A novel acoustic network model to study the influence of mean flow and axial temperature distribution on spinning limit cycles in annular combustors

The present article presents a novel acoustic network model accounting for mean flow and axial temperature distribution able to predict spinning limit cycles observed in an annular combustor. This corresponds to the limit cycle observed in the MICCA test facility, developed at EM2C laboratory, CNRS and CentraleSupélec for which experimental data for different azimuthal mode patterns are available. An acoustic network approach is used to model the combustor. At first the acoustic network modelling assumptions have been validated by comparing the predicted frequency of the pure acoustic modes of the system with those obtained by simulating the detailed geometry of the combustor in a Helmholtz solver. This is performed under the zero-Mach-number approximation since in the Helmholtz solver the convective terms are neglected. The analysis is restricted to the resonant modes from 100 to 1000 Hz, the frequency range in which unstable phenomena have been observed during experiments. Acoustic network predictions have been found to be in agreement with the Helmholtz solver results proving the validity of the modelling assumptions. Subsequently, the influence of convective terms and an axial temperature is investigated. In a second step, an experimental global Flame Describing Function (FDF) measured at the operative conditions in which the combustor dynamics were observed is coupled with the acoustic solver. In the frequency domain, the spinning limit cycle is predicted by means of a weakly nonlinear stability analysis. Simulations retrieve a spinning self-sustained mode at a resonant frequency and velocity amplitude level matching the experimental observation and previous numerical simulations proving that the proposed numerical approach is able to correctly model the combustion dynamics and damping level of the analysed combustor.