Nonlinear characterization of azimuthal combustion instability exhibi- ting flame transient phenomena Balasundaram Mohan 1 and Sathesh Mariappan 2 Department of Aerospace Engineering Indian Institute of Technology Kanpur Uttar Pradesh – 208016, India

ABSTRACT This article characterizes the nonlinear features observed in an annular combustor exhibiting self-excited azimuthal thermoacoustic instability. The annular combustor consists of 12 burn- ers with flames stabilized by bluff bodies protruding into the combustion chamber. This burner configuration closely resembles the flame stabilization geometry and flame shape in ramjet and afterburner configurations. As a first step, two different bluff bodies stabilize the flame: 1) cir- cular and 2) conical, and their associated instability dynamics are characterized. The combus- tor exhibit intermittent oscillations in pressure with dominant 1A-1L (first azimuthal – first longitudinal) acoustic mode at about 650 Hz. The duration of periodic oscillation in the pressure fluctuations varies non-monotonically with the airflow rate. Further, a relatively large ampli- tude pressure fluctuations are observed for intermediate values of airflow rate in both the flame stabilization. During these large-amplitude pressure fluctuations, localized flame extinction in certain burners is observed, leading to partial blow-off operation of the combustor. The flame extinction is subsequently followed by either successful or unsuccessful reignition, leading to an introduction of slow time scale large-amplitude heat release modulation in the problem. Fur- ther, the slow time scale heat release modulation is stochastic, leading to intermittent oscillation in pressure.

1. INTRODUCTION

Modern gas turbine engines operating with lean premixed prevaporized (LPP) combustion to reduce pollutant emission exhibits thermoacoustic instability for a particular operation envelope [1]. In ad- dition, the fuel-flexible operation, i.e., adding hydrogen with the existing fuels to minimize pollutant emission without significant modification to the combustor is detrimental. Especially, beyond a cer- tain percentage of hydrogen blending gives rise to thermoacoustic instability, flame stabilization in the upstream flow manifolds resulting in burnout of engine components and significant changes in the local heat release distributions are encountered [2]. For specific engine operating conditions, ther- moacoustic instability exhibits transient flame behavior such as flame flashback, extinction, near blow-off and reignition, which induces premature engine and component failures leading to compro- mise on engine performance. In this article, we examine the flame transient phenomena. In particular successful reignition event encountered in annular combustors while exhibiting self-excited thermo- acoustic instability. Further, we show that the large amplitude heat release oscillation associated with

1 mbala.kotti@gmail.com

2 sathesh@iitk.ac.in

worm 2022

this reignition introduces stochastic slow time to the thermoacoustic system. This stochastic slow time scale in turn manifests intermittent oscillation in pressure.

Azimuthal thermoacoustic instability in academic combustors was scrutinized in the recent past due to its practical relevance in modern gas turbine engines. For instance, the instability characteris- tics, modal dynamics, nonlinear saturation mechanism, and light around processes were examined in the annular combustor. The continuous transition between spinning and standing wave modes was observed by Worth and Dawson [3]. Symmetric and antisymmetric heat release distributions were observed in standing wave mode at the pressure node and antinode, respectively [4]. For spinning mode, the non-uniform heat release distribution was found in the annulus with a peak in heat release spinning at instability frequency. The spin ratio and quaternion ansatz were used to characterize the modal dynamics [5]. In addition to the spinning and standing wave modes, a slanted mode was ob- served in the MICCA combustor characterized by the presence of an antinode and a node in the annulus [6]. In the same combustor with liquid fuel and swirl burner, bursting oscillations in pressure was observed with local extinction of flames located in the vicinity of velocity antinode [7].

The majority of the experimental investigations available in the literature focused on the swirl stabilized flames relevant to practical gas turbine engines. However, fewer investigations were re- ported with matrix [6] and bluff-body stabilized flames without swirl. Nevertheless, as far as the authors' knowledge is concerned, most of the previous investigations have one similarity, i.e., the flames originate from the flush-mounted (to the base of combustion chamber) flame holders. In the present investigation, the flame holders protrude into the combustion chamber and offset from the combustion chamber base plate. Therefore, the flame base is inside the combustion chamber. Such a flame stabilization mechanism, i.e., the flame stabilization using bluff bodies in the flow path, finds application in ramjet and afterburner combustor configurations. Since the flame base is inside the combustion chamber, we expect an increased flame front distortion along the azimuthal direction caused by azimuthal pressure fluctuations. Hence, the flame dynamics analogous to that of a single burner truncated V-flame [8] are anticipated depending on the location of individual burners relative to the azimuthal pressure mode shape. Further in [8], the authors have shown that the flame is sensi- tive to forcing amplitude; even a low amplitude pressure fluctuation causes flame extinction. A sim- ilar localized flame extinction is observed in the present study, followed by a successful reignition leading to distributed slow time scale.

The rest of this article is structured as follows. In section 2, the experimental setup and data acqui- sition processes are discussed. Section 3 characterizes the observed instability and associated flame transient phenomenon. Key findings are summarized in section 4.

2. EXPERIMENTAL SETUP AND DATA ACQUISTION

In our experimental setup, the flames are stabilized by bluff bodies and operated with a fully premixed fuel-air mixture. Liquefied petroleum gas (LPG) is used as fuel comprising 60% butane and 40% propane by volume. The experimental setup consists of three major parts: a plenum, injection tube and combustion chamber, as depicted in Figure 1(a). The major parts of our experimental setup are designed by considering the annular combustor facility in [2]. Burner (see Figure 1b), i.e., the injection tube and flame holder specifications are adapted from the single-sector rig available in our laboratory [9]. Twelve such burners are azimuthally arranged 30 degrees apart to mimic the annular combustor. The combustor components, combustion chamber radii, injection tube length, and sensor locations are marked in Figure 1(a,c).

Fuel and air are supplied at the bottom of the plenum via a T-joint and mixing occur within the plenum. The plenum has provisions for acoustic forcing. Silencers (Festo 2130 U-1/2) are placed in (the converging portion) between T-joint and plenum to reduce upstream flow noise. Honeycomb is placed inside the plenum downstream of silencers which acts as a flow straightener. This premixed fuel-air mixture is fed through injection tubes into the combustion chamber. The 12 injection tubes with length and inner diameter of 200 mm and 14 mm, respectively, connect the plenum and com- bustion chamber. Figure 1(b) shows a cut section of an injection tube with components and dimen- sions marked. A constrictor is mounted over each injection tube, as shown in Figure 1(b), with an

inner diameter of 8 mm. This constrictor was shown to increase the lateral extent of the recirculation zone, local flow acceleration and strong vortex shedding [9]. Flame stabilization is achieved by either circular or conical bluff bodies, which are placed in injection tubes protruding into the combustion chamber. The length of the protrusion ( ℎ 𝑏𝑗 = 20 mm) is measured from the combustion chamber base, as depicted in Figure 1(b).

Figure 1: Schematic of the (a) annular combustion chamber, (b) cut section of an injection tube, and (c) top view of the combustion chamber. (a-c) Illustrate various parts of the test rig with all the di- mensions are in mm. The bluff-body flame holders, pressure (MC) and temperature (TC) sensors are shown in (c), numbered counterclockwise from the horizontal axis.

The axisymmetrically arranged bluff bodies are enclosed by two concentric cylinders made up of stainless steel, which forms an annular combustion chamber. The radius of outer and inner combus- tion chamber walls correspond to 178 mm and 113 mm, respectively, depicted in Figure 1(a-c). For the present study, the lengths of outer (𝑙 𝑜𝑐𝑤 ) and inner (𝑙 𝑖𝑐𝑤 ) combustion chamber walls are fixed at 300 mm. Further, the bluff-body diameters are the same and 13.6 mm. The conical bluff body has a full cone angle of 90 degrees. Note, in this article, the flames stabilized by circular and conical bluff bodies are referred interchangeably as circular and conical respectively in the text for ease.

Unsteady pressure data are acquired using condenser microphones and transducers, having nomi- nal sensitivities of 10.4 mV/Pa and 0.2 mV/Pa, respectively. The microphones are mounted using a stainless steel port in the combustion chamber and the pressure transducers are flush-mounted in the injection tubes. Unsteady pressure is acquired at six locations: four in the walls of the outer combus- tion chamber (see MC1-MC4 in Figure 1(c), 20 mm downstream of the combustion chamber base) and two in the injection tubes (see Figure 1(a), 55 mm from the bottom of the injection tube). The pressure recorded in the burner 4 injection tube is used for further analysis owing to its higher ampli- tude. Data are obtained at 32768 Hz for 15 s. The steady temperature of hot gas is measured at two azimuthal locations (at burners 2 and 8, for instance, refer to Figure 1c) inside the combustion cham- ber using a k-type thermocouple. These thermocouples are placed 20 mm downstream of the com- bustion chamber base. 𝐶𝐻 ∗ chemiluminescence imaging of the flame from the top view is captured using a 4 megapixel 12 bit CMOS high-speed camera fitted with a lens and narrow bandpass optical filter. This optical filter has a center wavelength of 430 nm. The flame images were captured with a resolution of 1024 × 1024, a frame rate of 100 fps and an exposure time of 9.998 ms, respectively. These chemiluminescence images show the location of the reaction zone and hence the position of the flame [10]. The top view of the flame is captured using a cooled angled mirror fixed downstream of the combustion chamber. The camera and pressure measurements are started at the same time instance by external triggering. For phase averaged flame images, high-speed images are captured with a resolution, frame rate and exposure time of 800 × 768 pixels, 5000 fps, and 0.20 ms, respec- tively, without filter.

The fuel and air volume flow rates are controlled using rotameters, model Eureka SSRS-MGS-13 and CIVF-PG-16(M). Fixed fuel flow rates of 16 and 18 slpm are used with circular and conical bluff bodies, respectively, yielding power outputs of 27.58 kW and 31.05 kW. In the present experiment, the airflow rate ( 𝑄 𝑎 ) is considered as a parameter and varied between 300-800 slpm with an increment

(b) Inner combustion chamber wall slutf-body outer combustion chamber wall Conbust son chanber base — Microphone Injection tube Plena 3 200 Air + fuel inlet | { li ‘Outer conbustion } chamber wall J Inner Combustion | chamber wall Mca| (c) | tut? body constrictor i) central rod Knisetian tule A siuft-boay Inner combustion chamber wail ~_Microphone.

of 25 slpm. A 20 s gap is given between the successive measurements to allow the system to reach flow and thermal equilibrium. 3. RESULTS AND DISCUSSION

The pressure time series acquired in burner 4 injection tube is shown in Figure 1(a). The red and blue lines correspond to the circular and conical bluff-body flame stabilizations, respectively (refer to leg- end in panel b). The pressure time series corresponds to the maximum normalized root mean square (RMS) value of the respective flame stabilizations. The pressure signal in panel (a) exhibits intermit- tent oscillations i.e., the presence of large-amplitude periodic pressure fluctuations amidst relatively low amplitude aperiodic fluctuations for circular bluff-body. On the other hand, the conical bluff- body manifests time-varying irregular amplitude with periodic pressure fluctuations. In the subse- quent paragraphs, we will show that this modulation in pressure fluctuations is caused by large am- plitude heat release oscillation associated with flame transient phenomena. In particular, we illustrate that the large-scale heat release modulation caused by the successful reignition of a burner causes irregular amplitude modulation.

The power spectral density (PSD) associated with panel (a) is shown in panel (b). In PSD, the first dominant peak occurs at 664 Hz and 644 Hz, respectively, for circular and conical bluff bodies. Sim- ilarly, the second dominant peak occurs at 331 Hz and 319 Hz, respectively. Using the mean of steady temperature obtained in burners 2 and 8 for circular (757.5 K) and conical (565 K) bluff bodies the theoretical value of 1A-1L mode is calculated as follows. The resonant frequency of 1A-1L mode is expressed as follows: 𝑓 1 𝐴−1𝐿 = 𝑎 𝑐 2 Τ ሾ(1 2𝑙 Τ ) 2 + (𝜆𝜋 Τ ) 2 ሿ 0.5 , Where 𝜆 (= 𝛼 𝑎 𝑟 Τ ) equals to 6.9334 for this combustor. Here 𝑎 𝑐 , 𝑙 , 𝛼 𝑎 and 𝑟 denotes the mean speed of sound, combustion chamber length, a coefficient related to the circumferential and radial modes and mean radius of the combustion cham- ber. The calculated 1A-1L mode frequencies are 751.46 Hz and 654.55 Hz, respectively, for circular and conical. These values are close to the experimental observations in panel (b). In addition, the frequency variation of the dominant peak (~ 650 Hz) is insensitive to combustion chamber lengths as compared to the secondary peak (~ 320 Hz) was shown experimentally using circular bluff body stabilized flame in our previous investigation [11].

Figure 2: (a) Pressure time series and (b) power spectral density (PSD) corresponding to the flames stabilized by circular and conical bluff bodies are shown by red and blue lines, respectively. The peak in (1A-1L mode) instability frequency occurs at about 664 Hz and 644 Hz, respectively, for circular and conical bluff bodies. Similarly, the second dominant peak (1L mode) occurs at 331 Hz and 319 Hz, respectively.

The phase averaged images corresponding to the conical bluff body for the airflow rate of 600 slpm is shown in Figure 3. These images show the maximum intensity variations occurring at burners 5 and 11 located azimuthally opposite to each other. This variation in intensity between burners 5 and 11 is out-of-phase (for instance, refer 3/8 phase). Negligible intensity variations occur at burners 7 and 8. Further, the burners 1 and 2 exhibit sustained flame extinction for this operating condition. The azimuthally fixed intensity variation among burners indicate the predominance of standing wave acoustic mode. The presence of longitudinal mode leads to in-phase intensity variation in all the burners (not observed in the present study). In addition, the reconstructed pressure mode shape (not shown here) shows pressure antinode located between burners 4, 5 and 10, 11. Similarly, the pressure node is located between burners 1, 2 and 7, 8. Further, the spin ratio associated with the pressure time

140 s fia 5 120 [=@, = 500 sipm, Circular 3 100 0% = 650 stm, Conical 2 80 60 - ; 0 500 1000 1500 2000 t (s) f (Hz

series of phase averaged images show a peak in probability at 0.212. This altogether indicates the presence of mixed clockwise standing wave 1A-1L acoustic mode in the combustor.

Figure 3: Phase averaged flame images (more than 1000 images in a bin) corresponding to 1A-1L mode associated with conical bluff-body for 𝑄 𝑎 = 600 slpm exhibiting mixed clockwise standing wave mode (associated with a peak in probability of spin ratio equals to 0.212±0.05). The maxi- mum intensity variations are observed in burners 5 and 11 with out-of-phase oscillation. Refer to Figure 1(c) or Figure 5(b) for burner numbers.

Figure 4: (a) Circular bluff-body and (b) conical bluff-body. The triangles and circles in (a,b) cor- responds to the normalized root mean square (RMS) value of pressure fluctuation and normalized occurrence time ( 𝒯 𝑑 ) of dominant 1A-1L mode respectively, for various airflow rates. In estimat- ing 𝒯 𝑑 , the threshold is set at ±15% of 1A-1L mode frequency.

1X VII TT °

The normalized RMS of pressure amplitude variation with airflow rate for circular and conical bluff bodies are shown in Figure 4(a,b), respectively, with triangles. The RMS envelope varies non- monotonically for airflow rate with intermediate airflow rate exhibiting maximum value. This non- monotonic variation in the RMS amplitude envelope is caused by the flame-acoustic coupling re- sulting from the axial extent of flames in individual burner and the number of active burner asso- ciated with rich to lean blow out operation encountered. The RMS amplitude having a non-zero values for low and high airflow rates indicate the presence of flow-induced turbulence. As dis- cussed in Figure 2(a), the presence of intermittent oscillation is quantified in the present study by estimating the fraction of the total time period of occurrence of the dominant 1A-1L mode. This sheds light on the proximity of full-blown thermoacoustic instability with respect to the operating condition. For this purpose, the normalized occurrence time (𝒯 𝑑 ) is estimated by following:

−1 𝑁 𝑝 −1 𝑗=1 , (1)

1

𝒯 𝑑 =

𝑡 𝑡𝑜𝑡 σ 𝑓 𝑗

Where 𝑓 𝑗 is the frequency falling within ±15% of the dominant instability frequency (for instance, refer to 1A-1L mode frequency in Figure 1b). Here 𝑓 𝑗 is calculated from the time difference asso- ciated with successive peak to peak amplitude in a pressure time series. The total time period and the total number of local peaks in a pressure time series are denoted by 𝑡 𝑡𝑜𝑡 (here 15 s of data is used) and 𝑁 𝑝 respectively. The estimated 𝒯 𝑑 for circular and conical bluff bodies are shown in

boo 11 (b) a ° Crreular 4°” A Conical ee 0.75 Ao & A200, A on 05 eo Aadag Aa A ‘ Tan} 025)" 4 ns] 8(rns) AF Hrs) 8 Bel Aaa ott ° 800 600 700 500 600 500 ° am Qa (slpm)

Figure 4 (a,b), respectively, with circle. The variation in pressure amplitude and 𝒯 𝑑 with airflow rate exhibits roughly similar trend for circular bluff-body (see panel a). This shows that the increase in pressure amplitude leads to an increase in 1A-1L mode instability cycle. Further, panel (a) shows the 𝒯 𝑑 values are always less than 1, indicating the presence of aperiodic or other acoustic and higher harmonic mode contributions. The above observations substantiate the presence of intermittent os- cillations in circular bluff-body. On the other hand, the conical bluff-body exhibits dominant 1A- 1L mode for the majority of the operating conditions indicated by 𝒯 𝑑 close to 1 (see panel b). This shows the presence of both intermittent oscillation (for low and high airflow rates) and irregular amplitude modulation (for intermediate airflow rates) in pressure fluctuations for conical bluff- body.

Figure 5: For airflow rate of 650 slpm corresponding to conical bluff-body, (a1) pressure time series exhibiting intermittent oscillation and (a2) normalized intensity of burner 12. Associated flame images exhibiting successful reignition of burner 12 are shown in panels (b-m). Red cross with alphabets b-m marked in panel (a1) corresponds to the time instance associated with the flame images shown in panels (b-m). The burner numbers are marked in panel (b) for ease of visualiza- tion. The successful reignition of burner 12 occurs through azimuthal flame propagation from burner 11. The active flame kernel propagating through the inner combustion chamber wall (see panel c) reignites the fresh fuel-air mixtures available in the proximity of burner 12 (see panel d). The subsequent flame spreading around burner 12 bluff-body leading to complete reignition are in panels (e-m). This successful reignition event spans approximately 0.20 s (5 Hz). The legend cor- responding to panels (b-m) is same as the legend in Figure 3.

To relate the flame transient phenomena with intermittent oscillation, the zoomed-in view of the pressure fluctuations in Figure 2(a) corresponding to conical bluff-body is shown in Figure 5(a1).

(al) 4 | k TTTAARATA THAT TTS RQ ARAN NH ee so MARA H | ea eons iH Dn 8 m c (a2) " Ex-Burner 12] * y ee ae L Pong e non e O ssful -STisxtinction x=. eee” necessary ” - reignition

The pressure fluctuations exhibit modulation in instability amplitude with nearly periodic oscilla- tions. The associated recurrence plot shows the presence of cell like structures (not shown here). The normalized heat release intensity of burner 12 is shown in panel (a2) with flame extinction and successful reignition marked using arrows. The successful reignition of burner 12 leads to a large increase in heat release. This large variation in heat release manifests in the form of modulation in pressure amplitude. The flame images showing the successful reignition of burner 12 are shown in panels (b-m). For further details, refer to the Figure 5 caption. By comparing panels (a1) and (a2), it is clear that the initiation of the flame kernel in burner 11 occurs when the pressure amplitude increases (reaches temporally a large amplitude, refer 𝑡= 9.79 s and panel c). The initiation of reignition occurs in burner 12 at 𝑡= 9.81 s, leading to increase in heat release. The sudden initia- tion of reignition leads to a reduction in instability amplitude in pressure. It is attributed to the out- of-phase contribution from burner 12 to the total acoustic energy. The successive flame spreading around the bluff-body depends on the local instability amplitude (i.e., the proximity of burner lo- cation relative to the velocity antinode), flame speed and availability of the unburned fuel-air mix- ture. The reduction in instability amplitude allows the flame to spread around the bluff-body (see panels e-l), leading to a gradual increase in heat release (see panel a2). The complete reignition occurs at 𝑡= 9.99 s leading to increase in pressure amplitude with more periodic oscillations. The successful reignition event spans approximately 200 ms leading to a frequency of 5 Hz. This time scale is relatively large in comparison to the dominant instability time scale (~ 1.6 ms) associated with the 1A-1L mode. Therefore, the successful reignition flame transient phenomenon introduces the slow time scale into the thermoacoustic system. In the past, Weng et al. [12] observed a similar slow time scale (1 Hz) mean flame oscillation in a laminar Rijke burner leading to a manifestation of low-frequency regular amplitude modulation in pressure. In the next paragraph, we show that the slow time scale observed in the present study is stochastic, which may lead to irregular ampli- tude modulations observed in the present experimental investigation.

The time span associated with a similar successful reignition events is collected for the Figure 4(a,b) from all the burners and shown in Figure 6(a,b) respectively. The event time span exhibits distributed behavior with maximum events occurring at 0.11 s and 0.07 s, respectively, for circular and conical bluff bodies. In addition, a relatively large number of events occur in circular bluff- body than conical. Since the occurrence of successful reignition leads to low amplitude pressure fluctuations, as shown in Figure 5(a1), the relatively stable operation of circular bluff body is re- lated to the frequent occurrence of the flame transient phenomena. In addition, the observed aperi- odic oscillation is attributed to the flow-induced turbulence present in this combustor. A similar order of slow time scales were observed in the past in the context light around process in annular combustors.

Figure 6: Histogram of the successful reignition event time span ( 𝜏 𝑚 ) corresponding to flames stabilized by (a) circular bluff-body and (b) conical bluff-body. The circular bluff-body stabilized flames exhibit a relatively more number of events (N). The event time span is estimated from the normalized heat release intensity associated with Figure 4(a,b) by considering all the burners.

0.2 b 6) Circular bluff-body 4 2 Ltt , 0.4 0.6 08 0 Tm, (s) Conical bluff-body 0.3

4. CONCLUSIONS

We characterized the nonlinear features observed in an annular combustor exhibiting self-excited dominant 1A-1L thermoacoustic mode. The flames were stabilized by 12 bluff bodies protruding into the combustion chamber. The combustor manifests intermittent oscillation in pressure with dominant instability frequency at about 650 Hz. The airflow rate was varied by keeping the fixed fuel flow rate. A comparison between the instability characteristics of two different bluff bodies was made: 1) cir- cular and 2) conical. The circular bluff-body exhibits relatively low amplitude pressure fluctuations compared to the conical bluff-body. The duration of periodic oscillation in the intermittent pressure fluctuation was found to vary non-monotonically with airflow rate in both cases. Further, relatively large amplitude pressure fluctuations were observed for intermediate airflow rates in both flame sta- bilization. These large-amplitude pressure fluctuations led to local flame extinction in certain burners, causing partial blow-off operation. This localized flame extinction was subsequently followed by either successful or unsuccessful reignition, leading to the introduction of slow time scale heat release modulation in the problem. Further, we have shown that this slow time scale heat release rate modu- lation was distributed and hence contributes to the appearance of intermittent oscillation in pressure. ACKNOWLEDGEMENTS

This work received financial support from Science and Engineering Research Board (SERB) India through grant number CRG/2019/000500. The authors greatly acknowledge the assistance provided by Manmohan (IIT Kanpur) and Vigneshwaran S (KAUST) while performing the experiments. REFERENCES

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