Prediction of Thermoacoustic Oscillations With a Linearised Euler Methodology

2015 ◽  
Author(s):  
C. F. Quaglia ◽  
R. S. Cant
Keyword(s):  
Acoustic Waves ◽  
High Frequency ◽  
Complex Geometry ◽  
Suitable Model ◽  
Mean Flow ◽  
Predictive Tool ◽  
Frequency Dependent ◽  
One Dimensional ◽  
Transverse Acoustic ◽  
Thermoacoustic Oscillations

Combustion instabilities in the aviation, aerospace and power generation industries have been a matter of concern for engineers since the 1950s, but with the increase in computer processing speed and the development of CFD it is now possible to attempt to predict frequencies and stability of a combustion system by numerical means, or by combining numerical, analytical and experimental approaches. Currently available analytical methods for the prediction of the frequency and stability of thermoacoustic oscillations make use of one-dimensional models where the frequency of oscillation is assumed to be low enough that only plane waves propagate in the burner, with higher order modes decaying quickly. While accurate and well-suited for longitudinal oscillations, these methods are unable to predict the frequency of instabilities where the unsteady heat release couples with the higher frequency transverse acoustic modes. Therefore a method is needed for applications where high frequency transverse oscillations are important. A method in which the linearised Euler equations are employed to calculate the propagation of acoustic waves is then suitable for solving this thermoacoustic problem. When a flame model that appropriately represents the frequency-dependent dynamics of the flame front is included, this method can predict the frequency of the oscillation resulting from the coupling between acoustics and combustion in an arbitrarily complex geometry. In this paper, a linearised Euler solver called INSTANT is introduced and validated against a well known theoretical model for the calculation of thermoacoustic oscillations in a one dimensional cylindrical duct with rigid walls and a radially uniform mean flow. The frequencies of oscillation and the modeshapes for this stable configuration match the theoretical ones well. An example calculation of transverse acoustic resonant mode is then presented. The ability of the code to predict the production of an entropy mode as a result of the interaction between an acoustic wave and a heat source region and its ability to predict frequencies of oscillation and modeshapes in a one dimensional configuration give confidence it can serve as a predictive tool for high frequency, transverse thermoacoustic oscillations in the more complex geometries of practical combustion systems once a suitable model for the frequency dependent flame response is included. The development of such a flame model is left for future work.

scholarly journals Damping and reflection coefficient measurements for an open pipe at low Mach and low Helmholtz numbers

1993 ◽  
Vol 256 ◽  
pp. 499-534 ◽  
Author(s):  
M. C. A. M. Peters ◽  
A. Hirschberg ◽  
A. J. Reijnen ◽  
A. P. J. Wijnands
Keyword(s):  
Experimental Data ◽  
Reflection Coefficient ◽  
Strouhal Number ◽  
Acoustic Waves ◽  
High Frequency ◽  
Nonlinear Behaviour ◽  
Mean Flow ◽  
Frequency Limit ◽  
Low Frequencies ◽  
Open Pipe

The propagation of plane acoustic waves in smooth pipes and their reflection at open pipe terminations have been studied experimentally. The accuracy of the measurements is determined by comparison of experimental data with results of linear theory for the propagation of acoustic waves in a pipe with a quiescent fluid. The damping and the reflection at an unflanged pipe termination are compared.In the presence of a fully developed turbulent mean flow the measurements of the damping confirm the results of Ronneberger & Ahrens (1977). In the high-frequency limit the quasi-laminar theory of Ronneberger (1975) predicts accurately the convective effects on the damping of acoustic waves. For low frequencies a simple theory combining the rigid-plate model of Ronneberger & Ahrens (1977) with the theoretical approach of Howe (1984) yields a fair prediction of the influence of turbulence on the shear stress. The finite response time of the turbulence near the wall to the acoustic perturbations has to be taken into account in order to explain the experimental data. The model yields a quasi-stationary limit of the damping which does not take into account the fundamental difference between the viscous and thermal dissipation observed for low frequencies.Measurements of the nonlinear behaviour of the reflection properties for unflanged pipe terminations with thin and thick walls in the absence of a mean flow confirm the theory of Disselhorst & van Wijngaarden (1980), for the low-frequency limit. It appears however that a two-dimensional theory such as proposed by Disselhorst & van Wijngaarden (1980) for the high-frequency limit underestimates the acoustical energy absorption by vortex shedding by a factor 2.5.The measured influence of wall thickness on the reflection properties of an open pipe end confirms the linear theory of Ando (1969). In the presence of a mean flow the end correction δ of an unflanged pipe end varies from the value at the high-Strouhal-number limit of δ/a = 0.61, with a the pipe radius, which is close to the value in the absence of a mean flow given by Levine & Schwinger (1948) of δ/a = 0.6133, to a value of δ/a = 0.19 in the low-Strouhal-number limit which is close to the value predicted by Rienstra (1983) of δ/a = 0.26.The pressure reflection coefficient is found to agree with the theoretical predictions by Munt (1977, 1990) and Cargill (1982b) in which a full Kutta condition is included. The accuracy of the theory is fascinating in view of the dramatic simplifications introduced in the theory. For a thick-walled pipe end and a pipe terminated by a horn the end correction behaviour is similar. It is surprising that the nonlinear behaviour at low frequencies and high acoustic amplitudes in the absence of mean flow does not influence the end correction significantly.The aero-acoustic behaviour of the pipe end is dramatially influenced by the presence of a horn. In the presence of a mean flow the horn is a source of sound for a critical range of the Strouhal number.The high accuracy of the experimental data suggests that acoustic measurements can be used for a systematic study of turbulence in unsteady flow and of unsteady flow separation.

Amplitude-Dependent Damping and Driving Rates of High-Frequency Thermoacoustic Oscillations in a Lab-Scale Lean-Premixed Gas Turbine Combustor

2021 ◽  
Author(s):  
Thomas Hofmeister ◽  
Thomas Sattelmayer
Keyword(s):  
Flow Field ◽  
Gas Turbine ◽  
Limit Cycle ◽  
High Frequency ◽  
Mean Flow ◽  
Gas Turbine Combustor ◽  
Cfd Simulations ◽  
The Mean ◽  
Amplitude Dependency ◽  
Thermoacoustic Oscillations

Abstract This paper presents numerical investigations of the amplitude-dependent stability behavior of thermoacoustic oscillations at screech level frequencies in a lean-premixed, swirl-stabilized, lab-scale gas turbine combustor. A hybrid Computational Fluid Dynamics / Computational AeroAcoustics (CFD / CAA) approach is applied to individually compute thermoacoustic damping and driving rates for various acoustic amplitude levels at the combustors' first transversal (T1) eigenfrequency. Forced CFD simulations with the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations mimic the real combustor's rotating T1 eigenmode. An increase of the forcing amplitude over time allows observation of the amplitude-dependent flow field and flame evolution. In accordance with measured OH*-chemiluminescence images, a pulsation amplitude-dependent flame contraction is reproduced in the CFD simulations. At several amplitude levels, period-averaged flow fields are then denoted as reference states, which serve as inputs for the CAA part. There, eigenfrequency simulations with linearized flow equations are performed with the Finite Element Method (FEM). The outcomes are damping and driving rates as a response to the amplitude-dependency of the mean flow field. It is found that driving due to flame-acoustics interactions governs a weak amplitude-dependency, which agrees with experimentally based studies at the authors' institute. This disqualifies the perception of heat release saturation as the root-cause for limit-cycle oscillations in this high-frequency thermoacoustic system. Instead, significantly increased dissipation due to the interaction of acoustically induced vorticity perturbations with the mean flow is identified, which may explain the formation of a limit-cycle.

A Time-Domain Network Model for Nonlinear Thermoacoustic Oscillations

2008 ◽  
Author(s):  
Simon R. Stow ◽  
Ann P. Dowling
Keyword(s):  
Heat Release ◽  
Frequency Domain ◽  
Limit Cycle ◽  
Network Model ◽  
Time Domain ◽  
Acoustic Waves ◽  
Mean Flow ◽  
The Mean ◽  
The Time Domain ◽  
Thermoacoustic Oscillations

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 linear oscillations grow into large amplitude self-sustained oscillations. The resulting limit cycles can cause structural damage. Thermoacoustic oscillations will have a low amplitude initially. Thus linear models can describe the initial growth and hence give stability predictions. An unstable linear mode will grow in amplitude until nonlinear effects become sufficiently important to achieve a limit cycle. While the frequency of the linear mode can often provide a good approximation to that of the resulting limit cycle, linear theories give no prediction of its resulting amplitude. In previous work, we developed a low-order frequency-domain method to model thermoacoustic limit cycles in LPP combustors. This was based on a ‘describing function’ approach and is only applicable when there is a dominant mode and the main nonlinearity is in the combustion response to flow perturbations. In this paper that method is extended into the time domain. The main advantage of the time-domain approach is that limit-cycle stability, the influence of harmonics, and the interaction between different modes can be simulated. 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. 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 while the combustion response to flow velocity and equivalence ratio fluctuations must be modelled nonlinearly, the flow perturbations generated as a result of the unsteady combustion can be treated as linear. In developing a time-domain network model for nonlinear thermoacoustic oscillations an initial frequency-domain calculation is performed. The linear network model, LOTAN, is used to categorise the combustor geometry by finding the transfer function for the response of flow perturbations (at the fuel injectors, say) to heat-release oscillations. This transfer function is then converted into the time domain through an inverse Fourier transform to obtain the Green’s function, which thus relates unsteady flow to heat release at previous times. By combining this with a nonlinear flame model (relating heat release to unsteady flow at previous times) a complete time-domain solution can be found by stepping forward in time. If an unstable mode is present, its amplitude will initially grow exponentially (in accordance with linear theory) until saturation effects in the flame model become significant, and eventually a stable limit cycle will be attained. The time-domain approach enables determination of the limit-cycle. In addition, the influence of harmonics and the interaction and exchange of energy between different modes can be simulated. These effects are investigated for longitudinal and circumferential instabilities in an example combustor system and results are compared to frequency-domain limit-cycle predictions.

Single-electron transport in a one-dimensional channel by high-frequency surface acoustic waves

1997 ◽  
Vol 56 (23) ◽  
pp. 15180-15184 ◽  
Author(s):  
V. I. Talyanskii ◽  
J. M. Shilton ◽  
M. Pepper ◽  
C. G. Smith ◽  
C. J. B. Ford ◽  
...  
Keyword(s):  
Electron Transport ◽  
Acoustic Waves ◽  
High Frequency ◽  
Surface Acoustic Waves ◽  
Single Electron ◽  
One Dimensional ◽  
Single Electron Transport

Pulsation-Amplitude-Dependent Flame Dynamics of High-Frequency Thermoacoustic Oscillations in Lean-Premixed Gas Turbine Combustors

2017 ◽  
Author(s):  
Frederik M. Berger ◽  
Tobias Hummel ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Heat Release ◽  
Gas Turbine ◽  
Growth Rates ◽  
High Frequency ◽  
Individual Growth ◽  
Mean Flow ◽  
Flame Dynamics ◽  
Pulsation Amplitude ◽  
The Mean ◽  
Thermoacoustic Oscillations

This paper presents the experimental investigation of pulsation-amplitude-dependent flame dynamics associated with transverse thermoacoustic oscillations at screech level frequencies in a generic gas turbine combustor. Specifically, the flame behavior at different levels of pulsation amplitudes is assessed and interpreted. Spatial dynamics of the flame are measured by imaging the OH* chemiluminescence signal synchronously to the dynamic pressure at the combustor’s face plate. First, linear thermoacoustic stability states, modal dynamics, as well as flame-acoustic phase relations are evaluated. It is found that the unstable acoustic modes converge into a predominantly rotating character in the direction of the mean flow swirl. Furthermore, the flame modulation is observed to be in phase with the acoustic pressure at all levels of the oscillation amplitude. Second, distributed flame dynamics are investigated by means of visualizing the mean and oscillating heat release distribution at different pulsation amplitudes. The observed flame dynamics are then compared against numerical evaluations of the respective amplitude-dependent thermoacoustic growth rates, which are computed using analytical models in the fashion of a non-compact flame-describing function. While results show a nonlinear contribution for the individual growth rates, the superposition of flame deformation and displacements balances out to a constant flame driving. This latter observation contradicts the state-of-the-art perception of root-causes for limit-cycle oscillations in thermoacoustic gas turbine systems, for which the heat release saturates with increasing amplitudes. Consequently, the systematic observations and analysis of amplitude-dependent flame modulation shows alternative paths to the explanation of mechanisms that might cause thermoacoustic saturation in high frequency systems.

Amplitude-Dependent Damping and Driving Rates of High-Frequency Thermoacoustic Oscillations in a Lab-Scale Lean-Premixed Gas Turbine Combustor

2021 ◽  
Author(s):  
Thomas Hofmeister ◽  
Thomas Sattelmayer
Keyword(s):  
Flow Field ◽  
Gas Turbine ◽  
High Frequency ◽  
Mean Flow ◽  
Gas Turbine Combustor ◽  
Cfd Simulations ◽  
Root Cause ◽  
The Mean ◽  
Amplitude Dependency ◽  
Thermoacoustic Oscillations

Abstract This paper presents the numerical investigations of amplitude-dependent stability behavior of thermoacoustic oscillations at screech level frequencies in a lean-premixed, atmospheric, swirl-stabilized, lab-scale gas turbine combustor. A hybrid Computational Fluid Dynamics / Computational AeroAcoustics (CFD / CAA) approach is applied to individually compute thermoacoustic damping and driving rates for various acoustic amplitude levels at the combustors’ first transversal (T1) eigenfrequency. Harmonically forced CFD simulations with the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations mimic the real combustor’s rotating T1 eigenmode. A slow and monotonous increase of the forcing amplitude over time allows observation of the amplitude-dependent flow field and flame evolution. In accordance with measured OH*-chemiluminescence images, a pulsation amplitude-dependent flame contraction is reproduced in the CFD simulations, where acoustically induced backflow at the combustion chamber inlet is identified as the root-cause of this phenomenon. At several amplitude levels, period-averaged flow fields are then denoted as reference states, which serve as inputs for the CAA part. There, eigenfrequency simulations with linearized flow equations are performed with the Finite Element Method (FEM). The outcomes are damping and driving rates as a response to the amplitude dependency of the mean flow field, which combined give the net thermoacoustic growth rate. It is found that driving due to flame-acoustics interactions only governs a weak amplitude dependency, which agrees with prior, experimentally based studies at the authors’ institute. This disqualifies the perception of heat release saturation as the root-cause for limit-cycle oscillations — at least in this high-frequency thermoacoustic system. Instead, significantly increased dissipation due to the interaction of acoustically induced vorticity perturbations with the mean flow is identified, which may explain the formation of a limit-cycle.

A Time-Domain Network Model for Nonlinear Thermoacoustic Oscillations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Simon R. Stow ◽  
Ann P. Dowling
Keyword(s):  
Heat Release ◽  
Frequency Domain ◽  
Limit Cycle ◽  
Network Model ◽  
Time Domain ◽  
Acoustic Waves ◽  
Mean Flow ◽  
The Mean ◽  
The Time Domain ◽  
Thermoacoustic Oscillations

Lean premixed prevaporized (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 linear oscillations grow into large-amplitude self-sustained oscillations. The resulting limit cycles can cause structural damage. Thermoacoustic oscillations will have a low amplitude initially. Thus linear models can describe the initial growth and hence give stability predictions. An unstable linear mode will grow in amplitude until nonlinear effects become sufficiently important to achieve a limit cycle. While the frequency of the linear mode can often provide a good approximation to that of the resulting limit cycle, linear theories give no prediction of its resulting amplitude. In previous work, we developed a low-order frequency-domain method to model thermoacoustic limit cycles in LPP combustors. This was based on a “describing-function” approach and is only applicable when there is a dominant mode and the main nonlinearity is in the combustion response to flow perturbations. In this paper that method is extended into the time domain. The main advantage of the time-domain approach is that limit-cycle stability, the influence of harmonics, and the interaction between different modes can be simulated. 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. 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 while the combustion response to flow velocity and equivalence ratio fluctuations must be modeled nonlinearly, the flow perturbations generated as a result of the unsteady combustion can be treated as linear. In developing a time-domain network model for nonlinear thermoacoustic oscillations an initial frequency-domain calculation is performed. The linear network model, LOTAN, is used to categorize the combustor geometry by finding the transfer function for the response of flow perturbations (at the fuel injectors, say) to heat-release oscillations. This transfer function is then converted into the time domain through an inverse Fourier transform to obtain Green’s function, which thus relates unsteady flow to heat release at previous times. By combining this with a nonlinear flame model (relating heat release to unsteady flow at previous times) a complete time-domain solution can be found by stepping forward in time. If an unstable mode is present, its amplitude will initially grow exponentially (in accordance with linear theory) until saturation effects in the flame model become significant, and eventually a stable limit cycle will be attained. The time-domain approach enables determination of the limit cycle. In addition, the influence of harmonics and the interaction and exchange of energy between different modes can be simulated. These effects are investigated for longitudinal and circumferential instabilities in an example combustor system and the results are compared with frequency-domain limit-cycle predictions.

Pulsation-Amplitude-Dependent Flame Dynamics of High-Frequency Thermoacoustic Oscillations in Lean-Premixed Gas Turbine Combustors

2017 ◽  
Vol 140 (4) ◽  
Author(s):  
Frederik M. Berger ◽  
Tobias Hummel ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Heat Release ◽  
Gas Turbine ◽  
Growth Rates ◽  
High Frequency ◽  
Individual Growth ◽  
Mean Flow ◽  
Flame Dynamics ◽  
Pulsation Amplitude ◽  
The Mean ◽  
Thermoacoustic Oscillations

This paper presents the experimental investigation of pulsation-amplitude-dependent flame dynamics associated with transverse thermoacoustic oscillations at screech level frequencies in a generic gas turbine combustor. Specifically, the flame behavior at different levels of pulsation amplitudes is assessed and interpreted. Spatial dynamics of the flame are measured by imaging the OH⋆ chemiluminescence (CL) signal synchronously to the dynamic pressure at the combustor's face plate. First, linear thermoacoustic stability states, modal dynamics, and flame-acoustic phase relations are evaluated. It is found that the unstable acoustic modes converge into a predominantly rotating character in the direction of the mean flow swirl. Furthermore, the flame modulation is observed to be in phase with the acoustic pressure at all levels of the oscillation amplitude. Second, distributed flame dynamics are investigated by means of visualizing the mean and oscillating heat release distribution at different pulsation amplitudes. The observed flame dynamics are then compared against numerical evaluations of the respective amplitude-dependent thermoacoustic growth rates, which are computed using analytical models in the fashion of a noncompact flame-describing function. While results show a nonlinear contribution for the individual growth rates, the superposition of flame deformation and displacement balances out to a constant flame driving. This latter observation contradicts the state-of-the-art perception of root-causes for limit-cycle oscillations in thermoacoustic gas turbine systems, for which the heat release saturates with increasing amplitudes. Consequently, the systematic observations and analysis of amplitude-dependent flame modulation shows alternative paths to the explanation of mechanisms that might cause thermoacoustic saturation in high frequency systems.

High-frequency, "quantum" and electromechanical effects in quasi-one-dimensional charge density wave conductors

2013 ◽  
Vol 183 (1) ◽  
pp. 33-54 ◽  
Author(s):  
Vadim Ya. Pokrovskii ◽  
Sergey G. Zybtsev ◽  
Maksim V. Nikitin ◽  
Irina G. Gorlova ◽  
Venera F. Nasretdinova ◽  
...  
Keyword(s):  
Charge Density ◽  
High Frequency ◽  
Charge Density Wave ◽  
Density Wave ◽  
One Dimensional ◽  
Electromechanical Effects
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