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Impact of Reynolds Number on the Drag Reduction Mechanism of Spanwise Travelling Surface Waves

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Abstract

The mechanism that provokes friction drag reduction in a turbulent boundary layer flow which is actively controlled by spanwise travelling transversal surface waves is investigated. The focus is on discussing the drag reducing mechanism for a low and a moderately high Reynolds number. At the low friction velocity based Reynolds number \(Re_\tau \approx 393\), the periodic secondary flow field induced by the surface actuation interacts with the quasi-streamwise vortices. An elliptic deformation of these vortices initiates their breakup and the reduced amount lowers the overall wall-shear stress level due to the consequently attenuated high-speed streaks. At the moderately high Reynolds number \(Re_\tau \approx 1525\), the effectiveness of this mechanism is reduced but a second contributor occurs, which manipulates the inner–outer interaction. The large-scale motions of the log layer can less effectively impose their footprint onto the near-wall flow field since large-scale ejections, which are introduced by the surface actuation in the near-wall region, balance the outer-layer sweeps. Since the outer-layer impact on the inner region is intensified by increasing Reynolds number, its disruption is beneficial as to a successful application of this drag reduction method to engineering relevant Reynolds numbers.

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Funding

The research was funded by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the research project SCHR-309/68 and by the European Commission’s Horizon 2020-Research and Innovation Framework Programme within the CoE RAISE project under Grant Agreement No. 951733. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GCS Supercomputer HAWK at the High-Performance Computing Center Stuttgart.

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Authors and Affiliations

  1. Institute of Aerodynamics, RWTH Aachen University, Wüllnerstraße 5a, 52062, Aachen, Germany

    Esther Lagemann, Marian Albers, Christian Lagemann & Wolfgang Schröder

  2. JARA Center for Simulation and Data Science, RWTH Aachen University, Seffenter Weg 23, 52074, Aachen, Germany

    Wolfgang Schröder

Authors
  1. Esther Lagemann
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  2. Marian Albers
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  3. Christian Lagemann
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  4. Wolfgang Schröder
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Contributions

MA performed the numerical simulations. EL and CL conducted the main physical analysis accompanied by discussions with MA and WS. The main manuscript text is written by EL. All authors reviewed the manuscript.

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Correspondence to Esther Lagemann.

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Lagemann, E., Albers, M., Lagemann, C. et al. Impact of Reynolds Number on the Drag Reduction Mechanism of Spanwise Travelling Surface Waves. Flow Turbulence Combust (2023). https://doi.org/10.1007/s10494-023-00507-1

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