A Bayesian Approach for Predicting Thermoacoustic Oscillations in an Electrically-Heated Rijke Tube

Predicting and eliminating thermoacoustic oscillations is a significant challenge in gas turbine design. Here we combine a thermoacoustic experiment with a thermoacoustic model and use data assimilation to infer the parameters of the model, rendering it predictive. The experiment is a vertical Rijke tube containing an electric heater (up to 300 Watts). The heater drives a base flow via natural convection, and thermoacoustic oscillations via velocity-driven heat release fluctuations. The growth/decay rates and frequencies of these oscillations are measured every few seconds. There are two models: one for the base flow and one for the acoustics. Both are unsteady. The parameters of the base flow model (Nusselt numbers and pressure loss coefficients) are estimated from many thousand measurements using an ensemble Kalman filter that accounts for both experimental and state and parameter errors. The parameters of the acoustic model are inferred by regression. This study shows that, with thorough Bayesian inference, a simple model with a few parameters can become a predictive model. The process reveals deficiencies in the model and, when combined with physical insight, shows how to improve it. This study proves the concept for small systems and prepares the ground for complex systems.