Investigation of gravity-driven infiltration instabilities in smooth and
rough fractures using a massively parallel smoothed particle
hydrodynamics (SPH) model
Abstract
This work investigates small-scale infiltration dynamics in smooth and
rough single fractures using a three-dimensional multiphase
pairwise-force smoothed particle hydrodynamics (PF-SPH) model.
Gravity-driven infiltration instabilities in fractures under unsaturated
conditions can significantly influence the arrival time of tracers or
contaminants, and the rapid and localized recharge dynamics in
fractured-porous aquifer systems. Here, we study the influence of
roughness and injection rate on fluid flow modes and flow velocity.
Three types of fractures are considered with different degrees of
roughness, including a smooth fracture. Both the rough and smooth
fractures exhibit flow instabilities, fingering, and intermittent flow
regimes for low infiltration rates. In agreement with theoretical
predictions, a flat fluid front is achieved when the flux q supplied to
a fracture is larger than the gravitationally driven saturated flux (q
> kρg/μ cosφ). To characterize the flow instability, we
calculate standard deviations of velocity along the fracture width. For
the considered infiltration rates, we find that an increase in roughness
decreases the flow velocity and increases the standard deviation of
velocity. This is caused by a higher likelihood of flow discontinuities
in the form of fingering and/or snapping rivulets. To validate our
unsaturated flow simulations in fractures, we estimate the scaling of
specific discharge with normalized finger velocity and compute the
relationship between fingertip length and scaled finger velocity, and
find a good agreement with experimental results.