Multi-Passage harmonic balance method for flutter prediction in multi-row configurations

Abstract

A multi-passage harmonic balance method is presented for flutter prediction in multi-row configurations, and particular focus is on simulation of more than two blade rows. The unsteady flows in such configurations contain two kinds of multiple perturbations: one refers to those who have different frequencies and the other one refers to those who have the same frequency but different inter-blade phase angles (IBPAs). Most of current harmonic balance methods only consider the former one and the applications have been restricted to two-blade-row configurations. In the few studies that consider more rows, a one-to-one correspondence assumption between frequency and IBPA is usually made putting extra limitation on the used modes. This motivates our work, and a simple but effective idea is proposed by adding passages adopted per row. The theoretical basis of this work is provided by the spinning mode analysis. The present method is developed based on the time-spectral and multi-frequential form of harmonic balance. The treatment of pitchwise and inter-row boundary conditions in the case of multi passages are particularly addressed. A recently-developed Jacobian-free Newton-Krylov method with a simplified LU-SGS preconditioner is employed to solve the resultant harmonic balance equations. For validation, two typical multi-row flutter cases are investigated. The numerical results show the validity and accuracy of the developed method.