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Various approaches to determine active regions in an unstable global mode: application to transonic buffet

Published online by Cambridge University Press:  25 October 2019

Edoardo Paladini Open the ORCID record for Edoardo Paladini [Opens in a new window] ,
Olivier Marquet Open the ORCID record for Olivier Marquet [Opens in a new window] ,
Denis Sipp Open the ORCID record for Denis Sipp [Opens in a new window] ,
Jean-Christophe Robinet Open the ORCID record for Jean-Christophe Robinet [Opens in a new window]  and
Julien Dandois Open the ORCID record for Julien Dandois [Opens in a new window]
Edoardo Paladini*
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190 Meudon, France
Olivier Marquet
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190 Meudon, France
Denis Sipp
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190 Meudon, France
Jean-Christophe Robinet
Affiliation:
DynFluid Laboratory, Arts et Métiers ParisTech, 75013 Paris, France
Julien Dandois
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190 Meudon, France
*
†Email address for correspondence: edoardo.paladini89@gmail.com
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Abstract

The transonic flow field around a supercritical airfoil is investigated. The objective of the present paper is to enhance the understanding of the physical mechanics behind two-dimensional transonic buffet. The paper is composed of two parts. In the first part, a global stability analysis based on the linearized Reynolds-averaged Navier–Stokes equations is performed. A recently developed technique, based on the direct and adjoint unstable global modes, is used to compute the local contribution of the flow to the growth rate and angular frequency of the unstable global mode. The results allow us to identify which zones are directly responsible for the existence of the instability. The technique is firstly used for the vortex-shedding cylinder mode, as a validating case. In the second part, in order to confirm the results of the first part, a selective frequency damping method is locally used in some regions of the flow field. This method consists of applying a low-pass filter on selected zones of the computational domain in order to damp the fluctuations. It allows us to identify which zones are necessary for the persistence of the instability. The two different approaches give the same results: the shock foot is identified as the core of the instability; the shock and the boundary layer downstream of the shock are also necessary zones while damping the fluctuations on the lower surface of the airfoil; and outside the boundary layer between the shock and the trailing edge or above the supersonic zone does not suppress the shock oscillation. A discussion on the several physical models, proposed until now for the buffet phenomenon, and a new model are finally offered in the last section.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 617 - 647
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© 2019 Cambridge University Press 

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