Analysis of Azimuthal Thermo-acoustic Modes in Annular Gas Turbine Combustion Chambers

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Mirko R. Bothien ◽  
Nicolas Noiray ◽  
Bruno Schuermans
Keyword(s):  
Gas Turbine ◽  
Network Model ◽  
Growth Rates ◽  
Linear Growth ◽  
Flame Temperature ◽  
Full Scale ◽  
Linear Growth Rate ◽  
Combustion Chambers ◽  
Engine Operation ◽  
Acoustic Modes

Modern gas turbine combustors operating in lean-premixed mode are prone to thermo-acoustic instabilities. In annular combustion chambers, usually azimuthal acoustic modes are the critical ones interacting with the flame. In case of constructive interference, high amplitude oscillations might result. In this paper, the azimuthal acoustic field of a full-scale engine is investigated in detail. The analyses are based on measurements in a full-scale gas turbine, analytical models to derive the system dynamics, as well as simulations performed with an in-house 3d nonlinear network model. It is shown that the network model is able to reproduce the behavior observed in the engine. Spectra, linear growth rates, as well as the statistics of the system's dynamics can be predicted. A previously introduced algorithm is used to extract linear growth rates from engine and model time domain data. The method's accuracy is confirmed by comparison of the routine's results to analytically determined growth rates from the network model. The network model is also used to derive a burner staging configuration, resulting in the decrease of linear growth rate and thus an increase of engine operation regime; model predictions are verified by full-scale engine measurements. A thorough investigation of the azimuthal modes statistics is performed. Additionally, the network model is used to show that an unfavorable flame temperature distribution with an amplitude of merely 1% of the mean flame temperature can change the azimuthal mode from dominantly rotating to dominantly standing. This is predicted by the network model that only takes into account flame fluctuations in axial direction.

Analysis of Azimuthal Thermoacoustic Modes in Annular Gas Turbine Combustion Chambers

2014 ◽  
Author(s):  
Mirko Bothien ◽  
Nicolas Noiray ◽  
Bruno Schuermans
Keyword(s):  
Gas Turbine ◽  
Network Model ◽  
Growth Rates ◽  
Linear Growth ◽  
Flame Temperature ◽  
Full Scale ◽  
Analytical Models ◽  
Linear Growth Rate ◽  
Combustion Chambers ◽  
Engine Operation

Modern gas turbine combustors operating in lean-premixed mode are prone to thermoacoustic instabilities. In annular combustion chambers, usually azimuthal acoustic modes are the critical ones interacting with the flame. In case of constructive interference, high amplitude oscillations might result. In this paper, the azimuthal acoustic field of a full-scale engine is investigated in detail. The analyses are based on measurements in a full-scale gas turbine, analytical models to derive the system dynamics, as well as simulations performed with an in-house 3d nonlinear network model. It is shown that the network model is able to reproduce the behaviour observed in the engine. Spectra, linear growth rates, as well as the statistics of the system’s dynamics can be predicted. A previously introduced algorithm is used to extract linear growth rates from engine and model time domain data. The method’s accuracy is confirmed by comparison of the routine’s results to analytically determined growth rates from the network model. The network model is also used to derive a burner staging configuration resulting in the decrease of linear growth rate and thus an increase of engine operation regime; model predictions are verified by full-scale engine measurements. A thorough investigation of the azimuthal modes statistics is performed. Additionally, the network model is used to show that an unfavorable flame temperature distribution with an amplitude of merely 1% of the mean flame temperature can change the azimuthal mode from dominantly rotating to dominantly standing. This is predicted by the network model that only takes into account flame fluctuations in axial direction.

Linear Growth Rate Estimation From Dynamics and Statistics of Acoustic Signal Envelope in Turbulent Combustors

2016 ◽  
Vol 139 (4) ◽  
Author(s):  
Nicolas Noiray
Keyword(s):  
Gas Turbine ◽  
Acoustic Signal ◽  
Growth Rates ◽  
Linear Growth ◽  
Dynamic Pressure ◽  
Linear Growth Rate ◽  
Case Scenario ◽  
Major Step ◽  
Worst Case ◽  
Signal Envelope

Considerable research and development efforts are required to meet the targets of future gas turbine technologies in terms of performance, emissions, and operational flexibility. One of the recurring problems is the constructive coupling between flames and combustor's acoustics. These thermoacoustic interactions can cause high-amplitude dynamic pressure limit cycles, which reduce the lifetime of the hot gas path parts or in the worst-case scenario destroy these mechanical components as a result of a sudden catastrophic event. It is shown in this paper that the dynamics and the statistics of the acoustic signal envelope can be used to identify the linear growth rates hidden behind the observed pulsations, and the results are validated against numerical simulations. This is a major step forward and it will contribute to the development of future gas turbine combustors, because the knowledge of these linear growth rates is essential to develop robust active and passive systems to control these combustion instabilities.

Linear Growth Rate Estimation From Dynamics and Statistics of Acoustic Signal Envelope in Turbulent Combustors

2016 ◽  
Author(s):  
Nicolas Noiray
Keyword(s):  
Gas Turbine ◽  
Acoustic Signal ◽  
Growth Rates ◽  
Linear Growth ◽  
Dynamic Pressure ◽  
Linear Growth Rate ◽  
Case Scenario ◽  
Major Step ◽  
Worst Case ◽  
Signal Envelope

Considerable research and development efforts are required to meet the targets of future gas turbine technologies in terms of performance, emissions and operational flexibility. One of the recurring problem is the constructive coupling between flames and combustor’s acoustics. These thermoacoustic interactions can cause high amplitude dynamic pressure limit cycles, which reduce the lifetime of the hot-gas-path parts or in the worst case scenario destroy these mechanical components as a result of a sudden catastrophic event. It is shown in this paper that the dynamics and the statistics of the acoustic signal envelope can be used to identify the linear growth rates hidden behind the observed pulsations, and the results are validated against numerical simulations. This is a major step forward and it will contribute to the development of future gas turbine combustors, because the knowledge of these linear growth rates is essential to develop robust active and passive systems to control these combustion instabilities.

scholarly journals Effect of Radial Wavevector on Collisional Drift Waves in a Toroidal Heliac

1999 ◽  
Vol 52 (1) ◽  
pp. 71 ◽  
Author(s):  
J. L. V. Lewandowski ◽  
R. M. Ellem
Keyword(s):  
Growth Rate ◽  
Electrostatic Potential ◽  
Growth Rates ◽  
Initial Value Problem ◽  
Linear Growth ◽  
Field Model ◽  
Linear Growth Rate ◽  
Drift Waves ◽  
Initial Value ◽  
Magnetic Shear

A 3-field model for collisional drift waves, in the ballooning representation, for a low-pressure stellarator plasma is presented. In particular, the effect of a finite radial mode number (≡ θk) is studied, and the linear growth rates for the fluctuating plasma density, electrostatic potential and electron temperature are computed numerically by solving the 3-field model as an initial-value problem. Numerical results for a 3-field period stellarator with low global magnetic shear are then presented. It is found that, in a system with small global magnetic shear, the case θk = 0 yields the fastest linear growth rate.

scholarly journals On the non-axisymmetric fragmentation of rings generated by the Secular Gravitational Instability

2021 ◽  
Author(s):  
Arnaud Pierens
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Linear Growth ◽  
Gravitational Instability ◽  
Dust Particles ◽  
Linear Growth Rate ◽  
Stability Parameters ◽  
Dust Density ◽  
Linear Evolution ◽  
Non Linear

Abstract Ringed structures have been observed in a variety of protoplanetary discs. Among the processes that might be able to generate such features, the Secular Gravitational Instability (SGI) is a possible candidate. It has also been proposed that the SGI might lead to the formation of planetesimals during the non-linear phase of the instability. In this context, we employ two-fluid hydrodynamical simulations with self-gravity to study the non-axisymmetric, non-linear evolution of ringed perturbations that grow under the action of the SGI. We find that the non-linear evolution outcome of the SGI depends mainly on the initial linear growth rate. For SGI growth rates smaller than typically σ ≳ 10−4 − 10−5Ω, dissipation resulting from dust feedback introduces a m = 1 spiral wave in the gas, even for Toomre gas stability parameters Qg > 2 for which non-axisymmetric instabilities appear in a purely gaseous disc. This one-armed spiral subsequently traps dust particles until a dust-to-gas ratio ε ∼ 1 is achieved. For higher linear growth rates, the dust ring is found to undergo gravitational collapse until the bump in the surface density profile becomes strong enough to trigger the formation of dusty vortices through the Rossby Wave Instability (RWI). Enhancements in dust density resulting from this process are found to scale with the linear growth rate, and can be such that the dust density is higher than the Roche density, leading to the formation of bound clumps. Fragmentation of axisymmetric rings produced by the SGI might therefore appear as a possible process for the formation of planetesimals.

On the Effect of Noise Induced Dynamics on Linear Growth Rates of Oscillations in an Electroacoustic Rijke Tube Simulator

2021 ◽  
Author(s):  
Neha Vishnoi ◽  
Pankaj Wahi ◽  
Aditya Saurabh ◽  
Lipika Kabiraj
Keyword(s):  
Gas Turbine ◽  
Turbulent Flows ◽  
Growth Rates ◽  
Noise Intensity ◽  
Linear Growth ◽  
Stochastic Dynamics ◽  
Decay Rates ◽  
System Stability ◽  
Rijke Tube ◽  
The Stability

Abstract Suppressing self-excited thermoacoustic oscillations in combustion chambers is essential for gas turbine system stability. Passive acoustic damping devices such as Helmholtz resonators are commonly employed in modern combustors to address the problem of thermoacoustic instabilities. The estimation of deterministic parameters characterizing flame-acoustic coupling, specifically the stability margins and linear growth/decay rates, is a prerequisite for designing these devices. As gas turbine combustors are typically noisy systems due to the presence of highly turbulent flows and unsteady combustion, it is essential to understand the role of noise and its impact on the estimated system stability. Recently several new results on the stochastic dynamics of thermoacoustic systems and the use of noise-induced dynamics to estimate system stability characteristics have been reported. In the present work, we study the different approaches previously reported on the estimation of linear growth/decay rates from noise-induced dynamics on an electroacoustic Rijke tube (a prototypical thermoacoustic system) simulator. We estimate the growth rates from noisy data obtained from the subthreshold, bistable, and linearly-unstable regions of the observed subcritical Hopf bifurcation and investigate the effect of additive noise intensity. We find that the noise intensity affects the stability boundaries and the estimated growth rates.

Autoradiographic studies of wool growth rate in Wensleydale crossbred lambs: absence of a marked circadian rhythm

1981 ◽  
Vol 33 (3) ◽  
pp. 259-263 ◽  
Author(s):  
G. C. Priestley ◽  
M. L. Ryder
Keyword(s):  
Growth Rate ◽  
Circadian Rhythm ◽  
Food Intake ◽  
Growth Rates ◽  
Linear Growth ◽  
Wool Fibre ◽  
Linear Growth Rate ◽  
Wool Growth

ABSTRACTThe linear growth rate of wool on three sites on each of six Wenslcydale × Blackface lambs was measured by wool fibre autoradiography following 11 injections of 35S-cystine. The first injection was given at 09.00 h, so that alternate 36h intervals between injections represented predominantly day (09.00 to 21.00h) or night (21.00 to 09.00 h). The overall mean growth rates on shoulder, mid-side and breech were 0·83, 0·96 and 0·95 mm/day. Differences between day and night growth rates were very small (proportionally<0·05) and inconsistent in 16 of the 18 samples; although breech samples from two sheep showed up to 0·14 faster growth in daytime, a circadian rhythm of wool growth seems unlikely on this evidence. Both linear wool growth rate and food intake increased steadily throughout the experiment.Mid-side wool growth rates in a second group of three crossbred longwool lambs averaged 0·79, 100 and 1·14 mm/day and were relatively stable over a period of several months.

scholarly journals Wind-wave amplification mechanisms: possible models for steep wave events in finite depth

2013 ◽  
Vol 1 (4) ◽  
pp. 3099-3127 ◽  
Author(s):  
P. Montalvo ◽  
R. Kraenkel ◽  
M. A. Manna ◽  
C. Kharif
Keyword(s):  
Wind Velocity ◽  
Deep Water ◽  
Growth Rates ◽  
Linear Growth ◽  
Wind Wave ◽  
Finite Depth ◽  
Wave Number ◽  
Linear Growth Rate ◽  
Wave Age ◽  
Wave Amplification

Abstract. We extend the Miles' mechanism of wind-wave generation to finite depth. A β-Miles linear growth rate depending on the depth and wind velocity is derived and allows the study of linear growth rates of surface waves from weak to moderate winds in finite depth h. The evolution of β is plotted, for several values of the dispersion parameter kh with k the wave number. For constant depths we find that no matter what the values of wind velocities are, at small enough wave age the β-Miles linear growth rates are in the known deep water limit. However winds of moderate intensities prevent the waves from growing beyond a critical wave age, which is also constrained by the water depth and is less than the wave age limit of deep water. Depending on wave age and wind velocity, the Jeffreys' and Miles' mechanisms are compared to determine which of them dominates. A wind-forced nonlinear Schrödinger equation is derived and the Akhmediev, Peregrine and Kuznetsov–Ma breather solutions for weak wind inputs in finite depth h are obtained.

scholarly journals Wind-wave amplification mechanisms: possible models for steep wave events in finite depth

2013 ◽  
Vol 13 (11) ◽  
pp. 2805-2813 ◽  
Author(s):  
P. Montalvo ◽  
R. Kraenkel ◽  
M. A. Manna ◽  
C. Kharif
Keyword(s):  
Wind Velocity ◽  
Deep Water ◽  
Growth Rates ◽  
Linear Growth ◽  
Wind Wave ◽  
Finite Depth ◽  
Wave Number ◽  
Linear Growth Rate ◽  
Wave Age ◽  
Wave Amplification

Abstract. We extend the Miles mechanism of wind-wave generation to finite depth. A β-Miles linear growth rate depending on the depth and wind velocity is derived and allows the study of linear growth rates of surface waves from weak to moderate winds in finite depth h. The evolution of β is plotted, for several values of the dispersion parameter kh with k the wave number. For constant depths we find that no matter what the values of wind velocities are, at small enough wave age the β-Miles linear growth rates are in the known deep-water limit. However winds of moderate intensities prevent the waves from growing beyond a critical wave age, which is also constrained by the water depth and is less than the wave age limit of deep water. Depending on wave age and wind velocity, the Jeffreys and Miles mechanisms are compared to determine which of them dominates. A wind-forced nonlinear Schrödinger equation is derived and the Akhmediev, Peregrine and Kuznetsov–Ma breather solutions for weak wind inputs in finite depth h are obtained.

scholarly journals Geometry of shoot apical dome and distribution of growth rates

2014 ◽  
Vol 51 (3-4) ◽  
pp. 389-402 ◽  
Author(s):  
Jerzy Nakielski
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Linear Growth ◽  
Linear Growth Rate ◽  
Rate Of Growth ◽  
Apical Dome ◽  
Subapical Region

The distribution of the relative elementary rate of growth (RERG) in apical domes of various shapes and patterns of displacement lines can be analytically examined. The geometry of these domes may be described by parabolas of <em>n</em>-th order, the variant of the distribution of linear growth rate should be established along any displacement line (e.g. along the axis) and then the RERG can be studied as the function depending on the position coordinates and the parameter n. Such investigations of several aplical domes of various shapes have been performed. The results confirm the occurrence of the minimum of relative, elementary growth rate (in volume) in the subapical region of the dome independently of the type of geometry (<em>n</em> parabola order).

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