This thesis is dedicated to the study of the turbulent fluid flow in rough-walled rock fractures. Fracture models were generated from 3D scans of fractured rock samples, while fluid flow was simulated numerically by means of FVM-based open-source CFD toolbox OpenFOAM, employing the high-performance computing cluster for the more demanding 3D models. First part of the thesis addresses the issue of fracture geometry. Realistic 2D and 3D fracture models were constructed from 3D scans of upper and lower halves of a fractured rock sample, taking both shear displacement and contact spots into account. Furthermore, we discuss the shortcomings of the available fracture aperture metrics and propose a new aperture metric based on the Hausdorff distance; imaging performance of the new metric is shown to be superior to the conventional vertical aperture, especially for rough fracture surfaces with abundant ridges and troughs. In the second part of the thesis we focus on the fluid flow through the rock fracture for both 2D and 3D cases. While previous studies were largely limited to the fully viscous Darcy or inertial Forchheimer laminar flow regimes, we chose to investigate across the widest possible range of Reynolds numbers from 0.1 to 10^6, covering both laminar and turbulent regimes, which called for a thorough investigation of suitable turbulence modeling techniques. Due to narrow mean aperture and high aspect ratio of the typical fracture geometry, meshing posed a particularly challenging problem. Taking into account limited computational resources and a sheer number of model geometries, we developed a highly-optimised workflow, employing the steady-state RANS simulation approach to obtain time-averaged flow fields. Our findings show that while flow fields remain mostly stationary and undisturbed for simpler contactless geometries, emergence of contact spots immediately triggers a transition to non-stationary flow starting from Re ∼ 10^2, which is reflected by the streamline tortuosity data. This transition disrupts the flow pattern across the fracture plane, causing strong channeling and large separation bubbles, with area of the latter being much larger than the generating contact spots. Adverse influence of the contact spots on the overall permeability is strong enough to override any benefits of aperture increase during shear and dilation. Contactless 3D models can to a certain degree be approximated by their 2D counterparts. Lastly, we investigate the influence of both shearing and contact spots on the overall permeability and friction factor of the fracture, drawing a parallel to the well-studied area of turbulent flow in rough-walled pipes and ducts. Unlike the latter, 3D curvilinear fracture geometries exhibit a gapless laminar–turbulent transition, behaving as a hydraulically rough channel in the turbulent range as the shear displacement increases.

Numerical solution of differential equations having multitude of scales in the solution field is one of the most challenging research areas, but highly demanded in scientific and industrial applications. One of the natural approaches for handling such problems is to separate the scales and approximate the solution of the segregated scales with appropriate numerical method. Variational multiscale method (VMS) is a predominant method in the paradigm of scale separation schemes. In our work we have used the VMS technique to develop a numerical scheme for computations of turbulent flows in time-dependent domains. VMS allows separation of the entire range of scales in the flow field into two or three groups, thereby enabling a different numerical treatment for the different groups. In the context of computational fluid dynamics(CFD), VMS is a significant new improvement over the classical large eddy simulation (LES). VMS does away with the commutation errors arising due to filtering in LES. Further, in a three-scale VMS approach the model for the subgrid scale can be contained to only a part of the resolved scales instead of effecting the entire range of resolved scales. The projection based VMS scheme that we have developed gives a robust and efficient method for solving problems of turbulent fluid flows in deforming domains, governed by incompressible Navier {Stokes equations. In addition to the existing challenges due to turbulence, the computational complexity of the problem increases further when the considered domain is time-dependent. In this work, we have used an arbitrary Lagrangian-Eulerian (ALE) based VMS scheme to account for the domain deformation. In the proposed scheme, the large scales are represented by an additional tensor valued space. The resolved large and small scales are computed in a single unified equation, and the effect of unresolved scales is confined only to the resolved small scales, by using a projection operator. The popular Smagorinsky eddy viscosity model is used to approximate the effects of unresolved scales. The used ALE approach consists of an elastic mesh update technique. Moreover, a computationally efficient scheme is obtained by the choice of orthogonal finite element basis function for the resolved large scales, which allows to reformulate the ALE-VMS system matrix into the standard form of the NSE system matrix. Thus, any existing Navier{Stokes solver can be utilized for this scheme, with modifications. Further, the stability and error estimates of the scheme using a linear model of the NSE are also derived. Finally, the proposed scheme has been validated by a number of numerical examples over a wide range of problems.