Linear state space interconnect modeling of acoustic systems

Linear,low-order network models, constructed from aset of interconnected acoustic subsystem elements, are an established tool in acoustic analysis. This paper introduces a generalized linear modeling framework for acoustic systems that is based on a state space formalism and linear system theory. It is shown how subsystem models retrieved from 1D low order modeling, 3D linearized perturbation equations as well as computational fluid dynamics or experiment can be translated into state space models. This translation does not involveany approximations beyond those made by the acoustic modeling in the first place. An algorithm to interconnect state space models is presented, which results in a single, joint state space model for the complete acoustic system. The resulting eigenvalue problem is linear,thus eigenvalues and eigenvectors can be determined for small and moderate problem sizes with very little effort, using standard numerical routines. In order to make possible the solution of larger problem sizes, as they result from 3D models, the framework exploits the sparse structure of the models. The methods and algorithms are exemplified and validated using simplistic configurations, but also a generic annular combustor test case with non trivial topology.