Exceptional points in thermoacoustic systems can be found for specific sets of parameters of the flame transfer function (FTF). They originate from the coalescence of two eigenvalue branches of purely acoustic and intrinsic origin, respectively. Since both the eigenvalues and the associated eigenfunctions coalesce at these points, it can be shown that the eigenvalue sensitivity to changes in parameters becomes infinitely large.  
Numerical detection of exceptional points and the associated flame transfer function based on the eigenvalue sensitivities can be very costly and requires an adequate initial guess. We, therefore, propose a new method that uses the coalescence of two eigenvalues at the exceptional point to determine the associated parameters of the FTF.  
Presuming that the exceptional point is located on a branch connecting an acoustic and an intrinsic thermoacoustic eigenvalue, the parameters of the FTF are updated iteratively such that the distance between the two eigenvalues decreases.  
To this end, an updated guess of the exceptional point is determined as the arithmetic mean of the two eigenvalues for each iteration. By using an adjoint solver to determine the associated parameters of the FTF for each guess, the exceptional eigenvalue can be determined efficiently and without prior knowledge of its location, enabling extensive investigations of more complex systems.  
Using the proposed method we investigate how exceptional points affect the results of thermoacoustic stability analysis, in particular regarding confidence intervals of eigenvalues in the vicinity of exceptional points. Owing to the infinite sensitivities at and close to exceptional points, uncertainties in numerically determined eigenvalues increase significantly. This may be critical, especially for eigenvalues approaching the unstable semi-plane, as the stability of the system can no longer be guaranteed.  
 


The Impact of Exceptional Points on the Reliability of Thermoacoustic Stability Analysis

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

Turbo Expo - Virtual Conference

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.