*3.3. Computational Mesh*

The computational mesh was divided into four regions, one for each runner and one for each of the contraction/expansion regions upstream and downstream the runners. The meshes of the runners were mostly block-structured, whereas the contraction/expansion regions consisted of 6 layers of prism boundary layer cells near the walls and unstructured tetrahedral core cells, as shown in Figure 3. The shroud tip clearance was 0.67 mm, and 8 layers of hexahedral and triangular prism cells were used in the tip clearance region. The mesh was finest at the runners, and gradually coarser further away from the runners. The surface mesh of one blade passage for the two runners is shown in Figure 3a, and the refined mesh regions close to the runners are shown in Figure 3b.

Table 2 presents a summary of the meshes for different regions. Note that the upstream and downstream regions utilised the same mesh. The total number of cells was 7.75 million, and the different regions contained roughly the same number of cells. The *y*<sup>+</sup> 90% values in Table 2 denote the maximum *y*<sup>+</sup> values in 90% of the region. They were obtained in pump mode at a time step before the transient operations had commenced. The *y*<sup>+</sup> value was less than 50 in 90% of the computational domain. Wall functions that adapted to all *y*+ values were used. In OpenFOAM-v1912, the wall boundary conditions kqRWallFunction for turbulent kinetic energy (*k*), omegaWallFunction for specific dissipation rate (*ω*) and nutkWallFunction for turbulent viscosity were applied.

**Figure 3.** Computational mesh regions, Runner 1 (red) and Runner 2 (blue). (**a**) Surface mesh of one blade passage. (**b**) Zoomed-in view of the refined mesh regions and surfaces of the runners.


**Table 2.** Mesh details.
