59972 - Comparison of Model Order Reduction Methods in Thermoacoustic Stability Analysis
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 Type
Technical Paper Publication
Description
Session: 04-09 Combustion Dynamics: Low-Order Modelling
Paper Number: 59972
Start Time: June 10th, 2021, 02:15 PM
Presenting Author: Naman Purwar
Authors: Naman Purwar TU Munich
Maximilian Meindl TU Munich
Wolfgang Polifke TU Munich