By discretizing convective terms with the HLLC scheme in the relative rotating coordinate system

a finite volume analysis code based on multi-block structured grids was developed independently

in order to numerically solve the internal flow fields of turbomachineries. The flow simulations of an unshrouded radial impeller and a shrouded backswept impeller were carried out respectively. The surface pressure at various blade heights calculated by the code and commercial software agrees well with the relative difference smaller than 1%

which verifies the accuracy of the algorithm. As for the diffusion terms of turbulence equations

full discretization and part discretization by neglecting cross-derivative terms were used respectively. Through comparisons of turbulence viscosity contour

aerodynamic force and moment

it indicates that neglecting cross-derivative terms exerts little impact of less than 1% on the results when the grid orthogonality is not too bad

and thus the calculation quantity of turbulence equations can be reduced obviously.