A two-way coupling for modeling thermoacoustic instabilities in a flat flame Rijke tube

Thermoacoustic instabilities are a serious problem for lean premixed combustion systems. Due to different time and length scales associated with the flow field, combustion, and acoustics, numerical computations of thermoacoustic phenomena are conceptually challenging. This work presents a coupled method for the simulation of thermoacoustic instabilities in low Mach number reacting flows. The acoustics are represented by a reduced order model that can be obtained from network techniques or finite element computations. A detailed chemistry finite-difference zero Mach number solver is used for the small scale flame dynamics. Under the assumption that the pressure is continuous across the flame, the acoustic model can be reduced to a time-domain relation mapping the velocity perturbation downstream of the flame to that upstream. Closure is obtained by the flame code, which delivers the jump in velocity across the combustion zone. The method is applied to an experimental laminar premixed burner-stabilized flat flame Rijke tube, that exhibits strong thermoacoustic oscillations associated with the 5k=4 mode of the geometrical set-up. In addition to the fundamental oscillation, a significant subharmonic response of the flame is observed. Results from the coupled simulation are compared to the experimental data. Good qualitative and quantitative agreement is found.

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