Two-Dimensional Digital Particle Tracking Velocimetry Algorithm Based on the Image of Particle Trace

Liu, C. and Tao, L. , 2007. Two-dimensional digital particle tracking velocimetry algorithm based on the image of particle trace. Journal of Coastal Research, SI 50 (Proceedings of the 9th International Coastal Symposium), pg – pg. Gold Coast, Australia, ISBN A digital method is developed to judge the instantaneous flow velocity by the image of the moving tracer particle formed during the exposure time. The grey-scale image of the particle trace is changed into the binary image and the pixels included in the particle trace image are marked. The length of the particle trace is obtained by determining the central principal axis of the particle trace image. The direction of the particle moving is determined by the fact that the flow velocities in a small local domain are almost the same. The instantaneous flow velocity field in the channel is measured by the method presented in this paper. The mean flow velocities along the vertical direction obtained by averaging the instantaneous velocities agree well with the logarithmic law. ADITIONAL INDEX WORDS: Particle Image Velocimetry (PIV), Image process, Central principal axis INTRODUCTION Particle tracking velocimetry (PTV) and particle image velocimetry (PIV) are non-intrusive optical technique to measure the instantaneous velocity of the whole flow field. Due to its great advantage in measuring complex flow field, it has been widely applied to study the turbulence and multiphase flows (e.g., TANAKA et al., 2003, ANGELE and MUHAMMAD, 2006). In the PTV system, the flow velocities are calculated by the displacement of tracer particles during the time interval. In general, there are two types of techniques to measure this displacement: (1) judging the particle images corresponding to the same particle at different exposures, (2) measuring the length of the particle trace formed at one exposure. Up to now, many digital PTV algorithms based on the first method are developed (for e.g., see COWEN, 1997, ISHIKAWA et al., 2000). However, few digital algorithms on the second method are reported. For many years, the length of the particle image and the direction of flow velocity are determined manually. Comparing to the PTV system based on the first method, that PTV system based on the second method has considerable advantages such as low-cost, real-time, and easy to use. Some research attempts and progress have been made recently in the development of the digital PTV algorithms based on the particle image formed at one exposure. BALDASSARRE et al. (2001) measured the length of the particle trace by identifying the intersections between the grid and trace and prevented the directional ambiguity of flow velocity due to the use of two CCD cameras to acquire particle images simultaneously. The PTV system using the algorithms developed by BALDASSARRE et al. (2001) is a low-cost, real-time, relatively easy to use, safe and flexible. However, the measuring precision of Baldassarre’s algorithm depends on the size of grid and the hardware system becomes a bit complex to acquire particle images simultaneously by two CCD cameras. To overcome such a weakness inherited in the technique of BALDASSARRE et al. (2001), in this paper, we presented a new approach: the central principal axes of the particle trace image are introduced to measure the length of the particle trace. Such a approach enables us to prevent the directional ambiguity of flow velocity due to the fact that flow velocities in a small local domain are approximately the same. The instantaneous flow velocity field in a channel presented in this paper demonstrates the validity of the method. The mean flow velocity profile obtained by averaging the instantaneous velocities agrees very well with the logarithmic law. MEASURING METHODS Flow tracer visualisation methods use tracer particles which are neutrally buoyant. By applying a PTV system, the velocity of each particle is assumed equal to the fluid velocity at the same location. So the flow velocities can be measured by the velocities of tracer particles. Since the size of seeding particles is always much smaller than the scale of flow structure, a suitable exposure time can be chosen to satisfy the following conditions: (1) the size of seeding particles is much smaller than the length of particle trace formed during the exposure time, (2) the particle trace is a straight line. Thus the particle trace image formed during the exposure time must be a rectangle in which the edges along one direction are much longer than that along another direction. Therefore, the vector of the particle trace can be obtained based on the particle trace image, and the velocity of the tracer particle can be calculated. Assuming that the vector of a particle trace is p ur and the exposure time is t Δ , the velocity of the particle u r can be calculated as p u t = Δ ur r (1) Journal of Coastal Research, Special Issue 50, 2007 Digital Particle Tracking Velocimetry Algorithm In practice, the vector of the particle trace is obtained by the following three steps: (1) image acquisition and processing, (2) particle trace marking, (3) particle trace vector calculation. Image acquiring and processing In order to obtain the particle trace image, a light sheet is used to illuminate the seeding particles. The particle trace images formed during the exposure time are recorded by CCD camera and transformed into digital image by a grabbing card. The ordinary grey-scale images are changed into binary images according to a certain threshold value. In order to obtain high quality binary images, the threshold value is set according to the mean grey value of the local area around the particle image trace. Particle trace marking It is important to mark the pixels included in a particle trace image in order to obtain the length of it. In this paper, the pixels included in a particle trace image are marked according to the binary images. In the binary images, the grey-scale at one pixel has only two values, 0 and 1. The grey value at the pixels of the particle trace images is 1 and the other is 0. The pixels included in a particle trace image can be defined as the connecting pixels whose values are 1. For two-dimensional images, the pixels connecting with the pixel (i, j) are (I,J+1), (I,J-1),( I+1,J+1), ( I+1,J), ( I+1,J-1), ( I-1,J+1), ( I-1,J), ( I-1,J-1). According to the above definition, an algorithm is devised to mark the pixels included in a particle trace image. Assuming that the pixels included in a particle trace image are (I1, J1 ), (I2, J2) ··· (IN,JN), the center of particle trace image (Ic,Jc) can be calculate by the following formula: