Modeling rough walls from surface topography to double averaged Navier-Stokes computation

Abstract

The discrete element method was recently revisited using a double averaged Navier-Stokes formulation [Chedevergne F. A double-averaged navier-stokes $k-\omega$ turbulence model for wall flows over rough surfaces with heat transfer. J Turbul. 2021 Sep;22(11):713–734. doi:10.1080/14685248.2021.1973014] and a new closure relation for the drag coefficient [Chedevergne F, Forooghi P. On the importance of the drag coefficient modelling in the double averaged navier-stokes equations for prediction of the roughness effects. J Turbul. 2020 Aug;21(8):463–482. doi:10.1080/14685248.2020.1817465]. The developed model lies on the notion of representative elementary roughness whose characterisation needs to be generalised to provide a rigorous definition for randomly distributed rough configurations. From 3D scans of rough surfaces and simple image processing, a procedure was proposed to compute the blockage factor and the elementary diameter, the two main parameters of the representative elementary roughness. The procedure was successfully applied to two experimental configurations [Squire D, Morrill-Winter C, Hutchins N, et al. Comparison of turbulent boundary layers over smooth and rough surfaces up to high reynolds numbers. J Fluid Mech. 2016;795:210–240; Croner E, Léon O, Chedevergne F. Industrial use of equivalent sand grain height models for roughness modelling in turbomachinery. In: 55th 3AF International Conference on Applied Conference; Poitiers, France; Apr 2021. https://hal.archives-ouvertes.fr/hal-03228846]. Computed velocity profiles match experimental ones when the Reynolds number is varied, showing at the same time the relevance of the procedure and the validity of the double averaged Navier-Stokes model across the different rough regimes.

Keywords:

• Roughness
• double averaged Navier-Stokes
• discrete element method
• turbulent boundary layers

Acknowledgments

The author is grateful to D. Chung, N. Hutchins (University of Melbourne) and M. MacDonalds (University of Auckland) for sharing their data on rough configurations. Sincere acknowledgments are also addressed to SafranTech for their support on roughness issues.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Cross-sections in planes perpendicular to the wall-normal coordinate y.

2 Since the Reynolds average is the ensemble average, the same notation is kept here for the mean height which is mean value over the ensemble of the discrete values of the elevations $y_{ij}$.