Energy-based drag decomposition analyses for a turbulent channel flow developing over convergent-divergent riblets

Direct numerical simulations of a turbulent channel flow developing over convergent-divergent (C-D) riblets are performed at a Reynolds number of Re-b = 2800, based on the half channel height delta and the bulk velocity. To gain an in-depth understanding of the origin of the drag generated by C-D riblets, a drag decomposition method is derived from kinetic energy principle for a turbulent channel flow with wall roughness. C-D riblets with a wavelength, lambda, ranging from 0.25 delta to 1.5 delta, are examined to understand the influence of secondary flow motions on the drag. It is found that as lambda increases, the intensity of the secondary flow motion increases first and then decreases, peaking at lambda / delta = 1. At lambda / delta & GE; 1, some heterogeneity appears in the spanwise direction for the turbulent kinetic energy (TKE) and vortical structures, with the strongest enhancement occurring around regions of upwelling. All the riblet cases examined here exhibit an increased drag compared to the smooth wall case. From the energy dissipation/production point of view, such a drag increase is dominated by the TKE production and the viscous dissipation wake component. While the drag contribution from the TKE production shear component decreases as lambda increases, the drag contribution from the wake component of both the TKE production and viscous dissipation follows the same trend as the intensity of the secondary flow motion. From the work point of view, the drag increase in the riblet case at lambda / delta = 0.25 comes mainly from the work of the Reynolds shear stresses, whereas at lambda / delta & GE; 1, the drag augmentation is dominated by the work of the dispersive stresses. At lambda / delta = 0.5, both components play an important role in the increase in the drag, which also exhibits a peak.

Automated summary

Direct numerical simulations were performed to investigate the influence of secondary flow motions on the drag generated by convergent-divergent (C-D) riblets in a turbulent channel flow. It was found that the intensity of the secondary flow motion increased with the wavelength of the riblets, peaking at a wavelength equal to the half channel height. The increase in drag was dominated by the turbulent kinetic energy production and viscous dissipation wake component. The work of the Reynolds shear stresses and dispersive stresses played important roles in the increase in drag at different wavelengths.