Unsteady Vortex Lattice Method of an Aeroelastic Airfoil with Aileron Structural Non-Linearities

This paper presents numerical simulations of fluid-structure interactions of a two dimensional airfoil-aileron configuration. The geometrical model is composed of two joint solids: a main airfoil which can pitch (α) and heave... [ view full abstract ]

This paper presents numerical simulations of fluid-structure interactions of a two dimensional airfoil-aileron configuration. The geometrical model is composed of two joint solids: a main airfoil which can pitch (α) and heave (h), and a hinged aileron (β). In a global goal of studying flutter, the present 3-dof aeroelastic model has been computed for linear and nonlinear structures.The aerodynamic model is based on the Unsteady Vortex Lattice Method (UVLM) valid for irrotational inviscid incompressible flow and small disturbances hypothesis. By considering the vortex shedding aligned with the airfoil (and choosing an appropriate non-dimensionalisation), the method can be cast in a linear discrete time domain form. Since the structural equations are expressed in the continuous time domain, it is convenient for computational reasons to express the aerodynamic model in the same form. The continuous time domain form of the aerodynamic model is obtained by integrating the homogenous part of the continuous model derived from the conservation of vorticity principle and by relating it to the discrete time domain model. A linear analytical relationship between the motion of the airfoil and the downwash at the collocation points allows for the formation of a fully coupled aeroelastic system. Validations of the numerical code on stiff linear weakly damped jointures are compared to the Theodorsen model and experimental data. Eigenvalues of the linear system are used to determine its stability. Flutter appears as a result of a Hopf bifurcation, when the real part of the first complex conjugate pair of eigenvalues of the aeroelastic system crosses the imaginary axis. Results are in very good agreement with those found in the literature is obtained. Secondly, freeplay and cubic structural nonlinearities were added to the linear model in order to predict the stability domain of a realistic airfoil-aileron configurations. Nonlinear terms require time integration of the aeroelastic system, using the RK45 numerical scheme. Depending on the ratio of the non-dimensionalized velocity to the linear flutter velocity, the non-linear aeroelastic response results in different types of motion: damped oscillations, limit cycle oscillations, chaotic motion or divergence. Phase trajectories and birfurcation diagrams were plotted. Good agreement with the experimental data and other numerical models is observed showing that the developed model is capable of predicting a non-linear response for an airfoil-aileron configuration with three degrees of freedom. Corrections of the aerodynamic model with high-fidelity aerodynamic data to account for aerodynamic nonlinearities (such as compressibility and viscosity effects) will be the subject of future work.