Acoustic modal analysis with heat release fluctuations using nonlinear eigensolvers

• Published in: Applied mathematics and computation Vol. 458; p. 128249
• Main Authors: Hiremath, Varun, Roman, Jose E.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2023
• Subjects: Helmholtz wave equation; Krylov methods; Nonlinear eigenvalue problem; SLEPc; Krylov methods; SLEPc; Nonlinear eigenvalue problem; Helmholtz wave equation
• ISSN: 0096-3003
• DOI: 10.1016/j.amc.2023.128249

Closed combustion devices like gas turbines and rockets are prone to thermoacoustic instabilities. Design engineers in the industry need tools to accurately identify and remove instabilities early in the design cycle. Many different approaches have been developed by the researchers over the years. In this work we focus on the Helmholtz wave equation based solver which is found to be relatively fast and accurate for most applications. This solver has been a subject of study in many previous works. The Helmholtz wave equation in frequency space reduces to a nonlinear eigenvalue problem which needs to be solved to compute the acoustic modes. Most previous implementations of this solver have relied on linearized solvers and iterative methods which as shown in this work are not very efficient and sometimes inaccurate. In this work we make use of specialized algorithms implemented in SLEPc that are accurate and efficient for computing eigenvalues of nonlinear eigenvalue problems. We make use of the n-tau model to compute the reacting source terms in the Helmholtz equation and describe the steps involved in deriving the Helmholtz eigenvalue equation and obtaining its solution using the SLEPc library. •Software for the early identification of thermoacoustic instabilities in closed combustion devices with arbitrary geometry.•Helmholtz wave equation in frequency space leading to a nonlinear eigenvalue formulation.•SLEPc's nonlinear eigensolver is fast and accurate, and can be run in parallel for large-scale problems.