Macroscopic model for unsteady flow in porous media
By D. Lasseux, Francisco J. Valdes-Parada, F. Bellet. Journal of Fluid Mechanics, 2019
48 citations recorded by the source corpus.
The present article reports on a formal derivation of a macroscopic model for unsteady one-phase incompressible flow in rigid and periodic porous media using an upscaling technique. The derivation is carried out in the time domain in the general situation where inertia may have a significant impact. The resulting model is non-local in time and involves two effective coefficients in the macroscopic filtration law, namely a dynamic apparent permeability tensor, $\unicode[STIX]{x1D643}_{t}$ , and a vector, $\unicode[STIX]{x1D736}$ , accounting for the time-decaying influence of the flow initial condition. This model generalizes previous non-local macroscale models restricted to creeping flow conditions. Ancillary closure problems are provided, which allow the effective coefficients to be computed. Symmetry and positiveness analyses of $\unicode[STIX]{x1D643}_{t}$ are carried out, showing that this tensor is symmetric only in the creeping regime. The effective coefficients are functions of time, geometry, macroscopic forcings and the initial flow condition. This is illustrated through numerical solutions of the closure problems. Predictions are made on a simple periodic structure for a wide range of Reynolds numbers smaller than the critical value characterizing the first Hopf bifurcation. Finally, the performance of the macroscopic model for a variety of macroscopic forcings and initial conditions is examined in several case studies. Validation through comparisons with direct numerical simulations is performed. It is shown that the purely heuristic classical model, widely used for unsteady flow, consisting of a Darcy-like model complemented with an accumulation term on the filtration velocity, is inappropriate.
Subfields: Computational Mechanics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/36f6b8d8a9756535c02a382c80fd0cbbb42aa4e3
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In Computational Mechanics
In Computational Theory and Mathematics
Citations in the corpus
- Modeling Turbulent Flows in Porous Media (2020, methodology): “…theory (Bennethum & Giorgi 1997), homogenization methods (Mei & Auriault 1991, Panfilov & Fourar 2006), thermodynamically constrained averaging theory (Gray & Miller 2014), and VAT (Breugem & Boersma 2005; de Lemos 2006; Finnigan 2000; Lasseux et al. 2011, 2019; Rosti et al. 2018; Travkin 2001).”