Global Stability Analysis of a Compressible Turbulent Flow Around a High-Lift Configuration

Abstract

The purpose of this work is to analyze a complex high lift configuration for which significant regions of separated flow are present. Current state of the art methods have some difficulty to predict the origin and the progression of this separated flow when increasing the angle of attack. The mechanisms responsible for the maximum lift limit on multielement wing configurations are not clear; this stability analysis could help to understand the physics behind the phenomenon and to find a relation between the flow separation and the instability onset. The methodology presented herein consists in the computation of a steady baseflow solution based on a finite volume discretization and a proposal of the solution for a generalized eigenvalue problem corresponding to the perturbed and linearized problem. The eigenvalue problem has been solved with the Arnoldi iterative method, one of the Krylov subspace projection methods. The described methodology was applied to the NACA0012 test case in subsonic and in transonic conditions and, finally, for the first time to the authors knowledge, on an industrial multi-component geometry, such as the A310 airfoil, in order to identify low frequency instabilities related to the separation. One important conclusion is that for all the analyzed geometries, one unstable mode related to flow separation appears for an angle of attack greater than the one correspondent to the maximum lift coefficient condition. Finally, an adjoint study was carried out in order to *Research Engineer, Airbus Operations S.L., maria-chiara.iorio@airbus.com. evaluate the receptivity and the structural sensitivity of the geometries, giving an indication of the domain region that could be modified resulting in the biggest change of the fiowfield.

Bifurcation scenario for a two-dimensional static airfoil exhibiting trailing edge stall

“…It is elongated in the streamwise direction, with largest magnitude close to the separation point of the base flow and in the shear layer of the recirculation region. This is in good agreement with the mode identified by Iorio et al (2016) on an NACA0012 at very high Reynolds number, Re = 6.0 × 10 6 . Superimposed onto the base flow, it modifies the location of the separation point and the size of the recirculation region.…”

“…The very low-frequency oscillation of the flow observed around stall ensures that this scale-decoupling is valid in the present case. Previously, Iorio et al (2016) observed by using a fully turbulent RANS model, that a low-frequency oscillation eigenmode was observed for the NACA0012 airfoil when the flow separates. We will show in the following that such a spatiotemporal structure is also observed for the OA209 aerofoil and that it may be linked to the low-frequency oscillation of the lift coefficient observed near stall (Zaman et al 1987).…”

“…This approach is preferred for industrial applications (Pailhas et al 2005;Jain et al 2018), due to the reduced computational cost, despite the addition of uncertainties in accurately predicting separated flows at stall conditions (Szydlowski & Costes 2004). In the fully turbulent regime, the URANS approach succeeds in predicting hysteresis (Mittal & Saxena 2001;Wales et al 2012;Richez, Leguille & Marquet 2016), low-frequency flow oscillations (Iorio, Gonzalez & Martinez-Cava 2016) around a static airfoil, and three-dimensional stall cells (Bertagnolio, Sørensen & Rasmussen 2005;Manni, Nishino & Delafin 2016;Plante, Dandois & Laurendeau 2020). For transitional flow regimes especially, the URANS approach fails to predict the development of the attached laminar boundary layer and the appearance of a laminar separation bubble.…”

“…Global stability analysis can also be performed on RANS steady solutions (fixed-points) to predict the origin of transonic buffet on airfoils (Crouch et al 2009;Sartor, Mettot & Sipp 2015b) or the broadband unsteadiness in transonic shock-wave/boundary-layer interactions (Sartor et al 2015a). Regarding airfoil stall, a global stability analysis of the subsonic turbulent flow around an NACA0012 profile at Re = 6.0 × 10 6 was recently performed by Iorio et al (2016) within the RANS framework. By analysing the development of two-dimensional perturbations around high lift solutions near stalling conditions, they found an unstable low-frequency two-dimensional mode whose temporal evolution and nonlinear saturation agrees with the low-frequency flow oscillations described above.…”

Pressure Bifurcation Phenomenon on Supersonic Blowing Trailing Edges

“…The analysis aims to identify which features can naturally appear in the flow and become dominant for some particular value of the parameters. Depending on the nature of the phenomenon, the analysis can be performed over a steady base flow solution [16][17][18], over an averaged mean flow [19][20][21], or using time-stepping or DMD techniques for the study of transient phenomena [22,23]. On this work, steady base flows were considered to characterize the stability behaviour of the system.…”