Numerical study of near-wall coherent structures and their control in turbulent boundary layers

Abstract

Using direct numerical simulations of turbulent channel flow, we present a new method for skin friction reduction by prevention of streamwise vortex formation near the wall. Instability of lifted, vortex-free low-speed streaks (above a critical strength ω_yc) is shown to generate new streamwise vortices, which dominate near-wall turbulence phenomena. This new vortex formation mechanism consists of: (i) instability-initiated streak waviness in the horizontal plane, (ii) generation of thin horizontal sheets of streamwise vorticity and induction of positive stretching ∂u/ϖx (i.e. positive VISA), inherent to streak waviness, and finally (iii) vorticity sheet collapse via stretching (rather than roll-up) into streamwise vortices. The instability mechanism is explained and its evolutionary dynamics are documented. Significantly, the 3D features of the (instantaneous) instability-generated vortices agree well with the coherent structures educed (i.e. ensemble-averaged) from fully turbulent flow, suggesting the prevalence of this mechanism.

Based on this crucial role of streak instability in vortex generation, we develop a new technique for drag reduction, enabling large-scale flow forcing without requiring instantaneous flow information. As proof-of-principle, we show that an x-independent forcing, with a wavelength of 400 wall units and an amplitude of only 6% of the centerline velocity, produces a significant sustained drag reduction: 20% for imposed counterrotating streamwise vortices and 50% for colliding, z-directed wall jets. The drag reduction results from weakened longitudinal vortices near the wall, due to forcing-induced suppression of the underlying streak instability. In particular, the forcing weakens the wall-normal vorticity flanking lifted low-speed streaks, lowering it below ω_yc, thereby arresting the streaks’ instability responsible for vortex generation. These results suggest promising new drag reduction strategies for practical situations, e.g. passive vortex generators or colliding spanwise jets from x-aligned slots, involving large-scale (hence more durable) actuation and requiring no wall sensors or control logic.

This research was supported by AFOSR grant F49620-97-1-0131 and the NASA Graduate Fellowship grant NGT-51022 of W.S. Supercomputer time was provided by the NASA Ames Research Center.