Direct numerical investigation of turbulent and laminar flow in karst conduits

Karst aquifers, characterised by extensive and intricate conduit networks, serve a critical role in groundwater flow and contaminant transport. These natural systems exhibit complex geometrical features, including branching conduits, variations in cross-sectional shape, and significant wall roughness (k/D≈10^-1). Such heterogeneity makes it challenging to understand and predict flow patterns, friction losses, and the onset of turbulent behaviour in karst environments. Accurate characterisation of flow dynamics at the conduit scale is therefore essential for developing robust numerical models and reliable management strategies.

This study aims to investigate flow behaviour within representative karst conduits to determine key geometrical and fluid mechanical parameters, such as average cross-sectional areas, cave centrelines, friction factors, and velocity distributions by means of direct numerical simulations in a wide range of flow conditions (Re=1-10⁴). These parameters are fundamental inputs for upscaling methodologies that aim to describe entire karst networks without resolving every conduit in detail. A combination of finite-volume and spectral element methods is employed, each chosen to capture specific flow regimes. At lower Reynolds numbers, a finite-volume approach is used to accurately resolve laminar flows, while at higher Reynolds numbers, a spectral element method is implemented to better capture the full range of turbulent flow scales.

The conduit geometries used in the simulations are reconstructed from high-resolution LiDAR scans of real karst formations. The provided STL files preserve critical features such as irregular walls, branching geometries, and variable cross-sections. To ensure accurate resolution of the boundary, an immersed boundary technique is applied in conjunction with a ray-tracing algorithm. This combined approach precisely identifies the conduit walls, thereby facilitating the correct imposition of boundary conditions in these complex geometries.

Preliminary results for low Reynolds number flows show that laminar assumptions can hold in certain portions of the conduit, leading to streamlined centreline velocities and predictable head losses. However, irregular conduit shapes disrupt the flow field, causing spatial variations that deviate significantly from classical smooth-channel results. As also observed in a previous wavy-channel investigation, transitional flows can occur much earlier than predicted by standard empirical correlations (Re ≤ 1500), suggesting that conventional methods for estimating friction factors may be insufficient for karst-specific conditions and to account for the marked heterogeneity of the systems. 

The implications of this study are crucial not only for single conduits but also for the better understanding of network-scale flow dynamics, which enables more accurate prediction of groundwater movement and contaminant dispersion in karst aquifers. Furthermore, the hydraulic parameters identified in this investigation are highly valuable for upscaling models, as they allow for their incorporation into comprehensive karst network simulations, thereby improving the assessment of these systems.