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

2025-10-08

AI Summary

This study addresses unsteady turbulent flow over a NACA 0012 airfoil at Re = 5×10⁴ and Ma = 0.4, for angles of attack ranging from 5° to 15°, in both two- and three-dimensional configurations. We propose a deep learning–based active flow control method that couples adjoint Navier–Stokes equations with automatic differentiation. A PDE-informed neural network maps real-time local wall pressure measurements to blowing/suction actuation commands, enabling adaptive regulation of separated flow. Key contributions include: (i) the first integration of adjoint sensitivity analysis into deep controller training—ensuring physical consistency and accurate gradient computation; and (ii) strong generalizability, with 2D-trained policies directly transferable to 3D large-eddy simulations. Results demonstrate significant separation suppression, yielding lift-to-drag ratio improvements of 18% (2D) and 22% (3D). Moreover, the 3D control exhibits superior energy efficiency compared to 2D and matches the performance of offline-optimized controllers.

Technology Category

• Machine Learning: Active Learning
• Multiagent Systems: Adversarial Agents
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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 $5 imes10^4$ 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.

Problem

• Optimizing lift-to-drag ratios in turbulent airfoil flows
• Reducing flow separation using neural network controllers
• Developing sensor-informed control for unsteady flow conditions

Innovation

• Adjoint-based deep learning optimizes turbulent airfoil flow control
• Neural network maps pressure to jet control for unsteady flows
• Automatic differentiation constructs adjoint Navier-Stokes sensitivity equations