Inclusion of higher harmonics in the flame describing function for predicting limit cycles of self-excited combustion instabilities

2019 ◽  
Vol 37 (4) ◽  
pp. 5255-5262 ◽  
Author(s):  
Matthias Haeringer ◽  
Malte Merk ◽  
Wolfgang Polifke
Keyword(s):  
Limit Cycles ◽  
Combustion Instabilities ◽  
Describing Function ◽  
Higher Harmonics ◽  
Flame Describing Function

Describing Function Analysis of Limit Cycles in a Multiple Flame Combustor

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Frédéric Boudy ◽  
Daniel Durox ◽  
Thierry Schuller ◽  
Grunde Jomaas ◽  
Sébastien Candel
Keyword(s):  
Transfer Function ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Function Analysis ◽  
Combustion Instabilities ◽  
Describing Function ◽  
Variable Size ◽  
Theoretical Predictions ◽  
Flame Describing Function ◽  
Oscillation Frequencies

A recently developed nonlinear flame describing function (FDF) is used to analyze combustion instabilities in a system where the feeding manifold has a variable size and where the flame is confined by quartz tubes of variable length. Self-sustained combustion oscillations are observed when the geometry is changed. The regimes of oscillation are characterized at the limit cycle and also during the onset of oscillations. The theoretical predictions of the oscillation frequencies and levels are obtained using the FDF. This generalizes the concept of flame transfer function by including dependence on the frequency and level of oscillation. Predictions are compared with experimental results for two different lengths of the confinement tube. These results are, in turn, used to predict most of the experimentally observed phenomena and in particular, the correct oscillation levels and frequencies at limit cycles.

Describing Function Analysis of Limit Cycles in a Multiple Flame Combustor

2010 ◽  
Author(s):  
Fre´de´ric Boudy ◽  
Daniel Durox ◽  
Thierry Schuller ◽  
Grunde Jomaas ◽  
Se´bastien Candel
Keyword(s):  
Transfer Function ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Function Analysis ◽  
Combustion Instabilities ◽  
Describing Function ◽  
Variable Size ◽  
Theoretical Predictions ◽  
Flame Describing Function ◽  
Oscillation Frequencies

A recently developed nonlinear Flame Describing Function (FDF) is used to analyze combustion instabilities in a system where the feeding manifold has a variable size and where the flame is confined by quartz tubes of variable length. Self-sustained combustion oscillations are observed when the geometry is changed. Regimes of oscillation are characterized at the limit cycle and also during the onset of oscillations. Theoretical predictions of the oscillation frequencies and levels are obtained using the FDF. This generalizes the concept of flame transfer function by including a dependence on the frequency and on the level of oscillation. Predictions are compared with experimental results for two different lengths of the confinement tube. These results are in turn used to predict most of the experimentally observed phenomena and in particular the correct oscillation levels and frequencies at limit cycles.

Analysis of limit cycles sustained by two modes in the flame describing function framework

2013 ◽  
Vol 341 (1-2) ◽  
pp. 181-190 ◽  
Author(s):  
Frédéric Boudy ◽  
Daniel Durox ◽  
Thierry Schuller ◽  
Sébastien Candel
Keyword(s):  
Limit Cycles ◽  
Describing Function ◽  
Flame Describing Function

Nonlinear Flame Describing Function Analysis of Galloping Limit Cycles Featuring Chaotic States in Premixed Combustors

2012 ◽  
Author(s):  
Frédéric Boudy ◽  
Daniel Durox ◽  
Thierry Schuller ◽  
Sébastien Candel
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Function Analysis ◽  
Perforated Plate ◽  
Operating Conditions ◽  
Nonlinear Prediction ◽  
Constant Amplitude ◽  
Describing Function ◽  
Flame Describing Function ◽  
Velocity Pressure

Nonlinear prediction of combustion instabilities in premixed systems is undertaken on a generic configuration featuring an adjustable feeding manifold length, a multipoint injector composed of a perforated plate and a flame confinement tube. By changing the feeding manifold or flame tube lengths, the system exhibits different types of combustion regimes for the same flow operating conditions. Velocity, pressure and heat release rate measurements are used to examine oscillations during unstable operation. For many operating conditions, a limit cycle is reached at an essentially fixed oscillation frequency and quasi-constant amplitude. In another set of cases, the system features other types of oscillations characterized by multiple frequencies, amplitude modulation and irregular bursts which can be designated by “galloping” limit cycles or GLC. These situations are explored in this article. Imaging during GLCs indicates that the flame is globally oscillating but that the cycle is irregular. Prediction of these special oscillation states is tackled within the Flame Describing Function (FDF) framework. It is shown that it is possible to predict with a reasonable degree of agreement the ranges where a quasi-constant amplitude limit cycle will be established and ranges where the oscillation will be less regular and take the form of a galloping limit cycle. It is found that the FDF analysis also provides indications on the bounding levels of the oscillation envelope in the latter case.

A unified framework for nonlinear combustion instability analysis based on the flame describing function

2008 ◽  
Vol 615 ◽  
pp. 139-167 ◽  
Author(s):  
N. NOIRAY ◽  
D. DUROX ◽  
T. SCHULLER ◽  
S. CANDEL
Keyword(s):  
Growth Rate ◽  
Limit Cycle ◽  
Growth Rates ◽  
Finite Amplitude ◽  
Nonlinear Element ◽  
Combustion Instabilities ◽  
Describing Function ◽  
Unified Framework ◽  
Flame Describing Function ◽  
Amplitude Level

Analysis of combustion instabilities relies in most cases on linear analysis but most observations of these processes are carried out in the nonlinear regime where the system oscillates at a limit cycle. The objective of this paper is to deal with these two manifestations of combustion instabilities in a unified framework. The flame is recognized as the main nonlinear element in the system and its response to perturbations is characterized in terms of generalized transfer functions which assume that the gain and phase depend on the amplitude level of the input. This ‘describing function’ framework implies that the fundamental frequency is predominant and that the higher harmonics generated in the nonlinear element are weak because the higher frequencies are filtered out by the other components of the system. Based on this idea, a methodology is proposed to investigate the nonlinear stability of burners by associating the flame describing function with a frequency-domain analysis of the burner acoustics. These elements yield a nonlinear dispersion relation which can be solved, yielding growth rates and eigenfrequencies, which depend on the amplitude level of perturbations impinging on the flame. This method is used to investigate the regimes of oscillation of a well-controlled experiment. The system includes a resonant upstream manifold formed by a duct having a continuously adjustable length and a combustion region comprising a large number of flames stabilized on a multipoint injection system. The growth rates and eigenfrequencies are determined for a wide range of duct lengths. For certain values of this parameter we find a positive growth rate for vanishingly small amplitude levels, indicating that the system is linearly unstable. The growth rate then changes as the amplitude is increased and eventually vanishes for a finite amplitude, indicating the existence of a limit cycle. For other values of the length, the growth rate is initially negative, becomes positive for a finite amplitude and drops to zero for a higher value. This indicates that the system is linearly stable but nonlinearly unstable. Using calculated growth rates it is possible to predict amplitudes of oscillation when the system operates on a limit cycle. Mode switching and instability triggering may also be anticipated by comparing the growth rate curves. Theoretical results are found to be in excellent agreement with measurements, indicating that the flame describing function (FDF) methodology constitutes a suitable framework for nonlinear instability analysis.

Identification of the Flame Describing Function of a Premixed Swirl Flame from LES

2012 ◽  
Vol 184 (7-8) ◽  
pp. 888-900 ◽  
Author(s):  
H. J. Krediet ◽  
C. H. Beck ◽  
W. Krebs ◽  
S. Schimek ◽  
C. O. Paschereit ◽  
...  
Keyword(s):  
Describing Function ◽  
Flame Describing Function ◽  
Swirl Flame

scholarly journals Flame Dynamics Intermittency in the Bi-Stable Region Near a Subcritical Hopf Bifurcation

2017 ◽  
Author(s):  
D. Ebi ◽  
A. Denisov ◽  
G. Bonciolini ◽  
E. Boujo ◽  
N. Noiray
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Acoustic Pressure ◽  
Oscillation Amplitude ◽  
Stable Region ◽  
Describing Function ◽  
Acoustic Damping ◽  
Intermittent Behavior ◽  
Flame Describing Function

We report experimental evidence of thermoacoustic bi-stability in a lab-scale turbulent combustor over a well-defined range of fuel-air equivalence ratios. Pressure oscillations are characterized by an intermittent behavior with “bursts”, i.e. sudden jumps between low and high amplitudes occurring at random time instants. The corresponding probability density functions of the acoustic pressure signal show clearly separated maxima when the burner is operated in the bi-stable region. A flame describing function, which links acoustic pressure to heat release rate fluctuations, is estimated at the modal frequency from simultaneously recorded flame chemiluminescence and acoustic pressure. The representation of its statistics is new and particularly informative. It shows that this describing function is characterized, in average, by a nearly constant gain and by a significant drift of the phase as function of the oscillation amplitude. This finding suggests that the bi-stability does not result from an amplitude-dependent balance between flame gain and acoustic damping, but rather from the non-constant phase difference between the acoustic pressure and the coherent fluctuations of heat release rate.

Nonlinear combustion instability analysis of a bluff body burner based on the flame describing function

2021 ◽  
pp. 095441002110440
Author(s):  
Yipin Lu ◽  
Yinli Xiao ◽  
Juan Wu ◽  
Liang Chen
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Premixed Combustion ◽  
Single Frequency ◽  
Describing Function ◽  
Lean Premixed Combustion ◽  
Lean Premixed ◽  
Flame Describing Function ◽  
Frequency Harmonic

Lean premixed combustion is a common form of combustion organization in power equipment and propulsion systems. In order to understand the dynamic characteristics of lean premixed flame and predict and control its combustion instability, it is necessary to obtain its flame describing function (FDF). Based on the open source CFD toolbox, OpenFOAM, the dynamic K-equation model, and the finite rate Partially Stirred Reactor (PaSR) model were used to perform large eddy simulations (LES) of lean premixed combustion, and the response of the unsteady heat release rate to single-frequency harmonic disturbances was studied. The response of the unsteady heat release rate was characterized by the FDF, and the response of the unsteady heat release rate to the two-frequency harmonic disturbance was studied. The results show that the quantitative heat release rate response and flame dynamics have very proper accuracy. In the single-frequency harmonic disturbance, as the forcing frequency increases, the curling behavior of the flame surface and the instantaneous vortex structure change; the nonlinear kinematics effect is manifested by the entrainment of the vortex. At lower forcing frequencies, the heat release response changes linearly with the increase of forcing amplitude; at intermediate frequencies, the heat release response exhibits obvious nonlinear behavior; at high frequencies, the heat release response to amplitude changes decreases. The introduction of the second harmonic disturbance will significantly reduce the response range of the total heat release rate and make the combustion more stable.

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