We consider turbulent flows in pressure-driven ducts with complex cross-section, with special reference to the case of square ducts. Direct numerical simulations (DNS) are carried out in a wide enough range of Reynolds number to reach flow conditions which are representative of fully developed turbulence. Extremely long integration times are required to achieve adequate convergence of the flow statistics, and specifically high-fidelity representation of the secondary motions which arise. The intensity of the latter is found to be in the order of 1-2% of the bulk velocity, and unaffected by Reynolds number variations. The smallness of the mean convection terms in the streamwise vorticity equation points to a simple characterization of the secondary flows, which in the asymptotic high-Re regime are found to be approximated with good accuracy by eigenfunctions of the Laplace operator. Despite their effect of redistributing the wall shear stress along the duct perimeter, we find that secondary motions do not have large influence on the mean velocity field, which can be characterized with good accuracy as that resulting from the concurrent effect of four independent flat walls, each controlling a quarter of the flow domain. As a consequence, we find that parametrizations based on the hydraulic diameter concept, and modifications thereof, are successful in predicting the duct friction coefficient. A theoretical predictive formula is presented for ducts with arbitrary cross-sectional shape, which includes corrections to the classical hydraulic diameter.

个人简介：

Sergio Pirozzoli is a professor of the departments of Mechanical and Aerospace Engineering in Sapienza University of Rome, Italy. He obtained his master and Ph.D. degrees in the departments of Mechanical and Aerospace Engineering in Sapienza University of Rome. He is the associate editor of several important journals: Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Theoretical and Computational Fluid Dynamics and ASME Journal of Fluids Engineering. He is the member of American Society of Mechanical Engineers and American Physical Society, Division of Fluid Dynamics.

His research focuses on the simulations of compressible or uncompressible turbulence and the relevant schemes. He has published over 70 papers on important journals of fluid mechanics, including Journal of Fluid Mechanics, Journal of Computational Physics and Journal of Computational Physics, etc. These papers focus on numerical schemes, boundary layer, compressible turbulence, turbulence structure and so on.