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Massimo Zanolini
Travelling waves as flow control technique have been extensively studied in incompressible literature and their performances in terms of drag reduction (DR) and net power saving are well known. This work for the first time addresses the natural extension of streamwise travelling waves of spanwise velocity to the compressible subsonic and supersonic regime. Three values of bulk Mach number Mb = [0.3; 0.8; 1.5] are investigated with a set of 126 direct numerical simulations (DNS) with fixed forcing amplitude A+ = 12 at a friction Reynolds number of Re = 400.
The maximum drag reduction is found to increase with the Mach number, and its peak to move towards higher frequencies and wavenumbers for a supersonic flow. The oscillating wall exhibits the opposite trend, since its peak moves to lower frequency, as confirmed by other results in recent compressible literature. The drag increase region becomes thinner and decentralized with respect to subsonic regime. The bulk density at the wall and the bulk temperature at the channel center increase when the travelling waves are applied to channel flow, and their values depend on the control parameters.
The drag reduction is further investigated in terms of vertical shift of the mean streamwise velocity profile, showing a similar trend to the incompressible data, but with an additional dependence on Mach number. The power budget is found to be particularly advantageous, since the regions of high DR and low power required are the same in the case of low Reynolds. As a consequence, the net power saving visibly increases in correspondence of the DR peak, with the noteworthy achievement of 31% after a maximum DR of 52% in supersonic conditions. The steady wave also gives a positive response, while the oscillating wall has negative saving, as expected for the relative large amplitude considered in this paper. The instantaneous flow field is visualized for both reference and controlled turbulent channel flows, showing the enlargement in low-speed streaks near the wall and the increment in mean streak spacing.