3 Quantitative Flow Visualization techniques

3.1 Introduction

For quantitative flow visualization techniques, a flow is visualized by seeding the fluid with small particles that allow to follow the instantaneous changes of the flow. The region in the flow to be researched is illuminated, mostly by a sheet of light. This light-sheet is generated by an expanding laser beam by means of a cylindrical lens or due to the projection of the beam on a rotating hexagonal mirror. The instantaneous flow is recorded at least twice by very short light flashes with a separation time (Dt) in between that is known. The flashes have to be sufficiently short in order image the particle shape. Too long illumination times will result into streaks of the particle images that will not allow to determine the exact particle location in the fluid. Several illuminations result in trace patterns of each particle on the image plane. Analyzing these particle traces result in local particle displacements. As the separation time between the recordings is known, the analyses directly result in velocities. Mainly two different techniques are known: Particle Tracking Velocimetry (PTV) and Particle Image Velocimetry (PIV). The difference is in the density of the seeding. In literature the particle density is often represented by two dimensionless parameters; the image particle density NI and source density NS. The source density represents whether the particle images are overlapping (NS > 1) or can be recogized individually (NS < 1). NI represents the ratio of the length of the particles tracks between successive illuminations and the distances between individual particles.

3.2 Particle Tracking Velocimetry

In case of PTV a sparse seeding is used (NS < 1 and NI < 1). Therefore, each particle trace can be analyzed individually. As the particles are present at random locations in the fluid, the velocity estimators are found at random locations in the flow, too. Velocities that have to be obtained in-between the points of observations will have to be interpolated. PTV is a relatively easy way for obtaining quantitative information of the flow. Interpolation, though, is only allowed if the smallest scales of the flow are much smaller than the distances between the points of observation. Mainly laminar flows may satisfy this demand.

3.3 Particle Image Velocimetry

In case of turbulent flows, a whole spectrum of eddies occur with maximum dimensions related to the flow domain and minimum dimensions in the order of the Kolmogorov length scale (a few millimeters for laboratorium experiments). In order to observe these large ranges of eddy sizes, a high particle density is needed (NI > 1). This means that it is impossible to track the individual particles. Therefore, the mean displacement of particles in a small region of the image(s) (the interrogation area) has to be calculated.
Actually, not the particle displacements are analyzed, but the image transparency as function of the relative translation within the interrogation area's. For computerized images the image density is represented by the pixel values. By locating the maximum transparancy the mean displacement of the particles in the interrogation area has been found. The transparancy can be obtained by shifting the two interrogation areas and subsequently plotting a two-dimensional histogram of the transparancy. This shifting may be performed physically, in case of analog images (i.e. photographic slides) or by means of a numeric algorithm, in case of digital PIV (DPIV). An other way to obtain the 2-dimensional transparancy function is by (auto) correlating the interrogation area's of the image. For analog images the correlation function may be obtained by optical Fourier Transformation techniques. The interrogation area, then, is determined by the diameter of the laser beam that interrogates the image. In case of DPIV, the calculation time of Fourier Transforming an interrogation area increases linearly with its dimension (NxN). Therefore, a more efficient method is mostly used by means of Fast Fourier Transformation (FFT) techniques. With FFT the calculation effort is related to Nlog(N), which means that it is advantagous for interrogation areas large than 16x16 points. Typical dimensions of an interrogation area for Digital PIV are 16x16 to 128x128 pixels.
In order to obtain a reliable estimator of the particle image displacement, about 10 to 15 particles in an interrogation area have to be present.
As the particle image density is very high, the entire image may be interrogated at arbitrary locations. Mostly, the interrogation process is performed on a rectangular grid of interrogation areas that are adjacent or partly overlapping. Therefore, in contrast to PTV, PIV results in a two dimensional velocity field on a rectangular grid.

3.4 Laser Speckle Velocimetry

In case particles are overlapping (Ns > 1) no individual particles can be recognized anymore. By using a coherent light source, a pattern of speckles is generated due to interferences of the coherent light. The speckel pattern, then, is imaged and recordered. Evaluations of interrogation areas from subsequent recordings, in a identical way as is done for PIV, will result into the displacements of the speckle patterns. As extremely high particle densities are needed, penetration of the light sheet is difficult and care should be taken that particles will not affect the flow itself. Laser Speckle Velocimetry is mostly used for determining of velocities of solid surfaces in transport mechanisms (photocopy machines, for example).

3.5 Other techniques

PIV has been evolved from photographic PIV in its beginning , some 15 to 20 years ago, that interrogates the slides by optical Fourier Transformation to digital PIV, that uses CCD cameras and computer techniques to carry out the interrogation. Nowadays, even three dimensional PIV within the light sheet is done by observing the flow with two or more cameras that are looking under different angels to the area of researchlight.
Holographic PIV does not have the restriction of the thickness of the light sheet. It allows to research a region in the flow that is defined by the coherence length of the laser source. Their analyses result in three-dimensional velocities on a three-dimensional grid.
An other technique that has been reported is 'Global Doppler Velocimetry'. It uses the doppler shift of the reflected light from the particles. The doppler shift is then recorded on an image. Time averaging is needed in order to obtain sufficiently signal So, this technique results in time averaged velocities at every pixel of the image, instead of every 16x16 or 128x128 pixels in case of PIV.

3.6 References

Ronald J. Adrian, 'Particle-imaging techniques for experimental fluid mechanics', Annu. Rev. Fluid Mech., 1991, 23, 261-304

'Particle Image Velocimetry', Measurement Science and Technology, vol 8, no 12, special issue

M. Raffel, C. Willert, J. Kompenhans, 'Particle Image Velocimetry', Springer, 1998

'Application of Particle Image Velocimtry, Theory and Practice', Course notes, March 2-6, 1998, Gottingen

J. Westerweel, 'Digital Particle Image Velocimetry, Theory and Application', PhD thesis, Delft University, 1993