Quantitative flow visualization was provided by a laser scanning version of particle image velocimetry (PIV). The ability of obtaining two-dimensional instantaneous velocity fields with high spatial resolution makes PIV a powerful tool for investigating separated, unsteady flows. A two-dimensional velocity field can be used for calculation of other flow properties such as vorticity distribution and streamline pattern, as well as other information. Comprehensive reviews of the PIV technique are presented by Adrian (1991), Landreth and Adrian (1988), Rockwell et al. (1993).
PIV tracks the motion of neutrally-buoyant particles suspended in the fluid to determine the velocity. In the present experiments, a mixture of metallic-coated glass particles with an average diameter of 14 mm and hollow glass spheres with an average diameter of 10 mm manufactured by Potters Industries Inc. was illuminated by a laser sheet, approximately 1 mm in thickness. The laser sheet is created using the laser-optical system described by Corcoran (1992). A continuous Argon-ion laser (Coherent Innova series) with a maximum power of 30 watts produces a multi-band beam which passes through a series of optical lenses. The beam is focused on a 72-facet rotating mirror manufactured by Lincoln Laser Corp. As the mirror rotates, reflections of the laser beam from its facets create a continuous vertical light sheet. In the case when the cylinder was moving with the zero phase shift with respect to the propagating wave, the rotating mirror was driven by a variable frequency motor at a frequency fm = 1.9 Hz to produce an effective scanning frequency fsc = 72, fm = 136.8 Hz. In all other cases, the rotating mirror was driven at a frequency fm = 2.9 Hz to produce an effective scanning frequency fsc = 208.8 Hz. The values of scanning frequency were chosen to optimize the distance between particle images on the PIV image. To minimize the unsteadiness in the laser scanning rate at lower rotational speeds, an external square function generator (Heath Co. SG-1274) was used to provide a high precision square wave to drive the motor.
The entire optical system is located under the wave tank (Figure 1c). The steering mirrors and the focusing lenses are positioned on a table that can be moved along the length of the tank. In addition, the entire system can be translated along the width of the wave tank to allow adjustment of the plane of interest. The circular support of the rotating mirror allows the laser sheet to be oriented at any angle with respect to the direction of wave propagation.
A Canon EOS-1 N RS camera with a 100 mm telephoto lens was used to capture the illuminated flow field on 35 mm Kodak TMAX 400 film. In the case of the cylinder moving with zero phase shift with respect to the propagating wave, a shutter speed of 1/40 sec and an f-number of 6.3 were used. In all the other cases, a shutter speed of 1/50 sec and an f-number of 4.0 were used. The maximum framing rate of the camera (approximately 8 frames/sec for these shutter speeds) allowed to take approximately 16 frames during one cycle of wave motion (T = 2 sec) providing a time resolution Dt/T = 0.0625.
The circular motion of the water in a propagating wave and large regions of the separated flow in the plane of interest causes directional ambiguity in the velocity field (Adrian, 1986). This ambiguity is eliminated by adding an artificial bias velocity to each image. The bias velocity also decreases the dynamic range to permit better interrogation of the image. The bias is added by using a 45° rotating mirror between the camera and the laser sheet. The frequency of the bias mirror oscillation was equal 10 Hz for all the experiments. The peak to peak amplitude of the ramp signal for the stationary cylinder cases was equal 0.432 V (depths of the cylinder submergence h = 20 mm and h = 7 mm) and 0.480 V (h = 0 mm). In the case of the cylinder moving with zero phase shift with respect to the propagating wave, the amplitude was equal to 0.272 V. In case of p radians phase shift, the amplitude was equal to 0.340 V. The actual bias velocity added to the flow ranged approximately from 2 to 6 times the velocity of the flow and was oriented in the direction of the wave propagation.
The use of a bias mirror to produce image shifting may give rise to systematic errors discussed by Raffel and Kompenhans (1995). This error is significant with sufficiently large rotation angles of the mirror, when the mirror is located close to the laser sheet, and with large magnification factors. In the present experiments, the bias mirror was located at a maximum distance from the laser sheet and was rotated much less than 1°. It has been assumed that the error associated with the use of a bias mirror is negligible with respect to other uncertainties involved in the PIV technique.
The proper choice of the parameters described in this section allows acquisition of multiple images of individual particles on the film negative. The spacing between the particles is proportional to the vector sum of the local and bias velocities.