Voronoï imaging methods for the measurement of granular flows

Abstract

A set of digital imaging methods derived from the Voronoõ È diagram is proposed and tested on various liquid±granular ¯ow applications. The methods include a novel pattern-based particle-tracking algorithm, as well as estimators of the three-dimensional granular concentration from two-dimensional images. The proposed algorithms are able to resolve individual grain motions even for rapid shear ¯ows involving dense, ¯uctuating granular ensembles. Full automation is achieved, allowing the derivation of accurate statistics from large sets of individual measurements, as well as the construction of complete sets of grain trajectories. Results are presented for different applications: homogeneous ¯uidization, steady uniform debris ¯ow, and unsteady debris surges.

Stereoscopic and velocimetric reconstructions of the free surface topography of antidune flows

“…3a. The expected root mean square accuracy on the X and Y image coordinates obtained with such a procedure is of the order of 0.1-0.25 pixels (Veber et al 1997;Capart et al 2002).…”

“…Local maxima of the highlighted images are then sought. The position of each maximum is finally refined to subpixel accuracy by way of a quadratic interpolation surface (for more details, see Capart et al 2002). Illustrating these steps, a filtered image with detected particle positions is shown in Fig.…”

“…In the present work, this operation is performed using the Voronoı¨algorithm of Capart et al (2002). This algorithm tracks local patterns of neighbouring particles using Voronoı¨cells as match templates.…”

Three-dimensional reconstruction of the oscillatory free-surfaces of a flow over antidunes: stereoscopic and velocimetric techniques

“…First, particles on one of the images are tracked in time using the Voronoï algorithm also employed for the velocimetric method [12]. Positions of the particles at any given instant can then be obtained by interpolation along the interframe displacements.…”

“…These steps are sketched in the next paragraphs. For more detail, the reader is referred to [14] and [12].…”