Effect of Turbulence and Roughness on Coupled Porous-Medium/Free-Flow Exchange Processes

Abstract

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, BeaversJoseph 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.

Experimental and Numerical Study of Evaporation From Wavy Surfaces by Coupling Free Flow and Porous Media Flow

“…Since different model concepts are used in the free flow and porous media regions, extra interfacial conditions are necessary to couple the two subdomains (Davarzani et al, ; Fetzer et al, ; Mosthaf & Baber et al, 2011) based on the assumption of local mechanical, chemical, and thermal equilibrium. Continuity of total mass flux Considering there is only a gas phase that exchanges between the free‐flow region and the porous media, the continuity of total mass flux in the normal direction of the interface should be where n denotes the normal vector of the interface.…”

Editorial

“…They perform a formal homogenization procedure to obtain upscaled equations. Fetzer et al (2016) extend a concept for the coupling of free and porous-medium flow to turbulent free-flow conditions and integrate eddy-viscosity and boundary layer models for a rough interface. Results demonstrate the effect of these extensions on the evaporation rate.…”

A domain decomposition method to couple nonisothermal compositional gas liquid Darcy and free gas flows

“…They both can depend on p, T ff and c but will be taken constant in the numerical experiments. The turbulent dynamic viscosity µ t is typically obtained using an algebraic turbulent model or a more advanced k − model [15] from which is also deduced the turbulent diffusivity d t and the turbulent thermal conductivity λ t . Note that, in the following numerical experiments, the turbulent dynamic viscosity, diffusivity and thermal conductivity will be computed from the stationary uncoupled gas flow.…”

“…At the interface Γ between the free-flow and the porous-medium domains, the coupling conditions are those stated in [7,15,5] where we have replaced the Beaver Joseph condition by the simpler no slip condition due to the low permeability of the porous medium in our application.…”

“…Firstly it allows to use different codes for the porous-medium and the free-flow problems. Secondly, it reduces the complexity of the nonlinear and linear systems and make it possible to use on-the shelves preconditioners which results in a better efficiency compared with a monolithic Newton algorithm solving the fully coupled system [7,15].…”