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

Influence of riblet shapes on the occurrence of Kelvin–Helmholtz rollers

“…For the present code we varied the channel width at (Endrikat et al. 2020), to verify that our minimal channels accurately resolve both the mean flow and fluctuations of size and for , in agreement with MacDonald et al. (2017).…”

“…A mesh refinement study (Endrikat et al. 2020) in all three directions for triangular riblets confirms that velocity fluctuations are resolved across all relevant scales and that is approximately mesh independent. For example, we made the mesh finer by factors of approximately , and in , and relative to our present mesh in figure 3( a ) and observed an increase in of , which cannot be discerned from the statistical uncertainty that we set to control the runtime of our simulations (details below).…”

“…Our domains with resolve all relevant fluctuations in the spectral and wall-normal region that may be affected by the Kelvin–Helmholtz instability and the energy in that spectral region matches that in wider domains, both for flows with and without Kelvin–Helmholtz rollers (Endrikat et al. 2020). Therefore, the constraint of the largest scales in the flow does not seem to affect the occurrence or strength of Kelvin–Helmholtz rollers, whose energy accumulates partly in the spanwise infinite wavelength of minimal-span channels.…”

Dispersive stresses in turbulent flow over riblets

“…We also note that at sufficiently high s + we expect that any riblet shape will eventually develop secondary flows inside the groove, but for certain geometries (e.g. triangular riblets with α = 30 • ) the value of s + for which this happens is well beyond the drag optimum and therefore for these cases inertial flow at the crest is responsible for the degradation of drag reduction (García-Mayoral & Jiménez 2011;Endrikat et al 2021).…”

“…Given the more recent date of the study on Kelvin-Helmholtz-like rollers, this mechanism has been considered the only cause of the linear-regime breakdown in recent years. However, Endrikat et al (2020Endrikat et al ( , 2021 recently used the present DNS dataset to study how the groove shape affects the Kelvin-Helmholtz-like rollers and found that they are only active for certain riblet geometries, namely sharp triangles and blades. Nevertheless, all riblet shapes exhibit the linear-regime breakdown eventually leading to a drag increase, thus pointing to a possible route to performance degradation that is unrelated to Kelvin-Helmholtz rollers.…”