The effect of spanwise wall oscillation on turbulent pipe flow structures resulting in drag reduction

Abstract

The results of a comparative analysis based upon a Karhunen–Loève expansion of turbulent pipe flow and drag reduced turbulent pipe flow by spanwise wall oscillation are presented. The turbulent flow is generated by a direct numerical simulation at a Reynolds number Reτ=150. The spanwise wall oscillation is imposed as a velocity boundary condition with an amplitude of A+=20 and a period of T+=50. The wall oscillation results in a 27% mean velocity increase when the flow is driven by a constant pressure gradient. The peaks of the Reynolds stress and root-mean-squared velocities shift away from the wall and the Karhunen–Loève dimension of the turbulent attractor is reduced from 2763 to 1080. The coherent vorticity structures are pushed away from the wall into higher speed flow, causing an increase of their advection speed of 34% as determined by a normal speed locus. This increase in advection speed gives the propagating waves less time to interact with the roll modes. This leads to less energy transfer and a shorter lifespan of the propagating structures, and thus less Reynolds stress production which results in drag reduction.

Drag reduction in turbulent boundary layers by in-plane wall motion

“…This points to an interaction between the Stokes layer and the near-wall structures, which can be described in terms of either a phase shift between the low-speed streaks and the quasi-streamwise vortical structures [11], or the creation of negative spanwise vorticity during the oscillation cycle [16]. Duggleby et al [17] observe that velocity fluctuations present an outward shift of the peak value of their root mean square (r.m.s.) profiles, and infer an outward shift of the turbulence structures, which thus convect at a faster speed, possibly explaining the shorter duration of sweeps and bursts events measured in experiments.…”

Introduction. Turbulence transition in pipe flow: 125th anniversary of the publication of Reynolds' paper

“…Proper orthogonal decomposition is another means of extracting large-scale coherent structures, and is used by Duggleby et al (2009) to identify these structures. They have related these structures to turbulent drag and drag reduction by wall manipulations (Duggleby et al 2007). Some of these structures might be related to the coherent travelling waves.…”

Direct numerical simulation of pipe flow using a solenoidal spectral method

“…6. In this plot, we present the results for a fixed oscillation frequency of Ω = 6π (frequency used in [3]) and vary the oscillation amplitude A. The skin friction coefficient, defined by…”

“…Drag reduction due to spanwise oscillations is a well-known phenomenon [2,3,9,17,21,22], and numerical studies routinely report a drag reduction on the order of 40%. Spanwise oscillations in the case of pipe flow are essentially azimuthal oscillations (about the pipe axis).…”