A new neural network for particle-tracking velocimetry

 We describe a new neural network designed to solve the correspondence problem of particle-tracking velocimetry. Given two successive pictures of marker-particles suspended in a fluid, it matches their images by approximately duplicating the fluid motion. We present the results of efficiency tests that reveal the excellence of its performance and its stability with respect to the presence of unmatchable particle images. We compare its success rate in image matching to that of the neural network of Grant and Pan (1995), and observe that it produces better results when the flows have more important changes in direction. It has the important advantages over the latter, of being better adapted to benefit from parallel computing, and of being self-starting, i.e. of not requiring to be taught about the fluid flow in advance. Received: 18 September 1997/Accepted: 11 August 1998     

A collision algorithm for anisotropic disperse flows based on ellipsoidal parcel representations

In this study, a new approach to the prediction of collision probabilities is proposed, which is specifically derived for Lagrangian Monte Carlo simulations of highly anisotropic disperse flows. The collision probability formulation eliminates the influence of the collision mesh by introduction of a parcel diameter. Two non-parametric parcel diameter estimators are given, an isotropic parcel diameter estimator for homogeneous droplet clouds, and an anisotropic parcel diameter estimator for inhomogeneous droplet clouds of reduced dimensionality, which obtains an ellipsoidal parcel representation from a weighted principal component analysis of the parcel population. The new formulation effectively reduces the parameters for spatial resolution from two (mesh size, number of parcels) to one (number of parcels only). For validation, simple synthetic test cases are run that allow a comparison of the collision probability formulation to purely stochastic and purely deterministic schemes. Dependence on numerical parameters is tested exemplary with a highly anisotropic hollow-cone spray for gasoline direct injection.     

Investigation on time scales in a low Reynolds number jet flow using particle-tracking velocimetry

The near flow field of an axisymmetric water jet at Reynolds numbers between 2000 and 5000 is investigated using Particle-Tracking Velocimetry. Measurements are taken in the longitudinal section (along the mean flow) and in cross-sections (orthogonal to the mean flow). From the former, correlation coefficients of the two in-plane velocity components in a Lagrangian framework are obtained: thus Lagrangian integral scales can be computed. Those of the streamwise velocity (axial) component increase on moving away from the centreline, whereas the opposite happens for the vertical velocity (radial) component: integral time scales of the two components are almost equal at the interface between jet and ambient fluids. On the other hand, integral scales are almost constant or increase slightly with the axial direction. In cross-sections, fluid ejection and injection from the jet centreline are observed to be connected to counter-rotating vortices (mushroom): their number and size change with Reynolds number in agreement with results from other authors. The maximum ejection velocity (orthogonal to the mean jet flow), at 3 nozzle diameters downstream of the outlet, is found to be one half of the mean outlet velocity.     

The structure of the head of an inertial gravity current determined by particle-tracking velocimetry

Digital particle-tracking velocimetry is used to obtain the two-dimensional structure of the head of inertial gravity currents propagating along a no-slip boundary. The early stage of development of lock-release gravity current experiments is recorded in the laboratory frame of reference and subsequently transformed by software to a frame moving with the current head. Time averages of these statistically stationary flows are computed, with the technique providing not only the mean two-dimensional velocity field but also the vorticity, shear stress and divergence fields, and streamlines of the flows. The distributions of the magnitude of the fluid velocity fluctuation and Reynolds stress complete the picture of the flow. Key features of the flow are broadly in line with earlier qualitative and quantitative investigations, and the detailed measurements presented here confirm some of the most recent findings from numerical simulations.     

Burnett equations for the ellipsoidal statistical BGK model

In order to discuss the agreement of the ellipsoidal statistical BGK (ES-BGK) model with the Boltzmann equation, Burnett equations are computed by means of the second-order Chapman-Enskog expansion of the ES-BGK model. It is found that the Burnett equations for the ES-BGK model with the correct Prandtl number are identical to the Burnett equations for the Boltzmann equation for Maxwell molecules (fifth-order power potentials). However, for other types of particle interaction, the Boltzmann Burnett equations cannot be reproduced from the ES-BGK model.Furthermore, the linear stability of the ES-BGK Burnett equations is discussed. It is shown that the ES-BGK Burnett equations are linearly stable for Prandtl numbers of and for , while they are linearly unstable for and .Received: 29 April 2003, Accepted: 20 June 2003PACS: 510.10.-y, 47.45.-n Correspondence to: Y. Zheng     

Spatially averaged time-resolved particle-tracking velocimetry in microspace considering Brownian motion of submicron fluorescent particles

A time-series measurement method is proposed to detect velocity fields in a microchannel taking into account Brownian motion of submicron tracer particles. The present study proposes spatially averaged time-resolved particle-tracking velocimetry (SAT–PTV), which can detect temporal variations of fluid flow and eliminate errors associated with Brownian motion without losing temporal resolution. Velocity vectors of tracer particles obtained by PTV are spatially averaged in each interrogation window of particle-image velocimetry, yielding full velocity field information with temporal resolution. Synthetic particle images, which include Brownian motion of submicron fluorescent particles in flow fields with linear velocity gradients, are generated to validate the ability of SAT–PTV to track particles. SAT–PTV correctly captures the velocity gradient profiles. The spatial resolution based on the size of the first interrogation window and the measurement depth of the microscope system is 6.7 m×6.7 m×1.9 m, within which several vectors are averaged. SAT–PTV is shown to measure the velocity field of a pulsating flow generated by an electrokinetic pump.An earlier version of this paper appeared in the Fourth International Symposium on Particle Image Velocimetry at Göttingen, Germany, 17–19 September 2001.     

New tracking algorithm for particle image velocimetry

The cross correlation tracking technique is widely used to analyze image data, in Particle Image Velocimetry (PIV). The technique assumes that the fluid motion, within small regions of the flow field, is parallel over short time intervals. However, actual flow fields may have some distorted motion, such as rotation, shear and expansion. Therefore, if the distortion of the flow field is not negligible, the fluid motion can not be tracked well using the cross correlation technique. In this study, a new algorithm for particle tracking, called the Spring Model technique, has been proposed. The algorithm can be applied to flow fields which exhibit characteristics such as rotation, shear and expansion.The algorithm is based on pattern matching of particle clusters between the first and second image. A particle cluster is composed of particles which are assumed to be connected by invisible elastic springs. Depending on the deformation of the cluster pattern (i.e., the particle positions), the invisible springs have some forces. The smallest force pattern in the second image is the most probable pattern match to the correspondent original pattern in the first image. Therefore, by finding the best matches, particle movements can be tracked between the two images. Three-dimensional flow fields can also be reconstructed with this technique.The effectiveness of the Spring Model technique was verified with synthetic data from both a two-dimensional flow and three-dimensional flow. It showed a high degree of accuracy, even for the three-dimensional calculation. The experimental data from a vortex flow field in a cylinder wake was also measured by the Spring model technique.     

Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow

Using a three-dimensional (3-D) particle-tracking velocimeter, detailed turbulent flow measurements were made in a plane channel with a one-sided 50% abrupt expansion, which acted as a backward-facing step. The turbulent channel flow reached a fully developed state well upstream of the step. The Reynolds number based on the upstream centerline velocity and the step height H was 5540. With the mean reattachment point located at 6.51H downstream of the step, the measurement region ranged from −2H upstream to 12H downstream of the step. Various turbulent statistics and the energy budget were calculated from numerous instantaneous vector distributions. As in previous experimental investigations, the Reynolds normal and shear stresses had maximum values upstream of the reattachment. The stress anisotropy tensor revealed a peculiar phenomenon near the reattachment wall, wherein the spanwise normal stress was the largest among the three normal stresses. The triple velocity correlations indicated large values in the separating shear layer, and hence the turbulent diffusion was a major term in the energy budget. Comparison was made between the present results and those of the direct numerical simulation (DNS) of Le et al. (1993), and it was found that the mean and fluctuating velocities, the Reynolds shear stress, and the turbulent energy budget were in excellent agreement, although there was a considerable difference in the inflow conditions.     

A non-Fickian,particle-tracking diffusion model based on fractional Brownian motion

The work is motivated by the recent discovery that ocean surface drifter trajectories contain fractal properties. This suggests that the dispersion of pollutants in coastal waters may also be described using fractal statistics. The paper describes the development of a fractional Brownian motion model for simulating pollutant dispersion using particle tracking. Numerical test cases are used to compare this new model with the results obtained from a traditional Gaussian particle-tracking model. The results seems to be significantly different, which may have implications for pollution modelling in the coastal zone. © 1997 John Wiley & Sons, Ltd.     

Parallel finite element algorithm based on full domain partition for stationary Stokes equations

Based on the full domain partition, a parallel finite element algorithm for the stationary Stokes equations is proposed and analyzed. In this algorithm, each subproblem is defined in the entire domain. Majority of the degrees of freedom are associated with the relevant subdomain. Therefore, it can be solved in parallel with other subproblems using an existing sequential solver without extensive recoding. This allows the algorithm to be implemented easily with low communication costs. Numerical results are given showing the high efficiency of the parallel algorithm.     

多体系统动力学方程的无违约数值计算方法

多体系统动力学方程为3阶微分代数方程,已有的约束违约稳定法存在位移违约问题,数值仿真准确性和稳定性不足。本文将求解高阶微分代数方程的降阶理论、ε嵌入处理方式与隐式龙格库塔法相结合,提出了直接满足位移约束条件的多体系统动力学方程的无违约算法,避免了约束违约问题。该方法先将多体动力学方程转化为2阶微分代数方程,并与位移约束方程联立;再应用ε嵌入隐式龙格库塔法进行数值求解。应用两种方法分别对单摆机构进行数值仿真,结果表明本文的方法不仅能适应较大步长,且准确性和稳定性均优于约束违约稳定法。     

基于全隐式无分裂算法求解三维N-S方程

基于多块结构网格,本文研究和发展了三维N-S方程的全隐式无分裂算法.对流项的离散运用Roe格式,粘性项的离散利用中心型格式.在每一次隐式时间迭代中,运用GMRES方法直接求解隐式离散引起的大型稀疏线性方组.为了降低内存需求以及矩阵与向量之间的运算操作数,Jacobian矩阵的一种逼近方法被应用在本文的算法之中.计算结果与实验结果基本吻合,表明本文的全隐式无分裂方法是有效和可行的.     

An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations

In this paper, an approach to improve the application of the differential quadrature method for the solution of Navier–Stokes equations is presented. In using the conventional differential quadrature method for solving Navier–Stokes equations, difficulties such as boundary conditions' implementation, generation of an ill conditioned set of linear equations, large memory storage requirement to store data, and matrix coefficients, are usually encountered. Also, the solution of the generated set of equations takes a long running time and needs high computational efforts. An approach based on the point pressure–velocity iteration method, which is a variant of the Newton–Raphson relaxation technique, is presented to overcome these problems without losing accuracy. To verify its performance, four cases of two‐dimensional flows in single and staggered double lid‐driven cavity and flows past backward facing step and square cylinder, which have been often solved by researchers as benchmark solution, are simulated for different Reynolds numbers. The results are compared with existing solutions in the open literature. Very good agreement with low computational efforts of the approach is shown. It has been concluded that the method can be applied easily and is very time efficient. Copyright © 2012 John Wiley & Sons, Ltd.     

Single-camera Doppler global velocimetry based on frequency modulation techniques

The main advantage of the described Doppler global velocimeter (DGV) systems based on frequency modulation (FM) or frequency shift keying (FSK) is that no reference detector is required. The frequency variation of the laser light during one modulation period additionally allows an on-line calibration of the complete DGV system. Thus, the new method has the potential to reduce the uncertainty of conventional DGV velocity measurements since time resolved velocity field measurements on a spinning disc have shown standard deviations down to 0.02 m/s. On investigating flow fields, velocity components notably less than 0.5 m/s were resolved.     

Particle tracking velocimetry with an ant colony optimization algorithm

A new concept algorithm based on the ant colony optimization is developed for the use in 2-D and 3-D particle tracking velocimetry (PTV). In the particle matching process of PTV, the ant colony optimization is usually aimed at minimization of the sum of the distances between the first-frame and second-frame particles. But this type of minimization often goes unsuccessfully in the regions where the particles are located very close to each other. In order to avoid this flaw, a new type of minimization is attempted using a physical property corresponding to the flow consistency or the quasi-rigidity of particle distribution patterns. Specifically, the ant colony optimization is now aimed at minimization of the sum of the relaxation of neighbor particles. In the present study, the new algorithm is applied to sets of 2-D and 3-D synthetic particle images as well as the experimental images with successful results.     

Rheological equations of state of weakly concentrated suspensions of rigid ellipsoidal particles

Rheological equations of state of dilute suspensions of rigid ellipsoidal particles (ellipsoids of revolution) are derived [1–4] from the vantage point of the structural-continuum approach, with attention given both to rotational Brownian motion of particles and to their inertia and the outer force fields. Interaction between particles is ignored in those treatments given the low concentration of the suspended particles. In this paper, the earlier findings [1–4] are generalized to higher concentrations. The effect of hydrodynamical interaction between particles on the rheological behavior of the suspension is treated in the light of the Simha approach [5].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 141–145, January–February, 1973.     

A molecular filter based velocimetry technique for high speed flows

A molecular absorption filter-based diagnostic technique has been developed to obtain instantaneous, planar velocity measurements in high speed flows. This paper presents the details of the technique and its application in high Reynolds number compressible mixing layers with convective Mach numbers of 0.51 and 0.86. Pressure broadening was used to tune the absorption profile of the filter to a given flow field/optical arrangement. It is shown that two filters can be used when background scattering is significant: one as the velocity-discriminating filter, the other to eliminate unwanted background light from the reference camera. Collected images show instantaneous variations in velocity within both the highly organized roller type structures of the M _c = 0.51 mixing layer and the unorganized structures found in both mixing layers. An uncertainty analysis showed that the measurement uncertainty was ±8.6% for the current measurements, but improvements to reduce the uncertainty to ±3% are suggested.The authors would like to acknowledge support for this research from NASA Lewis Research Center under Dr. K. B. M. Q. Zaman (NAG3-764) the Air Force Office of Scientific Research under Dr. L. Sakell (AFOSR-91-0412), and an equipment grant from NSF (CTS-9006879). A fellowship from NSF to S. A. Arnette is gratefully acknowledged. The authors also wish to thank the AARL staff and graduate students M.F. Reeder and V.M. Belovich for their help. Thanks go to Prof. R.B. Miles and J.N. Forkey of Princeton University for their cooperation in obtaining measurements of the absorption profiles.     

Soil flow analysis for grouser wheels based on a particle image velocimetry method

This paper presents an analysis, based on a particle image velocimetry method, of soil flow field beneath a grouser wheel traveling over loose soil. Although the grouser wheel is expected to have better traction and mobility over fine, loose soil, its interaction mechanisms with the soil remain to be elucidated. Thus, a particle image velocimetry-based soil flow analysis is conducted to directly observe soil behavior around the grouser wheel. In the experimental analysis, key parameters of the soil flow field, such as general shape, thickness, streamlines of the flow field, soil velocity on the streamlines, and soil failure angle are examined quantitatively. From the results, the soil flow shape periodically changes with wheel rotation, and this change appears, depending on wheel slip varying over time. Furthermore, the experimental result of the soil failure angle differs drastically from its typical theory. These results will contribute to modeling the mechanical interaction between the grouser wheel and soil.     

Rheological equations of state of weak solutions of polymers as rigid ellipsoidal macromolecules

Rheological equations of state are obtained for weak solutions of polymers as rigid ellipsoidal macromolecules, taking into account the rotational Brownian motion of the macromolecules, their energy, and the external force fields (electric and magnetic). As an example the effect of the inertia of the macromolecules on the rheological behavior of the solutions is examined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 125–129, March–April, 1972.