Combining a Helmholtz solver with the flame describing function to assess combustion instability in a premixed swirled combustor

Silva, Camilo F.; Nicoud, Franck; Schuller, Thierry; Durox, Daniel; Candel, Sébastien

doi:10.1016/j.combustflame.2013.03.020

Cited by 137 publications

(95 citation statements)

References 40 publications

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“…A mode is found at 429 Hz with a small growth rate, consistent with the LES result which showed a small amplitude mode at 435 Hz. In Silva et al (2013), authors mention that the growth rates assessed by a Helmholtz solver should be offset by a negative quantity which represents all the damping effects not included in the zero-Mach-number framework (acoustic boundary layers, vortex generation in shear layers, etc.). Consequently the mode predicted for case Hot at (+12 s −1 ) is consistent with the DMD analysis and experiments.…”

Section: Helmholtz/decbc Resultsmentioning

confidence: 99%

“…A posteriori results tend to show that the linear study is able to capture unstable/stable modes with a coherent estimation of the frequency. Recent studies (Selimefendigil & Polifke 2011;Silva et al 2013) demonstrate that it is possible to capture the non-linear behaviour when combining several transfer functions computed from the linear regime.…”

Section: Helmholtz Analysismentioning

confidence: 99%

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Mixed acoustic–entropy combustion instabilities in gas turbines

2014

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A combustion instability in a combustor terminated by a nozzle is analysed and modelled based on a low order Helmholtz solver. A Large Eddy Simulation (LES) of the corresponding turbulent, compressible and reacting flow is first performed and analysed based on Dynamic Mode Decomposition (DMD). The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approx. 320 Hz) and shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. The lowest purely acoustic mode being in the range 700 − 750 Hz, it is postulated that the instability observed around 320 Hz stems from a mixed entropy/acoustic mode where the acoustic generation associated with entropy spots being convected throughout the choked nozzle plays a key role. The DMD analysis allows to extract from the LES results a low-order model that confirms that the mechanism of the low-frequency combustion instability indeed involves both acoustic and convected entropy waves. The Delayed Entropy Coupled Boundary Condition (Motheau et al. 2014) is implemented into a numerical Helmholtz solver where the baseline flow is assumed at rest. When fed with appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz/DECBC solver predicts the presence of an unstable mode around 320 Hz, in agreement with both LES and experiments.

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Section: Helmholtz/decbc Resultsmentioning

confidence: 99%

Section: Helmholtz Analysismentioning

confidence: 99%

Mixed acoustic–entropy combustion instabilities in gas turbines

2014

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“…Recent examples of this include Noiray et al [9], who experimentally measured the FDF of an unconfined laminar burner; on combining with an acoustic model they obtained limit cycle predictions in excellent agreement with experiments. Palies et al [21] extended this to a turbulent premixed swirling flame, while Silva et al [22] combined a measured FDF for a premixed swirled combustor with a Helmholtz solver, predicting the limit cycle amplitude to within reasonable agreement with experimental data. Note that this approach has been used not only at lab scale, but also for real gas turbines operated at high pressure [20].…”

Section: Introductionmentioning

confidence: 99%

Simulation of the flame describing function of a turbulent premixed flame using an open-source LES solver

Han

Morgans

2015

Combustion and Flame

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Numerical simulations were used to characterise the non-linear response of a turbulent premixed flame to acoustic velocity fluctuations. The test flame simulated was the bluff body stabilised flame which has been the subject of a detailed experimental study (Balachandran et al., 2005, Combustion & Flame). Simulations were performed using Large Eddy Simulation (LES) via the open source Computational Fluid Dynamics (CFD) software, Code S aturne, with combustion modelled by combining a Flame Surface Density (FSD) method with a fractal approach for the wrinkling factor. The cold flow field and the unforced reacting flow were used for preliminary code validation. In order to characterise the non-linear response of the unsteady heat release rate to acoustic forcing, a harmonically varying velocity fluctuation, for which both the forcing frequency and normalised forcing amplitude were varied, was imposed. The flame response was characterised via a Flame Describing Function (FDF), also known as a nonlinear flame transfer function, for which the gain and phase shift depend on forcing amplitude as well as forcing frequency. The response at four frequencies was compared to experimental data in detail, confirming that the LES results captured both the qualitative flame dynamics and the quantitative response of the heat release rate with very reasonable accuracy. The full FDF was then obtained across more frequencies, again showing a good fit with the experimental data, other than for a slight under-prediction in gain, most probably due to neglecting the effect of wall heat loss and the effect of combustion modelling. The agreement was significantly better than has been obtained previously for this test case using numerical simulations. Finally, it was found that increasing combustor length had little affect on the flame response, which may prove useful for future long combustor stability and limit cycle analysis. This work thus confirms that LES, in this case via the open source Code S aturne, provides a useful tool for characterising the response of lean premixed turbulent flames.

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“…a flame which dimensions are much smaller than the acoustic wavelength, integration of Eq. (6) leads to [31]:…”

Section: Inclusion Of the Fdf In The Avsp Formalismmentioning

confidence: 99%

“…This type of simulation was already considered in a recent article [31] to investigate limit cycles of linearly unstable modes with simplified acoustic boundary conditions. It is used here to investigate linearly and nonlinearly unstable modes in a configuration featuring complex impedances and a complex response of the injection unit.…”

Section: Introductionmentioning

confidence: 99%

Prediction of the Nonlinear Dynamics of a Multiple Flame Combustor by Coupling the Describing Function Methodology With a Helmholtz Solver

Cuquel

Silva

Nicoud

et al. 2013

Volume 1B: Combustion, Fuels and Emissions

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This study focuses on the numerical determination of thermo-acoustic instabilities using a combination of the Flame Describing Function (FDF) methodology and a numerical code solving the Helmholtz equation. In this framework, the FDF is defined by a set of Flame Transfer Functions (FTF) that depend on both the frequency and amplitude of acoustic perturbations. The FDF methodology has been recently used in combination with acoustic network methods to examine the nonlinear stability of generic configurations with simplified geometries. Its extension to complex 3D geometries requires the use of numerical tools such as a Helmholtz solver. In the present work, that combination is validated on a multiple injection combustor. The implementation of the FDF methodology in the Helmholtz solver is detailed before examining numerical predictions obtained by the use of an experimentally determined FDF in the Helmholtz solver. The instability frequencies and growth rates are determined for each perturbation level and different nonlinear behaviors are exhibited depending on the combustor geometry. The case of linearly unstable modes reaching limit cycles is first examined. A more complex case involving mode switching is then examined when two unstable modes are present. In this situation, the most unstable mode in the linear regime triggers another * Address all correspondence to this author: alexis.cuquel@ecp.fr unstable mode at a higher perturbation level. These numerical calculations are compared with experimental data and exhibit a good match in terms of amplitude and frequency reached by the limit cycle.

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Combining a Helmholtz solver with the flame describing function to assess combustion instability in a premixed swirled combustor

Cited by 137 publications

References 40 publications

Mixed acoustic–entropy combustion instabilities in gas turbines

Mixed acoustic–entropy combustion instabilities in gas turbines

Simulation of the flame describing function of a turbulent premixed flame using an open-source LES solver

Prediction of the Nonlinear Dynamics of a Multiple Flame Combustor by Coupling the Describing Function Methodology With a Helmholtz Solver

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