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Stability and receptivity of the swept-wing attachment-line boundary layer : a multigrid numerical approach

Abstract : The goal of this study is the analysis of the stability and receptivity properties of the three-dimensional flow past the leading edge of a swept wing. The project is divided into two parts: (i) the computation of the steady base flow as a solution of the steady-state Navier-Stokes equations and (ii) the study of the direct and adjoint eigenvalue problems obtained by linearizing the time-dependent Navier-Stokes equation around the base flow. In order to address the first part, a DNS code has been developed based on a multigrid framework. The solution of the non-linear steady-state Navier-Stokes equation at various Reynolds numbers is obtained by continuation at a computational cost of nearly O(n), where n is the number of degrees of freedom (dof) of the problem. The study of the stability and receptivity properties is performed by numerically solving the eigenvalue/eigenvector problem. A Krylov-Schur algorithm, coupled with a shift-invert spectral transformation, is used to extract part of the spectrum. Two branches may be identified and one of these is associated with eigenvectors displaying a connection between attachment line and cross-flow modes. The wave-maker region for these eigenvectors is shown to be located close to the attachment line by computing the corresponding solution to the adjoint eigenvalue problem. The numerical global results are compared qualitatively with existing experimental observations and local stability analysis.
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Contributor : Gianluca Meneghello <>
Submitted on : Thursday, February 28, 2013 - 1:33:49 PM
Last modification on : Wednesday, March 27, 2019 - 4:39:25 PM
Long-term archiving on: : Sunday, April 2, 2017 - 7:14:18 AM


  • HAL Id : pastel-00795543, version 1



Gianluca Meneghello. Stability and receptivity of the swept-wing attachment-line boundary layer : a multigrid numerical approach. Mechanics of the fluids [physics.class-ph]. Ecole Polytechnique X, 2013. English. ⟨pastel-00795543⟩



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