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.

scholarly journals Flame Dynamics Intermittency in the Bistable Region Near a Subcritical Hopf Bifurcation

2018 ◽  
Vol 140 (6) ◽  
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 ◽  
Acoustic Damping ◽  
Intermittent Behavior ◽  
Flame Dynamics ◽  
Bistable Region ◽  
Subcritical Hopf Bifurcation

We report experimental evidence of thermoacoustic bistability 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 (PDFs) of the acoustic pressure signal show clearly separated maxima when the burner is operated in the bistable region. The gain and phase between acoustic pressure and heat release rate fluctuations are evaluated at the modal frequency from simultaneously recorded flame chemiluminescence and acoustic pressure. The representation of the corresponding statistics is new and particularly informative. It shows that the system is characterized, in average, by a nearly constant gain and by a drift of the phase as function of the oscillation amplitude. This finding may suggest that the bistability does not result from an amplitude-dependent balance between flame gain and acoustic damping, but rather from the nonconstant 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.

A Weakly Nonlinear Approach Based on a Distributed Flame Describing Function to Study the Combustion Dynamics of a Full-Scale Lean-Premixed Swirled Burner

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Davide Laera ◽  
Sergio M. Camporeale
Keyword(s):  
Heat Release ◽  
Limit Cycle ◽  
Heat Release Rate ◽  
Release Rate ◽  
Gas Turbines ◽  
Full Scale ◽  
Describing Function ◽  
Weakly Nonlinear ◽  
Lean Premixed ◽  
Flame Describing Function

Modern combustion chambers of gas turbines for power generation and aero-engines suffer of thermo-acoustic combustion instabilities generated by the coupling of heat release rate fluctuations with pressure oscillations. The present article reports a numerical analysis of limit cycles arising in a longitudinal combustor. This corresponds to experiments carried out on the longitudinal rig for instability analysis (LRIA) test facility equipped with a full-scale lean-premixed burner. Heat release rate fluctuations are modeled considering a distributed flame describing function (DFDF), since the flame under analysis is not compact with respect to the wavelengths of the unstable modes recorded experimentally. For each point of the flame, a saturation model is assumed for the gain and the phase of the DFDF with increasing amplitude of velocity fluctuations. A weakly nonlinear stability analysis is performed by combining the DFDF with a Helmholtz solver to determine the limit cycle condition. The numerical approach is used to study two configurations of the rig characterized by different lengths of the combustion chamber. In each configuration, a good match has been found between numerical predictions and experiments in terms of frequency and wave shape of the unstable mode. Time-resolved pressure fluctuations in the system plenum and chamber are reconstructed and compared with measurements. A suitable estimate of the limit cycle oscillation is found.

scholarly journals G-equation modelling of thermoacoustic oscillations of partially premixed flames

2017 ◽  
Vol 9 (4) ◽  
pp. 260-276 ◽  
Author(s):  
Bernhard Semlitsch ◽  
Alessandro Orchini ◽  
Ann P Dowling ◽  
Matthew P Juniper
Keyword(s):  
Heat Release ◽  
Limit Cycle ◽  
Heat Release Rate ◽  
Release Rate ◽  
Large Scale ◽  
Describing Function ◽  
Describing Functions ◽  
Wide Range ◽  
Flame Describing Function ◽  
Thermoacoustic Oscillations

Numerical simulations aid combustor design to avoid and reduce thermoacoustic oscillations. Non-linear heat release rate estimation and its modelling are essential for the prediction of saturation amplitudes of limit cycles. The heat release dynamics of flames can be approximated by a flame describing function. To calculate a flame describing function, a wide range of forcing amplitudes and frequencies needs to be considered. For this reason, we present a computationally inexpensive level-set approach, which accounts for equivalence ratio perturbations on flames with arbitrarily complex shapes. The influence of flame parameters and modelling approaches on flame describing functions and time delay coefficient distributions are discussed in detail. The numerically obtained flame describing functions are compared with experimental data and used in an acoustic network model for limit cycle prediction. A reasonable agreement of the heat release gain and limit cycle frequency is achieved even with a simplistic, analytical velocity fluctuation model. However, the phase decay is over-predicted. For sophisticated flame shapes, only the realistic modelling of large-scale flow structures allows the correct phase decay predictions of the heat release rate response.

Dynamical Characterization of Thermoacoustic Oscillations in a Hydrogen-Enriched Partially Premixed Swirl-Stabilized Methane/Air Combustor

2021 ◽  
Author(s):  
Abhishek Kushwaha ◽  
Praveen Kasthuri ◽  
Samadhan A. Pawar ◽  
R. I. Sujith ◽  
Ianko Chterev ◽  
...  
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Acoustic Pressure ◽  
Thermal Power ◽  
Frequency Locking ◽  
Thermoacoustic Instability ◽  
Period 2 ◽  
Partially Premixed ◽  
Hydrogen Enrichment

Abstract In this study, we systematically analyze the effects of hydrogen enrichment in the well-known PRECCINSTA burner, a partially premixed swirl-stabilized methane/air combustor. Keeping the equivalence ratio and thermal power constant, we vary the hydrogen percentage in the fuel. Successive increments in hydrogen fuel fraction increase the adiabatic flame temperature and also shift the dominant frequencies of acoustic pressure fluctuations to higher values. Under hydrogen enrichment, we observe the emergence of periodicity in the combustor resulting from the interaction between acoustic modes. As a result of the interaction between these modes, the combustor exhibits a variety of dynamical states, including period-1 limit cycle oscillations (LCO), period-2 LCO, chaotic oscillations, and intermittency. The flame and flow behavior is found to be significantly different for each dynamical state. Analyzing the coupled behavior of the acoustic pressure and the heat release rate oscillations during the states of thermoacoustic instability, we report the occurrence of 2:1 frequency-locking during period-2 LCO, where two cycles of acoustic pressure lock with one cycle of the heat release rate. During period-1 LCO, we notice 1:1 frequency-locking, where both acoustic pressure and heat release rate repeat their behavior in every cycle.

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

2018 ◽  
Author(s):  
José G. Aguilar ◽  
Matthew P. Juniper
Keyword(s):  
Sensitivity Analysis ◽  
Time Delay ◽  
Heat Release ◽  
Combustion Chamber ◽  
Heat Release Rate ◽  
Release Rate ◽  
Gas Turbines ◽  
Acoustic Pressure ◽  
Annular Combustor ◽  
Thermoacoustic Oscillations

In gas turbines, thermoacoustic oscillations grow if moments of high fluctuating heat release rate coincide with moments of high acoustic pressure. The phase between the heat release rate and the acoustic pressure depends strongly on the flame behaviour (specifically the time delay) and on the acoustic period. This makes the growth rate of thermoacoustic oscillations exceedingly sensitive to small changes in the acoustic boundary conditions, geometry changes, and the flame time delay. In this paper, adjoint-based sensitivity analysis is applied to a thermoacoustic network model of an annular combustor. This reveals how each eigenvalue is affected by every parameter of the system. This information is combined with an optimization algorithm in order to stabilize all thermoacoustic modes of the combustor by making only small changes to the geometry. The final configuration has a larger plenum area, a smaller premix duct area and a larger combustion chamber volume. All changes are less than 6% of the original values. The technique is readily scalable to more complex models and geometries and the inclusion of further constraints, such that the combustion chamber itself should not change. This demonstrates why adjoint-based sensitivity analysis and optimization could become an indispensible tool for the design of thermoacoustically-stable combustors.

scholarly journals Analytical approximations for heat release rate laws in the time- and frequency-domains

2020 ◽  
Vol 12 ◽  
pp. 175682772093049
Author(s):  
Sreenath M Gopinathan ◽  
Alessandra Bigongiari ◽  
Maria Heckl
Keyword(s):  
Transfer Function ◽  
Heat Release ◽  
Impulse Response ◽  
Release Rate ◽  
Time Domain ◽  
Time Lag ◽  
Coupling Coefficients ◽  
Describing Function ◽  
Flame Describing Function ◽  
The Time Domain

This paper focusses on the relationship between the heat release rate and the acoustic field, which is a crucial element in modelling thermoacoustic instabilities. The aim of the paper is twofold. The first aim is to develop a transformation tool, which makes it easy to switch between the time-domain representation (typically a heat release law involving time-lags) and the frequency-domain representation (typically a flame transfer function) of this relationship. Both representations are characterised by the same set of parameters n1, n2, …, nk. Their number is quite small, and they have a clear physical meaning: they are time-lag dependent coupling coefficients. They are closely linked to the impulse response of the flame in the linear regime in that they are proportional to the discretised (with respect to time) impulse response. In the nonlinear regime, the parameters n1, n2, …, nk become amplitude-dependent. Their interpretation as time-lag dependent coupling coefficients prevails; however, the link with the impulse response is lost. Nonlinear flames are commonly described in the frequency-domain by an amplitude-dependent flame transfer function, the so-called flame describing function. The time-domain equivalent of the flame describing function is sometimes mistaken for a ‘nonlinear impulse response’, but this is not correct. The second aim of this paper is to highlight this misconception and to provide the correct interpretation of the time-domain equivalent of the flame describing function.

Dynamical Characterization of Thermoacoustic Oscillations in a Hydrogen-Enriched Partially Premixed Swirl-Stabilized Methane/Air Combustor

2021 ◽  
Author(s):  
Abhishek Kushwaha ◽  
Praveen Kasthuri ◽  
Samadhan A. Pawar ◽  
R. I. Sujith ◽  
Ianko Chterev ◽  
...  
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Acoustic Pressure ◽  
Thermal Power ◽  
Frequency Locking ◽  
Thermoacoustic Instability ◽  
Period 2 ◽  
Partially Premixed ◽  
Hydrogen Enrichment

Abstract In this study, we systematically analyze the effects of hydrogen enrichment in the well-known PRECCINSTA burner, a partially premixed swirl-stabilized methane/air combustor. Keeping the equivalence ratio and thermal power constant, we vary the hydrogen percentage in the fuel. Successive increments in hydrogen fuel fraction increase the adiabatic flame temperature and also shift the dominant frequencies of acoustic pressure fluctuations to higher values. Under hydrogen enrichment, we observe the emergence of periodicity in the combustor resulting from the interaction between acoustic modes. As a result of the interaction between these modes, the combustor exhibits a variety of dynamical states, including period-1 limit cycle oscillations (LCO), period-2 LCO, chaotic oscillations, and intermittency. The flame and flow behavior is found to be significantly different for each dynamical state. Analyzing the coupled behavior of the acoustic pressure and the heat release rate oscillations during the states of thermoacoustic instability, we report the occurrence of 2:1 frequency-locking during period-2 LCO, where two cycles of acoustic pressure lock with one cycle of the heat release rate. During period-1 LCO, we notice 1:1 frequency-locking, where both acoustic pressure and heat release rate repeat their behavior in every cycle.

Thermoacoustic instability as mutual synchronization between the acoustic field of the confinement and turbulent reactive flow

2017 ◽  
Vol 827 ◽  
pp. 664-693 ◽  
Author(s):  
Samadhan A. Pawar ◽  
Akshay Seshadri ◽  
Vishnu R. Unni ◽  
R. I. Sujith
Keyword(s):  
Heat Release ◽  
Limit Cycle ◽  
Acoustic Field ◽  
Heat Release Rate ◽  
Release Rate ◽  
Bluff Body ◽  
Acoustic Pressure ◽  
Mutual Synchronization ◽  
Periodic Oscillations ◽  
Thermoacoustic Instability

Thermoacoustic instability is the result of a positive coupling between the acoustic field in the duct and the heat release rate fluctuations from the flame. Recently, in several turbulent combustors, it has been observed that the onset of thermoacoustic instability is preceded by intermittent oscillations, which consist of bursts of periodic oscillations amidst regions of aperiodic oscillations. Quantitative analysis of the intermittency route to thermoacoustic instability has been performed hitherto using the pressure oscillations alone. We perform experiments on a laboratory-scale bluff-body-stabilized turbulent combustor with a backward-facing step at the inlet to obtain simultaneous data of acoustic pressure and heat release rate fluctuations. With this, we show that the onset of thermoacoustic instability is a phenomenon of mutual synchronization between the acoustic pressure and the heat release rate signals, thus emphasizing the importance of the coupling between these non-identical oscillators. We demonstrate that the stable operation corresponds to desynchronized aperiodic oscillations, which, with an increase in the mean velocity of the flow, transition to synchronized periodic oscillations. In between these states, there exists a state of intermittent phase synchronized oscillations, wherein the two oscillators are synchronized during the periodic epochs and desynchronized during the aperiodic epochs of their oscillations. Furthermore, we discover two different types of limit cycle oscillations in our system. We notice a significant increase in the linear correlation between the acoustic pressure and the heat release rate oscillations during the transition from a lower-amplitude limit cycle to a higher-amplitude limit cycle. Further, we present a phenomenological model that qualitatively captures all of the dynamical states of synchronization observed in the experiment. Our analysis shows that the times at which vortices that are shed from the inlet step reach the bluff body play a dominant role in determining the behaviour of the limit cycle oscillations.

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