Consistent Flow Structure Evolution in Accelerating Flow Through Hexagonal Sphere Pack

Direct numerical simulation based on incompressible Navier–Stokes equations with an immersed boundary method is used to simulate accelerating porous media flow through a bed of uniform spheres arranged in hexagonal close packing order. The transient flow is realised by driving initially resting fluid by a constant pressure gradient. A wide spectrum of Reynolds number based on the sphere diameter and volume-averaged velocity is considered, which ranges from creeping flow up to a Reynolds number of approximately 350, where turbulent flow structures are evident inside the pores. It is found that nonlinear dependence of the volume-averaged velocity with respect to the applied pressure gradient is the consequence of emergence of streamwise jets and the accompanying streamwise vortices, as previously observed for other sphere pack arrangements. Furthermore, two distinct flow modes are identified in the steady flow regime which satisfy full geometric symmetries. The flow then becomes unsteady around Reynolds number of 90 which coincides with a partial breaking of the symmetries, and pore-scale turbulence emerges once all the symmetries vanish when Reynolds number is larger than 200. For all the considered unsteady flow, independent of being turbulent or not, we observe a consistent sequence of flow structure evolution during the flow development with progressively broken symmetries albeit at widely varying instantaneous Reynolds numbers. Moreover, we show that the symmetry breaking takes place in larger pore spaces first, then propagate into smaller pores located in downstream.