Low-Order Modeling of Dynamic Stall and Bifurcation Analysis of Highly Flexible Wing

Highly flexible wings can experience complex aerodynamic phenomena, such as dynamic stall, which induce nonlinear forces and lead to instabilities or limit-cycle oscillations that are challenging to predict and mitigate. A low-order accurate and efficient numerical model is in demand to give near real-time on-site nonlinear aeroelastic prediction during the wind tunnel testing, to help ensure that suitable tests are safely conducted. For this purpose, reducing the states of either the aerodynamic or structural model is extremely important in lowering the computation cost for numerical continuation. This paper explores a low-order modeling approach to analyze dynamic stall and bifurcation behavior in highly flexible wings, with applications in the design and control of next-generation highly efficient air transport. In this paper, the low-order unsteady aerodynamic model is derived by reducing the order of the attached flow portion of the original Beddoes-Leishman model (BLM). The reduced set of governing equations is tailored to retain significant aerodynamic and structural couplings while minimizing computational overhead; the nonlinear beam shape (NBS) formulation is used to model the flexible wing structure. Numerical comparisons for a NACA 0012 airfoil show that the modified BLM with six states is close to matching the original BLM with twelve states when prescribed periodic motion is given. The caveat is that the model is useful in a relatively low-frequency range; however, this is considered to be enough to cover the frequency range of aerodynamic phenomena associated with limit cycle oscillations (LCOs) related to highly flexible wings. The numerical model is expected to quickly identify and predict parameter regimes where stable, unstable, and oscillatory behaviors emerge, enabling a deeper understanding of aerodynamic load variations and structural deformation patterns. To further validate the low-order aerodynamic model, the final version of the paper will incorporate open-sourced experimental data to assess the model's accuracy and evaluate the capability of the developed numerical tool to predict the nonlinear aeroelastic behavior of the high-aspect-ratio wing. This includes key features such as dynamic stall characteristics and post-stall behavior.