Methods for Digital Particle Image Sizing (DPIS): Comparisons and improvements

Abstract

This paper explores the accuracy of particle image sizing using direct processing of digitally recorded images. Traditional methods for particle image sizing were considered and, four new algorithms were developed to deliver improved accuracy and robustness. Statistical error analysis was performed using Monte Carlo simulations in order to quantify the dependence of these methods on noise, discretization, and particle size distribution. The performance of these methods were compared against Phase Doppler Analyzer measurements of spray atomization. We introduce a novel two-dimensional four-point Gaussian estimator and an alternative Gaussian estimator based on a local least squares (LLS) fit. These methods were further advanced to account for pixel discretization effects using integral formulations (continuous methods). All new methods were compared against conventional pixel counting and the established three-point Gaussian estimator. The new methods significantly reduced the total error in the diameter estimation compared to the three-point Gaussian estimator and pixel counting. The least squares Gaussian estimator and its continuous version demonstrated almost identical results and superior performance for diameters over 4 pixels. For smaller diameters, the continuous four-point Gaussian estimator delivered the highest accuracy. For uniform particle size distribution between 2–14 pixels image diameter, the least squares estimators delivered error less than 5% with respect to the true diameter for 80% of the particles. The remaining methods demonstrated error of 5% (or better) for less than 60% of the particles. Validation in an experiment of high-pressure spray atomization showed that the Gaussian local least squares methods and the continuous four-point method delivered similar particle size distribution compared to PDA. The particle mean diameter estimated by the two methods differed only by 3% and 6% respectively with respect to the PDA measurements. The novel particle image sizing schemes developed here can deliver accurate, robust, and computationally efficient apparent diameter measurement, thus providing a viable, simple and inexpensive solution for performing sizing on conventional particle image velocimetry images. This capability enables simultaneous measurements of both velocity and particle size for a wide range of multi-phase flows.