Turbulent flows in square ducts: physical insight and suggestions for turbulence modellers

We carry out Direct Numerical Simulation (DNS) of flows in a straight duct with square cross-section. At high-friction Reynolds numbers, the Reynolds number dependence is similar to turbulent plane channels, hence flows in a square duct allows to investigate the Reynolds number dependency through a reduced number of simulations. Secondary motion play a minor role in this regime. At low Re, the profiles of the statistics differ from those in the two-dimensional channel due to the interaction of flow structures with different size. Large flow scales due to the mean motion are responsible for creating turbulence anisotropy in wall-bounded flows, causing serious difficulties for RANS turbulence closures. Projection of velocity vectors and of the Reynolds stress tensor along the eigenvectors of the mean strain-rate tensor yields reduced Reynolds stress anisotropy, and simple turbulence kinetic energy budgets. We show that the isotropic rate of dissipation is more difficult to model than the full dissipation rate, whose distribution does not largely differ from that of turbulence kinetic energy production. We expect that this information may be exploited for the development of advanced RANS models for complex flows.