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;

Numerical simulation of axisymmetric unsteady incompressible flow by a vorticity-velocity method

A new numerical method for solving the axisymmetric unsteady incompressible Navier-Stokes equations using vorticity-velocity variables and a staggered grid is presented. The solution is advanced in time with an explicit two-stage Runge-Kutta method. At each stage a vector Poisson equation for velocity is solved. Some important aspects of staggering of the variable location, divergence-free correction to the velocity held by means of a suitably chosen scalar potential and numerical treatment of the vorticity boundary condition are examined. The axisymmetric spherical Couette flow between two concentric differentially rotating spheres is computed as an initial value problem. Comparison of the computational results using a staggered grid with those using a non-staggered grid shows that the staggered grid is superior to the non-staggered grid. The computed scenario of the transition from zero-vortex to two-vortex flow at moderate Reynolds number agrees with that simulated using a pseudospectral method, thus validating the temporal accuracy of our method.

刚性充液容器内竖直激励表面波研究进展

受外激励的充液刚性容器中流体的波动问题有实际的工程应用背景.竖直方向的受周期性外激励的充液容器的自由表面波问题--Faraday波问题是流体力学三大不稳定性难题之一(另外两个不稳定性问题是RayleighBénard对流和Taylor-Couette流).本文综述了在理想流体中和弱粘性流体中Faraday波的研究成果;介绍了作者在底部垂直激励的圆柱形容器中流体表面波图谱的实验研究和理论分析的结果.最后提出有待进一步研究的问题.

Rarefied gas dynamics: fundamentals, simulations and micro flows

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

 

稀薄气体动力学

通常的气体动力学方法，当气体分子的平均自由程与流场特征长度相比不可忽略时，不再适用，要采用稀薄气体动力学的方法。这适用于航天飞行器在高空飞行时受的力和热，也适用于微机电系统和真空系统等离子体材料加工等21世纪技术前沿领域。本书系统、简明地阐述稀薄气体动力学方法，给出方法的基础并着重介绍直接模拟Monte Carlo(DSMC)方法以及与低速稀薄气体流动相关的前沿课题。全书共分7章。前两章是作为学科的基础引入的，第1章以空气为对象对于分子能态结构、能态分布以极小篇幅作了简要概括的叙述，以作为了解稀薄气流非平衡现象物理基础的初步。第2章对包括双体碰撞、Boltzmann方程以及气体的平衡态等分子动理论的基础做了必要的讨论，其中包括了对唯像论分子相互作用模型、变径硬球（VHS）、变径软球（VSS）和概括化硬球（GHS）等模型的介绍。第3章讨论了各种分子和表面的相互作用模型，包括反映细致平衡的互易原理和基于此原理的CLL模型的阐述。第4章讨论自由分子流。第5章讨论应用于滑流领域的各连续介质方程及滑流边界条件，一些简单解以及热泳问题。第6章则较全面、概括地介绍了求解过程领域中的各种解析和数值方法。第7章介绍了直接模拟Monte Carlo(DSMC)方法，讨论了非平衡流动及低速稀薄流动等前沿课题，包括处理内能松弛、化学反应的方法、用于复杂流场通用软件的方法、低速稀薄流动的信息保存（IP）方法等。　　本书适合高等学校力学一航空航天专业高年级学生、研究生及从事气动力学和航天研究的科研人员参考阅读。

通常的气体动力学方法，当气体分子的平均自由程与流场特征长度相比不可忽略时，不再适用，要采用稀薄气体动力学的方法。这适用于航天飞行器在高空飞行时受的力和热，也适用于微机电系统和真空系统等离子体材料加工等21世纪技术前沿领域。本书系统、简明地阐述稀薄气体动力学方法，给出方法的基础并着重介绍直接模拟Monte Carlo(DSMC)方法以及与低速稀薄气体流动相关的前沿课题。

符号表
绪论
第1节 稀薄气体动力学的提出
第2节 气体的分子模型
第3节 分子平均自由程
第4节 流动的领域划分
第5节 非平衡现象与稀薄气体动力学
第6节 相似准则
第1章 分子结构与能态
第1节 双原子分子
第2节 分子的能态分布
第3节 分子的内能、内自由度和内能分布函数
第2章 分子动理论基础
第1节 速度分布函数
第2节 宏观量的表达
第3节 分子的双体碰撞模型
第4节 碰撞截面与分子模型
第5节 Boltzmann方程
第6节 碰撞积分与气体分子的总碰撞数
第7节 碰撞积分的计算
第8节 Maxwell输运方程——矩方程
第9节 Maxwell分布
第10节 气体的平衡态
第11节 8速度气体模型
第12节 混合气体
第3章 分子表面相互作用
第1节 引言
第2节 镜面反射与漫反射，适应系数
第3节 互易性原理
第4节 CLL分子表面相互作用模型
第4章 自由分子流
第1节 气体中的分子数目通量和动量通量
第2节 作用于物体的气动力
第3节 表面元素的热传导
第4节 自由分子流出与热流逸
第5节 Couette流动与平板间的传热问题
第6节 无碰撞Boltzmann方程的通解，非定常流动
第5章 连续介质模型
第1节 引言
第2节 基本方程
第3节 滑流边界条件
第4节 一些简单问题的求解
第5节 热蠕动与热泳
第6章 过渡领域
第1节 概述
第2节 线化的BoltzmanN方程
第3节 矩方法
第4节 模型方程
第5节 有限差分法
第6节 间断纵坐标方法
第7节 积分方法
第8节 直接模拟方法
第7章 直接模拟Monte方法
第1节 引言
第2节 碰撞的取样
第3节 DSMC方法求解问题实例
第4节 内能的激发与松弛
第5节 化学反应的模拟
第6节 复杂流场的计算，位置元方法
第7节 微尺度低速气体流动，信息保存法
附录I 气体的性质和分子性质
附录II 分布函数求矩遇到的积分
附录III 具有给定分布的随机数的取样
附录IV Couette问题程序
参考文献
主题词索引

An Atomistic-Continuum Hybrid Simulation Of Fluid Flows Over Superhydrophobic Surfaces

Recent experiments have found that slip length could be as large as on the order of 1 mu m for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper, an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces, in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths, which cannot be obtained by molecular dynamics simulation alone.

An atomistic-continuum hybrid simulation of fluid flows over superhydrophobic surfaces

Recent experiments have found that slip length could be as large as on the order of 1 mu m for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths which cannot be obtained by molecular dynamics simulation alone.

Experimental study on inertial effects in liquid-solid flows

This thesis presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Reynolds (defined by the shear rate and particle diameter) and Stokes numbers, ranging from 3 ≤ Re ≤ 1.6 × 10³ and 0.4 ≤ St ≤ 195. The experiments use a specifically designed Couette cylindrical rheometer that allows for probing the transition from transporting a pure liquid to transporting a dense suspension of particles. Measurements of the shear stress are presented for a wide range of particle concentration (10 to 60% in volume) and for particle to fluid density ratio between 1 and 1.05. The effective relative viscosity exhibits a strong dependence on the solid fraction for all density ratios tested. For density ratio of 1 the effective viscosity increases with Stokes number (St) for volume fractions (φ) lower than 40% and becomes constant for higher φ. When the particles are denser than the liquid, the effective viscosity shows a stronger dependance on St. An analysis of the particle resuspension for the case with a density ratio of 1.05 is presented and used to predict the local volume fraction where the shear stress measurements take place. When the local volume fraction is considered, the effective viscosity for settling and no settling particles is consistent, indicating that the effective viscosity is independent of differences in density between the solid and liquid phase. Shear stress measurements of pure fluids (no particles) were performed using the same rheometer, and a deviation from laminar behavior is observed for gap Reynolds numbers above 4× 10³, indicating the presence of hydrodynamic instabilities associated with the rotation of the outer cylinder. The increase on the effective viscosity with Stokes numbers observed for mixtures with φ ≤ 30% appears to be affected by such hydrodynamic instabilities. The effective viscosity for the current experiments is considerably higher than the one reported in non-inertial suspensions.

I. Studies on bacteriophage DNA's and minicircular DNA's in M. lysodeikticus and E. coli 15. II. Flow dichroism of DNA solutions

Part I

Chapter 1.....A physicochemical study of the DNA molecules from the three bacteriophages, N1, N5, and N6, which infect the bacterium, M. lysodeikticus, has been made. The molecular weights, as measured by both electron microscopy and sedimentation velocity, are 23 x 10⁶ for N5 DNA and 31 x 10⁶ for N1 and N6 DNA's. All three DNA's are capable of thermally reversible cyclization. N1 and N6 DNA's have identical or very similar base sequences as judged by membrane filter hybridization and by electron microscope heteroduplex studies. They have identical or similar cohesive ends. These results are in accord with the close biological relation between N1 and N6 phages. N5 DNA is not closely related to N1 or N6 DNA. The denaturation T_m of all three DNA's is the same and corresponds to a (GC) content of 70%. However, the buoyant densities in CsCl of Nl and N6 DNA's are lower than expected, corresponding to predicted GC contents of 64 and 67%. The buoyant densities in Cs₂SO₄ are also somewhat anomalous. The buoyant density anomalies are probably due to the presence of odd bases. However, direct base composition analysis of N1 DNA by anion exchange chromatography confirms a GC content of 70%, and, in the elution system used, no peaks due to odd bases are present.

Chapter 2.....A covalently closed circular DNA form has been observed as an intracellular form during both productive and abortive infection processes in M. lysodeikticus. This species has been isolated by the method of CsC1-ethidium bromide centrifugation and examined with an electron microscope.

Chapter 3.....A minute circular DNA has been discovered as a homogeneous population in M. lysodeikticus. Its length and molecular weight as determined by electron microscopy are 0.445 μ and 0.88 x 10⁶ daltons respectively. There is about one minicircle per bacterium.

Chapter 4.....Several strains of E. coli 15 harbor a prophage. Viral growth can be induced by exposing the host to mitomycin C or to uv irradiation. The coliphage 15 particles from E. coli 15 and E, coli 15 T^- appear as normal phage with head and tail structure; the particles from E. coli 15 TAU are tailless. The complete particles exert a colicinogenic activity on E.coli 15 and 15 T^-, the tailless particles do not. No host for a productive viral infection has been found and the phage may be defective. The properties of the DNA of the virus have been studied, mainly by electron microscopy. After induction but before lysis, a closed circular DNA with a contour length of about 11.9 μ is found in the bacterium; the mature phage DNA is a linear duplex and 7.5% longer than the intracellular circular form. This suggests the hypothesis that the mature phage DNA is terminally repetitious and circularly permuted. The hypothesis was confirmed by observing that denaturation and renaturation of the mature phage DNA produce circular duplexes with two single-stranded branches corresponding to the terminal repetition. The contour length of the mature phage DNA was measured relative to φX RFII DNA and λ DNA; the calculated molecular weight is 27 x 10⁶. The length of the single-stranded terminal repetition was compared to the length of φX 174 DNA under conditions where single-stranded DNA is seen in an extended form in electron micrographs. The length of the terminal repetition is found to be 7.4% of the length of the nonrepetitious part of the coliphage 15 DNA. The number of base pairs in the terminal repetition is variable in different molecules, with a fractional standard deviation of 0.18 of the average number in the terminal repetition. A new phenomenon termed "branch migration" has been discovered in renatured circular molecules; it results in forked branches, with two emerging single strands, at the position of the terminal repetition. The distribution of branch separations between the two terminal repetitions in the population of renatured circular molecules was studied. The observed distribution suggests that there is an excluded volume effect in the renaturation of a population of circularly permuted molecules such that strands with close beginning points preferentially renature with each other. This selective renaturation and the phenomenon of branch migration both affect the distribution of branch separations; the observed distribution does not contradict the hypothesis of a random distribution of beginning points around the chromosome.

Chapter 5....Some physicochemical studies on the minicircular DNA species in E. coli 15 (0.670 μ, 1.47 x 10⁶ daltons) have been made. Electron microscopic observations showed multimeric forms of the minicircle which amount to 5% of total DNA species and also showed presumably replicating forms of the minicircle. A renaturation kinetic study showed that the minicircle is a unique DNA species in its size and base sequence. A study on the minicircle replication has been made under condition in which host DNA synthesis is synchronized. Despite experimental uncertainties involved, it seems that the minicircle replication is random and the number of the minicircles increases continuously throughout a generation of the host, regardless of host DNA synchronization.

Part II

The flow dichroism of dilute DNA solutions (A₂₆₀≈0.1) has been studied in a Couette-type apparatus with the outer cylinder rotating and with the light path parallel to the cylinder axis. Shear gradients in the range of 5-160 sec.^-1 were studied. The DNA samples were whole, "half," and "quarter" molecules of T4 bacteriophage DNA, and linear and circular λb₂b₅c DNA. For the linear molecules, the fractional flow dichroism is a linear function of molecular weight. The dichroism for linear A DNA is about 1.8 that of the circular molecule. For a given DNA, the dichroism is an approximately linear function of shear gradient, but with a slight upward curvature at low values of G, and some trend toward saturation at larger values of G. The fractional dichroism increases as the supporting electrolyte concentration decreases.

Desenvolvimento de um simulador numérico empregando o método Smoothed Particle Hydrodynamics para a resolução de escoamentos incompressíveis. Implementação computacional em paralelo (CUDA)

Neste trabalho, foi desenvolvido um simulador numérico baseado no método livre de malhas Smoothed Particle Hydrodynamics (SPH) para a resolução de escoamentos de fluidos newtonianos incompressíveis. Diferentemente da maioria das versões existentes deste método, o código numérico faz uso de uma técnica iterativa na determinação do campo de pressões. Este procedimento emprega a forma diferencial de uma equação de estado para um fluido compressível e a equação da continuidade a fim de que a correção da pressão seja determinada. Uma versão paralelizada do simulador numérico foi implementada usando a linguagem de programação C/C++ e a Compute Unified Device Architecture (CUDA) da NVIDIA Corporation. Foram simulados três problemas, o problema unidimensional do escoamento de Couette e os problemas bidimensionais do escoamento no interior de uma Cavidade (Shear Driven Cavity Problem) e da Quebra de Barragem (Dambreak).

Simulação de escoamentos incompressíveis empregando o método Smoothed Particle Hydrodynamics utilizando algoritmos iterativos na determinação do campo de pressões

Nesse trabalho, foi desenvolvido um simulador numérico (C/C++) para a resolução de escoamentos de fluidos newtonianos incompressíveis, baseado no método de partículas Lagrangiano, livre de malhas, Smoothed Particle Hydrodynamics (SPH). Tradicionalmente, duas estratégias são utilizadas na determinação do campo de pressões de forma a garantir-se a condição de incompressibilidade do fluido. A primeira delas é a formulação chamada Weak Compressible Smoothed Particle Hydrodynamics (WCSPH), onde uma equação de estado para um fluido quase-incompressível é utilizada na determinação do campo de pressões. A segunda, emprega o Método da Projeção e o campo de pressões é obtido mediante a resolução de uma equação de Poisson. No estudo aqui desenvolvido, propõe-se três métodos iterativos, baseados noMétodo da Projeção, para o cálculo do campo de pressões, Incompressible Smoothed Particle Hydrodynamics (ISPH). A fim de validar os métodos iterativos e o código computacional, foram simulados dois problemas unidimensionais: os escoamentos de Couette entre duas placas planas paralelas infinitas e de Poiseuille em um duto infinito e foram usadas condições de contorno do tipo periódicas e partículas fantasmas. Um problema bidimensional, o escoamento no interior de uma cavidade com a parede superior posta em movimento, também foi considerado. Na resolução deste problema foi utilizado o reposicionamento periódico de partículas e partículas fantasmas.

Aerodynamic effects in ink-jet printing on a moving web

The airflow between the fast-moving substrate and stationary print heads in a web print press may cause print quality issues in high-speed, roll-to-roll printing applications. We have studied the interactions between ink drops and the airflow in the gap between the printhead and substrate, by using an experimental flow channel and high-speed imaging. The results show: 1) the gap airflow is well approximated by a standard Couette flow profile; 2) the effect of gap airflow on the flight paths of main drops and satellites is negligible; and 3) the interaction between the gap airflow and the wakes from the printed ink drops should be investigated as the primary source of aerodynamically- related print quality issues. ©2012 Society for Imaging Science and Technology.

Global modes with multiple saddle points

Significant progress has been made towards understanding the global stability of slowly-developing shear flows. The WKBJ theory developed by Patrick Huerre and his co-authors has proved absolutely central, with the result that both the linear and the nonlinear stability of a wide range of flows can now be understood in terms of their local absolute/convective instability properties. In many situations, the local absolute frequency possesses a single dominant saddle point in complex X-space (where X is the slow streamwise coordinate of the base flow), which then acts as a single wavemaker driving the entire global linear dynamics. In this paper we consider the more complicated case in which multiple saddles may act as the wavemaker for different values of some control parameter. We derive a frequency selection criterion in the general case, which is then validated against numerical results for the linearized third-order Ginzburg-Landau equation (which possesses two saddle points). We believe that this theory may be relevant to a number of flows, including the boundary layer on a rotating disk and the eccentric Taylor-Couette-Poiseuille flow. © 2014 Elsevier Masson SAS. All rights reserved.

Statistical analysis of microscale gas flows and stock price changes

First, recent studies on the information preservation (IP) method, a particle approach for low-speed micro-scale gas flows, are reviewed. The IP method was validated for benchmark issues such as Couette, Poiseuille and Rayleigh flows, compared well with measured data for typical internal flows through micro-channels and external flows past micro flat plates, and combined with the Navier-Stokes equations to be a hybrid scheme for subsonic, rarefied gas flows. Second, the focus is moved to the microscopic characteristic of China stock market, particularly the price correlation between stock deals. A very interesting phenomenon was found that showed a reverse transition behaviour between two neighbouring price changes. This behaviour significantly differs from the transition rules for atomic and molecular energy levels, and it is very helpful to understand the essential difference between stock markets and nature.