A novel method for the simulation of combustion instabilities in annular combustors is presented. It is based on the idea to solve the equations governing the acoustics in the time domain and couple them to a model for the heat release in the flames. The linear wave equation describing the temporal and spatial evolution of the pressure fluctuations is implemented in a finite element code. Providing high flexibility, this code in principle allows both the computational domain to be of arbitrary shape and the mean flow to be included. This yields applicability to realistic technical combustors. The fluctuating heat release acting as a volume source appears as a source term in the equation to be solved. Employing a time-lag model, the heat release rate at each individual burner is related to the velocity in the corresponding burner at an earlier time. As saturation also is considered, a non-linearity is introduced into the system. Starting the simulation from a random initial perturbation with suitable values for the parameters of the heat release model, a self-excited instability is induced, leading to a finite-amplitude limit cycle oscillation. The feasiblity of the approach is demonstrated with 3D-simulations of a simple model annular combustor. The effect of the model parameters and of axial mean flow on the stability and the shape of the excited modes is shown.

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