Flame features and oscillation characteristics in near-blowout swirl-stabilized flames using highspeed OH-PLIF and mode decomposition methods

Zhen CAO, Xin YU, Jiangbo PENG,*, Bin HU, Zhonghao WANG,Yang YU, Long GAO, Minghong HAN, Xun YUAN, Guohua WU

a National Key Laboratory of Science and Technology on Tunable Laser, Harbin Institute of Technology, Harbin 150001, China

b Institute of Opt-Electronics, Harbin Institute of Technology, Harbin 150001, China

c Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China

d School of Aeronautics and Astronautics, University of Chinese Academy of Sciences, Beijing 100190, China

KEYWORDS Dynamic mode decomposition (DMD);High-speed OH-PLIF;Moment descriptors;Near-blowout;Proper orthogonal decomposition (POD)

Abstract Flame features and dynamics are important to the explanation and prediction of a lean blowout(LBO)phenomenon.In this paper,recognition of near-LBO flame features and oscillation characterization methods were proposed based on flame spectroscopic images. High-speed planar laser-induced fluorescence measurements of OH were used to capture unique dynamic features such as the local extinction and reignition feature and entrained reactant pockets. The Zernike moment demonstrated a good performance in recognition of stability and near-LBO conditions,though the geometric moment had more advantages to characterize frequency characteristics. Low-frequency oscillations, especially at the obvious self-excited oscillation frequency around 200 Hz, were found when approaching an LBO condition,which can be expected to be used as a novel prediction characteristic parameter of the flameout limit. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) were used to conduct dynamic analysis of near-LBO flames. POD modes spectra showed the unique frequency characteristics of stable and near-LBO flames, which were basically in line with those at the heat-release frequency. The primary POD modes demonstrated that the radial vibration mode dominated in a stable flame, while the rotation mode was found to exist in a near-LBO flame.Analysis of modal decomposition showed that flame shedding and agminated entrained reactant pockets were responsible for generating self-excited flame oscillations.

1. Introduction

In recent years, high-dynamic flame state diagnosis has generally been an active field of research in aero-engine combustors for state-of-the-art systems that extend the performance envelope.1-4Flame evolution features including flame ignition,stabilization, propagation, and extinction have provided a lot of convenience for understanding complex combustion phenomena and developing high-precision prediction models.5-7Due to the complex turbulence-chemistry interaction,it is challenging to achieve accurate theoretical prediction of lean blowout(LBO),8-10which plays a significant role in the operational envelope of engines. The instability close to LBO conditions can be associated with changes in flame shape, area, and heat-release rate.11With the explosive development of stateof-the-art laser spectroscopy, several LBO semi-empirical corrections can be obtained based on the unique and universal features of phenomenological observations, further enabling the prediction of LBO limits.8Non-intrusive spectroscopy techniques such as OH* or CH* chemiluminescence imaging have been stimulated and developed to monitor combustion processes for the recognition of flame instability.12-14However, due to the multi-dimensional nature of the flow field and signal-integral characteristics, chemiluminescence measurements results are not only difficult to individuate and understand the regime of stability and instability,but also sensitive to background emission noise. In general, continuous high-speed planar laser-induced fluorescence (PLIF) imaging has great advantages to acquire abundant local flame features that can be used for mechanism analysis and prediction,which has been the top interest of performance and enablement evaluation of industrial-type combustors.15Therefore,the focus of this paper is the recognition of flame features and oscillation characterization using the high-speed OH-PLIF technique and advanced mode decomposition methods, which plays a major role in the explanation and prediction of complex combustion phenomena.

Swirl-stabilized flame is expected to be the main combustion mode in aero and stationary gas turbines. To reduce pollutant discharge, especially NOx, advanced gas turbine combustors usually operate under a lean condition due to the temperature limit. Unfortunately, lean flames at a low equivalence ratio are susceptible to dynamic instabilities, and global blowout occurs easily.16At present, the complexity of engine geometries makes the air flow rate not measured accurately,so the equivalence ratio can no longer be used as a reliable indicator for evaluating LBO.Shanbogue et al.16reviewed the dynamics and phenomenology of the LBO process in bluff body stabilized flames,and two dynamic features were considered as two distinct stages when recirculation stabilized flames approached blowoff.The first stage was characterized by local extinction along the flame sheet, but the flame structure and flow field were not largely influenced.The second stage demonstrated the phenomena of flame flapping and large-scale wake disruption. To accurately assess the LBO safety margin, several quantitative detection indices have been presented to predict the proximity to LBO, including the normalized CH*chemiluminescence root mean square(NRMS)and normalized cumulative duration.17Furthermore, near-LBO features including obvious low-frequency oscillations and a uniform heat-release distribution have been reported by Yi et al.18Furthermore, several studies have been conducted to investigate the dynamics of a near-LBO swirl-stabilized flame in a gas turbine model combustor using chemiluminescence imaging and simultaneous OH and CH2O-PLIF measurements.19Similarly,results have demonstrated that a near-LBO flame has some unique features relative to a stable flame,such as the extinction of the flame root and more entrained reactant pockets. The flame root played a significant role in flame stability,featuring frequent extinction and reignition near an LBO condition,which has been considered as an oscillation cycle. However,detailed oscillation process and frequency spectrum characteristics have not been reported when approaching LBO. Potential oscillation modes and flame morphology during the transition from a stable flame to an unstable one should be investigated in further study.

Spectral, statistical, and wavelet-based methods have been developed to correlate extracted parameters with physical quantities that characterize unstable flame behaviors.11,21It is generally discussed around the acquired signal intensity.However, the physical meanings represented are difficult to demonstrate or require a rigorous and careful calibration process.22Nowadays,some novel feature extraction methods have been developed to obtain the most relevant features of an image and analyze the properties of an image feature, which are used for the final classification or identification of specific features.For instance,moment descriptors based on the shape feature have been widely used in the image recognition field because of their excellent ability to express global features.The Zernike moment23and Hu’s seven moments24have been confirmed to be highly sensitive to the shape features of an image, and further the grayscale distribution and boundary shape of an interest area can be well described. Khare et al.25used the Zernike moment to conduct object classification and confirmed that translation and rotation-invariance properties were especially beneficial for describing the shapes and orientations of objects. Yadav et al.26proposed a moment invariants feature extraction technique and achieved an intelligent identification of moving object detection. They used Hu’s seven moments invariants as the input feature quantity of the classifier. To our knowledge, the recognition and oscillation characterization of a flame state based on moment features have not been reported, which is expected to provide a new insight into flame dynamics close to an LBO condition.Recently, advanced modal decomposition methods have risen in response to the understanding of flame dynamics.For example, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have been widely applied in the turbulent combustion environment to explain complex interaction details.27,28Kopp-Vaughan et al.29applied the POD method to quantitatively investigate flame front dynamics through a blowoff process in bluff body stabilized flames,and primary POD modes demonstrated Benard-von Karman vortex shedding just prior to blowoff. Zhang et al.30studied the flame structures and dynamics of kerosene fuel under stable and near-LBO conditions in a laboratory-scale aerocombustor. POD analysis results of OH* chemiluminescence showed the transitions from the rotation mode to the vibration mode,and identified the important fluctuation modes of staged lean premixed pre-vaporized (LPP) combustion near LBO.Han et al.31illustrated the interactions between pilot and main flames in a stratified swirl burner. Results showed a phenomenon of beating oscillation with two frequencies (198 Hz and 223 Hz),and the coherent structures during the oscillation were extracted by means of the DMD method to demonstrate the heat release dynamics, which attributed to the so-called bulk oscillation and a convective motion. Nakaya et al.32investigated supersonic combustion behaviors by a POD and DMD conjoint analysis of high-speed imaging of CH*chemiluminescence.DMD analysis results showed the same frequency range as that of the fast Fourier transform(FFT) of low-rank POD modes, and fundamental combustion frequencies and typical combustion modes were obtained.

As the above discussed, most studies associated with swirlstabilized flame dynamics aimed at a phenomenological observation of a near-LBO condition, and eventually characterized its main features. However, detailed oscillation frequency characteristics and dominant pulsation modes were rarely mentioned, especially the transition from a stable condition to instability, i.e., a near-LBO condition. The present study aimed to conduct frequency analysis and identify the effects of the global equivalence ratio on flame local features, oscillation frequencies,and pulsation modes,as a fundamental study of lean swirl-stabilized combustion. The OH-PLIF technique with a repetition of 1 kHz was used to capture the unique flame dynamic information during stable and near-LBO conditions.Moment descriptors based on the flame shape feature were used for the recognition and oscillation characterization. The frequency characteristic was demonstrated using the Zernike moment invariants and Hu’s seven moments invariants for the first time. Finally, POD and DMD methods were applied to analyze frequency characteristics and flame pulsation modes.Time and spatial pulsation characteristics were investigated. The present study aimed to characterize the unique oscillation characteristics of a near-LBO flame. Obtained results were expected to predict the onset of LBO and conduct active LBO control according to the phenomenological observation in an engineering application.

2. Experimental details

2.1. Optics and combustor

A schematic representation of the optical measurement system is shown in Fig. 1. Details of the high-speed OH-PLIF system have already been reported in our previous work,33and therefore only a brief description will be provided here. The key of the high-speed PLIF system is a pumped laser, and a highspeed Nd:YAG laser with high output energy was selfresearched,which generated 30 mJ/pulse at 532 nm with a repetition of 1 kHz. A high-speed dye laser (Sirah Credo, with Rhodamine 6G) was pumped to obtain UV(UltraViolet)pulses of 1.6 mJ at 1 kHz.High-energy ultraviolet pulses allow to obtain spectroscopic images with high signal-to-noise ratios and tolerate the transmittance loss of combustor window segments in engineering applications. To investigate detailed flame dynamics, a nearly 6-cm laser sheet was generated by the sheet forming optics to cover the entire swirl flame area.Then, the intensified CMOS (Complementary Metal-Oxide-Semiconductor)array has 1856×970 pixels with an operation rate of 1 kHz. The field of view was set to a 70 m (width)×50 m (height) region above the nozzle, giving a spatial resolution of about 67 μm per pixel. In our experiment, an optically accessible gas turbine model combustor was employed. The design of this swirl-stabilized burner was based on the double swirl burner model of German Aerospace Center (DLR).34However, the difference was that the fuel nozzle outlet of the burner model used here was in the same plane as the air nozzle outlet, resulting in that swirl methane fuel carried out nonpremixed combustion with the swirl air. The burning onset or the flame root behavior can be captured by optical measurement techniques. Furthermore, the non-premixed combustion mode also widely exists in aero-engine combustors, which can be used to study non-premixed flame behaviors in different combustion states. It is beneficial to extend the stable operation limit and drive the innovation of engine design.The injector assembly consisted of a circular air nozzle,an annular fuel nozzle, and a co-annular outer air nozzle. The outlet diameter of the circular air nozzle was 15 mm, which was connected to the internal swirl generator with an inner swirl angle of 45°.The internal diameter of the annular air nozzle connected to the external swirl generator was 17 mm,and the external diameter was gradually expanded from 27 mm to 30 mm.The outer swirl angle was 60°. The fuel CH4was transported into the annular fuel intake chamber in three strands, and the inlet chamber was connected to the fuel nozzle (an inner diameter of 15.6 mm and an outer diameter of 16.4 mm) through six oblique cut holes.Eventually,both fuel and air were in a swirling state. By reducing the flow of methane while keeping the total flow of air constant,a series of equivalence ratios ranging from 0.1-0.6 was established to investigate the flame dynamics during stable and near-LBO conditions.

Fig. 1 Experimental setup for OH-PLIF measurements.

2.2. Feature extraction and mode decomposition methods

Continuous high-speed PLIF measurements have great advantages in obtaining large amounts of flame data with short time intervals.High-resolution two-dimensional planar information is frequently used to analyze the dynamic characteristics of flames. However, the huge amount of data with large redundancy undoubtedly increases the analysis difficulty. In the paper, some efficient feature extraction and analysis methods were proposed to meet the research demand for flame state recognition and combustion oscillation characterization. The Zernike moment and Hu’s seven moments were used to recognize the flame state between stable and near-LBO flames. The principal component analysis (PCA) method was used to reduce the dimension of raw data and reveal the main data features.Then,the data set was mapped into a new feature space to achieve state classification.The PCA method is a multivariate statistical analysis method that realizes the transformation from high-dimensional variables to unrelated low-dimensional variables without changing the original information. The method can select fewer variables to reflect the original information as much as possible. The moment invariants usually introduce a set of complex polynomials to form a feature set.For example, the Zernike moment is a complete orthogonal moment defined in the interior of the unit circle ofx2+y2=1, and the calculation form can be expressed as follows:

where Anmis the amplitude of the Zernike moment, and the variants n and m represent the order and multiplicity of the moment, respectively; ρ and θ represent the polar diameter and polar angle in polar coordinates, respectively; Vnmis the kernel function, and the detailed description of the algorithm can be found in Refs.23,25. In principle, the Zernike moment can construct a moment of any order,and the higher the order is, the more details it can represent. Meanwhile, Hu’s seven geometric invariant moments are constructed using the central moment orders 2 and 3,which can also effectively describe the features of an image.24,26On the other hand, two advanced mode decomposition methods, i.e., POD and DMD, were adopted to conduct dynamic analysis, which are based on a snapshot-based method for the high-speed OH-PLIF technique at 1 kHz.The mode analysis objective is the flame structure and obtaining a significant coherent structure for dynamic analysis. A total of 2000 images were provided as POD and DMD analysis data. The mechanism of both being used here is based on the idea of singular value decomposition. In DMD analysis, the detailed algorithm of the DMD can be found in Refs.35,36.The effect of data noise on DMD analysis has been considered preliminarily in our previous work.37The extraction accuracy of singular values can be estimated to address the effect of noise on experimental results. As for the POD process,38firstly, flame images were vectorized to form a matrixX= ［x1，x2，...，xn-1］, and then the singular value decomposition of X is represented as.

where the matrix U represents the spatial distribution of different POD modes. The diagonal matrix Σ expresses the singular value of data and reflects the pulsating energy of different POD modes. Traditionally, the diagonal matrix was arranged in the order from large to small,so the higher the order is,the greater the pulsation energy is. In the dynamic analysis process, the first few modes played a significant role in the flame pulsation or oscillation process, which should be paid attention to in further study.Each column in the matrix V consisted of the time coefficient vectors of each mode. Therefore, by FFT analysis of the time coefficients, the time characteristics of each mode pulsation could be characterized to analyze the periodic oscillation characteristics of modes.

3. Results and discussions

3.1. Flame feature and oscillation characterization

Fig. 2 Typical time-series OH-PLIF images at stable (φ=0.6) and near-LBO (φ=0.2) conditions.

The high-speed PLIF technique has great potential to describe the highly dynamic spatial-temporal evolution of flame features. Dynamic features including periodic flame behavior and local extinction can be found based on unique phenomenological observations, enabling to further uncover the underlying mechanisms using post-processing algorithms. In the present paper, by decreasing the global equivalence ratio φ, favored flame conditions were investigated. Note that the flame could not be built below the equivalence ratio of the experimental study. Therefore, unique LBO features were allowed to be investigated based on phenomenological detections. In Fig. 2, instantaneous time-series OH-PLIF images for a swirl-stabilized flame during stable and near-LBO conditions are demonstrated. The reaction zones of the two conditions took place in different locations. In the stable condition, the flame front was widely distributed than that of the near-LBO condition. It could be seen that the major part of OH radicals existed in the inner recirculation zone (IRZ)and the inner shear layer(ISL)belonging to obvious characteristics of swirling flow. Similar results have been reported by Sto¨hr et al.39A local extinction feature was clearly found in the flame root, indicated by a red arrow, corresponding to the decreasing OH concentration. The flame root has been confirmed to suffer the effect of a high strain rate and tend to cause a stretch extinction of the flame.34Meanwhile,a reignition phenomenon occurred in a short time interval of 1 ms.In general,it is difficult to observe the fine structure nature of a swirl-stabilized flame by means of chemiluminescence measurements. Fig. 2(b) shows the unique features of near-LBO flames, for example, individual helical flame zones were found in the overall combustion process (indicated by red circles),which mainly attributed to the reduced stretch extinction limit.Prior studies showed that the loop of flame extinction and reignition processes might induce the instability of a flame.18The dynamic characteristics of the wrinkled vortex structure in a swirl flame are very important for analyzing the mechanism of flame stability and excavating the inherent law of the interaction between the flow field and the combustion field. In the whole combustion process, the flame shape expressed broken,and there was no large-scale and continuous flame front formation, indicating that the flame was close to the blowout edge. The results also showed that the flame stability became worse at a low equivalence ratio level.

To quantify the flame dynamics characteristics when approaching an LBO condition and evaluate the available flame shape feature,moment descriptors including the Zernike moment and the Hu moments were used to establish the correlation between the flame feature and instability characteristics.Furthermore, the variation of the flame area was used to describe the heat release fluctuation.In Fig.3(a),the classification result based on the 7-order Zernike moment invariants demonstrated a good performance in recognition of different combustion conditions, especially stable and near-LBO conditions.The principal component 1(PC1)represented the principal component with the largest information content, to which all selected moment invariants contributed. The physical meaning of the principal component represented was not clear because of the mathematical description.However,the present work tried to establish the relationship between moment descriptors and flame conditions. In the future, simplified moment characteristics are expected to conduct the monitor and analysis of the combustion state based on advanced algorithms such as machine learning. In the current study, the selected 7 orders were enough to achieve the recognition objective according to the analysis results. In Fig. 3(b), the classification effect based on Hu’s seven moment invariants was not ideal. It could be seen that the Zernike moment as a widely used orthogonal moment had superior ability to identify the combustion state than that of the Hu moments as geometric moments. The oscillation frequency spectrums close to the LBO flames were extracted by the FFT of three flame features as shown in Fig. 3(c) and 3(d). The FFT results of the flame area and principal component feature of the moment had good consistency and revealed obvious low-frequency oscillations during the near-LBO condition. In describing the characteristics of oscillations, geometric moment descriptors had more advantages characterized by a stronger amplitude. Similar low-frequency oscillations phenomena have been reported by previous studies,40,41and the underlying mechanism might correlate with local flame extinction and reignition events. However, the above results also expressed an interesting phenomenon, that is, a self-excited frequency oscillation around 200 Hz. The results demonstrated that the intensified low-frequency phenomenon gradually disappeared at a very low equivalence ratio of φ=0.1.Fig.3(e)shows that the other aspect for the near-LBO features was a narrowed reaction zone by the observation of time-averaged OH-PLIF images. With an extension of the LBO limit margin, intensified lowfrequency oscillations at a few hertz to tens of hertz have ceased to be the dominant oscillation modes,while the specific and self-excited frequency oscillation might play a major role in the combustion instability. It can be expected to be used as a novel prediction characteristic parameter of the flameout limit.It could be speculated that the near-LBO flame displayed more unstable flow features such as entrained reactant pockets(seen in Fig.2(b))relative to a stable flame,which triggered the self-excited flame oscillation and further influenced the global heat-release pulsation. Meanwhile, flame local extinction and reignition due to a high strain rate of the flame root had a significant effect on how the combustion responded to the selfexcited flame oscillation.Therefore,investigating the transition process from stability to instability helped to understand how recirculation zone-stabilized flames ultimately blow off. Furthermore, considering the complexities of interaction between flow,chemistry,and transport,an observation of unique instability features was critical for the prediction of LBO events and the extension of the operation margin of the gas turbine combustor.

Fig. 3 Correlation analysis between image moment features and combustion condition, including the PCA results and oscillation frequency spectrums.

3.2. Mode decomposition analysis

As the above analysis, the selected target flames were associated with the stable and near-LBO flames. The flames of φ = 0.6 and φ = 0.4 corresponded to stable conditions, and the flames of φ=0.2 and φ=0.1 represented near-LBO conditions. The above results only revealed the one-dimensional time oscillation characteristic of the near LBO flame, and the spatial oscillation characteristic could not be described. The dominant POD modes were used to study the main spatial pulsation region of combustion. Fig. 4 shows the analysis results of 2000 OH-PLIF images by POD, and the four dominant POD modes were extracted and analyzed. In POD modes,the red or blue color bar represented the direction of the pulsation, while the depth reflected the intensity of the pulsation.The pulsation regions were believed to be related to the flame oscillations. During a stable flame condition, the flame pulsation mainly existed in the inner recirculation region and inner shear layer through observing POD mode 1.Reducing the global equivalence ratio made the pulsation region narrow, and the oscillation intensity of the inner recirculation region strengthened. The axisymmetric feature of the flame pulsation showed that the radial vibration mode was the dominant pulsation mode.POD mode 2 showed that the outer recirculation region also exhibited strong instability features. It should be noted that a flame shedding phenomenon occurred in the region when the global equivalence ratio was 0.1. Therefore,the near-LBO swirl-stabilized flame consists of three flame pulsation modes: flame oscillation along the shear layer, rotation motion, and flame shedding mode. The rotation mode corresponds to the rotation motion in the swirl flame. When the flame transitions from the stable to LBO state, the vibration mode changes, and the rotation and flame shedding modes gradually play an important role in the flame dynamics of the near-LBO swirl-stabilized flame. The conjoint analysis of the flame structure and POD modes demonstrated that the entrained reaction pockets might play a significant role in the rotation pulsation feature. Further, with a decrease of the global equivalence ratio, the gradually agminated entrained reaction pockets got more and more obvious (seen in POD mode 4). However, whether the rotation mode was caused by the processing vortex core (PVC) cannot be determined. The role of the PVC should be studied in more detail by means of simultaneous PIV and OH-PLIF measurements.The mode analysis results by POD showed different flame pulsation structures,which could confirm that flame shedding and agminated entrained reaction pockets were responsible for generating flame oscillations.

Fig. 4 Comparison of dynamic modes by POD analysis of OH-PLIF image.

Fig. 5 Power spectra of FFT for the primary POD modes coefficients.

The time pulsation characteristics of each POD mode could be extracted by FFT analysis of the time coefficient matrix,and then the frequency spectrum characteristics of combustion oscillation could be investigated as shown in Fig. 5. Results showed that each POD mode contained multiple pulsation frequencies. In a stable condition, frequency spectrum results demonstrated that there existed low-frequency oscillation characteristics.The advantage of this method is that it can initially correlate the flow structure with the characteristics of the spectrum. For example, only modes 1 and 2 had obvious lowfrequency oscillation as shown in Fig. 5(a). It could be seen that the low-frequency oscillation mainly occurred in the recirculation zone and the shear layer.POD modes 3 and 4 demonstrated entrained reaction pockets,but the smaller size has not caused the flame to pulsate at a certain frequency. With a decrease of the equivalence ratio, the shift to a high frequency happened at the transition from stability to instability. The original low-frequency characteristics of a few hertz to tens of hertz gradually weakened, and the single or dominant frequency oscillation characteristic of the flame was more obvious. A similar oscillation frequency range around 200 Hz was captured by POD analysis as shown in Fig. 5(c). By comparing the mode structure and the corresponding frequency feature, we could see that the 200-Hz frequency attributed to the flame shedding indicated in POD mode 2 of Fig. 5(d).The pulsation region where the second harmonic frequency appeared had the characteristic of the rotation mode. The rotation phenomenon might be due to the helical vortex located in the ISL region.39In the transition from stability to instability, the oscillation frequency shifted from a low frequency to a relatively higher frequency, along with the generation of a second harmonic frequency.

Fig. 6 DMD spectra of two near-LBO flames, corresponding to the dominant coherent structures.

Although the POD method could investigate the dominant pulsation region,each mode had an individual frequency spectrum, allowing to analyze the flame dynamic characteristics.However, a multiple-frequency spectrum was difficult to distinguish the corresponding flow structure at each frequency.The association analysis of POD and DMD could provide a new insight for revealing instability details.The DMD method could decompose the modes corresponding to the eigenvalues,and identify the combustion mode related to the specific frequency information. The coherent structure could reflect the sub-flame structure based on the mode decomposition, and the color depth expressed the oscillation intensity.Fig.6 shows the DMD analysis results for two typical near-LBO conditions. In Fig. 6(a), four main frequency peaks were obtained,namely 15 Hz, 192 Hz, 342 Hz, and 447 Hz. On the right was the corresponding DMD mode. The intensified lowfrequency oscillation characteristics were basically consistent with the FFT results of the POD time coefficients. It should be noted that the FFT results reflect the whole flame oscillation, and the DMD frequencies correspond to the dominant combustion modes. Therefore, it can be speculated that the self-excited oscillation frequency of around 200 Hz is probably closer to a combination frequency of the four dominant frequencies, but this needs to be verified in subsequent work.According to the statistical analysis results of the flame area,heat release frequencies were mainly distributed in low frequencies of around tens of hertz and 192 Hz. Therefore, the DMD method can distinguish the individual structures for 15 Hz and 192 Hz,allowing to be discussed separately.Aiming at the research interest of heat-release pulsation, the twodimensional spatial distribution characteristics were investigated based on the DMD mode structure. The spatial locations of the flame root and the reactant pocket could be visualized by the OH-PLIF images (seen in Fig. 2). However, the spatial location of heat-release structures needed to match the DMD mode image around the heat-release frequency,which could be reflected by the fluctuation of the flame area.The results showed that the oscillation characteristics of the recirculation zone and the flame root were dominant in the low-frequency range. Focusing on the self-excited frequency of 192 Hz, the coherent structure was distributed in the recirculation zone and near the combustor outlet, and it could be seen that the heat-release structure fell off, which was similar to the flame shedding. Furthermore, the coherent structure at a high frequency exhibited entrained reactant pockets in the flame arm zone. Entrained reactant pockets have been found in a near-LBO flame due to high-probability extinction events along the flame front.20The results further confirmed that frequent quenching and reignition events along the flame arm zone activated oscillation behaviors, forming oscillatory cycles. Similarly, in Fig. 6(b), the heat-release distribution was concentrated near the two flame arms according to the DMD mode at 214 Hz. It could also express that the flame arm zone played a significant role in the heat release of the ultra-lean swirl-stabilized flame, and a similar phenomenon has also been reported by Renaud et al.41At a higher frequency, the flame root zone showed a weak oscillation structure, showing that the oscillation of the flame root zone was relatively weak.However,at a lower frequency,a strong mode structure existed in the flame root zone, indicating that the flame root zone expressed low-frequency oscillation characteristics. The results expressed the great potential for POD and DMD to conduct dynamic analysis for unstable flames. In future work,the preheat and reaction zones should be investigated by CH2O PLIF and CH-PLIF measurements in current experimental conditions. Meanwhile, the flow field and acoustic data should also be included in the oscillation characteristics analysis to reveal the thermal-fluid-acoustic multi-field coupling process by means of simultaneous PIV, OH-PLIF,and pressure measurements. Furthermore, an attempt will be made to reconstruct the whole combustion mode using dominant DMD modes,and as a result,the difference between FFT results and DMD frequencies can also be explained. To address the effect of noise on experimental results, real-time monitoring devices of laser pulse energy and distribution should be established to optimize the DMD algorithm. The study is expected to propose a novel LBO indicator and provide a significant reference and guideline for optimization and design of more advanced gas turbine combustors in the future.

4. Conclusions

This paper utilized a high-speed OH-PLIF technique to characterize stable and near-blowout flame dynamics in a swirlstabilized gas turbine model combustor. Dynamic features including the local extinction and reignition feature and entrained reactant pockets were obtained through phenomenological observations.Moment descriptors were used for recognition and oscillation characterization for the first time.Dynamic analysis processes were conducted by advanced mode decomposition methods including POD and DMD,and obtained conclusions are as follows:

(1) The Zernike moment demonstrated a good performance in recognition of stability and near-LBO conditions,though Hu’s seven moments had more advantages to characterize the oscillation frequency spectrum.Obvious low-frequency oscillations were found similar to those of prior studies, but the heat-release frequency tended to develop around 200 Hz near an LBO flame, indicating a self-excited combustion oscillation feature. Results showed that the intensified low-frequency phenomenon gradually disappeared at an ultra-lean flame condition.With the extension of the LBO limit margin, intensified low-frequency oscillations at a few hertz to tens of hertz have ceased to be the dominant oscillation modes,while potential thermoacoustic instabilities around 200 Hz might play a major role in the eventual blowout. This unique frequency phenomenon can be expected to be used as a novel prediction characteristic parameter of the flameout limit.

(2) Mode decomposition analysis showed that the radial vibration mode was dominant in a stable flame, while the rotation mode was found to exist in a near-LBO flame. Frequency analysis of the primary POD modes also showed the unique frequency characteristics of stable and near-LBO flames. Furthermore, flame shedding and agminated entrained reactant pockets were responsible for generating self-excited flame oscillations.The intensified low-frequency oscillation characteristics were basically consistent with the FFT results of the POD time coefficients. With an increase of the oscillation frequency, the flame root oscillation weakened,while the dynamic structure expressed entrained reactant pockets caused by frequent extinction and reignition events. The results expressed the great potential for POD and DMD to analyze flame dynamics.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This study was supported by the Heilongjiang Provincial Natural Science Foundation of China (No. LH2021F028).