Link between subsonic stall and transonic buffet on swept and unswept wings: from global stability analysis to nonlinear dynamics

Plante, Frédéric; Dandois, Julien; Beneddine, Samir; Laurendeau, Éric; Sipp, Denis

doi:10.1017/jfm.2020.848

Cited by 28 publications

(33 citation statements)

References 91 publications

(170 reference statements)

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“…Two distinct branches of modes can be observed; one outboard branch which describes modes travelling outboard along the wing in a sense of positive sweep angle and another inboard branch describing propagation in the opposite direction instead. Overall, the trend resembles what was discussed by Crouch et al (2019Crouch et al ( , 2020 and Plante et al (2021). The inboard branch (visualised by dashed lines in the figure) has higher growth rates than the outboard branch, which would suggest that the inboard behaviour is more dominant.…”

Section: Triglobal Instability Of Spanwise-uniform Base Flow On Swept Wingsupporting

confidence: 77%

“…In previous biglobal studies on infinite wings (Crouch et al 2019;Paladini et al 2019;Plante et al 2021), the frequency range of those dominant modes related to the shock-buffet instability on swept wings was found to be up to an order of magnitude higher compared with the aerofoil mode on a straight wing, depending on the particular configuration, specifically the sweep angle. Figure 14(a) presents the eigenspectra resulting from the stability analysis on wings with sweep angles between Λ = 0 • and 30 • and aspect ratio A = 3.…”

Section: Triglobal Instability Of Spanwise-uniform Base Flow On Swept Wingmentioning

confidence: 85%

“…Interestingly, the description of the time-marching simulations on the straight wing in Crouch et al (2019) would suggest that they observed a similar event of high activity of the otherwise seemingly dormant, spanwise-periodic monotone (shock-distortion) mode. The reader is also referred to Plante et al (2020Plante et al ( , 2021, where nonlinear time-marching simulations are discussed.…”

Section: Time-domain Interpretation Of Global Modesmentioning

confidence: 99%

“…Shock buffet brings a challenge to the wing design of modern large aircraft when flying in the commercially interesting transonic regime. Essentially, shock buffet is a manifestation of strong shock-wave/boundary-layer interaction, revealed through shock oscillations using either an operator-based global stability method (Crouch et al 2007;Sartor et al 2015;Crouch, Garbaruk & Strelet 2019;Paladini et al 2019;Timme 2020;Plante et al 2021) or data-driven algorithms such as proper orthogonal decomposition and dynamic mode decomposition (Masini et al 2020a;Masini, Timme & Peace 2020b;Zhao et al 2020) can be used to explore the flow mechanism.…”

Section: Introductionmentioning

confidence: 99%

“…Those transonic-flow stability results on a NACA0012 aerofoil demonstrated good agreement with earlier experimental data (McDevitt & Okuno 1985). More recently, the ideas were successfully applied in the analysis of other aerofoils (Sartor et al 2015;Zauner & Sandham 2020) and three-dimensional infinite (Crouch et al 2019;Paladini 2019;Paladini et al 2019;Plante et al 2021) and finite (Timme & Thormann 2016;Timme 2020) wings. In those infinite-wing shock-buffet studies, the authors predicted both the quasi-two-dimensional aerofoil mode and presented spatial spanwise-periodic modes in the framework of biglobal stability analysis.…”

Section: Introductionmentioning

confidence: 99%

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Triglobal infinite-wing shock-buffet study

Timme

2021

J. Fluid Mech.

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This article uses triglobal stability analysis to address the question of shock-buffet unsteadiness, and associated modal dominance, on infinite wings at high Reynolds number, expanding upon recent biglobal work, aspiring to elucidate the flow phenomenon's origin and characteristics. Infinite wings are modelled by extruding an aerofoil to finite aspect ratios and imposing a periodic boundary condition without assumptions on spanwise homogeneity. Two distinct steady base flows, spanwise uniform and non-uniform, are analysed herein on straight and swept wings. Stability analysis of straight-wing uniform flow identifies both the oscillatory aerofoil mode, linked to the chordwise shock motion synchronised with a pulsation of its downstream shear layer, and several monotone (non-oscillatory), spatially periodic shock-distortion modes. Those monotone modes become outboard travelling on the swept wing with their respective frequencies and phase speeds correlated with the sweep angle. In the limiting case of very small wavenumbers approaching zero, the effect of sweep creates branches of outboard and inboard travelling modes. Overall, triglobal results for such quasi-three-dimensional base flows agree with previous biglobal studies. On the contrary, cellular patterns form in proper three-dimensional base flow on straight wings, and we present the first triglobal study of such an equilibrium solution to the governing equations. Spanwise-irregular modes are found to be sensitive to the chosen aspect ratio. Nonlinear time-marching simulations reveal the flow evolution and distinct events to confirm the insights gained through dominant modes from routine triglobal stability analysis.

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Section: Triglobal Instability Of Spanwise-uniform Base Flow On Swept Wingsupporting

confidence: 77%

Section: Triglobal Instability Of Spanwise-uniform Base Flow On Swept Wingmentioning

confidence: 85%

Section: Time-domain Interpretation Of Global Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Triglobal infinite-wing shock-buffet study

Timme

2021

J. Fluid Mech.

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Experimental assessment of wing lower surface buffet effects induced by the installation of a UHBR nacelle

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Rudnik

2022

CEAS Aeronaut J

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The installation of large bypass ratio engines on classical under wing configurations may lead to shock/boundary layer interaction on the wing lower surface, limiting the flight envelope in a similar way to classical buffet occurring on the wing suction side at high incidences in transonic flight. In this study, buffet effects on the lower surface of the wing induced by the installation of a Ultra-High-Bypass-Ratio through flow nacelle are assessed by means of wind tunnel testing. Unsteady pressure sensitive paint measurements were used to assess the pressure field on the wing with high temporal and spatial resolution. Strong unsteady shock motion associated with shock induced separation was found on the wing lower surface for various combinations of Mach number, Reynolds number and angle of attack. The wing lower surface buffet effects are found to increase with reducing angle of attack and are present over a wide range of Reynolds numbers. Preliminary spectral analysis suggests an upper limit for the buffet frequency at a Strouhal number of about 0.4.

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

et al. 2021

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We numerically investigate stalling flow around a static airfoil at high Reynolds numbers using the Reynolds-averaged Navier–Stokes equations (RANS) closed with the Spalart–Allmaras turbulence model. An arclength continuation method allows to identify three branches of steady solutions, which form a characteristic inverted S-shaped curve as the angle of attack is varied. Global stability analyses of these steady solutions reveal the existence of two unstable modes: a low-frequency mode, which is unstable for angles of attack in the stall region, and a high-frequency vortex shedding mode, which is unstable at larger angles of attack. The low-frequency stall mode bifurcates several times along the three steady solutions: there are two Hopf bifurcations, two solutions with a two-fold degenerate eigenvalue and two saddle-node bifurcations. This low-frequency mode induces a cyclic flow separation and reattachment along the airfoil. Unsteady simulations of the RANS equations confirm the existence of large-amplitude low-frequency periodic solutions that oscillate around the three steady solutions in phase space. An analysis of the periodic solutions in the phase space shows that, when decreasing the angle of attack, the low-frequency periodic solution collides with the unstable steady middle-branch solution and thus disappears via a homoclinic bifurcation of periodic orbits. Finally, a one-equation nonlinear stall model is introduced to reveal that the disappearance of the limit cycle, when increasing the angle of attack, is due to a saddle-node bifurcation of periodic orbits.

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Link between subsonic stall and transonic buffet on swept and unswept wings: from global stability analysis to nonlinear dynamics

Abstract: Abstract

Cited by 28 publications

References 91 publications

Triglobal infinite-wing shock-buffet study

Triglobal infinite-wing shock-buffet study

Experimental assessment of wing lower surface buffet effects induced by the installation of a UHBR nacelle

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

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