DYNAMICS OF ROTORS IMMERSED IN ECCENTRIC ANNULAR FLOW. PART 1: THEORY

A theoretical model is developed for predicting the dynamic behaviour and stability of a rotating shaft immersed in both a concentric or eccentric fluid annulus. Of specific concern here are geometries presenting a moderate flow-confinement, for which scarce results exist. Theoretical results show that moderate gap configurations lead to quite distinct flow forces, when compared to typical bearing configurations. Also, the annulus eccentricity is shown to be a very important parameter, controlling rotor dynamics and stability. In a companion paper (Part 2), experimental results are reported and favourably compared with the present theory.     

环形截面螺旋管道内二次流动特性的研究

从曲线柱坐标系下的N-S方程出发,以曲率和挠率为小参数,采用摄动法求解了环形截面螺旋管道内的黏性流动,给出了完全二阶摄动解,结果表明：当挠率为零时,二次流表现为上下对称的四个涡;当挠率不为零,涡的对称性遭到破坏,二次涡的强度和个数受De数和环形截面内外径之比δ的影响,轴向速度最大值在De数较小时靠近管道的内侧,随着De数的增加,其最大值向外侧移动。     

ANALYSIS OF VELOCITY ANNULAR EFFECT OF OSCILLATORY FLOW INSIDE PARALLEL PLATE CHANNEL

为了分析管内交变流动速度环状效应的特性,通过数值模拟对平板流道内可压缩交变流动的速度环状效应进行研究．根据速度环状效应的产生机理,分析得出在黏性流体管内交变流动中必然存在速度环状效应,并且在流道截面中心速度为零相位下最容易观察到速度环状效应．为了定量描述速度环状效应,根据流道中心速度为零相位下的速度分布曲线的斜率情况,提出定量评价指标速度环状效应系数,并针对平行平板流道内层流交变流动,利用该评价指标定量分析了无量纲参数（包括瓦伦西数Va和最大雷诺数Remax）对速度环状效应的影响．     

PERTURBATION SOLUTION OF NON-NEWTONIAN FLUID AXIAL LAMINAR FLOW THROUGH ECCENTRIC ANNULI

Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity ε is taken as a perturbation parameter, and the first order perturbation solutions of the problem, such as velocity field, limit velocity and pressure gradient, are all obtained.     

燃烧室两相流场亚网格燃烧模型的研究

在三维任意曲线坐标系下采用不同的亚网格燃烧模型对环形燃烧室火焰筒气液两相湍流瞬态反应流进行大涡模拟．计算中所采用的数学度模型有：k方程亚网格尺度模型估算亚网格湍流黏性;热通量辐射模型估算辐射换热,分别采用亚网格EBU燃烧模型（E-A model）、亚网格二阶矩输运方程模型（SOM）和亚网格二阶矩代数模型（SOM-A）估算化学反应速率．并在非交错网格系统下气相采用SIMPLE算法和混合差分格式求解,液相采用Lagrange处理,并用PSIC算法对其进行求解．通过实验结果和计算结果的比较,表明在三维任意曲线坐标系下对燃烧室火焰简两相湍流油雾燃烧流场进行大涡模拟,3种不同的亚网格燃烧模型都能真实反映两相湍流化学反应流流动及实际燃烧过程,而采用亚网格二阶矩输运方程模型稍优于其他两种亚网格燃烧模型．     

FLOW DYNAMICS OF GAS-SOLID FLUIDIZED BEDS WITH EVAPORATIVE LIQUID INJECTION

1. Introduction Injections of evaporative liquids into fluidized solid parti- cles are routinely practiced in industrial processes involv- ing gas-solid fluidization systems such as fluid catalytic cracking, polymerization, and plastic coating (Fan et al., 2001). In the FCC riser system, heavy oil is injected into the system to evaporate rapidly by contact with the hot catalyst particles. Simultaneously, thermal and catalytic cracking reactions take place. During a polymerization process, a …     

THE FLOW-INDUCED VIBRATION OF A FLEXIBLE STRIP HANGING VERTICALLY IN A PARALLEL FLOW PART 1: TEMPORAL AEROELASTIC INSTABILITY

The effect of several parameters in a fluid–strip system are studied for linear/nonlinear models in detail. Such parameters are: the number of modes in the Galerkin discretization, the length of the strip, and the flow velocity. The present simulation clearly shows that when nonlinear forces are considered the response approaches a flutter-type limit cycle at supercritical flow speeds. The Reynolds number at which the strip begins to oscillate is about 10⁴–10⁵. With a further increase of the flow velocity the strip oscillates regularly. At higher flow velocities the oscillation becomes violent and irregular. The amplitude, frequency and drag coefficient at the limit cycle are presented as functions of the flow velocity for a given strip. The numerical predictions are in qualitative agreement with previous experimental data.     

界面动力学研究近况

界面动力学主要包括界面波动力界面动态断裂两人部分，本文评述了其主要研究课题的最新进展，并在此基础上展望了其发展趋势，指出界面模型研究、界面无损检测、界面动态损伤与破坏机理、界面动态断裂韧性及弹塑性面裂纹动态扩展等是当前最关心且急待解决的问题。     

FRACTURE ANALYSIS OF AN ANNULAR CRACK IN A PIEZOELECTRIC LAYER

A flat annular crack in a piezoelectric layer subjected to electroelastic loadings is investigated under electrically impermeable boundary condition on the crack surface. Using Hankel transform technique, the mixed boundary value problem is reduced to a system of singular integral equations. With the aid of Gauss-Chebyshev integration technique, the integral equations are further reduced to a system of algebraic equations. The field intensity factor and energy release rate are determined. Numerical results reveal the effects of electric loadings and crack configuration on crack propagation and growth. The results seem useful for design of the piezoelectric structures and devices of high performance.     

VIBRATION AND STABILITY OF VERTICAL UPWARD-FLUID-CONVEYING PIPE IMMERSED IN RIGID CYLINDRICAL CHANNEL

A theoretical model is developed for the vibration and stability of a vertical pipe subjected concurrently to two dependent axial flows. The external fluid, after exiting the outer annular region between the pipe and a rigid cylindrical channel, is conveyed upwards inside the pipe. This configuration thus resembles of a pipe that aspirating fluid. The equation of planar mo- tion is solved by means of the differential quadrature method （DQM）. Calculations are conducted for a slender drill-string-like and a bench-top-size system, for different confinement conditions of the outer annular channel. It is shown that the vibrations of these two systems are closely related to the degree of confinement of the outer annular channel. For a drill-string-like system with narrow annuli, buckling instability may occur in the second and third modes. For a bench-top-size system, however, both buckling and flutter may occur in the lowest three modes. The form of instability depends on the annuli size.     

多刚体系统动力学的旋量-矩阵方法

本文将经典力学中的旋量概念以矩阵形式表示,用以建立多刚体系统的动力学方程。这种旋量-矩阵方法能保留旋量融矢量与矢量矩于一体的优点,却避免以往对偶数记法的缺点。结合 Roberson/wittenburg的图论工具,旋量-矩阵方法的应用范围可扩大到一般多刚体系统。对于树形系统,利用旋量通路矩阵推导各个由第i铰联结的全部外侧刚体组成的第i子系统的动力学方程,可避免出现铰的约束反力,对于非树系统,则利用回路矩阵导出各子系统动力学方程及运动学相容条件,全部计算过程统一为矩阵运算,以操作机器人作为具体算例。     

LINEAR INSTABILITY OF THE ANNULAR HAGEN-POISEUILLE FLOW WITH SMALL INNER RADIUS BY A CHEBYSHEV PSEUDOSPECTRAL METHOD

Abstract

A new eigenvalue search procedure using the Chebyshev pseudospectral technique has been developed for the solution of the Orr-Sommerfeld equations. It can deal accurately and flexibly with various velocity profiles. The axisymmetric linear instability characteristics oflhe annular Hagen-Poiseuille Bow have been studied with this procedure. Neutral curves were obtained for 1 > R = R₁/R₀ > 0.06 where R_l is the inner radius and R₀ is the outer radius. When R = 1 which is the plane Poiseuille flow, the corresponding critical Reynolds number is 5772.22 α_r; = 1.0209. As R decreases to 0.06, the critical Reynolds number increases to 2.6 × 10₆ and the wave speed decreases to 0.0573. The wavenumber first decreases gradually from a, = 1.0209 at R = 1.0 to α _r, = 0.90 at R = 0.3. and then it increases rapidly to α _r, = 1.73 at R = 0.06.     

BIFURCATIONS OF AIRFOIL IN INCOMPRESSIBLE FLOW

Bifurcations of an airfoil with nonlinear pitching stiffness in incompressible flow are investigated. The pitching spring is regarded as a spring with cubic stiffness. The motion equations of the airfoil are written as the four dimensional one order differential equations. Taking air speed and the linear part of pitching stiffness as the parameters, the analytic solutions of the critical boundaries of pitchfork bifurcations and Hopf bifurcations are obtained in 2 dimensional parameter plane. The stabilities of the equilibrium points and the limit cycles in different regions of 2 dimensional parameter plane are analyzed. By means of harmonic balance method, the approximate critical boundaries of 2-multiple semi-stable limit cycle bifurcations are obtained, and the bifurcation points of supercritical or subcritical Hopf bifurcation are found. Some numerical simulation results are given.     

环形液池内中等Pγ数流体的浮力-热毛细对流

为了了解水平温度梯度作用时环形液池内的浮力-热毛细对流特性,利用有限差分法进行了非稳态三维数值模拟,环形液池外壁被加热,半径为40 mm,内壁被冷却,半径为20 mm,液池深度为3～17mm,液池内流体为0.65cSt的硅油,其Pr数为6.7.模拟结果表明,当水平温度梯度较小时,流动为轴对称稳态流动,随着温度梯度的增加,流动将会失去其稳定性,在浅的液池内(d=3 mm),转化成三维振荡流动,在深的液池内(d≥6mm),转化成三维稳定流动;模拟计算的临界温差及表面温度分布图像与实验结果基本吻合.     

多刚体系统动力学的子系统递推法

本文采用递归推导并定义铰基矢阵得到以相对速度或伪速度表示的动力学方程。对非树系统利用回路转换矩阵及铰基矢阵自动建立约束方程,并用奇异值分解缩聚法得到以独立伪速度为变量的动力学方程。并导出递推计算公式便于程序执行。相应的通用程序SNERM已产生。     

PREDICTION OF FLOW REGIMES IN SPOUT-FLUIDIZED BEDS

Five main flow regimes in spout-fluidized bed were identified in this study, namely, fixed bed, spout with aeration, spout-fluidization, jet in fluidized bed and slugging, together with their corresponding major frequencies translated from pressure signals. The empirical equation A=aBb, in which A=Fr* /(H/Di) and B=(Fr*/(H/D))/(μg/μmf) are respectively the spout-geometry and spout-geometry-fluidization dimensionless numbers, was proposed to distinguish these flow regimes.