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.