Simulation, analysis and modeling of unsteady flow in porous media

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Unsteady porous media flow establish an important class of flow phenomena. There is a number of technical applications and environmental flow problems in which the flow is unsteady, e.g. flows through plant canopies in atmospheric boundary layers and under the influence of waves underwater or the interaction of a turbulent boundary layer flow with the flow and transport in the upper layer of the soil or a snow layer. The flow of blood and mass transport in living organisms can as well be considered as unsteady flow through porous media. So far, a unique description and modeling of these unsteady flow problems can not be found in the literature and different concepts on how to treat them exist.In most cases, flows in porous media are described on the scale of a representative elementary volume (REV). On this scale it is necessary to model the interaction between flow and solid by suitable models. The well known Darcy and Forchheimer equations are widely accepted for steady flows in porous media, although the coefficients depend strongly on the flow state. In unsteady flows, the steady-state interaction models can not be used as they strongly vary during unsteady flow. For unsteady flow in the linear regime (Re<<1), the applicant was able to demonstrate that the volume averaged equation for the kinetic energy provides a correction to the time constant in the unsteady Darcy equation that agrees well with fully resolved solutions of Navier-Stokes equations in the pore space.The goal of this proposal is to analyze unsteady flow in porous media in the non-linear and turbulent regime. We intend to study transient flow after a step change in pressure gradient and oscillatory flow. A direct numerical simulation in fully resolved pore space will be undertaken using our own Navier-Stokes solver. We plan to do simulations in two-dimensional geometries (cylinder packs) and three-dimensional geometries (sphere packs). Our interest is on macroscopic modeling of interaction terms, dissipation and time constant in unsteady porous media flow. A special focus will be on the transition from linear to non-linear and from non-linear to turbulent states in unsteady porous media flow.