Abstract
Direct numerical simulations of fully developed turbulent channel flows with wavy walls are undertaken. The wavy walls, skewed with respect to the mean flow direction, are introduced as a means of emulating a Spatial Stokes Layer (SSL) induced by in-plane wall motion. The transverse shear strain above the wavy wall is shown to be similar to that of a SSL, thereby affecting the turbulent flow and leading to a reduction in the turbulent skin-friction drag. However, some important differences with respect to the SSL case are brought to light too. In particular, the phase variations of the turbulent properties are accentuated and, unlike in the SSL case, there is a region of increased turbulence production over a portion of the wall, above the leeward side of the wave, thus giving rise to a local increase in dissipation. The pressure- and friction-drag levels are carefully quantified for various flow configurations, exhibiting a combined maximum overall-drag reduction of about 0.6%. The friction-drag reduction is shown to behave approximately quadratically for small wave slopes and then linearly for higher slopes, whilst the pressure-drag penalty increases quadratically. The transverse shear-strain layer is shown to be approximately Reynolds-number independent when the wave geometry is scaled in wall units.
Highlights
In the context of greener and more cost-effective aviation, industrial and academic researchers have proposed and studied a wide range of drag-reducing control methods mainly over the past three decades
In the present study, skewed wavy-wall channels have been investigated by means of direct numerical simulation as a potential passive open-loop drag-reduction device
The spanwise shear-strain profiles generated by the wavy wall were shown to resemble closely those of the wellestablished method of drag reduction by in-plane wall motions and to depend only weakly on the Reynolds number when expressed in wall units
Summary
In the context of greener and more cost-effective aviation, industrial and academic researchers have proposed and studied a wide range of drag-reducing control methods mainly over the past three decades. This method was studied by Viotti et al. by means of direct numerical simulation (DNS) for various forcing amplitudes ASSL and wavelengths λx. The premise is that the wavy geometry will generate a spanwise shear strain, somewhat away from the wall, that will weaken turbulence in a similar manner to that affected by the SSL Such a passive device would benefit from the favourable actuation characteristics of the SSL (large wavelength), resulting in a practical solution, from a manufacturing and maintenance standpoint. The present study will focus on selected direct numerical simulations of turbulent wavy-channel flows with the aim of examining the degree of Stokes-layer emulation achieved, and the degree to which the drag is reduced relative to the plane channel. As part of this study, some major similarities and differences between the flow arising from in-plane wall motions and that past a wavy wall, as shown in Fig. 2, will be brought to light, including the impact on the near-wall turbulence
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