Verification and validation of Reynolds-averaged Navier–Stokes turbulence models for external flow

The Spalart–Allmaras (S-A) turbulence model in the NASA-Langley CFL3D and FUN3D flow solvers has been previously verified 2nd-order accurate. For low subsonic 2-D applications (turbulent flat plate and NACA 0012 airfoil at α = 0 ° ), solutions from the S-A, S-A with Rotation and Curvature (SARC), Menter Shear-Stress Transport (SST), and Wilcox 1998   k - ω turbulence models in commercial flow solvers, Cobalt and RavenCFD, are compared with NASA results for code verification. Of 36 case evaluations, each of which uses 5 systematically refined computational meshes, only 7 approach 2nd-order observed accuracy, but 27 cases show 1st-order or better, indicating the formal order may be less than 2 for these applications. Since Cobalt and RavenCFD turbulence models perform comparable to NASAʼs verified models and since rigorous code verification is not possible without access to source code, the presented evidence suggests these turbulence models are implemented correctly for these or similar flow conditions and configurations. For solution verification, estimates of numerical uncertainty are less than 0.5% for 94% of the cases and less than 0.1% for 61% of the cases. For validation, the turbulent flat plate solutions match experiment skin friction within 4.8% for x / L > 0.05 , and for airfoil drag coefficient, S-A and SST agree within 1.2% of experiment, SARC 2%, and k - ω 4%.