Unified low-order modeling approach to can-annular combustors

We present a unified, physics-based low-order modeling approach to can-annular combustors, combining a linear stability analysis and a nonlinear Langevin approach to unravel the highly complex, multi-physical dynamics in this type of system. In the linear part, Howe's Rayleigh conductivity model is combined with the projected Helmholtz equation and a Bloch wave ansatz to arrive at a single equation for the frequency spectrum of an N-can combustor. Starting from first principles, we illustrate and give a physical explanation for the coupling-induced amplification and suppression of thermoacoustic instabilities. Adding another layer of complexity, we then take into account nonlinearities in the flame response and the aeroacoustic coupling. The nonlinear dynamics of a symmetric model combustor are explored by exploiting the gradient structure of the averaged slow-flow dynamics. We obtain exact analytical expressions for the steady-state statistics, highlighting the connection between different emergent patterns and the resistive coupling between the cans. We leverage our analysis to explain the intermittent energy transfer between Bloch modes observed in real-world gas turbines.