Homogeneous turbulence subjected to rotation-dominated plane distortion

A new configuration of distorted homogeneous turbulence is investigated in the domain of rotation-dominated elliptical flows. The experimental results are compared with exact numerical solutions obtained in Fourier space for the linear part of the problem. The inherently periodic character of the flow results in typical oscillatory variations of the anisotropy and the pressure-strain correlations. A new two-point closure approach of the EDQNM type is proposed for the nonlinear problem; it is based on a representation of the spectral tensor by scalar functions expanded in terms of spherical harmonics.     

The dynamic performance of the Weissenberg Rheogoniometer

The dynamic performance of a standard Model R18 Weissenberg Rheogoniometer has been studied in detail. The Rheogoniometer was carefully calibrated and used to measure accurately the rheological behaviour of a highly nonlinear viscoelastic polymer solution (1% polyacrylamide in 50% glycerol/water).In this paper the elaborate procedures that were used to calibrate the electronic signal processing equipment are described. The various static and dynamic calibration/correction factors are defined and incorporated into a computer implemented calculation scheme for evaluating the linear dynamic properties from the raw digital transfer function analyser readings.The linear dynamic properties of the polymer solution are presented together with the corresponding steady shearing properties. Both cone and plate and parallel plates geometries were used and good agreement was obtained over the wide range (six decades) of frequencies and shear rates employed.Fluid inertia effects were found to become important when the modified Reynolds number,Re _c ² orRe(H/R)², exceeded a value of about 0.1. These effects had a strong influence on the phase angle() which could readily be detected by varying the gap angle/width. The Walters-Kemp equations were found to give consistently accurate values for the linear dynamic properties for modified Reynolds numbers up to 11.6 which was the highest reached.     

STABILITY OF NON-CONSERVATIVE LINEAR GYROSCOPIC SYSTEMS

ＳＴＡＢＩＬＩＴＹ　ＯＦ　ＮＯＮ－ＣＯＮＳＥＲＶＡＴＩＶＥ　ＬＩＮＥＡＲ　ＧＹＲＯＳＣＯＰＩＣ　ＳＹＳＴＥＭＳＬｉＪｕｎｆｅｎｇ（李俊峰）；ＷａｎｇＺｈａｏｌｉｎ（王照林）（ＲｅｃｅｉｖｅｄＮｏｖ．３，１９９５，ＲｅｖｉｓｅｄＡｐｒｉｌ２１，１９９６...     

各向异性两相材料尖劈奇性场的非协调元分析

提出了一个基于位移的、分析柱状各向异性两相材料尖劈端部邻域的奇性位移场和应力场问题的非协调元特征分析法. 该方法从柱状扇区的散度定理出发，将柱状扇区控制方程的弱式化为一个与虚功原理相同形式的方程，采用一种新的非协调元技术把所导出的``虚功原理'转化为标准一阶特征方程的求解问题. 非协调元法中，尖劈端部邻域的位移场假定没有采用奇异变换技术，有限元的单元形式是一维的. 将柱状各向异性两相材料尖劈视为``广义平面应变'问题，位移场与坐标z无关，只关注界面端的幂奇异性而不考虑对数奇异性. 运用该方法给出了柱状各向异性两相材料尖劈端部奇性应力指数、奇性位移角分布和应力角分布的算例. 所有的计算结果表明，该方法使用的单元少而且精度较高.     

HIGH PERFORMANCE SPARSE SOLVER FOR UNSYMMETRICAL LINEAR EQUATIONS WITH OUT-OF-CORE STRATEGIES AND ITS APPLICATION ON MESHLESS METHODS

A new direct method for solving unsymmetrical sparse linear systems(USLS) arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin (MLPG) method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests.     

Instability of small-amplitude convective flows in a rotating layer with free boundaries

The stability of steady convective flows in a horizontal layer with free boundaries, heated from below and rotating about a vertical axis, is studied in the Boussinesq approximation (Rayleigh-Bénard convection). The flows considered are convective rolls or square cells that are sums of two perpendicular rolls with equal wave numbers k. It is assumed that the Rayleigh number is almost critical in order for convective flows with a wave number k: R = R _c (k) + ε² to arise, the amplitude of the supercritical states being of the order of ε. It is shown that the flows are always unstable relative to perturbations that are the sum of one long-and two short-wave modes corresponding to linear rolls turned through small angles in opposite directions.     

Thermocapillary convection in an absorbing-scattering medium subjected to irradiation

The criteria for the onset of thermocapillary convection in a horizontal radiating fluid layer heated by an incident thermal radiative energy source are determined. The fluid layer is an absorbing and isotropically scattering medium confined between a free upper surface and an insulated rigid lower surface. Linear analysis is performed on the continuity, momentum, energy, and approximate radiative equations. The resulting disturbance equations are solved using a numerical optimization technique to obtain the eigenvalues governing the onset of convective motion. The influence of thermal radiation on the critical Marangoni number is examined. Attention is drawn to the physical significance of the heat transfer mode, gravitational force, the scattering effect, and the surface radiative properties. The conditions leading to the onset of convection are presented as functions of the optical thickness, scattering albedo, Planck number, surface emissivities, and transmissivities.     

On Determining the Percolation Reynolds Number and the Characteristic Linear Dimension for Ideal and Fictitious Porous Media

Various versions of representations of the percolation Reynolds number for porous media with isotropic and anisotropic flow properties are considered. The formulas are derived and the variants are analyzed with reference to model porous media with a periodic microstructure formed by systems of capillaries and packings consisting of spheres of constant diameter (ideal and fictitious porous media, respectively). A generalization of the Kozeny formula is given for determining the capillary diameter in an ideal porous medium equivalent to a fictitious medium with respect to permeability and porosity and it is shown that the capillary diameter is nonuniquely determined. Relations for recalculating values of the Reynolds number determined by means of formulas proposed earlier are given and it is shown that taking the microstructure of porous media into account, as proposed in [1, 2], makes it possible to explain the large scatter of the numerical values of the Reynolds number in processing the experimental data.     

The Stress Response of Functionally Graded Isotropic Linearly Elastic Rotating Disks

The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic solid circular disks or cylinders, rotating at constant angular velocity about a central axis. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic problem for a homogeneous isotropic rotating solid disk or cylinder is considered. The special case of a body with Young"s modulus depending on the radial coordinate only, and with constant Poisson"s ratio, is examined. For the case when the Young"s modulus has a power-law dependence on the radial coordinate, explicit exact solutions are obtained. It is shown that the stress response of the inhomogeneous disk (or cylinder) is significantly different from that of the homogeneous body. For example, the maximum radial and hoop stresses do not, in general, occur at the center as in the case for the homogeneous material. Furthermore, for the case where the Young"s modulus increases with radial distance from the center, it is shown that radially symmetric solutions exist provided the rate of growth of the Young"s modulus is, at most, cubic in the radial variable. It is also shown for the general inhomogeneous isotropic case how the material inhomogeneity may be tailored so that the radial and hoop stress are identical throughout the disk. This revised version was published online in August 2006 with corrections to the Cover Date.     

线性系统模态控制及其时滞补偿

对线性系统模态控制及其时滞补偿进行研究。模态控制分控制全部模态和控制有限模态两种情况 ,时滞补偿采用移相补偿。最后结合算例对两种控制模态下的控制效果和控制有限模态时的时滞补偿进行了数值计算和结果对比