Abstract
Lean premixed combustion chambers are susceptible to combustion instabilities arising from the coupling between the heat release rate perturbations and the acoustic disturbances. These instabilities are not desirable and knowledge of this complex mechanism is necessary in order to prevent or at least suppress them. A low order model is developed comprising a linear acoustic network and an improved analytical form for a flame describing function (FDF). The latter includes both the saturation of the amplitude of heat release rate perturbations and the change of phase lag relative to oncoming acoustic velocity fluctuations when the instability grows into a limit cycle. A stability map is constructed by moving the flame along the Rijke tube based on the eigenvalues resolved from the network. The acoustic model is then converted into the time domain and combined with the flame describing function to determine the evolutions of the heat release rate disturbances and velocity perturbations within the tube. It is shown that this method can be used to capture some quite intricate nonlinear behaviour of combustion instabilities and the results in the time domain are consistent with those predicted in the frequency domain.
Highlights
Lean premixed combustion chambers are susceptible to combustion instabilities arising from the coupling between the heat release rate perturbations and the acoustic disturbances
The stability of a combustion chamber is determined by the balance between the energy gain from the heat released from unsteady combustion and the dissipation due to the viscous thermal damping [6,5], radiation from the boundaries [7] and various relaxation processes in flows with particles or droplets [2], which are considered to be proportional to the acoustic disturbance level [8,9,10]
This paper has presented an improved analytical form for a flame describing function (FDF)
Summary
The experimentally determined FDF for the premixed flames of a matrix burner was recently combined with an acoustic network to predict the stability map, in which the eigenfrequency is varied by changing the length of combustion chamber [30,41,42] This method was extended to predict the evolution of the eigenfrequencies and corresponding growth rates with the increase of modulation level for turbulent swirling flames [43,44]. A combined analytical/numerical approach is employed in this work to systematically analyse different features of nonlinear behaviour of combustion instabilities, based on a proposed analytical form for a flame model accounting for both the nonlinearities of the gain and the time delay This nonlinear flame model is applied to a Rijke tube where the perturbations can be treated as longitudinal waves to simplify the complex nonlinear mechanism.
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