Sensitivity Analysis for Forced Response in Turbomachinery using an adjoint Harmonic Balance Method

Abstract

The analysis of aeroelastic properties is an important aspect in the design of turbomachinery components. In this study we focus on vibrations caused by the interaction of adjacent blade rows (forced response). This is an inherently unsteady phenomenon. But due to its periodic nature it can be efficiently treated by numerical methods formulated in the frequency domain, e.g. the harmonic balance method. When going from the analysis of individual designs using CFD to CFD-based optimisation it is desirable to compute also sensitivities of objective functions (targets and restrictions for the optimisation) with respect to design parameters. Since in typical applications the number of design parameters is much larger than the number of objective functions, it is advantageous to use the adjoint method for the computation of these sensitivities. An adjoint solver based on the harmonic balance method has been implemented in the framework of the flow solver TRACE. This is now extended and used to compute the sensitivities of aeroelastic objective functions to the amplitudes of a harmonic perturbation at the entry or exit of the respective blade row. These sensitivities can be validated by comparing to finite differences obtained from harmonic balance computations with different perturbations. We apply the method to model problems which are representative for turbomachinery configurations.