Adjoint Harmonic Sensitivities for Forced Response Minimization

Abstract

This paper presents an adjoint analysis for three-dimensional unsteady viscous flows aimed at the calculation of linear worksum sensitivities involved in turbomachinery forced response predictions. The worksum values are normally obtained from linear harmonic flow calculations but can also be computed using the solution to the adjoint of the linear harmonic flow equations. The adjoint method has a clear advantage over the linear approach if used within a rotor forced vibration minimization procedure which requires the structural response to a large number of different flow excitation sources characterized by a unique frequency and interblade phase angle. Whereas the linear approach requires a number of linear flow calculations at least equal to the number of excitation sources, the adjoint method reduces this cost to a single adjoint solution for each structural mode of rotor response. A practical example is given to illustrate the dramatic computational saving associated with the adjoint approach.