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Efficient numerical methods for global linear instability. Analysis and modeling of non-orthogonal swept attachment-line boundary layer flow

  • Autores: José Miguel Pérez Pérez
  • Directores de la Tesis: Vassilios Theofilis (dir. tes.), Dani Rodríguez Álvarez (codir. tes.)
  • Lectura: En la Universidad Politécnica de Madrid ( España ) en 2012
  • Idioma: español
  • Materias:
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  • Resumen
    • The aim of this thesis is to study the mechanisms of instability that occur in swept wings when the angle of attack increases.

      For this, a simplified model for the a simplified model for the non-orthogonal swept leading edge boundary layer has been used as well as different numerical techniques in order to solve the linear stability problem that describes the behavior of perturbations superposed upon this base flow. Two different approaches, matrix-free and matrix forming methods, have been validated using direct numerical simulations with spectral resolution.

      In this way, flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via the solution of the pertinent global (Bi-Global) PDE-based eigenvalue problem. Subsequently, a simple extension of the extended Görtler-Hämmerlin ODE-based polynomial model proposed by Theofilis, Fedorov, Obrist & Dallmann (2003) for orthogonal flow, which includes previous models as particular cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the stability results and unravel the limits of validity basic flow models analyzed.

      The effect of the angle of attack, AoA, on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from AoA = 0 (orthogonal flow) up to values close to ¿ / 2 which make the assumptions under which the basic flow in derived questionable, in found to systematically destabilize the flow. The critical conditions of non-orthogonal flows al 0 ¿ AoA ¿ ¿ / 2 are shown to be recoverable from those or orthogonal flow, via a simple analytical transformation involving AoA.

      These results can help to understand the mechanisms of destabilization that occurs in the attachment line of wings at finite angle of attack. Studies taking into account variations of the pressure field in the basic flow or the extension to compressible floes are issues that remain open.

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