Viscoplastic dambreak waves: review of simple computational approaches and comparison with experiments

We investigated the dam-break problem for Herschel-Bulkley fluids: a fixed volume of a viscoplastic material (a polymeric gel called Carbopol ultrez 10) was released and flowed down an inclined flume. Using Particle Image Velocimetry techniques, we measured the velocity profiles far from the sidewalls, the front position as a function of time, and the flow depth evolution at a given place. The experimental data were compared to three models of increasing complexity: the kinematic wave model, an advection diffusion model (lubrication theory), and the one-layer Saint-Venant equations. Surprisingly, the best agreement was obtained with the simplest model (kinematic wave model) even though it could not capture the details of the head profile (regarded as a shock wave, i.e., a discontinuity). Lubrication theory (the advection diffusion model) performed well from a qualitative viewpoint. Computed velocity profiles and depth evolution were in reasonably good agreement with data, but this model overestimated initial acceleration, which resulted in a systematic difference between theoretical and experimental curves of the front position over time. This shortcoming was not fixed when using a more elaborate model (Saint-Venant equations), rather it was exacerbated. The relatively modest performance of the more elaborate models was intriguing (for Newtonian liquids, the best agreement was obtained with the most sophisticated model).

Dam Break of Newtonian Fluids and Granular Suspensions

Nicolas Andreini

The objective of this thesis was to increase our understanding of two-phase geophysical flows (e.g. debris flows) by providing velocity profiles in idealized laboratory avalanches. To that end, we developed a new experimental platform made up of an inclined flume coupled to an imaging system to measure velocity in granular suspension. The inclined flume was 3.5 m long and 10 cm wide and could be inclined from 0 to 35°. A reservoir with the capacity for 10 l of fluid was located in the upper part of the flume and closed with a pneumatic controlled gate. Velocity profiles were obtained using Particle Image Velocimetry (PIV) and index-of-refraction matching of the solid and liquid phases. We used transparent PMMA beads with mean diameters of 200 µm and the interstitial fluid was composed of a mixture of three fluids. The interstitial fluid was adapted in order to match the refraction index and the density of the solid phase. Using pulsed laser and a high speed camera we were able to measure velocity profiles at frequencies up to 1000 Hz with very good precision. Two additional cameras tracked the front position along the flume with a frequency of 30 Hz and a spatial resolution of 1 mm. Prior to acquiring data on the granular suspension, we tested our system on Newtonian fluids. Eight flow configurations were selected with different fluids (glycerol and triton X100), different slopes and different released masses. Velocity profiles were found to be parabolic far from the front as well as very close to the contact line. However, near the front, quantitative theoretical predictions given by lubrication theory diverged from experimental results. Velocities were significantly overestimated (∼ 400%) by the theory at low Reynolds numbers (Re < 2) and slightly underestimated (∼ 10%) at high Reynolds numbers (Re > 8). Very good agreement with theory far from the front indicated that the accuracy of the setup was good (reliable calibration procedure and image processing methods). Experiments on granular suspensions revealed a variety of behaviors depending on the particle concentration, the slope and the mass released. At solid fractions up to 45%, suspensions behaved as homogeneous viscous fluids. For the duration of the experiment, it was not possible to detect any inhomogeneity due to migration or sedimentation. In the range of shear rate tested and with the precision allowed by the setup no shear thickening or shear thinning was observed since velocity profiles remained perfectly Newtonian. For slightly more concentrated suspensions (up to 55%), we found that the flow dynamics at the bulk scale could still be described using a viscous theory. However, at the local scale, migration gave rise to concentration inhomogeneities producing a blunted velocity profile. The shape of the blunted profile was well described by the Mills and Snabre migration model coupled to a Krieger-Dougherty effective viscosity. However, magnitudes of the velocities were largely overestimated, most probably because we fitted the effective viscosity at higher shear rates. Above 55%, small released masses with high solid fractions stopped after a finite time and separation between fluid and solid phases occurred. The solid frame stayed at rest while the fluid seeped through the granular media eroding the front. For larger released masses, we observed successions of different regimes: After an inertial regime and a pseudo-viscous regime, the flow slowed down, corresponding to a new regime in which the shearing was localized in a thin layer at bottom and there was no shearing of the front. At the same time, we observed that the free surface deformed and became wavy. Fractures developed on the top of the flow and, if they grew sufficiently, modified the local velocity field substantially. Finally, at longer time (≥ 4 min) an intermittent motion (stick-slip) was observed with phases during which the suspension was flowing in a quasi-steady regime and phases during which the suspension was at a halt.

EPFL2012

Internal dynamics of Newtonian and viscoplastic fluid avalanches down a sloping bed

Christophe Ancey, Nicolas Andreini, Gaël Epely Chauvin

We experimentally investigated the spreading of fluid avalanches (i.e., fixed volumes of fluid) down an inclined flume. Emphasis was given to the velocity field within the head. Using specific imaging techniques, we were able to measure velocity profiles within the flowing fluid far from the sidewalls. We studied the behavior of Newtonian and viscoplastic fluids for various flume inclinations and initial masses. For the Newtonian fluids tested (glycerol and Triton X100), we compared the measured velocity field with that predicted by lubrication theory. Provided that the flow Reynolds number Re was sufficiently low (typically Re < 1), there was excellent agreement between theory and experiment except for the very thin region just behind the contact line. For higher Reynolds numbers (typically Re similar to 10), the discrepancy between theory and experiment was more marked (relative errors up to 17% for the body). As viscoplastic materials, we used Carbopol ultrez 10. For the body, agreement between theoretical and measured velocity profiles was fairly satisfactory whereas it was very poor for the tip region as the curvature of the free surface became more pronounced: the velocities were not only much lower than those predicted by lubrication theory, but there was also evidence of slipping in the flow part adjacent to the contact line. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4718018]

2012

Basal entrainment by Newtonian gravity-driven flows

Christophe Ancey, Nicolas Andreini, Belinda Margaret Bates

Gravity-driven flows can erode the bed along which they descend and increase their mass by a factor of 10 or more. This process is called "basal entrainment." Although documented by field observations and laboratory experiments, it remains poorly understood. This paper examines what happens when a viscous gravity-driven flow generated by releasing a fixed volume of incompressible Newtonian fluid encounters a stationary layer (composed of fluid with the same density and viscosity). Models based on depth-averaged mass and momentum balance equations deal with bed-flow interfaces as shock waves. In contrast, we use an approach involving the long-wave approximation of the Navier-Stokes equations (lubrication theory), and in this context, bed-flow interfaces are acceleration waves that move quickly across thin stationary layers. The incoming flow digs down into the bed, pushing up downstream material, thus advancing the flow front. Extending the method used by Huppert ["The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface," J. Fluid Mech. 121, 43-58 (1982)] for modeling viscous dam-break waves, we end up with a nonlinear diffusion equation for the flow depth, which is solved numerically. Theory is compared with experimental results. Excellent agreement is found in the limit of low Reynolds numbers (i.e., for flow Reynolds numbers lower than 20) for the front position over time and flow depth profile. Published by AIP Publishing.

Amer Inst Physics2016

Dam Break of Newtonian Fluids and Granular Suspensions

Nicolas Andreini

EPFL2012