Modeling and analysis of the movement of fluid-fluid interfaces ín porous media coupled with free flow
Final Report Abstract
This project aimed on numerical modeling of coupled porous-medium free flow exchange processes. A coupling concept, developed in MUSIS 1, has been implemented into the numerical framework DuMux. In a next step several extensions have been made and their effect has been analyzed. First the model was extended to turbulent conditions in the free flow by using algebraic turbulence models. In that scope the influence of roughness, parametrized a so-called sand grain roughness has been investigated. Both, turbulence and roughness, enhance the exchange fluxes compare to a purely laminar system. The model has been simplified by using the boundary layer theory and replacing the full free flow model by a model only describing the boundary layer and the fluxes through it. For cases in which the assumptions for the boundary development are valid, the results are in good agreement with the ones obtained by coupling to a full free flow model. Good agreements are also achieved, when the effect of surface water content is included. Radiation has been included for both, the coupled and the uncoupled model, and shows a significant influence on the resulting exchange fluxes. Thermal non-equilibrium influences the temperature distribution within the fluids and the solid material, which affects the fluid flow, transport, and partitioning processes. This may be especially relevant under high velocities in the free flow. In summary, evaporation processes are influenced by a great variety of parameters within both flow compartments which reveal a dynamical interplay. The boundary layer at the interface of the two compartments influences decisively the exchange of mass, momentum and energy. All fluid-structure parameters (capillary pressure, relative permeability, effective thermal conductivity and diffusivity), are non-linear. Their representation on averaged volumes contains severe uncertainties considering their values at the porous-medium surface. This holds also for the surface water content, which is approximated by the volumetric quantities water saturation and porosity, and which is determining the transition from stage-1 to stage-2. The influence of the volumetric approximation of surface quantities can be reduced by a high grid vertical grid resolution in the vicinity of the interface. The interface processes are restricted to a relatively small region and do in general not scale, if a larger domain is considered. However, they crucially influence the evaporation behavior and have to be properly accounted for in REV-scale and field-scale models. Usually, area-specific quantities are not available, but would give a better representation of the processes happening at fluid-fluid and fluid-solid interfaces. A good agreement between measured and computed drying curves was achieved on two different ways: with a statistical distribution of soil parameters and using a saturation-dependent transfer coefficient. The statistical distribution of the porous-medium parameters leads to a nonuniform drying behavior at the surface. However, information about small-scale heterogeneities is usually not available and, thus, the choice of the variance and and correlation length is somehow arbitrary. Furthermore, the introduction of a heterogeneous distribution does not account for the processes happening in the boundary layer, and are further independent of the flow velocity. Hence, the scaling of the diffusive fluxes with a well- founded transfer coefficient that depends on the surface water content is the more promising approach.
Publications
- Model concepts for heat and water transport in soils and across the soil-atmosphere interface – Part 1: Theory Water Resources Research, 2017, accepted
Vanderborght, J.; Fetzer, T.; Mosthaf, K.; Smits, K. and R. Helmig
(See online at https://doi.org/10.1002/2016WR019982) - A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow. Water Resources Research, 2011, 47, W10522
Mosthaf, K.; Baber, K.; Flemisch, B.; Helmig, R.; Leijnse, A.; Rybak, I. and B. Wohlmuth
(See online at https://doi.org/10.1029/2011WR010685) - Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow. IMA Journal of Applied Mathematics, 2012, 77, 887-909
Baber, K.; Mosthaf, K.; Flemisch, B.; Helmig, R.; Müthing, S. and B. Wohlmuth
(See online at https://doi.org/10.1093/imamat/hxs048) - Simulation of infiltration processes in the unsaturated zone using a multiscale approach. Vadose Zone Journal, 2012, 11, 3
Kissling F.; Helmig R. and C. Rohde
(See online at https://doi.org/10.2136/vzj2011.0193) - Modeling and Analysis of Coupled Porous-Medium and Free Flow with Application to Evaporation Processes
K. Mosthaf
(See online at https://doi.org/10.18419/opus-519) - Modeling and analysis of evaporation processes from porous media on the REV scale. Water Resources Research, 2014, 50, 1059-1079
Mosthaf, K.; Helmig, R. and D. Or
(See online at https://doi.org/10.1002/2013WR014442)
