An Approximate Time Domain Nonlinear Harmonic Method for Analyzing Unsteady Flows With Multiple Fundamental Modes

In this article, a new hybrid time and frequency domain method called the approximate time domain nonlinear harmonic method is proposed for a robust and efficient analysis of turbomachinery unsteady flow with more than one fundamental mode. The proposed method combines the features of the nonlinear harmonic method and the time domain harmonic balance method. Unsteady flow components are grouped according to their fundamental frequencies and inter blade phase angles, and separate unsteady flow governing equations are constructed for each mode group. These mode groups are connected using the least squares method based Fourier transform. The proposed method is expected to be exact for a linear problem but approximate for a nonlinear problem. Three sets of analyses with increasing levels of difficulties are presented to demonstrate the validity and effectiveness of the proposed method by comparing it with the time domain harmonic balance method based on the almost periodic Fourier transform.