DIRECT NUMERICAL-SIMULATION OF TURBULENT-FLOW IN A SQUARE DUCT

A direct numerical simulation of a fully developed, low-Reynolds-numbe r turbulent flow in a square duct is presented. The numerical scheme e mploys a time-splitting method to integrate the three-dimensional, inc ompressible Navier-Stokes equations using spectral/high-order finite-d ifference discretization on a staggered mesh; the nonlinear terms are represented by fifth-order upwind-biased finite differences. The unste ady flow field was simulated at a Reynolds number of 600 based on the mean friction velocity and the duct width, using 96 x 101 x 101 grid p oints. Turbulence statistics from the fully developed turbulent field are compared with existing experimental and numerical square duct data , providing good qualitative agreement. Results from the present study furnish the details of the comer effects and near-wall effects in thi s complex turbulent flow field; also included is a detailed descriptio n of the terms in the Reynolds-averaged streamwise momentum and vortic ity equations. Mechanisms responsible for the generation of the stress -driven secondary flow are studied by quadrant analysis and by analysi ng the instantaneous turbulence structures. It is demonstrated that th e mean secondary flow pattern, the distorted isotachs and the anisotro pic Reynolds stress distribution can be explained by the preferred loc ation of an ejection structure near the comer and the interaction betw een bursts from the two intersecting walls. Comer effects are also man ifested in the behaviour of the pressure-strain and velocity-pressure gradient correlations.