Particle Image Velocimetry

Human beings are extremely interested in the observation of nature, as this was and still is of utmost importance for their survival. Human senses are especially well adapted to recognize moving objects as in many cases they mean eventual danger. One can easily imagine how the observation of moving objects has stimulated first simple experiments with set-ups and tools easily available in nature. Today the same primitive behavior becomes obvious, when small children throw little pieces of wood down from a bridge in a river and observe them floating downstream. Even this simple experimental arrangement allows them to make a rough estimate of the velocity of the running water and to detect structures in the flow such as swirls, wakes behind obstacles in the river, water shoots, etc.

It is clear from the principle of PIV as described that PIV — in contrast to hotwire or pressure probe techniques — is based on the direct determination of the two fundamental dimensions of the velocity: length and time. On the other hand, the technique measures indirectly, because it is the particle velocity which is determined instead of fluid velocity. Therefore, fluid mechanical properties of the particles have to be checked in order to avoid significant discrepancies between fluid and particle motion.

A detailed mathematical description of statistical PIV evaluation has been given by Adrian [36]. This early work from 1988 concentrated on autocorrelation methods and was later expanded to cross-correlation analysis [65]. Most of the characteristics and limitations of the statistical PIV evaluation have been described therein. The most complete and careful mathematical description of digital PIV has been given by Westerweel [7]. In this chapter a simplified mathematical model of the recording and subsequent statistical evaluation of PIV images will be presented. For this purpose the two-dimensional spatial estimator for the correlation will be referred to as the correlation. First, we analyze the cross-correlation of two frames of singly exposed recordings, then we expand the theory for the evaluation of doubly exposed recordings. The motivation for why auto- and cross-correlation methods are employed in PIV evaluation will be given in chapter 5.

In this chapter different approaches to PIV recording are introduced. It is important to realize that the various recording methods are not necessarily defined by the recording medium. The same approach may for instance be applied using either photography or digital recording. The PIV recording modes can be separated into two main branches: (1) methods which capture the illuminated flow on to a single frame and (2) methods which provide a single illuminated image for each illumination pulse. These branches are referred to as single frame/multi-exposure PIV and multi-frame/single exposure PIV, respectively [28].

This chapter treats the fundamental techniques for statistical PIV evaluation. In spite of the fact that most realizations of PIV evaluation systems axe quite similar — in nearly every case they are based on digitally performed Fourier algorithms — we will also consider optical techniques because they are still important for the classification and understanding of existing set-ups.

The recording and evaluation of PIV images has been described in the previous two chapters. Investigations employing the PIV technique usually result in a great number of images which must be further processed. If looking for statistical quantities the recorded data can easily amount to some gigabytes, which is now possible with today’s computer hardware. Even more data per investigation are to be expected in future. Thus, it is quite obvious that a fast, reliable and fully automatic further processing of the PIV data is essential.

In spite of all its advantages, the PIV method underlies some shortcomings that make further developments on the basis of instrumentation necessary. One of these disadvantages is the fact that the “classical” PIV method is only capable of recording the projection of the velocity vector into the plane of the light sheet; the out-of-plane velocity component is lost while the in-plane components are affected by an unrecoverable error due to the perspective transformation as described in section 2.4.3. For highly three-dimensional flows this can lead to substantial measurement errors of the local velocity vector. This error increases as the distance to the principal axis of the imaging optics increases. Thus it is often advantageous to select a large viewing distance in comparison to the imaged area to keep the projection error to a minimum. This is easily achieved using long focal length lenses.

In this chapter some of the applications of DLR’s mobile PIV system will be described. For each experiment the most important parameters of the flow field under investigation, of the illumination and recording set-up will be given. If not stated otherwise, the evaluation has been carried out by means of cross-correlation methods, i.e. in the case of photographic recording the negatives have been scanned and digitized prior to evaluation.