弹性理论
12·5 位错塑性理论
12·6 一般缺陷塑性理论
12·7 晶体塑性位错理论
12·8 Nye张量及缺陷塑性理论小结
12·9 位错塑性理论二维公式及算例
第十三章 非黎曼几何及流形简介
13·1 Euler空间张量场的绝对微分
13·2 曲率张量
13·3 线性空间
13·4 仿射联络空间
13·5 非完整变换
13·6 拓扑空间
13·7 微分流形
第十四章 缺陷连续统的非线性理论
14·1 非Niemann物质流形的构造
14·2 缺陷的几何意义
14·3 缺陷连续统的弹性理论
14·4 缺陷连续统的塑性理论
14·5 晶体塑性位错理论
第十五章 理性力学若干应用
15·1 有限变形的精确描述
15·2 曲线坐标的相应公式
15·3 本构方程的客观性原理
15·4 物质对称性
15·5 主轴法
15·6 客观应力率
附录 曲线坐标
1 基向量与度量张量
2 逆变导数
3 应力张
4 运动方程

 

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.