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

Christophe Ancey, Steve Cochard
2009
Journal paper

Abstract

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.

Official source

https://infoscience.epfl.ch/record/134645?ln=en

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts

Related publications

, ,

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.

Cambridge University Press2009

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

, ,

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. We look into this issue by studying eroding dam-break waves. More specifically we would like to determine what happens when a viscous gravity-driven flow generated by releasing a fixed volume of incompressible Newtonian fluid encounters a stationary erodible 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 [J. Fluid Mech. 121, 43–58 (1982)] for modelling 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. The Newtonian model has sometimes been used to describe the flow behaviour of natural materials such as snow and debris suspensions, but the majority of existing approaches rely on more elaborate constitutive equations. So there is no direct application of the results presented here to real flow conditions. Yet, our study sheds light on the mechanisms involved in basal entrainment. We provide evidence that the whole layer of loose material is entrained quickly once the flow makes contact with the erodible layer. As this process occurs on very short times, we can consider that the whole layer underneath the incoming flow is mobilized instantaneously.

2016

, ,

2016