Dynamics of fluid circulation in coupled free and heterogeneous porous domains

Abstract

Fluid flow in coupled free and porous domain, particularly when the porous medium is heterogeneous, is encountered in many hydro-environmental conditions, e.g., leakage from underground pipe, combined groundwater lake–subsurface interactions. One of the most difficult problems in the study of coupled flow behaviour has been the development of a universally applicable modelling scheme for combining the flow regimes. This is because the free/porous interfacial properties (e.g., shear-stress; velocity slip) that govern the coupled flow behaviour are difficult to determine experimentally under hydro-environmental conditions. On the other hand, the implications of various forms of heterogeneity in the porous media properties can be very different on the fluid-flow behaviour. Difficulties may also arise in direct coupling of the model equations that govern the fluid flow in the individual regions (e.g., Navier–Stokes for free-flow region and the Darcy's equation for the porous flow region). Consequently, models of coupled free and porous flow for hydro-environmental conditions are not very well developed at the moment. While there are some indications that fluids in coupled free and porous domains may circulate (i.e., development of flow cells), there is a lack of appropriate 3D analysis on how heterogeneities in porous media may affect such flow patterns. In this paper, we aim to analyse how porous media heterogeneity affects the dynamics of flow circulation in the porous side of a coupled free and porous domain. For this purpose, we analyse flow patterns in several model domains made up of two porous layers with differing permeabilities. The governing model equations are discretised and solved using the standard finite volume method on a staggered cell-centred mesh. The temporal discretisation is done using the explicit method. An in-house graphical user interface (GUI) has been created specifically to aid in the visualisation of otherwise complex flow patterns. The GUI contains many post-processing options and provides a comprehensive tool for the analysis of hydrodynamics and contaminant motion (not discussed in this paper) in coupled free and porous flow domains. This GUI is described in this paper briefly. The effects of altering the aspect ratio (i.e., multi-scale) of the domain on the coupled flow pattern have also been discussed.