Imaging Techniques for Fluid Mechanics-- Algorithms and Software

Background

Particle Image Velocimetry (PIV) was first developed into a workable technique around 1985 at the University of Illinois, Urbana-Champaign, where Dr. Prasad was a post-doctoral fellow during 1989-92. Partly through his efforts, PIV now represents the foremost technique for making non-intrusive velocity measurements over global domains in fluid flows, instantaneously and with high accuracy. The technique is a quantitative extension of the qualitative flow-visualization technique which was practiced for several decades. In PIV, fluid flows are seeded with minute passive tracer particles, which are then illuminated by short, intense bursts of laser light formed into a sheet. A camera oriented orthogonally to the light sheet records the location of the same particles at successive instants in time. In post-processing, a step known as ``interrogation,'' image fields are digitized and particle displacements are extracted using correlation algorithms. Given the time separation between laser pulses, the velocity field over the recorded domain is instantaneously mapped at thousands of grid-points providing a detailed, quantitative view of the flow.

A world-class PIV laboratory has been established at UDel from the ground up, with the purchase of major equipment and the design and fabrication of experimental facilities. Laser illumination for the suspended particles is provided by twin Continuum Nd:YAG pulsed lasers, each operating at 10 Hz and providing 6 ns pulses at 300 mJ/pulse in the green (532 nm). Photographs are acquired using conventional 35 mm cameras, scientific format (4'' by 5''), and high-resolution (Kodak ES 1.0) digital cameras. Recorded images are interrogated on a high-speed interrogation system which consists of two Intel-860 processors incorporated into a 486-PC platform. The 860 processors perform Fast Fourier Transforms with extreme efficiency, which is an essential step in our correlation algorithms. The effective speed of the interrogation system is 200 Mflops, which translates to the interrogation of up to 50 vectors/second. All of our algorithms are written in-house by Dr. Prasad's research team, which allows for continuous improvements and innovations.

The following works have been completed:

Boillot, A., and Prasad, A.K., "Optimization Procedure for Pulse Separation in Cross-Correlation PIV," Experiments in Fluids, Vol. 21, pp. 87-93 (1996).

In PIV, the optimal time separation between successive laser pulses is influenced by a number of parameters. In the present paper, only two kinds of errors affecting the choice of pulse separation are studied: (i) random error arising from noise during recording of the flow seeded with tracer particles and subsequent interrogation of the particle images, and (ii) acceleration error arising from approximation of the local Eulerian velocity based on small (but non-zero) particle displacements. These two kinds of errors place conflicting requirements on the pulse separation. A model to optimize pulse separation with respect to these two errors is described, and the model is confirmed by the results of a Monte Carlo simulation. The model for optimal pulse separation is extended to various acceleration distributions. An estimate for the spatial resolution of the velocity field resulting from cross-correlation PIV is proposed.
Prasad, A.K., Adrian, R.J., Landreth, C.C., and Offutt, P.W., "Effect of Resolution on the Speed and Accuracy of Particle Image Velocimetry Interrogations," Experiments in Fluids, Vol. 13, No. 2-3, pp. 105-116, 1992.

Particle Image Velocimetry (PIV) incorporates a process by which an image of a flow field, bearing double images of seeding particles is analyzed in small regions called "interrogation spots." Each spot is imaged on to a photodetector array whose digitized output is evaluated computationally using the auto-correlation technique. This paper examines the effects of resolving the spot using arrays of various resolutions, motivated primarily by a gain in speed. For this purpose, two specially created test-photographs representing (i) uniform flow, and (ii) solid body rotation, were interrogated using array sizes ranging from 32 by 32 to 256 by 256. Each reduction in resolution by a factor of 2 gains a factor of four in interrogation speed, but this benefit is counteracted by a loss in accuracy. The particle image diameter strongly influences accuracy through two distinct error mechanisms. When the particle image diameter is small compared to the pixel size, mean bias error becomes significant due to finite numerical resolution of the correlation function. Conversely, when the particle image is large, random error due to irregularities in the electronic images predominates. The optimum image size, therefor, lies not at either extreme, but at an intermediate value such that the particle image is small in an absolute sense, and yet large enough relative to the pixel size.