Tomographic particle image velocimetry

This paper describes the principles of a novel 3D PIV system based on the illumination, recording and reconstruction of tracer particles within a 3D measurement volume. The technique makes use of several simultaneous views of the illuminated particles and their 3D reconstruction as a light intensity distribution by means of optical tomography. The technique is therefore referred to as tomographic particle image velocimetry (tomographic-PIV). The reconstruction is performed with the MART algorithm, yielding a 3D array of light intensity discretized over voxels. The reconstructed tomogram pair is then analyzed by means of 3D cross-correlation with an iterative multigrid volume deformation technique, returning the three-component velocity vector distribution over the measurement volume. The principles and details of the tomographic algorithm are discussed and a parametric study is carried out by means of a computer-simulated tomographic-PIV procedure. The study focuses on the accuracy of the light intensity field reconstruction process. The simulation also identifies the most important parameters governing the experimental method and the tomographic algorithm parameters, showing their effect on the reconstruction accuracy. A computer simulated experiment of a 3D particle motion field describing a vortex ring demonstrates the capability and potential of the proposed system with four cameras. The capability of the technique in real experimental conditions is assessed with the measurement of the turbulent flow in the near wake of a circular cylinder at Reynolds 2,700.     

Tomographic particle tracking velocimetry using telecentric imaging

The goal of this article is to discuss 3D Particle Tracking Velocimetry (PTV) in a tomographic reconstructed voxel space with at least doubling the spatial resolution compared to classical 3D PTV. For this purpose, a new tomographic reconstruction technique based on telecentric imaging in combination with the epipolar geometry is presented. The method overcomes the need for memory intensive weighting matrices or cost intensive iterations, which are necessary in iterative algebraic reconstruction techniques. A characteristic of tomographic reconstruction is the reconstruction of ghost particles. As the aim of PTV is the reconstruction of true particle paths, this article focuses on the removal of ghost particles and ghost trajectories. The method is validated via a synthetic turbulent flow field and via the benchmark experiment of a vortex ring.     

Three-dimensional tomographic reconstruction of unstable ejection phenomena of droplets for electrohydrodynamic jet

The electrohydrodynamic (EHD) jet is becoming increasingly popular within industrial printing areas based on phenomena induced by electrical potentials. Regardless of the physical observations of unstable ejection phenomena in regions possessing high electric potential, quantitative visualization is still necessary; no report exists exemplifying quantitative visualization. Thus, the size, shape and position of EHD droplets were reconstructed in this study using developed three-dimensional tomography methods. Two computer-synthesized phantoms for the liquid meniscus containing small satellite droplets were generated according to actual images captured by two high-speed cameras. These droplets were made in order to numerically reconstruct droplet behavior. Four three-dimensional tomography methods, such as the algebraic reconstruction technique (ART), the adaptive algebraic reconstruction technique (AART), the simultaneous iterative reconstruction technique (SIRT) and the multiplicative algebraic reconstruction technique (MART), were developed to accurately mimic droplet movement using multiple image views. Four basis functions including the cubic B-spline, cosine, o-Moms and Keys basis functions were adopted in order to improve the performance of the tomographic reconstructions. After completing a comparison of the four tomography results, the MART method in association with the cubic cosine basis function was selected as the means to significantly improve reconstruction accuracy. Additionally, it was the applied method for the reconstruction of the droplet behavior from experimental projections by two cameras.     

Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005). This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.     

解三维摩擦接触问题的一个二阶锥线性互补法

针对三维摩擦接触问题的求解,给出了一种基于参变量变分原理的二阶锥线性互补法. 首先,基于三维Coulomb摩擦锥在数学表述上属于二阶锥的事实,利用二阶锥规划对偶理论,建立了三维Coulomb摩擦接触条件的参变量二阶锥线性互补模型,它是二维Coulomb摩擦接触条件参变量线性互补模型在三维情形下的自然推广;随后,利用参变量变分原理与有限元方法,建立了求解三维摩擦接触问题的二阶锥线性互补法. 较之于将三维Coulomb摩擦锥进行显式线性化的线性互补法,该方法无需对三维Coulomb摩擦锥进行线性化,因而在保证精度的前提下所解问题的规模要小很多. 最后通过算例展示了该方法的特点.      

Computed tomographic X-ray velocimetry for simultaneous 3D measurement of velocity and geometry in opaque vessels

Computed tomographic X-ray velocimetry has been developed for simultaneous three-dimensional measurement of flow and vessel geometry. The technique uses cross-correlation functions calculated from X-ray projection image pairs acquired at multiple viewing angles to tomographically reconstruct the flow through opaque objects with high resolution. The reconstruction is performed using an iterative, least squares approach. The simultaneous measurement of the object’s structure is performed with a limited projection tomography method. An extensive parametric study using Monte Carlo simulation reveals accurate measurements with as few as 3 projection angles, and a minimum required scan angle of only 30°. When using a single/source detector system, the technique is limited to measurement of periodic or steady flow fields; however, with the use of a multiple source/detector system, instantaneous measurement will be possible. Synchrotron experiments are conducted to demonstrate the simultaneous measurement of structure and flow in a complex geometry with strong three-dimensionality. The technique will find applications in biological flow measurement, and also in engineering applications where optical access is limited, such as in mineral processing.     

Application of the maximum entropy technique in tomographic reconstruction from laser diffraction data to determine local spray drop size distribution

This work proposes a new deconvolution technique to obtain local drop size distributions from line-of-sight intensity data measured by laser diffraction technique. The tomographic reconstruction, based on the maximum entropy (ME) technique, is applied to forward scattered light signal from a laser beam scanning horizontally through the spray on each plane from the center to the edge of spray, resulting in the reconstructed scattered light intensities at particular points in the spray. These reconstructed intensities are in turn converted to local drop size distributions. Unlike the classical method of the onion peeling technique or other mathematical transformation techniques that yield unrealistic negative scattered light intensity solutions, the maximum entropy constraints ensure positive light intensity. Experimental validations to the reconstructed results are achieved by using phase Doppler particle analyzer (PDPA). The results from the PDPA measurements agree very well with the proposed ME tomographic reconstruction.     

A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate

This paper investigates the plane problem of a frictional receding contact formed between an elastic functionally graded layer and a homogeneous half space, when they are pressed against each other. The graded layer is assumed to be an isotropic nonhomogeneous medium with an exponentially varying shear modulus and a constant Poisson’s ratio. A segment of the top surface of the graded layer is subject to both normal and tangential traction while rest of the surface is devoid of traction. The entire contact zone thus formed between the layer and the homogeneous medium can transmit both normal and tangential traction. It is assumed that the contact region is under sliding contact conditions with the Coulomb’s law used to relate the tangential traction to the normal component. Employing Fourier integral transforms and applying the necessary boundary conditions, the plane elasticity equations are reduced to a singular integral equation in which the unknowns are the contact pressure and the receding contact lengths. Ensuring mechanical equilibrium is an indispensable requirement warranted by the physics of the problem and therefore the global force and moment equilibrium conditions for the layer are supplemented to solve the problem. The Gauss–Chebyshev quadrature-collocation method is adopted to convert the singular integral equation to a set of overdetermined algebraic equations. This system is solved using a least squares method coupled with a novel iterative procedure to ensure that the force and moment equilibrium conditions are satisfied simultaneously. The main objective of this paper is to study the effect of friction coefficient and nonhomogeneity factor on the contact pressure distribution and the size of the contact region.     

求解Rayleigh阻尼系数的加权最小二乘法

在地震反应分析过程中,提出了一种优化方法以解决Rayleigh阻尼系数计算时选择两阶合理参考频率的难题。该方法是以反应谱理论为基础,以结构位移峰值误差最小为目标函数。将位移反应谱用一阶Taylor级数近似计算,从而将目标函数简化为加权最小二乘法的方程。随后以框架结构为例,讨论了模态个数和阻尼比模型对Rayleigh阻尼系数计算的影响,并与传统方法、最小二乘法及基于多参考振型的加权最小二乘法进行比较。计算结果表明,最小二乘法由于忽略了模态贡献的影响,不是计算Rayleigh阻尼系数的合理方法。当模态个数所包含的累积振型参与质量达90%以上,本文方法所得Rayleigh阻尼系数计算结果稳定,结构动力反应的计算精度高。     

A new computational algorithm for contact friction modeling of large plastic deformation in powder compaction processes

In this paper, the large deformation frictional contact of powder forming process is modeled based on a new computational algorithm by imposing the contact constraints and modifying the contact properties of frictional slip. A simple and efficient numerical algorithm is presented for imposing the contact constraints and frictional contact properties based on the node-to-surface contact technique to simulate the large deformation contact problem in the compaction process of powder. The Coulomb friction law is used to simulate the friction between the rigid punch and the workpiece by the use of penalty approach. A double-surface cap plasticity model is employed together with the nonlinear contact friction algorithm within the framework of large FE deformation in order to predict the non-uniform relative density distribution during large deformation of powder die-pressing. Finally, the numerical schemes are examined for accuracy and efficiency in modeling of a set of powder components.     

Friction measurement at low sliding speed using a servohydraulic tension-torsion machine

A method is presented for the determination of the coefficient of friction at low sliding speeds down to 3 nm/s. It is also possible to vary the contact pressure. The maximum average contact pressure is 40 MPa in the present test configuration, where a servohydraulic tension-torsion machine is used. The method, involving test equipment, measurement and the principles of evaluation, is exemplified by a study where the variation of the coefficient of friction with sliding velocity contact pressure and surface roughness is investigated for the material combination steel and concrete. The measurements have been performed as a 2³ factorial design. An error analysis was performed and the relative measurement uncertainty when determining the coefficient of friction was estinated to be 1.2 percent.     

Electromagnetic tomography (EMT): Theoretical analysis of the forward problem

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EFFECT OF INTERGRANULAR FRICTION ON THE BOTTOM FORCE CHAIN OF TWO-DIMENSIONAL PARTICLE PILES WITH POINT DEFECTS1)

力链对颗粒物质的宏观与微观力学性质起着决定性的作用。在离散元法的基础上,建立二维规则排列的颗粒物质系统,分别研究无缺陷颗粒系统在集中载荷变化与有缺陷颗粒系统在缺陷区域改变时,粒间摩擦系数对颗粒系统底部接触力分布规律的影响。结果表明：在无缺陷颗粒系统中,颗粒系统底部接触力的分布形式受摩擦系数和集中载荷的大小影响。随摩擦系数的增大,底部接触力由双峰形式经平台过渡,逐渐向单峰形式转变。在有缺陷颗粒系统中,摩擦系数和缺陷尺寸对底部接触力分布均有影响。同种载荷作用下,随缺陷尺寸的增大,底部接触力峰值显著增大;底部平均力被明显削弱,力向边界的传递增强。系统中轴线上缺陷的存在使底部中间区域受力削弱,当缺陷尺寸超过2 层以上时,底部中间力随摩擦系数的变化特征由递增曲线演变为线形衰减曲线。     

HC轧机辊间接触与辊系变形的Taylor级数多极边界元数学规划解析

分析HC轧机辊间接触分布和辊系弹性变形对于改善辊间压力分布状态,减少轧故褂檬倜案纳瓢逍畏浅Ｖ匾?醯捎诩扑懔亢艽?使用传统数值方法(有限元法或边界元法)分析辊间接触和辊系变形是非常困难的.本文描述了一种基于点-面接触模型的三维弹性接触Taylor级数多极边界元法,给出了数学规划解析方法,适合大规模弹性接触问题的求解....     

高速列车制动闸片摩擦块形状对制动界面摩擦学行为的影响

在自行研制的高速列车制动缩比试验台上,对六边形、五边形和圆形摩擦块进行拖曳制动试验,研究摩擦块形状对高速列车制动界面摩擦学行为的影响,并采用有限元方法分析了不同摩擦块形状下制动界面接触行为的差异,探讨了摩擦块形状对接触压力分布及表面热分布的影响. 结果表明:摩擦块形状显著影响了制动界面磨损特性及接触压力分布,使得制动盘产生不同的温度分布现象. 在本试验条件下,六边形摩擦块表面磨损轻微,接触平台大小较为均匀,而五边形和圆形摩擦块表面呈现明显的犁沟和剥落特征,且大接触平台占比较高;六边形摩擦块与制动盘拖曳制动过程,界面具有较大的接触面积,使得接触压力分布较为均匀,表现出较好的接触行为,而五边形和圆形摩擦块的接触行为相对较为复杂,与之对摩的制动盘产生明显的热聚集现象.      

正畸弓丝与托槽间摩擦力建模及试验研究

正畸矫治过程中,正畸弓丝与托槽间的相对滑动趋势将产生摩擦力,进而降低有效矫治力,影响矫治的性能和效率. 针对目前正畸摩擦力预测方法量化预测精度低的问题,依据正畸弓丝与托槽间的几何关系、力学关系及物理参数,提出一种基于分力叠加原理的计及接触角度的正畸摩擦力预测模型建立方法. 探究影响正畸摩擦力的主要因素以及变化规律,提出采用有限滑动法测量正畸摩擦力,搭建了基于六维力传感器的正畸摩擦力测量系统,进行了不同弓丝-托槽组合和不同接触角度的摩擦力测量,试验数据与预测模型的理论数据间误差率处于0.55%~9.65%之间,证明该预测模型可为医师明确正畸矫治器参数-摩擦力-矫治力的关系提供理论依据,为实现数字化正畸提供理论支撑,保证个性化正畸方案的高效、高可靠性和高舒适度,最终达到轻力矫治的效果.      

Fretting contact of two elastic solids with graded coatings under torsion

In this paper, the fretting contact problem for two elastic solids with graded coatings is investigated. We assume a conventional axisymmetric Hertzian contact takes place between two elastic solids under the action of the normal pressure. The application of the torque produces an annulus of slip. It is assumed that the surface shear traction within the contact area is limited by Coulomb’s friction law and the torsion angel was produced within the central adhesion zone as a rigid body. The linear multi-layer model is used to model the functionally graded coating with arbitrarily varying shear modulus. This model divides the coating into a series of sub-layers with the elastic modulus varying linearly in each sub-layer and continuous on the sub-interfaces. By using the transfer matrix method and Hankel integral transform technique, this problem is formulated as the solution of the Cauchy singular integral equations. The contact tractions are calculated by solving the equations numerically. The results show that the appropriate gradual variation of the shear modulus can significantly alter the contact tractions. Therefore, graded coatings may have potential applications in improving the resistance to fretting contact damage at the contact surfaces.     

A weighted least squares method for first-order hyperbolic systems

The paper presents a generalization of the classical L²-norm weighted least squares method for the numerical solution of a first-order hyperbolic system. This alternative least squares method consists of the minimization of the weighted sum of the L² residuals for each equation of the system. The order of accuracy of global conservation of each equation of the system is shown to be inversely proportional to the weight associated with the equation. The optimal relative weights between the equations are then determined in order to satisfy global conservation of the energy of the physical system. As an application of the algorithm, the shallow water equations on an irregular domain are first discretized in time and then solved using Laplace modification and the proposed least squares method.     

Contact analysis in presence of spherical inhomogeneities within a half-space

This paper presents a fast method of solving contact problems when one of the mating bodies contains multiple heterogeneous inclusions, and numerical results are presented for soft or stiff inhomogeneities. The emphasis is put on the effects of spherical inclusions on the contact pressure distribution and subsurface stress field in an elastic half-space. The computing time and allocated memory are kept small, compared to the finite element method, by the use of analytical solution to account for the presence of inhomogeneities. Eshelby’s equivalent inclusion method is considered in the contact solver. An iterative process is implemented to determine the displacements and stress fields caused by the eigenstrains of all spherical inclusions. The proposed method can be seen as an enrichment technique for which the effect of heterogeneous inclusions is superimposed on the homogeneous solution in the contact algorithm. 3D and 2D Fast Fourier Transforms are utilized to improve the computational efficiency. Configurations such as stringer and cluster of spherical inclusions are analyzed. The effects of Young’s modulus, Poisson’s ratio, size and location of the inhomogeneities are also investigated. Numerical results show that the presence of inclusions in the vicinity of the contact surface could significantly changes the contact pressure distribution. From a numerical point of view the role of Poisson’s ratio is found very important. One of the findings is that a relatively ‘soft’ and nearly incompressible inclusion – for example a cavity filled with a liquid – can be more detrimental for the stress state within the matrix than a very hard inclusion with a classical Poisson’s ratio of 0.3.     

The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field

Three-dimensional density information of a double free air jet was acquired using optical tomography. The projections of the density field were measured using the background oriented schlieren method (BOS). Preceding the free jet measurements, the sensitivity, accuracy and resolution of the BOS method were investigated. The sensitivity depends mostly on the focal length of the lens used, the relative position of the object between camera and background and the smallest detectable shift in the image plane. The accuracy was found to be sufficiently high to apply a tomographic reconstruction process. The resolution is determined by the transfer function of the BOS-method. It is not constant and depends on the size of the interrogation windows used for the cross-correlation-algorithm. The reconstruction of the free jet was computed, using filtered back projection. The reconstructed 3D density field shows with good resolution the typical diamond structure of the density distribution in under-expanded free jets.