Prediction of Turbulent Secondary Flows in Ducts Using Equilibrium Wall-Modeled LES

Abstract

For many practical applications, large eddy simulation (LES) and direct numerical simulation (DNS) are still too computationally expensive to be viable engineering tools. By modeling the small scales within the boundary layer, wall-modeled LES (WMLES) reduces this cost and enables high Reynolds number calculations. For a WMLES approach that relies on the assumption of an equilibrium boundary layer, however, a primary concern is the extent to which the set of simplified equations solved by the wall-model may be insufficient to predict boundary layer separation or three-dimensional behavior. Additionally, most equilibrium WMLES approaches rely on some type of eddy viscosity term to parameterize the effects of unresolved turbulence near the wall. In many flows of interest, however, the anisotropy of the Reynolds stress tensor violates the assumptions inherent to the most common eddy viscosity models. Hence, the accuracy of WMLES for these types of flows is not yet fully established. This research attempts to identify some of the potential deficiencies in the equilibrium WMLES methodology for turbulent flows through non-circular ducts and demonstrates how certain straightforward modifications can significantly improve the calculation of shear stress. The shear stress distributions are then shown to be influential in the development of the secondary vortices which can significantly alter the primary, axial flow. Several model variations are initially evaluated using two streamwise-periodic, incompressible test cases before being applied to a spatially-evolving, compressible flow. These modifications are shown to improve the prediction of the secondary flows found in turbulent ducts across a range of Reynolds and Mach numbers.