Oscillatory forcing of flow through porous media. Part 1. Steady flow

• Published in: Journal of fluid mechanics Vol. 465; pp. 213 - 235
• Main Authors: GRAHAM, D. R., HIGDON, J. J. L.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.08.2002
• Subjects: Anisotropy; Computational methods in fluid dynamics; Exact sciences and technology; Flow pattern; Flow rates; Flows through porous media; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Nonhomogeneous flows; Oscillators; Physics; Porous materials; Porous media; Steady flow; Finite element method; Streamlines; Porous medium flow; Forced oscillation; Digital simulation; Steady flow; Bifurcation; Modelling; Constricted tube; Cylinder set; Mesh generation
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112002001155

Oscillatory forcing of a porous medium may have a dramatic effect on the mean flow rate produced by a steady applied pressure gradient. The oscillatory forcing may excite nonlinear inertial effects leading to either enhancement or retardation of the mean flow. Here, in Part 1, we consider the effects of non-zero inertial forces on steady flows in porous media, and investigate the changes in the flow character arising from changes in both the strength of the inertial terms and the geometry of the medium. The steady-state Navier–Stokes equations are solved via a Galerkin finite element method to determine the velocity fields for simple two-dimensional models of porous media. Two geometric models are considered based on constricted channels and periodic arrays of circular cylinders. For both geometries, we observe solution multiplicity yielding both symmetric and asymmetric flow patterns. For the cylinder arrays, we demonstrate that inertial effects lead to anisotropy in the effective permeability, with the direction of minimum resistance dependent on the solid volume fraction. We identify nonlinear flow phenomena which might be exploited by oscillatory forcing to yield a net increase in the mean flow rate. In Part 2, we take up the subject of unsteady flows governed by the full time-dependent Navier–Stokes equations.