FDF-based combustion instability analysis for evolution of mode shapes and eigenfrequency in the multiple flame burner

In this work, the FDF (flame describing function)-based combustion instability analysis together with the Helmholtz solver has been made for the wide range of velocity perturbation and plenum length in the multiple premixed burner. The Helmholtz solver is based on the commercial software COMSOL and the present numerical analysis is made for the two-dimensional axisymmetric geometry. This study has been mainly motivated to systematically analyze the effects of the velocity perturbation on the detailed evolution of eigenfrequency and mode transformation characteristics versus the variation of the plenum length. Due to the realistic treatment for the acoustic boundary conditions as well as the pressure jump condition across the perforated plate, the present study is able to predict the continuous transformation of the mode shapes according to the variation of the plenum length. To precisely analyze the nonlinear combustion instability phenomena in the multiple flame combustor, computations are made for the wide range of velocity perturbation and plenum length. In terms of stable and unstable ranges of frequency, numerical results yield the comparable results with measurements. Moreover, the present numerical results for the higher velocity perturbation ratios clearly reveal the frequency locking phenomenon which does not change the eigenfrequency even for the condition transforming the acoustic modes several times. Based on numerical results, the detailed discussions are made for effects of the velocity perturbation on the evolution of eigenfrequency and mode transformation characteristics versus the variation of the plenum length.