An Integrated Loads Analysis Model for Wake Vortex Encounters

When a plane crosses the wake generated by a preceding aircraft, large dynamical loads in the order of the design loads may be induced. Loads analysis models for such wake vortex encounters need to consider aspects important for manoeuvre, as well as gust type responses. If the angle between the path and the trailing vortices is small, the encounter is manoeuvre like due to large induced roll motion. When the vortices are crossed almost perpendicularly, a gust type response is to be expected, where unsteady aerodynamic effects are significant. In [1] a modeling approach of an integrated loads analysis model suitable for wake vortex encounters was presented. This contribution will further investigate the requirements for such flight loads models for wake vortex encounters. One important aspect is, that the bandwidth of the excitation due to gust type wake vortex encounters is considerably larger compared to classical design gusts. Hence, the convergence behavior for high reduced frequencies of the doublet lattice models needs to be examined in more detail. A rational function approximation (RFA) is required to make the unsteady aerodynamics amendable for nonlinear time domain simulations. Previously, a ”physical” RFA could significantly improve the results for incompressible flow at high reduced frequencies by explicit approximation of the added mass term. The ”physical” RFA scheme is now extended to the compressible regime. The results are compared to the solution of the Possio equation and a velocity potential method for unsteady motion of airfoils in compressible flow. Further, the (time domain) integral loads analysis model is compared to a frequency domain approach. Induced velocities due to a pre-described trajectory for a wake crossing are determined. A subsequent Fourier transformation yields the excitation spectrum for the frequency domain calculations. Various encounter angles with wake vortices are computed and compared to time domain simulations, where the trajectory is determined as a nonlinear response during the simulation. Results show that in some encounter scenarios these nonlinearities can become crucial.