Acoustic modal analysis with heat release fluctuations using nonlinear eigensolvers

TL;DR

This paper improves the accuracy and efficiency of acoustic modal analysis in thermoacoustic systems by applying nonlinear eigensolvers from SLEPc to solve the Helmholtz wave equation with heat release fluctuations.

Contribution

It introduces the use of specialized nonlinear eigensolvers in SLEPc for Helmholtz equation-based thermoacoustic mode analysis, surpassing previous linearized methods.

Findings

Nonlinear eigensolvers provide more accurate eigenvalues.

The approach is computationally efficient.

Enhanced detection of thermoacoustic instabilities.

Abstract

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.