Flutter Analysis of an Embedded Blade Row with a Harmonic Balance Solver

Abstract

Commonly, in the flutter analysis of a turbomachine blade row the blade row studied for stability is treated as isolated from its neighbouring blade rows. This approach neglects the effects caused by the reflection of upstream and downstream propagating waves at the neighbouring blade rows. These reflected waves are the source of additional unsteady forces at the blade surface which may have significant effects on the aeroelastic stability of the blade row. To take this influence in the flutter analysis of a blade row into account a coupled unsteady simulation of all rows considered has to be performed. The usual approach to solve for the unsteady flow with a non-linear time-domain solver is expen-sive in terms of computational resources. Especially if in a multi-row configuration the blade counts of the blade rows considered do not allow restricting the simulation to a few passages in each row. To solve for the unsteady flow field, in this paper an alternative ap-proach based on the nonlinear frequency domain Harmonic Balance method is presented. In the frequency-domain the unsteady flow field can be approximated with a small number of relevant frequencies and the circumferential and temporal periodicity of the problem reduces the computational domain to a single passage per blade row only. The efficiency of this approach for flutter analysis in a multi-row configuration is demonstrated by applying it to an embedded rotor blade row.