- In this work, flow through synthetic arrangements of contacting spheres is studied
as a model problem for porous media and packed bed type flows. Direct numerical
simulations are performed for moderate pore Reynolds numbers in the range,
10 ≤ Re ≤ 600, where non-linear porescale flow features are known to contribute
significantly to macroscale properties of engineering interest.
To first choose and validate appropriate computational models for this problem,
the relative performance of two numerical approaches involving body conforming
and non-conforming grids for simulating porescale flows is examined. In the first
approach, an unstructured solver is used with tetrahedral meshes, which conform
to the boundaries of the porespace. In the second approach, a fictitious domain
formulation (Apte et al., 2009. J Comput. Phys. 228 (8), 2712-2738) is used, which
employs non-body conforming Cartesian grids and enforces the no-slip conditions
on the pore boundaries implicitly through a rigidity constraint force. Detailed
grid convergence studies of both steady and unsteady flow through prototypical
arrangements of spheres indicate that for a fixed level of uncertainty, significantly lower grid densities may be used with the fictitious domain approach, which also does not require complex grid generation techniques.
Next, flows through both random and structured arrangements of spheres are
simulated at pore Reynolds numbers in the steady inertial ( 10 ≲ Re ≲ 200)
and unsteady inertial (Re ≈ 600) regimes, and used to analyze the characteristics
of porescale vortical structures. Even at similar Reynolds numbers, the vortical
structures observed in structured and random packings are remarkably different.
The interior of the structured packings are dominated by multi-lobed vortex rings
structures that align with the principal axes of the packing, but perpendicular to
the mean flow. The random packing is dominated by helical vortices, elongated
parallel to the mean flow direction. The unsteady dynamics observed in random
and structured arrangements are also distinct, and are linked to the behavior of
the porescale vortices.
Finally, to investigate the existence and behavior of transport barriers in packed
beds, a numerical tool is developed to compute high resolution finite-time Lyapunov
exponent (FTLE) fields on-the-fly during DNS of unsteady flows. Ridges
in this field are known to correspond to Lagrangian Coherent Structures (LCS),
which are invariant barriers to transport and form the skeleton of time dependent
Lagrangian fluid motion. The algorithm and its implementation into a parallel
DNS solver are described in detail and used to explore several flows, including
unsteady inertial flow in a random sphere packing. The resulting FTLE fields
unambiguously define the boundaries of dynamically distinct porescale features
such as counter rotating helical vortices and jets, and capture time dependent
phenomena including vortex shedding at the pore level.