Particle image velocimetry

Particle image velocimetry (PIV) is an optical method used to obtain instantaneous velocity measurements and related properties in fluids. The fluid is seeded with tracer particles which, for the purposes of PIV, are generally assumed to faithfully follow the flow dynamics. It is the motion of these seeding particles that is used to calculate velocity information of the flow being studied. Other techniques used to measure flows are Laser Doppler velocimetry and Hot-wire anemometry. The main difference between PIV and those techniques is that PIV produces two dimensional vector fields, while the other techniques measure the velocity at a point.

With PIV is generally considered cases where the particle concentration is such that it is possible to identify individual particles in an image, but not with certainty to track it between images. When the particle concentration is so low that it is possible to follow an individual particle it is called Particle tracking velocimetry, while Laser speckle velocimetry is used for cases where the particle concentration is so high that it is difficult to observe individual particles in an image.

Typical PIV apparatus consists of a camera (normally a digital camera with a CCD chip in modern systems), a high power laser, for example a double-pulsed Nd:YAG laser or a copper vapour laser, an optical arrangement to convert the laser output light to a thin light sheet (normally using a cylindrical lens and a spherical lens), a synchronizer to act as an external trigger for control of the camera and laser, the seeding particles and the fluid under investigation. A fibre optic cable or liquid light guide often connects the laser to the lens setup.

History

While the method of adding particles or objects to a fluid in order to observe its flow is likely to have been used from time to time through the ages no sustained application of the method is known. The first to use particles to study fluids in a more systematic manner was Ludwig Prandtl, who did so in the early 20th Century.

Laser Doppler Velocimetry was predates PIV as a laser-digital analysis system to become widespread for research and industrial use. Able to obtain all of a fluid's velocity measurements at a specific point, it can be considered the 2-dimensional PIV's immediate preecessor. PIV itself found its roots in Laser speckle velocimetry, a technique that several groups began experimenting with in the late 1970s. In the early 1980s it was found that it was advantageous to decrease the particle concentration down to levels where individual particles could be observed. At these particle densities it was further noticed that it was easier to study the flows if they were split into many small 'interrogation' areas, that could be analysed individually to generate one velocity for each area. The images were usually recorded using analog cameras and needed immense amount of computing power to be analyzed.

With the increasing power of computers and widespread use of CCD cameras it became tempting to do everything digitally. The implications of doing so was analysed during 1990s and over time digital PIV became increasingly common, to the point that it today totally dominates.

Equipment and Aparatus

Seeding Particles

The seeding particles an inherently critical component of the PIV system. Depending on the fluid under investigation, the particles must be able to match the fluid properties reasonably well. Otherwise they will not follow the flow satisfactorily enough for the PIV analysis to be considered accurate. While the actual particle choice is dependent on the nature of the fluid, generally for macro PIV investigations they are glass beads, polystyrene, aluminum flakes or oil droplets (if the fluid under investigation is a gas). They must be inherently reflective, so that the laser sheet incident on the fluid flow will reflect off of the particles and be scattered towards the camera.

The particles are typically of a diameter on the order of 10 to 100 micrometers. As for sizing, the particles should be small enough so that response time of the particles to the motion of the fluid is reasonably small to accurately follow the flow, yet large enough to scatter a significant quantity of the incident laser light. Due to the small size of the particles, the particles motion is dominated by stokes drag and settling or rising affects. Approximating the particles as spherical particles of very low Reynolds number, then the ability of the particles to follow the fluid's flow is directly proportional to the difference in density between the particles and the fluid and directly proportional to the square of the particles' diameters. The scattered light from the particles is also dominated by Reynolds scattering and so is also proportional to the square of the particles' diameters. Thus the particle size needs to be balanced to scatter enough light to accurately visualize all particles within the laser sheet plane but small enough to accurately follow the flow.

The seeding mechanism needs to also be designed so as to sufficiently seed the flow to a sufficient degree without overly disturbing the flow.

Camera

To perform PIV analysis on the flow, two exposures of laser light are required upon the camera from the flow. Originally, with the inability of cameras to capture multiple frames at high speeds, both exposures were captured on the same frame and this single frame was used to determine the flow. A process called auto correlation was used for this analysis. However, as a result of autocorrelation the direction of the flow becomes unclear, as it is not clear which particle spots are from the first pulse and which are from the second pulse. Faster digital cameras using CCD chips were developed since then that can capture two frames at high speed with a few hundred ns difference between the frames. This has allowed each exposure to be isolated on its own frame for more accurate cross-correlation analysis. The limitation of typical cameras is that this fast speed is limited to a pair of shots. This is because each pair of shots must be transferred to the computer before another pair of shots can be taken. Typical cameras can only take a pair of shots at a much slower speed. High speed CCD cameras are available but are much more expensive.

A new camera is under development that can take shots as fast as a laser can fire them. It is not yet available for usage outside of the development group.

Laser and Optics

For macro PIV setups, Nd-YAG lasers are predominant due to their ability to produce high-power, high-speed pulses. They emit primarily at 1064 nm wavelength and its harmonics (532, 266, etc.) For safety reasons, the laser emission is typically bandpassed to isolate the 532 nm harmonics (this is green light, the only harmonic able to be seen by the naked eye). A fiber optic cable or liquid light guide might be used to direct the laser light to the experimental setup.

The optics consist of a spherical and cylindrical lens combination. The cylindrical lens expands the laser into a plane while the spherical lens compresses the plane into a thin sheet. This is critical as the PIV technique cannot generally measure motion normal to the laser sheet and so ideally this is eliminated by maintaining an entirely 2-dimensional laser sheet. It should be noted though that the spherical lens cannot compress the laser sheet into an actual 2-dimensional plane. The minimum thickness is on the order of the wavelength of the laser light and occurs at a finite distance from the optics setup (the focal point of the cylindrical lens). This is the ideal location to place the analysis area of the experiment.

Correct lens for the camera should also be selected to properly focus on and visualize the particles within the investigation area.

Synchronizer

The synchronizer acts as an external trigger for both the camera(s) and the laser. While analogue systems in the form of a photosensor, rotating aperture and light have been used in the past, most systems in use today are digital. Controlled by a computer, the synchronizer can dictate the timing of each frame of the CCD camera's sequence in conjunction with the firing of the laser to within 1 ns precision. Thus the time between each pulse of the laser and the placement of the laser shot in reference to the camera's timing can be accurately controlled. Knowledge of this timing is critical as it is needed to determine the velocity of the fluid in the PIV analysis.

Analysis

The frames are split into a large number of interrogation areas, or windows. It is then possible to calculate a displacement vector for each window with help of signal processing and autocorrelation or cross-correlation techniques. This is converted to a velocity using the time between laser shots and the physical size of each pixel on the camera. The size of the interrogation window should be chosen to have at least 6 particles per window on average.

The synchronizer controls the timing between image exposures and also permits image pairs to be acquired at various times along the flow. For accurate PIV analysis, it is ideal that the region of the flow that is of interest should display an average particle displacement of about 8 pixels. This is a compromise between a longer time spacing which would allow the particles to travel further between frames, making it harder to identify which interrogation window traveled to which point, and a shorter time spacing, which could make it overly difficult to identify any displacement within the flow.

The scattered light from each particle should be in the region of 2 to 4 pixels across on the image. If too large an area is recorded, particle image size drops and peak locking might occur with loss of sub pixel precision. There are methods to overcome the peak-locking effect, but they require some additional work.

If there is in house PIV expertise and time to develop a system, even though it is not trivial, it is possible to build a custom PIV system. Research grade PIV systems do, however, have high power lasers and high end camera specifications for being able to take measurements with the broadest spectrum of experiments required in research. If, for example, you want to spend less money, of course you get less resolution and lower framerates. There are also PIV analysis software available in the open source community. The results can have similar or even better quality compared to the expensive commercial PIV systems. Some of the commercial PIV companies include TSI [2], LaVision [3], Dantec [4], Etalon Research [5] and IDT [6]. Commercial timing electronics come in varying resolutions. A typical example is Berkeley Nucleonics [7].

Pros/Cons

Advantages

The method is to a large degree nonintrusive. The added tracers (if they are properly chosen) generally cause negligible distortion of the fluid flow.

Optical measurement avoids the need for Pitot tubes, hotwires anemometers or other intrusive Flow measurement probes. Additionally the method is capable of measuring an entire two-dimensional cross section (geometry) of the flow field simultaneously.

High speed data processing allows the generation of large numbers of image pairs which, on a modern personal computer may be analysed in real time or at a later time. Thus a high quantity of near continuous information may be gained.

Sub pixel displacement values allow a high degree of accuracy, since each vector is the statistical average for many particles within a particular tile. Displacement can typically be accurate down to 10% of one pixel on the image plane.

Drawbacks

In some cases the particles will, due to their higher density, not perfectly follow the motion of the fluid (gas/liquid). If experiments are done e.g. in water, it is easily possible to find very cheap particles (e.g. plastic powder with a diameter of ~60 µm) with the same density as water. If the density still does not fit, the density of the fluid can be tuned by increasing/ decreasing its temperature. This leads to slight changes in the Reynolds number, so the fluid velocity or the size of the experimental object has to be changed to account for this.

Particle image velocimetry methods will in general not be able to measure components along the z-axis (towards to/away from the camera). These components might not only be missed, they might also introduce an interference in the data for the x/y-components. Some new methods also allow to measure three-dimensional flow though.

Since the resulting velocity vectors are based on cross-correlating the intensity distributions over small areas of the flow, the resulting velocity field is a spatially averaged representation of the actual velocity field. This obviously has consequences for the accuracy of spatial derivatives of the velocity field, vorticity, and spatial correlation functions that are often derived from PIV velocity fields.

Commercial research grade PIV systems include a Class IV laser and high resolution/speed digital camera that make the systems potentially unsafe and very expensive. Commercial systems are prohibitively expensive (around US$100K).

More Complex PIV Setups

Molecular Tagging Velocimetry

molecular tagging velocimetry, or MTV, uses molecule sized tags, which are often already a part of the flow. Small molecules being much closer to the size and density of a flow minimize the error of particles not following the flow. One example used in humid air flows uses a laser to dissociate the water (H2O) in the flow into H + OH. The hydroxyl (OH) molecule serves as the tag. This method is known as hydroxyl tagging velocimetry (HTV).

The molecules used as tracers in MTV are subject to Brownian motion. This limits the method to ultra-high speed or steady flows.

Stereoscopic PIV

Stereoscopic PIV utilises two cameras with separate viewing angles to extract the z-axis displacement. Both cameras must be focused on the same spot in the flow and must be properly calibrated to have the same point in focus.

In fundamental fluid mechanics, displacement within a unit time in the X, Y and Z directions are commonly defined by the variables U, V and W. As was previously described, basic PIV extracts the U and V displacements as functions of the in-plane X and Y directions. This enables calculations of the $U_{x}$, $V_{y}$, $U_{y}$ and $V_{x}$ velocity gradients. However, the other 5 terms of the velocity gradient tensor are unable to be found from this information. The stereoscopic PIV analysis also grants the Z-axis displacement component, W, within that plane. Not only does this grant the Z-axis velocity of the fluid at the plane of interest, but two more velocity gradient terms can be determined: $W_{x}$ and $W_{y}$. The velocity gradient components $U_{z}$, $V_{z}$, and $W_{z}$ can not be determined. The velocity gradient components form the tensor:

${\begin{bmatrix}U_{x}&U_{y}&U_{z}\\V_{x}&V_{y}&V_{z}\\W_{x}&W_{y}&W_{z}\end{bmatrix}}$

Dual Plane Stereoscopic PIV

This is an expansion of stereoscopic PIV by adding a second plane of investigation directly offset from the first one. This allows the determination of the three acceleration components single-plane stereoscopic PIV could not calculate. With this technique, all fluid properties within a 2-dimensional plane can be quantified.

Micro PIV

With the use of an epifluorescent microscope, microscopic flows can be analyzed. MicroPIV makes use of fluorescing particles that excite at a specific wavelength and emit at another wavelength. Laser light is reflected through a dichroic mirror, travels through an objective lens that focuses on the point of interest, and illuminates a regional volume. The emission from the particles, along with reflected laser light, shines back through the objective, the dichroic mirror and through an emission filter that blocks the laser light. Where PIV draws its 2-dimensional analysis properties from the planar nature of the laser sheet, microPIV utilizes the ability of the objective lens to focus on only one plane at a time, thus creating a 2-dimensional plane of viewable particles.

It should be noted that microPIV particles are on the order of several hundred nm in diameter, meaning they are extremely susceptible to Brownian motion. Thus, a special ensemble averaging analysis technique must be utilized for this technique. The cross-correlation of a series of basic PIV analysis are averaged together to determine the actual velocity field. Thus, only steady flows can be investigated. Special preprocessing techniques must also be utilized since the images tend to have a zero-displacement bias from background noise and low signal-noise ratios. Usually, high numerical aperture objectives are also used to capture the maximum emission light possible. Optic choice is also critical for the same reasons.

Holographic PIV

Holographic PIV extracts the entirety of the motion of the particles in all planes. It does so by using the interference patterns of two laser beams of the seem frequency but out of phase to visualize all the particles within a volume with their respective interference patterns. However, large difficulties in this technique arise from isolating the z-component (out of plane) of the particles. It is still in development but has so far not been reliably successful.

Scanning PIV

By using a rotating mirror, a high-speed camera and correcting for geometric changes, PIV can be performed nearly instantly on a set of planes throughout the flow field. Fluid properties between the planes can then be interpolated. Thus a quasi-volumetric analysis can be performed on a target volume.

Tomographic PIV

A volumetric analysis technique, like holographic PIV, that utilizes four cameras oriented at different angles but focused on the same point to determine all of the acceleration properties of a fluid.

Particle Tracking Velocimetry

By utilizing PIV analysis as an initial guess for a PTV analysis, more accurate analysis can be obtained than the spatial averaging of the cross-correlation method that typifies PIV analysis alone.

Applications

PIV has been applied to a wide range of flow problems, varying from the flow over an aircraft wing in a wind tunnel to vortex formation in prosthetic heart valves. 3-Dimensional techniques have been sought to analyze turbulent flow and jets.

Rudimentary PIV algorithms based on cross-correlation can be implemented in a matter of hours, while more sophisticated algorithms may require a significant investment of time. Several open source implementations are available including URAPIV [8] and mpiv [9] (a Matlab Toolbox), PyPIV [10] (an implementation in Python), JPIV [11] (a Java implementation), OSIV [12] and Gpiv [13] (both implementations in C).

Granular PIV: Velocity measurement in granular flows and avalanches

Particle image velocimetry (PIV) measurement technique is also introduced and used to measure the dynamics of the velocity distribution of free surface and unsteady flows of granular avalanches of non-transparent sand and quartz particles down channels and curved chutes merging into a horizontal plane from initiation to the run-out zone. Velocity distributions at the free surface are determined, and also at the bottom from below. These results can be applied to estimate impact pressures exerted by granular flows and avalanches on defence structures and infrastructures along the channel and in run-out zones.

PIV is used to measure the velocity field of the free surface and basal boundary in a granular flow and avalanche. This analysis is particularly designed for nontransparent fluids such as sand, gravel, quartz, or other granular materials that we can find in geophysical scenarios. This PIV system is called the “granular PIV.” The set-up of the granular PIV differs from the usual PIV in that the optical surface structure which is produced by illumination of the surface of the granular flow is already sufficient to detect the motion. This means one does not need to add tracer particles in the bulk material.

See also

• Particle tracking velocimetry
• Laser Doppler velocimetry
• Hot-wire anemometry
• Molecular tagging velocimetry

References

• Particle Image Velocimetry: A Practical Guide, Raffel M., Willert C., Wereley, S. and Kompenhans J. 2007. Heidelberg: Springer-Verlag. ISBN 3-540-72307-3
• Digital Particle Image Velocimetry — Theory and Application, Westerweel, J. 1993. Delft: Delft University Press. [14]
• Avalanche Dynamics: Dynamics of Rapid Flows of Dense Granular Avalanches, Shiva P. Pudasaini and Kolumban Hutter, 2007. Springer, Berlin, New York, ISBN 3-540-32686-3
• Adrian, R.J., "Twenty years of particle image velocimetry". Experiments in Fluids 39:159–169 (2005).

External links

• from "Online Resource Center".
• from "The Art of Laser Velocimetry", an explanation of DPIV, and an explanation of holographic PIV.
• Acoustic Particle-Image Velocimetry — Development and Applications
• Educational Particle Image Velocimetry (e-PIV) - resources and demonstrations
• Matlab PIV toolbox
• OpenPIV
• Gpiv, Gpivtools, PyGpiv
• JPIV
• Particle Image Velocimetry - General Information and Applications