Linear frequency domain and harmonic balance predictions of dynamic deritvates

Dynamic derivatives are used to represent the influence of the aircraft rates on the aerodynamic forces and moments needed for flight dynamics studies. These values have traditionally been estimated by processing measurements made from periodic forced motions applied to wind tunnel models. The use of Computational Fluid Dynamics has potential to supplement this approach. This paper considers the problem of the fast computation of forced periodic motions using the Euler equations. Three methods are evaluated. The first is computation in the time domain, and this provides the benchmark solution in the sense that the time accurate solution is obtained. Two acceleration techniques in the frequency domain are compared. The first uses an harmonic solution of the linearised problem(referred to as the linear frequency domain approach). The second uses the Harmonic Balance method, which approximates the nonlinear problem using a number of Fourier modes. These approaches are compared in the sense of their ability to predict dynamic derivatives and their computational cost. The standard NACA aerofoil CT cases, the SDM fighter model geometry and the DLR F12 passenger jet wind tunnel model are used as test cases. Compared to time accurate simulations an orderof- magnitude reduction in CPU costs is achieved for flows with a narrow frequency spectrum and moderate amplitudes, as the solution does not evolve through transients to reach periodicity