Modal Analysis of Annular Combustors: Effect of Burner Impedance

Krebs, Werner; Walz, Günther; Flohr, Patrick; Hoffmann, Stefan

doi:10.1115/2001-gt-0042

Cited by 11 publications

(7 citation statements)

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“…Similarly, results from other annular combustors have shown both standing and traveling waves [106,107,111,115,134] and several investigators have analyzed the reason for the preference of one modal structure over another [109,120,122].…”

Section: Transverse Modes In Circular Geometriesmentioning

confidence: 89%

Transverse combustion instabilities: Acoustic, fluid mechanic, and flame processes

O’Connor

Acharya

Lieuwen

2015

Progress in Energy and Combustion Science

301

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Thermoacoustic oscillations associated with transverse acoustic modes are routinely encountered in combustion chambers. While a large literature on this topic exists for rockets, no systematic reviews of transverse oscillations are available for airbreathing systems, such as in boilers, aircraft engines, jet engine augmentors, or power generating gas turbines. This paper reviews work on the problem for air-breathing systems, summarizing experimental, modeling, and active control studies of transverse oscillations. It then details the key physical processes controlling these oscillations by describing transverse acoustic wave motions, the effect of transverse acoustic waves on hydrodynamic instabilities, and the influence of acoustic and hydrodynamic fluid motions on the unsteady heat release. This paper particularly emphasizes the distinctions between the direct and indirect effect of transverse wave motions, by arguing that the dominant effect of the transverse acoustics is to act as the "clock" that controls the frequency and modal structure of the disturbance field. However, in many instances, it is the indirect axial flow disturbances at the nozzles (driven by pressure oscillations from the transverse mode), and the vortices that they excite, that cause the dominant heat release rate oscillations. Throughout the review, we discuss issues associated with simulating or scaling instabilities, either in subscale experimental geometries or by attempting to understand instability physics using identical nozzle hardware during axial oscillations of the same frequency as the transverse mode of interest. This review closes with a model problem that integrates many of these controlling elements, as well as recommendations for future research needs.

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Section: Transverse Modes In Circular Geometriesmentioning

confidence: 89%

Transverse combustion instabilities: Acoustic, fluid mechanic, and flame processes

O’Connor

Acharya

Lieuwen

2015

Progress in Energy and Combustion Science

301

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“…A detailed explanation of the Helmholtz equation as applied to thermoacoustics is given by Nicoud et al [40,197]. The advantage of the Helmholtz-equation framework is that it can tackle three-dimensional geometries, with the con that it holds for very small mean-flow Mach numbers and requires numerical discretization, such as finite elements (e.g., [40,166,172,[199][200][201][202]), finite volumes (e.g., [164]) or finite difference. This model is applied in Sec.…”

Section: Helmholtz Equationmentioning

confidence: 99%

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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“…th annular sector Pressure and velocity fluctuations can be written at any location x in the annular chamber as [15,28]:…”

Section: Propagation In the Imentioning

confidence: 99%

A theoretical study of mean azimuthal flow and asymmetry effects on thermo-acoustic modes in annular combustors

Bauerheim

Cazalens

Poinsot

2015

Proceedings of the Combustion Institute

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To cite this version:Michaël Bauerheim, Michel Cazalens, Thierry Poinsot. A theoretical study of mean azimuthal flow and asymmetry effects on thermo-acoustic modes in annular combustors. Proceedings of the Combustion Institute, Elsevier, 2015, vol. 35 (n°3) AbstractThe objective of this paper is to develop an analytical model to capture two symmetry breaking effects controlling the frequency and nature (spinning, standing or mixed) of azimuthal modes appearing in annular chambers: (1) Using two different burner types distributed along the chamber (2) Considering the mean azimuthal flow due to the swirlers or to effusion cooling. The ATACAMAC (Analytical Tool to Analyze and Control Azimuthal Modes in Annular Chambers) methodology is applied using the linearized acoustic equations with a steady and uniform azimuthal mean flow. It provides an analytical implicit dispersion relation which can be solved numerically. A fully analytical resolution is possible when the annular chamber is weakly coupled to the burners. Results show that symmetry breaking, either by mixing burners types or with a mean azimuthal flow, splits the azimuthal modes into two waves with different frequencies and structures. Breaking symmetry promotes standing modes but adding even a low azimuthal mean flow fosters spinning modes so that the azimuthal mean flow must be taken into account to study azimuthal modes.

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Modal Analysis of Annular Combustors: Effect of Burner Impedance

Cited by 11 publications

References 0 publications

Transverse combustion instabilities: Acoustic, fluid mechanic, and flame processes

Transverse combustion instabilities: Acoustic, fluid mechanic, and flame processes

Adjoint Methods as Design Tools in Thermoacoustics

A theoretical study of mean azimuthal flow and asymmetry effects on thermo-acoustic modes in annular combustors

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