Principles

The Particle Image Velocimetry is a well established, non intrusive technique for measuring the spatial distribution of the velocity within a single plane inside the flow, indirectly via the displacement of moving particles groups within a certain time, see figure 2.1 and [85]. For this purpose the flow region under consideration is homogeneously seeded with appropriate tracer-particles such that their injection and presence does not affect the flow or fluid properties. The

2 Particle Image Velocimetry

concentration of the particles must be well adjusted with regard to the finest flow structures, in order to sample the flow properly, and the deviation of the particle velocity

?

pfrom the real flow motion must be negligible compared to the uncertainty of the imaging and recording system and to the uncertainty due to the evaluation procedure. In this case the difference between the following expressions is negligible.

i After the required seeding concentration has been obtained, a desired plane inside the flow is illuminated twice by a thin laser light-sheet. The light scattered by the tracer-particles at time^m and ^{m o} in the direction of the recording optics is usually stored on individual frames of a single frame transfer CCD camera, whose optical axis is perpendicular to the light-sheet.

It is obvious that the fluid must be optically accessible and sufficiently transparent for the wavelength under consideration. Furthermore, the light-sheet intensity and field of view must be well balanced to the scattering properties of the particles, the performance of the optical system and the sensitivity of the camera.

particles

Particle image positions at t

∆ Particle image positions at t+ t∆

t+ t

X Y

FIGURE 2.1: Schematic set-up of particle image velocimetry system after [85]. A desired plane in-side the flow is illuminated twice by a thin laser light-sheet and the scattered light emerging from the homogeneously distributed particles in the direction of the imaging optics is recorded.

The local in-plane particle image displacement component ^u of the double exposed particles is finally determined from the two single exposed recordings by means of spatial cross-correlation techniques and afterwards divided by

m

and the magnification factor ^v of the imaging system to calculate the first order approximation of the velocity field according to the following equation.

2.1 Principles It is of fundamental importance to realize that the particle displacement must be small relative to the finest flow scales, as only phenomena that occur over a time interval which is longer than^{md€m o b m} and that have a spatial extent larger than the absolute displacement can be resolved, but the particle image displacement

hu

, on the other hand, must be large for accurate measurements.

This brief overview already implies that the complexity of the technique arises basically from the technical components involved and their mutual dependence on each other and less on the principles of the technique itself. In terms of accuracy, for example, the particles should be sufficiently small and their density should exactly match the density of the surrounding fluid. Unfortunately, this is not often feasible for a desired field of view and a given laser power, light sheet thickness, transparency of the fluid, imaging optics and sensitivity of the digital camera, as the scattering intensity decreases rapidly with decreasing particle diameter as shown in figure 2.2. Decreasing the light-sheet width or thickness may partially help but

Light

0^o 180^o

5 10⁷

3 10 10 Light 10

0^o 180^o

FIGURE 2.2: Light intensity scattered by spherical oil particles of different size in air (left: ^ p ^‚

ƒ…„

m, right: ^ _p ‚

ƒa†„

m), illuminated from left with a plane monochromatic wave front, after [85].

The complex spatial intensity distribution, with a maximum in forward direction, results from the interference between the reflected, refracted and diffracted wave front.

the size of the largest resolvable scales will decrease as well and the three dimensionality of the flow may cause further problems as will be explained later. To use a powerful laser seems to be the appropriate solution but beside the costs, strong reflections from model surfaces or undesirable disturbances of the flow due to acoustic excitation or thermal response of the flow have to be taken into account [48]. An intensified camera could be applied as well but a reduced spatial resolution and an increased noise level must be accepted. Alternatively, the evaluation procedure could be adapted but then the accuracy of the velocity estimation and the validity of the well established principles may become questionable. Furthermore, it cannot be recommended to analyse data where the desired fluid mechanical information, hidden in the particle image displacement, cannot be uniquely determined. So increasing the particle size may be the appropriate solution at the end, but how this can be achieved is unknown.

Anyway, in order to make the right decision while setting up and aligning the experiment, a clear understanding of the basic components is essential. For this reason the production of desired particles, the problems associated with the recording of the particle images and the determination of the image displacement will be treated in chapter 2. In chapter 3 and 4 the more sophisticated recording techniques are considered which have been applied for the fluid mechanical investigations presented in the second part of the thesis.

2 Particle Image Velocimetry