DNS investigation on anisotropy and inhomogeneity of Reynolds stress in rhombic ducts

In non-circular ducts, such as rhombic ducts, anisotropy and inhomogeneity of Reynolds stress induce secondary flow of the second kind. In the present study, Direct Numerical Simulation of turbulent flow in rhombic ducts have been carried out to investigate effects of the corner angle on anisotropy and inhomogeneity of the Reynolds stress. Near diagonal lines not only from acute corner, but also from obtuse corner, turbulent kinetic energy is suppressed. In order to clarify the suppression mechanisms of turbulent kinetic energy, the budgets of Reynolds-stress transport are evaluated. Suppression of turbulent kinetic energy near the diagonal line from the acute corners is attributed to small production term due to low mean velocity gradient. On the other hand, mean velocity gradient near the diagonal line from the obtuse corner is as high as that away from the corners. However, the production term is small near the obtuse corner bisector. The main reason is that redistribution to the turbulent energy component in the diagonal direction is strongly suppressed. It is found that redistribution to turbulent energy components in the cross section from that in the streamwise direction is suppressed near acute and obtuse bisectors.