Thermoacoustic instabilities are a major challenge in the development of modern low-emission gas 
turbines. Thermoacoustic stability analysis is a crucial step in the design phase of these turbines. 
Uncertainty quantification and parametric studies for this analysis require repeated computations of 
models with large degrees of freedom, which can be prohibitively expensive. Model order reduction 
(MOR) plays a pivotal role in reducing this computational cost by finding a reduced order model 
(ROM) with significantly less degrees of freedom than the full order model (FOM), but featuring 
approximately the same dynamics. In this proof-of-concept study, the acoustic wave propagation is 
modeled by a 1D network approach, while the flow-flame interaction is accounted for by a Flame 
Transfer Function (FTF). We employ MOR to the acoustic subsystem, which usually contributes 
most to the degrees of freedom to the overall setup, and couple it to the FTF after the reduction. 
Projective MOR techniques employ projection of the FOM onto an appropriate subspace to obtain 
the ROM. It is the choice of this subspace that differentiates the various techniques. This study 
demonstrates the application of three reduction techniques to the acoustic subsystem - modal 
reduction, truncated balanced realization (TBR) and iterative rational Krylov algorithm (IRKA). 
Modal reduction, a commonly used MOR method in thermoacoustics, is based on building a modal 
basis using the eigenmodes of the full order acoustic model. Instead of preserving the eigenmodes, 
TBR and IRKA are based on preserving the transfer behavior of the FOM. TBR uses balancing of 
controllability and observability Grammians of the full system to obtain the ROM, whereas, IRKA 
iteratively finds the expansion points to optimally match moments of the transfer function of the full 
system. The modes computed from reduced systems coupled to the FTF are compared with the 
modes from the coupled FOM system to assess the suitability of the reduction techniques. Results 
show that although the reduced system from the modal reduction method correctly captures the 
thermoacoustic cavity modes, it fails to capture the intrinsic thermoacoustic mode, which is a 
marginally stable mode for the FOM coupled system. On the contrary, ROMs from TBR and IRKA 
methods accurately predict both cavity and intrinsic thermoacoustic modes. Thus, model order 
reduction methods based on transfer behavior of the system are more suitable than the methods 
based on the eigenmodes for thermoacoustic stability analysis.

Comparison of Model Order Reduction Methods in Thermoacoustic Stability Analysis

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2021/volume/84898

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