Numerical Calculation of Impulsive and Indicial Aerodynamic Responses Using Computational Aerodynamics Techniques

A Non-Parametric Technique for Aerodynamic State Identification for Flutter Prediction

“…However, as shown in Ref. [1], there is an amplitude range in which the aerodynamic response due to the unsteady motion can be considered linear with respect to the mode shapes, even in the transonic regime. Therefore, assuming that the motion amplitude is sufficiently small, one can formulate the problem as a linear dynamic system in the frequency domain and, as such, write the input-output relation as…”

“…Further details on the approach here used for the numerical discretization of the Euler equations and on the construction of the present code can be seen in Ref. [1].…”

“…Another possibility, also described in Ref. [1], consists in employing exponentiallyshaped signals which attempt to approximate smooth impulsive functions. As the exponentiallyshaped input is not a unit sample excitation, the real unit sample response, in this case, is evaluated using a well-known property of the convolution theorem [19],…”

“…Hence, the actual issue addressed in the present work is the matter of reducing the computational cost of such CFD calculations such that the overall cost of an aeroelastic study would be acceptable in industrial conditions. The present effort builds upon previous work by Marques and Azevedo [1,2], which used unsteady CFD solutions to impulsive and indicial perturbations in each structural mode of the configuration in order to build the required aerodynamic transfer functions and, then, identify aerodynamic states that would allow aeroelastic stability analyses in the frequency domain. The drawback with such approach is that the construction of an aeroelastic stability root locus, for a given flight condition, costs one steady CFD run, in order to obtain the initial steady state solution at the flight condition of interest, plus as many unsteady CFD runs as the number of mode shapes considered in the analysis.…”

“…As will be further discussed along the text, if the system inputs are uncorrelated, the transfer functions can be estimated by a division, in the frequency domain, of the cross power spectral density of the corresponding input and output, and the power spectral density of the input. Results are compared to the previous capability [1,2] in which the aerodynamic transfer functions are computed with an unsteady simulation for each modal movement.…”