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Theoretical and numerical study of free-surface flow of viscoplastic fluids : 2D dambreaks, axisymmetrical slumps and surges down an inclined slope

University of British Columbia

Abstract: The dynamics of free surface flow of yield stress fluid under gravity has been an open problem, both in theory and in computation. The contribution of this thesis comes in three parts. First, we report the results of computations for two dimensional dambreaks of viscoplastic fluid, focusing on the phenomenology of the collapse, the mode of initial failure, and the final shape of the slump. The volume-of-fluid method (VOF) is used to evolve the surface of the viscoplastic fluid, and its rheology is captured by either regularizing the viscosity or using an augmented-Lagrangian scheme. The interface is tracked by the Piecewise-Linear-Interface-Calculation (PLIC) scheme, modified in order to avoid resolution issues associated with the over-ridden finger of ambient fluid that results from the no slip condition and the resulting inability to move the contact line. We establish that the regularized and augmented-Lagrangian methods yield comparable results. The numerical results are compared with asymptotic theories valid for relatively shallow or vertically slender flow, with a series of previously reported experiments, and with predictions based on plasticity theory. Second, we report computations of the axisymmetric slump of viscoplastic fluid, with the PLIC scheme improved for mass conservation. The critical yield stress for failure is computed and bounded analytically using plasticity methods. The simulations are compared with experiments either taken from existing literature or performed using Carbopol. The comparison is satisfying for lower yield stresses; discrepancies for larger yield stresses suggest that the mechanism of release may affect the experiments. Finally, we report asymptotic analyses and numerical computations for surges of viscoplastic fluid down an incline with low inertia. The asymptotic theory applies for relatively shallow gravity currents. The anatomy of the surge consists of an upstream region that converges to a uniform sheet flow, and over which a truly rigid plug sheaths the surge. The plug breaks further downstream due to the build up of the extensional stress acting upon it, leaving instead a weakly yielded superficial layer, or pseudo-plug. Finally, the surge ends in a steep flow front that lies beyond the validity of shallow asymptotics.

Text

2019-04-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69809

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/