The influence of image analysis methodology on the calculation of granular temperature for granular flows

Abstract

The granular temperature is an index of the level of collisional activity in a granular flow, and increasingly important in the verification of extended kinetic theories. The granular temperature is related to the square of the difference between a particle’s velocity and that of the group mean. Image analysis of high-speed video is the most common method to measure granular temperature in experimental flows and depends on correlation of a search mask or a portion of the original image to the next image frame to determine the particle’s movement. This invariably involves some level of estimation of the location at a resolution finer than the pixels that make up the image. However, errors in determining particle movement at the subpixel level can be shown to have a significant impact on granular temperature identification. We show that taking particle movement to be a chain of displacement vectors provides context to the apparent impulses on the particle. Here we propose two novel methods for determining the granular temperature of experimental flows, namely a novel method of initializing Particle Image Velocimetry (PIV) for granular systems where each search subset is centred on a previously determined particle location to reduce bias, and a method of filtering the apparent impulses on a particle on a frequency basis. We term these methods Guided-PIV and Impulse Frequency Filtering (IFF), respectively. In a verification exercise using synthetically generated images, we show Guided-PIV to produce substantially more accurate results than ordinary applications of PIV. The IFF method is shown to greatly reduce the influence of analyzed framerate on granular temperature results. Our results demonstrate practical improvements for granular temperature identification from image analysis, throughout a range of experimental image quality levels, and we anticipate that these improvements will enable experimental assessment towards verification of theorized models of collisional-frictional granular flows.