A practical application of the bode criterion for prediction of thermoacoustic combustion instabilities

The work presented summarizes a simplified approach to prediction of thermoacoustic instabilities employed at Virginia Tech, based on a control system model of a lean-premixed turbulent combustor. Separate transfer functions representing the flame dynamics and the combustor acoustics were measured. Though the transfer functions used in this work were experimentally obtained, in concept, flame and acoustic transfer functions obtained from theoretical means would have also been suitable. The acoustic transfer function was considered to be constant with respect to operating condition, while flame transfer function variations were realized by generating a prototype flame transfer function from experimental flame transfer function data. The flame and acoustic transfer functions were then combined in a closed loop system model to obtain the system open loop transfer function (OLTF), representing the closed loop feedback between the flame and the acoustics. The OLTF was analyzed using the Bode criterion, which tests for amplifying gain at frequencies where the acoustic and flame oscillations occur in phase. The gain margin was used when necessary as an additional criterion to select single prediction of instability at each given operating condition. Predictions were then validated in a laboratory combustor and showed reasonable accuracy in identifying frequencies at which instabilities occurred.