Imposing virtual origins on the velocity components in direct numerical simulations

摘要

The relative wall-normal displacement of the origin perceived by different components of near-wall turbulence is known to produce a change in drag. This effect is produced for instance by drag-reducing surfaces of small texture-size like riblets and superhydrophobic surfaces. To facilitate the research on how these displacements alter near-wall turbulence, this paper studies different strategies to model such displacement effect through manipulated boundary conditions. Previous research has considered the effect of offsetting the virtual origins perceived by the tangential components of the velocity from the reference, boundary plane, where the wall-normal velocity was set to zero. These virtual origins are typically characterised by slip-length coefficients in Robin, slip-like boundary conditions. In this paper, we extend this idea and explore several techniques to define and implement virtual origins for all three velocity components on direct numerical simulations (DNSs) of channel flows, with special emphasis on the wall-normal velocity. The aim of this work is to provide a suitable foundation to extend the existing understanding on how these virtual origins affect the near-wall turbulence, and ultimately aid in the formulation of simplified models that capture the effect of complex surfaces on the overlying flow and on drag, without the need to resolve fully the turbulence and the surface texture. From the techniques tested, Robin boundary conditions for all three velocities are found to be the most satisfactory method to impose virtual origins, relating the velocity components to their respective wall-normal gradients linearly. Our results suggest that the effect of virtual origins on the flow, and hence the change in drag that they produce, can be reduced to an offset between the virtual origin perceived by the mean flow and that perceived by the overlying turbulence, and that turbulence remains otherwise smooth-wall-like, as proposed by Luchini (1996). The origin for turbulence, however, would not be set by the spanwise virtual origin alone, but by a combination of the spanwise and wall-normal origins. These observations suggest the need for an extension of Luchini's virtual-origin theory to predict the change in drag, accounting for the wall-normal transpiration when its effect is not negligible.