A Nonlinear Frequency Domain Aerodynamic Model for Continuous Turbulence Encounter based on Functional Series Expansion

Kurzfassung

In this paper a nonlinear Reduced Order Model (ROM) for a frequency domain aerodynamic model based on functional or Volterra series expansion is presented. It relies on the numerical identification of the higher order Volterra Kernels by a continuous time impulse method and the transformation into the frequency domain with multidimensional Fourier transforms. This frequency domain ROM allows the nonlinear computation of the output power spectra as function of the input power spectra, showing an independence on the randomness of the phase for Gaussian stationary processes. Gust and continuous turbulence encounters are considered for a rigid wing empennage configuration flying in the transonic regime. Results obtained with the nonlinear frequency domain ROM are compared against CFD Euler computations for a discrete gust case showing a very good agreement. For continuous turbulence encounters the influence of the nonlinearity in the root mean square of the output when increasing the turbulence intensity is considered, showing a cubic dependency with the root mean square value of the turbulence for a second order Volterra series expansion. Additionally, convergence issues experienced by full-order CFD simulations when the turbulence intensity is increased are pointed out.