Theory of non-isotropic spatial resolution in PIV

The spatial resolution of the PIV interrogation technique is discussed from an analytical standpoint and assessed with Monte Carlo numerical simulation of particle image motion. The PIV measurement error associated with lack of spatial resolution is modelled associating the cross-correlation operator to a moving average filter. The error associated with the "low-pass filtering" effect is investigated by adopting a second-order polynomial expression for the velocity spatial distribution. According to the present error analysis, the measurement error is proportional to the second-order spatial derivative of the velocity field and increases with the square of the window linear size. The strategy for the selection of the window size and properties (aspect ratio and orientation) so as to minimize the error is discussed. The principle is based on nonisotropic interrogation windows of elliptical shape, with a constant area and elongated in the direction of the largest curvature radius. The nonisotropic parameters are defined as eccentricity and orientation, which are based on the local eigenvalues/vectors of the Hessian tensor of the displacement spatial distribution. The technique is implemented in a recursive PIV interrogation method. The performance of nonisotropic interrogation technique is assessed by means of synthetic PIV images, which simulate three situations: first, a one-dimensional sinusoidal shear displacement, which allows comparison of the cross-correlation spatial response with the transfer function of linear filters. Second, the stream-wise exponential velocity decay is simulated, which simulates the particle tracers decelerating downstream of a shock wave and gives an example of a flow with main velocity differences aligned with the velocity direction. The results show that keeping the image density fixed, the error caused by insufficient spatial resolution can be reduced by a factor two when a preferential direction is found in the flow field. Finally, a Lamb–Oseen vortex flow is presented, which shows the complex pattern formed by the interrogation windows in a two-dimensional case. In this case, the improvement in interrogation performance is limited due to the isotropic nature of the velocity spatial fluctuation.     

Limits on the resolution of correlation PIV iterative methods. Fundamentals

The spatial resolution of correlation particle image velocimetry (PIV) is a frequently addressed issue that still raises scientific interest. In conventional non-iterative PIV, the spatial resolution limits are of common knowledge (Willert and Gharib (1991) Exp Fluids 10:181–193; Raffel et al. (1998) ISBN 3-540-63683-8, Springer, Berlin Heidelberg New York, among others). On the contrary, those advanced iterative multipass methods that use image distortion techniques or multigrid techniques present a more complex scenario. One of the concepts that raises more debate is the limiting effect of the interrogation window size. This paper focuses on the subject, trying to clarify key points. The results indicate that iterative algorithms using an appropriate weighting function eliminate the window size from the ensemble of spatial resolution limits.     

动高压加载下锆基金属玻璃强度测量

为了研究Zr₅₁Ti₅Ni₁₀Cu₂₅Al₉金属玻璃的高压强度特性,进行了平靶冲击实验。采用反向碰撞方式,运用DISAR技术测量金属玻璃样品/LiF窗口界面粒子速度剖面,分析粒子速度剖面获得了37~66GPa压力范围锆基金属玻璃的屈服强度和剪切模量。实验结果表明,在上述压力范围金属玻璃的屈服强度和剪切模量均显示出一定程度的压力硬化效应,分析表明金属玻璃冲击加载波阵面剪应力衰减并非由损伤/破坏或温度软化等因素导致。     

A new particle tracking algorithm based on deterministic annealing and alternative distance measures

We describe a new particle tracking algorithm for the interrogation of double frame single exposure data, which is obtained with particle image velocimetry. The new procedure is based on an algorithm which has recently been proposed by Gold et al. (Gold et al., 1998) for solving point matching problems in statistical pattern recognition. For a given interrogation window, the algorithm simultaneously extracts: (i) the correct correspondences between particles in both frames and (ii) an estimate of the local flow-field parameters. Contrary to previous methods, the algorithm determines not only the local velocity, but other local components of the flow field, for example rotation and shear. This makes the new interrogation method superior to standard methods in particular in regions with high velocity gradients (e.g. vortices or shear flows). We perform benchmarks with three standard particle image velocimetry (PIV) and particle tracking velocimetry (PTV) methods: cross-correlation, nearest neighbour search, and image relaxation. We show that the new algorithm requires less particles per interrogation window than cross-correlation and allows for much higher particle densities than the other PTV methods. Consequently, one may obtain the velocity field at high spatial resolution even in regions of very fast flows. Finally, we find that the new algorithm is more robust against out-of-plane noise than previously proposed methods. Received: 1 March 1999 / Accepted: 29 July 1999     

Turbulent transport dissimilarity with modulated turbulence structure in channel flow of viscoelastic fluid

This experimental study investigated the turbulent transport dissimilarity with a modulated turbulence structure in a channel flow of a viscoelastic fluid using simultaneous particle image velocimetry and planar laser-induced fluorescence measurements. An instantaneous dye concentration field with fluctuating velocity vectors showed that mass was transferred by hierarchically large-scale wavy motions with inclination. A co-spectral analysis showed that the spatial phase modulation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation corresponded to the relaxation time. The occurrence of intense dye concentration fluctuation and small streamwise velocity fluctuation in a thin boundary layer caused dissimilar turbulent transport because of the non-zero negative correlation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation only on large scales. This explains the turbulent transport dissimilarity which leads to the zero averaged Reynolds shear stress and non-zero wall-normal turbulent mass flux.     

The unsteadiness of shock waves propagating through gas-particle mixtures

A shock wave which is incident onto a gas-particle mixture or initiated within such a mixture needs a certain distance to reach a constant velocity. This effect is due to the inertia and the heat capacity of the particles. In general the shock wave is decelerated and the frozen pressure jump is decaying. A vertical shock tube was used in order to produce a plane shock wave incident onto a homogeneous gas-particle mixture. In addition to measurements of the shock velocity and the pressure history along the total low pressure section, the particle velocity was measured within the relaxation zone far downstream of the diaphragm using a laser-Doppler-velocimeter. Thus a drag law describing the particle acceleration within the relaxation zone was derived from the measurements. To compare the experiments with theoretical results, calculations were performed by the random-choice method.     

Direct measurement of local instantaneous laminar burning velocity by a new PIV algorithm

This paper presents a new experimental approach using PIV technique to measure the local instantaneous laminar burning velocity of a stretched premixed flame. Up to now, from experimental techniques, this physical property was only accessible in average and the instantaneous interactions of flame with flow structures, mixture variations and walls could not be considered. In the present work, the local burning velocity is measured as the difference between the local flame speed and the local fresh gas velocity at the entrance of the flame zone. Two original methods are proposed to deduce these quantities from pair of particle images. The local flame speed is measured from the distance between two successive flame positions. For the flame localization, a new extraction tool combined with a filtering technique is proposed to access to the flame front coordinates with sub-pixel accuracy. The local fresh gas velocity near the flame front is extracted from the maximum of the normal velocity profile, located within 1 mm ahead of the flame front. To achieve the required spatial resolution, a new algorithm based on adaptive interrogation window scheme has been developed by taking into account the flow and flame front topologies. The accuracy and reliability of our developments have been evaluated from two complementary approaches based, respectively, on synthetic images of particle and on the well-established configuration of outwardly propagating spherical flames. In the last part of the paper, an illustration of the potentials of our new approach is shown in the case of a laminar flame propagating through a stratified mixture.     

A closed model of fluctuating particle motion in a turbulent flow

Random particle motion in a turbulent and molecular velocity fluctuation field is considered. Using a spectral representation of the carrier-phase Eulerian velocity fluctuation correlations, a closed system of integral equations for calculating the carrier-phase velocity correlation along the particle trajectory and the particle Lagrangian velocity fluctuation correlation is obtained. Based on this system, the fluctuations of the particle parameters are analyzed. In the limiting case of a passive admixture, an estimate is found for the ratio of the integral Lagrangian and Eulerian time scales and the Kolmogorov constant for the Lagrangian structure function of the carrier-phase velocity fluctuations.     

PIV measurements of turbulent flow in planar mixing layer

A turbulent mixing layer consists of two different flow types, i.e. shear layer (shear-flow turbulence) and free stream regions (nearly homogeneous turbulence). The inherent non-uniform seeding tracer distributions observed around the interfaces between the shear layer and two free stream regions usually lead to a difficulty in particle image velocimetry (PIV) measurements. A parametric study on the application of PIV to the measurement of velocity field in a planar mixing layer is made by means of six factors, including interrogation window size, aspect ratio of interrogation window, interrogation window offset, threshold of data validation, sharpening spatial filters (Prewitt and Sobel masks), and smoothing spatial filter (median mask). The objective of this study is to obtain accurate turbulent measurements in both mean and fluctuating velocities using PIV under an appropriate parametric setting. The optimal levels, which are trade-off in between the accuracy and fine spatial resolution of velocity field measurements, are determined with the aid of the Taguchi method. It is shown that the PIV measurements made with this optimal set of parameters are in good agreement with the measurements made by a two-component hot-wire anemometer. Case independency of the proposed optimal set of parameters on the flow condition of the mixing layer is validated through the applications to two additional tests under the different experimental conditions in changing solely either velocity ratio of high-speed to low-speed free stream velocities or Reynolds number.     

Particle tracer response across shocks measured by PIV

The experimental approach used for the evaluation of the particle response time across a stationary shock wave is assessed by means of PIV measurements. The study focuses on the experimental requirements for a reliable and unbiased measurement of the particle response time τ _p and length ξ _p based on a single-exponent decaying law. A numerical simulation of the particle response experiment returns the parameters governing the measurement: namely the normalized spatial and temporal resolution, shock strength, and digital resolution. Representing the velocity decay in logarithmic coordinates it is shown that measurements performed with laser pulse separation time up to τ _p and interrogation window up to ξ _p still yield unbiased results for the particle response. A set of experiments on the particle response across a planar oblique shock wave was conducted to verify the results from the numerical assessment. Liquid droplets of DEHS and solid tracer particles of silicon and titanium dioxide with different primary crystal size are compared. The resulting temporal response ranges from 2 to 3 μs, corresponding to values commonly reported in literature, to almost 0.3 μs when particles are properly dehydrated and a filter is applied before injection into the wind tunnel. It is the first experimental evidence of particle tracers with a measured response time lower than 0.4 μs. The same procedure is applied to attempt the measurement of individual particle tracers by particle tracking velocimetry to estimate the spread in the distribution of tracer time response. The latter analysis is limited by the particle image tracking precision error, which biases the results introducing a wider broadening of the particle velocity distribution.     

[100]LiF单晶在60 GPa以内冲击加载下的高压屈服强度特性

获取光学窗口自身的高压强度特性是开展材料高压高应变率冲击响应行为精密测量和数据反演的重要基础。利用平板撞击和双屈服面法,通过冲击-卸载、冲击-再加载原位粒子速度剖面精细测量和数据反演,获得了约60 GPa范围内[100]LiF屈服强度特性随冲击压力的变化规律。结果表明:在实验压力范围内,[100]LiF的屈服强度随加载压力的提高而显著提高,压力硬化效应显著;同时,LiF在冲击加载下的屈服强度高于磁驱准等熵加载结果,应变率硬化效应强于热软化效应。采用Huang-Asay模型确定了可描述冲击加载[100]LiF强度特性的本构模型参数,为LiF在强度、相变、层断裂等加窗测量实验中的深入应用和数据准确解读提供了重要支撑。     

Theory of cross-correlation analysis of PIV images

To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability.For the direct cross-correlation method of single-exposure, double-frame systems which model video array detector interrogation and of double-exposure single-frame systems which generalize earlier direct auto-correlation methods of interrogation of photographic recordings, optimal system parameters are recommended for a range of velocity fields in order to eliminate signal bias and to minimize loss of signal strength. The signal bias resulting from velocity gradients in auto-correlation analysis can be eliminated in cross-correlation interrogation by appropriate choice of the optimal parameters. Resolution, detection rate, accuracy and reliability are compared with direct auto-correlation methods for double- and multiple-pulsed systems.     

Particle image velocimetry measurements of a shock wave/turbulent boundary layer interaction

Particle image velocimetry is used to investigate the interaction between an incident shock wave and a turbulent boundary layer at Mach 2.1. A particle response assessment establishes the fidelity of the tracer particles. The undisturbed boundary layer is characterized in detail. The mean velocity field of the interaction shows the incident and reflected shock wave pattern, as well as the boundary layer distortion. Significant reversed flow is measured instantaneously, although, on average no reversed flow is observed. The interaction instantaneously exhibits a multi-layered structure, namely, a high-velocity outer region and a low-velocity inner region. Flow turbulence shows the highest intensity in the region beneath the impingement of the incident shock wave. The turbulent fluctuations are found to be highly anisotropic, with the streamwise component dominating. A distinct streamwise-oriented region of relatively large kinematic Reynolds shear stress magnitude appears within the lower half of the redeveloping boundary layer. Boundary layer recovery towards initial equilibrium conditions appears to be a gradual process.     

On improvement of PIV image interrogation near stationary interfaces

In this paper the problem posed by interfaces when present in PIV measurements is addressed. Different image pre-processing, processing and post-processing methodologies with the intention to minimize the interface effects are discussed and assessed using Monte Carlo simulations. Image treatment prior to the correlation process is shown to be incapable of fully removing the effects of the intensity pedestal across the object edge. The inherent assumption of periodicity in the signal causes the FFT-based correlation technique to perform the worst when the correlation window contains a signal truncation. Instead, an extended version of the masking technique introduced by Ronneberger et al. (Proceedings of the 9th international symposium on applications of laser techniques to fluid mechanics, Lisbon, 1998) is able to minimize the interface-correlation, resolving only the particle displacement peak. Once the displacement vector is obtained, the geometric center of the interrogation area is not the correct placement. Instead, the centre of mass position allows an unbiased representation of the wall flow (Usera et al. in Proceedings of the 12th international symposium on applications of laser techniques to fluid mechanics, Lisbon, 2004). The aforementioned concepts have been implemented in an adaptive interrogation methodology (Theunissen et al. in Meas Sci Technol 18:275–287, 2007) where additionally non-isotropic resolution and re-orientation of the correlation windows is applied near the interface, maximizing the wall-normal spatial resolution. The increase in resolution and robustness are demonstrated by application to a set of experimental images of a flat-plate, subsonic, turbulent boundary layer and a hypersonic flow over a double compression ramp.     

在球面散心冲击波作用下JB-9014炸药冲击引爆过程实验研究

采用双灵敏度VISAR对JB-9014炸药在20 GPa的球面散心冲击波作用下冲击引爆过程开展了实验研究。测得的不同厚度JB-9014炸药/窗口界面的粒子速度历程表明,到爆轰距离为2~3 mm,在3~5mm处反应冲击波已发展为稳定爆轰波。开展了相应的初步数值计算工作,计算结果与实验基本吻合。     

Two-color particle image velocimetry technique for an internal combustion engine

A two-color particle image velocimetry (PIV) technique has been applied to a single-cylinder motored research engine. Two-color PIV is a quantitative planar velocity measurement technique that can unambiguously determine the velocity magnitude and direction.

The work includes the development of an interrogation system, a series of computer simulations to determine the performance of the technique under various conditions, the comparison of these results to similar ones obtained for an autocorrelation PIV system, and a test of the technique by reconstructing the velocity field of a uniform jet flow.

The technique was then applied to the in-cylinder flow field of a motored single-cylinder, cup-in-head, research engine. A total of 27 instantaneous velocity fields were obtained at a single measurement plane for a single operating condition of the engine. The data were analyzed to yield ensemble-averaged velocity and velocity fluctuation.     

Stereo particle image velocimetry of nonequilibrium turbulence relaxation in a supersonic boundary layer

Measurements using stereo particle image velocimetry are presented for a developing turbulent boundary layer in a wind tunnel with a Mach 2.75 free stream. As the boundary layer exits from the tunnel nozzle and moves through the wave-free test section, small initial departures from equilibrium turbulence relax, and the boundary layer develops toward the equilibrium zero-pressure-gradient form. This relaxation process is quantified by comparison of first and second order mean, fluctuation, and gradient statistics to classical inner and outer layer scalings. Simultaneous measurement of all three instantaneous velocity components enables direct assessment of the complete turbulence anisotropy tensor. Profiles of the turbulence Mach number show that, despite the M = 2.75 free stream, the incompressibility relation among spatial gradients in the velocity fluctuations applies. This result is used in constructing various estimates of the measured-dissipation rate, comparisons among which show only remarkably small differences over most of the boundary layer. The resulting measured-dissipation profiles, together with measured profiles of the turbulence kinetic energy and mean-flow gradients, enable an assessment of how the turbulence anisotropy relaxes toward its equilibrium zero-pressure-gradient state. The results suggest that the relaxation of the initially disturbed turbulence anisotropy profile toward its equilibrium zero-pressure-gradient form begins near the upper edge of the boundary layer and propagates downward through the defect layer.     

Mirror particle-tracking-velocimetry in a strip-coded light-sheet: a new method to determine the wall-shear-stress field

In this paper we present a new technique to measure the wall-shear-stress named mirror PTV (MPTV). The basic principle is the use of a reflective coated surface to record the flow in the very near wall region in such way, that the original particle and its mirror image are detected. The distance between the original particle image and its corresponding mirror image is used to calculate the wall-normal distance of the particle. With the information of particle motion between successive illuminations it is possible to determine the wall-shear-stress with high temporal and spatial resolution from the velocity gradient at the wall to a first order approximation, i.e. assuming a linear velocity profile. To validate the technique, the wall-shear-stress-distribution in a wall-bounded jet is measured and compared with the theoretical solution of Glauert (1956). The results agree well with the theoretical solution.     

Numerical simulation of expansion/compression effect on shock induced turbulent flow

The interaction of homogeneous and isotropic turbulence with a shock wave is observed by solving the Reynolds-averaged Navier–Stokes equations with the k–? turbulence model. All turbulent fluctuations are measured at the period of expansion in the turbulent field and during compression by the reflected shock on turbulent field, and it is observed that the longitudinal turbulent velocity fluctuation is enhanced more at the period of expansion due to incident shock wave movement far from the turbulent field. The amplification of the turbulent kinetic energy (TKE) level in the shock/turbulence interaction depends on the shock wave strength and the longitudinal velocity difference across the shock wave. On decreasing the longitudinal velocity difference across the shock, the turbulent kinetic energy (TKE) level is less amplified. The TKE level is amplified by the factor of 1.5–1.8 in the shock/turbulence interaction where the dissipation rate of TKE decreases in all cases of shock/turbulence interaction. After the shock/turbulence interaction, the turbulent dissipative-length scale is amplified slightly and the amplification of the length scales decreases when increasing the shock strength. To cite this article: M.A. Jinnah, K. Takayama, C. R. Mecanique 333 (2005).     

Simultaneous measurements of velocity and density in buoyancy-driven mixing

A variant of the particle image velocimetry (PIV) technique is described for measuring velocity and density simultaneously in a turbulent Rayleigh-Taylor mixing layer. The velocity field is computed by the usual PIV technique of cross-correlating two consecutive images, and deducing particle displacements from correlation peaks of intensity fields. Different concentrations of seed particles are used in the two streams of different temperature (density) fluids, and a local measure of the density is obtained by spatially averaging over an interrogation window. Good agreement is reported between the first- and second-order statistics for density obtained from this technique and from a thermocouple. Velocity-density correlations computed by cross-correlating individual time series are presented. The errors in the density measurements are quantified and analyzed, and the issue of spatial resolution is also discussed. Our purpose for this paper is to introduce the PIV-S method and validate its accuracy against corresponding thermocouple measurements.