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Adjoint-based sensitivity analysis of low-order thermoacoustic networks using a wave-based approach

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Aguilar, JG 
Juniper, MP 


Strict pollutant emission regulations are pushing gas turbine manufacturers to develop devices that operate in lean conditions, with the downside that combustion instabilities are more likely to occur. Methods to predict and control unstable modes inside combustion chambers have been developed in the last decades but, in some cases, they are computationally expensive. Sensitivity analysis aided by adjoint methods provides valuable sensitivity information at a low computational cost. This paper introduces adjoint methods and their application in wave-based low order network models, which are used as industrial tools, to predict and control thermoacoustic oscillations. Two thermoacoustic models of interest are analyzed. First, in the zero Mach number limit, a nonlinear eigenvalue problem is derived, and continuous and discrete adjoint methods are used to obtain the sensitivities of the system to small modifications. Sensitivities to base-state modification and feedback devices are presented. Second, a more general case with non-zero Mach number, a moving flame front and choked outlet, is presented. The influence of the entropy waves on the computed sensitivities is shown.



thermoacoustic stability, adjoint methods, sensitivity analysis, network models, nonlinear eigenvalue problems

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Journal of Computational Physics

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Royal Academy of Engineering (RAEng)
J.G.A. is grateful to Alessandro Orchini for fruitful discussions and comments on this paper, and thankfully acknowledges CONACyT and Cambridge Trust for funding this project. L.M. gratefully acknowledges the financial support from the Royal Academy of Engineering Research Fellowships scheme.