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.

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.

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.

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 Heat-Release/Acoustic Model for Thermoacoustic Instability in Lean Premixed Combustors

1999 ◽  
Vol 121 (3) ◽  
pp. 415-421 ◽  
Author(s):  
A. A. Peracchio ◽  
W. M. Proscia
Keyword(s):  
Heat Release ◽  
Limit Cycle ◽  
Gas Turbines ◽  
Pressure Fluctuations ◽  
Parametric Model ◽  
Operating Conditions ◽  
Cycle Frequency ◽  
Thermoacoustic Instability ◽  
Lean Premixed ◽  
Industrial Gas Turbines

Lean premixed combustors, such as those used in industrial gas turbines to achieve low emissions, are often susceptible to the thermoacoustic combustion instabilities, which manifest themselves as pressure and heat release oscillations in the combustor. These oscillations can result in increased noise and decreased durability due to vibration and flame motion. A physically based nonlinear parametric model has been developed that captures this instability. It describes the coupling of combustor acoustics with the rate of heat release. The model represents this coupling by accounting for the effect of acoustic pressure fluctuations on the varying fuel/air ratio being delivered to the flame, causing a fluctuating heat release due to both fuel air ratio variations and flame front oscillations. If the phasing of the fluctuating heat release and pressure are proper, an instability results that grows into a limit cycle. The nonlinear nature of the model predicts the onset of the instability and additionally captures the resulting limit cycle. Tests of a lean premixed nozzle run at engine scale and engine operating conditions in the UTRC single nozzle rig, conducted under DARPA contract, exhibited instabilities. Parameters from the model were adjusted so that analytical results were consistent with relevant experimental data from this test. The parametric model captures the limit cycle behavior over a range of mean fuel air ratios, showing the instability amplitude (pressure and heat release) to increase and limit cycle frequency to decrease as mean fuel air ratio is reduced.

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.

An Experimental Validation of Heat Release Rate Fluctuation Measurements in Technically Premixed Flames

2013 ◽  
Author(s):  
Poravee Orawannukul ◽  
Bryan D. Quay ◽  
Domenic A. Santavicca
Keyword(s):  
Transfer Function ◽  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Equivalence Ratio ◽  
Premixed Flames ◽  
Reconstruction Technique ◽  
Chemiluminescence Intensity ◽  
Lean Premixed ◽  
Rate Of Heat Release

Knowledge of the effects of inlet velocity and inlet equivalence ratio fluctuations on the rate of heat release in lean premixed gas turbine combustors is essential for predicting combustor instability characteristics. This information is typically obtained from independent velocity-forced and fuel-forced flame transfer function measurements, where the global chemiluminescence intensity is used as a measure of the flame’s overall rate of heat release. The flame in an actual lean premixed combustor is referred to as a technically premixed flame and is exposed to both velocity and equivalence ratio fluctuations. Under these conditions the chemiluminescence intensity does not provide a reliable measure of the flame’s rate of heat release. The objective of this work is to experimentally assess the validity of a technique for making heat release rate measurements in technically premixed flames based on the linear superposition of fuel-forced and velocity-forced flame transfer function measurements. In the absence of a technique for directly measuring the heat release rate fluctuations in an air-forced technically premixed, the heat release reconstruction is validated indirectly by comparing measured to reconstructed chemiluminescence intensity fluctuations. Results are reported for a range of operating conditions and forcing frequencies which demonstrate the capabilities and limitations of this technique. A variation of this technique, referred to as a reverse reconstruction, is proposed which does not require a measurement of the fuel-forced flame transfer function. The air-forced flame transfer function gain and phase obtained using the reverse reconstruction technique are presented and compared to the results from the direct reconstruction technique.

scholarly journals The Effect of Fuel Staging on the Structure and Instability Characteristics of Swirl-Stabilized Flames in a Lean Premixed Multinozzle Can Combustor

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Janith Samarasinghe ◽  
Wyatt Culler ◽  
Bryan D. Quay ◽  
Domenic A. Santavicca ◽  
Jacqueline O'Connor
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Pressure Fluctuation ◽  
Equivalence Ratio ◽  
Flame Structure ◽  
Fuel Flow ◽  
Lean Premixed ◽  
Fuel Staging ◽  
Rate Oscillations

Fuel staging is a commonly used strategy in the operation of gas turbine engines. In multinozzle combustor configurations, this is achieved by varying fuel flow rate to different nozzles. The effect of fuel staging on flame structure and self-excited instabilities is investigated in a research can combustor employing five swirl-stabilized, lean-premixed nozzles. At an operating condition where all nozzles are fueled equally and the combustor undergoes a self-excited instability, fuel staging successfully suppresses the instability: both when overall equivalence ratio is increased by staging as well as when overall equivalence ratio is kept constant while staging. Increased fuel staging changes the distribution of time-averaged heat release rate in the regions where adjacent flames interact and reduces the amplitudes of heat release rate fluctuations in those regions. Increased fuel staging also causes a breakup in the monotonic phase behavior that is characteristic of convective disturbances that travel along a flame. In particular, heat release rate fluctuations in the middle flame and flame–flame interaction region are out-of-phase with those in the outer flames, resulting in a cancelation of the global heat release rate oscillations. The Rayleigh integral distribution within the combustor shows that during a self-excited instability, the regions of highest heat release rate fluctuation are in phase-with the combustor pressure fluctuation. When staging fuel is introduced, these regions fluctuate out-of-phase with the pressure fluctuation, further illustrating that fuel staging suppresses instabilities through a phase cancelation mechanism.

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