A computational framework based on the harmonic balance method for nonlinear bulk-flow analysis

This study presents a harmonic balance method for nonlinear bulk-flow analysis of rotor–stator clearance flows. The steady-state response is represented by a truncated Fourier series, and the governing equations are formulated in the frequency domain. The proposed framework is further extended to a coupled analysis with rotor systems. This interaction arises from shaft motion that alters the film thickness and from fluid forces generated by the pressure field. Numerical results demonstrate that the proposed framework accurately predicts steady-state pressure and velocity fields in comparison with direct time integration. Fluid forces are also reliably estimated, whereas the perturbation approach exhibits limitations depending on static eccentricity and dynamic whirling amplitude. The coupled analysis confirms that the harmonic balance method can predict steady-state rotor responses without time-domain simulations. Finally, rotor orbit results highlight the significance of nonlinear coupling, in contrast to relying on linear rotordynamic coefficients. • A frequency-domain framework for nonlinear bulk-flow analysis is presented. • Harmonic balance method represents pressure and velocity fields via Fourier series. • Fluid forces under large eccentricity and whirling motion are accurately approximated. • Prediction of nonlinear rotor response is achieved through two-way coupling.