We numerically analyze fluid flow through porous media up to a limiting Reynolds number of scriptO(103). Due to inertial effects, such processes exhibit a gradual transition from laminar to turbulent flow for increasing magnitudes of Re. On the macroscopic scale, inertial transition implies nonlinearities in the relationship between the effective macroscopic pressure gradient and the filter velocity, typically accounted for in terms of the quadratic Forchheimer equation. However, various inertia‐based extensions to the linear Darcy equation have been discussed in the literature; most prominently cubic polynomials in velocity. The numerical results presented in this contribution indicate that inertial transition, as observed in the apparent permeability, hydraulic tortuosity, and interfacial drag, is inherently of sigmoidal shape. Based on this observation, we derive a novel filtration law which is consistent with Darcy's law at small Re, reproduces Forchheimer's law at large Re, and exhibits higher‐order leading terms in the weak inertia regime.

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A comparative study on mesh-based and mesh-less Computational Fluid Dynamics (CFD) approaches coupled with the Discrete Element Method (DEM) is presented. As the mesh-based CFD approach a Finite Volume Method (FVM) is used. A Smoothed Particle Hydrodynamics (SPH) method represents mesh-less CFD. The unresolved fluid model is governed by the locally averaged Navier-Stokes equations. A newly developed model for applying boundary conditions in the SPH is described and validation tests are performed. With the help of the presented comparative tests, the similarities and differences of DEM-FVM and DEM-SPH methods are discussed. Three test cases, comprised of a single solid particle sedimentation test, flow through a porous block and sedimentation of a porous block, are performed using both methods. Drag forces acting on solid particles highly depend on local fluid fractions. For comparative reasons, the size of a cell in FVM is chosen such that fluid fractions match those computed in SPH. In general, DEM-FVM and DEM-SPH methods exhibit good agreement with analytic reference results. Differences between DEM-SPH and DEM-FVM approaches were found mostly due to differences in computed local fluid fractions.

We perform pore-scale resolved direct numerical simulations of immiscible two-phase flow in porous media to study the evolution of fluid interfaces. Using a Smoothed-Particle Hydrodynamics approach, we simulate saturation-controlled primary drainage in heterogeneous, partially wettable 2D porous microstructures. While imaging the evolution of fluid interfaces near capillary equilibrium becomes more feasible as fast X-ray tomography techniques mature, imaging methods with suitable temporal resolution for viscous-dominated flow have only recently emerged. In this work, we study viscous fingering and stable displacement processes. During viscous fingering, pore-scale flow fields are reminiscent of Bretherton annular flow, that is, the less viscous phase percolates through the core of a pore-throat forming a hydrodynamic wetting film. Even in simple microstructures wetting films have major impact on the evolution of fluid interfacial area and are observed to give rise to nonnegligible interfacial viscous coupling. Although macroscopically appearing flat, saturation fronts during stable displacement extend over the length of the capillary dispersion zone. While far from the dispersion zone fluid permeation obeys Darcy's law, the interplay of viscous and capillary forces is found to render fluid flow within complex. Here we show that the characteristic length scale of the capillary dispersion zone increases with the heterogeneity of the microstructure.

Shape-Memory Polymers (SMPs) have the ability to be deformed and memorize this deformation until an external activation stimulus (e.g., heat) is applied. Therefore, they have attracted great interest in many areas, especially for applications where reconfigurable structures are required (e.g., Shape-Memory (SM) stents or micro air vehicles). Nevertheless, prior to technical application, the effective thermomechanical behavior of SMPs must be thoroughly understood. In the current contribution, an assessment of thermorheological properties of the commercially available polyurethane system ESTANE is presented. Thermorheological properties were investigated using Dynamic Mechanical Thermal Analysis (DMTA) and complementary uniaxial stress relaxation experiments. Upon material parameter optimization, a finite viscoelastic and incompressible material model was used to model experimentally observed viscoelastic properties.