Nonlinear aeroelastic study of a three-degrees-of-freedom airfoil with control surface hysteresis stiffness in a dynamic stall flow
image: Considering the characteristics of large slenderness ratio structure, it is reasonable to simplify the dynamics of a HALE aircraft as the plunge, pitch, and flap motions of a planar airfoil. The dynamic behavior of the 3-DOF airfoil can be obtained via nonlinear aeroelastic analysis. The theoretical results are beneficial for the optimization design of HALE vehicles under coupled nonlinear conditions.
Credit: Chinese Journal of Aeronautics
High altitude long endurance (HALE) aircraft, in pursuit of excellent aerodynamic performance and dwell time, usually suffers structural hysteresis nonlinearity due to the imperfection of control surfaces. In addition to structural nonlinearity, the effect of aerodynamic nonlinearity should be considered in HALE aircrafts with high aspect-ratio wings during severe environments, owing to significant torsional deformation. These coupled nonlinearities may trigger adverse aeroelastic responses, posing a potential threat to structural integrity and flight safety. However, the aeroelastic response of a HALE vehicle is generally predicted with isolated aerodynamic or structural nonlinearity. Since the combined nonlinearities can cause significantly different aeroelastic signatures that cannot be captured in an isolated nonlinear case, it is necessary to study the dynamic behavior of the coupled nonlinear aeroelastic model.
Recently, a team of aeroelastic scientists led by Junqiang Bai from Northwestern Polytechnical University, China first reported an aeroelastic study of a coupled nonlinear airfoil with control surface hysteresis stiffness in a dynamic stall flow. This work not only improves the classical Office National d’Etudes et de Recherches Aérospatiales (ONERA) dynamic stall model, but also explains the effect of coupled nonlinearities on the post-flutter behavior of the three-degrees-of-freedom (3-DOF) airfoil.
The team published their work in Chinese Journal of Aeronautics recently (https://doi.org/10.1016/j.cja.2025.103533).
“In this report, we proposed a 3-DOF aeroelastic model that combines control surface hysteresis stiffness and dynamic stall aerodynamics. A control surface hysteretic model is applied to represent the nonlinear structural dynamics. The ONERA dynamic stall model is extended to a 3-DOF airfoil, considering the dynamic behavior of the control surface. The nonlinear aeroelastic model of a 3-DOF airfoil is described using a monolithic state-space equation. Henon’s event-driven scheme is used to investigate the post-flutter behavior of the 3-DOF airfoil.” said Junqiang Bai, professor at School of Aeronautics at Northwestern Polytechnical University (China), a senior expert whose research interests focus on the field of nonlinear aeroelastic modeling and control.
“The proposed aerodynamic model has been unexpectedly found to improve the numerical precision of nonlinear aerodynamic load by almost double that of the classical ONERA model that does not consider the dynamic behavior of the control surface.” said Junqiang Bai.
“Moreover, we found the decoupling nonlinear method has strong conservatism.” said Junqiang Bai. In their results, the flutter onset speed of the coupled nonlinear aeroelastic airfoil is overestimated by 10% using decoupled nonlinear analysis.
“Based on the results of bifurcation diagrams, spectral waterfall plots, and aerodynamic power, we observed the coupled nonlinear airfoil maintained small-amplitude limit cycle oscillation (LCO) and was dominated by the structural hysteresis nonlinearity and aerodynamic energy from the plunge motion at low airspeeds. With an increase in the airspeed, the LCO amplitude of the pitch motion increased, and the stall aerodynamic nonlinearity became stronger than the structural hysteresis nonlinearity. The switch of dominant nonlinearity induced a sharp increase in the aerodynamic power. Excited by the increased energy, the airfoil underwent a period-doubling bifurcation and switched to a higher-amplitude LCO.” said Junqiang Bai.
In the control field, it has been found that active control technology can suppress classical flutter as well as nonlinear aeroelastic vibrations. In this regard, Bai will combine the closed-loop controller with the coupled nonlinear aeroelastic model to study the suppression of nonlinear vibration.
Other contributors include Jiahua Liang from the School of Aeronautics at Northwestern Polytechnical University in Xi'an, China; Zhiwei Sun from the Research Institute of Unmanned Aerial Vehicle at Northwestern Polytechnical University in Xi'an, China; Heye Xiao, Min Chang from the Unmanned System Research Institute at Northwestern Polytechnical University in Xi'an, China.
Original Source
Jiahua LIANG, Junqiang BAI, Zhiwei SUN, Heye XIAO, Min CHANG. Nonlinear aeroelastics of a three-degree-of-freedom airfoil with control surface hysteresis stiffness in a dynamic stall flow [J]. Chinese Journal of Aeronautics, 2025, https://doi.org/10.1016/j.cja.2025.103533.
About Chinese Journal of Aeronautics
Chinese Journal of Aeronautics (CJA) is an open access, peer-reviewed international journal covering all aspects of aerospace engineering, monthly published by Elsevier. The Journal reports the scientific and technological achievements and frontiers in aeronautic engineering and astronautic engineering, in both theory and practice. CJA is indexed in SCI (IF = 5.3, top 4/52, Q1), EI, IAA, AJ, CSA, Scopus.