Frequency-Domain Gust Response Simulation Using Computational Fluid Dynamics

Abstract

The numerical investigation of dynamic responses to atmospheric turbulence is an important task during the aircraft design and certification process. Efficient methods are desirable because large parameter spaces spanned by, for example, Mach number, flight altitude, load case, and gust shape need to be covered. Aerodynamic nonlinearities such as shocks and boundary-layer separation should be included to account for transonic flight conditions. A linearized frequency-domain method is outlined to efficiently obtain gust responses using computational fluid dynamics. The Reynolds-averaged Navier–Stokes equations are linearized around a steady-state solution and solved for discrete frequencies. The resulting large but sparse system of linear equations can then be evaluated significantly faster than its time-domain counterpart. The method is verified analyzing sinusoidal gust responses for an airfoil and a large civil aircraft considering a broad range of reduced frequencies. Derivatives of aerodynamic coefficients and complex-valued surface pressures are compared for time- and frequency-domain approaches. Next, 1-cos gusts are investigated using an incomplete inverse Fourier transform in conjunction with a complex-valued weighting function to discuss time histories of lift coefficients as well as surface pressures. Finally, introduced techniques are applied to conditions arising from certification requirements to demonstrate the technical readiness. The methods discussed present an important step to establish computational fluid dynamics in the routine aircraft loads process.