Browsing by Author "Baber, Katherina"

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Coupling free flow and flow in porous media in biological and technical applications : from a simple to a complex interface description
(2014) Baber, Katherina; Helmig, Rainer (Prof. Dr.-Ing.)
The objective of this work is the development of model concepts and methods for the coupling of free flow and flow in porous media. Coupling concepts of varying complexity ranging from a simple to a pore-scale to a complex interface approach are derived. The main focus is the development and testing of an REV-scale coupling concept that accounts for drop dynamics at the interface. The developed coupling concepts are based on the assumption of thermodynamic equilibrium and on flux balances. The formulation of mechanical equilibrium in the pore-scale and complex interface concept is challenging due to the scale-dependent definition of pressure. The combination of microscopic and macroscopic pressure formulations causes pressure jumps at the interface and non-physical pressure gradients. Hence, an extensive discussion of the pressure conditions is given. The coupled model is implemented in the C++ simulator DuMux (Flemisch et al., 2011) using the mortar method. The applicability of the developed concepts is assessed on the basis of two applications: transvascular exchange and drop dynamics in PEM fuel cells. In Mosthaf et al. (2011) and Baber et al. (2012), we develop a simple interface concept for coupling non-isothermal compositional two-phase flow in the porous-medium with a non-isothermal compositional single-phase system in the free-flow region. The concept is based on the two-domain approach with a simple interface devoid of thermodynamic properties. In this work, the simple interface concept is applied to model transvascular exchange. The simulations reproduce filtration and reabsorption and reveal the influence of wall and tissue parameters on the final distribution of therapeutic agents. However, the complex structure of the micro-vascular wall and the influence of the different pathways cannot be resolved by the presented approach. In some applications, the complex structure of the interface and the processes happening therein cannot be described by a simple interface devoid of thermodynamic properties. In such cases, it might be beneficial to resolve the interface layer or interface region on the pore-scale. We present a first step towards a resulting coupled pore-/REV-scale model where the interface is described by a bundle-of-tubes approach. The coupling concept between the one-phase free-flow, the pore-scale and the two-phase porous-medium model is based on flux continuity and the assumption that pore-and REV-scale pressure are equal. We develop an REV-scale interface concept - the complex interface concept - that describes drop formation, growth and detachment on hydrophobic interface between free and porous-medium flow. The interface stores the mass and energy of the drops without resolving them. The direct exchange between free-flow and porous-medium region next to the drop is also part of the coupling concept since it preserves the exchange processes described by the simple interface concept. The fraction of the interface which is covered by drops is used to obtain an area-weighted average of the coupling conditions with and without drop so that coupling conditions for the whole interface are obtained. The complex interface concept captures drop formation, growth and detachment. These processes are influenced by the conditions of both the free-flow and porous-medium region. The temporal evolution of the drop volume is an outcome of the model. The number of drops that can form on the interface is defined a priori by choosing the size of a drop REV. Neither the influence of the drops on the free-flow conditions nor film flow or sliding and merging of drops is included since the focus is on the interface description. The model is applied to simulate drop formation in the cathode of PEM fuel cells. In fuel cells, water is generated by the electro-chemical reaction in the catalyst layer and flows through the hydrophobic porous fibre structure of the GDL. Reaching the GC, water forms drops on the hydrophobic interface between GC and GDL. The drops significantly influence the water management in fuel cells which must be optimised to achieve good performance and durability. The numerical results show that it is possible to include drop dynamics in the REV-scale coupling conditions between free and porous-medium flow. Drop formation, growth and detachment are represented correctly, if the evaporation from the drop surface is neglected. The interface-coverage ratio, which is an indicator for the quality of the water management, can be predicted. The simulations for a higher number of drops suggest that the interface conditions dominate the system. A parameter study shows that interface wettability and free-flow velocity have a significant influence on the drop growth and detachment. In summary, this work reveals the potential of the developed coupling concepts to deal with realistic problems and exposes the need for further improvement and development.