CFD simulation of a transonic compressor cascade: mesh sensitivity analysis for steady-state RANS simulations

The aerodynamic optimization of modern turbomachinery requires a solid understanding of transonic flows, which are characterized by complex interactions between shock waves and boundary layers near solid walls. This thesis aims to assess the capability of a two-dimensional Reynolds Averaged Navier–Stokes (RANS) simulations to accurately reproduce the experimental behaviour of a transonic compressor cascade under Unique Incidence conditions. Particular attention is devoted to the influence of spatial discretization strategies and turbulence modelling on the accuracy and reliability of the numerical predictions. To accurately reproduce the U Ioperating condition, a Python script was developed to automatically determine the inlet flow angle (β1) corresponding to a target inlet Mach number (M1 = 1.21) and to compute the back pressure upstream of the spill point, ensuring consistency with the experimental boundary conditions. Using the meshing software, a structured grid was generated by applying a constant spatial refinement factor √2 and constraining the distributions in the wall-normal direction to ensure boundary layer resolution (y+ < 1.5). Three different meshes have been created: coarse (50000 cells), medium mesh(100000 cells), fine mesh (200000 cells). Simulations were performed in ANSYS Fluent using different turbulence models: K−ωSST model, K−ε Realizable, SST Transition Model. The mesh sensitivity analysis was performed using the Grid Convergence Index (GCI) method, while the turbulence models were evaluated by comparing Richardson-extrapolated quantities with experimental measurements. The results showed that the KWSST model provided the best overall agreement with the experimental data.The validation process demonstrated that the RANS approach is able to accurately reproduce the main aerodynamic performance parameters of the transonic compressor cascade, in fact the comparison between the Richardson-extrapolated results and the experimental measurements showed very good agreement for the integral quantities, confirming the reliability of the numerical approach for the prediction of the overall flow behavior. However, some discrepancies were observed in the local prediction of the shock wave position. Although the shock structure and the transonic flow features were correctly captured, the exact shock location was not fully reproduced. This deviation may be attributed to the limitations of a two-dimensional RANS approach, which neglects three-dimensional effects present in the experimental cascade, such as spanwise flow variations and three-dimensional shock/boundary-layer interactions. A sensitivity analysis on the outlet back pressure was also performed to investigate whether the shock displacement could be related to the imposed boundary condition. However, the variation of the back pressure did not eliminate the observed discrepancy, suggesting that other physical effects are responsible for the remaining difference.