Simulation of Indexing and Clocking with a New Multidimensional Time Harmonic Balance Approach

Alongside the capability to simulate rotor–stator interactions, a central aspect within the development of frequency-domain methods for turbomachinery flows is the ability of the method to accurately predict rotor–rotor and stator–stator interactions on a single-passage domain. To simulate such interactions, state-of-the-art frequency-domain approaches require one fundamental interblade phase angle, and therefore it can be necessary to resort to multi-passage configurations. Other approaches neglect the cross-coupling of different harmonics. As a consequence, the influence of indexing on the propagation of the unsteady disturbances is not captured. To overcome these issues, the harmonic balance approach based on multidimensional Fourier transforms in time, recently introduced by the authors, is extended in this work to account for arbitrary interblade phase angle ratios on a single-passage domain. To assess the ability of the approach to simulate the influence of indexing on the steady, as well as on the unsteady, part of the flow, the proposed extension is applied to a modern low-pressure fan stage of a civil aero engine under the influence of an inhomogeneous inflow condition. The results are compared to unsteady simulations in the time-domain and to state-of-the-art frequency-domain methods based on one-dimensional discrete Fourier transforms.