Toward the simulation of complex 3D shear flows using unsteady statistical turbulence models Joongcheol Paik, Liang Ge, Fotis Sotiropoulos * School of Civil and Environmental Engineering, Georgia Institute of Technology, 790 Atlantic Drive, Atlanta, GA 30332-0355, USA Abstract 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–e 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. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Unsteady RANS; DES; Overset grids; 3D separation; Concave wall turbulence 1. Introduction Most flows of engineering relevance take place in complex, multi-connected domains and are dominated by large-scale unsteadiness and coherent vortex shed- ding. Unsteady statistical turbulence models constitute the only feasible modeling framework for quantitatively accurate predictions of such flows at real-life Reynolds numbers (Spalart, 2000). Such models include unsteady Reynolds-averaged Navier–Stokes (URANS) and hy- brid URANS/LES formulations. Turbulence models in the former category solve the RANS and turbulence closure equations in a time-accurate fashion and thus resolve directly contributions to the time-averaged Reynolds stresses from large-scale, low-frequency deterministic fluctuations in the flow. Therefore, UR- ANS models would in principle work well in flows in which slowly varying coherent structures contribute a considerable portion of the total turbulence kinetic en- ergy (Durbin, 1995; Spalart, 2000). Hybrid modeling strategies are essentially LES models designed to asymptote to a URANS model near solid walls. Such models exploit the ability of LES to resolve all turbulent scales larger than the grid spacing in the bulk of the flow domain while requiring only relatively modest compu- tational resources, which are comparable to those re- quired in a URANS simulation (see Spalart, 2000, for a detailed discussion). A very popular hybrid approach is the so-called Detached-Eddy Simulation (DES), which was proposed by Spalart et al. (1997) and has recently attracted considerable attention due to its simplicity and preliminary success in various complex, massively sep- arated flows. The standard DES model employs a gen- eralized version of the Spalart–Allmaras (SA), one- equation, eddy-viscosity model (Spalart and Allmaras, 1994). The turbulence length scale in the DES model is dependent on the distance from the wall. Sufficiently close to the wall the length scale is set equal to the dis- tance from the wall and the model operates in a UR- ANS mode while far from the wall the length scale is proportional to the local grid spacing and the model switches to the LES mode. * Corresponding author. Tel.: +1-404-894-4432; fax: +1-404-385- 1131. E-mail address: fs30@ce.gatech.edu (F. Sotiropoulos). 0142-727X/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.ijheatfluidflow.2004.02.002 International Journal of Heat and Fluid Flow 25 (2004) 513–527 www.elsevier.com/locate/ijhff