Viscous drag reduction: Groove-texturing applied to naturally developing boundary-layer flow

Abstract

The concept of a micropatterned surface morphology capable of producing self-stabilization of turbulence in wall-bounded flows is considered which act to restructure fluctuations towards the limiting state where these must be entirely suppressed. Direct numerical simulations of turbulence in a groove-modified channel consisting of flat and grooved walls were performed at a Reynolds number \mathrm{Re_m} $ \simeq $ 5000 based on the bulk velocity and the full channel height. Simulations were performed for highly disturbed initial flow conditions leading to the almost instantaneous appearance of turbulence in channels with flat walls. In an attempt to insure persistence of laminar flow, the surface morphology was designed in the form of profiled grooves aligned with the flow direction and embedded in the wall. Such grooves are presumed to allow development of only the statistically axisymmetric disturbances. In contrast to the rapid production of turbulence along a flat wall, it was found that such development was suppressed over a grooved wall for a remarkably long period of time. Owing to the difference in the flow structure, friction drag over the grooved wall was more than 60% lower than that over the flat wall. Using simulation databases, anisotropy of turbulence was evaluated to yield insights into structural changes in the flow permitting self-sustaining of the laminar regime, leading to the drag reduction effect. Anisotropy-invariant mapping supports the conclusion, emerging from analytic considerations, that persistence of the laminar regime is due to statistical axisymmetry in the velocity fluctuations.