Active Control of Turbulent Airfoil Flows Using Adjoint-based Deep Learning

TL;DR

This work tackles efficient control of turbulent airfoil flows by coupling adjoint-based optimization with a PDE-augmented neural controller (DPM) to maximize time-averaged lift-to-drag at Re=$5\times10^4$ and Ma=$0.4$. By solving the compressible Navier–Stokes equations (DNS for 2D and LES for 3D) and embedding a neural network that maps local pressure measurements to jet total pressure, the approach yields sensor-informed, adaptive boundary-layer blowing/suction actuators. In 2D, adaptive controllers trained on DNS markedly improve $\overline{C_l/C_d}$ across $\alpha=5^{\circ},10^{\circ},15^{\circ}$, with qualitative flow changes delaying separation; in 3D, controllers trained directly on turbulent flows (LC3) consistently outperform 2D-trained variants, achieving substantial gains in $C_l/C_d$ and energy-weighted metrics. The results demonstrate the potential of adjoint-based, model-consistent learning for robust, transferable aerodynamic control, including effective spanwise line-actuation and improved efficiency in realistic 3D turbulent regimes.

Abstract

We train active neural-network flow controllers using a deep learning PDE augmentation method to optimize lift-to-drag ratios in turbulent airfoil flows at Reynolds number $5\times10^4$ and Mach number 0.4. Direct numerical simulation and large eddy simulation are employed to model compressible, unconfined flow over two- and three-dimensional semi-infinite NACA 0012 airfoils at angles of attack $α= 5^\circ$, $10^\circ$, and $15^\circ$. Control actions, implemented through a blowing/suction jet at a fixed location and geometry on the upper surface, are adaptively determined by a neural network that maps local pressure measurements to optimal jet total pressure, enabling a sensor-informed control policy that responds spatially and temporally to unsteady flow conditions. The sensitivities of the flow to the neural network parameters are computed using the adjoint Navier-Stokes equations, which we construct using automatic differentiation applied to the flow solver. The trained flow controllers significantly improve the lift-to-drag ratios and reduce flow separation for both two- and three-dimensional airfoil flows, especially at $α= 5^\circ$ and $10^\circ$. The 2D-trained models remain effective when applied out-of-sample to 3D flows, which demonstrates the robustness of the adjoint-trained control approach. The 3D-trained models capture the flow dynamics even more effectively, which leads to better energy efficiency and comparable performance for both adaptive (neural network) and offline (simplified, constant-pressure) controllers. These results underscore the effectiveness of this learning-based approach in improving aerodynamic performance.

Figures (16)

• Figure 1: Instantaneous dimensionless vorticity magnitude in uncontrolled 2D airfoil flows (G1 mesh).
• Figure 2: Two-dimensional NACA 0012 flows: Time-averaged friction coefficient $C_f$ (left) and pressure coefficient $C_p$ (right) at $\alpha=5^\circ$ compared to data of Jones et al.jones2008direct.
• Figure 3: Three-dimensional NACA 0012 flows: Time-averaged G1 (DNS) and G3 (LES) friction coefficients $C_f$ (left) and pressure coefficients $C_p$ (right) at $\alpha=5^\circ$ compared to DNS data of Jones et al.jones2008direct.
• Figure 4: Illustration of the DPM-based active-control framework. Left: location of pressure sensor ($p_s$) and active jet controller ($p_{0J}$) along the airfoil suction surface. Right: feedforward neural network structure with a factor $C_\mathrm{out}=0.5$ on the hyperbolic-tangent output layer.
• Figure 5: Velocity magnitudes and streamlines of time-averaged uncontrolled and controlled 2D airfoil flows.