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Linear instability in the wake of an elliptic wing

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Abstract

Linear global instability analysis has been performed in the wake of a low aspect ratio three-dimensional wing of elliptic cross section, constructed with appropriately scaled Eppler E387 airfoils. The flow field over the airfoil and in its wake has been computed by full three-dimensional direct numerical simulation at a chord Reynolds number of \(Re_{c}=1750\) and two angles of attack, \(\mathrm{{AoA}}=0^\circ \) and \(5^\circ \). Point-vortex methods have been employed to predict the inviscid counterpart of this flow. The spatial BiGlobal eigenvalue problem governing linear small-amplitude perturbations superposed upon the viscous three-dimensional wake has been solved at several axial locations, and results were used to initialize linear PSE-3D analyses without any simplifying assumptions regarding the form of the trailing vortex system, other than weak dependence of all flow quantities on the axial spatial direction. Two classes of linearly unstable perturbations were identified, namely stronger-amplified symmetric modes and weaker-amplified antisymmetric disturbances, both peaking at the vortex sheet which connects the trailing vortices. The amplitude functions of both classes of modes were documented, and their characteristics were compared with those delivered by local linear stability analysis in the wake near the symmetry plane and in the vicinity of the vortex core. While all linear instability analysis approaches employed have delivered qualitatively consistent predictions, only PSE-3D is free from assumptions regarding the underlying base flow and should thus be employed to obtain quantitative information on amplification rates and amplitude functions in this class of configurations.

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Authors and Affiliations

  1. School of Aeronautics, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, Madrid, 28040, Spain

    Wei He, Juan Ángel Tendero & Pedro Paredes

  2. School of Engineering, University of Liverpool, The Quadrangle, Browlow Hill, Liverpool, L69 3GH, UK

    Vassilis Theofilis

  3. Theoretical and Applied Mechanics Laboratory, Department of Mechanical Engineering, Universidade Federal Fluminense, Rua Passo da Patria 156, Niterói, RJ, 24210-240, Brazil

    Vassilis Theofilis

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  1. Wei He
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  2. Juan Ángel Tendero
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  4. Vassilis Theofilis
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Correspondence to Wei He.

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Communicated by Dr. Theofilis and Dr. Sharma.

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He, W., Tendero, J.Á., Paredes, P. et al. Linear instability in the wake of an elliptic wing. Theor. Comput. Fluid Dyn. 31, 483–504 (2017). https://doi.org/10.1007/s00162-016-0400-2

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  • DOI: https://doi.org/10.1007/s00162-016-0400-2

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