Time domain modelling and stability analysis of complex thermoacoustic systems

Abstract

A methodology allowing for a modular setup of complex acoustic systems is developed. The transfer behaviour of the individual subsystems is formulated in time domain. Subsystem descriptions can be obtained by analytical considerations, numerical methods, or experimental data. Once the complex subsystems have been characterized experimentally, changes in system geometry can be implemented easily by exchanging or adding subsystems. To validate the modelling approach, experiments are conducted in an acoustic test rig with a combustor-type geometry. Results are compared to predictions from the model, demonstrating accuracy in frequency and time domain. Application to thermoacoustic instabilities arising in lean-premixed combustion is given. The influence of a modified fuel distribution on an unstable operating point of a lean-premixed combustor is studied and validated with experimental data. Additionally, a study on the parameters governing the flame transfer function is performed to generate a stability map of a model combustor. An advantage of the state-space approach is that stability of a thermoacoustic system can be determined by simply solving a matrix eigenvalue problem. This is in strong contrast to the traditional approach, where the complete model is formulated in frequency domain with infinite-dimensional transfer functions. The time domain approach is based on the methodology presented by Schuermans et al. [1]. In contrast to their work, however, subsystems are not obtained from modal expansions but are characterized by using system identification techniques. Additionally, accuracy of the time domain model is verified by experiments.