Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part I. Sensitivity

TL;DR

This paper introduces an adjoint-based method for efficiently computing sensitivities of eigenvalues in nonlinear, degenerate, and non self-adjoint eigenproblems, applied to thermo-acoustic combustor stability analysis.

Contribution

It develops a novel adjoint-based approach to calculate first- and second-order sensitivities in complex eigenproblems, reducing computational effort significantly.

Findings

Adjoint method matches finite difference sensitivities with fewer computations.

The method effectively analyzes stability sensitivities in different combustor configurations.

Significant reduction in computational cost compared to traditional finite difference approaches.

Abstract

We present an adjoint-based method for the calculation of eigenvalue perturbations in nonlinear, degenerate and non self-adjoint eigenproblems. This method is applied to a thermo-acoustic annular combustor network, the stability of which is governed by a nonlinear eigenproblem. We calculate the first- and second-order sensitivities of the growth rate and frequency to geometric, flow and flame parameters. Three different configurations are analysed. The benchmark sensitivities are obtained by finite difference, which involves solving the nonlinear eigenproblem at least as many times as the number of parameters. By solving only one adjoint eigenproblem, we obtain the sensitivities to any thermo-acoustic parameter, which match the finite-difference solutions at much lower computational cost.