scholarly journals Weakly nonlinear analysis of thermoacoustic instabilities in annular combustors

2016 ◽  
Vol 805 ◽  
pp. 52-87 ◽  
Author(s):  
G. Ghirardo ◽  
M. P. Juniper ◽  
J. P. Moeck
Keyword(s):  
Gas Turbines ◽  
Practical Importance ◽  
Industrial Applications ◽  
Local Pressure ◽  
Weakly Nonlinear ◽  
Acoustic Damping ◽  
Thermoacoustic Instabilities ◽  
Rotationally Symmetric ◽  
Flame Response ◽  
Annular Combustor

Rotationally symmetric annular combustors are of practical importance because they generically resemble combustion chambers in gas turbines, in which thermoacoustically driven oscillations are a major concern. We focus on azimuthal thermoacoustic oscillations and model the fluctuating heat release rate as being dependent only on the local pressure in the combustion chamber. We study the dynamics of the annular combustor with a finite number of compact flames equispaced around the annulus, and characterize the flames’ response with a describing function. We discuss the existence, amplitude and the stability of standing and spinning waves, as a function of: (i) the number of the burners; (ii) the acoustic damping in the chamber; (iii) the flame response. We present the implications for industrial applications and the future direction of investigations. We then present as an example the first theoretical study of thermoacoustic triggering in annular combustors, which shows that rotationally symmetric annular chambers that are thermoacoustically unstable do not experience only stable spinning solutions, but can also experience stable standing solutions. We finally test the theory on one experiment with good agreement.

Stability Criteria for Standing and Spinning Waves in Annular Combustors

2015 ◽  
Author(s):  
Giulio Ghirardo ◽  
Matthew P. Juniper ◽  
Jonas P. Moeck
Keyword(s):  
Gas Turbines ◽  
Practical Importance ◽  
Industrial Applications ◽  
Describing Function ◽  
Combustion Chambers ◽  
Rotationally Symmetric ◽  
Annular Combustor ◽  
Flame Describing Function ◽  
The Stability ◽  
Future Direction

Rotationally symmetric annular combustors are of practical importance because they generically resemble combustion chambers in gas turbines and aeroengines, in which thermoacoustically driven oscillations are a major concern. We focus on thermoacoustic oscillations of azimuthal type, neglect the effect of the transverse acoustic velocity in the azimuthal direction, and model the heat release rate as being dependent only on the pressure in the combustion chamber. We study the dynamics of the annular combustor with a finite number of compact flames equi-spaced along the annulus, and characterise the flames’ response with a describing function. We discuss with broad generality the existence, amplitudes and the stability of standing and spinning waves, as a function of: 1) the number of the burners; 2) the damping in the chamber; 3) the flame describing function. These have implications on industrial applications, the future direction of investigations, and for what to look for in experimental data. We then present as an example of application the first theoretical study of triggering in annular combustors, and show that rotationally symmetric annular chambers can experience stable standing solutions.

Acoustic Energy Balance During the Onset, Growth and Saturation of Thermoacoustic Instabilities

2020 ◽  
Author(s):  
R. Gaudron ◽  
D. Yang ◽  
A. S. Morgans
Keyword(s):  
Energy Balance ◽  
Network Models ◽  
Acoustic Energy ◽  
Dimensionless Numbers ◽  
Weakly Nonlinear ◽  
Acoustic Damping ◽  
Thermoacoustic Instabilities ◽  
Wide Range ◽  
Acoustic Absorption Coefficient ◽  
Flame Describing Function

Abstract Thermoacoustic instabilities can occur in a wide range of combustors and are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, it does not provide any physical insight in terms of the acoustic energy balance of the system. On the other hand, Rayleigh’s criterion may be used to quantify the losses, sources and transfers of acoustic energy within and at the boundaries of a combustor. However, this approach is cumbersome for most applications because it requires computing volume and surface integrals and averaging over an oscillation cycle. In this work, a new methodology for studying the acoustic energy balance of a combustor during the onset, growth and saturation of thermoacoustic instabilities is proposed. The two cornerstones of this new framework are the acoustic absorption coefficient Δ and the cycle-to-cycle acoustic energy ratio λ, both of which do not require computing integrals. Used along with a suitable acoustic network model, where the flame frequency response is described using the weakly nonlinear Flame Describing Function (FDF) formalism, these two dimensionless numbers are shown to characterize: 1) the variation of acoustic energy stored within the combustor between two consecutive cycles, 2) the acoustic energy transfers occurring at the combustor’s boundaries and 3) the sources and sinks of acoustic energy located within the combustor. The acoustic energy balance of the well-documented Palies burner is then analyzed during the onset, growth and saturation of thermoacoustic instabilities using this new methodology. It is demonstrated that this new approach allows a deeper understanding of the physical mechanisms at play. For instance, it is possible to determine when the flame acts as an acoustic energy source or sink, where acoustic damping is generated, and if acoustic energy is transmitted through the boundaries of the burner.

Acoustic Damper Placement and Tuning for Annular Combustors: An Adjoint-Based Optimization Study

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Georg A. Mensah ◽  
Jonas P. Moeck
Keyword(s):  
Helmholtz Equation ◽  
Gas Turbines ◽  
Algebraic Models ◽  
Combustion Chambers ◽  
Thermoacoustic Instabilities ◽  
Helmholtz Resonators ◽  
Major Threat ◽  
Optimization Study ◽  
Annular Combustor ◽  
Parameter Values

Thermoacoustic instabilities pose a major threat to modern gas turbines. The use of acoustic dampers, like Helmholtz resonators, has proven useful for the mitigation of such instabilities. However, assessing the effect of acoustic dampers on thermoacoustic modes in annular combustion chambers remains an intricate task. This results from the implicit nature of the thermoacoustic Helmholtz equation associated with the high number of possible parameter values for the positioning of the dampers and their impedance design. In the present work, the principal challenges of the effective placement and the design of the impedance of acoustic dampers in annular chambers are discussed. This includes the choice of an appropriate objective function for the optimization, the combinatorial challenges when dealing with different possible damper arrangements, and the numerical complexities when using the thermoacoustic Helmholtz equation to approach this issue. As a key aspect, the paper proposes a new adjoint-based approach to tackle these problems. The new algorithm establishes algebraic models that predict the effect of acoustic dampers on the growth rates of the thermoacoustic modes. The theory is exemplified on the basis of a generic annular combustor model with 12 burners.

Investigation of Thermoacoustic Stability Limits of an Annular Gas Turbine Combustor Test-Rig With and Without Helmholtz-Resonators

2005 ◽  
Author(s):  
Joachim Lepers ◽  
Werner Krebs ◽  
Bernd Prade ◽  
Patrick Flohr ◽  
Giacomo Pollarolo ◽  
...  
Keyword(s):  
Gas Turbine ◽  
Gas Turbines ◽  
Thermal Power ◽  
Power Input ◽  
Test Rig ◽  
Combustion Chambers ◽  
Thermoacoustic Instabilities ◽  
Helmholtz Resonators ◽  
Annular Combustor ◽  
Computational Analyses

Providing gas turbine combustion chambers with Helmholtz-resonators is a promising approach for extending the operating range of gas turbines towards higher thermal power input whilst minimizing the risk of thermoacoustic instabilities. The work currently being reported gives an overview of experimental and computational analyses carried out for a full annular combustor test-rig located at Gioia del Colle in Italy. The thermoacoustic stability characteristics of this test-rig were thoroughly analyzed both for a base configuration without Helmholtz-resonators and for an extended configuration with 14 Helmholtz-resonators. An increase of power input to the combustor by 8.5–20% can be realized when the test-rig is equipped with resonators. The experimental analyses are reproduced by a computational model.

Prediction of Thermoacoustic Instabilities With Focus on the Dynamic Flame Behavior for the 3A-Series Gas Turbine of Siemens KWU

1999 ◽  
Author(s):  
Uwe Krüger ◽  
Jens Hüren ◽  
Stefan Hoffmann ◽  
Werner Krebs ◽  
Dieter Bohn
Keyword(s):  
Gas Turbine ◽  
Gas Turbines ◽  
Analytical Data ◽  
Flow Distribution ◽  
Transient Behavior ◽  
Axial Direction ◽  
Step Function ◽  
Lean Premixed Combustion ◽  
Thermoacoustic Instabilities ◽  
Annular Combustor

Self-induced combustion driven oscillations are a crucial challenge in the design of advanced gas turbine combustors. Lean premixed combustion, typically used in modern gas turbines, has a pronounced tendency to produce these instabilities. Thus, the prediction of these thermoacoustic instabilities in the design phase of an engine becomes more and more important. A method based on linear acoustic four-pole elements to predict the instabilities of the ring combustor of the Siemens 3A-series gas turbines will be presented in this paper. The complex network includes the entire system starting from both compressor outlet and fuel supply system and ending at the turbine inlet. Most of the transfer elements can be described by analytical data. Nevertheless, the most important elements, “flame” and “combustion chamber”, have to be investigated more in detail due to their complex 3D acoustics. For the turbulent, premixed and swirled flame, a numerical simulation of the transient behavior after a sudden jump in mass flow at the inlet (step-function approach) is used to obtain the flame frequency response for axial direction as well as circumferential direction. This method has been verified for numerous different flame types (Krüger et al. (1998), Bohn et al. (1997), Bohn et al. (1996)). The four-pole element of the annular combustor is derived by an eigenfrequency analysis of the chamber, including a numerical predicted temperature and flow distribution. The results show the principle possibilities of the instability analysis described. The frequencies predicted correspond well with experience from engine test fields. The importance of several elements for self-induced combustion driven oscillations is pointed out clearly.

Acoustic Damper Placement and Tuning for Annular Combustors: An Adjoint-Based Optimization Study

2016 ◽  
Author(s):  
Georg A. Mensah ◽  
Jonas P. Moeck
Keyword(s):  
Helmholtz Equation ◽  
Gas Turbines ◽  
Algebraic Models ◽  
Combustion Chambers ◽  
Thermoacoustic Instabilities ◽  
Helmholtz Resonators ◽  
Major Threat ◽  
Optimization Study ◽  
Annular Combustor ◽  
Parameter Values

Thermoacoustic instabilities pose a major threat to modern gas turbines. The use of acoustic dampers, like Helmholtz resonators, has proven useful for the mitigation of such instabilities. However, assessing the effect of acoustic dampers on thermoacoustic modes in annular combustion chambers remains an intricate task. This results from the implicit nature of the thermoacoustic Helmholtz equation associated with the high number of possible parameter values for the positioning of the dampers and their impedance design. In the present work, the principal challenges of the effective placement and the design of the impedance of acoustic dampers in annular chambers are discussed. This includes the choice of an appropriate objective function for the optimization, the combinatorial challenges when dealing with different possible damper arrangements, and the numerical complexities when using the thermoacoustic Helmholtz equation to approach this issue. As a key aspect, the paper proposes a new adjoint-based approach to tackle these problems. The new algorithm establishes algebraic models that predict the effect of acoustic dampers on the growth rates of the thermoacoustic modes. The theory is exemplified on the basis of a generic annular combustor model with 12 burners.

An Experimental Investigation of the Nonlinear Response of an Atmospheric Swirl-Stabilized Premixed Flame

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
Sebastian Schimek ◽  
Jonas P. Moeck ◽  
Christian Oliver Paschereit
Keyword(s):  
Gas Turbines ◽  
Oscillation Amplitude ◽  
Network Models ◽  
Mean Flow ◽  
Test Rig ◽  
Linear Network ◽  
Modeling Tools ◽  
Velocity Fluctuations ◽  
Thermoacoustic Instabilities ◽  
Flame Response

Due to stringent emission restrictions, modern gas turbines mostly rely on lean premixed combustion. Since this combustion mode is susceptible to thermoacoustic instabilities, there is a need for modeling tools with predictive capabilities. Linear network models are able to predict the occurrence of thermoacoustic instabilities but yield no information on the oscillation amplitude. The prediction of the pulsation levels and hence an estimation whether a certain operating condition has to be avoided is only possible if information on the nonlinear flame response is available. Typically, the flame response shows saturation at high forcing amplitudes. A newly constructed atmospheric test rig, specifically designed for the realization of high excitation amplitudes over a broad frequency range, is used to generate extremely high acoustic forcing power with velocity fluctuations of up to 100% of the mean flow. The test rig consists of a generic combustor with a premixed swirl-stabilized natural gas flame, where the upstream part has a variable length to generate adaptive resonances of the acoustic field. The OH∗ chemiluminescence response, with respect to velocity fluctuations at the burner, is measured for various excitation frequencies and amplitudes. From these measurements, an amplitude dependent flame transfer function is obtained. Phase-averaged OH∗ pictures are used to identify changes in the flame shape related to saturation mechanisms. For different frequency regimes, different saturation mechanisms are identified.

An Experimental Investigation of the Nonlinear Response of an Atmospheric Swirl-Stabilized Premixed Flame

2010 ◽  
Author(s):  
Sebastian Schimek ◽  
Jonas P. Moeck ◽  
Christian Oliver Paschereit
Keyword(s):  
Gas Turbines ◽  
Oscillation Amplitude ◽  
Network Models ◽  
Mean Flow ◽  
Test Rig ◽  
Linear Network ◽  
Modeling Tools ◽  
Velocity Fluctuations ◽  
Thermoacoustic Instabilities ◽  
Flame Response

Due to stringent emission restrictions, modern gas turbines mostly rely on lean premixed combustion. Since this combustion mode is susceptible to thermoacoustic instabilities, there is a need for modeling tools with predictive capabilities. Linear network models are able to predict the occurrence of thermoacoustic instabilities but yield no information on the oscillation amplitude. The prediction of the pulsation levels and hence an estimation whether a certain operating condition has to be avoided is only possible if information on the nonlinear flame response is available. Typically, the flame response shows saturation at high forcing amplitudes. A newly constructed atmospheric test rig, specifically designed for the realization of high excitation amplitudes over a broad frequency range, is used to generate extremely high acoustic forcing power with velocity fluctuations of up to 100% of the mean flow. The test rig consists of a generic combustor with a premixed swirl-stabilized natural gas flame, where the upstream part has a variable length to generate adaptive resonances of the acoustic field. The OH* chemiluminescence response, with respect to velocity fluctuations at the burner is measured for various excitation frequencies and amplitudes. From these measurements, an amplitude dependent flame transfer function is obtained. Phase-averaged OH* pictures are used to identify changes in the flame shape related to saturation mechanisms. For different frequency regimes, different saturation mechanisms are identified.

scholarly journals Design and Optimization of a Centrifugal Pump for Slurry Transport Using the Response Surface Method

Machines ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 60
Author(s):  
Khaled Alawadhi ◽  
Bashar Alzuwayer ◽  
Tareq Ali Mohammad ◽  
Mohammad H. Buhemdi
Keyword(s):  
Response Surface ◽  
Centrifugal Pump ◽  
Industrial Applications ◽  
Pump Efficiency ◽  
Optimized Design ◽  
Centrifugal Pumps ◽  
Local Pressure ◽  
Design And Optimization ◽  
Geometry Characteristic ◽  
Line Design

Since centrifugal pumps consume a mammoth amount of energy in various industrial applications, their design and optimization are highly relevant to saving maximum energy and increasing the system’s efficiency. In the current investigation, a centrifugal pump has been designed and optimized. The study has been carried out for the specific application of transportation of slurry at a flow rate of 120 m3/hr to a head of 20 m. For the optimization process, a multi-objective genetic algorithm (MOGA) and response surface methodology (RSM) have been employed. The process is based on the mean line design of the pump. It utilizes six geometric parameters as design variables, i.e., number of vanes, inlet beta shroud, exit beta shroud, hub inlet blade draft, Rake angle, and the impeller’s rotational speed. The objective functions employed are pump power, hydraulic efficiency, volumetric efficiency, and pump efficiency. In this reference, five different software packages, i.e., ANSYS Vista, ANSYS DesignModeler, response surface optimization software, and ANSYS CFX, were coupled to achieve the optimized design of the pump geometry. Characteristic maps were generated using simulations conducted for 45 points. Additionally, erosion rate was predicted using 3-D numerical simulations under various conditions. Finally, the transient behavior of the pump, being the highlight of the study, was evaluated. Results suggest that the maximum fluctuation in the local pressure and stresses on the cases correspond to a phase angle of 0°–30° of the casing that in turn corresponds to the maximum erosion rates in the region.

Predicting the Influence of Damping Devices on the Stability Margin of an Annular Combustor

2017 ◽  
Author(s):  
Max Zahn ◽  
Michael Betz ◽  
Moritz Schulze ◽  
Christoph Hirsch ◽  
Thomas Sattelmayer
Keyword(s):  
Resonance Frequency ◽  
Stability Margin ◽  
Numerical Approach ◽  
Acoustic Mode ◽  
Acoustic Properties ◽  
Azimuthal Mode ◽  
Acoustic Damping ◽  
Linearized Euler Equations ◽  
Annular Combustor ◽  
The Impact

A numerical modeling approach based on linearized Euler equations is applied to predict the linear stability of an annular combustor with and without dampers. The acoustic properties of all relevant combustor components such as damping devices, swirl burner characteristics, swirl flame dynamics, and combustor exit are individually evaluated via experimental and numerical approaches. All of the components are incorporated subsequently into the combustor model using impedances and acoustic transfer matrices to obtain an efficient procedure. This study focuses on using this approach to predict an annular combustor’s stability margin and to assess how dampers influence the modal dynamics of the first azimuthal mode. Stability predictions are successfully validated with experimental data. Different combustor components’ contributions to the acoustic damping of the entire system is also determined based on that numerical approach. Damper application in combustors can engender uncertainties in resonance frequency in the case of hot-gas ingestion. The impact of “detuned” resonators on the predicted damping rates with respect to a deviation in the resonance frequency and the eigenfrequency of the attenuated acoustic mode is therefore evaluated. The influence of dampers on the annular combustor’s stability margin is also determined.

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