Bernhard Ćosić

Nonlinear Instability Analysis for Partially Premixed Swirl Flames

Limit-cycle prediction of thermoacoustic instabilities for unstable practical gas turbine combustion systems is still a challenge for the gas turbine industry. The nonlinear stability analysis is especially demanding for highly turbulent swirling flames with significant equivalence ratio fluctuations. In the present study, a partially premixed swirl-stabilized flame at a Reynolds number of approximately 35,000 is investigated. An experimentally obtained flame describing function (FDF) is used for the determination of the thermoacoustic oscillation frequency and amplitude. Damping is obtained directly from measurements. The multi-microphone method is used to determine the amplitude dependent transfer function of the flame as well as the transfer function of the burner and the acoustic response of the boundary conditions. Solving the thermoacoustic modeling framework, with the measured transfer functions incorporated, yields frequency and amplitude of the self-excited limit cycle oscillation. The error between model and experimental results is thoroughly assessed. Measurements were made for various lengths of the combustion chamber exhaust gas tube to verify the results for different frequencies and amplitudes. Good agreement is found for the entire range of combustor lengths investigated. A sensitivity analysis of the linear flame transfer function to several operational parameters is provided allowing for an assessment of the limits of the nonlinear stability analysis approach. Furthermore, the effect of amplitude dependent damping is addressed.

Acoustic Response of a Helmholtz Resonator Exposed to Hot-Gas Penetration and High Amplitude Oscillations

Helmholtz resonators are often used in the gas turbine industry for the damping of thermoacoustic instabilities. To prevent thermal destruction, these devices are usually cooled by a purging flow. Since the acoustic velocity inside the neck of the resonator becomes very high already at moderate pressure oscillation levels, hot-gas penetration cannot always be fully avoided. This study extends a well-known nonlinear impedance model to include the influence of hot-gas intrusion into the Helmholtz resonator neck. A time-dependent but spatially averaged density function of the volume flow in the neck is developed. The steady component of this density function is implemented into the nonlinear impedance model to account for the effect of hot-gas intrusion. The proposed model predicts a significant shift in the resonance frequency of the damper towards higher frequencies, depending on the amplitude of the acoustic velocity in the neck and the temperature of the penetrating hot gas. Subsequently, the model is verified by the experimental investigation of two resonance frequencies (86 Hz and 128 Hz) for two hot gas temperatures (1470 K and 570 K) and various pressure oscillation amplitudes. The multimicrophone method, in combination with a microphone flush-mounted in the resonator volume, is used to determine the impedance of the Helmholtz damper. Additionally, a movable ultra-thin thermocouple was used to determine the degree of hot-gas penetration and the change of the mean temperature at various axial positions in the neck. A very good agreement between the model and the experimental data is obtained for all levels of pressure amplitudes and of hot-gas penetration depths. The mean air temperatures in the neck were accurately predicted too.

Optical Measurement of Local and Global Transfer Functions for Equivalence Ratio Fluctuations in a Turbulent Swirl Flame

Equivalence ratio fluctuations are known to be one of the key factors controlling thermoacoustic stability in lean premixed gas turbine combustors. The mixing and thus the spatio-temporal evolution of these perturbations in the combustor flow is, however, difficult to account for in present low-order modeling approaches. To investigate this mechanism, experiments in an atmospheric combustion test rig are conducted. To assess the importance of equivalence ratio fluctuations in the present case, flame transfer functions for different injection positions are measured. By adding known perturbations in the fuel flow using a solenoid valve, the influence of equivalence ratio oscillations on the heat release rate is investigated. The spatially and temporally resolved equivalence ratio fluctuations in the reaction zone are measured using two optical chemiluminescence signals, captured with an intensified camera. A steady calibration measurement allows for the quantitative assessment of the equivalence ratio fluctuations in the flame. This information is used to obtain a mixing transfer function, which relates fluctuations in the fuel flow to corresponding fluctuations in the equivalence ratio of the flame. The current study focuses on the measurement of the global, spatially integrated, transfer function for equivalence ratio fluctuations and the corresponding modeling. In addition, the spatially resolved mixing transfer function is shown and discussed. The global mixing transfer function reveals that despite the good spatial mixing quality of the investigated generic burner, the ability to damp temporal fluctuations at low frequencies is rather poor. It is shown that the equivalence ratio fluctuations are the governing heat release rate oscillation response mechanism for this burner in the low-frequency regime. The global transfer function for equivalence ratio fluctuations derived from the measurements is characterized by a pronounced low-pass characteristic, which is in good agreement with the presented convection–diffusion mixing model.Copyright

Impact of Shear Flow Instabilities on the Magnitude and Saturation of the 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.Copyright

Prediction of Pressure Amplitudes of Self-Excited Thermoacoustic Instabilities for a Partially Premixed Swirl-Flame

The prediction of the limit-cycle amplitude of thermoacoustically unstable practical gas turbine combustion systems remains a challenge for the gas turbine industry. The present study uses an experimentally obtained Flame Describing Function (FDF) for the determination of the thermoacoustic oscillation frequency and amplitude. In contrast to other studies, which investigated perfectly premixed laminar or marginally turbulent flames, this study deals with a highly turbulent swirl flame with spatial and temporal fuel???air unmixedness in an order of practical interest. A partially premixed swirl-stabilized flame is investigated at a Reynolds number of approximately 35 000. The Multi-Microphone-Method is used to determine the amplitude dependent transfer function of the flame as well as the transfer function of the burner and the acoustic response of the boundary conditions. The results are compared to OH* chemiluminescence measurements, which show a significant deviation in terms of the flame transfer function gain due to equivalence ratio fluctuations. The measured transfer functions are incorporated into a thermoacoustic modeling framework to determine frequency and amplitude of the self-excited limit cycle oscillation. Measurements were made for various lengths of the exhaust gas tube to verify the results for different frequencies and amplitudes. Good agreement is found for the entire range of combustor lengths investigated. The error between model and experimental results is thoroughly assessed.Copyright ?? 2013 by ASME

Amplitude-Dependent Flow Field and Flame Response to Axial and Tangential Velocity Fluctuations

The current paper investigates the nonlinear interaction of the flow field and the unsteady heat release rate and the role of swirl fluctuations. The test rig consists of a generic swirl-stabilized combustor fed with natural gas and equipped with a high-amplitude forcing device. The influence of the phase between axial and azimuthal velocity oscillations is assessed on the basis of the amplitude and phase relations between the velocity fluctuations at the inlet and the outlet of the burner. These relations are determined in the experiment with the multimicrophone-method and a two component laser Doppler velocimeter (LDV). Particle image velocimetry (PIV) and OH*-chemiluminescence measurements are conducted to study the interaction between the flow field and the flame. For several frequency regimes, characteristic properties of the forced flow field and flame are identified, and a strong amplitude dependence is observed. It is found that the convective time delay between the swirl generator and the flame has an important influence on swirl-number oscillations and the flame dynamics in the low-frequency regime. For mid and high frequencies, significant changes in the mean flow field and the mean flame position are identified for high forcing amplitudes. These affect the interaction between coherent structures and the flame and are suggested to be responsible for the saturation in the flame response at high forcing amplitudes.

Open-Loop Control of Combustion Instabilities and the Role of the Flame Response to Two-Frequency Forcing

Controlling combustion instabilities by means of open-loop forcing at non-resonant frequencies is attractive because neither a dynamic sensor signal nor a signal processor is required. On the other hand, since the mechanism by which this type of control suppresses an unstable thermoacoustic mode is inherently nonlinear, a comprehensive explanation for success (or failure) of open-loop control has not been found. The present work contributes to the understanding of this process in that it interprets open-loop forcing at non-resonant frequencies in terms of the flame’s nonlinear response to a superposition of two approximately sinusoidal input signals. For a saturation-type nonlinearity, the fundamental gain at one frequency may be decreased by increasing the amplitude of a secondary frequency component in the input signal. This effect is first illustrated on the basis of an elementary model problem. In addition, an experimental investigation is conducted at an atmospheric combustor test-rig to corroborate the proposed explanation. Open-loop acoustic and fuel-flow forcing at various frequencies and amplitudes is applied at unstable operating conditions that exhibit high-amplitude limit-cycle oscillations. The effectiveness of specific forcing parameters in suppressing self-excited oscillations is correlated with flame response measurements that include a secondary forcing frequency. The results demonstrate that a reduction in the fundamental harmonic gain at the instability frequency through the additional forcing at a non-resonant frequency is one possible indicator of successful open-loop control. Since this mechanism is independent of the system acoustics, an assessment of favorable forcing parameters, which stabilize thermoacoustic oscillations, may be based solely on an investigation of burner and flame.Copyright

Resonance Frequency of Helmholtz Dampers in the Presence of High-Temperature Grazing Flows

Thermoacoustic instabilities limit the operation of a gas turbine combustor under very lean conditions, which are required to achieve the strict regulations of emissions of NOx and CO2. An effective means to extend the operation window is a Helmholtz resonator, which provides a narrow-band damping of acoustic pressure amplitudes. While the prediction of the damping characteristic of a single volume Helmholtz resonator is well known under isothermal conditions, uncertainties still exist for non-isothermal conditions as they prevail in gas tubine combustors where the resonator volume and its neck are purged with colder air from the compressor that is released eventually through the neck mouth into the hot grazing flow in the combustion chamber. Based on the multi-microphone method, the reflection coefficent of a purged Helmholtz resonator mounted to a combustion test rig has been determined experimentally for different grazing flow temperatures. On basis of the results the change of the length correction of the resonator neck is modeled, being a function of the temperature difference and the excitation amplitude. Latter is provided by loudspeakers plugged to the combustor rig downstream of the Helmholtz resonator. It is shown, that the decay of the length correction for higher grazing flow temperatures basically scales with the density ratio between the hot combustion gases and the colder gas in the resonator neck, as suggested in recent publications. Small deviations are detected which can be explained by physical phenomena that have been observed by optical measurement methods. If these phenomena are incorporated into the model, the accuracy of estimation of the resonance frequency improves considerably.