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Abstract
Turbulence control in the form of a streamwise travelling wave of transverse wall motion was studied numerically by employing direct numerical simulations (DNS). Both total and phase averaging were utilised to examine the statistical behaviour of the turbulence affected by the wall forcing, with a focus on the skin friction. Comparison with results from pure temporal and spatial wall forcing are conducted, and a compilation of data is used to explore analogies with drag-reduced channel flow.
Highlights
An interesting observation from the temporal wall oscillation case with the long period of T + = 176 is the wave occurring in the skin friction profile, from the onset of the wall-forcing, as illustrated in Figure 5, where C f is plotted for two phases (φ = 0◦ and φ = 90◦ )
There is a propagation wave originating from the onset of the oscillating wall, travelling downstream with a decreasing amplitude, until vanishing roughly where the skin friction stabilises to its drag-reduced levels
The compilation of data presented provided evidence for the close resemblance of the drag reduction (DR) in boundary layer and channel flow, the effects of the variation downstream are lacking in the latter case
Summary
The amplitude of the wall velocity does usually not depend on the streamwise coordinate (x) in computational studies of channel flow, while the forcing (1) is complemented with a function describing the spatial distribution when applied to a limited section of the wall in the boundary layer experiments and simulations. Researchers [3,5,12,13,14,15] considered a steady variation in the streamwise direction along the plate instead of a time-dependent forcing In this case, the wall velocity (W) is imposed in the form of. The only experimental data to date for this type of wall forcing are provided by [17], who applied the streamwise travelling wave on the pipe flow, and by [18] for the highReynolds number boundary layer.
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