  We examine the time-dependent flow dynamics inside an idealised renal pelvis
in the context of a surgical procedure for kidney stone removal, extending
previous work by Williams et al. (2020,2021), who showed how vortical flow
structures can hinder mass transport in a canonical two-dimensional domain.
Here, we examine the time-dependent evolution of these vortical flow structures
in three-dimensions, and incorporate the presence of rigid kidney stones. We
perform direct numerical simulations, solving the transient Navier-Stokes
equations in a spherical domain. The results shed light on the crucial role of
flow circulation in the renal cavity and its effect on the trajectories of
rigid stones. We demonstrate that stones can either be washed out of the cavity
along with the fluid, or be trapped in the cavity via their interaction with
vortical flow structures. Additionally, we study the effect of multiple stones
in the flow field within the cavity in terms of the kinetic energy, entrapped
fluid volume, and the clearance rate of a passive tracer modelled via an
advection--diffusion equation. We demonstrate that the flow in the presence of
stones features a higher vorticity production within the cavity compared with
the stone-free cases.

Fluid Dynamics