Limits on rough-particle sizing with low-defocus interferometric imaging

We present a rigorous theoretical model for the influence of the aperture in interferometric out-of-focus imaging.We investigate the role of this effect on the properties of speckle-like patterns generated by irregular,rough particles.Finally,we determine the conditions under which these patterns are no longer representative of particle size but of the aperture itself and the defocus parameter.     

孔径尺寸对干涉配合铆接件超高周疲劳性能的影响

合理的干涉配合铆接工艺可以有效提高构件疲劳性能,本文通过试验研究与数值模拟相结合分析孔径尺寸对干涉配合铆接件超高周疲劳性能的影响。利用20kHz超声疲劳试验系统测试了三种不同孔径尺寸下干涉配合铆接件的超高周疲劳性能;基于ABAQUS模拟分析了铆接工艺过程以及孔径尺寸对干涉量和孔边残余应力的影响,通过分析高频低幅加载下孔边应力分布,结合超高周疲劳试验及断口形貌观察,分析了孔径尺寸对铆接件超高周疲劳性能的影响。结果表明:不同孔径尺寸铆接件的裂纹萌生扩展方式类似,疲劳裂纹萌生均发生在孔边距表面1.5mm最大残余拉应力处;适当减小孔径尺寸所形成的合理干涉量可以提高铆接件疲劳寿命,φ4.10mm的孔径可以形成0.66%的孔边平均干涉量,铆接件疲劳寿命最高达到3.63×108周。     

Non-Newtonian Flow in a Variable Aperture Fracture

The transmissivity of a variable aperture fracture for flow of a non-Newtonian, purely viscous power-law fluid with behavior index n is studied. The natural logarithm of the fracture aperture is considered to be a two-dimensional, spatially homogeneous and correlated Gaussian random field. We derive an equivalent fracture aperture for three flow geometries: (1) flow perpendicular to aperture variation; (2) flow parallel to aperture variation; (3) flow in an isotropic aperture field. Under ergodicity, results are obtained for cases 1 and 2 by discretizing the fracture into elements of equal aperture and assuming that the resistances due to each aperture element are, respectively, in parallel and in series; for case 3, the equivalent aperture is derived as the geometric mean of cases 1 and 2. When n=1 all our expressions for the equivalent aperture reduce to those derived in the past for Newtonian flow and lognormal aperture distribution. As log-aperture variance increases, the equivalent aperture is found to increase for case 1, to decrease for case 2, and to be a function of flow behavior index n for case 3.     

Effects of the Correlation Length on the Hydraulic Parameters of a Fracture Network

We consider the influences of correlation length and aperture variability on the REV, the equivalent permeability of a fracture network, and the uncertainty in the equivalent permeability using a two-dimensional orthogonal bond percolation model. The percolation threshold, correlation length, effective conductivity, and coefficient of variation of the effective conductivity are investigated over statistically representative multiple realizations with Monte Carlo simulations in 2D fracture networks that have log-normally distributed individual fracture permeabilities. We show that although the aperture variability is large, the REV and the correlation length are similar near the percolation threshold. In contrast, when the fracture density is much larger than the percolation threshold they diverge as the aperture variability increases. We characterize the effects of correlation length and aperture variability on effective conductivity with a simple function. From the coefficient of variation analysis, the correlation length can be a criterion for evaluating which conceptual model is appropriate for describing the flow system for a given fracture network when aperture variability is sufficiently small. However, discrete fracture network models are recommended for flow simulation models because of the difficulty of REV estimation and the uncertainty in equivalent hydraulic parameters when aperture variability is large.     

Numerical modeling of discrete multi-crack growth applied to pattern formation in geological brittle media

We describe a finite element-based method to propagate multiple fractures simultaneously. The algorithm is iterative and it simulates sub-critical quasi-static crack propagation. The matrix is homogeneous and isotropic, and behaves linear elastically. The algorithmic cornerstones are a failure criterion, a propagation criterion, and a propagation angle. Fracture geometries are kept track of independently of the mesh allowing geometric handling of fracture arrest, closure, and coalescence. Fracture aperture is an emergent property of the model. The mesh is adaptively remeshed to capture variations in the geometry and displacement field. Generated patterns reproduce observed crack paths in physical experiments. Algorithm efficiency scales linearly. The model reproduces en-echelon crack linkage, fracture hooking, and orthogonal tip approximation patterns. Our numerical experiments closely match physical experiments. Remeshing consumes <2% of the total computational time demonstrating current computational capabilities allow for discrete crack propagation to be viable for multiple crack propagation.     

Ecoulement visqueux entre deux cones coaxiaux

A numerical method of resolution of laminar incompressible flows in cones of revolution is proposed by asymptotic expansions in powers of 1/r (r radius vector). Remarks on linearity allow to calculate all wanted terms, function after function, by fourth-order Runge-Kutta process. Two examples are selected: the flow between two symmetric cones and one between a cone and a plane. The study of the flow between two symmetric cones as a function of the aperture angle reveals the existence of two patterns separated by a discontinuity at approximately 156°.     

Spark-generated bubble collapse near or inside a circular aperture and the ensuing vortex ring and droplet formation

This paper aims to study the oscillation of a sparkgenerated submerged bubble located near or inside a circular aperture made in a flat plate using high-speed visualization technique. In the case of a bubble oscillating near an aperture the initial free surface of the water was set at the bottom surface of the plate. The effects of aperture size and bubblefree surface distance on the bubble behavior as well as on the ensuing droplet dynamics are investigated. It was found that the direction of the bubble reentrant jet was towards the aperture or away from it respectively when the normalized aperture size was smaller or greater than a certain critical value. In addition, a toroidal vortex ring was observed to form, which rotated inwards as it moved away from the aperture. It was also found that if the bubble was incepted at a distance sufficiently away from a supercritical size aperture a single droplet could be produced. In the case of a bub- ble initiated in the middle of a circular aperture submerged just beneath the water free surface, the bubble was found to take the shape of an ellipsoid during its expansion. Then a reentrant jet was initiated and pierced the bubble from its top side.     

基于紊流状态的阻尼阀缝隙节流解析计算

提出了一种基于紊流状态的缝隙节流解析计算方法. 运用边界层理论给出紊流状态下流体的三层速度分布表达式,通过积分定理推导出平行平板的缝隙流量解析式,与CFD 软件数值解对比偏差很小,验证了方程的正确性. 以此为基础根据阻尼阀的结构特点又推导出同心环形缝隙的紊流流量公式,并分析不同物性参数对缝隙压差和流量的影响规律,填补了工程设计中没有紊流状态下缝隙节流解析式的空白,为提高阻尼阀的设计精度奠定了基础.     

散斑照相孔径优化的研究

本文提出了三种新的散斑照相孔径方法:一维调频孔径法,交叉孔径法和旋转孔径法。给出了理论分析和实验证明。这些方法简单实用,能有效地改变衍射晕的能量分布。适当选择孔径的参数,实验者能相当任意地控制散斑图的空间频率成份。新方法兼顾了突出某一频率成份、灵敏度连续可调、获得多个方向散斑场运动信息等各方面的特性。     

Transport of Neutrally Buoyant and Dense Variably Sized Colloids in a Two-Dimensional Fracture with Anisotropic Aperture

The transport of monodisperse as well as polydisperse colloid suspensions in a two-dimensional, water saturated fracture with spatially variable and anisotropic aperture is investigated with a particle tracking model. Both neutrally buoyant and dense colloid suspensions are considered. Although flow and transport in fractured subsurface formations have been studied extensively by numerous investigators, the transport of dense, polydisperse colloid suspensions in a fracture with spatially variable and anisotropic aperture has not been previously explored. Simulated snapshots and breakthrough curves of ensemble averages of several realizations of a log-normally distributed aperture field show that polydisperse colloids exhibit greater spreading than monodisperse colloids, and dense colloids show greater retardation than neutrally buoyant colloids. Moreover, it is demonstrated that aperture anisotropy oriented along the flow direction substantially increases colloid spreading; whereas, aperture anisotropy oriented transverse to the flow direction retards colloid movement.     

On the Rayleigh conductivity of a bias-flow aperture

An analysis is made of the attenuation of sound by vorticity production in a bias flow aperture. A modified form of the Cummings equation describing unsteady flow through a small aperture is used to extend the linear theory of the bias flow conductivity of a circular aperture in a thin wall of Howe (1979. On the theory of unsteady high Reynolds number flow through a circular aperture. Proceedings of the Royal Society of London A 366, 205–233) to a wall of arbitrary thickness and to examine the influence acoustic nonlinearity within the aperture. Numerical results are compared with existing analytic predictions of linear theory. It is shown that attenuations predicted by both linear and nonlinear theories agree over a wide range of incident acoustic pressures, approaching in amplitude that required to maintain the steady mean flow through the aperture. The dominant nonlinear effect is a small reduction (less than about 5%) in the mean bias flow velocity. Application of the Cummings equation in the linear regime leads to a new, simple formula for the bias flow conductivity for a screen of finite thickness.     

Hydraulic conductivity of rock fractures

The flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of fluid mechanics. The derivation of the cubic law is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates - the only fracture geometry that is amenable to exact treatment. The various geometric and kinematic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. In general, this requires a sufficiently low flow rate, and some restrictions on the spatial rate of change of the aperture profile. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area.     

Shock-Induced Borehole Waves and Fracture Effects

We perform wave experiments using a vertical shock tube setup. Shock waves are generated by the rupture of a thin membrane. In the test section, the incident pressure waves generate borehole-guided waves along water-saturated samples. The tube is equipped with side wall gages and a mobile pressure probe, so that the attenuation and reflection of the wave can be measured. The computation for a single horizontal fracture intersecting a vertical borehole gives a quantitative prediction of reflection and transmission of borehole-guided waves. Three different fracture apertures are used for the calculation. Fracture aperture significantly affects both reflection and transmission coefficients. Large fractures increase reflectivity and decrease transmissivity. In the experiment, we found that both pressures above and below the fracture are influenced by the fracture aperture indeed, thus indicating the potential for fracture detection by borehole waves.     

Shock-Induced Borehole Waves and Fracture Effects

We perform wave experiments using a vertical shock tube setup. Shock waves are generated by the rupture of a thin membrane. In the test section the incident pressure waves generate borehole-guided waves along water-saturated samples. The tube is equipped with side wall gages and a mobile pressure probe, so that the attenuation and reflection of the wave can be measured. The computation for a single horizontal fracture intersecting a vertical borehole gives a quantitative prediction of reflection and transmission of borehole-guided waves. Three different fracture apertures are used for the calculation. Fracture aperture significantly affects both reflection and transmission coefficients. Large fractures increase reflectivity and decrease transmissivity. In the experiment, we found that both pressures above and below the fracture are influenced by the fracture aperture indeed, thus indicating the potential for fracture detection by borehole waves.     

水力压裂解析模型裂缝扩展参数敏感性分析

水力压裂形成复杂裂缝网络是致密储层油气开采的重要技术,掌握水压裂缝扩展机理是控制压裂行为和优化压裂效果的关键．水压裂缝动态扩展行为涉及储层岩体、注入压裂液、压裂实施工艺等方面,其中水力压裂扩展时间、压裂液流体动力粘度系数、压裂液流体注入流速、储层岩石剪切模量成为决定裂缝扩展长度和裂缝开度的重要因素．本研究采用KGD、PKN两类等高解析模型对主控因素的参数敏感性进行分析,直观、快速、可靠地获得水压裂缝扩展长度、张开度动态演化行为的量化数值．研究发现,压裂持续开展过程中水压裂缝扩展长度呈线性增长、开度逐渐趋于稳定,高流体动力粘度导致裂缝难扩展、形成较大裂缝开度,通过增加压裂液流体注入流速可同时增加裂缝扩展长度和开度,较高的岩石剪切模量将降低水压裂缝的开度．通过对比两类解析模型在不同参数下的水压裂缝扩展结果,分析压裂参数与裂缝扩展的相关性和敏感系数,讨论水力压裂解析模型的裂缝扩展参数敏感性．     

Comparison of Symmetric and Asymmetric Schemes with Arithmetic and Harmonic Averaging for Fracture Flow on Cartesian Grids

Performance of four finite-difference schemes for fluid flow in rough-walled fractures on regular Cartesian grids is evaluated numerically. The four schemes are an asymmetric scheme with arithmetic averaging, an asymmetric scheme with harmonic averaging, a symmetric scheme with arithmetic averaging, and a symmetric scheme with harmonic averaging. The schemes are compared with respect to their simulated hydraulic aperture and the mass balance error. 1320 flow simulations with different grid sizes, mean fracture aperture and root mean square (RMS)/mean aperture ratio are completed. The asymmetric scheme with arithmetic averaging arises naturally, without any extra assumptions about the correct transmissivity averaging procedure, when one uses second-order finite differences to approximate the generalized Laplace operator expanded as a derivative of a product. Hydraulic apertures obtained with harmonic averaging are found to usually be smaller than those obtained with arithmetic averaging, especially when the ratio of aperture RMS to the mean aperture is larger. The traditionally used asymmetric schemes are found to be superior to symmetric schemes in terms of mass balance accuracy.

     

Exact solution of problem of deflection of an anisotropic plate with an aperture

The exact solution of the problem of the deflection of an anisotropic plate weakened by an aperture is known only for the case in which the aperture has the shape of a circle or an ellipse [1, 2]. An exact solution has not been derived for any other aperture shapes. Approximate methods [3–6] which are widespread for the case of multiply connected anisotropic plates [7] are applied to the determination of the bending moments in an anisotropic plate near an aperture differing little from an elliptical or circular one.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 168–177, September–October, 1977.     

A Dynamic Systems Approach to Understanding Reaching Movements with a Prosthetic Arm

A case study was conducted on an experienced upper extremity prosthetic user that required him to perform a reaching and grasping task with both his prosthetic and normal anatomical hand. We used a scanning task (Wallace, Stevenson, Spear, & Weeks, 1994; Button, Bennett, & Davids, 1998) that required the participant to perform a wide range of coordination patterns defined by the relative phasing between the aperture of the fingers (or artificial prehensor) and the arm. Visual templates of the required finger trajectories in the various required phase conditions served as environmental information for the subject to follow. Based on previous work, we hypothesized that the participant would exhibit at least one stable reaching and grasping pattern in both his anatomical and prosthetic arm. In support of this hypothesis, the results showed a negative sloping relationship between the required relative phase and the mean delta relative phase (required relative phase minus the actual relative phase). The smallest delta relative phase occurred at approximately 80° and 115° relative phase for the anatomical and prosthetic arm, respectively during the scanning task. These results confirm our previous work of the presence of only one attractor in reaching and grasping movements using either the anatomical or prosthetic arm.     

Focusing of an ultrasonic beam by a curved interface

We calculate the wavefields near the caustics, and their cusps, formed when a well collimated, ultrasonic beam scatters from a concave fluid-solid interface. The radius of curvature of the interface is assumed to be sufficiently large and the angle of incidence sufficiently small that only reflection and transmission of the beam need be considered. The incident beam is modeled as a two-dimensional wavefield whose initial profile is rectangular. The aperture is assumed to be sufficiently large (in wavelengths) that a well collimated beam is radiated, and the interface is assumed to lie close enough to the aperture that it is struck by a wavefield that has not yet evolved into a cylindrical wave. The scattered wavefields are represented as multiple integrals and are evaluated using a combination of asymptotic and numerical analysis. Special attention is given to the sometimes competing effects of the shadow boundary of each scattered beam with its corresponding caustic, and cusp if one is formed.     

Experimental study of oblique circular cylindrical apertures in plates

Ten steel plates weakened by the penetration of an oblique circular cylindrical aperture have been tested. The generator of the aperture makes 0-, 15-, 30- and 45-deg angles with the normal to the plate surface. In the case of the first seven models, the tractions were applied in the direction normal and parallel to the plane of symmetry. The strain distributions around the aperture are presented in nondimensional forms along three generators 45 deg apart. The last three models, with large aperture diameter, were tested to investigate the effect of thickness-to-diameter ratio for the three angles of skewness. The experimental results are compared with the theoretical predictions. It is noted that, for most of the plates, there was a fairly good agreement for the stress distribution throughout the thickness. The results of the experiments for uniaxial state of stress have been superimposed in order to obtain the response for various biaxial conditions.