System rotation and streamline curvature correction for the ℓ2−ω delayed detached eddy simulation model

In flows with system rotation and streamline curvature, the inability of the underlying Reynolds-averaged Navier–Stokes (RANS) branch to sense the curvature/rotation effect may result in inaccurate near-wall prediction for a hybrid RANS/large eddy simulation (LES) model. The rotation and curvature (RC) correction by Arolla and Durbin [Int. J. Heat Fluid Flow 39, 78–89 (2013)] is introduced to the ℓ2−ω delayed detached eddy simulation (DDES) model [K. Reddy, J. Ryon, and P. Durbin, J. Heat Fluid Flow 50, 103–113 (2014)] to overcome the limitations of traditional linear eddy viscosity-based hybrid RANS/LES approaches in complex flows, denoted as ℓ2−ω DDES-RC. The ℓ2−ω DDES-RC formulation modifies the RANS length scale using a rotation and curvature-dependent eddy viscosity coefficient, while keeping the RANS-LES coupling mechanism unaltered. It allows the near-wall RANS region to respond to rotation and curvature effects. Additionally, it facilitates earlier switching from RANS to LES modes when needed. Validation through spanwise rotating turbulent channel flows, infinite serpentine passage flows, and wall-mounted hump simulations demonstrates the model's superiority over the original DDES model which cannot sense rotation or curvature. Key results include accurate predictions of asymmetric velocity profiles, Reynolds stress anisotropy, and separation bubble dynamics in rotating and curved flows, aligned closely with direct numerical simulation (DNS) and experimental data. The model maintains computational efficiency while circumventing the convergence issue that usually occurs in second-moment closure, offering a robust tool for simulating complex turbulent flows in rotating machinery and aerodynamic applications.