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

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.

arXiv comment27 pages, 10 figures

References in corpus (5)

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• Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach
• Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part II. Uncertainty quantification
• Global modes, receptivity, and sensitivity analysis of diffusion flames coupled with duct acoustics
• Adjoint-based linear analysis in reduced-order thermo-acoustic models

Cited by in corpus (7)

• Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part II. Uncertainty quantification
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• Combined State and Parameter Estimation in Level-Set Methods
• Learning thermoacoustic interactions in combustors using a physics-informed neural network
• Degenerate perturbation theory in thermoacoustics: high-order sensitivities and exceptional points
• A real-time digital twin of azimuthal thermoacoustic instabilities
• Adjoint characteristic decomposition of one-dimensional waves