Matched Volterra reduced-order model for an airfoil undergoing periodic translation

This paper is devoted to application of the Reduced-Order Model (ROM) based on Volterra series to prediction of lift and drag forces due to airfoil periodic translation in transonic flow region. When there is large amplitude oscillation of the relative Mach number, as appeared in helicopter rotor movement in forward flight, the conventional Volterra ROM is found to be unsatisfactory. To cover such applications, a matched Volterra ROM, inspired from previous multistep nonlinear indicial response method based on Duhamel integration, is thus considered, in which the step motions are defined inside a number of equal intervals with both positive and negative step motions to match the airfoil forward and backward movement, and the kernel functions are constructed independently at each interval. It shows that, at least for the translation movement considered, this matched Volterra ROM greatly improves the accuracy of prediction. Moreover, the matched Volterra ROM, with the total number of step motions and thus the computational cost close to those of the conventional Volterra ROM method, has the additional advantage that the same set of kernels can match various translation motions with different starting conditions so the kernels can be predesigned without knowing the specific motion of airfoil.