Viscoplastic flows over topographies: an experimental - numerical cross-comparison
Résumé
Numerous industrial and geophysical applications involve free-surface flows of viscoplastic materials over topographies. The interplay between inertia, rheological effects and topographical features can give rise to particular flow patterns, such as the formation of possibly unyielded accumulation zones ahead of obstacles, the formation of dry zones downstream of obstacles, etc. We report on laboratory experiments specifically designed to study these complex processes. Finite volumes of a viscoplastic material (Carbopol) are released from a rectangular reservoir onto 3D-printed topographies characterized by different configurations of ridges and mounds. The evolution of flow thickness over time is monitored with a temporal resolution of 250 Hz and a typical accuracy of 0.5 mm through a Moiré projection technique. The influence of release position, release volume, and fluid rheology on flow dynamics are investigated. In all case, an abrupt transition is observed between an inertia-dominated regime at short times, and a regime mainly controlled by plasticity and rheological effects at longer times. Interactions with the topography affect this transition by either promoting or delaying the deceleration of the flow. Experimental results are then compared to numerical simulations based on depth-averaged shallow-flow models. In this approach, which is widely used for practical applications, the vertical structure of the flow is not resolved, such that properly representing complex rheological effects can be challenging. Different formulations proposed in the literature for accounting for the internal shearing of the flow and the friction with the bed surface have been tested. Systematic cross-comparisons with the experimental data provides a unique benchmark to assess the predictive capabilities of these models. Once validated, the models can then be used to further explore the dynamical properties of the flows in a wider range of parameters.