Thermo-acoustic eigenmodes of annular or can-annular combustion chambers, which typically feature a discrete rotational symmetry, may be computed in an efficient manner by utilizing the Bloch-wave theory. Unfortunately, the application of the Bloch-wave theory to combustion dynamics has hitherto been limited to the frequency domain.
In this study we present a time domain formulation of Bloch boundary conditions (BBC), which allows to employ them in time domain simulations, e.g. CFD simulations. The BBCs are expressed as acoustic scattering matrices and translated to complex-valued state-space systems. In a hybrid approach an unsteady, compressible CFD simulation of the burner-flame zone is coupled via characteristic-based state-space boundary-conditions to a reduced order model of the combustor acoustics that includes BBCs. The acoustic model with BBC accounts for cross-can acoustic coupling and the discrete rotational symmetry of the configuration, while the CFD simulation accounts for the nonlinear flow-flame-acoustic interactions. This approach makes it possible to model limit cycle oscillations of (can-)annular combustors at drastically reduced computational cost compared to CFD simulations of the full configuration, and without the limitations of weakly nonlinear approaches that utilize a flame describing function.
In the current study the suggested approach is applied to a generic multi-can combustor. Results agree well with a fully compressible CFD simulation of the complete configuration.