Resolving turbulence and drag over textured surfaces using texture-less simulations: the case of slip/no-slip textures
arxiv(2024)
摘要
We study the effect of surface texture on an overlying turbulent flow for the
case of textures made of an alternating slip/no-slip pattern, a common model
for superhydrophobic surfaces but also a particularly simple form of texture.
For texture sizes L^+ ≲ 20, we have previously reported that
turbulence remained smooth-wall-like, other than experiencing an apparent
origin offset for different flow components. For slip/no-slip textures, this
effect reduced to the flow experiencing slip conditions in the streamwise and
spanwise directions and zero transpiration at the surface. The overlying
turbulence effectively perceived such boundary conditions at least up to
texture sizes L^+ ≈ 50. However, beyond L^+ ≈ 20 the texture
interacted with the overlying turbulence in a non-homogeneous fashion,
additional Reynolds stresses arose and turbulence was no longer
smooth-wall-like. This is the typical effect of surface texture observed for
rough surfaces, and results in an increase in drag relative to smooth-wall
flows. In this paper, we argue that this occurs because the texture modifies
the overlying turbulence through non-linear, cross-advective terms between the
background turbulence and the texture-coherent flow directly induced by the
surface topology. To verify this, we conduct homogeneous-slip-length
simulations where we introduce additional, forcing terms in the Navier-Stokes
equations to capture the effect of this non-linear interaction on the
background turbulence. The interaction can then be accounted for without the
need to resolve the surface texture. We show that the additional terms
quantitatively capture the changes in the flow up to texture sizes L^+ ≈
70–100, including not just the roughness function but also the flow
statistics and structure.
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