Shock-Boundary Layer Interaction in Transonic Flows: Evaluation of Grid Resolution and Turbulence Modeling Effects on Numerical Predictions

This study investigates the influence of mesh resolution and turbulence model selection on the accuracy of numerical simulations for transonic flow, with particular emphasis on shock-boundary layer interaction phenomena. Accurate prediction of such flows is notoriously difficult due to the sensitivity to near-wall resolution, global mesh density, and turbulence model assumptions, and this problem motivates the present work. Two solvers were employed, rhoCentralFoam (unsteady) and TSLAeroFoam (steady-state), both are compressible and density-based and implemented within the OpenFOAM framework. The investigation focuses on three different non-dimensional wall distance ( $y^{+}$) values of 1, 2.5 and 5, each implemented with both moderate and fine mesh resolutions. Three turbulence models—Spalart-Allmaras (SA), $k$- $\omega$ Shear Stress Transport (SST), and $k$- $ϵ$ Realizable—were evaluated at M = 0.74, Re = 2.7 $\times$ ${\mathrm{10}}^6$, and $\alpha$ = ${\mathrm{3.19}}^{\circ }$. Results showed that while both solvers achieved good overall agreement with experimental data, particularly in terms of pressure distribution, lift coefficient, and shock location, noticeable differences still emerged. The $k$- $\omega$ SST model consistently delivered the most robust performance across all cases, capturing the shock position on $y^{+}\approx 1$ meshes with deviations below 0.02 $c$ compared to the experiment, and maintaining accuracy even at $y^{+}\approx 5$. The $k$- $ϵ$ Realizable model was highly sensitive to near-wall resolution, displacing shocks downstream at higher $y^{+}$ values, whereas Spalart-Allmaras remained broadly comparable to the $k$- $\omega$ SST model in predictive performance. The rhoCentralFoam solver achieved consistently better lift predictions, staying within about 2% of the experimental value on average, whereas TSLAeroFoam overpredicted it by around 4%. For transonic Reynolds-Averaged Navier-Stokes (RANS) simulations, unsteady $k$- $\omega$ SST with $y^{+}\approx 1$ is recommended for maximum fidelity, whereas steady $k$- $\omega$ SST or SA simulations offer a practical option for quick and reasonably accurate aerodynamic predictions.