Scale-resolving simulations and data-driven modal analysis of turbulent transonic buffet cells on infinite swept wings

TL;DR

This study resolves transonic buffet on swept infinite wings up to $AR=3$ using scale-resolving ILES/QDNS and analyzes the resulting data with SPOD to separate 2D shock oscillations from 3D spanwise buffet cells. It demonstrates that sweep transforms a stationary 3D separation mode on unswept wings into a spanwise-travelling mode whose frequency increases with sweep, while the 2D shock mode remains largely sweep-insensitive. A clear link is established between mean flow separation at the SBLI and the emergence of strong 3D buffet dynamics, with the 3D wavelength governed by the spanwise domain (approximately $1$–$1.5c$ for $AR=3$). The work also provides a practical convection-velocity scaling, $V_c\approx0.78\tan(\lambda)$, and confirms that buffet is a coupled superposition of 2D shock motion and 3D separation-driven instabilities, offering insights into finite-wing behavior and informing design and control strategies for transonic aircraft.

Abstract

Transonic airfoil buffet is a class of shock-wave/boundary-layer interaction (SBLI) known to exhibit self-sustained two-dimensional (2D) chordwise shock wave oscillations (Strouhal number St=0.05-0.1), and three-dimensional (3D) spanwise-modulated flow separation/reattachment (St=0.2-0.4). Due to computational cost, scale-resolving simulations of span-periodic configurations to date have been limited to narrow airfoils, insufficient to accommodate the 3D buffet cell instability reported in low-fidelity simulations and experiments. In this work, implicit large-eddy simulations (ILES) and modal analysis are performed on infinite wings up to AR=3 with sweep effects for the first time. Two flow conditions are examined, corresponding to minimally and largely separated mean flow at the shock location. For the minimally separated case, the shock dynamics remain essentially spanwise-uniform (quasi-2D), with only weak and intermittent separation cells confined to the trailing-edge region and exhibiting negligible interaction with the shock. In contrast, increased mean separation leads to the emergence of pronounced 3D buffet cells with a characteristic spanwise wavelength: 1-1.5c. Spectral proper orthogonal decomposition reveals that a stationary low-frequency 3D separation mode previously identified on unswept wings (St=0.02) becomes a spanwise travelling mode as sweep is imposed, shifting monotonically to intermediate frequencies (St=0.06-0.35). The 2D shock mode is largely insensitive to sweep, whereas the frequency and energy content of the 3D mode increase with sweep while its wavelength remains unchanged. The results demonstrate that transonic buffet arises from the superposition of distinct but coupled 2D shock motion and separation-driven 3D instabilities, with mean flow separation at the shock identified as a necessary condition for dominant 3D buffet dynamics to emerge.

Figures (13)

• Figure 1: (left) Example spanwise separation 'buffet cells' in a low-fidelity steady RANS-based transonic airfoil simulation and (right) a high-fidelity simulation of the same phenomenon in the present study at a wing aspect ratio $AR = L_z / c$ equal to three chord lengths. Scale-resolved fine-scale turbulent structures at $w \pm 0.075$ are coloured by Mach number. The $\lambda$-shock wave is also visible on the Mach number contours imposed on the back panel. The flow is tripped to turbulence at 10% chord.
• Figure 2: Span- and time-averaged mean $(a)$ pressure coefficient and $(b)$ skin-friction, for two unswept $\lambda = 0^{\circ}$ cases corresponding to (blue, $\alpha=5^{\circ}$) minimally-, and (black, $\alpha=6^{\circ}$) largely-separated flow at the SBLI $(x \approx 0.4-0.5)$.
• Figure 3: Sectional evaluation at $z = L_z / 2$ of the $(a)$ lift coefficient and $(b)$ power spectral density of lift fluctuations. Showing the low-frequency unsteadiness in $\alpha=5^{\circ}$ cases at different aspect ratios and sweep angles.
• Figure 4: Instantaneous flow visualisations over the suction side of the airfoil surface at $\lambda = 25^{\circ}$ and $\alpha = 5^{\circ}$. The top/bottom plots show the off-wall streamwise/spanwise velocity at $y=0.003c$. The shock front is observed to be quasi-2D across the span for all time instances at this angle of attack, despite the chordwise low-frequency buffet unsteadiness.
• Figure 5: Sectional evaluation of $(a,c)$ lift coefficient and $(b,d)$ PSD of lift fluctuations. Showing $\alpha=6^{\circ}$ buffet cases at $(a,b)$ zero/low- and $(c,d)$ high-sweep angles, demonstrating the monotonic frequency increase of the 3D buffet cell mode with sweep.