The effect of texture granularity on turbulence

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 super- hydrophobic surfaces. For texture sizes L⁺ ≤ 20, it has been previously discussed that turbulence remains smooth-wall-like, other than experiencing an apparent origin offset for different flow components. For slip/no-slip textures, this effect reduces to the flow experiencing slip conditions in the streamwise and spanwise directions and zero transpiration at the surface. It has been reported that the overlying turbulence effectively perceives such boundary conditions at least up to texture sizes L⁺ ≈ 50. However, beyond L⁺ ≈ 20 the texture interacts with the overlying turbulence in a non-homogeneous fashion, and turbulence is no longer smooth-wall-like. This is the typical effect of surface texture observed in rough surfaces, and results in a degradation of drag. In this thesis, we argue that the texture modifies the overlying turbulence through cross-advective terms between the background turbulence and the flow directly induced by the texture. To verify this, we conduct homogeneous-slip-length simula- tions where we introduce additional, forcing terms in the Navier-Stokes equations that capture the effect of the 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, including both the roughness function and the turbulent statistics up to texture sizes L⁺ ≈ 70. Apart from the square-post textures in a collocated arrangement, we also validate the forcing model with staggered texture arrangement as well as slip/no-slip longitudinal ridges. The results further confirm that the additional terms are able to capture the modification in turbulence for different texture geometries. As the first step, we investigate calculating the additional terms a priori by using a modified laminar flow field, instead of texture-coherent flow from DNS, into the forcing model.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2022

Author dc:creator

• Xie, Wenxiong

Advisor dc:contributor.advisor

• García-Mayoral, Ricardo

• drag reduction
• flow control
• near-wall turbulence
• surface texturing

Licence

• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.91262

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/343840