Analysis of secondary motions in square duct flow

Abstract

We carry out direct numerical simulations (DNS) of square duct flow spanning the friction Reynolds number range , to study the nature and the role of secondary motions. We preliminarily find that secondary motions are not the mere result of the time averaging procedure, but rather they are present in the instantaneous flow realizations, corresponding to large eddies persistent in both space and time. Numerical experiments have also been carried out whereby the secondary motions are suppressed, hence allowing to quantifying their effect on the mean flow field. At sufficiently high Reynolds number, secondary motions are found to increase the friction coefficient by about 3%, hence proportionally to their relative strength with respect to the bulk flow. Simulations without secondary motions are found to yield larger deviations on the mean velocity profiles from the standard law-of-the-wall, revealing that secondary motions act as a self-regulating mechanism of turbulence whereby the effect of the corners is mitigated.