Reduced-order models based on CFD impulse and step responses

Abstract

Reduced-order models (ROM), which are based on the Volterra theory for nonlinear systems, for the evaluation of nonlinear unsteady aerodynamic forces are presented. The ROMs provide a means for rapid evaluation of frequency-domain generalized aerodynamic forces, which can then be used in traditional flutter analysis schemes to calculate flutter characteristics about nonlinear steady flows. Two ROMs are formulated, an impulse-type ROM that is based on the convolution of ROM kernels with the input signal, and a step-type ROM that is based on convolution with the derivative of the input signal. Linear, first-, and second-order kernels are identified for these two ROMs from direct CFD impulse and step responses. The ROM methodology is demonstrated with the heave and elastic modes of the AGARD 445.6 wing. It was found that the accuracy of the CFD-based impulse response is dependent on the choice of input amplitude and computational time step, and that the impulse-type kernels are highly sensitive to inaccuracies in the impulse responses used for their identification. The step-type ROM was found to be robust, and resulted in good predictions of direct responses. The introduction of second-order kernels did not significantly improve the predictions, indicating a difficulty in performing true nonlinear identification. The use of first-order step-type ROM offered a significant computational time saving compared to the full CFD frequency response analysis.