Acoustic Transfer Functions Derived from Finite Element Modeling for Thermoacoustic Stability Predictions of Gas Turbine Engines

Design and prediction of thermoacoustic instabilities is a major challenge in aerospace propulsion and the operation of power generating gas turbine engines. This is a complex problem in which multiple physical systems couple together. Traditionally, thermoacoustic models can be reduced to dominant physics which depend only on flame dynamics and acoustics. This is the general approach adopted in this research. The primary objective of this thesis is to describe how to obtain acoustic transfer functions using finite element modeling. These acoustic transfer functions can be coupled with flame transfer functions and other dynamics to predict the thermoacoustic stability of gas turbine engines. Results of this research effort can go beyond the prediction of instability and potentially can be used as a tool in the design stage. Consequently, through the use of these modeling tools, better gas turbine engine designs can be developed, enabling expanded operating conditions and efficiencies.

This thesis presents the finite element (FE) methodology used to develop the acoustic transfer functions of the Combustion System Dynamics Laboratory (CSDL) gaseous combustor to support modeling and prediction of thermoacoustic instabilities. In this research, several different areas of the acoustic modeling were addressed to develop a representative acoustics model of the hot CSDL gaseous combustor. The first area was the development and validation of the cold acoustic finite element model. A large part of this development entailed finding simple but accurate means for representing complex geometries and boundary conditions. The cold-acoustic model of the laboratory combustor was refined and validated with the experimental data taken on the combustion rig.

The second stage of the research involved incorporating the flame into the FE model and has been referred to in this thesis as hot-acoustic modeling. The hot-acoustic model also required the investigation and characterization of the flame as an acoustic source. The detailed mathematical development for the full reacting acoustic wave equation was investigated and simplified sufficiently to identify the appropriate source term for the flame. It was determined that the flame could be represented in the finite element formulation as a volumetric acceleration, provided that the flame region is small compared to acoustic wavelengths. For premixed gas turbine combustor flames, this approximation of a small flame region is generally a reasonable assumption.

Both the high temperature effects and the flame as an acoustic source were implemented to obtain a final hot-acoustic FE model. This model was compared to experimental data where the heat release of the flame was measured along with the acoustic quantities of pressure and velocity. Using these measurements, the hot-acoustic FE model was validated and found to correlate with the experimental data very well.

The thesis concludes with a discussion of how these techniques can be utilized in large industrial-size combustors. Insights into stability are also discussed. A conclusion is then presented with the key results from this research and some suggestions for future work.