Direct Numerical Simulations of Turbulent Flow Over Various Riblet Shapes in Minimal-Span Channels

Riblets reduce skin-friction drag until their viscous-scaled size becomes large enough for turbulence to approach the wall, leading to the breakdown of drag-reduction. In order to investigate inertial-flow mechanisms that are responsible for the breakdown, we employ the minimal-span channel concept for cost-efficient direct numerical simulation (DNS) of rough-wall flows (MacDonald et al. in J Fluid Mech 816: 5-42, 2017). This allows us to investigate six different riblet shapes and various viscous-scaled sizes for a total of 21 configurations. We verify that the small numerical domains capture all relevant physics by varying the box size and by comparing to reference data from full-span channel flow. Specifically, we find that, close to the wall in the spectral region occupied by drag-increasing Kelvin-Helmholtz rollers (Garcia-Mayoral and Jimenez in J Fluid Mech 678: 317-347, 2011), the energy-difference relative to smooth-wall flow is not affected by the narrow domain, even though these structures have large spanwise extents. This allows us to evaluate the influence of the Kelvin-Helmholtz instability by comparing fluctuations of wall-normal and streamwise velocity, pressure and a passive scalar over riblets of different shapes and viscous-scaled sizes to those over a smooth wall. We observe that triangular riblets with a tip angle alpha=30 degrees and blades appear to support the instability, whereas triangular riblets with alpha = 60 degrees- 90 degrees and trapezoidal riblets with alpha = 30 degrees show little to no evidence of Kelvin-Helmholtz rollers.

Automated summary

The study investigates the breakdown of drag-reduction mechanisms in riblets as their viscous-scaled size becomes large enough for turbulence to approach the wall. Using the minimal-span channel concept, cost-efficient direct numerical simulation of rough-wall flows was conducted to study the inertial-flow mechanisms. Different shapes and sizes of riblets were examined, with findings indicating varying influences on the Kelvin-Helmholtz instability.