Tracking the free surface of time-dependent flows: image processing for the dam-break problem

Abstract

The dam-break problem (i.e., the sudden release of a given volume of fluid down a slope) has attracted a great deal of attention from mechanicians and physicists over the past few years, with particular interest devoted to the free-surface profile and the spreading rate. Experimentally, impediments to accurate measurements of the free-surface evolution are numerous because of the significant variations in its curvature and velocity. To accurately measure the surge's free-surface variations with time, we have developed a new imaging system, consisting of a digital camera coupled with a synchronized micromirror projector. The object's surface is imaged into a camera and patterns are projected onto the surface under an angle of incidence that differs from the imaging direction. From the deformed pattern recorded by the camera, the phase can be extracted and, by using unwrapping algorithms, the height can be computed and the free surface reconstructed. We were able to measure the free surface of the flow to within 1 mm over a surface of 1.8 · 1.1 m 2 . Although the techniques used in our system are not new when taken individually, the system in its entirety is innovative and more efficient than most methods used to-date in practical applications.

Experimental investigation of the spreading of viscoplastic fluids on inclined planes

“…We developed algorithms to process the image data, determine the spreading rate, and reconstruct whole-field three-dimensional shapes of the free surface. The free surface was reconstructed with an accuracy of 1 mm over a surface of 1.4 m × 1.4 m at a rate of 45 Hz (further details of the experimental procedure are provided by [40]). In terms of computation time, for a typical 3-min experiment, the post-processing phase required almost one week on a singleprocessor machine.…”

“…To take up this challenge, we built a new imaging system, which makes it possible to accurately reconstruct the free surface of an avalanching mass of fluid. In Section 2.1, we outline the techniques developed for this purpose; the interested reader is referred to an earlier publication for further information [40]. Another substantial challenge posed by non-Newtonian fluids lies in the proper characterization and control of rheological properties.…”

The dam-break problem for Herschel–Bulkley viscoplastic fluids down steep flumes

“…where h front = h f is their overlap value, i.e., the flow depth at the front of the outer solution, h outer the solution to (45), and h inner the solution to (53). The composite solution provided a uniform approximation of the solution to leading order.…”

“…The object's surface was imaged into a camera and patterns were projected onto the surface under an angle of incidence that differed from the imaging direction [44,45]. From the deformed pattern recorded by the camera, the phase could be extracted and, using unwrapping algorithms, the height was computed and the free surface reconstructed.…”

“…Second, tracking the free surface of a timedependent flow remains a challenging task. Here we take advantage of sophisticated image processing techniques [44,45] to measure the flow-depth profiles and front velocity of finite volumes of Carbopol Ultrez 10. In Section 3, we present our experimental data and compare them with theoretical predictions.…”