A New Explicit Algebraic Wall Model for LES of Turbulent Flows Under Adverse Pressure Gradient

Abstract

A new explicit algebraic wall law for the Large Eddy Simulation of flows with adverse pressure gradient is proposed. This new wall law, referred as adverse pressure gradient power law (APGPL), is developed starting from the power-law of Werner and Wengle (Turbulent Shear Flows, vol 8, Springer, New York, pp 155–168, 1993) in order to mimic an implicit non-equilibrium log-law based on Afzal’s law (Afzal, IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows at High Reynolds Numbers, Kluwer Academic Publishers, Bochum, pp 95–118, 1996). No iterative method is needed for the evaluation of the wall shear stress from the APGPL contrary to the majority of models available in the literature. The APGPL model relies on the definition of three modes: the equilibrium power-law is used in regions of no or favourable pressure gradient, the APGPL is used in regions of adverse pressure gradient, and no wall model is used in separated flow regions. This model is assessed via Large Eddy Simulations of flows involving adverse pressure gradient and boundary layer separation using the Lattice Boltzmann Method on uniform nested grids. The flow around a clean and iced NACA23012 airfoil at Reynolds number \(Re = 1.88 \times 10^6\) and the flow over the LAGOON landing gear at \(Re = 1.59 \times 10^6\) are considered. Results are found in good agreement with those obtained by the non-equilibrium log-law and experimental and numerical data available in the literature.

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Acknowledgements

The authors acknowledge C.Gacherieu from Airbus for the eslA reference data. The authors would like to thank J.Basirico for his help on this study.

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Correspondence to Sylvia Wilhelm.

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Conflicts of interest

P. Sagaut has received research grants from Airbus, Renault, Safran and CS. Other authors declare no conflict of interest.

Funding

This work was supported by the project OMEGA3 ”Outil de ModElisation de nouvelle Génération pour l’Aérodynamique Appliquée à l’Aéronautique“ (No. 2018-16), with the financial support of DGAC. This work was performed using HPC resources from GENCI-TGCC/CINES (Grant 2018-A0052A07679).

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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by S. Wilhelm, J. Jacob and P. Sagaut. The first draft of the manuscript was written by S. Wilhelm and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Wilhelm, S., Jacob, J. & Sagaut, P. A New Explicit Algebraic Wall Model for LES of Turbulent Flows Under Adverse Pressure Gradient. Flow Turbulence Combust (2020). https://doi.org/10.1007/s10494-020-00181-7

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Keywords

  • Wall modelling
  • Large Eddy simulation
  • Lattice Boltzmann method
  • Aerodynamics