Nonlinear Reduced Order Models for the Structural Dynamics of Combustor Systems With Prestress and Friction

Abstract

An efficient methodology to capture the nonlinear responses of combustor systems with prestress and Coulomb friction is developed. The combustor systems experience wear at the interfaces between components due to flowinduced vibrations. In particular, wear has been observed at the interface between the transition piece and the hula seal, and at the interface between the hula seal and the liner. These interfaces are prestressed, and their vibratory response has a softening nonlinearity caused by Coulomb friction combined with microslip. In addition, the contact between the hula seal and the transition piece is that between a convex surface and a concave surface. Hence, geometric nonlinearity of the contact stiffness in the normal direction is present also. These phenomena are hard to capture by fullorder finite element (FE) approaches because they require time marching or harmonic balancing of very large models. To address this issue, we develop reduced order models (ROMs) which are specifically designed to capture Coulomb friction (combined with microand macroslip). To demonstrate the proposed approach, a simplified hula seal is placed between two very rigid plates (which relate to the transition piece and the liner). For validation, contact elements are used to model the interface between the plates and the hula seal. Transient dynamic analysis (TDA) in ansys is applied to the fullorder model. The model is shown to exhibit softening nonlinearity and microslip at all levels of prestress. To show that ROMs for this system are possible (i.e., they exist), we use proper orthogonal decomposition (POD) to show that the dynamics is dominated by a low number of spatial coherences. For a variety of frequency ranges and prestress levels, we show that a single such coherence is dominant. Next, low order models are proposed and their parameters are identified. A systematic method to identify these parameters is developed. Particular attention is paid to the amount of calculations needed for obtaining these parameters. Finally, the ROMs are validated by comparing their predictions with results from TDA for the fullorder model. We show that these ROMs can accurately predict the nonlinear response of the system.