Characterization and Modeling of a Spinning Thermoacoustic Instability in an Annular Combustor Equipped With Multiple Matrix Injectors

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Jean-François Bourgouin ◽  
Daniel Durox ◽  
Jonas P. Moeck ◽  
Thierry Schuller ◽  
Sébastien Candel
Keyword(s):  
High Speed ◽  
Stable Limit Cycle ◽  
Turbulent Flames ◽  
Linear Growth Rate ◽  
Stable Limit ◽  
Acoustic Oscillations ◽  
Describing Function ◽  
Azimuthal Mode ◽  
Thermoacoustic Instability ◽  
Annular Combustor

Oscillations in fully annular systems coupled by azimuthal modes are often observed in gas turbine combustors but not well documented. One objective of the present study is to characterize this type of oscillation in a laboratory scale system, allowing detailed pressure measurements and high speed visualization of the flame motion. The experiment is designed to allow detailed investigations of this process at a stable limit cycle and for an extended period of time. Experiments reported in the present article are carried out in the MICCA facility which was used in our previous work to analyze instabilities arising when the chamber backplane was equipped with multiple swirling injectors (Bourgouin et al., 2013, “Self-Sustained Instabilities in an Annular Combustor Coupled by Azimuthal Acoustic Modes,” ASME Paper No. GT2013-95010). In the present study, these units are replaced by a set of matrix injectors. The annular plenum feeds 16 such devices confined by two cylindrical quartz tubes open to the atmosphere. The multiple flames formed by the matrix injectors are laminar and have a well documented describing function. This constitutes an ideal configuration allowing systematic investigations of thermo-acoustic oscillations coupled by longitudinal or azimuthal modes while avoiding complexities inherent to swirling turbulent flames studied previously. Optical access to the chamber allows high speed imaging of light emission from the flames providing instantaneous flame patterns and indications on the heat release rate fluctuations. Eight waveguide microphones record the pressure signal at the combustor injection plane and in the plenum. Among the unstable modes observed in this setup, this analysis focuses on situations where the system features a spinning azimuthal mode. This mode is observed at a frequency which is close to that associated with the 1A mode of the plenum. A theoretical analysis is then carried out to interpret the angular shift between the nodal lines in the plenum and chamber, and the measured flame describing function (FDF) is used to quantify this shift and determine the linear growth rate.

Characterization and Modeling of a Spinning Thermoacoustic Instability in an Annular Combustor Equipped With Multiple Matrix Injectors

2014 ◽  
Author(s):  
Jean-François Bourgouin ◽  
Daniel Durox ◽  
Jonas P. Moeck ◽  
Thierry Schuller ◽  
Sébastien Candel
Keyword(s):  
High Speed ◽  
Stable Limit Cycle ◽  
Turbulent Flames ◽  
Linear Growth Rate ◽  
Stable Limit ◽  
Acoustic Oscillations ◽  
Describing Function ◽  
High Speed Imaging ◽  
Azimuthal Mode ◽  
Thermoacoustic Instability

Oscillations in fully annular systems coupled by azimuthal modes are often observed in gas turbine combustors but not well documented. One objective of the present study is to characterize this type of oscillation in a laboratory scale system allowing detailed pressure measurements and high speed visualization of the flame motion. The experiment is designed to allow detailed investigations of this process at a stable limit cycle and for an extended period of time. Experiments reported in the present article are carried out in the MICCA facility which was used in our previous work to analyze instabilities arising when the chamber backplane was equipped with multiple swirling injectors (Bourgouin et al. ASME Paper GT2013-95010). In the present study, these units are replaced by a set of matrix injectors. The annular plenum feeds sixteen such devices confined by two cylindrical quartz tubes open to the atmosphere. The multiple flames formed by the matrix injectors are laminar and have a well documented describing function. This constitutes an ideal configuration allowing systematic investigations of thermo-acoustic oscillations coupled by longitudinal or azimuthal modes while avoiding complexities inherent to swirling turbulent flames studied previously. Optical access to the chamber allows high speed imaging of light emission from the flames providing instantaneous flame patterns and indications on the heat release rate fluctuations. Eight waveguide microphones record the pressure signal at the combustor injection plane and in the plenum. Among the unstable modes observed in this setup, this analysis focuses on situations where the system features a spinning azimuthal mode. This mode is observed at a frequency which is close to that associated with the 1A mode of the plenum. A theoretical analysis is then carried out to interpret the angular shift between the nodal lines in the plenum and chamber and the measured flame describing function is used to quantify this shift and determine the linear growth rate.

Intermittency, Secondary Bifurcation and Mixed-Mode Oscillations in a Swirl-Stabilized Annular Combustor: Experiments and Modeling

2020 ◽  
Author(s):  
Samarjeet Singh ◽  
Amitesh Roy ◽  
Reeja K. V. ◽  
Asalatha Nair ◽  
Swetaprovo Chaudhuri ◽  
...  
Keyword(s):  
Mixed Mode ◽  
Equivalence Ratio ◽  
High Amplitude ◽  
The State ◽  
Turbulent Flames ◽  
Bulk Velocity ◽  
Thermoacoustic Instability ◽  
Mixed Mode Oscillations ◽  
Annular Combustor ◽  
Low Amplitude

Abstract We experimentally study thermoacoustic transitions in an annular combustor consisting of sixteen premixed, swirl-stabilized turbulent flames. We show the changes in the characteristics of bifurcations leading to the state of longitudinal thermoacoustic instability (TAI) when equivalence ratio and bulk velocity are systematically varied. Depending upon the bulk velocity, we observe different states of combustor operation when the equivalence ratio is varied. These states include combustion noise, intermittency, low-amplitude TAI, mixed-mode oscillations (MMO), and high-amplitude TAI. We closely examine the special case of MMO that is encountered during the transition from low-amplitude TAI to high-amplitude TAI. We also discuss the global and local flame dynamics observed during the state of MMO. We find that during epochs of low-amplitude oscillations of MMO, all the flames are partially synchronized, while during epochs of high-amplitude oscillations, all the flames are perfectly synchronized. Finally, we replicate the criticalities of bifurcation of the annular combustor in a phenomenological model containing sixth-order nonlinearities.

scholarly journals Non Linear Control System Based Modeling of Cardiac Muscle using Describing Function and Lyapnuov Stability.

2020 ◽  
Vol 9 (2) ◽  
pp. 1815-1820
Keyword(s):  
Cardiac Muscle ◽  
Dead Zone ◽  
Research Work ◽  
Stable Limit Cycle ◽  
Function Technique ◽  
Lag Phase ◽  
Stable Limit ◽  
Describing Function ◽  
Mass Spring ◽  
Transportation Delay

Main focus of this research work is aims towards the nonlinear analysis of human cardiac muscle by describing function technique and finding stability using lyapnuov stability theory. The nature of cardiac muscle can be modeled by mass, spring with a damper where for simplicity spring and damper are considered a linear element. In reality, it has been observed that, the characteristics of spring and damper are not linear rather nonlinear. Not only that, transportation delay (non-zero reaction time) or lag phase of cardiac muscle plays an important role to make the overall model nonlinear. The range of transportation delay for which the system is stable has been calculated here to ensure the presence of dead zone type nonlinearity in cardiac muscle. In this paper a nonlinear characteristics of the model has been analyzed considering dead zone combined with saturation. The describing function technique is used here to represent the nonlinearity. A converging stable limit cycle has been found after the analysis. Finally, lyapnuov stability theorem is applied on our proposed model and it has been that the system is asymptotically stable in the sense of lyapnuov

Intermittency, Secondary Bifurcation and Mixed-Mode Oscillations in a Swirl-Stabilized Annular Combustor: Experiments and Modeling

2020 ◽  
Author(s):  
Samarjeet Singh ◽  
Amitesh Roy ◽  
K. V. Reeja ◽  
Asalatha Nair ◽  
Swetaprovo Chaudhuri ◽  
...  
Keyword(s):  
Mixed Mode ◽  
Equivalence Ratio ◽  
High Amplitude ◽  
The State ◽  
Turbulent Flames ◽  
Bulk Velocity ◽  
Thermoacoustic Instability ◽  
Mixed Mode Oscillations ◽  
Annular Combustor ◽  
Low Amplitude

Abstract We experimentally study thermoacoustic transitions in an annular combustor consisting of sixteen premixed, swirl-stabilized turbulent flames. We show the changes in the characteristics of bifurcations leading to the state of longitudinal thermoacoustic instability (TAI) when equivalence ratio and bulk velocity are systematically varied. Depending upon the bulk velocity, we observe different states of combustor operation when the equivalence ratio is varied. These states include combustion noise, intermittency, low-amplitude TAI, mixed-mode oscillations (MMO), and high-amplitude TAI. We closely examine the special case of MMO that is encountered during the transition from low-amplitude TAI to high-amplitude TAI. We also discuss the global and local flame dynamics observed during the state of MMO. We find that during epochs of low-amplitude oscillations of MMO, all the flames are partially synchronized, while during epochs of high-amplitude oscillations, all the flames are perfectly synchronized. Finally, we replicate the criticalities of bifurcation of the annular combustor in a phenomenological model containing sixth-order nonlinearities.

Self-Sustained Instabilities in an Annular Combustor Coupled by Azimuthal and Longitudinal Acoustic Modes

2013 ◽  
Author(s):  
Jean-Francois Bourgouin ◽  
Daniel Durox ◽  
Jonas P. Moeck ◽  
Thierry Schuller ◽  
Sébastien Candel
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
High Speed ◽  
High Amplitude ◽  
Acoustic Mode ◽  
Azimuthal Mode ◽  
Longitudinal Acoustic ◽  
Acoustic Modes ◽  
Annular Combustor

Annular combustors may give rise to various types of combustion instabilities. Some of the resulting oscillations coupled by transverse acoustic modes are commonly observed in practice and their suppression or reduction is an important issue which needs to be considered. The present study is carried out in a system comprising an annular plenum feeding 16 swirling injectors confined by two cylindrical quartz tubes opened to the atmosphere. Calculations based on a Helmholtz solver provide a suitable estimate of frequencies observed experimentally and reveal the modal structure corresponding to the longitudinal and transverse oscillations. High speed images obtained under reactive conditions are then processed to extract the structure of heat release rate perturbations and match this structure with that of the coupling acoustic mode. It is found that the transverse instability is coupled by a first azimuthal mode which is characterized by a time varying spin ratio. This index gives the respective levels of rotating components in the azimuthal mode. Another instability arising at a lower frequency is coupled by a longitudinal acoustic mode giving rise to high-amplitude oscillations in heat release rate in which most of the flames (but not all) are synchronized and in phase with the pressure perturbation.

Amplitude statistics prediction in thermoacoustics

2018 ◽  
Vol 844 ◽  
pp. 216-246 ◽  
Author(s):  
G. Ghirardo ◽  
F. Boudy ◽  
M. R. Bothien
Keyword(s):  
Acoustic Pressure ◽  
Combustion Noise ◽  
Pressure Amplitude ◽  
Describing Function ◽  
Thermoacoustic Instability ◽  
Design Change ◽  
Describing Functions ◽  
Annular Combustor ◽  
Acoustic Losses ◽  
Thermoacoustic Oscillations

We discuss the statistics of acoustic pressure of thermoacoustic oscillations, either axial or azimuthal in nature. We derive a model where the describing functions of the fluctuating heat release rate of the flame and of the acoustic losses appear directly in the equations. The background combustion noise is assumed to be additive, and we show how one can recover, from the measurement of the acoustic pressure at the flame location, the projected describing function of the flame minus the acoustic losses. Using the same equations, one can predict the statistics of the amplitude of acoustic pressure for a certain system. The theory is then tested on an azimuthal thermoacoustic instability in an industrial annular combustor by measuring the state of the system, predicting the acoustic pressure amplitude statistics after a design change and comparing the prediction with the measured statistics after the design change has been implemented.

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

The Structure and Propagation Mechanism of Turbulent Flames in High Speed Flow

1955 ◽  
Vol 25 (8) ◽  
pp. 377-384 ◽  
Author(s):  
MARTIN SUMMERFIELD ◽  
SYDNEY H. REITER ◽  
VICTOR KEBELY ◽  
RICHARD W. MASCOLO
Keyword(s):  
High Speed ◽  
Turbulent Flames ◽  
Propagation Mechanism ◽  
High Speed Flow ◽  
Speed Flow

The Effect of Lewis Number on Instantaneous Flamelet Speed and Position Statistics in Counter-Flow Flames With Increasing Turbulence

2017 ◽  
Author(s):  
Sean D. Salusbury ◽  
Ehsan Abbasi-Atibeh ◽  
Jeffrey M. Bergthorson
Keyword(s):  
Flame Front ◽  
Turbulence Intensity ◽  
High Speed ◽  
Rayleigh Scattering ◽  
Turbulent Flame ◽  
Lewis Number ◽  
Turbulent Flames ◽  
Flame Speed ◽  
Laminar Flames ◽  
Counter Flow

Differential diffusion effects in premixed combustion are studied in a counter-flow flame experiment for fuel-lean flames of three fuels with different Lewis numbers: methane, propane, and hydrogen. Previous studies of stretched laminar flames show that a maximum reference flame speed is observed for mixtures with Le ≳ 1 at lower flame-stretch values than at extinction, while the reference flame speed for Le ≪ 1 increases until extinction occurs when the flame is constrained by the stagnation point. In this work, counter-flow flame experiments are performed for these same mixtures, building upon the laminar results by using variable high-blockage turbulence-generating plates to generate turbulence intensities from the near-laminar u′/SLo=1 to the maximum u′/SLo achievable for each mixture, on the order of u′/SLo=10. Local, instantaneous reference flamelet speeds within the turbulent flame are extracted from high-speed PIV measurements. Instantaneous flame front positions are measured by Rayleigh scattering. The probability-density functions (PDFs) of instantaneous reference flamelet speeds for the Le ≳ 1 mixtures illustrate that the flamelet speeds are increasing with increasing turbulence intensity. However, at the highest turbulence intensities measured in these experiments, the probability seems to drop off at a velocity that matches experimentally-measured maximum reference flame speeds in previous work. In contrast, in the Le ≪ 1 turbulent flames, the most-probable instantaneous reference flamelet speed increases with increasing turbulence intensity and can, significantly, exceed the maximum reference flame speed measured in counter-flow laminar flames at extinction, with the PDF remaining near symmetric for the highest turbulence intensities. These results are reinforced by instantaneous flame position measurements. Flame-front location PDFs show the most probable flame location is linked both to the bulk flow velocity and to the instantaneous velocity PDFs. Furthermore, hydrogen flame-location PDFs are recognizably skewed upstream as u′/SLo increases, indicating a tendency for the Le ≪ 1 flame brush to propagate farther into the unburned reactants against a steepening average velocity gradient.

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