Impact of tip rounding on riblet drag-reduction performance

The present paper investigates the effect of tip rounding on the performance of riblets in turbulent flows. The rounding impact is investigated both with Stokes and turbulent simulations, to evaluate the protrusion heights difference Δ⁢ℎ and the roughness function Δ⁢𝑈$^+$, respectively. Three different cross section shapes are considered through inexpensive Stokes simulations, triangular riblets with a 30°,60° and 90° tip angle, and an exponential decay in the Δ⁢ℎ value for increasingly larger tip roundings is observed. For the turbulent problem we employ an innovative, cost-effective immersed-boundary method that uses the pre-computed Stokes solution to assemble the immersed-boundary coefficients, enabling an accurate representation of the near-tip flow on relatively coarse grids. Turbulent direct numerical simulations carried out for the 60° geometry reproduce the same trend observed in Stokes calculations, showing that the loss of turbulent drag-reduction due to tip rounding is explained by the geometry’s diminished viscous efficiency.