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High Reynolds Number Airfoil: From Wall-Resolved to Wall-Modeled LES

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Abstract

This paper presents an in-depth study, using wall-resolved Large-Eddy Simulation (wrLES), of a high Reynolds number airfoil in a near-stall condition. The flow around the NACA4412 airfoil, a widely used test case for turbulence modeling validation, is computed at Reynolds number Re = 1.64 × 106 and angle of attack α = 12∘. In the first part of the paper, the results are compared to previous experimental and numerical results, showing close agreement with both. In order to aid wall-model development, the second part of the paper characterizes the effect of the adverse pressure-gradient (APG) on the turbulent boundary layer development, and evaluates different wall-models in an a priori manner. It appears that the simple models, which assume an equilibrium flow, provide a better match to the mean flow velocity than allegedly more advanced models. The study reveals also that the often used simplification of the “Two-Layer Model”(TLM) that takes the pressure-gradient into account but neglects the convective terms, is not adequate. This simplification applied to the TLM indeed leads to a higher error than the simple equilibrium models. Therefore, it is argued that if the convective terms are neglected, the pressure-gradient term needs to be neglected as well.

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Notes

  1. i.e. using the local wall shear stress \(\tau _{w} = \rho u_{\tau }^{2}\) to non-dimensionalize the tangential velocity u+ = u/uτ and the normal wall distance y+ = yuτ/ν with ν the kinematic viscosity.

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Acknowledgments

The first author thanks Prof. Piomelli and Prof. Schlatter for the fruitful discussions during DLES11 conference, as well as J.-S. Cagnone, A. Johnen, M. Rasquin and J. Lacabanne for their judicious advices and support in the analysis, meshing, and post-processing of this work. She also would like to thank the reviewers for their thorough analyses of the text and their insightful remarks.

Funding

This research has been financed by the Walloon Region through the FirstDoCA framework (grant number ECV320600FD016F/1217882). The study benefited from computational resources made available on the Tier-1 supercomputer of the Fédération Wallonie-Bruxelles (n∘1117545).

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Authors and Affiliations

  1. Cenaero, Gosselies, Belgium

    A. Frère & K. Hillewaert

  2. Institute of Mechanics, Materials and Civil Engineering (iMMC), Université catholique de Louvain (UCL), Louvain-la-Neuve, Belgium

    A. Frère, P. Chatelain & G. Winckelmans

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  1. A. Frère
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  2. K. Hillewaert
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Correspondence to A. Frère.

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Frère, A., Hillewaert, K., Chatelain, P. et al. High Reynolds Number Airfoil: From Wall-Resolved to Wall-Modeled LES. Flow Turbulence Combust 101, 457–476 (2018). https://doi.org/10.1007/s10494-018-9972-9

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