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

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 micro-mirror 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 1mm over a surface of 1.8 × 1.1m2. 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 application

Measurements of time-dependent free-surface viscoplastic flows down steep slopes

The objective of this thesis was to increase our understanding of gravity-driven geophysical flows by developing a new platform to simulate avalanches of fluid in the laboratory. To simulate flow avalanches in the laboratory, we created a unique experimental setup consisting of a metallic frame supporting a reservoir, an inclined aluminum plane, and a horizontal run-out zone. At 6-m long, 1.8-m wide, and 3.5-m high, the structure is probably the largest laboratory setup of its kind in the world. In a dam-break experiment, up to 120 liters of fluid can be released from the reservoir down the 4-m long inclined plane. We precisely control initial and boundary conditions. To measure the free-surface profile, a novel imaging system consisting of a high-speed digital camera coupled to a synchronized micro-mirror projector was developed. The camera records how regular patterns projected onto the surface are deformed when the free surface moves. We developed algorithms to post-process the image data, determine the spreading rate, and generate whole-field 3-dimensional shape measurements of the free-surface profile. We compute the phase of the projected pattern, unwrap the phase, and then apply a calibration matrix to extract the flow thickness from the unwrapped phase. 56 different flow configurations, with a wide range of inclinations, were finally tested with Newtonian and viscoplastic fluids. For each test, the evolution of the free surface was recorded in 3 dimensions. Different flow regimes were observed, which depend on: the plane inclination, the setup geometry, the volume, and characteristics of the fluid. Partial agreements were found between theoretical models and our results

The dam-break problem for viscous fluids in the high-capillary-number limit

Experiments were undertaken to investigate dam-break flows where a finite volume of highly viscous fluid (glucose with viscosity μ ≈ 350 Pa s) maintained behind a lock gate was released into a horizontal or inclined flume. The resulting sequence of flow-depth profiles was tracked using a three-dimensional visualization system. In the low-Reynolds-number and high-capillary-number limits, analytical solutions can be obtained from the Navier–Stokes equations using lubrication theory and matched asymptotic expansions. At shallow slopes, similarity solutions can also be worked out. While the variation in the front position scaled with time as predicted by theory for both horizontal and sloping flumes, there was a systematic delay in the front position observed. Moreover, taking a closer look at the experimental flowdepth profiles shows that they were similar, but they noticeably deviated from the theoretical similarity form for horizontal planes. For sloping beds, the flow-depth profile is correctly predicted provided that different scalings are used at shallow and large slopes

Volumetric measurements by tomographic PIV of grid generated turbulence in an open channel flow

International audienceThis paper investigates the energy dissipation rate behind two combinations of trash racks (or meshes) in an open channel flow. Five trash rack assemblies divided the flume into four identical pools in the downstream direction. The global characteristics of the flow were compared with Tomo-PIV measurements that were taken in the water column of the flow. From the Tomo-PIV measurements, the instantaneous structures in the flow were visualised and the decay of turbulent kinetic energy and energy dissipation analysed

Volumetric Measurements by Tomographic PIV of an Open Channel Flow Behind a Turbulent Grid

National audienceThis paper investigates the energy dissipation rate behind two combinations of trash racks (or meshes) in an open channel flow from tomo-PIV measurements. Five trash rack assemblies divided the flume into four identical pools. Each trash rack assembly is composed of a fine wire mesh and two regular square grids, characterised by their mesh size M. The Reynolds numbers with respect to M were 4300 and 9600 corresponding to a mean velocity ¯U through each pool between 0.35 and 0.315 m/s. This aim of this paper is to investigate the turbulent energy dissipation behind two configurations of regular grids in an open channel

Mesure volumique par tomo-PIV d'un écoulement dans un canal turbulent de surface libre derrière une grille

National audienceLa mesure directe de la dissipation dans les écoulements n'est pas possible mais les nouvelles techniques de mesure volumique comme la tomo-PIV permettre de calculer le tenseur des gradients de vitesse et par la même la dissipation instantanée. Cet article présente des mesures de vitesse par tomo-PIV d'un écoulement à surface libre pour un nombre de Reynolds de 36000 dans un canal incliné à l'aval d'un assemblage de grilles. La faisabilité des mesures est réalisée et deux configurations de grilles sont comparées. On montre notamment que la dissipation n'est pas homogène et isotrope dans la région de l'écoulement mesurée

Front dynamics of supercritical non-Boussinesq gravity currents

In this paper, we seek similarity solutions to the shallow water (Saint-Venant) equations for describing the motion of a non-Boussinesq, gravity-driven current in an inertial regime. The current is supplied in fluid by a source placed at the inlet of a horizontal plane. Gratton and Vigo (1994) found similarity solutions to the Saint-Venant equations when a Benjamin-like boundary condition was imposed at the front (i.e., nonzero flow depth); the Benjamin condition represents the resisting effect of the ambient fluid for a Boussinesq current (i.e., a small-density mismatch between the current and the surrounding fluid). In contrast, for non-Boussinesq currents the flow depth is expected to be zero at the front in absence of friction. In this paper, we show that the Saint-Venant equations also admit similarity solutions in the case of non-Boussinesq regimes provided that there is no shear in the vertical profile of the streamwise velocity field. In that case, the front takes the form of an acute wedge with a straight free boundary and is separated from the body by a bore

Existence and features of similarity solutions for non-Boussinesq gravity currents

In this paper, the flow dynamics of gravity currents on a horizontal plane is investigated from a theoretical point of view by seeking similarity solutions. The current is generated by unleashing a varying volume of heavy fluid within an ambient fluid of much lower density. Unlike earlier investigators, we assume that the ambient fluid exerts no significant resisting action on the current, and therefore the flow depth is expected to drop to zero at the front in the absence of friction. In this context, the shallow-water equations are highly appropriate for computing the mean velocity and flow depth of the current. The boundary condition imposed at the front leads to technical mathematical difficulties. Indeed, unlike in the Boussinesq case, no regular solution to the shallow-water equations satisfies the downstream condition, but when the flow is supercritical at the channel inlet, it is possible to construct a piecewise solution by patching a regular solution to an exceptional solution, which represents the head behavior. To better understand this result and make sure that the result is physically relevant, we consider the Navier–Stokes equations within the high-Reynolds-number limit. Approximate similarity solutions can be worked out, which support our earlier analysis on the shallow-water equations. While the flow body is self-similar and weakly rotational, the head is not self-similar, but tends toward a self-similarity shape at long times. It is characterized by a strong vorticity, a straight free surface, and a nonuniform velocity profile, which becomes flatter and flatter with time