Determining Sizes of Particles in a Flow from DPIV Data
A proposed method of measuring the size of particles entrained in a flow of a liquid or gas would involve utilization of data from digital particle-image velocimetry (DPIV) of the flow. That is to say, with proper design and operation of a DPIV system, the DPIV data could be processed according to the proposed method to obtain particle sizes in addition to particle velocities. As an additional benefit, one could then compute the mass flux of the entrained particles from the particle sizes and velocities. As in DPIV as practiced heretofore, a pulsed laser beam would be formed into a thin sheet to illuminate a plane of interest in a flow field and the illuminated plane would be observed by means of a charge-coupled device (CCD) camera aimed along a line perpendicular to the illuminated plane. Unlike in DPIV as practiced heretofore, care would be taken to polarize the laser beam so that its electric field would lie in the illuminated plane, for the reason explained in the next paragraph. The proposed method applies, more specifically, to transparent or semitransparent spherical particles that have an index of refraction different from that of the fluid in which they are entrained. The method is based on the established Mie theory, which describes the scattering of light by diffraction, refraction, and specular reflection of light by such particles. In the case of a particle illuminated by polarized light and observed in the arrangement described in the preceding paragraph, the Mie theory shows that the image of the particle on the focal plane of the CCD camera includes two glare spots: one attributable to light reflected toward the camera and one attributable to light refracted toward the camera. The distance between the glare spots is a known function of the size of the particle, the indices of refraction of the particle material, and design parameters of the camera optics. Hence, the size of a particle can be determined from the distance between the glare spots. The proposed method would be implemented in an algorithm that would automatically identify, and measure the distance between, the glare spots for each particle for which a suitable image has been captured in a DPIV image frame. The algorithm (see figure) would begin with thresholding of data from the entire image frame to reduce noise, thereby facilitating discrimination of particle images from the background and aiding in the separation of overlapping particles. It is important not to pick a threshold level so high that the light intensity between a given pair of glare spots does not fall below the threshold value, leaving the glare spots disconnected. The image would then be scanned in a sequence of rows and columns of pixels to identify groups of adjacent pixels that contain nonzero brightnesses and that are surrounded by pixels of zero brightness. Each such group would be assumed to constitute the image of one particle. Each such group would be further analyzed to determine whether the image was saturated; saturated particle images must be rejected because the locations of glare spots in saturated images cannot accurately be determined. Within each unsaturated particle image, the centroids (deemed to be the locations) of the glare spots would be determined by means of gradients of brightness distributions and three-point horizontal and three-point vertical Gaussian estimates based on the brightness values of the brightest pixels and the pixels adjacent to them. If the brightness of a given particle image contained only one peak, then it would be assumed that a second glare spot did not exist and that image would be rejected.