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     

Time-series PIV measurements in a very large rotating tank

 We describe a non-intrusive PIV system developed for performing high-resolution measurements in a field of view of 2 m×3 m, as required on the LEGI-Coriolis 13 m diameter rotating platform. Particle preparation, laser illumination, photographic digitization, and cross-correlation analysis techniques are explained. Some results on the wake behind a cylinder illustrate the possibilities of this PIV system. Received: 29 October 1996/Accepted: 5 April 1997     

Quantum nanospheres for sub-micron particle image velocimetry

Quantum Nanospheres™ (QNs) have been developed as a new type of flow-tracing particle for micron resolution particle image velocimetry (PIV). The 70 nm diameter QNs were created by conjugating quantum dots to polystyrene beads. The fluorescent QNs have a large Stokes’ shift and are impervious to photobleaching. The use of QNs as flow-tracing particles for micro-PIV was demonstrated by measuring fluid motion in a 30 × 300 μm channel. Using an interrogation region of 1 × 1,024 pixels and ensemble averaging 1,800 image pairs, the physical volume of the interrogation region was 117 μm × 117 μm × 2 μm.     

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.     

Investigation of boundary layers in internal combustion engines using a hybrid algorithm of high speed micro-PIV and PTV

Heat transfer properties vary locally and temporally in internal combustion engines due to variations in the boundary layer flow. In order to characterize the dynamics in the boundary layer, crank-angle resolved high-speed micro particle image velocimetry (μPIV) and particle tracking velocimetry (PTV) have been used for near-wall velocity measurements in a spark-ignition direct-injection single cylinder engine. A 527-nm dual cavity green Nd:YLF laser was used for velocity measurements near the cylinder head wall between the intake and exhaust valves in the tumble mean flow plane parallel to the cylinder axis. A long-distance microscope was used to obtain a spatial resolution of 45 μm. Flow fields were determined from 180 to 490 CAD in the compression and expansion strokes. The data show significant variation in the flow during the compression and expansion strokes and from cycle to cycle. Flow deceleration was observed during the end of the compression that continued during the expansion stroke until 400 CAD when the flow direction reverses. Sub-millimeter-sized vortical structures were observed within the boundary layer over extended periods of time.     

Application of the PIV technique to measurements around and inside a forming drop in a liquid–liquid system

A particle image velocimetry (PIV) method has been developed to measure the velocity field inside and around a forming drop with a final diameter of 1 mm. The system, including a microscope, was used to image silicon oil drops forming in a continuous phase of water and glycerol. Fluorescent particles with a diameter of 1 μm were used as seeding particles. The oil was forced through a 200 μm diameter glass capillary into a laminar cross-flow in a rectangular channel. The velocity field was computed with a double-frame cross-correlation function down to a spatial resolution of 21 × 21 μm. The method can be used to calculate the shear stress induced at the interface by the cross-flow of the continuous phase and the main forces involved in the drop formation process.     

Stereoscopic PIV measurements of a turbulent boundary layer with a large spatial dynamic range

The flow in a streamwise/wall-normal plane of a turbulent boundary layer at moderate Reynolds number (Re _θ = 2,200) is characterized using two stereo PIV systems just overlapping in the streamwise direction. The aim is to generate SPIV data for near-wall turbulence with enough spatial dynamic range to resolve most of the coherent structures present in the flow and to facilitate future comparisons with direct numerical simulations. This is made possibly through the use of four cameras with large CCD arrays (4,008 px × 2,672 px) and through a rigorous experimental procedure designed to minimize the impact of measurement noise on the resolution of the small scales. For the first time, both a large field of view [S _x ; S _y ] = [2.6δ; 0.75δ] and a high spatial resolution (with an interrogation window size of 13.6⁺) have been achieved. The quality of the data is assessed through an analysis of some of the statistical results such as the mean velocity profile, the rms and the PDF of the fluctuations, and the power spectra.     

Interfacial PIV to resolve flows in the vicinity of curved surfaces

PIV measurements near a wall are generally difficult due to low seeding density, low velocity, high velocity gradient, and strong reflections. Such problems are often compounded by curved boundaries, which are commonly found in many industrial and medical applications. To systematically solve these problems, this paper presents two novel techniques for near-wall measurement, together named Interfacial PIV, which extracts both wall-shear gradient and near-wall tangential velocity profiles at one-pixel resolution. To deal with curved walls, image strips at a curved wall are stretched into rectangles by means of conformal transformation. To extract the maximal spatial information on the near-wall tangential velocity field, a novel 1D correlation function is performed on each horizontal pixel line of the transformed image template to form a “correlation stack”. This 1D correlation function requires that the wall-normal displacement component of the particles be smaller than the particle image diameter in order to produce a correlation signal. Within the image regions satisfying this condition, the correlation function yields peaks that form a tangential velocity profile. To determine this profile robustly, we propose to integrate gradients of tangential velocity outward from the wall, wherein the gradient at each wall-normal position is measured by fitting a straight line to the correlation peaks. The capability of Interfacial PIV was validated against Particle Image Distortion using synthetic image pairs generated from a DNS velocity field over a sinusoidal bed. Different velocity measurement schemes performed on the same correlation stacks were also demonstrated. The results suggest that Interfacial PIV using line fitting and gradient integration provides the best accuracy of all cases in the measurements of velocity gradient and velocity profile near wall surfaces.     

Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries

The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise–wall-normal plane of a 536 μm capillary over the Reynolds-number range 1,800 ≤ Re ≤ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re ≅ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 ≤ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non-laminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these “trains” of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the non-laminar subsets at each transitional Re, including root-mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.     

Turbulent flow measurement in a square duct with hybrid holographic PIV

 A hybrid holographic system has been developed for three-dimensional particle image velocimetry. With unique high pass filters, the system combines advantages of both in-line and off-axis holography without having their draw-backs. It improves the signal to noise ratio of the reconstructed image, allows use of 3–15 μm particles in water at high population and achieves large dynamic ranges in both velocity and space. With an automated image acquisition and processing system it has been used for measuring the velocity distributions in a square duct at Re=1.23×10⁵. The data consists of 97×97×87 vectors (with 50% overlapping of adjacent interrogation windows). The quality of the results is evaluated using the continuity equation. The deviation from the equation decreases rapidly with increasing control volume and reaches a level of less than 10%. Mean velocities, r.m.s. velocity fluctuations and turbulence spectra are estimated using the data. Received: 16 December 1996/Accepted: 6 March 1997     

A microfluidic-based nanoscope

 A novel technique for noninvasively measuring the shapes of walls with resolution approaching tens of nanometers is presented. The nanoscope measures local wall position by measuring the velocity of a fluid with micron-scale spatial resolution as it flows over a surface. The location of the wall is estimated by assuming the no-slip velocity condition at the wall and extrapolating the velocity profile to zero. Nanoscope measurements were obtained in a 30 × 300-μm channel. The wall shape of the glass microchannel was determined to be flat to within a root mean square uncertainty of 62 nm. Numerical simulations show that noise in the velocity measurements contributes significantly to uncertainty in wall position. The technique can be used to measure surfaces that are immersed in liquids and in geometries that do not provide exposed surfaces, where traditional nanoscope techniques such as scanning probe microscopes (SPM) are not applicable. Received: 2 March 2001 / Accepted: 19 October 2001     

A high-resolution laser Doppler anemometer for three-dimensional turbulent boundary layers

 A new laser Doppler anemometer optimized for high spatial resolution near a wall is described. The instrument uses short focal length optics, a mirror probe in the flow, and side-scatter collection to produce a measuring volume 35 μm in diameter by 66 μm long. Data are presented for a two-dimensional boundary layer, demonstrating the instrument’s ability to measure Reynolds shear stresses as close to the wall as 0.1 mm, or y ⁺≈3. Received: 6 October 1995/Accepted: 9 April 1996     

Generating arbitrarily sized interrogation windows for correlation-based analysis of particle image velocimetry recordings

 We describe a technique that allows an arbitrary size of the interrogation window when using the traditional FFT algorithm in analysing PIV recordings by either cross- or auto-correlation methods. The length and width of the effective interrogation window are no longer required to be composed of a number of pixels making a power of 2 (16, 32, 64 etc). This gives a higher flexibility in selecting the appropriate window size. Received: 28 January 1997/Accepted: 11 August 1997     

Transient temperature measurements in a convectively cooled droplet

 The transient cooling of an evaporating water droplet, suspended in a jet of dry air, was experimentally investigated in this study using thermochromic liquid crystal thermography. Microencapsulated beads of thermochromic liquid crystals, suspended in the water droplets, enabled the visualization of the transient temperature fields within the droplets. Digital movies of the convectively cooled droplets reveal spatial and temporal temperature gradients resolved down to length scales of ∼100 μm and time scales of ∼0.03 s. The transient temperature measurements were analyzed to yield total droplet convective heat transfer rates. Droplet heat transfer rates determined from a heat balance on the droplets compare favorably to previously published measurements. Received: 11 June 1997/Accepted: 26 March 1998     

Assessment of dual plane PIV measurements in wall turbulence using DNS data

Experimental dual plane particle image velocimetry (PIV) data are assessed using direct numerical simulation (DNS) data of a similar flow with the aim of studying the effect of averaging within the interrogation window. The primary reason for the use of dual plane PIV is that the entire velocity gradient tensor and hence the full vorticity vector can be obtained. One limitation of PIV is the limit on dynamic range, while DNS is typically limited by the Reynolds number of the flow. In this study, the DNS data are resolved more finely than the PIV data, and an averaging scheme is implemented on the DNS data of similar Reynolds number to compare the effects of averaging inherent to the present PIV technique. The effects of averaging on the RMS values of the velocity and vorticity are analyzed in order to estimate the percentage of turbulence intensity and enstrophy captured for a given PIV resolution in turbulent boundary layers. The focus is also to identify vortex core angle distributions, for which the two-dimensional and three-dimensional swirl strengths are used. The studies are performed in the logarithmic region of a turbulent boundary layer at z ⁺ = 110 from the wall. The dual plane PIV data are measured in a zero pressure gradient flow over a flat plate at Re _τ = 1,160, while the DNS data are extracted from a channel flow at Re _τ = 934. Representative plots at various wall-normal locations for the RMS values of velocity and vorticity indicate the attenuation of the variance with increasing filter size. Further, the effect of averaging on the vortex core angle statistics is negligible when compared with the raw DNS data. These results indicate that the present PIV technique is an accurate and reliable method for the purposes of statistical analysis and identification of vortex structures.     

Micro- and Nanoscale Deformation Measurement of Surface and Internal Planes via Digital Image Correlation

The digital image correlation (DIC) technique is successfully applied across multiple length scales through the generation of a suitable speckle pattern at each size scale. For microscale measurements, a random speckle pattern of paint is created with a fine point airbrush. Nanoscale displacement resolution is achieved with a speckle pattern formed by solution deposition of fluorescent silica nanoparticles. When excited, the particles fluoresce and form a speckle pattern that can be imaged with an optical microscope. Displacements are measured on the surface and on an interior plane of transparent polymer samples with the different speckle patterns. Rigid body translation calibrations and uniaxial tension experiments establish a surface displacement resolution of 1 μm over a 5×6 mm scale field of view for the airbrushed samples and 17 nm over a 100×100 μm scale field of view for samples with the fluorescent nanoparticle speckle. To demonstrate the capabilities of the method, we characterize the internal deformation fields generated around silica microspheres embedded in an elastomer under tensile loading. The DIC technique enables measurement of complex deformation fields with nanoscale precision over relatively large areas, making it of particular relevance to materials that possess multiple length scales.     

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.     

Second-order accurate particle image velocimetry

 An adaptive, second-order accurate particle image velocimetry (PIV) technique is presented. The technique uses two singly exposed images that are interrogated using a modified cross-correlation algorithm. Consequently, any of the equipment commonly available for conventional PIV (such as dual head Nd: YAG lasers, interline transfer CCD cameras, etc.) can be used with this more accurate algorithm. At the heart of the algorithm is a central difference approximation to the flow velocity (accurate to order Δt ²) versus the forward difference approximation (accurate to order Δt) common in PIV. An adaptive interrogation region-shifting algorithm is used to implement the central difference approximation. Adaptive shifting algorithms have been gaining popularity in recent years because they allow the spatial resolution of the PIV technique to be maximized. Adaptive shifting algorithms also have the virtue of helping to eliminate velocity bias errors. The second- order accuracy resulting from the central difference approximation can be obtained with relatively little additional computational effort compared to that required for a standard first-order accurate forward difference approximation. The adaptive central difference interrogation (CDI) algorithm has two main advantages over adaptive forward difference interrogation (FDI) algorithms: it is more accurate, especially at large time delays between camera exposures; and it provides a temporally symmetric view of the flow. By comparing measurements of flow around a single red blood cell made using both algorithms, the CDI technique is shown to perform better than conventional FDI-PIV interrogation algorithms near flow boundaries. Cylindrical Taylor–Couette flow images, both experimental and simulated, are used to demonstrate that the CDI algorithm is significantly more accurate than conventional PIV algorithms, especially as the time delay between exposures is increased. The results of the interrogations are shown to agree quite well with analytical predictions and confirm that the CDI algorithm is indeed second-order accurate while the conventional FDI algorithm is only first-order accurate. Received: 15 June 2000/Accepted: 2 February 2001     

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.     

The influence of peak-locking errors on turbulence statistics computed from PIV ensembles

The influence of peak-locking errors on turbulence statistics computed from ensembles of PIV data is considered. PIV measurements are made in the streamwise–wall-normal plane of turbulent channel flow. The PIV images are interrogated in three distinct ways, generating ensembles of velocity fields with absolute, moderate, and minimal peak locking. Turbulence statistics computed for all three ensembles of data indicate a general sensitivity to peak locking in the single-point statistics, except for the mean velocity profile. Peak-locking errors propagate into the fluctuations of velocity, rendering single-point statistics inaccurate when severe peak locking is present. Multi-point correlations of both streamwise and wall-normal velocity are also found to be influenced by severe levels of peak locking. The displacement range of the measurement, defined by the PIV time delay, appears to affect the influence of peak-locking errors on turbulence statistics. Smaller displacement ranges, particularly those that produce displacement fluctuations that are less than one pixel in magnitude, yield inaccurate turbulence statistics in the presence of peak locking.