Direct Numerical Simulations of Turbulent Flow Over Various Riblet Shapes in Minimal-Span Channels
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Direct Numerical Simulations of Turbulent Flow Over Various Riblet Shapes in Minimal‑Span Channels S. Endrikat1 · D. Modesti1,2 · M. MacDonald3 · R. García‑Mayoral4 · N. Hutchins1 · D. Chung1 Received: 19 May 2020 / Accepted: 5 October 2020 © Springer Nature B.V. 2020
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 dragincreasing 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 𝛼 = 30◦ and blades appear to support the instability, whereas triangular riblets with 𝛼 = 60◦–90◦ and trapezoidal riblets with 𝛼 = 30◦ show little to no evidence of Kelvin–Helmholtz rollers. Keywords Riblets · Minimal-span channel · DNS · Kelvin–Helmholtz
* S. Endrikat [email protected] 1
Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia
2
Faculty of Aerospace Engineering, Delft University of Technology, Delft, Netherlands
3
Department of Mechanical Engineering, University of Auckland, Auckland 1010, New Zealand
4
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
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Flow, Turbulence and Combustion
1 Drag‑Reduction Performance of Riblets Riblets are small streamwise-aligned grooves on a surface that have been shown to reduce skin-friction drag compared to a smooth wall (Walsh and Weinstein 1978; Walsh 1982; Luchini et al. 1991; Bechert et al. 1997). The skin-friction coefficient Cf = 2∕U𝛿+2 is defined by the friction-scaled mean streamwise velocity U + ≡ U∕uτ at the half-channel or boundary-layer height 𝛿 . The superscript √ + denotes viscous scaling with the kinematic fluid viscosity 𝜈 and friction velocity uτ ≡ τw ∕𝜌 , where 𝜌 is the fluid density and τw the wall shear stress (drag per unit plan area), such that Cf = 2τw ∕(𝜌U𝛿2 ) . Drag reduction of a riblet surface c
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