A note on fitting a generalised Moody diagram for wall modelled large-eddy simulations

ABSTRACT

Motivated by the needs of wall modelled Large Eddy Simulation (LES), we introduce fits to numerical solutions of the Reynolds Averaged Navier–Stokes equations in their simplest near-wall, boundary layer approximation including a mixing-length model. We formulate the problem such that independent dimensionless variables are those directly available in LES. We provide practical fits for the dependent variable, fits that encompass a smooth transition between the viscous sublayer and inertial logarithmic layer, and then progress first considering moderate pressure gradients as well as roughness effects under the assumption that the mixing-length is not affected by the pressure gradient. An alternative fit based on the empirical wall model of Nickels (Inner scaling for wall-bounded flows subject to large pressure gradients. J Fluid Mech. 2004;521:217–239) is also provided, taking into account possible effects of pressure gradient on turbulence near-wall structure. We then consider the case of general pressure gradients, both favourable and adverse, up to conditions of separation, for both smooth and rough surfaces. The proposed fitting functions constitute a generalised Moody chart, comply with analytical solutions valid in various asymptotic regimes, and obviate the need for numerical iterative solution methods or near-wall numerical integration of ordinary differential equations during LES.

Keywords:

• Turbulence
• wall model
• large-eddy simulations

Acknowledgments

The author thanks M. Fowler, Y. Hue, G. Narasimhan, T. Zaki, P. Luchini, J. Larsson and X.I.A. Yang for insightful conversations and comments and is grateful to the Office of Naval Research and the National Science Foundation for financial support.

Disclosure statement

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

Additional information

Funding

Financial support for the present work was provided by the Office of Naval Research [grant number N00014-17-1-2937] and the Division of Chemical, Bioengineering, Environmental, and Transport Systems – National Science Foundation [grant number CBET-1738918].