A Reduced-Order Model of an Aeroelastic Wing Exhibiting a Sub-Critical Hopf Bifurcation

Reduced-order aeroelastic models have been formulated for an AGARD 445.6 wing that exhibits limit cycle oscillations and a sub-critical Hopf bifurcation. The nonlinear aeroelastic behavior and sensitivity to initial conditions requires a nonlinear model. The flow dynamics are approximated with a low-dimensional set of eigenmodes, utilizing the method of proper orthogonal decomposition. The reduced-order flow model is coupled to a modal representation of the structural dynamics, forming a small set of nonlinear ordinary differential equations that comprise the aeroelastic model. The physics-based, reduced-order model is constructed with data from a subset of aeroelastic CFD simulations. The method is evaluated by comparing predictions of bifurcating responses (stability or limit cycle oscillations) from a much larger set of aeroelastic CFD simulations that includes on-design conditions used to construct the model and off-design conditions that were not used for model construction. The reduced-order model correctly predicts the sensitivity to initial perturbations and is four orders of magnitude smaller than the aeroelastic CFD model with a commensurate reduction in computational overhead.