*3.5. Solver*

The numerical simulation was performed using the commercial software ANSYS Fluent. The present simulation used a RANS approach for the liquid phase through a realizable *k* − model. The dispersed phase was estimated using the discrete phase model in the commercial CFD software ANSYS Fluent. The numerical simulation was performed coupling all the subdomains with the following imposed boundary conditions:


A setup used previously in [32] was used for the solid phase, where the injection was applied at the domain inlet and fully elastic collision was assumed at the walls. An analysis of the adequate number of particle injections was also carried out to generate a statistically meaningful sampling. One-hundred stochastic tracking tries were determined to be adequate to ensure that erosion on the walls of the turbine flow passage was independent of the number of injected particles.

The steady-state simulations were carried out using spatial derivatives discretized through a second-order upwind scheme. Full pressure–velocity coupling was enabled using the SIMPLE algorithm. Further, double precision was considered to improve the computational accuracy. A quantitative assessment of the discharge difference was made between the inlet and the outlet, which was lower than the order of 9 × <sup>10</sup><sup>−</sup>3.

The postprocessing phase was carried out in ANSYS CFD-Post, obtaining estimations of the erosion rate on the surfaces of the studied components. Additionally, the pressure and velocity of the flow were determined. Turbine efficiency was calculated based on these results.
