A procedure for studying transient flows near boundaries using high-resolution, high-speed particle image velocimetry (PIV) is described here. PIV is a non-intrusive measurement technique applicable to any optically accessible flow by optimizing several parameter constraints such as the image and recording properties, the laser sheet properties, and analysis algorithms.
Multi-dimensional and transient flows play a key role in many areas of science, engineering, and health sciences but are often not well understood. The complex nature of these flows may be studied using particle image velocimetry (PIV), a laser-based imaging technique for optically accessible flows. Though many forms of PIV exist that extend the technique beyond the original planar two-component velocity measurement capabilities, the basic PIV system consists of a light source (laser), a camera, tracer particles, and analysis algorithms. The imaging and recording parameters, the light source, and the algorithms are adjusted to optimize the recording for the flow of interest and obtain valid velocity data.
Common PIV investigations measure two-component velocities in a plane at a few frames per second. However, recent developments in instrumentation have facilitated high-frame rate (> 1 kHz) measurements capable of resolving transient flows with high temporal resolution. Therefore, high-frame rate measurements have enabled investigations on the evolution of the structure and dynamics of highly transient flows. These investigations play a critical role in understanding the fundamental physics of complex flows.
A detailed description for performing high-resolution, high-speed planar PIV to study a transient flow near the surface of a flat plate is presented here. Details for adjusting the parameter constraints such as image and recording properties, the laser sheet properties, and processing algorithms to adapt PIV for any flow of interest are included.
Multi-dimensional measurements of velocities and the ability to track the flow field in time provide critical information in many areas of science, engineering, and health sciences. Amongst the most widely used techniques for flow imaging is particle image velocimetry (PIV). Initially established as a planar technique that measured snapshots of the two in-plane velocity components, PIV variants have been developed to provide three-component and volumetric measurement capabilities. All PIV systems consist of tracer particles, one or more light sources, and one or more cameras. Solid particles or droplets are commonly used as tracer particles but bubbles inherent in the flow may also be used as tracer particles. The camera(s) then image(s) scattered or emitted light from the tracer particles after they are irradiated by the light source(s). Amongst the broad range of variations 1,2 the most common one captures two velocity components in a plane at a rate of a few frames per second. More recently, new instrumentation has enabled high-frame rate measurements (> 1 kHz) that follow the flow at turbulent time scales in the kHz range.
PIV determines a velocity field by tracking the average motion of particle groups from a pair of images that are separated by a known time delay. Each image is divided into a grid of regularly spaced interrogation windows. The most common interrogation window size is 32 x 32 pixels. An algorithm computes the cross-correlation function for all interrogation windows, resulting in one displacement vector per interrogation window and therefore produces a regular grid of vectors. Dividing the displacement vector field by time delay then determines the velocity vector field.
When planning PIV measurements it is important to realize that typically the choice of experimental settings is a compromise between conflicting requirements. In other words, the experimental conditions need to be carefully planned to capture the aspects of the flow that are of importance for the study at hand. The books by Raffel et al. 1 and Adrian and Westerweel 2 provide excellent in-depth discussions of these constraints. Here we highlight several that are most critical in the present context.
The choice of the field-of-view (FOV) will set the starting point for the parameter selection here. The number of pixels on the camera chip then determines the spatial resolution and the number of vectors that are obtained, assuming that one chooses to use interrogation window sizes of 32 x 32 pixels, often with a 50% overlap during the cross-correlation procedure. A seeding density of 8-10 particles per interrogation window is generally desired to aid the cross-correlation function. However, there are special algorithms, such as particle tracking velocimetry (PTV) and time-averaged correlation approaches, that may be used to address situations with low seeding density (1-3 particles/interrogation window) as is the case with imaging near surfaces. Note that the velocity gradients within each interrogation window should be small to avoid a bias in the resulting representative vector for that window.
An established rule-of-thumb is that the particle displacements between the first and second frame should not exceed 8 pixels (¼ of the interrogation window size) to reduce the number of pairing losses (loss of particle images within the interrogation window from the first frame to the second frame) for the correlation. As a result, the time between the two consecutive laser pulses (dt) has to be adjusted accordingly. However, reducing dt below the equivalent of 8-pixel displacements will reduce the velocity dynamic range because the lower end resolution limit is on the order of 0.1 pixel displacement.
Similar to the 8-pixel displacement within the imaging plane, the highest velocity particles should not traverse more than ¼ of the light sheet thickness, again to reduce the number of pairing losses. Since the time delay between the two laser pulses is used to ensure the best correlations within the light sheet plane, the thickness of the sheet is a variable in this context. While the uniformity of the light intensity is not as critical as it is for intensity-based measurements such as planar laser-induced fluorescence imaging 3, a near top-hat beam profile helps PIV quality, especially for higher resolution imaging.
In general, some assumptions about the nature of the flow under study can be used as a starting point in the selection of experimental parameters. Then, exploratory experiments might be needed to refine the settings.
Here we describe how to set up a PIV experiment that allows high frame rate imaging measurements of two velocity components with spatial resolution that is adequate to resolve boundary layer structures. This is accomplished with the use of a high-repetition rate TEM 00 diode-pumped solid-state laser, a long-distance microscope, and a high frame rate CMOS camera. A few details on imaging near surfaces are also included.
1. Lab Safety
2. Benchtop Set-up
3. Flow Set-up
4. Optimizing the Set-up
5. Running the Experiment
6. Data Processing
A photo of the set-up is shown in Figure 1. Raw particle images of a 32 x 32 pixel interrogation window near the wall from two consecutively captured images are shown in Figure 2. The particles in Figure 2a are displaced 2-3 pixels to the right in Figure 2b and satisfy the “one-quarter rule,” which states that in-plane and out-of-plane particle displacements should not exceed ¼ of the interrogation window size. Additionally, the particle density per interrogation window should be roughly 8-10 particles since PIV correlation algorithms track groups of particles. However, the seeding density in near-wall PIV investigations is often on the order of 1-3 particles. Thus, special algorithms should be used to address studies with lower seeding density, such as particle tracking velocimetry (PTV) algorithms which track individual particles 1,2,4-6. A time-averaged correlation approach 7,8 may also be used to address low seeding density issues but this generally results in the loss of temporal resolution. Additionally, imaging near walls is impacted by bright laser reflections that may adversely affect PIV correlations and produce false vectors. These bright reflections also limit the position of the first valid velocity vector in the wall normal direction. Pre-processing the raw particle images is necessary to reduce the impact of background noise from sources such as laser reflections. In this demonstration the first valid vector was located 23 μm from the wall.
After raw particle images are processed using the PIV correlation algorithms, the quality and validity of the resulting velocity vector fields should be assessed. Spurious vectors are unavoidable in the raw vector fields but there are a few distinguishing characteristics. Incorrect vectors are common near surfaces, at the edges of the light sheet, and at the edges of a flow. In addition, the magnitude and direction of invalid vectors differ significantly from neighboring vectors and will not make physical sense. In the case of this boundary layer flow example, the valid velocity vectors should point from left to right as the particle displacements from Figure 2 indicate. Additionally, the velocities should decrease near the wall due to the no-slip condition 9. The instantaneous velocity fields shown in Figure 3 fit both of these physical criteria. Another useful metric to assess the validity of PIV results is to determine the vector choice of each vector in the velocity vector field. In general, the vector field should consist of >= 95% first choice vectors, i.e. those that required no post-processing, so that robust post-processing algorithms may be used to detect and replace spurious vectors without producing considerable artifacts 2. The instantaneous vector fields shown in Figure 3 are composed entirely of 1st choice vectors.
The significance of high-speed, or cinematographic, PIV measurements becomes evident from an inspection of a time sequence of flow images. Instantaneous velocity (Vi) and velocity fluctuation (V’) vector fields at the beginning, middle, and end of the recording sequence are shown in Figure 3. Using a Reynolds decomposition, Vi is the sum of the averaged velocity field () and V’ 10. For this experiment, was determined by temporally averaging all images in the sequence. The instantaneous vector fields throughout the recording sequence are very similar and show the flow moving from the left to the right. These results also indicate that the flow is predominantly in the horizontal direction since the horizontal velocity component (u) is much larger than the vertical velocity component (v). The fluctuation vector fields also indicate that the horizontal velocity fluctuations (u’) are larger than the vertical velocity fluctuations (V’). However, the fluctuations also indicate that the flow is slowing down since u’ reverses its direction throughout the recording sequence.
The time-averaged and instantaneous u – profiles at several different times throughout the recording sequence are shown in Figure 4 and verify that the flow is slowing down over time. The u – profiles were determined by averaging four adjacent vector columns together to improve the statistical significance of the results close to the wall. The procedure was used in previous work 6,8. The error bars indicate twice the standard deviation of the four adjacent vector columns. The largest error bar occurs near the surface of the plate and reaffirms the difficulty of using PIV correlation algorithms for areas of low seeding density. Several analysis algorithms are designed to address low seeding density such as PTV 5,6 and time-averaged correlation approaches 7,8.
Figure 1. Benchtop assembly.
Figure 2. Particle images in a 32 x 32 pixel interrogation near the wall at a) t = 0.2 msec and b) t = 0.4 msec. The physical dimensions of the interrogation window are 96 x 96 μm2.
Figure 3. On the left: instantaneous (Vi), and on the right: fluctuation (V’) velocity fields at the beginning, middle, and end of the recording sequence. Vector fields are composed entirely of first-choice vectors. A smaller subset of the vector fields is shown for clarity. The Vi fields indicate flow moving from left to right while V’ reverse direction. Please note that only every fourth vector column in the horizontal direction is shown for clarity. Additionally, the velocity scale between the Vi and V’ fields is different as indicated in the top left corner of each image.
Figure 4. Horizontal velocity (u) profiles at different times throughout the flow. Time-averaged u – profile is shown with circles. Error bars shown on t = 0.1 msec profile are representative of error bars for all other times. The time history of the u – profiles shows a decrease in the flow over time.
As with any optical flow measurement technique, planning the setup of high-speed particle image velocimetry (PIV) requires assessment of constraints and the evaluation of best compromises for the measurement task at hand. The selection of image magnification, frame rate, laser sheet properties, and analysis algorithms depend on details of the flow under study. If need be, exploratory measurements must be conducted to identify parameter settings for high fidelity measurements.
This article describes the general procedure and some sample results for high-speed PIV to study the boundary layer of a flow along a flat plate. A sequence of 500 images was recorded at 5 kHz. A long-distance microscope was used to achieve a 2.4 x 1.8 mm2 field-of-view located at the plate surface. High quality illumination of the seed oil droplets was achieved with a beam from a pulsed diode-pumped solid-state laser that was expanded into a light sheet using a beam homogenizer. The beam homogenizer contains a micro-lens array made up of small cylindrical lenses and an additional, integrated telescope. The micro-lens array expands the circular beam in the vertical direction by splitting the incoming beam into beamlets. Then the following telescope superimposes the beamlets to create a light sheet with an even light intensity distribution in the light sheet plane normal to the beam propagation. Images were processed using a PIV cross-correlation algorithm. It should be noted that a homogenized beam is helpful, especially when working near surfaces, but it is not crucial to the application described here.
The method outlined in this procedure enables non-intrusive high-resolution, high-speed investigations of flows using robust correlation algorithms. The key advantages of this high-resolution, high-speed measurement technique are high spatial and temporal resolution and the ability to identify and track the evolution of structures within the flow. Using these techniques, Alharbi 6 and Jainski et al. 8 have demonstrated the ability to visualize and track vortex structures within the boundary layer of an internal combustion engine. These key features enable investigations on the structure and dynamics of highly transient flows. Furthermore, PIV may be expanded beyond the two-dimensional, two-component (2D-2C) velocity fields (as described here) to resolve 3-components (3C) in a plane (stereo-PIV) and in a volume (tomographic PIV, scanning PIV, holographic PIV). Additionally, PIV may be implemented with other techniques such as planar laser-induced fluorescence (PLIF), filtered Rayleigh scattering (FRS), and thermographic phosphors to achieve simultaneous 2D measurements of velocity and other scalars (temperature, species concentration, equivalence ratios) 11-14. These optical, laser-based methods can be directly applied to investigate mass and energy exchange processes in many applications, such as the near-wall flows in an internal combustion engine.
The authors have nothing to disclose.
This material is based upon work supported by the US National Science Foundation under Grant No. CBET-1032930 and work performed at the University of Michigan’s Quantitative Laser Diagnostics Laboratory.
Name of Equipment | Company | Model | Comments |
High-speed 532 nm Nd:YAG laser | Quantronix | Model: Hawk I | |
Long distance microscope (QM-100) | Questar | Model: QM-100 | |
High-speed CMOS camera (Phantom v7.3) | Vision Research | Model: Phantom v7.3 | |
Atomizer (TSI 9306) | TSI | Model: 9306 | |
Silicone oil | Dow Corning CST 510 | CST 510 Fluid | |
Beam homogenizer | Fraunhofer | Custom made part | |
45° high-reflectivity (HR) 532 nm turning mirror | Laser Optik | Multiple suppliers | |
Aperture | Multiple suppliers | ||
Calibration target | Custom made part | ||
PIV recording and processing software | LaVision | Software: Da Vis | |
High-speed controller (HSC) | LaVision | ||
Optical rail and carriers | Multiple suppliers | ||
Laser beam blocks and traps | Multiple suppliers | ||
Mounts for optical elements | Multiple suppliers | ||
Translation stage | Newport | ||
Metal tubing to create jet flow | McMaster-Carr | Multiple suppliers | |
Combination square and centering square | Multiple suppliers |