A genetic algorithm particle pairing technique for 3D velocity field extraction in holographic particle image velocimetry

 This research explores a novel technique, using Genetic Algorithm Particle Pairing (GAPP) to extract three-dimensional (3D) velocity fields of complex flows. It is motivated by Holographic Particle Image Velocimetry (HPIV), in which intrinsic speckle noise hinders the achievement of high particle density required for conventional correlation methods in extracting 3D velocity fields, especially in regions with large velocity gradients. The GA particle pairing method maps particles recorded at the first exposure to those at the second exposure in a 3D space, providing one velocity vector for each particle pair instead of seeking statistical averaging. Hence, particle pairing can work with sparse seeding and complex 3D velocity fields. When dealing with a large number of particles from two instants, however, the accuracy of pairing results and processing speed become major concerns. Using GA’s capability to search a large solution space parallelly, our algorithm can efficiently find the best mapping scenarios among a large number of possible particle pairing schemes. During GA iterations, different pairing schemes or solutions are evaluated based on fluid dynamics. Two types of evaluation functions are proposed, tested, and embedded into the GA procedures. Hence, our Genetic Algorithm Particle Pairing (GAPP) technique is characterized by robustness in velocity calculation, high spatial resolution, good parallelism in handling large data sets, and high processing speed on parallel architectures. It has been successfully tested on a simple HPIV measurement of a real trapped vortex flow as well as a series of numerical experiments. In this paper, we introduce the principle of GAPP, analyze its performance under different parameters, and evaluate its processing speed on different computer architectures. Received: 7 September 1997/Accepted: 3 February 1998     

How to get spatial resolution inside probe volumes of commercial 3D LDA systems

In laser Doppler anemometry (LDA) it is often the aim to determine the velocity profile for a given fluid flow. The spatial resolution of such velocity profiles is limited in principal by the size of the probe volume. The method of using time of flight data from two probe volumes allows improvements of the spatial resolution by at least one order of magnitude and measurements of small-scale velocity profiles inside the measuring volume along the optical axis of commercial available 3D anemometers without moving the probe. No change of the optical set-up is necessary. An increased spatial resolution helps to acquire more precise data in areas where the flow velocity changes rapidly as shown in the vicinity of the stagnation point of a cuboid. In the overlapping region of three measuring volumes a spatially resolved 3D velocity vector profile is obtained in the direction of the optical axis in near plane flow conditions. In plane laminar flows the probe volume is extended by a few millimetres. The limitation of the method to a plane flow is that it would require a two-component LDA in a very special off-axis arrangement, but this arrangement is available in most commercial 3D systems.     

Measurement of Dean flow in a curved micro-tube using micro digital holographic particle tracking velocimetry

Digital micro holographic particle tracking velocimetry (HPTV) was used to measure the three-dimensional (3D) velocity field of a laminar flow in a curved micro-tube with a circular cross-section. The micro HPTV system consists of a high-speed camera and a single laser with an acoustic optical modulator (AOM) chopper. We obtained the temporal evolution of the instantaneous velocity field of water flow within curved micro-tubes with inner diameters of 100 and 300 μm. The 3D mean velocity-field distribution was obtained quantitatively by statistically averaging the instantaneous velocity fields. At low Dean numbers (De), a secondary flow was not generated in the curved tube; however, with increasing Dean number a secondary flow consisting of two large-scale counter-rotating vortices arose due to enhanced centrifugal force. To reveal the flow characteristics at high Dean numbers, the trajectories of fluid particles were evaluated experimentally from the 3D velocity-field data measured using the HPTV technique. The present experimental results, especially the 3D particle trajectories, are likely to be helpful in understanding mixing phenomena in curved sections of various 3D curved micro-tubes or micro-channels, as well as in the design of such structures.     

Measurement of laminar,transitional and turbulent pipe flow using Stereoscopic-PIV

Stereoscopic particle image velocimetry (SPIV) is applied to measure the instantaneous three component velocity field of pipe flow over the full circular cross-section of the pipe. The light sheet is oriented perpendicular to the main flow direction, and therefore the flow structures are advected through the measurement plane by the mean flow. Applying Taylor’s hypothesis, the 3D flow field is reconstructed from the sequence of recorded vector fields. The large out-of-plane motion in this configuration puts a strong constraint on the recorded particle displacements, which limits the measurement accuracy. The light sheet thickness becomes an important parameter that determines the balance between the spatial resolution and signal to noise ratio. It is further demonstrated that so-called registration errors, which result from a small misalignment between the laser light sheet and the calibration target, easily become the predominant error in SPIV measurements. Measurements in laminar and turbulent pipe flow are compared to well established direct numerical simulations, and the accuracy of the instantaneous velocity vectors is found to be better than 1% of the mean axial velocity. This is sufficient to resolve the secondary flow patterns in transitional pipe flow, which are an order of magnitude smaller than the mean flow.     

A tomographic PIV resolution study based on homogeneous isotropic turbulence DNS data

In order to accurately assess measurement resolution and measurement uncertainty in DPIV and TPIV measurements, a series of simulations were conducted based on the flow field from a homogeneous isotropic turbulence data set (Re _λ = 141). The effect of noise and spatial resolution was quantified by examining the local and global errors in the velocity, vorticity and dissipation fields in addition to other properties of interest such as the flow divergence, topological invariants and energy spectra. In order to accurately capture the instantaneous gradient fields and calculate sensitive quantities such as the dissipation rate, a minimum resolution of x/η = 3 is required, with smoothing recommended for the TPIV results to control the inherently higher noise levels. Comparing these results with experimental data showed that while the attenuation of velocity and gradient quantities was predicted well, higher noise levels in the experimental data led increased divergence.     

A particle image velocimetry system for microfluidics

 A micron-resolution particle image velocimetry (micro-PIV) system has been developed to measure instantaneous and ensemble-averaged flow fields in micron-scale fluidic devices. The system utilizes an epifluorescent microscope, 100–300 nm diameter seed particles, and an intensified CCD camera to record high-resolution particle-image fields. Velocity vector fields can be measured with spatial resolutions down to 6.9×6.9×1.5 μm. The vector fields are analyzed using a double-frame cross-correlation algorithm. In this technique, the spatial resolution and the accuracy of the velocity measurements is limited by the diffraction limit of the recording optics, noise in the particle image field, and the interaction of the fluid with the finite-sized seed particles. The stochastic influence of Brownian motion plays a significant role in the accuracy of instantaneous velocity measurements. The micro-PIV technique is applied to measure velocities in a Hele–Shaw flow around a 30 μm (major diameter) elliptical cylinder, with a bulk velocity of approximately 50 μm s^-1. Received: 26 November 1997/Accepted: 26 February 1998     

PIV measurements of a microchannel flow

 A particle image velocimetry (PIV) system has been developed to measure velocity fields with order 1-μm spatial resolution. The technique uses 200 nm diameter flow-tracing particles, a pulsed Nd:YAG laser, an inverted epi-fluorescent microscope, and a cooled interline-transfer CCD camera to record high-resolution particle-image fields. The spatial resolution of the PIV technique is limited primarily by the diffraction-limited resolution of the recording optics. The accuracy of the PIV system was demonstrated by measuring the known flow field in a 30 μm×300 μm (nominal dimension) microchannel. The resulting velocity fields have a spatial resolution, defined by the size of the first window of the interrogation spot and out of plane resolution of 13.6 μm× 0.9 μm×1.8 μm, in the streamwise, wall-normal, and out of plane directions, respectively. By overlapping the interrogation spots by 50% to satisfy the Nyquist sampling criterion, a velocity-vector spacing of 450 nm in the wall-normal direction is achieved. These measurements are accurate to within 2% full-scale resolution, and are the highest spatially resolved PIV measurements published to date. Received: 29 October 1998/Accepted: 10 March 1999     

Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer

A digital holographic microscope is used to simultaneously measure the instantaneous 3D flow structure in the inner part of a turbulent boundary layer over a smooth wall, and the spatial distribution of wall shear stresses. The measurements are performed in a fully developed turbulent channel flow within square duct, at a moderately high Reynolds number. The sample volume size is 90 × 145 × 90 wall units, and the spatial resolution of the measurements is 3–8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The paper describes the data acquisition and analysis procedures, including the particle tracking method and associated method for matching of particle pairs. The uncertainty in velocity is estimated to be better than 1 mm/s, less than 0.05% of the free stream velocity, by comparing the statistics of the normalized velocity divergence to divergence obtained by randomly adding an error of 1 mm/s to the data. Spatial distributions of wall shear stresses are approximated with the least square fit of velocity measurements in the viscous sublayer. Mean flow profiles and statistics of velocity fluctuations agree very well with expectations. Joint probability density distributions of instantaneous spanwise and streamwise wall shear stresses demonstrate the significance of near-wall coherent structures. The near wall 3D flow structures are classified into three groups, the first containing a pair of counter-rotating, quasi streamwise vortices and high streak-like shear stresses; the second group is characterized by multiple streamwise vortices and little variations in wall stress; and the third group has no buffer layer structures.     

A three-velocity-component laser-Doppler velocimeter for measurements inside the linear compressor cascade

A 24′′ (610 mm) access laser-Doppler velocimeter (LDV) system was developed to make simultaneous three-velocity-component measurements in a low speed linear cascade wind tunnel with moving wall simulation. The probe has a 610 mm access length and achieves a measurement spatial resolution of 100 μm by using off-axis optical heads. With the relatively large access length, the LDV probe allows for measurements from the side of a wind tunnel instead of through the tunnel floor, while the high spatial resolution allows for quality near-wall measurements. The probe has been tested in a zero-pressure gradient 2D turbulent boundary layer and the test results agree well with the experimental data measured with different LDV systems and hot-wire anemometery for the boundary layer flows. The energy spectral density was estimated using a slot correlation, and Von Kármán’s model for the energy-spectrum function was used to analyze the measured spectral data to estimate the turbulent kinetic energy dissipation rate, which compares favorably with the measured production values in the log-layer region of the turbulent boundary layer. Measurements are presented for the moving endwall boundary layer at the inlet of the linear compressor cascade facility to validate the capability of this LDV for tip leakage flow measurements. These results indicate that the moving endwall reduces velocity gradients in the near-wall region and results in less production of Reynolds stresses and turbulent kinetic energy compared to the stationary endwall case.     

A new facility for time-resolved PIV measurements in rotating channels

A new facility to measure the time evolution of 2D velocity fields in a rotating channel is presented, and the accuracy is discussed in detail. Measurements are made by means of a time-resolved PIV system composed of a continuous laser diode, coupled by a fiber optics cable to a laser plane optical module, and a CMOS high-speed camera. Both the PIV system and divergent channel are fixed on a 2.5 m rotating disk. This allows a direct measurement of the relative velocity of flows with Reynolds numbers between 3 × 10³ and 3 × 10⁴ and Rotation numbers between 0.0 and 0.52. These values correspond to the flow conditions in small radial impellers and can be independently adjusted by a change of the relative flow velocity and RPM. It is shown that this new facility allows high signal-to-noise ratios, and that the direct acquisition of the data in a rotating frame drastically reduces the measurement error. The accuracy and high spatial and temporal resolution of the measurements allow a detailed analysis of boundary layer characteristics in stationary and rotating conditions.     

Stereoscopic micro particle image velocimetry

A stereoscopic micro-PIV (stereo-μPIV) system for the simultaneous measurement of all three components of the velocity vector in a measurement plane (2D–3C) in a closed microchannel has been developed and first test measurements were performed on the 3D laminar flow in a T-shaped micromixer. Stereomicroscopy is used to capture PIV images of the flow in a microchannel from two different angles. Stereoscopic viewing is achieved by the use of a large diameter stereo objective lens with two off-axis beam paths. Additional floating lenses in the beam paths in the microscope body allow a magnification up to 23×. The stereo-PIV images are captured simultaneously by two CCD cameras. Due to the very small confinement, a standard calibration procedure for the stereoscopic imaging by means of a calibration target is not feasible, and therefore stereo-μPIV measurements in closed microchannels require a calibration based on the self-calibration of the tracer particle images. In order to include the effects of different refractive indices (of the fluid in the microchannel, the entrance window and the surrounding air) a three-media-model is included in the triangulation procedure of the self-calibration. Test measurement in both an aligned and a tilted channel serve as an accuracy assessment of the proposed method. This shows that the stereo-μPIV results have an RMS error of less than 10% of the expected value of the in-plane velocity component. First measurements in the mixing region of a T-shaped micromixer at Re = 120 show that 3D flow in a microchannel with dimensions of 800 × 200 μm² can be measured with a spatial resolution of 44 × 44 × 15 μm³. The stationary flow in the 200 μm deep channel was scanned in multiple planes at 22 μm separation, providing a full 3D measurement of the averaged velocity distribution in the mixing region of the T-mixer. A limitation is that this approach requires a stereo-objective that typically has a low NA (0.14–0.28) and large depth-of-focus as opposed to high NA lenses (up to 0.95 without immersion) for standard μPIV.     

Stereoscopic PIV on multiple color-coded light sheets and its application to axial flow in flapping robotic insect wings

Non-scanning volume flow measurement techniques such as 3D-PTV, holographic and tomographic particle image velocimetry (PIV) permit reconstructions of all three components (3C) of velocity and vorticity vectors in a fluid volume (3D). In this study, we present a novel 3D3C technique termed Multiple-Color-Plane Stereo Particle-Image-Velocimetry (color PIV), which allows instantaneous measurements of 3C velocity vectors in six parallel, colored light sheets. We generated the light sheets by passing white light of two strobes through dichroic color filters and imaged the slices by two 3CCD color cameras in Stereo-PIV configuration. The stereo-color images were processed by custom software routines that sorted each colored fluid particle into one of six gray-scale images according to its hue, saturation, and luminance. We used conventional Stereo PIV cross-correlation algorithms to compute a 3D planar vector field for each light sheet and subsequently interpolated a volume flow map from the six vector fields. As a first application, we quantified the wake and axial flow in the vortical structures of a robotic insect (fruit fly) model wing. In contrast to previous findings, the measured data indicate strong axial flow components on the upper wing surface, including axial flow in the leading-edge vortex core. Collectively, color PIV is robust against mechanical misalignments, avoids laser safety issues, and computes instantaneous 3D vector fields in a fraction of the time typical for other 3D systems. Color PIV might thus be of value for volume measurements of highly unsteady flows.     

Effect of particle number density in in-line digital holographic particle velocimetry

A digital in-line holographic particle tracking velocimetry (HPTV) system was developed to measure 3D (three-dimensional) velocity fields of turbulent flows. The digital HPTV (DHPTV) procedure consists of four steps: recording, numerical reconstruction, particle extraction and velocity extraction. In the recording step, a digital CCD camera was used as a recording device. Holograms contained many unwanted images or noise. To get clean holograms, digital image processing techniques were adopted. In the velocity extraction routine, we improved the HPTV algorithm to extract 3D displacement information of tracer particles. In general, the results obtained using HPTV were not fully acceptable due to technical limitations such as low spatial resolution, small volume size, and low numerical aperture (NA). The problems of spatial resolution and NA are closely related with a recording device. As one experimental parameter that can be optimized, we focused on the particle number density. Variation of the reconstruction efficiency and recovery ratio were compared quantitatively with varying particle number density to check performance of the developed in-line DHPTV system. The reconstruction efficiency represented the particle number distribution acquired through the numerical reconstruction procedure. In addition the recovery ratio showed the performance of 3D PTV algorithm employed for DHPTV measurements. The particle number density in the range of C _o = 13–17 particles/mm³ was found to be optimum for the DHPTV system tested in this study.     

Experimental scanning for simplifying the model of a stirred-tank flow

 Velocity measurements by two-component laser Doppler velocimetry (LDV) and laser sheet visualizations were used to analyze the 3D turbulent flow field in a stirred tank, for the purpose of reducing the intricacy of the hydrodynamics to more simple models. We first deal with the mean flow field measured, and the instantaneous visualized patterns, to appreciate the deviation from steadiness and predict the dispersion of particles from the mean motion alone. The study then focuses on the discharge flow from the agitator (Rushton turbine). The jet at the exit from the turbine is modeled in mean values. The flow instability as shown experimentally indicates that the Reynolds number plays no part in this phenomenon. A study based on dynamical system theory, considering a frequency modulation of the flow, shows the possibility of describing rather simply the deterministic component in the velocity fluctuation due to the blades. Received: 29 July 1997/Accepted: 11 November 1997     

Near-wall measurements of turbulence statistics in a fully developed channel flow with a novel laser Doppler velocity profile sensor

This paper reports on the measurements of the near-wall turbulence statistics in a fully developed channel flow. The flow measurements were carried out with a novel laser Doppler velocity profile sensor with a high spatial resolution. The sensor provides both the information of velocity and position of individual tracer particles inside the measurement volume. Hence, it yields the velocity profile inside the measurement volume, in principle, without the sensor being mechanically traversed. Two sensor systems were realized with different techniques. Typically the sensor has a relative accuracy of velocity measurement of 10⁻³ and the spatial resolution of a few micrometers inside the measurement volume of about 500 μm long. The streamwise velocity was measured with two independent sensor systems at three different Reynolds number conditions. The resulting turbulence statistics show a good agreement with available data of direct numerical simulations up to fourth order moment. This demonstrates the velocity profile sensor to be one of the promising techniques for turbulent flow research with the advantage of a spatial resolution more than one magnitude higher than a conventional laser Doppler technique.     

A-priori testing of an eddy viscosity model for the density-weighted subgrid scale stress tensor in turbulent premixed flames

In this study, we report on the direct measurement of the density-weighted subgrid scale (SGS) stress tensor in turbulent premixed flames. In large-eddy simulations (LES), this unresolved tensor is typically modelled using eddy viscosity approaches. Additionally to the direct measurement, we provide a pure experimentally based a-priori test of the commonly used eddy viscosity model suggested by Smagorinsky. For two turbulent premixed V-shaped methane–air flames, a statistical analysis is presented where the correlation between the directly measured SGS stress tensor and the eddy viscosity model following Smagorinsky is tested. The measurement strategy is based on the application of a dual-plane stereo-PIV technique which enables the measurement of the 3D flow field in two parallel planes. This allows the determination of velocities as well as velocity gradients in all three directions. Here, a vector resolution of 118 μm was achieved. For a priori testing, the data are subjected to a spatial filtering procedure that reproduces the application of the filter function in LES. The calculation of velocity gradients is performed after the application of this spatial averaging. Additionally to the velocity field, the flame front position is deduced from the clearly observable step in the tracer particle number density between burnt and unburnt regions of the flame. This facilitates the direct single-shot-based evaluation of all components of the density-weighted SGS stress tensor. Additionally, the model expressions related to these terms can be determined, which is done in this first study for the static Smagorinsky model. With that, the instantaneous local comparison between directly measured stress terms and modelled terms is possible, based on the instantaneous local evaluation procedure. The measurement procedure is described, and first results are presented and discussed. They show a rather poor performance of the static form of the Smagorinsky model (with fixed Smagorinsky constant). Our future aims are to use the directly measured SGS data for the a-priori comparison with more advanced models.     

In vivo whole-field blood velocity measurement techniques

In this article a number of whole-field blood velocity measurement techniques are concisely reviewed. We primarily focus on optical measurement techniques for in vivo applications, such as laser Doppler velocimetry (including time varying speckle), laser speckle contrast imaging and particle image velocimetry (including particle tracking). We also briefly describe nuclear magnetic resonance and ultrasound particle image velocimetry, two techniques that do not rely on optical access, but that are of importance to in vivo whole-field blood velocity measurement. Typical applications for whole-field methods are perfusion monitoring, the investigation of instantaneous blood flow patterns, the derivation of endothelial shear stress distributions from velocity fields, and the measurement of blood volume flow rates. These applications require individual treatment in terms of spatial and temporal resolution and number of measured velocity components. The requirements further differ for the investigation of macro-, meso-, and microscale blood flows. In this review we describe and classify those requirements and present techniques that satisfy them.     

Spatially adaptive PIV interrogation based on data ensemble

This paper proposes a specific application of the approach recently proposed by the authors to achieve an autonomous and robust adaptive interrogation method for PIV data sets with the focus on the determination of mean velocity fields. Under circumstances such as suboptimal flow seeding distribution and large variations in the velocity field properties, neither multigrid techniques nor adaptive interrogation with criteria based on instantaneous conditions offer enough robustness for the flow field analysis. A method based on the data ensemble to select the adaptive interrogation parameters, namely, the window size, aspect ratio, orientation, and overlap factor is followed in this study. Interrogation windows are sized, shaped and spatially distributed on the basis of the average seeding density and the gradient of the velocity vector field. Compared to the instantaneous approach, the ensemble-based criterion adapts the windows in a more robust way especially for the implementation of non-isotropic windows (stretching and orientation), which yields a higher spatial resolution. If the procedure is applied recursively, the number of correlation samples can be optimized to satisfy a prescribed level of window overlap ratio. The relevance and applicability of the method are illustrated by an application to a shock-wave-boundary layer interaction problem. Furthermore, the application to a transonic airfoil wake verifies by means of a dual-resolution experiment that the spatial resolution in the wake can be increased by using non-isotropic interrogation windows.     

Time-resolved velocity field measurements of separated flow in front of a vertical fence

 An experimental investigation of the velocity fields of the turbulent shear flow in front of a vertical fence was performed using a hybrid particle tracking velocimetry technique. The vertical fence, with an aspect ratio of 10, was embedded in a thin laminar boundary layer. The Reynolds number of the flow based on the fence height was about 5,000. The measured instantaneous velocity fields and flow visualization results revealed a complex but organized flow structure in front of the fence. The stagnation point detached from the surface of the fence, increasing the streamline curvature near the fence. Time resolved turbulence statistics were obtained and compared with those of a 3D junction flow. Received: 23 August 2000/Accepted: 1 February 2001     

圆柱尾流雷诺应力与平均运动变形率的空间弛豫效应

针对圆柱尾流中沿流向存在的Karman涡街周期性涡旋结构,对湍流雷诺应力与平均运动变形率之间的空间弛豫效应进行了实验研究.在回流式水槽中,放入不同直径的圆柱模型,获得不同雷诺数下的圆柱尾流,利用二维高时间分辨率粒子图像测速(TRPIV)技术测量圆柱尾流二维瞬时速度空间分布图像的时间序列.经过数字图像处理,获得二维雷诺应...