Nonlinear Aeroelastic Formulation and Postflutter Analysis of Flexible High-Aspect-Ratio Wings

The nonlinear aeroelastic modeling and the post-flutter behavior of high-altitude long-endurance wings are discussed. A parametric structural model of wings based on an exact kinematic approach is formulated and coupled with an incompressible unsteady aerodynamic model that is obtained via an indicial formulation accounting for viscous effects, including dynamic stall and flow separation. To this end, a modified Beddoes-Leishman model is employed, and the equations of motion, together with the equations governing the aerodynamic states, are obtained via a total Lagrangian formulation. The critical and post-critical dynamic aeroelastic response is evaluated, and the limit cycles occurring in the post-flutter condition past the Hopf bifurcation are studied. Together, with comparisons from the available data of an experimental wing model with tip store, the effects of the unsteady loads and dynamic stall are evaluated and compared with predictions obtained from a model using a classical quasi-steady aerodynamic formulation. Aeroelastic simulations are concurrently performed within a finite element solution platform. Space and time integrations are conducted using a numerical scheme that directly discretizes the partial differential equations, which are associated with the equations of motion of the flexible wing, and the ordinary differential equations, which are associated with the added lag-state formulation pertinent to the unsteady aerodynamic loads, in a hybrid solution form. The aim is the study of the aeroelastic behavior of these highly nonlinear wings for an improved understanding of the nonlinear phenomena occurring particularly in the neighborhood of the flutter boundary and in the post-critical regime when the unsteady aerodynamic effects and dynamic stall contribute more significantly to the wing dynamic behavior.