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Simulation d'écoulements non-newtoniens en milieu poreux macroscopique par la méthode de lattice-Boltzmann

Abstract : A non-newtonian fluid is a fluid which relation between it's shear rate and the stress under which it is put, is not linear. In a porous medium, the stress imposed to the fluid depends on the imposed pressure, but also on the pores size, and therefore on the macroscopic scale permeability. Some fluids have a rheology such that the fluid show a change of behaviour reaching a yield stress. If the pore size is random, then the fluid will present heterogeneous regime changes in the medium. The flow will then show a first regime where the whole fluid will be under the threshold, a regime where the whole fluid will be far above the threshold, and an intermediate regime for which both rheologies coexists. We are interested in intermediate regime for the flow of non-newtonian fluids in macroscopic porous media, and study it with numerical simulations. More particularly, we look at the flow of a Bingham fluid and that of a Carreau fluid. The Bingham fluid doesn't flow under a yield stress. Under the threshold, it behaves as a solid. Beyond, it's shear-rate/stress relation is an affine law. Carreau fluids have a shear-rate/stress relation that change regime between that of a newtonian fluid, and a power law. The macroscopic scale study is done simulating a Darcy-Brinkman law in a heterogeneous permeability field. We use for our simulations the lattice-Boltzmann method, on a regular node grid, and more specifically Irina Ginzburg two relaxation-time scheme. For each fluid, we study the flow-pressure relationship, as well as the geometric properties and the multi-scale properties in the fluid regions in the same flow regime (clusters), properties such as their size and shape. We also link these geometrical properties to the percolation theory, which studies the behaviour of randomly opening node maps and predicts fractal properties.
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Romaric Kostenko. Simulation d'écoulements non-newtoniens en milieu poreux macroscopique par la méthode de lattice-Boltzmann. Mécanique des fluides [physics.class-ph]. Université Paris-Saclay, 2019. Français. ⟨NNT : 2019SACLS561⟩. ⟨tel-02495355⟩

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