Toward the simulation of complex 3D shear flows using unsteady statistical turbulence models

Recent progress in the numerical simulation of complex, 3D incompressible flows with unsteady statistical turbulence models is reviewed. A second-order accurate, overset grid, numerical method is developed for carrying out unsteady Reynolds-averaged Navier–Stokes (URANS) and detached-eddy simulations (DES) of flows in complex multi-connected domains. Results are reported for three test cases: (1) flow in a channel with four bottom-mounted rectangular piers; (2) flow in a channel with a corner-mounted rectangular block; and (3) flow in a strongly curved rectangular bend. Comparisons between the computed results and laboratory measurements and flow visualization experiments lead to the conclusion that even relatively simple turbulence closure models (such as the standard k–ε model or the one-equation Spalart–Allmaras model) can simulate complex, 3D flows dominated by geometry-induced, large-scale instabilities and unsteady coherent structures with reasonable accuracy. The results for the curved duct case further show that exciting and resolving directly with unsteady statistical turbulence models the low-frequency, large-scale, vortical rolls in a concave wall boundary layer is critical prerequisite for simulating the dramatic effects of concave curvature on the structure of turbulence.