Our SFB 1313 doctoral researcher Edward N. Coltman (Central Project Z, Associated Project AX-3) successfully defended his doctoral thesis "Coupled Free-Flow and Porous-Medium Flow Systems: An Analysis of Soil Water Evaporation on Multiple Scales" on 16 July 2024. Congratulations!
Edward N. Coltman was a researcher at the Department of Hydromechanics and Modelling of Hydrosystems.
Abstract
Throughout our natural and engineered environments, dynamic flows, transporting mass, momentum, and energy, define the conditions in which we live. Although many of these flows can be described with individual mathematical models, some of the most interesting and relevant applications are best described as a system of coupled flow
domains. Free flows, such as turbulent atmospheric flows, often come in contact with porous-medium flows, such as sub-surface groundwater flows or flows through filters. In many contexts, these flows, when in contact with each other, exhibit a significant coupling, where conditions in one domain affect the conditions in the other domain, as well as the exchange between the two. Some examples of real-world applications that display this coupled behavior are proton-exchange membrane fuel cells, transpiration cooling, and hyporheic flows. Simulating the dynamics of these coupled systems becomes a challenge; mathematical models for each domain must be developed and the coupling between models must be incorporated. Additionally, the scale of evaluation must be considered. While large scale models may be useful for larger applications, some mechanisms relevant to the system may be neglected.
Within this thesis, we focus on a relevant but complex example of these coupled systems: soil water evaporation. This application, both extensively common and environmentally critical, is difficult to describe well due to the complexity of the flows on either side of the interface, as well as various scales of evaluations. Partially saturated porous surfaces cover much of the Earth’s surface and their exchange of mass and heat with the atmosphere influences the atmospheric water cycle and surface energy balance. While evaluations must be efficient and capable of handling such a large system, complex mechanisms at smaller scales play a large role in the development of exchange rates. Within the subsurface, capillary forces counteracting gravitational forces, thermal phase change aspects, and the interplay of multiphase conditions affecting mass and heat transport near the evaporation front complicate the mass and energy conditions at the interface. In the atmosphere, turbulence, variations in temperature or humidity, as well as the development of boundary layers and near-surface flow structures, further complicate the evaporational demand at the interface. Even for a homogeneous system with a simple flat surface, models to describe this evaporation can become quite complicated, but for rough or formed interfaces, both the conditions beneath the surface and above the surface change and spatially vary. Including all of these mechanisms in larger and more simplified models becomes a challenge.
In this work, we analyze soil water evaporation across scales with increasing levels of complexity. Large-scale models, typically resolved for individual measured data points, provide rough estimates of exchange rates using resistance functions. In comparison, laboratory-scale models offer more detailed insights. Uncoupled homogeneous or spatially variant models can be used to resolve some dynamics, but variations in the atmosphere are ignored. Using a coupled model, we investigate the effects of interfacial roughness and interfacial forms on evaporation rates. With these investigations and experimental work done in a wind tunnel environment, we can see how interfacial forms
have a large effect on local and total evaporation rates.
While these evaluations at an averaged scale can be very useful, even at this focused scale, some significant mechanisms from smaller scales are ignored. In this thesis, we outline these missing mechanisms and define a framework for incorporating these missing sub-scale mechanisms at the averaged scale. As “enhanced diffusion” is often used to describe missing pore-scale mechanisms, a velocity driven dispersion model is developed using this framework, where pore-scale simulations, volume averaging, data-driven models, and metrics analysis combine to form a data-driven multi-scale dispersive transport model. These results demonstrate the importance of accurate parameters and model concepts when capturing sub-scale phenomena.
In summary, this work advances the understanding of soil water evaporation by developing and comparing coupled models that account for complex interactions between free-flow and porous media at different scales. The findings provide a foundation for more accurate and comprehensive models, enhancing our ability to predict and manage critical environmental and engineering processes.