Viscoplastic fluid impacting a body of water: predicting wave features from the fluid properties

We investigate viscoplastic fluids (described using a Herschel–Bulkley model) striking a body of water: a fixed volume of a viscoplastic material (a polymeric gel called Carbopol ultrez 10) initially contained in a box is released on a slope and flows down under gravity. When it enters flume filled with water, it generates an impulse wave. The problem is to determine impulse waves’ features from the viscoplastic fluid properties. First, we use momentum and mass conservation in a control volume for modeling the interaction between the viscoplastic flow and water [1]. To close the resulting equations, we calculate the flow depth and average velocity of the viscoplastic fluid (at the shoreline) using an approximate model (based on lubrication theory and matched asymptotic expansions) [2]. We then solve the mass and momentum balance equations numerically. The scale analysis of these equations allows us to define 5 dimensionless groups, which are used to correlate wave features and fluid properties. Second, we compare the theoretical model with experimental data specifically acquired for this purpose. Figure 1 shows the experimental facility. Using PIV techniques, we measure the velocity profile of the viscoplastic fluid near the shoreline and its velocity field after immersion. This makes it possible to determine the water velocity field and the interface between the solid, water, and air phases. Good agreement is found between the measured and predicted wave characteristics (e.g. amplitude and height).

Impulse waves generated by snow avalanches: Momentum and energy transfer to a water body

Christophe Ancey

When a snow avalanche enters a body of water, it creates an impulse wave whose effects may be catastrophic. Assessing the risk posed by such events requires estimates of the wave’s features. Empirical equations have been developed for this purpose in the context of landslides and rock avalanches. Despite the density difference between snow and rock, these equations are also used in avalanche protection engineering. We developed a theoretical model which describes the momentum transfers between the particle and water phases of such events. Scaling analysis showed that these momentum transfers were controlled by a number of dimensionless parameters. Approximate solutions could be worked out by aggregating the dimensionless numbers into a single dimensionless group, which then made it possible to reduce the system’s degree of freedom. We carried out experiments that mimicked a snow avalanche striking a reservoir. A lightweight granular material was used as a substitute for snow. The setup was devised so as to satisfy the Froude similarity criterion between the real-world and laboratory scenarios. Our experiments in a water channel showed that the numerical solutions underestimated wave amplitude by a factor of 2 on average. We also compared our experimental data with those obtained by Heller and Hager (2010), who used the same relative particle density as in our runs, but at higher slide Froude numbers.

Wiley-Blackwell2016

Intermittent motion and sediment transport -- experimental and theoretical insight

Christophe Ancey

We investigate the entrainment, deposition, and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope. This is an idealization of bed-load transport in mountain streams. Earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics. The intermittent character of particle transport at low water discharges led us to consider it as a random process. Sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles. We develop a birth-death immigration-emigration Markov process to describe the particle exchanges between the bed and the water stream. A key feature of the model is its long autocorrelation times and wide, frequent fluctuations in the solid discharge, a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments. We present experimental data obtained using a nearly two-dimensional channel and glass beads as a substitute for sediment. Entrainment, trajectories, and deposition were monitored using a high-speed digital camera. The empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model. Experiments confirmed the existence of wide and frequent fluctuations of the solid discharge, and revealed the existence of long autocorrelation time, but theory overestimates the autocorrelation times by a factor of around three. Particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model, which performs well when a single particle is moving. For our experiments, the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity. We also noted significant changes in the behavior of particle transport when the bed slope or the water discharge was increased. The more vigorous the stream was, the more continuous the solid discharge became. Moreover, while 90% of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10%, particles dissipate more and more energy when the bed slope is increased, but surprisingly, the dissipation rate is nearly independent of fluid velocity.

2007

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

Christophe Ancey, Steve Cochard

In this paper we investigate the dam-break problem for viscoplastic (Herschel- Bulkley) fluids down a sloping flume: a fixed volume of fluid initially contained in a reservoir is released onto a slope and flows driven by gravitational forces until these forces are unable to overcome the fluid’s yield stress. Like in many earlier investigations, we use lubrication theory and matched asymptotic expansions to de- rive the evolution equation of the flow depth, but with a different scaling for the flow variables, which makes it possible to study the flow behavior on steep slopes. The evolution equations takes on the form a nonlinear diffusion-convection equation. To leading order, this equation simplifies into a convection equation and reflects the balance between gravitational forces and viscous forces. After presenting analytical and numerical results, we compare theory with experimental data obtained with a long flume. We explore a fairly wide range of flume inclinations from 6° to 24° , while the initial Bingham number lies in the 0.07–0.26 range. Good agreement is found at the highest slopes, where both the front position and flow-depth profiles are properly described by theory. In contrast, at the lowest slopes, theoretical pre- dictions substantially deviate from experimental data. Discrepancies may arise from the formation of unsheared zones or lateral levees that cause slight flow acceleration.

2009

Intermittent motion and sediment transport -- experimental and theoretical insight

Christophe Ancey

2007