2.2 Mesh generation
The geometry of the real machine was reproduced by means of a coordinate measuring tri-optic machine. The Hexahedral mesh blocks were distributed to have fine meshing near the leading edge and trailing edge and the hub and shroud of vane and blade. refinements around the vanes and blades were made for 15 mesh lines nearest the wall and with minimum volume distortion to get accuracy for the boundary layers resolution. A refinment to the tip clearance of 15 mesh lines to capture the details of leakage flow. A minimum number of nodes was secured inside the boundary layers so that kω-SST turbulence [23] can be used. An automatic wall function control [23] allowed to switch from the wall function for 20<y+ <100 and the low reynolds model for y+ < 2. Based on simulations at the nominal operating point (N=6000 rpm, m=5.06 kg/s), the first layer of nodes from a wall is estimated by\(\ y=\frac{\ y^{+}\mu}{\rho V_{t}}\), where\(\text{\ \ }V_{t}=V_{\infty}\ \sqrt{\frac{C_{f}}{2}}\) and\(C_{f}=0.026\text{Re}_{c}^{\frac{-1}{7}}\ \)[27]for Reynolds number \(\text{Re}_{c}=\frac{\rho V_{\infty}c}{\mu}\) based on vane/blade chord.\(y=y^{+}\sqrt{80}C_{\text{av}}\text{Re}_{C_{\text{av}}}^{-0.92}\), where the chord \(c_{\text{av}}=89\ mm\) and the maximum flow velocity equal to \(150\ m/s\). For y+ about 2 the nearest meshline is about 5 µm. The study of grid size dependency was conducted at the nominal operating conditions for five meshes of the runner blade, revealed stabilized steady state performance for a total mesh size of 2.75 million nodes For the complete circumerential components of this axial fan stage. Figure 2 presents part views of used meshes per sectors.