An Arnoldi approach for generation of reduced-order models for turbomachinery

Abstract

Abstract A linear reduced-order aerodynamic model is developed for aeroelastic analysis of turbomachines. The basis vectors are constructed using a block Arnoldi method. Although the model is cast in the time domain in state-space form, the spatial periodicity of the problem is exploited in the frequency domain to obtain these vectors efficiently. The frequency domain proper orthogonal decomposition is identified as a special case of the Arnoldi method. We show an application where the aerodynamic model is coupled with a simple structural model that has two degrees of freedom for each blade. The technique is applicable to viscous and three-dimensional problems as well as multi-stage problems with inlet and exit disturbance flows, although here results are presented for two-dimensional, inviscid flow through a 20-blade single-stage rotor. In this case, the number of states of the model is on the order of 10 per blade passage, making it appropriate for control applications.