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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 [1,2], 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. Our numerical predictions for the flow dynamics in the absence of stones are validated with experimental and 2D numerical data from [1], and the governing parameters and flow regimes are chosen carefully in order to satisfy several clinical constraints. 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.

Original publication




Journal article


J Biomech Eng

Publication Date



1 - 16