Computation of turbulent flow and secondary motions in a square duct using a forced generalized lattice Boltzmann equation

Abstract

Turbulent flow in a straight square duct driven by a pressure gradient exhibits remarkable flow structures such as the presence of mean streamwise vorticity or secondary flows. These secondary circulations take the form of two counter-rotating vortices near each corner of the duct. Even though their magnitudes are small compared with primary streamwise motions, they have a significant influence on flow and scalar transport and are challenging to accurately predict using computational approaches. In this paper, we employ a recently developed formulation of the generalized lattice Boltzmann equation (GLBE) with forcing term to perform large eddy simulation of fully developed turbulent flow in a square duct at a shear Reynolds number based on duct width equal to 300. Subgrid scale effects are represented by the Smagorinsky eddy viscosity model, which is modified by the van Driest damping function in the near-wall regions, in this GLBE approach, which is based on multiple relaxation times. It was found that the GLBE is able to correctly reproduce the existence of mean secondary motions and the computed detailed structure of first- and second-order statistics of main and secondary motions are in good agreement with prior direct numerical simulations based on the solution of the Navier-Stokes equations and experimental data.