This article describes a nonlinear frequency domain method for the simulation of unsteady blade row interaction problems across several blade rows in turbomachinery. The capability to efficiently simulate such interactions is crucial for the improvement of the prediction of blade vibrations, tonal noise, and the impact of unsteadiness on aerodynamic performance.
The simulation technique presented here is based on the harmonic balance approach and has been integrated into an existing flow solver. A nontrivial issue in the application of harmonic balance methods to turbomachinery flows is the fact that various fundamental frequencies may occur simultaneously in one relative system, each one being due to the interaction of two blade rows. It is shown that, considering the disturbances corresponding to different fundamental frequencies as mutually uncoupled, one can develop an unsteady simulation method which from a practial view point turns out to be highly attractive. On the one hand, it is possible to take into account arbitrarily many nonlinear interaction terms. On the other, the computational efficiency can be increased considerably once it is known that the nonlinear coupling between certain subsets of the harmonics plays only a minor role.
To validate the method and demonstrate its accuracy and efficiency a multistage compressor configuration is simulated using both the method described in this article and a conventional time-domain solver.