Compact representation of transonic airfoil buffet flows with observable-augmented machine learning

TL;DR

This work addresses the challenge of representing the complex, high-dimensional transonic buffet of airfoils in a low-dimensional form. The authors develop an observable-augmented lift-based nonlinear autoencoder that compresses a sectional pressure field into a three-dimensional latent space, capturing key buffet dynamics such as shock motion and wall-bounded separation. The latent space enables both interpretable physics and sparse-sensor reconstruction of aerodynamic responses, with sensitivity-guided sensor selection and comparison to QR-pivot methods. Importantly, a model trained at wind-tunnel-scale Reynolds number $Re=3\times10^6$ demonstrates transferable phase dynamics to $Re=3\times10^7$, highlighting potential for real-time flight-envelope analysis and suggesting a data-fusion path across LES, unsteady RANS, and experiments for broader applicability.

Abstract

Transonic buffet presents time-dependent aerodynamic characteristics associated with shock, turbulent boundary layer, and their interactions. Despite strong nonlinearities and a large degree of freedom, there exists a dominant dynamic pattern of a buffet cycle, suggesting the low dimensionality of transonic buffet phenomena. This study seeks a low-dimensional representation of transonic airfoil buffet at a high Reynolds number with machine learning. Wall-modeled large-eddy simulations of flow over the OAT15A supercritical airfoil at two Mach numbers, $M_\infty = 0.715$ and 0.730, respectively producing non-buffet and buffet conditions, at a chord-based Reynolds number of $Re = 3\times 10^6$ are performed to generate the present datasets. We find that the low-dimensional nature of transonic airfoil buffet can be extracted as a sole three-dimensional latent representation through lift-augmented autoencoder compression. The current low-order representation not only describes the shock movement but also captures the moment when the separation occurs near the trailing edge in a low-order manner. We further show that it is possible to perform sensor-based reconstruction through the present low-dimensional expression while identifying the sensitivity with respect to aerodynamic responses. The present model trained at $Re = 3\times 10^6$ is lastly evaluated at the level of a real aircraft operation of $Re = 3\times 10^7$, exhibiting that the phase dynamics of lift is reasonably estimated from sparse sensors. The current study may provide a foundation toward data-driven real-time analysis of transonic buffet conditions under aircraft operation.

Figures (18)

• Figure 1: The computational grid used in the present wall-modeled large-eddy simulations of two-dimensional transonic airfoil buffet at a high Reynolds number fukushima2018wall. An instantaneous streamwise velocity field $u$ near the wall and the density gradient magnitude $|\nabla \rho|$ are superposed. The gray grid lines are displayed every fifth point in the $g_1$ and $g_2$ (wall-normal) directions. The subfigure is focused on the region of the shock wave-turbulent boundary layer interactions with the gray grid lines plotted every fifteenth point in the $g_1$ direction and every fifth point in the $g_2$ direction.
• Figure 2: Lift coefficient and pressure fields at $M_\infty=0.715$ (top) and 0.730 (bottom). A note for the shock location is provided underneath each contour of $M_\infty = 0.730$. The arrow in each subcontour represents the direction of shock movement.
• Figure 3: Lift-augmented nonlinear autoencoder FT2023.
• Figure 4: Comparison of compression performance for transonic airfoil buffet flow data between linear POD and a standard nonlinear autoencoder (AE, $\beta=0$). $(a)$ The relationship between the latent dimension $n_{\bm \xi}$ and the $L_2$ reconstruction error $\varepsilon$. $(b)$ Representative reconstructed pressure snapshots with $n_{\bm \xi} = (1,3,5)$ for $M_\infty = 0.730$ with $(c)$ the reference field. $(d)$ The absolute error field $e_{L_1} = |{\bm q}-\hat{\bm q}|$ corresponding to figures $(b)$.
• Figure 5: Latent subspace identified by a standard autoencoder ($\beta=0$) and the lift-augmented autoencoder ($\beta=0.03$ and 0.05) colored by the cases of different Mach numbers $M_\infty = (0.715, 0.730)$ (top) and the time-varying lift coefficient $C_L(t)$ (bottom). The pressure fields over time corresponding to the points $\rm (i-iv)$ in the latent space are also shown. The arrow in each subcontour represents the direction of shock movement. The zoomed-in view of wake and the downstream region visualized with a different color scheme are also depicted to emphasize the interaction between the wake, shock, and turbulent boundary layer.