Large-eddy simulations and modal reconstruction of laminar transonic buffet

Abstract

Transonic buffet refers to the self-sustained periodic motion of shock waves observed in transonic flows over wings and can limit the flight envelope of aircraft. Based on the boundary layer characteristics at the shock foot, buffet has been classified as laminar or turbulent and the mechanisms underlying the two have been proposed to be different (Dandois et al., J. Fluid Mech., vol. 18, 2018, pp. 156–178). The effect of various flow parameters (freestream Mach and Reynolds numbers and sweep and incidence angles) on laminar transonic buffet on an infinite wing (Dassault Aviation's supercritical V2C aerofoil) is reported here by performing large-eddy simulations (LES) for a wide range of parameters. A spectral proper orthogonal decomposition identified the presence of a low-frequency mode associated with buffet and high-frequency wake modes related to vortex shedding. A flow reconstruction based only on the former shows periodic boundary-layer separation and reattachment accompanying shock wave motion. A modal reconstruction based only on the wake mode suggests that the separation bubble breathing phenomenon reported by Dandois et al. is due to this mode. Together, these results indicate that the physical mechanisms governing laminar and turbulent buffet are the same. Buffet was also simulated at zero incidence. Shock waves appear on both aerofoil surfaces and oscillate out of phase with each other indicating the occurrence of a Type I buffet (Giannelis et al., Aerosp. Sci. Technol., vol. 18, 2018, pp. 89–101) on a supercritical aerofoil. These results suggest that the mechanisms underlying different buffet types are the same.

Resolvent analysis of a finite wing in transonic flow

“…This mode, shown in figures 3( c ) and 6, corresponds to a wake mode, extensively discussed in Sartor et al. (2015) and Moise et al. (2022).…”

“…The bump at angular frequency 𝜔 = 19.3 is discussed next. This mode, shown in figures 3(c) and 6, corresponds to a wake mode, extensively discussed in Sartor et al (2015) and Moise et al (2022). The unsteady wake manifests itself over the same spatial region as the coherent structures of the finite-wing buffet modes, emanating from the separation region behind the shock foot, resulting in downstream vortex shedding.…”

“…Despite being first identified in the 1960s, a complete explanation incorporating the diverse inherent multidisciplinary aspects is still elusive, even though the body of experimental research continues to grow (Dandois, 2016;Jacquin, Molton, Deck, Maury, & Soulevant, 2009;Sugioka et al, 2018;Tijdeman, 1977). A hydrodynamic/acoustic feedback loop sustaining the shock oscillations was one of the first explanations for aerofoil buffet given by Lee (1990), which has been corroborated but also disputed by different experimental and numerical studies (Feldhusen-Hoffmann, Statnikov, Klaas, & Schröder, 2018;Jacquin et al, 2009;Moise, Zauner, & Sandham, 2022). At the same time, numerous experimental and numerical studies have found spanwise outboard propagation of buffet cells, a distinct feature of shock buffet on swept infinite and finite wings.…”

Global stability analysis of elastic aircraft in edge-of-the-envelope flow

“…2009; Feldhusen-Hoffmann et al. 2018; Moise, Zauner & Sandham 2022). The first global stability study on an aerofoil in turbulent flow linked shock buffet to an unstable eigenmode (Crouch et al.…”

“…Although it was first identified in the 1960s, a complete multidisciplinary explanation remains elusive, despite progress made continually by experiments and numerical investigations (Tijdeman 1977;Jacquin et al 2009;Dandois 2016). One of the first theoretical models by Lee (1990) proposed an acoustic feedback loop that sustained the shock oscillations, which was corroborated in experimental studies, although contradictory results and theories have also been put forward (Jacquin et al 2009;Feldhusen-Hoffmann et al 2018;Moise, Zauner & Sandham 2022). The first global stability study on an aerofoil in turbulent flow linked shock buffet to an unstable eigenmode (Crouch et al 2009), soon followed by similar findings on infinite straight and swept wings (Crouch, Garbaruk & Strelets 2019;Paladini et al 2019a;He & Timme 2021).…”