Symmetry-Breaking of Turbulent Flow in Porous Media Composed of Periodically Arranged Solid Obstacles

Microscale turbulence in porous media is a new physical phenomenon that exhibits unique properties unlike those in classical turbulence flows. At low values of porosity, the surface forces on the solid obstacles compete with the inertial force of the fluid flow to result in the formation of flow instabilities. In this paper, we report the origin and mechanism of a symmetry-breaking phenomenon in periodic porous media that causes a deviation in the direction of the mean flow from that of the applied pressure gradient. Large Eddy Simulation (LES) is used to simulate turbulent flow in a homogeneous porous medium consisting of a periodic, square lattice arrangement of cylindrical solid obstacles. Direct Numerical Simulation (DNS) is used to simulate the transient stages during symmetry breakdown and also to validate the LES method. Quantitative and qualitative observations are made from the following approaches: (1) macroscale momentum budget, (2) 2D & 3D flow visualization. The phenomenon draws its roots from the amplification of a flow instability that emerges from the vortex shedding process. The symmetry-breaking phenomenon is a pitchfork bifurcation that can exhibit multiple modes depending on the local vortex shedding process. The phenomenon is observed to be sensitive to the porosity, solid obstacle shape, and the Reynolds number. It is a source of macroscale turbulence anisotropy in porous media for symmetric solid obstacle geometries. The resulting macroscale flow field is oriented such that it does not align with the plane of symmetry of the porous matrix geometry. The principal axis of the Reynolds stress tensor is not aligned with any of the geometric axes of symmetry, nor with the direction of flow. Thus, symmetry-breaking in porous media involves new flow physics that should be taken into consideration while modeling flow inhomogeneity in the macroscale.
Comment: Version 3 includes new information that shows that the conservation of momentum is satisfied during symmetry-breaking