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Laminar shallow viscoplastic fluid flowing through an array of vertical obstacles

Abstract : A new Bingham-Darcy shallow depth approximation flow model is proposed in this paper. This model is suitable for a laminar shallow viscoplastic fluid flowing on a general topography and crossing an array of vertical obstacles. An analogous porous medium is first introduced for reducing the array of obstacles. It bases on a continuum model similar to the Brinkman equations, where the usual Darcy model is extended for viscoplastic Bingham fluids. Next, a specific asymptotic analysis of this Bingham-Darcy porous medium in the case of shallow depth flows leads to a new reduced model. The resulting highly nonlinear parabolic equation in terms of the flow height only is efficiently solved by a Newton method, without any regularization. The numerical predictions compares both qualitatively and quantitatively well with both some experimental measurements and full tridimensional simulations. Finally, a new experiment for a viscoplastic flow over an inclined plane through a network of obstacle is proposed and numerical simulations are provided for future comparisons with experiments.
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Submitted on : Monday, March 19, 2018 - 12:57:02 PM
Last modification on : Thursday, December 2, 2021 - 9:02:08 PM

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Noé Bernabeu, Pierre Saramito, Andrew Harris. Laminar shallow viscoplastic fluid flowing through an array of vertical obstacles. Journal of Non-Newtonian Fluid Mechanics, Elsevier, 2018, 257, pp.59-70. ⟨10.1016/j.jnnfm.2018.04.001⟩. ⟨hal-01646766v2⟩

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