Direct measurement of fluid velocity gradients at a wall by PIV image processing with stereo reconstruction

Velocity gradient is typically estimated in Particle Image Velocimetry (PIV) by differentiating a measured velocity field, which amplifies noise in the measured velocities. If gradients near a boundary are sought, such noise is usually greater than in bulk fluid, because of small tracer displacement, uncertainty in the effective positions of velocity vectors, intense deformation of tracer patterns, and laser reflection. We consider here a modified form of the Particle Image Distortion (PID) method todirectly calculate velocity gradients at a fixed wall, and refer it as “PIV/IG” (“Interface Gradiometry”). Results from synthetic 2D PIV images suggest our method achieves higher SNR and accuracy than velocity differentiation. Also, we have developed a procedure to reconstruct three-dimensional velocity gradient at a fixed wall the two non-zero components from PIV/IG data obtained in stereo views; these equations simplify considerably thanks to the no-slip condition. Experimental data from the bottom wall of turbulent open channel flow appear to suffer from a form of pixel locking. As with standard PIV, this underlines the importance of adequate tracer diameter in the images, sufficient seeding density, and of dynamic range of the camera sensor.     

Particle pairing using genetic algorithms for PIV

This paper presents a new particle pairing algorithm using “Genetic Algorithms” for DPIV (Digital Particle Image Velocimetry), which are searching algorithms for obtaining an optimal solution based on the mechanism of evolution. The particle pairing between two tracer images with a constant time interval is needed to obtain a velocity vector field. Since the algorithm adopts a fitness function which totally evaluates the similarity between respective small particle patterns in the two tracer images over the field, it promises to give a more correct velocity vector distribution than the conventional PTV (Particle Tracking Velocimetry) which identifies each particle based on its local information. In addition, a particle pattern matching for the similarity is performed after correcting fluid rotation. It therefore is robust against a high particle density and an increase in the time interval. The algorithm is applied to the PIV standard images distributed through the Internet (http://www.vsj.or.jp/piv). It gives a correct velocity vector distribution as a result even if a pair of the successive images has a large time interval.     

Dynamic analysis of bubble-driven liquid flows using time-resolved particle image velocimetry and proper orthogonal decomposition techniques

Abstract  

An experimental study to evaluate dynamic structures of flow motion and turbulence characteristics in bubble-driven water flow in a rectangular tank with a varying flow rate of compressed air is conducted. Liquid flow fields are measured by time-resolved particle image velocimetry (PIV) with fluorescent tracer particles to eliminate diffused reflections, and by an image intensifier to acquire enhanced clean particle images. By proper orthogonal decomposition (POD) analysis, the energy distributions of spatial and temporal modes are acquired. Time-averaged velocity and turbulent kinetic energy distributions are varied with the air flow rates. With increasing Reynolds number, bubble-induced turbulent motion becomes dominant rather than the recirculating flow near the side wall. Detailed spatial structures and the unsteady behavior of dominant dynamic modes associated with turbulent kinetic energy distributions are addressed.     

On the origins of decoherence and extinction contrast in phase-contrast imaging

A theoretical formalism describing the formation of images in a linear shift invariant X-ray optical system is derived within the wave-optical theory. It is applicable to a non-crystalline object consisting of two types of features, with the characteristic sizes which are respectively not smaller and much smaller than the resolution of the imaging system. This formalism is then applied to two phase-contrast imaging techniques, the propagation-based and analyser-based imaging. The obtained formulae for the intensity distribution in the image well explain the “decoherence effect” which is observed in the former technique and the “extinction contrast” which is a characteristic of the latter technique. This formalism is shown to be in good agreement with the results of the accurate numerical simulations, using rigorous wave-optical theory, of the propagation-based and analyser-based phase-contrast images of the model objects.     

水洞流场PIV显示与分析系统离轴测试校正

粒子图像测速技术(PIV)通过测量被测流场截面上每一位置点的速度,获得整个被测流场的信息.在PIV一般应用中所使用的照明激光片光与成像CCD装置的拍摄方向是垂直的,在某些应用场合受测试条件的限制,需要采用离轴方式进行测量,此时CCD成像方向与照明的激光片光不垂直,而是有一定夹角.离轴测试方式将对PIV系统的光学成像系统、示踪粒子选择和粒子图像处理带来影响.实验采用Scheimpflug离轴聚焦的方法对表面镀银高反射率的示踪粒子进行成像,通过调整成像透镜与CCD像面的夹角可获得清晰的粒子成像,并利用网格校正板和软件计算处理等方法有效校正了由于离轴测试带来的影响.     

Pipe flow measurement by using a side-scattering holographic particle imaging technique

A side scattering holographic particle imaging technique has been developed and demonstrated to be a capable tool for obtaining good quality images of a particle field in a high Reynolds number pipe flow. Instantaneous three-dimensional velocity components can be measured. The streamwise velocity error is estimated to be about 5%. Limitations of this optical set-up are discussed. The methodology and results presented will be of use for designing a pulsed laser holographic technique for turbulent velocity measurement or particle diagnostics in a pipe flow.     

Stereoscopic flow-tagging velocimetry

A laser-based method for measuring the three components of the velocity in a plane simultaneously and instantaneously without seed particles is presented. This is achieved by combining a laser flow-tagging technique with stereoscopic detection, in which the tagged flow is viewed from two different directions. A single CCD camera is employed for this purpose by using a new optical detection system. The flow tagging is performed by two consecutive laser pulses, i.e., “write” and “read” laser pulses. The write laser creates a grid of tracer molecules (NO) by inducing a photodissociation process. The three-dimensional motion of the tracer molecules is measured by a thick read laser sheet. Received: 22 July 1999 / Revised version: 5 August 1999 / Published online: 30 September 1999     

Phase contrast, phase retrieval and aberration balancing in shift-invariant linear imaging systems

We treat the problems of phase-contrast image formation, deterministic phase retrieval and aberration balancing, in the imaging of weak objects using two-dimensional shift-invariant linear imaging systems. Three classes of model sample are considered: weak phase objects, weak phase-amplitude objects and single-material weak phase-amplitude objects. For each class of sample we show how the various aberration coefficients, which characterise a given imaging system, contribute to the structure of the associated phase-contrast image. The corresponding inverse problem, of obtaining a closed-form expression for the input wave-field given one or more aberrated phase-contrast images of the same, is then examined. Two sample applications are considered: analyser-crystal phase-contrast imaging of weak objects using hard X-rays, and Zernike-type phase-contrast imaging. We close with a discussion of how coherent and incoherent aberrations may be “balanced” against one another, briefly mentioning the applications of this idea to both “deblur by defocus” and proximity-corrected X-ray lithography.     

On the Existence of Invariant Measure for Lagrangian Velocity in Compressible Environments

We study transport of a passive tracer particle in a time dependent turbulent flow in the medium with positive molecular diffusivity. We show that there exists then a probability measure equivalent to the underlying physical probability, corresponding to the Eulerian velocity field, under which the particle Lagrangian velocity observations are stationary. As an application we derive the existence of the Stokes drift and the effective diffusivity—the characteristics of the long time behavior of the particle motion.     

Application of PIV to over-expanded supersonic flows: Possibilities and limits

Two-dimensional velocity distributions outside a Mach 2.0 supersonic nozzle have been investigated using a digital particle im age velocimetry (PIV). Mean velocities , vor ticity field and volume dilatation field were obtained from PIV images using 0 .33 μm titanium dioxide (TiO₂) particle. The seeding particle of larger size , 1.4 μrn Ti0₂, was also used for the experimental comparison of velocity lag downstream of shock waves. The results have been compared and analyzed with schlieren photographs for the locations of shock waves and over-expanded shock structure to inspect possibilities and limits of a PIV technique to over-expanded supersonic flows. It is found that although the quantitative velocity measurement using PIV on over-expanded supersonic flows with large velocity and pressure gradients is limited, the locations of normal shock and oblique shock waves can be resolved by the axial/radial velocity fields, and over-expanded shock structure can be predicted by vorticity field and volume dilatation field which are acquired from the spatial differential of the velocity field.     

Quantitative phase-contrast imaging of cells with phase-sensitive optical coherence microscopy

We describe a method for en face phase-contrast imaging of cells with a fiber-based differential phase-contrast optical coherence microscopy system. Recorded en face images are quantitative phase-contrast maps of cells due to spatial variation of the refractive index and (or) thickness of various cellular components. Quantitative phase-contrast images of human epithelial cheek cells obtained with the fiber-based differential phase-contrast optical coherence microscopy system are presented.     

On the Asymptotic Behavior of an Ornstein-Uhlenbeck Process with Random Forcing

We study the asymptotic behavior of an inertial tracer particle in a random force field. We show that there exists a probability measure, under which the process describing the velocity and environment seen from the vantage point of the moving particle is stationary and ergodic. This measure is equivalent to the underlying probability for the Eulerian flow. As a consequence of the above we obtain the law of large numbers for the trajectory of the tracer. Moreover, we prove also some decorrelation properties of the velocity of the particle, which lead to the existence of a non-degenerate asymptotic covariance tensor. The research of both authors was supported by the Polish Committee for Scientific Research (KBN) grant No. 2PO3A03123.     

Particle velocity field measurement using an ultra-light membrane

The aim of this paper, is to present an innovative experimental approach to assess images of the acoustic particle velocity field using a laser vibrometer scanning an ultra-light membrane. Firstly, a theoretical part is devoted to the infinite membrane governing equations, and to its response to an acoustic incident plane wave. An impedance of the membrane is defined, and a mass correction factor is obtained for a plane wave in normal incidence, allowing to assess the particle velocity of the acoustic field without membrane from the measured velocity of the membrane. The practical realization of a finite membrane is reported in a second section, showing difficulties linked to membrane modes generated by an uncontrolled residual tension, also showing how those difficulties are overcome by weighing down the membrane and by applying the mass correction. Third and fourth parts of the article are dedicated to two-dimension applications, illustrating the implementation of the membrane approach in the case of a plate excited by a shaker, and in the case of a loudspeaker driven with a white noise. Results are encouraging, showing that a “heavy” membrane should be used in low frequency to avoid difficulties due to membrane modes, and a light one in high frequency to minimize the mass effect (that can be corrected only for plane wave in normal incidence) and to avoid potential interactions between the membrane and the air gap between the membrane and the source, when the membrane is placed in the near field.     

Mixing in a model gas turbine combustor studied by panoramic optical techniques

Using planar optical methods based on laser-induced fluorescence and particle image velocimetry instantaneous velocity fields and passive tracer concentration are measured simultaneously in a model of GT-combustor at realistic flow rates. Spatial distributions of velocity pulsations and passive tracer concentration pulsations are measured at air flow rate about 0.4 kg/s. Correlations of velocity and concentration pulsations are measured. The most intense turbulent mass flux in the region of swirling flow mixing layer was observed. The contribution of advective and turbulent components in the transfer of a passive tracer in the axial direction was estimated.     

Einstein Relation for a Tagged Particle in Simple Exclusion Processes

 It is known that the rescaled position of a tagged particle in symmetric simple exclusion processes converges to a diffusion. If now the tracer particle is driven by a small force, then it picks up a velocity. The Einstein relation states that in the limit, this velocity is proportional to the small force, and the constant of proportionality can be computed from the diffusion matrix of the tracer particle with no driving force. Such a relation is believed to be generally valid. In this article we establish its validity for all symmetric simple exclusion processes in dimension and we prove a density property for certain invariant states of the driven system. Received: 2 September 2001 / Accepted: 28 March 2002 Published online: 31 July 2002     

Stationarity of Lagrangian Velocity¶in Compressible Environments

We study the transport of a passive tracer particle by a random d-dimensional, Gaussian, compressible velocity field. It is well known, since the work of Lumley, see [13], and Port and Stone, see [20], that the observations of the velocity field from the moving particle, the so-called Lagrangian velocity process, are statistically stationary when the field itself is incompressible. In this paper we study the question of stationarity of Lagrangian observations in compressible environments. We show that, given sufficient temporal decorrelation of the velocity statistics, there exists a transformation of the original probability measure, under which the Lagrangian velocity process is time stationary. The transformed probability is equivalent to the original measure. As an application of this result we prove the law of large numbers for the particle trajectory. Received: 1 May 2001 / Accepted: 4 December 2001     

动态微粒场双脉冲全息图再现像的分离技术

双脉全息图可应用于动态微粒场中粒子形状、尺寸、密度和速度等分布参数的测定。但由于两个脉冲时刻所拍摄的粒子像只能同时再现,不能判断粒子运动速度的方向,在运动情况较复杂时,粒子的“配对”也很困难。本文提出一种技术,可以分别再现两个脉冲时刻的粒子场图像,从而实现粒子速度方向的判定,同时减小了配对困难。     

Dynamic behavior of non-uniform granular gases system with the fractal characteristic in one dimension

A one-dimensional dynamic model of polydisperse granular mixture with a power-law size distribution is presented, in which the particles are subject to inelastic mutual collisions and driven by Gaussian white noise. The particle size distribution of the mixture has the fractal characteristic, and a fractal dimension D as a measurement of the inhomogeneity of the particle size distribution is introduced. We define the global granular temperature and the kinetic pressure of the mixture, and obtain their expressions. By molecular dynamics simulations, we have mainly investigated how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the steady-state dynamic properties of the system, focusing on the global granular temperature, kinetic pressure, velocity distribution and distribution of interparticle spacing. Some novel results are found that, with the increase of the fractal dimension D, the global granular temperature and the kinetic pressure decrease, the velocity distribution deviates more obviously from the Gaussian one and the particles cluster more pronouncedly at the same value of the restitution coefficient e (0<e<1). On the other hand, as the restitution coefficient e decreases, the dynamic behavior has the similar evolution as above at the fixed fractal dimension D. The dynamic behavior changing with e and D is, respectively, presented.     

Dynamic and quantitative phase-contrast imaging of living cells under simulated zero gravity by digital holographic microscopy and superconducting magnet

The experiment of dynamic and quantitative phase-contrast imaging of living cells in simulated zero gravity environment were performed by using digital holographic microscopy (DHM) combined with a superconducting magnet (SM). The SM with large gradient high magnetic field was used to simulate zero gravity by levitating biological living samples. The proposed DHM system provided highly efficient and versatile means for dynamically and quantitatively phase-contrast imaging MC3T3-E1 cells. To our knowledge, the phase images of living cells undergoing modifications and division under simulated zero gravity were firstly obtained by using DHM-SM prototype.