Abstract
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 (García-Mayoral and Jiménez 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 \(\alpha =30^{\circ }\) and blades appear to support the instability, whereas triangular riblets with \(\alpha =60^{\circ }\)–\(90^{\circ }\) and trapezoidal riblets with \(\alpha =30^{\circ }\) show little to no evidence of Kelvin–Helmholtz rollers.
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Acknowledgements
The authors gratefully acknowledge the support of the Australian Research Council Discovery Project DP170102595. This research is undertaken with the assistance of resources from NCI that is supported by the Australian Government and from Pawsey that is funded by the Australian Government and the Government of Western Australia. D. Modesti was partially funded by Ermenegildo Zegna, through the “EZ Founder’s Scholarship”. The authors are grateful to the anonymous reviewers for their helpful comments which improved the quality of the manuscript.
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This project was supported by the Australian Research Council Discovery Project DP170102595. D. Modesti was partially funded through the “EZ Founder’s Scholarship”.
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The authors declare that they have no conflict of interest.
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Simulations for this project were conducted using the commercial solver Cliff by Cascade Technologies Inc.
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Endrikat, S., Modesti, D., MacDonald, M. et al. Direct Numerical Simulations of Turbulent Flow Over Various Riblet Shapes in Minimal-Span Channels. Flow Turbulence Combust 107, 1–29 (2021). https://doi.org/10.1007/s10494-020-00224-z
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DOI: https://doi.org/10.1007/s10494-020-00224-z