Evaporation is an important component of the soil water balance. It is composed of water flow and transport processes in a porous medium that are coupled with heat fluxes and free air flow. This work ...provides a comprehensive review of model concepts used in different research fields to describe evaporation. Concepts range from nonisothermal two‐phase flow, two‐component transport in the porous medium that is coupled with one‐phase flow, two‐component transport in the free air flow to isothermal liquid water flow in the porous medium with upper boundary conditions defined by a potential evaporation flux when available energy and transfer to the free airflow are limiting or by a critical threshold water pressure when soil water availability is limiting. The latter approach corresponds with the classical Richards equation with mixed boundary conditions. We compare the different approaches on a theoretical level by identifying the underlying simplifications that are made for the different compartments of the system: porous medium, free flow and their interface, and by discussing how processes not explicitly considered are parameterized. Simplifications can be grouped into three sets depending on whether lateral variations in vertical fluxes are considered, whether flow and transport in the air phase in the porous medium are considered, and depending on how the interaction at the interface between the free flow and the porous medium is represented. The consequences of the simplifications are illustrated by numerical simulations in an accompanying paper.
Key Points
We review theory and model concepts for evaporation from porous media
We discuss the underlying assumptions and simplifications of different approaches
Approaches differ in the description of lateral transport, transport in the air phase of the porous medium, and coupling at the porous medium free flow interface
Turbulence transportation across permeable interfaces is investigated using direct numerical simulation, and the connection between the turbulent surface flow and the pore flow is explored. The ...porous media domain is constructed with an in-line arranged circular cylinder array. The effects of Reynolds number and porosity are also investigated by comparing cases with two Reynolds numbers (
R
e
≈
3000
,
6000
) and two porosities (
φ
=
0.5
,
0.8
). It was found that the change of porosity leads to the variation of flow motions near the interface region, which further affect turbulence transportation below the interface. The turbulent kinetic energy (TKE) budget shows that turbulent diffusion and pressure transportation work as energy sink and source alternatively, which suggests a possible route for turbulence transferring into porous region. Further analysis on the spectral TKE budget reveals the role of modes of different wavelengths. A major finding is that mean convection not only affects the distribution of TKE in spatial space, but also in scale space. The permeability of the wall also have an major impact on the occurrence ratio between blow and suction events as well as their corresponding flow structures, which can be related to the change of the Kármán constant of the mean velocity profile.
Multicomponent gas transport in porous media and at the interface between porous media and free flow occurs in a wide range of technical and environmental systems. Modeling tools are required for the ...quantitative description of such coupled environmental compartments. We present a benchmark study to compare different diffusion models as well as different coupling concepts employed for the description of multicomponent gas flow and transport at the porous medium/free-flow interface. The benchmark problems allowed us to compare two diffusion models (Fickian and Maxwell-Stefan formulations) for predicting the transport behavior of multicomponent mixtures in porous media and in presence of a free flow. The examples highlighted the importance of interaction between different diffusing components by applying the Maxwell-Stefan formulation, as well as the impact of the free flow velocity on gas migration at the interface under diffusion- and advection-dominated conditions. The problems were solved using two simulation tools, incorporating different coupling concepts to describe the physics of flow and transport processes. In COMSOL Multiphysics, we implemented a single-domain Brinkman approach, whereas in the DuMu
X
simulator we used a two-domain approach with the Navier-Stokes equation for the free flow and Darcy’s law for the porous medium. Also, the formulation of the Maxwell-Stefan equation for multicomponent transport was different between the two codes. Despite the different modeling concepts, mathematical descriptions and numerical schemes implemented in the two simulators, their outcomes demonstrate excellent agreement for all benchmark problems, as well as the capability to reproduce the results of previous modeling and experimental studies.
The model for microbially induced calcite precipitation (MICP) published by Ebigbo et al. (2012) has been improved based on new insights obtained from experiments and model calibration. The challenge ...in constructing a predictive model for permeability reduction in the underground with MICP is the quantification of the complex interaction between flow, transport, biofilm growth, and reaction kinetics. New data from Lauchnor et al. (2015) on whole‐cell ureolysis kinetics from batch experiments were incorporated into the model, which has allowed for a more precise quantification of the relevant parameters as well as a simplification of the reaction kinetics in the equations of the model. Further, the model has been calibrated objectively by inverse modeling using quasi‐1D column experiments and a radial flow experiment. From the postprocessing of the inverse modeling, a comprehensive sensitivity analysis has been performed with focus on the model input parameters that were fitted in the course of the model calibration. It reveals that calcite precipitation and concentrations of
NH4+ and
Ca2+ are particularly sensitive to parameters associated with the ureolysis rate and the attachment behavior of biomass. Based on the determined sensitivities and the ranges of values for the estimated parameters in the inversion, it is possible to identify focal areas where further research can have a high impact toward improving the understanding and engineering of MICP.
Key Points:
Revision of the model based on recent experiments
Model recalibration using calcite and in situ concentration measurements
Identification of areas for further research
Exchange processes between a turbulent free flow and a porous media flow are sensitive to the flow dynamics in both flow regimes, as well as to the interface that separates them. Resolving these ...complex exchange processes across irregular interfaces is key in understanding many natural and engineered systems. With soil–water evaporation as the natural application of interest, the coupled behavior and exchange between flow regimes are investigated numerically, considering a turbulent free flow as well as interfacial forms and obstacles. Interfacial forms and obstacles will alter the flow conditions at the interface, creating flow structures that either enhance or reduce exchange rates based on their velocity conditions and their mixing with the main flow. To evaluate how these interfacial forms change the exchange rates, interfacial conditions are isolated and investigated numerically. First, different flow speeds are compared for a flat surface. Second, a porous obstacle of varied height is introduced at the interface, and the effects the flow structures that develop have on the interface are analyzed. The flow parameters of this obstacle are then varied and the interfacial exchange rates investigated. Next, to evaluate the interaction of flow structures between obstacles, a second obstacle is introduced, separated by a varied distance. Finally, the shape of these obstacles is modified to create different wave forms. Each of these interfacial forms and obstacles is shown to create different flow structures adjacent to the surface which alter the mass, momentum, and energy conditions at the interface. These changes will enhance the exchange rate in locations where higher velocity gradients and more mixing with the main flow develop, but will reduce the exchange rate in locations where low velocity gradients and limited mixing with the main flow occur.
A channel flow coupled with a transversal stream through porous structures is investigated numerically in this study. Velocity profiles are obtained on the pore scale and averaged to the macroscale ...in order to evaluate the validity of the Beavers–Joseph interface condition. For this purpose, different ratios between the velocity at the inlet of the channel and the velocity at the base of the porous structure are considered. The effects of Reynolds number, velocity ratio, and geometrical arrangement of the porous structure on the Beavers–Joseph constant are then examined. A critical velocity ratio is found where, for lower ratios, the interface momentum transfer is mainly affected by the channel flow and, for higher ratios, the flow in the porous structure governs. The uniformity of the Beavers–Joseph constant at the interface is found to decrease with increasing velocity ratios. The present results have then been compared with simulations from a coupled Navier–Stokes/Darcy–Forchheimer model.
•Systematic evaluation of lattice Boltzmann models for porous media simulation, from creeping to turbulent flow regimes.•Evaluation of collision models and boundary schemes in terms of parallel ...effciency and numerical accuracy.•Effect of the lattice model on permeability and drag force.•Parallel simulation of pore scale resolved flow scenarios.
The lattice Boltzmann method has become a popular tool for determining the correlations for drag force and permeability in porous media for a wide range of Reynolds numbers and solid volume fractions. In order to achieve accurate and relevant results, it is important not only to implement very efficient code, but also to choose the most appropriate simulation setup. Moreover, it is essential to accurately evaluate the boundary conditions and collision models that are effective from the Stokes regime to the inertial and turbulent flow regimes. In this paper, we compare various no-slip boundary schemes and collision operators to assess their efficiency and accuracy. Instead of assuming a constant volume force driving the flow, a periodic pressure drop boundary condition is employed to mimic the pressure-driven flow through the simple sphere pack in a periodic domain. We first consider the convergence rates of various boundary conditions with different collision operators in the Stokes flow regime. Additionally, we choose different boundary conditions that are representatives of first- to third-order schemes at curved boundaries in order to evaluate their convergence rates numerically for both inertial and turbulent flow. We find that the multi-reflection boundary condition yields second order for inertial flow while it converges with third order in the Stokes regime. Taking into account the both computational cost and accuracy requirements, we choose the central linear interpolation bounce-back scheme in combination with the two-relaxation-time collision model. This combination is characterized by providing viscosity independent results and second-order spatial convergence. This method is applied to perform simulations of touching spheres arranged in a simple cubic array. Full- and reduced-stencil lattice models, i.e., the D3Q27 and D3Q19, respectively, are compared and the drag force and friction factor results are presented for Reynolds numbers in the range of 0.001 to 2,477. The drag forces computed using these two different lattice models have a relative difference below 3% for the highest Reynolds number considered in this study. Using the evaluation results, we demonstrate the flexibility of the models and software in two large scale computations, first a flow through an unstructured packing of spherical particles, and second for the turbulent flow over a permeable bed.
Core Ideas
We present a locally mass‐conservative flow, transport, and root–soil interaction model.
We include a sustainable, flexible research software framework for plant‐scale model development.
...This is an improved model concept for fluid dynamic processes, evaporation, root water uptake.
We have developed a general model concept and a flexible software framework for the description of plant‐scale soil–root interaction processes including the essential fluid mechanical processes in the vadose zone. The model was developed in the framework of non‐isothermal, multiphase, multicomponent flow and transport in porous media. The software is an extension of the open‐source porous media flow and transport simulator DuMux to embedded mixed‐dimensional coupled schemes. Our coupling concept allows us to describe all processes in a strongly coupled form and adapt the complexity of the governing equations in favor of either accuracy or computational efficiency. We have developed the necessary numerical tools to solve the strongly coupled nonlinear partial differential equation systems that arise with a locally mass conservative numerical scheme even in the context of evolving root architectures. We demonstrate the model concept and its features, discussing a virtual hydraulic lift experiment including evaporation, root tracer uptake on a locally refined grid, the simultaneous simulation of root growth and root water uptake, and an irrigation scenario comparing different models for flow in unsaturated soil. We have analyzed the impact of evaporation from soil on the soil water distribution around a single plant's root system. Moreover, we have shown that locally refined grids around the root system increase computational efficiency while maintaining accuracy. Finally, we demonstrate that the assumptions behind the Richards equation may be violated under certain conditions.
The interactions between turbulent free flow and flow in a porous medium are of key interest in different fields, e.g., meteorology, agriculture, building physics, and aerospace engineering. Properly ...understanding the strongly coupled exchange processes between the two domains is crucial to describing these interactions. In (Mosthaf et al. in Water Resour Res 47(10):W10522,
2011
. doi:
10.1029/2011WR010685
), a concept for coupling laminar compositional single-phase free flow to compositional two-phase porous-medium flow under non-isothermal conditions was presented. In this study, the existing coupling concept is first extended to turbulent free-flow conditions. This includes the interface conditions between a Reynolds-averaged Navier–Stokes free flow using algebraic turbulence models and a Darcy porous-medium flow. Second, eddy viscosity and boundary layer models for a rough interface are integrated into this model concept. Results from laboratory evaporation experiments are used for comparison of the developed model concept. A sensitivity analysis of the evaporation rate and porous-medium quantities on different model setups, boundary conditions, Beavers–Joseph coefficients, and roughness lengths is performed. Results demonstrate how including turbulence, either with eddy viscosity or boundary layer models, affects the evaporation rate. The model concept is able to predict early stage-I and intermediate to later stage-II evaporation rates. Sand-grain roughness concepts are successfully included into the model and show the desired qualitative effect.
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