Validation of Flame Transfer Function Reconstruction for Perfectly Premixed Swirl Flames

2004 ◽  
Author(s):  
A. Gentemann ◽  
C. Hirsch ◽  
K. Kunze ◽  
F. Kiesewetter ◽  
T. Sattelmayer ◽  
...  
Keyword(s):  
Transfer Function ◽  
Heat Release ◽  
Dynamic Behavior ◽  
Broad Band ◽  
Combustion Process ◽  
Single Frequency ◽  
Mean Flow ◽  
Swirl Number ◽  
Absolute Value ◽  
The Absolute

The introduction of lean premix combustion increases the susceptibility of the combustor to thermoacoustic instabilities. To control these instabilities, information about the dynamic behavior of the combustion process is necessary. The flame transfer function offers one possibility to describe the dynamic behavior of the combustion process. It relates velocity fluctuations through the burner to an overall heat release fluctuation caused by the flame. As the transfer function for turbulent premix swirl flames can not be derived accurately from first principles, an alternative approach is needed. This paper introduces and validates a method, based on computational fluid dynamics (CFD), to reconstruct flame transfer functions. A transient simulation of the turbulent reacting flow is performed with broad band excitation of the flow variables on the boundaries. On the basis of the resulting time series for velocity and heat release, the transfer function of the flame is reconstructed by application of a system identification procedure based on the Wiener-Hopf equation. This method is applied to a lean perfectly premixed swirl burner. The resulting transfer function is validated with experimental data up to frequencies of f = 400 Hz. Good qualitative agreement is observed between the two approaches. Remarkably, the absolute value of the flame transfer function (the ‘gain’ of the flame) is found to be larger than unity over a range of frequencies, even though fluctuations of heat release and velocity are normalized with their mean flow values. To gain insight into this phenomenon, the dynamic behavior of the flame is investigated in detail. This concerns in particular the interaction of velocity, heat release fluctuations, the swirl number, and fluctuations of flame position and shape. Instead of broad band excitation, single frequency excitation is applied on the boundary for these investigations. It is found that swirl number fluctuations are convected into the flame. At the frequency where the wavelength of those fluctuations agrees with the length scale of the flame, unburned gases accumulate in the combustor. The excess heat is released periodically, which causes the overshoot in the absolute value of the flame transfer function.

Flame Transfer Function Calculations for Combustion Oscillations

2001 ◽  
Author(s):  
M. Zhu ◽  
A. P. Dowling ◽  
K. N. C. Bray
Keyword(s):  
Transfer Function ◽  
Heat Release ◽  
Hot Spots ◽  
Mixture Fraction ◽  
Low Frequency ◽  
Single Frequency ◽  
Fuel Spray ◽  
Chamber Pressure ◽  
Iir Filter ◽  
Rate Of Combustion

Combustors with fuel-spray atomisers are particularly susceptible to a low-frequency oscillation at idle and sub-idle conditions. For aero-engine combustors, the frequency of this oscillation is typically in the range 50-120Hz and is commonly called ‘rumble’. The mechanism involves interaction between the plenum around the burner and the combustion chamber. Pressure variations in the plenum or the combustor alter the inlet air and fuel spray characteristics, thereby changing the rate of combustion. This in turn leads to local ‘hot spots’ which generate pressure oscillations as they convect through the downstream nozzle. In order to eliminate the combustion oscillations, it is essential to determine which fuel atomisers are particularly likely to lead to instability by quantifying their sensitivity to flow perturbations. This can be done by identifying the system through understanding the transfer function, which represents the relationship between the unsteadiness of combustion and the inlet fuel and air. In the present work, various types of signals are applied to produce a small change the inlet fuel and air flow rates, the response in the rate of heat release caused downstream was calculated and stored for subsequent analysis. Afterwards, the system transfer function is calculated by determining the coefficients of an IIR filter (Infinite Impulse Response) for which the output signal is the downstream heat release rate and the input signal is the inlet flow rate. The required transfer function then follows from the Fourier transform of this relationship. The resulting transfer functions are compared with those obtained by the forced harmonic oscillations at a fixed given frequency. Suitably chosen input signals accurately recover the results for harmonic forcing at a single frequency, but also give detailed information about the combustor response over a wide frequency range. There are two distinct forms to the low-frequency quasi-steady response. In the primary zone, the rate of combustion is influenced by the turbulence and is enhanced when the inlet air velocity is large. Near the edge of combustion zone, the rate of combustion depends on the mixture fraction and is high when the mixture fraction is close to the stoichiometric value. This generates ‘hot spots’ which convect into the dilution zone. At higher frequencies, the combustion lags this quasi-steady response through simple lag-laws and the relevant time delays have been identified.

Study of Combustion Instabilities Imposed by Inlet Velocity Disturbance in Combustor Using LES

2009 ◽  
Author(s):  
Kenji Sato ◽  
Ed Knudsen ◽  
Heinz Pitsch
Keyword(s):  
Transfer Function ◽  
Flow Field ◽  
Heat Release ◽  
Combustion Chamber ◽  
Combustion Process ◽  
Variable Density ◽  
Combustion Model ◽  
Combustion Instabilities ◽  
Inlet Velocity ◽  
Good Agreement

Stable combustion is one of the most important requirements for the development of heavy duty gas turbine engines that comply with stringent environmental regulations at high firing temperatures. In this research, one of the typical combustion instabilities which is caused by an acoustically forced velocity disturbance is investigated using variable density LES simulations. The G-equation approach for LES is used as the combustion model [1], and an experiment by Balachandran et al. [2, 3] is selected for case study. The velocity profiles in the experimental combustion chamber are compared with experimentally measured data at non-reacting conditions and it is confirmed that these are in good agreement. At the reacting conditions, predicted flame shapes are compared with OH PLIF measurements. The transfer function of the heat release due to inlet velocity forcing at 40 Hz and 160 Hz frequencies is also compared with the experimental data. These are in good agreement, including the nonlinear response of heat release. The transfer function is highly related to the flow field. The non-linearity of the transfer function can be traced to the interaction of the flow field in the combustion chamber with the combustion process itself.

Low-Order Modelling of Thermoacoustic Limit Cycles

2004 ◽  
Author(s):  
Simon R. Stow ◽  
Ann P. Dowling
Keyword(s):  
Transfer Function ◽  
Heat Release ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Acoustic Waves ◽  
Mean Flow ◽  
Velocity Perturbation ◽  
Linear Mode ◽  
The Mean ◽  
Low Order

Lean premixed prevaporised (LPP) combustion can reduce NOx emissions from gas turbines, but often leads to combustion instability. Acoustic waves produce fluctuations in heat release, for instance by perturbing the fuel-air ratio. These heat fluctuations will in turn generate more acoustic waves and in some situations self-sustained oscillations can form. The resulting limit cycles can have large amplitude causing structural damage. Thermoacoustic oscillations will have a low amplitude initially. Thus linear models can give stability predictions. An unstable linear mode will grow in amplitude until nonlinear effects become important and a limit cycle is achieved. While the frequency of the linear mode can provide a good approximation to that of the resulting limit cycle, linear theories give no prediction of its amplitude. A low-order model for thermoacoustic limit cycles in LPP combustors is described. The approach is based on the fact that the main nonlinearity is in the combustion response to flow perturbations. In LPP combustion, fluctuations in the inlet fuel-air ratio have been shown to be the dominant cause of unsteady combustion: these occur because velocity perturbations in the premix ducts cause a time-varying fuel-air ratio, which then convects downstream. If the velocity perturbation becomes comparable to the mean flow, there will be an amplitude-dependent effect on the equivalence ratio fluctuations entering the combustor and hence on the rate of heat release. A simple nonlinear flame model for this dependence is developed and is assumed to be the major non-linear effect on the limit cycle. Since the Mach number is low, the velocity perturbation can be comparable to the mean flow, with even reverse flow occurring, while the disturbances are still acoustically linear in that the pressure perturbation is still much smaller than the mean. Hence elsewhere the perturbations are treated as linear. In this nonlinear flame model, the flame transfer function describing the combustion response to changes in inlet flow is a function of both frequency and amplitude. The nonlinear flame transfer function is incorporated into a linear thermoacoustic network model for plane waves. Frequency, amplitude and modeshape predictions are compared with results from an atmospheric test rig. The approach is extended to circumferential waves in a thin annular geometry, where the nonlinearity leads to modal coupling.

Transfer Function Calculations for Aeroengine Combustion Oscillations

2005 ◽  
Vol 127 (1) ◽  
pp. 18-26 ◽  
Author(s):  
M. Zhu ◽  
A. P. Dowling ◽  
K. N. C. Bray
Keyword(s):  
Transfer Function ◽  
Heat Release ◽  
Hot Spots ◽  
Mixture Fraction ◽  
Low Frequency ◽  
Single Frequency ◽  
Fuel Spray ◽  
Chamber Pressure ◽  
Iir Filter ◽  
Rate Of Combustion

Combustors with fuel-spray atomizers are particularly susceptible to a low-frequency oscillation at idle and subidle conditions. For aeroengine combustors, the frequency of this oscillation is typically in the range 50–120 Hz and is commonly called “rumble.” The mechanism involves interaction between the plenum around the burner and the combustion chamber. Pressure variations in the plenum or the combustor alter the inlet air and fuel spray characteristics, thereby changing the rate of combustion. This in turn leads to local “hot spots” which generate pressure oscillations as they convect through the downstream nozzle. In order to eliminate the combustion oscillations, it is essential to determine which fuel atomizers are particularly likely to lead to instability by quantifying their sensitivity to flow perturbations. This can be done by identifying the system through understanding the transfer function, which represents the relationship between the unsteadiness of combustion and the inlet fuel and air. In the present work, various types of signals are applied to produce a small change in the inlet fuel and air flow rates, the response in the rate of heat release caused downstream was calculated and stored for subsequent analysis. Afterwards, the system transfer function is calculated by determining the coefficients of an IIR filter (Infinite Impulse Response) for which the output signal is the downstream heat release rate and the input signal is the inlet flow rate. The required transfer function then follows from the Fourier transform of this relationship. The resulting transfer functions are compared with those obtained by the forced harmonic oscillations at a fixed given frequency. Suitably chosen input signals accurately recover the results for harmonic forcing at a single frequency, but also give detailed information about the combustor response over a wide frequency range. There are two distinct forms to the low-frequency quasisteady response. In the primary zone, the rate of combustion is influenced by the turbulence and is enhanced when the inlet air velocity is large. Near the edge of combustion zone, the rate of combustion depends on the mixture fraction and is high when the mixture fraction is close to the stoichiometric value. This generates ‘hot spots’ which convect into the dilution zone. At higher frequencies, the combustion lags this quasi-steady response through simple lag-laws and the relevant time delays have been identified.

scholarly journals Effects of the Injector Design on the Transfer Function of Premixed Swirling Flames

2017 ◽  
Author(s):  
M. Gatti ◽  
R. Gaudron ◽  
C. Mirat ◽  
T. Schuller
Keyword(s):  
Transfer Function ◽  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Bluff Body ◽  
Transfer Functions ◽  
Thermal Power ◽  
Phase Lag ◽  
Swirl Number ◽  
Injector Design

This article reports a series of experiments on the dynamics of lean-premixed swirl-stabilized flames submitted to harmonic flowrate modulations. The flame transfer function is analyzed for different injector designs with a specific focus on conditions leading to the lowest heat release rate response for a given flowrate perturbation. Experiments are carried out at a fixed equivalence ratio and fixed thermal power. Transfer functions are measured for radial swirling vanes by modifying the diameter of the swirler injection holes, the diameter of the injection tube at the top of the swirler and the end piece diameter of a central insert serving as a bluff body. It is found that the lowest response depends on the forcing frequency and is obtained when the injector design features the largest swirl number. The transfer function of the studied flames features a minimum gain value which decreases for increasing swirl levels. This minimum value is found to be independent of the velocity forcing level and is only controlled by the level of swirl. An excessive swirl level however leads to flash-back of the perturbed flames inside the injector. The way the flame behaves at this forcing frequency is analyzed for a set of injectors featuring the same radial swirling vane design and different injection tube diameters or conical end pieces. It is found that at the condition corresponding to the lowest FTF gain, i.e. the injector with the largest swirl number, the upper and lower parts of the flame contribute to out of phase heat release oscillations, but they also both feature a reduced level of fluctuations. When the swirl number decreases, the FTF gain increases due to a reduction of the phase lag between heat release rate oscillations in the lower and the upper parts of the flame and more importantly due to a general increase of the level of heat release oscillations in both parts of the flame.

Impact of Shear Flow Instabilities on the Magnitude and Saturation of the Flame Response

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
Steffen Terhaar ◽  
Bernhard Ćosić ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Transfer Function ◽  
Shear Flow ◽  
High Speed ◽  
Transfer Functions ◽  
Flow Fields ◽  
Shear Layers ◽  
Flow Instabilities ◽  
Mean Flow ◽  
Swirl Number ◽  
Flame Response

Amplitude-dependent flame transfer functions, also denoted as flame describing functions, are valuable tools for the prediction of limit-cycle amplitudes of thermoacoustic instabilities. However, the effects that govern the transfer function magnitude at low and high amplitudes are not yet fully understood. It is shown in the present work that the flame response at perfectly premixed conditions is strongly influenced by the growth rate of vortical structures in the shear layers. An experimental study in a generic swirl-stabilized combustor was conducted in order to measure the amplitude-dependent flame transfer function and the corresponding flow fields subjected to acoustic forcing. The applied measurement techniques included the multi-microphone-method, high-speed OH*-chemiluminescence measurements, and high-speed particle image velocimetry. The flame response and the corresponding flow fields are assessed for three different swirl numbers at 196 Hz forcing frequency. The results show that forcing leads to significant changes in the time-averaged reacting flow fields and flame shapes. A triple decomposition is applied to the time-resolved data, which reveals that coherent velocity fluctuations at the forcing frequency are amplified considerably stronger in the shear layers at low forcing amplitudes than at high amplitudes, which is an indicator for a nonlinear saturation process. The strongest saturation is found for the lowest swirl number, where the forcing additionally detached the flame. For the highest swirl number, the saturation of the vortex amplitude is weaker. Overall, the amplitude-dependent vortex amplification resembles the characteristics of the flame response very well. An application of a linear stability analysis to the time-averaged flow fields at increasing forcing amplitudes yields the decreasing growth rates of shear flow instabilities at the forcing frequency. It therefore successfully predicts a saturation at high forcing amplitudes and demonstrates that the mean flow field and its modifications are of utmost importance for the growth of vortices in the shear layers. Moreover, the results clearly show that the amplification of vortices in the shear layers is an important driver for heat release fluctuations and their saturation.

Impact of Shear Flow Instabilities on the Magnitude and Saturation of the Flame Response

2013 ◽  
Author(s):  
Steffen Terhaar ◽  
Bernhard Ćosić ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Transfer Function ◽  
Shear Flow ◽  
High Speed ◽  
Transfer Functions ◽  
Flow Fields ◽  
Shear Layers ◽  
Flow Instabilities ◽  
Mean Flow ◽  
Swirl Number ◽  
Flame Response

Amplitude-dependent flame transfer functions, also denoted as flame describing functions, are valuable tools for the prediction of limit-cycle amplitudes of thermoacoustic instabilities. However, the effects that govern the transfer function magnitude at low and high amplitudes are not yet fully understood. It is shown in the present work that the flame response at perfectly premixed conditions is dominated by the growth rate of vortical structures in the shear layers. An experimental study in a generic swirl-stabilized combustor was conducted in order to measure the amplitude-dependent flame transfer function and the corresponding flow fields subjected to acoustic forcing. The applied measurement techniques included the Multi-Microphone-Method, high-speed OH*-chemiluminescence measurements, and high-speed Particle Image Velocimetry. The flame response and the corresponding flow fields are assessed for three different swirl numbers at 196 Hz forcing frequency. The results show that forcing leads to significant changes in the time-averaged reacting flow fields and flame shapes. A triple decomposition is applied to the time-resolved data, which reveals that coherent velocity fluctuations at the forcing frequency are amplified considerably stronger in the shear layers at low forcing amplitudes than at high amplitudes, an indicator for a nonlinear saturation process. The strongest saturation is found for the lowest swirl number, where the forcing additionally detached the flame. For the highest swirl number, the saturation of the vortex amplitude is weaker. Overall, the amplitude-dependent vortex amplification resembles the characteristics of the flame response very well. An application of linear stability analysis to the time-averaged flow fields at increasing forcing amplitudes yields decreasing growth rates of shear flow instabilities at the forcing frequency. It therefore successfully predicts a saturation at high forcing amplitudes and demonstrates that the mean flow field and its modifications are of utmost importance for the growth of vortices in the shear layers. Moreover, the results clearly show that the amplification of vortices in the shear layers is a dominant driver for heat release fluctuations and their saturation.

Linearised Theory for LPP Combustion Dynamics

2003 ◽  
Author(s):  
C. A. Armitage ◽  
R. S. Cant ◽  
A. P. Dowling ◽  
T. P. Hynes
Keyword(s):  
Heat Release ◽  
Combustion Chamber ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Broad Band ◽  
Mode Shapes ◽  
Complex Frequency ◽  
Mean Flow ◽  
Combustion Dynamics ◽  
Forcing Function

Gas turbines which are operated under lean, premixed, pre–vaporised (LPP) conditions are notoriously susceptible to self–excited oscillations. In the combustion chamber the unsteady heat released by combustion processes interacts with pressure fluctuations. The challenge is to develop a tool which can determine the frequency and stability characteristics of self–excited oscillations in realistic gas–turbine geometries. To this end, the flow through the gas turbine is described as far as possible by taking advantage of linearised theory and analytical models of the behaviour in the combustion chamber. First, a steady, mean flow solution for an idealised axi–symmetric combustor geometry is calculated using the inviscid Euler equations for continuity, momentum and energy with a specified distributed mean heat release. Superimposed on this is a linearised, three–dimensional perturbed flow in which the time and circumferential variation are described by a complex frequency and mode number respectively. Within this numerical model of the combustor a ‘flame model’ is used to describe the change in the rate of combustion due to inlet flow perturbations. The flame model may be given by an analytical expression—for example using a simple time lag with an expression proportional to the mean heat release in order to describe the unsteady heat release. An alternative approach would be to use a localised and detailed unsteady CFD calculation to determine the flow downstream of a generic premix duct geometry. If the flow is perturbed at the inlet a relationship between these fluctuations and the unsteady heat release may be obtained. In order to capture the response of the system to a wide frequency range an appropriately chosen broad–band forcing function may be used to perturb the flow. System identification techniques allow the transfer function to be extracted and a suitable flame model for the linearised Euler calculations may be constructed. Sample calculations of each aspect of the research will be presented to demonstrate the capabilities of each technique and the viability of combining the approaches towards the goal of aiding the design of gas–turbine combustors. Calculations using the linearised Euler methodology with analytical expressions for the flame model will demonstrate the capability of the approach to identify the frequencies of oscillation, mode shapes and zones of stability of particular combustor geometries.

scholarly journals Incentive Function of Audit Opinion for the Increase of Regional Operational Expenditure and Own-Source Revenues Through Sensitivity Analysis in Indonesia

2020 ◽  
Vol 11 (1) ◽  
pp. 20
Author(s):  
Muhammad Ikbal Abdullah ◽  
Andi Chairil Furqan ◽  
Nina Yusnita Yamin ◽  
Fahri Eka Oktora
Keyword(s):  
Sensitivity Analysis ◽  
Significant Influence ◽  
Provincial Government ◽  
Sensitivity Testing ◽  
Audit Opinion ◽  
Absolute Value ◽  
Operating Expenditure ◽  
The Absolute ◽  
Operational Expenditure

This study aims to analyze the sensitivity testing using measurements of realization of regional own-source revenues and operating expenditure and to analyze the extent of the effect of sample differences between Java and non-Java provinces by using samples outside of Java. By using sensitivity analysis, the results found the influence of audit opinion on the performance of the provincial government mediated by the realization of regional operating expenditure. More specifically, when using the measurement of the absolute value of the realization of regional operating expenditure it was found that there was a direct positive and significant influence of audit opinion on the performance of the Provincial Government. However, no significant effect of audit opinion was found on the realization value of regional operating expenditure and the effect of the realization value of regional operating expenditure on the performance of the Provincial Government. This result implies that an increase in audit opinion will be more likely to be used as an incentive for the Provincial Government to increase the realization of regional operating expenditure.

Die Bedeutung der Homogenisationsart und -intensität für die Größe und Konstanz der Sauerstoffaufnahme von Meerschweinchen-Leberhomogenat / The Influence of Mode and Intensity of Homogenization on the Absolute Value and Stability of Oxygen Consumption of Guinea Pig Liver Homogenates

1977 ◽  
Vol 32 (11-12) ◽  
pp. 908-912 ◽  
Author(s):  
H. J. Schmidt ◽  
U. Schaum ◽  
J. P. Pichotka
Keyword(s):  
Oxygen Uptake ◽  
Guinea Pig ◽  
Measuring Time ◽  
Pig Liver ◽  
Absolute Value ◽  
Modified Method ◽  
Simultaneous Measurements ◽  
Liver Homogenates ◽  
The Absolute ◽  
Guinea Pig Liver

Abstract The influence of five different methods of homogenisation (1. The method according to Potter and Elvehjem, 2. A modification of this method called Potter S, 3. The method of Dounce, 4. Homogenisation by hypersonic waves and 5. Coarce-grained homogenisation with the “Mikro-fleischwolf”) on the absolute value and stability of oxygen uptake of guinea pig liver homogenates has been investigated in simultaneous measurements. All homogenates showed a characteristic fall of oxygen uptake during measuring time (3 hours). The modified method according to Potter and Elvehjem called Potter S showed reproducible results without any influence by homogenisation intensity.

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