Sparse surface pressure-based reconstruction of the flow around a thick airfoil over a range of angles of attack

TL;DR

This work tackles reconstructing instantaneous flow fields around a thick airfoil from sparse wall-pressure measurements at high Reynolds number. It combines Proper Orthogonal Decomposition with two shallow neural networks (SNN-POD) to map limited surface pressure to steady and unsteady POD amplitudes, enabling velocity-field recovery via a reduced-order basis. Sensor placement is optimized by a variance-maximization strategy, and the model demonstrates accuracy with a small sensor count (e.g., 7 sensors representing ~55% of the Cp variance) and generalization to unseen angles of attack within $[10^{\circ},20^{\circ}]$, achieving a maximum mean-squared error of $2.9\%$ for seen angles and $6.6\%$ for interpolated angles. The study also shows that combining a global model with a local, regime-specific model (SNN-POD-C) improves instantaneous-flow reconstruction in transitional AoA regimes, highlighting the framework’s potential for adaptive, data-driven flow estimation in wind-energy applications.

Abstract

We present an efficient neural-based approach to estimate the instantaneous flow field around an airfoil from limited surface pressure measurements. The model, denoted SNN-POD, relies on two independent shallow neural networks to predict the instantaneous flow over a wide range of angles of attack [10{\textdegree},20{\textdegree}]. At all angles the global model correctly recovers the average characteristics of the flow from single-time sensor data, thus allowing combination with local, angle-dependent models. The method is applied to 2D URANS simulations of a thick airfoil at a Reynolds number of Re=4.5e6. The training set consists of snapshots obtained from a coarse sampling (1-2{\textdegree}) of the angle of attack range. A variance-based criterion is used to determine the number and positions of sensors. Tests are carried out for unseen snapshots at angles of attack within the set (sampled angles) as well as outside the set (interpolated angles). The maximum MSE error of attack for sampled and interpolated angles is respectively 2.9% and 6.6%. This makes it possible to develop adaptive strategies to improve the estimation if necessary.

Figures (17)

• Figure 1: a) Time-averaged pressure coefficient $C_p$ distribution around the airfoil b) Standard deviation $\sigma_{C_p}$ of $C_p$ (suction side only) in chordwise direction for angles of attack from $10^\circ$ to $20^\circ$. Vertical dashed lines correspond to the chordwise location of the Intermittent Separation Point (ISP), which is defined as the local maximum of $\sigma_{C_p}$ on the mid-chord pressure suction side
• Figure 2: Pre-multiplied time spectrograms of $C_p$ for AoA = $10^\circ$ (a), AoA = $14^\circ$ (b), AoA = $20^\circ$ (c). Black dashed lines corresponds to the location of the ISP
• Figure 3: Streamwise evolution of the time-averaged wake width $\delta(x)/c$ (a) and streamwise evolution of the time-averaged wake deflection angle $\alpha$ (b). The profiles are shown for $x/c \in [1;7]$, where $x/c = 1$ corresponds to the streamwise location of the trailing edge
• Figure 4: Snapshots of the normalized instantaneous streamwise velocity field $u/U_\infty$ (top) and spectrograms of the pre-multiplied velocity spectra $f S_u$ for the cases AoA $=10^\circ$ (a), AoA $= 14^\circ$ (b), and AoA $= 20^\circ$ (c). The vertical white dashed lines in the snapshots denote the $x/c=2$ section where the spectrograms are computed. The horizontal yellow dashed lines in the spectrograms indicate the wake width
• Figure 5: Sensor layouts selected with the variance-maximization strategy for different threshold levels