Adjoint-based perturbation theory

Quantitative prediction on the variation in a modeshape by exploiting high-order adjoint-based perturbation theory.

 

Thermoacoustic eigenvalues are known to be very sensitive to small variations in the operating conditions and geometry. The first order (linear) sensitivity of the eigenvalues can be estimated by exploiting adjoint methods. Even for small but finite parametric variations, however, the trajectories that the eigenvalues follow in the complex plane are far from linear. By exploiting perturbation theory, it is possible to derive high-order power-series that quantitatively represent the effect of real-world finite perturbations to the (thermo)acoustic eigenvalues, and well-approximate nonlinear variations in the thermoacoustic spectrum and its modeshapes, a fundamental information for accurate uncertainty quantification.

• PI: Dr. Alessandro Orchini
• Funding: Alexander von Humboldt Foundation
• Collaborators: Dr. Georg Mensah, Prof. Luca Magri, Prof. Jonas Moeck

Related Publications

A. Orchini, G. Mensah, J. Moeck, "Perturbation theory of nonlinear, non-self-adjoint eigenvalue problems: Semisimple eigenvalues" Journal of Sound and Vibration, 2021, Vol. 507, pp. 116150. [link]

A. Orchini, L. Magri, C. Silva, G. Mensah, J. Moeck, "Degenerate perturbation theory in thermoacoustics: high-order sensitivities and exceptional points" Journal of Fluid Mechanics, 2020, Vol. 903, pp. A37. [link]

G. Mensah, A. Orchini, J. Moeck, "Perturbation theory of nonlinear, non-self-adjoint eigenvalue problems: Simple eigenvalues" Journal of Sound and Vibration, 2020, Vol. 473, pp. 115200. [link]

G. Mensah, L. Magri, A. Orchini, J. Moeck, "Effects of asymmetry on thermoacoustic modes in annular combustors: a higher-order perturbation study" Journal of Engineering for Gas Turbines and Power, 2019, Vol. 141, pp. TP-18-1358. [link]