A Quantitative Comparison between a Low Order Model and a 3D FEM Code for the Study of Thermoacoustic Combustion Instabilities

The study of thermoacoustic combustion instabilities has an important role for safety operation in modern gas turbines equipped with lean premixed dry low emission combustion systems. Gas turbine manufacturers often adopt simulation tools based on low order models for predicting the phenomenon of humming. These simulation codes provide fast responses and good physical insight, but only one-dimensional or two-dimensional simplified schemes can be generally examined. The finite element method can overcome such limitations, because it allows to examine three-dimensional geometries and to search the complex eigenfrequencies of the system. Large Eddy Simulation (LES) techniques are proposed in order to investigate the instability phenomenon, matching pressure fluctuations with turbulent combustion phenomena to study thermoacoustic combustion oscillations, even if they require large numerical resources. The finite element approach solves numerically the Helmholtz equation problem converted in a complex eigenvalue problem in the frequency domain. Complex eigenvalues of the system allow us to identify the complex eigenfrequencies of the combustion system analyzed, so that we can have a valid indication of the frequencies at which thermoacoustic instabilities are expected and of the growth rate of the pressure oscillations at the onset of instability. Through the collaboration among Ansaldo Energia, University of Genoa and Polytechnic University of Bari, a quantitative comparison between a low order model, called LOMTL and the three-dimensional finite element method has been examined, in order to exploit the advantages of both the methodologies.