Adjoint Methods for Elimination of Thermoacoustic Oscillations in a Model Annular Combustor via Small Geometry Modifications

Aguilar, José G.; Juniper, Matthew P.

doi:10.1115/gt2018-75692

Cited by 11 publications

(23 citation statements)

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“…Different symmetry-breaking perturbations to the burners were studied with higher-order perturbation adjoint theory in [171]. In eigenvalue optimization, Mensah and Moeck [172] calculated the optimal placement and tuning of acoustic dampers in an annular combustor; while Aguilar and Juniper [173,174] eliminated thermoacoustic oscillations by shape optimization. Recently, Silva et al [175] applied adjoint methods to calculated the critical flame index with relevance to intrinsic thermoacoustic modes.…”

Section: Thermoacousticsmentioning

confidence: 99%

“…Base-flow sensitivity was applied in thermoacoustics in [158] in a ducted diffusion flame to find the optimal changes to stabilize a thermoacoustic instability. Recently, the effect of shape modifications of annular and longitudinal combustors were calculated in [173,174] to stabilize all the thermoacoustic eigenvalues with adjoint-based optimization. 36 More precisely, a norm of such a sensitivity was originally called structural sensitivity in [67].…”

Section: Sensitivity To the Thermoacoustic Matrixmentioning

confidence: 99%

“…In the first example, the instability is suppressed by passive devices (Helmholtz resonators, which are acoustic dampers), which are optimally placed and tuned in the combustor [172]. In the second example, the instability is suppressed by modifying the shape of the combustor [173]. Both examples are applied to annular combustors.…”

Section: Applications Of Srs Analysis To Optimizationmentioning

confidence: 99%

“…The authors of [173] stabilized a thermoacoustic annular configuration by optimizing the geometry of the sectors of the combustor by a wave approach (Sec. 2.2.3) combined with a flame response model (Sec.…”

Section: Shape Optimizationmentioning

confidence: 99%

“…n indicates the wave number of the mode. Adapted from [173]. Units are dimensional as in the original paper, to which the reader may refer for details.…”

Section: Combining Bloch Theory With Adjoints: the Inclination Rule Imentioning

confidence: 99%

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Adjoint Methods as Design Tools in Thermoacoustics

Magri

2019

Applied Mechanics Reviews

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In a thermoacoustic system, such as a flame in a combustor, heat release oscillations couple with acoustic pressure oscillations. If the heat release is sufficiently in phase with the pressure, these oscillations can grow, sometimes with catastrophic consequences. Thermoacoustic instabilities are still one of the most challenging problems faced by gas turbine and rocket motor manufacturers. Thermoacoustic systems are characterized by many parameters to which the stability may be extremely sensitive. However, often only few oscillation modes are unstable. Existing techniques examine how a change in one parameter affects all (calculated) oscillation modes, whether unstable or not. Adjoint techniques turn this around: They accurately and cheaply compute how each oscillation mode is affected by changes in all parameters. In a system with a million parameters, they calculate gradients a million times faster than finite difference methods. This review paper provides: (i) the methodology and theory of stability and adjoint analysis in thermoacoustics, which is characterized by degenerate and nondegenerate nonlinear eigenvalue problems; (ii) physical insight in the thermoacoustic spectrum, and its exceptional points; (iii) practical applications of adjoint sensitivity analysis to passive control of existing oscillations, and prevention of oscillations with ad hoc design modifications; (iv) accurate and efficient algorithms to perform uncertainty quantification of the stability calculations; (v) adjoint-based methods for optimization to suppress instabilities by placing acoustic dampers, and prevent instabilities by design modifications in the combustor's geometry; (vi) a methodology to gain physical insight in the stability mechanisms of thermoacoustic instability (intrinsic sensitivity); and (vii) in nonlinear periodic oscillations, the prediction of the amplitude of limit cycles with weakly nonlinear analysis, and the theoretical framework to calculate the sensitivity to design parameters of limit cycles with adjoint Floquet analysis. To show the robustness and versatility of adjoint methods, examples of applications are provided for different acoustic and flame models, both in longitudinal and annular combustors, with deterministic and probabilistic approaches. The successful application of adjoint sensitivity analysis to thermoacoustics opens up new possibilities for physical understanding, control and optimization to design safer, quieter, and cleaner aero-engines. The versatile methods proposed can be applied to other multiphysical and multiscale problems, such as fluid–structure interaction, with virtually no conceptual modification.

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Section: Thermoacousticsmentioning

confidence: 99%

Section: Sensitivity To the Thermoacoustic Matrixmentioning

confidence: 99%

Section: Applications Of Srs Analysis To Optimizationmentioning

confidence: 99%

Section: Shape Optimizationmentioning

confidence: 99%

“…n indicates the wave number of the mode. Adapted from [173]. Units are dimensional as in the original paper, to which the reader may refer for details.…”

Section: Combining Bloch Theory With Adjoints: the Inclination Rule Imentioning

confidence: 99%

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Adjoint Methods as Design Tools in Thermoacoustics

Magri

2019

Applied Mechanics Reviews

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Optimisation of chaotically perturbed acoustic limit cycles

Huhn

Magri

2020

Nonlinear Dyn

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In an acoustic cavity with a heat source, the thermal energy of the heat source can be converted into acoustic energy, which may generate a loud oscillation. If uncontrolled, these acoustic oscillations, also known as thermoacoustic instabilities, can cause mechanical vibrations, fatigue and structural failure. The objective of manufacturers is to design stable thermoacoustic configurations. In this paper, we propose a method to optimise a chaotically perturbed limit cycle in the bistable region of a subcritical bifurcation. In this situation, traditional stability and sensitivity methods, such as eigenvalue and Floquet analysis, break down. First, we propose covariant Lyapunov analysis and shadowing methods as tools to calculate the stability and sensitivity of chaotically perturbed acoustic limit cycles. Second, covariant Lyapunov vector analysis is applied to an acoustic system with a heat source. The acoustic velocity at the heat source is chaotically perturbed to qualitatively mimic the effect of the turbulent hydrodynamic field. It is shown that the tangent space of the acoustic attractor is hyperbolic, which has a practical implication: the sensitivities of time-averaged cost functionals exist and can be robustly calculated by a shadowing method. Third, we calculate the sensitivities of the time-averaged acoustic energy and Rayleigh index to small changes to the heat-source intensity and time delay. By embedding the sensitivities into a gradient-update routine, we suppress an existing chaotic acoustic oscillation by optimal design of the heat source. The analysis and methods proposed enable the reduction of chaotic oscillations in thermoacoustic systems by optimal passive control. Because the theoretical framework is general, the techniques presented can be used in other unsteady deterministic multi-physics problems with virtually no modification.

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A novel modal expansion method for low-order modeling of thermoacoustic instabilities in complex geometries

Laurent

Bauerheim

Poinsot

et al. 2019

Combustion and Flame

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This work proposes an improvement to existing methods based on modal expansions used for the prediction of thermoacoustic instabilities in zero Mach number flow conditions. Whereas the orthogonal basis made of the acoustic eigenmodes of the domain bounded by rigid walls is classically used, an alternative method based on a modal expansion onto an over-complete set of acoustic eigenmodes is proposed. This allows avoiding the misrepresentation of the acoustic velocity field often observed near non rigid-wall boundaries. A Low Order Model network utilizing a state-space framework is then built upon this novel type of modal expansion. Several test cases, going from non reacting ducts to a complex geometry with combustion, are studied to assess the potential of the approach. The methodology not only successfully mitigates the misrepresentation in the acoustic field in the presence of non-rigid-wall boundaries, but it also drastically improves the convergence speed. The modularity of the method and its ability to handle complex geometries are illustrated by considering a configuration featuring an annular chamber, an annular plenum, as well as multiple burners. This novel technique is expected to bring worthy improvements to existing Low Order Models using modal expansions for the prediction of combustion instabilities.

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Adjoint Methods for Elimination of Thermoacoustic Oscillations in a Model Annular Combustor via Small Geometry Modifications

Cited by 11 publications

References 0 publications

Adjoint Methods as Design Tools in Thermoacoustics

Adjoint Methods as Design Tools in Thermoacoustics

Optimisation of chaotically perturbed acoustic limit cycles

A novel modal expansion method for low-order modeling of thermoacoustic instabilities in complex geometries

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