The technique described herein offers a low cost and relatively simple method to simultaneously measure particle kinematics and turbulence in flows with low particle concentrations. The turbulence is measured using particle image velocimetry (PIV), and particle kinematics are calculated from images obtained with a high-speed camera in an overlapping field-of-view.
Numerous problems in scientific and engineering fields involve understanding the kinematics of particles in turbulent flows, such as contaminants, marine micro-organisms, and/or sediments in the ocean, or fluidized bed reactors and combustion processes in engineered systems. In order to study the effect of turbulence on the kinematics of particles in such flows, simultaneous measurements of both the flow and particle kinematics are required. Non-intrusive, optical flow measurement techniques for measuring turbulence, or for tracking particles, exist but measuring both simultaneously can be challenging due to interference between the techniques. The method presented herein provides a low cost and relatively simple method to make simultaneous measurements of the flow and particle kinematics. A cross section of the flow is measured using a particle image velocimetry (PIV) technique, which provides two components of velocity in the measurement plane. This technique utilizes a pulsed-laser for illumination of the seeded flow field that is imaged by a digital camera. The particle kinematics are simultaneously imaged using a light emitting diode (LED) line light that illuminates a planar cross section of the flow that overlaps with the PIV field-of-view (FOV). The line light is of low enough power that it does not affect the PIV measurements, but powerful enough to illuminate the larger particles of interest imaged using the high-speed camera. High-speed images that contain the laser pulses from the PIV technique are easily filtered by examining the summed intensity level of each high-speed image. By making the frame rate of the high-speed camera incommensurate with that of the PIV camera frame rate, the number of contaminated frames in the high-speed time series can be minimized. The technique is suitable for mean flows that are predominantly two-dimensional, contain particles that are at least 5 times the mean diameter of the PIV seeding tracers, and are low in concentration.
There exist a large number of applications in both scientific and engineering fields that involve the behavior of particles in turbulent flows, for example, aerosols in the atmosphere, contaminants and/or sediments in engineered systems, and marine micro-organisms or sediment in the ocean1,2,3. In such applications, it is often of interest to understand how the particles respond to turbulence, which requires simultaneous measurement of the particle kinematics and the fluid dynamics.
Existing technologies to measure particle motions, called particle tracking (PT), which tracks individual particle trajectories, and the statistical technique of particle image velocimetry4,5 (PIV), used to measure flow velocities, both incorporate non-intrusive optical techniques. The main challenge in using these non-intrusive optical techniques to measure both the flow and particle kinematics simultaneously is the separate illumination required for each imaging technique that cannot interfere with the other's measurement accuracy (e.g., the illumination source for measuring the particle kinematics cannot act as a significant noise source in the fluid velocity measurement and vice-versa). The image contrast in both sets of images needs to be sufficient to obtain reliable results. For example, the PT images are converted to black and white images in order to perform a blob analysis to determine particle positions; thus, insufficient contrast leads to errors in particle position. Poor contrast in PIV images amounts to a low signal-to-noise ratio that will cause inaccuracies in estimation of the fluid velocities.
Here, a relatively low cost and simple method to simultaneously measure both particle kinematics and flow velocities is described. Through use of a high-power monochromatic light emitting diode (LED) line light, where the line refers to the light aperture, and dual-head high-intensity laser, both the particles of interest and the flow field are imaged in the same region simultaneously. The high power of the LED is sufficient for the imaging of the (tracked) particles by the high-speed camera but does not impact the PIV images because the light intensity scattered from PIV tracers is too low. When the dual-head high-intensity laser illuminates the flow field for the PIV images, it occurs over a short time interval and these images are easily identified and removed from the time series obtained by the high-speed PT camera when they are registered. PIV laser pulses recorded in the high-speed image (used for particle tracking) time series can be minimized by not running the two systems at frame acquisition rates that are commensurate with each other. In more advanced setups, one could externally trigger the PT and PIV cameras with a delay that would ensure this does not happen. Finally, by careful consideration of the amount of particles being tracked within the PIV field of view (FOV), any errors introduced by these tracked particles in the correlation analysis of PIV images are already taken into account by the overall error estimation, including errors associated with non-uniform size distribution of PIV tracers within the interrogation window. The vast majority of the PIV seeding tracers are following the flow, yielding accurate flow velocity estimates. These techniques enable the simultaneous direct measurement of both the particle kinematics and flow field in a two-dimensional plane.
This technique is demonstrated by applying it to determine particle settling characteristics in a turbulent flow, similar to that used in studies by Yang and Shy6 and Jacobs et al.7. Particle settling is the final stage in sediment transport, which generally consists of sediment suspension, transport, and settling. In most prior studies that have addressed particle settling in turbulent flows, either particle trajectories or turbulent velocities are not directly measured but inferred theoretically or modeled8,9,10. Details on the interactions between particles and turbulence have most often been investigated using theoretical and numerical models due to the experimental limitations in measuring both simultaneously6,11. We present a particle-turbulence interaction case study in an oscillating grid facility, where we study the settling velocity of particles and their coupling with turbulence. For clarity, hereafter we will refer to the particles under investigation as "particles" and the seeding particles used for the PIV technique as "tracers"; additionally, we will refer to the camera used for the high-speed imaging of the particle trajectories as the "particle tracking", "PT", or "high-speed" camera, which measures "high-speed images" and the camera used for the PIV method the "PIV camera", which measures "images". The method described herein enables the simultaneous measurement of particles kinematics and fluid dynamics over a pre-defined field of interest within the facility. The obtained data provides a two-dimensional description of the particle-turbulence interaction.
Note: All personnel should be trained in the safe use and operation of Class IV lasers as well as in the safe use and operation of hand and power tools.
1. Experimental Set-up
2. Image Analysis
Note: There are numerous software packages available to perform both the PIV and PT image analysis – both commercial and freeware. For PIV analysis, freeware codes are OpenPIV (http://www.openpiv.net/) and MatPIV (http://folk.uio.no/jks/matpiv/index2.html). Commercial companies also sell PIV analysis software. For PT analysis, numerous particle tracking codes exist in both 3D and 2D such as Particle Tracker (https://omictools.com/particle-tracker-tool); a full listing of various software platforms can be found here: https://omictools.com/particle-tracking-category or http://tacaswell.github.io/tracking/html/. Most analysis packages, e.g., MATLAB, have built in tools that make it relatively easy to implement your own tracking code. For the results presented in this study, OpenPIV, TSI Insight, and MATLAB custom-written tracking codes were used.
3. Analysis
A schematic of the experimental setup is shown in Figure 1. The figure shows the arrangement of light sheets (LED and laser), the overlap in the FOVs, and the position of the FOVs relative to the oscillating grid and tank walls. The turbulence and particles are measured simultaneously as described in the protocol section. Figure 2 shows example results of the measurements of instantaneous velocity and vorticity along with sample particle trajectories. The results of the PIV analysis are evaluated based on computing the RMS of the turbulent fluctuations. For this oscillating grid facility, the magnitude of the spatial mean of the RMS velocity fluctuation over the PIV FOV should increase with grid frequency for both velocity components7,15. If this result is not obtained, then the grid facility, PIV setup, or PIV analysis contain errors and should be repeated. An example of the vertical profile of RMS velocity fluctuations for different grid frequencies is provided in Figure 3, where it is shown that the RMS turbulent fluctuations increase with grid frequency.
The particle trajectories are evaluated by examining the distribution of velocities obtained from the particle trajectories, as shown in Figure 4. These distributions should be approximately Gaussian in distribution. If they are not, then there may be a problem with the acquisition of the high-speed images depending on the specific flow conditions, an issue with the analysis of the high-speed images, or an insufficient number of particle trajectories. In this particular application of the method, the validation of the trajectory results can also be achieved by comparison to the Dietrich16 curves for stagnant water. Trajectory computations in still water using the same procedures outlined here for the particles should yield a settling velocity that is approximately consistent with these empirical curves as shown in Figure 5, where the results for the stagnant flow condition show agreement with the Dietrich16 curves. Figure 5 also demonstrates that particles tend to have increased settling speeds in turbulence as discussed in Jacobs et al.7.
Figure 1: Schematic description of the experimental setup, which consists of a grid turbulence tank, particle image velocimetry setup (using a CCD (PIV) camera and laser), and 2D high-speed imaging particle tracking setup (using a CMOS (PT) camera and LED light). Dimensions on the schematic are provided in centimeters. This figure has been modified from that shown in Jacobs et al.7 Please click here to view a larger version of this figure.
Figure 2: Velocity distribution and trajectories. (A) An example instantaneous fluid velocity distribution represented by vectors in pixels/s overlaid on instantaneous vorticity characterized by color. The red scale vector in the lower left corner represents 500 pixels/s. (B) An example of time-lapse (over 30 PT images) trajectories of particles with a 261 µm mean diameter at 5 Hz grid oscillations. Panel B of this figure has been modified from that shown in Jacobs et al.7 Please click here to view a larger version of this figure.
Figure 3: Horizontally averaged vertical profiles of the RMS of the (a) horizontal and (b) vertical turbulent fluctuations for all grid frequencies (see legend). Turbulent RMS velocities increase with grid frequency. RMS values are based on 500 vector maps computed at all locations and then subsequently averaged over all horizontal positions (50 points) at each vertical position to obtain the vertical profiles shown. This figure has been modified from that shown in Jacobs et al.7 Please click here to view a larger version of this figure.
Figure 4: Histograms of the particles' measured horizontal and vertical velocities in stagnant water and turbulent conditions (see subtitles) for (A, left two panels) a natural (irregularly shaped) sand particle with 261 µm mean diameter and (B, right two panels) a spherical synthetic particle with a 71 µm mean diameter. The lines in the subplots are Gaussian fits to the histograms. This figure has been modified from that shown in Jacobs et al.7 Please click here to view a larger version of this figure.
Figure 5: Settling velocities in stagnant and turbulent flow conditions versus particle size for several different types of particles. As illustrated in the legend, the colors represent different sediment types: synthetic or manufactured particles, several industrial sand types (120, 100, 35), and sand from a local beach in Myrtle Beach, SC-see Table 1 in Jacobs et al.7 for more details. The symbols, including the filled circle, indicate the flow conditions represented as grid frequency in the legend, where stagnant refers to zero frequency. As grid frequency increases, the RMS turbulent velocity fluctuations increase. The empirical curves of Dietrich16 for particle settling velocity in stagnant water are also shown for several different shape factors. This figure has been modified from that shown in Jacobs et al.7 Please click here to view a larger version of this figure.
The method described herein is relatively inexpensive and provides a simple way to simultaneously measure particle trajectories and turbulence in order to examine the influence of flow on particle kinematics. It is noteworthy to mention that flows or particle motions that are strongly three-dimensional are not well-suited for this technique. The out-of-plane motion will result in errors17 in both the 2D tracking and the PIV analysis and should be minimized. In addition, the method requires the concentration of tracked particles to be relatively low (on the order of tens of particles per PT image). This restriction is important in order to maximize confidence that the same particle is being tracked in consecutive images. If too many particles exist simultaneously in the FOV of the PT camera, then inaccuracies in the trajectory calculations and early termination of trajectories can occur as well as increased errors in the PIV image analysis. Consequently, problems associated with particle flocculation would be challenging for this technique to investigate because large particle concentrations are usually needed. Finally, this technique is best suited for tracking larger particles (>50 µm). There must be sufficient separation between the PIV tracers (~10 µm) from the particles that are being tracked. A factor of at least 5 is suggested.
The most critical steps in the protocol for the particle tracking are the calibration steps, selection of the frame rate, particle concentration in the images, and ensuring high signal-to-noise ratio in the high-speed images. The blob analysis requires conversion of the gray scale image to a black-and-white image upon which the particle trajectories are computed. If the contrast in the high-speed images is such that this conversion is difficult, then errors in the trajectories are likely because there will be uncertainty in identification of the particles. Insufficient particle displacement, too large of displacement between frames, or too many particles can lead to errors in the particle trajectories and/or early termination of particle trajectories. For the PIV, the calibration of the image size, setting of the time between image pairs, proper selection of the tracers, and detailed alignment between the PIV camera and the laser are the most important steps to ensuring a good result in the PIV correlation analysis, which is key for obtaining accurate statistics on the turbulence.
Here, we demonstrated the results of the technique by applying it to examine the settling velocity of various types and sizes of sediment particles in varying turbulent conditions. The results show a nearly Gaussian distribution of particle settling velocities (as well as horizontal velocities) of which the mean is considered a typical settling velocity for that particle in different conditions. The RMS of the turbulent velocity fluctuations show an increase with grid frequency as expected7,15 and are approximately uniform over the FOV vertical height (aside from one low turbulence case – 2 Hz grid frequency, see Figure 3). Together, these results demonstrate that the simultaneous measurement of the particles and flow field were successful. They also demonstrate that there are increased settling speeds with increasing turbulence7, which is consistent with the "fast-tracking" theory of particle settling behavior in turbulent flow11.
The utilization of the method herein is one example of addressing a scientific question involving particle-turbulence interaction; the method can be utilized in other research disciplines and applications. In addition to examining trends in a particular aspect of particle behavior in varying flow conditions, it is also feasible to examine the flow velocities at particular instances in time along the trajectory of a particle. The integration of the flow velocity information with the particle trajectory data depends on the specific question investigated and offers a potential wealth of information regarding particle kinematics in flows for a large range of applications. In summary, this technique offers a low-cost solution to simultaneous measurement of particle trajectories and turbulence relevant in a number of applications where fluid flow interacts with natural or man-made particulates.
The authors have nothing to disclose.
Portions of this work were supported by the II-VI Foundation and the Coastal Carolina Professional Enhancement Grant. We would also like to acknowledge Corrine Jacobs, Marek Jendrassak and William Merchant for help with the experimental setup.
Optical lenses | CVI LASER OPTICS | Y2-1025-45, RCC-25.0-15.0-12.7-C, PLCC-25.4-515.1-UV | Other optics companies are acceptable. Spherical and cyclindrical lenses for generating PIV light sheet. |
Camera lens for PIV | Nikon | Nikkor 105mm f/2D | Other camera lens companies are acceptable. Camera lens for PIV imaging. |
Camera lens for high-speed | Nikon | Nikkor 50mm f/1.8D | Other camera lens companies are acceptable. Camera lens for high-speed imaging. |
Dual-head pulsed laser | Quantel | EverGreen: 532nm, 70mJ@15Hz | Other laser companies are acceptable. Dual-head Pulsed-laser for PIV: Nd:YAG |
LED line light | Gardasoft Vision, Ltd. | VLX2 LED Line Lighting – Green – GAR-VLX2-250-LWD-G-T04 | Other companies are acceptable. Line light for LED. |
PIV seeding particles/tracers | Potters Industries | SPHERICAL Hollow Glass Spheres: 11 mm average diameter | Other companies are acceptable. PIV seeding particles |
CCD cross-correlation camera | TSI, Inc. | POWERVIEW 11M: CCD, Double-exposure, 4008×2672 pixels @ 4.2 Hz with 12bit dynmic range | Other companies are acceptable. Double-exposurem, CCD camera for PIV imaging. |
High-speed camera | Photron | FASTCAM SA3; Model 60K: 1024×1024 pixels @ 1kHz | Other companies are acceptable. CMOS camera for high speed imaging. |
Synchronizer | TSI, Inc. | LASERPULSE SYNCHRONIZER 610036 | Other companies are acceptable. Synchronize the acquisition of the PIV camera and laser. |
Calibration target | TSI, Inc. | Other companies are acceptable. Precision target for image calibration. |