Numerical Simulation of Turbulent Fluid Flow in Rough Rock Fracture: 2D Case

We investigate both laminar and turbulent flow regimes in a rough-walled rock fracture via numerical CFD simulations. While previous studies were limited to either fully viscous Darcy or inertial Forchheimer laminar flow regimes, we chose to cover the widest possible Reynolds number range of 0.1–106\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^6$$\end{document}. We introduce CFD simulation of a turbulent flow for rough-walled fractures, implementing RANS approach to turbulence modeling. We focus on 2D fracture geometries and implement changes in both shear displacement and wall roughness, systematically examining their effect on fracture permeability and friction factor in a manner similar to the fundamental studies of the flow in rough-walled pipes. For a curvilinear fracture, laminar flow becomes non-stationary between Re∼102\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re \, {\sim } \, 10^2$$\end{document}–103\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^3$$\end{document}, earlier for larger shear displacement and wall roughness. Laminar–turbulent transition starting at Recr∼2300\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re_{\textrm{cr}} \, {\sim } \, 2300$$\end{document} may lead to a sharp drop in permeability depending on the fracture geometry; this gap vanishes for larger shear displacement and wall roughness. Depending on the fracture geometry, bottlenecks closing with shear become a major negative factor for the overall permeability.