Nonlinearities in off-diagonal GAF matrix elements in the scope of T-tail flutter

Kurzfassung

Assessment of T-tail flutter requires unsteady aerodynamic forces beyond the scope of the conventional DLM, usually accounted for by means of correctional terms computed by external methods and superposed with the DLM aerodynamics. The increasingly employed CFD methods as high-fidelity alternatives to potential flow solutions inherently capture the aerodynamic forces to their full extent. However, literature has shown that the full description of the unsteady aerodynamic terms in combination with a linear modal approach for the representation of the dynamical system of T-tails may lead to spurious stiffness terms. For a physically more accurate flutter assessment, it is suggested to include quadratic deformation components in the modal representation. While the effect of higher order deformation components on the stiffness of the vertical tail plane out-of-plane bending mode shape is known from literature, their impact on the aerodynamic coupling terms has not been studied in depth so far. As these are driving factors for flutter, this paper works out the impact of quadratic mode shape components on the aerodynamic coupling terms with regard to frequency of oscillation and deformation amplitude. The two mode shapes studied in this paper are vertical tail plane out-of-plane bending and torsion. Both mode shapes are approximated as rigid body rotations of the horizontal tail plane w.r.t. the longitudinal and vertical axes, respectively. This allows for an analytical description of the linear and quadratic deformations. In order to exclude aerodynamic interference between horizontal and vertical tail plane, only the isolated horizontal tail plane is studied. The aerodynamics is restricted to inviscid flow at a Mach number of 0.4 and atmospheric conditions at mean sea level according to the International Standard Atmosphere. Converged solutions to harmonic excitation of the geometry's CFD surface mesh are studied which enables the evaluation of aerodynamic stiffness and damping from magnitude and phase angle of the input and output signals. Fourier transformation of the signals as well as a curve fitting approach is used to address the frequency content of the aerodynamic response. The impact of the quadratic mode shape components is most notable for the aerodynamic influence of the horizontal tail plane roll motion on itself and on the yaw motion. Here, the change in stiffness regarding the roll motion, as outlined above, is observed as well as a striking impact on the stiffness and damping regarding the yaw motion, i.e. the aerodynamic coupling term at non-infinitesimal deformation amplitudes. Concerning the yaw motion, the quadratic deformation components affect the stiffness of the aerodynamic influence on itself. The damping terms, however, are insensitive to the quadratic deformation components. For the amplitude dependency, a nonlinearity in the coupling term of horizontal tail plane roll motion on yaw motion is identified, which is fundamentally different between a linear and a quadratic deformation approach. In addition, a third harmonic content in the generalized aerodynamic forces is observed. All other aerodynamic terms behave linearly w.r.t. the deformation amplitude.