THE NONLINEAR THERMOACOUSTIC EIGENVALUE PROBLEM AND ITS RATIONAL APPROXIMATIONS: ASSESSMENT OF SOLUTION STRATEGIES

Moritz Merk, Philip E. Buschmann, Jonas P. Moeck, Wolfgang Polifke

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Nonlinear eigenvalue problems (NLEVPs) arise in thermoacoustics by considering the temporal evolution of small perturbations in the relevant governing equations. In this work, two solution strategies are compared: (i) a contour-integration-based method that guarantees to provide all eigenvalues in a given domain and (ii) a method that approximates the NLEVP by a rational eigenvalue problem, which is generally easier to solve. The focus lies on numerical speed, the completeness of the computed spectrum, and the appearance of spurious modes, i.e., modes that are not part of the original spectrum but appear as a result of the approximation. To this end, two prototypical thermoacoustic systems are considered: a single-flame Rijke tube and an annular model combustor. The comparison of both methods is preceded by a detailed analysis of the user-defined input parameters in the contour-integration-based method. Our results show that both methods can resolve all types of considered eigenvalues with sufficient accuracy for applications. However, the recast linear problem is overall faster to solve and allows a priori precision estimates – unlike the contour-integration-based method. Spurious modes as a by-product of the NLEVP approximation are found to play a minor role, and recommendations are given on how to eliminate them.

Original languageEnglish
Title of host publicationCombustion, Fuels, and Emissions
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791885994
DOIs
StatePublished - 2022
EventASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition, GT 2022 - Rotterdam, Netherlands
Duration: 13 Jun 202217 Jun 2022

Publication series

NameProceedings of the ASME Turbo Expo
Volume3-A

Conference

ConferenceASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition, GT 2022
Country/TerritoryNetherlands
CityRotterdam
Period13/06/2217/06/22

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