Particle image velocimetry

Particle image velocimetry (PIV) is an optical method used to measure velocities and related properties in fluids. The fluid is seeded with 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.

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History

For a recent overview of the history of PIV technique see: Adrian, R.J., "Twenty years of particle image velocimetry". Experiments in Fluids 39:159–169 (2005).

Technique

Typical PIV apparatus consists of a camera (normally a digital camera in modern systems), a high power laser, for example a double-pulsed Nd-YAG laser laser or a copper vapour laser, an optical arrangement to convert the laser output light to a light sheet (normally using a cylindrical lens), and the fluid/gas under investigation. A fibre optic cable often connects the laser to the cylindrical lens setup. The laser acts as a photographic flash for the digital camera, and the particles in the fluid scatter the light. It is this scattered light that is detected by the camera.

In order to measure the velocity at least two exposures are needed. They can be recorded on one or several frames.

The frames are split in a large number of interrogation areas, often called tiles. It is then possible to calculate a displacement vector for each tile with help of signal processing (auto-correlation/cross-correlation). This is converted to a velocity using the time between image exposures.

Timing electronics allows one to control the spacing between image exposures. The electronics also permits image pairs to be acquired at various times along the flow. These digital delay and pulse generators provide several outputs that can be delayed and referenced to each other.

Advantages

The method is to a large degree nonintrusive. The added tracers (if they are properly chosen, see for the reference Melling, 1997 [1]) generally cause negligible distortion of the fluid flow.

Optical measurement avoids the need for Pitot tubes, hotwires 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

The particles will, due to their higher density, not exactly follow the motion of the fluid (gas/liquid).

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.

The size of the recordable flow field is limited by the size of the tracer particles. 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 will occur with loss of sub pixel resolution. The typical maximum size of the recordable plane is in the region of 10cm to 50cm square, depending on the technology and complexity of the analysis algorithms used.

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.

Improvements to basic PIV

Each of the above limitations have been addressed by specialist techniques. For example, a similar velocimetry method known as 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).

Stereoscopic PIV utilises two cameras with separate viewing angles to extract the z-axis velocity component. Holographic PIV similarly extracts the third component. However Both these techniques drastically increase cost and complexity of the system.

Recent research has outlined the possibility of treating the flow images as a continuous system of flow structures, instead of a system of quasi-random points. This allows the imaging of a limitless size of flow field, provided appropriate seeding is ensured.

The molecules used as tracers in MTV are subject to Brownian motion. This limits the method to ultra-high speed flows. A typical example of the successful application of MTV is the investigation the intake flow in engines. Here the spray is very dense and flow speeds are high enough to allow accurate results for MTV.

The effect of the spatial averaging can be reduced by the use of more complicated algorithms based on deforming the interrogation areas or based on Particle tracking velocimetry using PIV as an initial estimate for the position where individual particles are advected.

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. Though less common, PIV can also be used for quantifying the deformation and motion of solid materials and tissues that have embedded markers or are in some other way visually heterogeneous (e.g. using fluorescent speckles or particle grains).

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 [2] and mpiv [3] (a Matlab Toolbox), PyPIV [4] (an implementation in Python), OSIV [5] and Gpiv [6] (both implementations in C).

See also

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

References

• Particle Image Velocimetry, Raffel M., Willert C. and Kompenhans J. 1998. Heidelberg: Springer-Verlag.
• Digital Particle Image Velocimetry — Theory and Application, Westerweel, J. 1993. Delft: Delft University Press.