On the importance of the drag coefficient modelling in the double averaged Navier-Stokes equations for prediction of the roughness effects

ABSTRACT

The Discrete Element Method (DEM) for modelling of flow over rough walls is revised in the framework of the DANS (Double Averaged Navier-Stokes) equations, with a special focus on the drag term appearing in the mean momentum equation as a key to the robustness of the model. A set of 14 Direct Numerical Simulations (DNS) of channel flows with systematically varying roughness topographies is considered to assess the performances of different drag coefficient closures. While the standard model of Taylor et al. [J. Fluids Eng. 107 (1985), 251–257] is found not to be successful in reproducing the distribution of the drag force, a new model is derived. The new model along with the model recently proposed by Kuwata  et al. [Int. J. Heat Fluid Flow 77 (2019), 186–201] are employed for the solution of channel flow along with a simple mixing length model. Both models are shown to be successful in prediction of roughness function as long as a constant in the latter model is readjusted. The velocity profiles are also well recovered and in particular the roughness sublayers are accurately reproduced.

Keywords:

• Discrete element method
• roughness modelling
• double averaged Navier-Stokes
• direct numerical simulations

Acknowledgments

PF gratefully acknowledges financial support from German Research Foundation (DFG) through the project SFB/TRR 150 for this research.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

PF gratefully acknowledges financial support from German Research Foundation (DFG) through the project SFB/TRR 150 for this research.