Including Flow–Acoustic Interactions in the Helmholtz Computations of Industrial Combustors

Ni, Franchine; Nicoud, Franck; Méry, Yoann; Staffelbach, Gabriel

doi:10.2514/1.j057093

Cited by 7 publications

(3 citation statements)

References 51 publications

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“…Extensive experimental studies have been carried out by Palies [12] et al to investigate the influence of swirler structure and swirl number on flame response. Furthermore, FTFs can be further incorporated into acoustic calculations, such as low-order network models (LONM) [13][14][15] or Helmholtz solvers [16,17], to obtain detailed thermoacoustic stability data by including them as a source term representing non-steady heat release.…”

Section: Introductionmentioning

confidence: 99%

Experimental Study on Flame Response Characteristics of a Non-Premixed Swirl Model Combustor

Yang,

Liu,

Zhang

et al. 2023

Energies

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Non-premixed swirl combustion has been widely used in pieces of industrial combustion equipment such as industrial boilers, furnaces, and certain specific gas turbine combustors. In recent years, the combustion instability of non-premixed swirl flames has begun receiving attention, yet there is still a lack of related research in academia. Therefore, in this study, we conducted experimental research on a swirl stabilized gas flame model combustor and studied the heat release response characteristics of the swirl combustor through the flame transfer function. Firstly, the flame transfer function (FTF) was measured under different inlet velocities and equivalence ratios, and the experimental results showed that the FTF gain curve of the non-premixed swirl flame exhibited a significant “bimodal” shape, with the gain peaks located around 230 Hz and 330 Hz, respectively. Secondly, two oscillation modes of the flame near the two gain peaks were identified (the acoustic induced vortex mode Mv and the thermoacoustic oscillation mode Ma), which have not been reported in previous studies on swirl non-premixed flames. In addition, we comprehensively analyzed the flame pulsation characteristics under the two oscillation modes. Finally, the coupling degrees between velocity fluctuations, fuel pressure fluctuations, and heat release fluctuations were analyzed using the Rayleigh Index (RI), and it was found that in the acoustic-induced vortex mode, a complete feedback loop was not formed between the combustor and the fuel pipeline, which was the main reason for the significant difference in the pressure fluctuation amplitude near 230 Hz and 330 Hz.

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Section: Introductionmentioning

confidence: 99%

Experimental Study on Flame Response Characteristics of a Non-Premixed Swirl Model Combustor

Yang,

Liu,

Zhang

et al. 2023

Energies

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“…15 By reason of the low computational cost and the high availability of open-source and commercial solvers, the Helmholtz equation had been extensively used to investigate thermoacoustic stability. 16–22 In the presence of mean flow, the advection of acoustic waves leads to a decrease of the eigenfrequencies proportional to M 2. 15 With its zero Mach number assumption, this shift is not incorporated by the Helmholtz equation.…”

Section: Introductionmentioning

confidence: 99%

On the convective wave equation for the investigation of combustor stability using FEM-methods

Heilmann

Sattelmayer

2022

International Journal of Spray and Combustion Dynamics

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Solving the Helmholtz equation with spatially resolved finite element method (FEM) approaches is a well-established and cost-efficient methodology to numerically predict thermoacoustic instabilities. With the implied zero Mach number assumption all interaction mechanisms between acoustics and the mean flow velocity including the advection of acoustic waves are neglected. Incorporating these mechanisms requires higher-order approaches that come at massively increased computational cost. A tradeoff might be the convective wave equation in frequency domain, which covers the advection of waves and comes at equivalent cost as the Helmholtz equation. However, with this equation only being valid for uniform mean flow velocities it is normally not applicable to combustion processes. The present paper strives for analyzing the introduced errors when applying the convective wave equation to thermoacoustic stability analyses. Therefore, an acoustically consistent, inhomogeneous convective wave equation is derived first. Similar to Lighthill’s analogy, terms describing the interaction between acoustics and non-uniform mean flows are considered as sources. For the use with FEM approaches, a complete framework of the equation in weak formulation is provided. This includes suitable impedance boundary conditions and a transfer matrix coupling procedure. In a modal stability analysis of an industrial gas turbine combustion chamber, the homogeneous wave equation in frequency domain is subsequently compared to the Helmholtz equation and the consistent Acoustic Perturbation Equations (APE). The impact of selected source terms on the solution is investigated. Finally, a methodology using the convective wave equation in frequency domain with vanishing source terms in arbitrary mean flow fields is presented.

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“…One of the most straightforward approaches is the direct discretization of the Helmholtz equation that is then solved thanks to a Finite Element Method (FEM) solver. State-of-the-art FEM Helmholtz solvers are able to solve for thermaoustic eigenmodes in complex geometries comprising active flames and dissipative effects [5,6] , and can also incorporate the FDF formalism to capture nonlinear limit-cycle behaviors [7,8] . However, direct discretization FEM Helmholtz solvers often result in a large number of Degrees of Freedom (DoF), synonym of a considerable computational cost, and only permit little modularity, as any change in the geometrical parameters requires a new geometry and mesh generation.…”

Section: Introductionmentioning

confidence: 99%

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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Including Flow–Acoustic Interactions in the Helmholtz Computations of Industrial Combustors

Cited by 7 publications

References 51 publications

Experimental Study on Flame Response Characteristics of a Non-Premixed Swirl Model Combustor

Experimental Study on Flame Response Characteristics of a Non-Premixed Swirl Model Combustor

On the convective wave equation for the investigation of combustor stability using FEM-methods

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

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