An Experimental Study on Flame Pufﬁng of a Swirl Partially Premixed Combustion under Varying Mass Flow Rate of Primary Air

: It is of practical signiﬁcance to understand the ﬂame pufﬁng behavior under varying mass ﬂow rate of primary air ˙m pri . An experiment was conducted to study the impact of ˙m pri on ﬂame pufﬁng in a swirl partially premixed combustor, the pufﬁng behavior of six signiﬁcant ﬂame properties was examined. The results showed that almost every spectrum had two fundamental frequencies, which is different from the single-peak spectrum of non-swirl ﬂame. The ﬂame heat-release rate, ﬂame area, and ﬂame equivalent width had identical dominant frequency and sub-dominant frequency, both decreased with the increasing of ˙m pri . It was attributed to the decreased overall ﬂame temperature caused by the improved mixing of fuel and primary air. All measured frequencies were in the range of 3–14 Hz, but the predicted frequencies from the theoretical models based on non-swirl ﬂame were larger than the measured. This indicates the pufﬁng frequency of swirl ﬂame was much more sensitive to the variation in ˙m pri than the frequency of non-swirl ﬂame. Moreover, the amplitude of ﬂame length was the smallest in all properties, with the most weakened oscillating intensity. While the amplitude of the ﬂame area and ﬂame equivalent width were the largest, with the strongest oscillation level. Consequently, the ﬂame pufﬁng is mainly attributed to the oscillation in width direction.


Introduction
Observation of many combustion processes shows that the state of flame is not stationary at any moment, it displays a substantial oscillating characteristic which is generally termed as 'flame puffing', 'flame flickering', or 'flame pulsation' [1]. Flame puffing is a consequence of the interaction between the flame surface and large vortices, these vortices are formed due to the buoyant force, and they move downstream along the flame front thus inducing flame oscillation [2]. With the existence of flame puffing, the structure of the flame is always changed with time, which influences some important combustion properties, e.g., the entrainment velocity of oxidizer into the flame, flame radiation, flame size, and the efficiency of combustion. With severe conditions, the puffing even can cause flame extinction and the failure of combustion instruments [3]. So it is of practical significance to understand flame puffing behavior in the fields of combustion instability and flame monitoring.
In recent decades, the characteristics of flame puffing have been explored in many researches. Bahadori et al. [4] and Durox et al. [5] investigated the effects of gravitational level on flame flickering respectively; they found that the flickering frequency f has a proportional relationship with g n (g is gravitational acceleration), the exponent n is 0.5 from the former, while n is 0.67 from the latter.
These combustion tests were conducted on a 20 kW design power facility which can investigate high pressure combustion [28]. This test rig has three main sections, as displayed in Figure 1. (1) First of all, there is a supply section which comprises of several parts including an air compressor, mass flow rate controller (MFC), and a high-pressure gas holder. The air compressor provides the air for combustion with a maximum capacity of 2.5 kg/min. The flow rate of air is measured by a flow meter while air flow is regulated by an electronic control valve. An MFC, having a maximum capacity of 36 g/min, was installed after the gas holder measures and controls fuel (methane) flow rate. (2) The second section of this facility is the combustion section which contains an axisymmetric cylindrical chamber (combustor) and a swirl burner, as shown in Figures 2 and 3. The length of the combustor is 1.35 m and the diameter is 0.3 m. Figure 3 illustrates the swirl burner that contains a radial swirler which improves the fuel/air mixing quality. Ten straight vanes having setting angle α of 50° constitute the swirler. To enhance flame stability, a convergent divergent nozzle was designed, having an angle of 42° between its divergent side face and vertical line. Primary air, which is a fraction of main air, flows tangentially through the swirler where fuel is delivered by the central fuel. Primary air carrying fuel then enters into the combustion chamber where the combustion process takes place. Flame length is controlled by primary air which mixes with fuel before combustion and is only 5% (on mass basis) of the total air supplied by the compressor. The mixing quality of primary air and methane is still insufficient because this mixing process occurs in a shorter distance. The remaining fraction of air/secondary air flows through a wind distributing plate and then from an annular slot it enters the combustor flowing adjacent to the inner walls. Secondary air not only supports combustion but also cools down the wall and metallic parts to avert damages caused by overheating. On the combustor wall an optically accessible window is attached for monitoring and recording the flame structure. (3) Lastly, there is an exhaust section which draws exhaust gas out into the atmosphere with the help of an induced draught system. It also includes a device to control the operating pressure of the combustor and is termed as the pressure regulating valve. (1) First of all, there is a supply section which comprises of several parts including an air compressor, mass flow rate controller (MFC), and a high-pressure gas holder. The air compressor provides the air for combustion with a maximum capacity of 2.5 kg/min. The flow rate of air is measured by a flow meter while air flow is regulated by an electronic control valve. An MFC, having a maximum capacity of 36 g/min, was installed after the gas holder measures and controls fuel (methane) flow rate. (2) The second section of this facility is the combustion section which contains an axisymmetric cylindrical chamber (combustor) and a swirl burner, as shown in Figures 2 and 3. The length of the combustor is 1.35 m and the diameter is 0.3 m. Figure 3 illustrates the swirl burner that contains a radial swirler which improves the fuel/air mixing quality. Ten straight vanes having setting angle α of 50 • constitute the swirler. To enhance flame stability, a convergent divergent nozzle was designed, having an angle of 42 • between its divergent side face and vertical line. Primary air, which is a fraction of main air, flows tangentially through the swirler where fuel is delivered by the central fuel. Primary air carrying fuel then enters into the combustion chamber where the combustion process takes place. Flame length is controlled by primary air which mixes with fuel before combustion and is only 5% (on mass basis) of the total air supplied by the compressor. The mixing quality of primary air and methane is still insufficient because this mixing process occurs in a shorter distance. The remaining fraction of air/secondary air flows through a wind distributing plate and then from an annular slot it enters the combustor flowing adjacent to the inner walls. Secondary air not only supports combustion but also cools down the wall and metallic parts to avert damages caused by overheating. On the combustor wall an optically accessible window is attached for monitoring and recording the flame structure. (3) Lastly, there is an exhaust section which draws exhaust gas out into the atmosphere with the help of an induced draught system. It also includes a device to control the operating pressure of the combustor and is termed as the pressure regulating valve.

Measurement Methods
To examine the dynamic behavior of flame, the flame zone was detected by recording the chemiluminescence image of the CO2* species. For this purpose, a high-speed COMS (Complementary Metal Oxide Semiconductor) camera named Olympus i speed 3 (Olympus, Essex, UK) was installed near the optical window and a band filter BG 38 (HB-OPTICAL, Shengyang, China) with a bandwidth of 340-600 nm was attached to the camera.
Samaniego et al. [29] reviewed the CO2* chemiluminescence method which is often employed for determination of the flame zone. Although several species like CH, OH, and PAH may exist within the range of the 340-600 nm wavelength, their impact is trivial and can be ignored as CO2* is the prime emitter for hydrocarbon flames. As suggested in the review [29], more than 95% of chemiluminescence comprises CO2* emission when integrated over the 340-600 nm range. Thus from the whole 340-600 nm wavelength range, chemiluminescence can be captured and construed as CO2* emission. CO2* is produced in three fundamental steps as given in Equation (1) [29] and it indicates the reaction zone.
In the first step of the reaction CO2* is produced, while in the second step CO2* emits light and returns to its ground state (CO2), where M is a kind of intermediate product of combustion. The final

Measurement Methods
To examine the dynamic behavior of flame, the flame zone was detected by recording the chemiluminescence image of the CO2* species. For this purpose, a high-speed COMS (Complementary Metal Oxide Semiconductor) camera named Olympus i speed 3 (Olympus, Essex, UK) was installed near the optical window and a band filter BG 38 (HB-OPTICAL, Shengyang, China) with a bandwidth of 340-600 nm was attached to the camera.
Samaniego et al. [29] reviewed the CO2* chemiluminescence method which is often employed for determination of the flame zone. Although several species like CH, OH, and PAH may exist within the range of the 340-600 nm wavelength, their impact is trivial and can be ignored as CO2* is the prime emitter for hydrocarbon flames. As suggested in the review [29], more than 95% of chemiluminescence comprises CO2* emission when integrated over the 340-600 nm range. Thus from the whole 340-600 nm wavelength range, chemiluminescence can be captured and construed as CO2* emission. CO2* is produced in three fundamental steps as given in Equation (1) [29] and it indicates the reaction zone.
In the first step of the reaction CO2* is produced, while in the second step CO2* emits light and returns to its ground state (CO2), where M is a kind of intermediate product of combustion. The final

Measurement Methods
To examine the dynamic behavior of flame, the flame zone was detected by recording the chemiluminescence image of the CO 2 * species. For this purpose, a high-speed COMS (Complementary Metal Oxide Semiconductor) camera named Olympus i speed 3 (Olympus, Essex, UK) was installed near the optical window and a band filter BG 38 (HB-OPTICAL, Shengyang, China) with a bandwidth of 340-600 nm was attached to the camera.
Samaniego et al. [29] reviewed the CO 2 * chemiluminescence method which is often employed for determination of the flame zone. Although several species like CH, OH, and PAH may exist within the range of the 340-600 nm wavelength, their impact is trivial and can be ignored as CO 2 * is the prime emitter for hydrocarbon flames. As suggested in the review [29], more than 95% of chemiluminescence comprises CO 2 * emission when integrated over the 340-600 nm range. Thus from the whole 340-600 nm wavelength range, chemiluminescence can be captured and construed as CO 2 * emission. CO 2 * is produced in three fundamental steps as given in Equation (1) [29] and it indicates the reaction zone.
In the first step of the reaction CO 2 * is produced, while in the second step CO 2 * emits light and returns to its ground state (CO 2 ), where M is a kind of intermediate product of combustion. The final Energies 2018, 11, 1916 5 of 14 stage of the reaction is a quenching step which contends with the second step of the reaction. In this stage, CO 2 * returns to its ground state, as it can be seen in Equation (1).

Flame Properties
The measured flame zone based on the method of CO 2 * chemiluminescence is used to obtain the flame properties. We examined the flame properties under varying the mass flow rate of primary air (i.e.,ṁ pri = 95 g/min, 100 g/min, 105 g/min) while the fuel's mass flow rate remained constant (16 g/min). These flame properties include flame heat-release rate H, flame area A, flame length L, flame equivalent width W, flame center length L c , and image correlation coefficient R. Some of them are shown in Figure 4; all properties are determined as follows: Energies 2018, 11, x 5 of 14 stage of the reaction is a quenching step which contends with the second step of the reaction. In this stage, CO2* returns to its ground state, as it can be seen in Equation (1).

Flame Properties
The measured flame zone based on the method of CO2* chemiluminescence is used to obtain the flame properties. We examined the flame properties under varying the mass flow rate of primary air (i.e., ṁpri = 95 g/min, 100 g/min, 105 g/min) while the fuel's mass flow rate remained constant (16 g/min). These flame properties include flame heat-release rate H, flame area A, flame length L, flame equivalent width W, flame center length Lc, and image correlation coefficient R. Some of them are shown in Figure 4; all properties are determined as follows: (1) Flame heat-release rate H is usually determined by integrating the intensity of the chemiluminescence over the entire image, i.e., summing the gray values of all pixels in that image [30][31][32]. The gray value is a parameter which reflects the luminosity of a grayscale image, and it has a range of 0-255. The luminance enhances gradually from 0 to 255 where 0 corresponds to black color while 255 corresponds to a white color (note that Figure 4 is a little saturated, which may have influence on the determination of H). While it is not the Figure we employed to obtain the signal in the paper, we used it to clearly present flame geometric properties because it is bright. The Figures corresponding to the cases we explored in the present work are not saturated, and the relevant heat-release rate signal was found to have a significant and regular variation with time, so it can be a qualitative indicator of flame oscillation. (2) Flame area A is obtained by calculating the amount of all luminous pixels, whose gray value is larger than a threshold. After comparing various results based on different thresholds, we choose 100 as the threshold in the present calculation, which is enough to determine the flame area accurately. (3) Flame length L is defined as the distance between the injector exit and the flame tip. It is obtained by calculating the number of pixels from the nozzle exit to the flame tip (the visual tip of the flame). (4) Flame equivalent width W is defined as the flame average diameter and it is calculated as the ratio between flame area A and flame length L [33], namely W = A/L. (5) Flame center C is employed to intensively describe flame position by considering the flame as a point [31,34,35] (displayed as a red point in Figure 5), it is determined by employing the gravity center concept which is calculated by treating each pixel as a local position and considering each individual pixel's intensity as its mass. In this way, the flame center can be obtained. (1) Flame heat-release rate H is usually determined by integrating the intensity of the chemiluminescence over the entire image, i.e., summing the gray values of all pixels in that image [30][31][32]. The gray value is a parameter which reflects the luminosity of a grayscale image, and it has a range of 0-255. The luminance enhances gradually from 0 to 255 where 0 corresponds to black color while 255 corresponds to a white color (note that Figure 4 is a little saturated, which may have influence on the determination of H). While it is not the Figure we employed to obtain the signal in the paper, we used it to clearly present flame geometric properties because it is bright. The Figures corresponding to the cases we explored in the present work are not saturated, and the relevant heat-release rate signal was found to have a significant and regular variation with time, so it can be a qualitative indicator of flame oscillation. (2) Flame area A is obtained by calculating the amount of all luminous pixels, whose gray value is larger than a threshold. After comparing various results based on different thresholds, we choose 100 as the threshold in the present calculation, which is enough to determine the flame area accurately.
where A and B are the average values of A and B respectively.

Puffing Dynamics
The flame zone was recorded in time sequence, with a recording frame rate of 400 frames per second (fps). Under this rate, the interval time between two sequential frames is 2.5 ms. The image has a resolution of 1280 H × 1024 V pixels. To analyze the flame dynamics, a sequence of continuous flame surface topography of the flame zone is displayed in Figure 5 [28]. It can be noticed that the flame surface is wrinkled because of the effect of large vortices around the flame front, these vortices are generated due to the buoyant force caused by combustion. During the combustion, high-temperature gas is produced in the flame zone and accelerated into the cool ambient air. As the flow velocity of heated gas is larger than that of surrounding air, a vortex V1 outside the flame surface is formed at 0 ms, which facilitates the entrainment of air into the flame. As V1 moves upward along the flame front, a characteristic necking is observed. At the same time, a low-pressure region behind V1 is created and immediately filled by the burning gas from upstream, resulting in the production of a bulge. When this bulge rises, another vortex V2 is generated below the bulge at 10 ms; it convects as V1. The movement of vortices causes the flame puffing.
Where A and B are the average values of A and B respectively.

Puffing Dynamics
The flame zone was recorded in time sequence, with a recording frame rate of 400 frames per second (fps). Under this rate, the interval time between two sequential frames is 2.5 ms. The image has a resolution of 1280 H × 1024 V pixels. To analyze the flame dynamics, a sequence of continuous flame surface topography of the flame zone is displayed in Figure 5 [28]. It can be noticed that the flame surface is wrinkled because of the effect of large vortices around the flame front, these vortices are generated due to the buoyant force caused by combustion. During the combustion, high-temperature gas is produced in the flame zone and accelerated into the cool ambient air. As the flow velocity of heated gas is larger than that of surrounding air, a vortex V1 outside the flame surface is formed at 0 ms, which facilitates the entrainment of air into the flame. As V1 moves upward along the flame front, a characteristic necking is observed. At the same time, a low-pressure region behind V1 is created and immediately filled by the burning gas from upstream, resulting in the production of a bulge. When this bulge rises, another vortex V2 is generated below the bulge at 10 ms; it convects as V1. The movement of vortices causes the flame puffing.  In addition, we also observed some attractive phenomena during the puffing process, which can give more insights to understand the puffing. At 10 ms, the flame base appeared a local auto-ignition, which caused a processive increase in the burning zone at the flame root in succedent images from 10 ms to 17.5 ms. Subsequently, the flame base is lifted off downstream from 17.5 ms to 30 ms, during which time, the liftoff height slightly became higher. Afterward, at 32.5 ms, a local re-ignition was found at the flame root. Which indicates that the behavior of auto-ignition and liftoff around the flame base alternately occur during the process of flame puffing. Another noticeable phenomenon is the flame extinction which appears at flame tip, as shown at 30 ms. This is attributed to the excessive air entrainment toward the flame tip due to the movement of the vortex, and thus the local temperature dropped significantly to extinguish the flame tip. It leads to a sudden shortening of the flame length. Moreover, some isolated small flame regions were found which are cut off from the main body by the entrained air, as displayed in 0-5 ms. These segmental regions also play an important indispensable role in the pulsation of flame.

Puffing Signal and Spectrum
The time variation in flame properties is displayed in Figure 6. For each case, the length of time is 1.28 s, a total of 512 sequential images were analyzed. The signal of flame heat-release rate was from our previous research [28]. It was seen that the curves of flame heat-release rate, flame area, and flame equivalent width are almost the same for any case, which indicates the flame heat-release rate is proportional to flame area and flame equivalent width. While, other properties including flame length, flame center length, and correlation coefficient display different varying behaviors with time. These signals were processed by Fast Fourier Transform (FFT) to obtain the characteristic frequency of flame puffing. Their amplitude-frequency curves are shown in Figure 7. In addition, we also observed some attractive phenomena during the puffing process, which can give more insights to understand the puffing. At 10 ms, the flame base appeared a local auto-ignition, which caused a processive increase in the burning zone at the flame root in succedent images from 10 ms to 17.5 ms. Subsequently, the flame base is lifted off downstream from 17.5 ms to 30 ms, during which time, the liftoff height slightly became higher. Afterward, at 32.5 ms, a local re-ignition was found at the flame root. Which indicates that the behavior of auto-ignition and liftoff around the flame base alternately occur during the process of flame puffing. Another noticeable phenomenon is the flame extinction which appears at flame tip, as shown at 30 ms. This is attributed to the excessive air entrainment toward the flame tip due to the movement of the vortex, and thus the local temperature dropped significantly to extinguish the flame tip. It leads to a sudden shortening of the flame length. Moreover, some isolated small flame regions were found which are cut off from the main body by the entrained air, as displayed in 0-5 ms. These segmental regions also play an important indispensable role in the pulsation of flame.

Puffing Signal and Spectrum
The time variation in flame properties is displayed in Figure 6. For each case, the length of time is 1.28 s, a total of 512 sequential images were analyzed. The signal of flame heat-release rate was from our previous research [28]. It was seen that the curves of flame heat-release rate, flame area, and flame equivalent width are almost the same for any case, which indicates the flame heat-release rate is proportional to flame area and flame equivalent width. While, other properties including flame length, flame center length, and correlation coefficient display different varying behaviors with time. These signals were processed by Fast Fourier Transform (FFT) to obtain the characteristic frequency of flame puffing. Their amplitude-frequency curves are shown in Figure 7.   In Figure 7, almost every spectrum has several oscillation frequencies with a certain amount of amplitude. This is different with the amplitude-frequency characteristics of non-swirl flame, which always has a single-peak spectrum as can be found in previous researches [1,3]. The appearance of multiple frequencies for present swirl flame may be due to the occurrence of spiral flow field (e.g., the precessing vortex core (PVC)), which leads to the complex flame oscillation behavior. All the frequencies exist in a low-frequency range, mainly in 0-50 Hz. Nearly each spectrum has two fundamental frequencies: dominant frequency (denoted as d) and sub-dominant frequency (denoted as s). Other frequencies in the same spectrum are found to be their harmonic frequencies (denoted as 2d, 3d, 4d; or 2s, 3s, 4s). For example, 2d represents the second order harmonic frequency of the In Figure 7, almost every spectrum has several oscillation frequencies with a certain amount of amplitude. This is different with the amplitude-frequency characteristics of non-swirl flame, which always has a single-peak spectrum as can be found in previous researches [1,3]. The appearance of multiple frequencies for present swirl flame may be due to the occurrence of spiral flow field (e.g., the precessing vortex core (PVC)), which leads to the complex flame oscillation behavior. All the frequencies exist in a low-frequency range, mainly in 0-50 Hz. Nearly each spectrum has two Energies 2018, 11,1916 9 of 14 fundamental frequencies: dominant frequency (denoted as d) and sub-dominant frequency (denoted as s). Other frequencies in the same spectrum are found to be their harmonic frequencies (denoted as 2d, 3d, 4d; or 2s, 3s, 4s). For example, 2d represents the second order harmonic frequency of the dominant frequency (d); while 2s represents the second order harmonic frequency of the sub-dominant frequency (s). As the fundamental frequencies (dominant frequency (d) and sub-dominant frequency (s)) in each case are the primary ones, we choose them for each condition to investigate the frequency behavior with the varying mass flow rate of primary air. Note that there are three spectrums which do not have the sub-dominant frequency, their corresponding conditions areṁ pri = 105 g/min in Figure 7c, m pri = 95 g/min in Figure 7e andṁ pri = 105 g/min in Figure 7f.

Puffing Frequency
As illustrated in Figure 8, the flame heat-release rate (Figure 8a), flame area (Figure 8b), and flame equivalent width (Figure 8d) have identical dominant frequency and sub-dominant frequency, this is consistent with the observation in Figure 6 that they have similar time traces. The dominant frequency and sub-dominant frequency both decreased with the increasing ofṁ pri . The enhanced mixing between primary air and fuel probably is the cause for this result. The probability for relatively distant fuel and primary air particles to mix with each other before burning increased whenṁ pri increased, resulting in the broadened region of fuel-lean/rich mixture. Thus, burning initiated in the premixing state enhanced low-temperature regions of flame. Meanwhile, reducing the high-temperature regions produced by the pure diffusion combustion of entirely separated fuel and air [36]. Consequently, the overall flame temperature lowered, that caused weaker buoyancy, inducing low velocity vortex movement and thus triggered lowered frequency.
Energies 2018, 11, x 9 of 14 dominant frequency (d); while 2s represents the second order harmonic frequency of the sub-dominant frequency (s). As the fundamental frequencies (dominant frequency (d) and sub-dominant frequency (s)) in each case are the primary ones, we choose them for each condition to investigate the frequency behavior with the varying mass flow rate of primary air. Note that there are three spectrums which do not have the sub-dominant frequency, their corresponding conditions are ṁpri = 105 g/min in Figure 7c, ṁpri = 95 g/min in Figure 7e and ṁpri = 105 g/min in Figure 7f.

Puffing Frequency
As illustrated in Figure 8, the flame heat-release rate (Figure 8a), flame area (Figure 8b), and flame equivalent width (Figure 8d) have identical dominant frequency and sub-dominant frequency, this is consistent with the observation in Figure 6 that they have similar time traces. The dominant frequency and sub-dominant frequency both decreased with the increasing of ṁpri. The enhanced mixing between primary air and fuel probably is the cause for this result. The probability for relatively distant fuel and primary air particles to mix with each other before burning increased when ṁpri increased, resulting in the broadened region of fuel-lean/rich mixture. Thus, burning initiated in the premixing state enhanced low-temperature regions of flame. Meanwhile, reducing the high-temperature regions produced by the pure diffusion combustion of entirely separated fuel and air [36]. Consequently, the overall flame temperature lowered, that caused weaker buoyancy, inducing low velocity vortex movement and thus triggered lowered frequency. Different properties display different puffing behaviors. As for flame length in Figure 8c, its dominant frequency reduced but sub-dominant frequency increased with the increasing of ṁpri; but for flame center length in Figure 8e, both the dominant and sub-dominant frequency have an ascending trend as ṁpri increased; while for image correlation coefficient in Figure 8f, its dominant frequency increased but sub-dominant frequency declined at larger ṁpri. Although their frequencies and the varying trends of the frequency with ṁpri are diverse, yet all dominant and sub-dominant frequencies of flame properties are in the range of 3-14 Hz. These frequencies were compared with the frequencies predicted by some existing theoretical models based on non-swirl flames. The frequency f in these models merely relies on the injector diameter dj, as introduced before, f = Cdj −0.5 , where C is a constant but varying in different models. The models and their predicted results are shown in Table 1, where dj is 0.01 m (the diameter of the nozzle throat which is considered as the exit of injector). As displayed in Table 1, the calculated frequencies from the theoretical models are larger than the present measurement of swirl flame (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). This indicates that the puffing frequency of swirl flame does not only depend on the diameter of injector but also relies on the mass flow rate of primary air, that is to say, it was much more sensitive to the variation in ṁpri than the frequency of non-swirl flame. In addition, an accurate scaling of the puffing frequency with the mass flow rate of primary air may not be acquired at present as the current data is not much, while we will measure more experimental data to develop the scaling in the future.

Puffing Mean Value
To calculate the normalized puffing amplitude in the next section, the time-mean value of flame properties was first determined. Each time-mean value can be obtained as the ratio between the integration of the corresponding property to time and the time length (1.28 s). The results are shown in Figure 9; one can see that all flame properties except the correlation coefficient have an overall decreasing trend with the increment of the mass flow rate of primary air. The decreasing flame area, flame length, and flame equivalent width are attributed to the declined air entrainment needed for dilution of the fuel to stoichiometric levels as ṁpri increased. Which resulted in the reduction of the Different properties display different puffing behaviors. As for flame length in Figure 8c, its dominant frequency reduced but sub-dominant frequency increased with the increasing ofṁ pri ; but for flame center length in Figure 8e, both the dominant and sub-dominant frequency have an ascending trend asṁ pri increased; while for image correlation coefficient in Figure 8f, its dominant frequency increased but sub-dominant frequency declined at largerṁ pri . Although their frequencies and the varying trends of the frequency withṁ pri are diverse, yet all dominant and sub-dominant frequencies of flame properties are in the range of 3-14 Hz. These frequencies were compared with the frequencies predicted by some existing theoretical models based on non-swirl flames. The frequency f in these models merely relies on the injector diameter d j , as introduced before, f = Cd j −0.5 , where C is a constant but varying in different models. The models and their predicted results are shown in Table 1, where d j is 0.01 m (the diameter of the nozzle throat which is considered as the exit of injector). As displayed in Table 1, the calculated frequencies from the theoretical models are larger than the present measurement of swirl flame (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). This indicates that the puffing frequency of swirl flame does not only depend on the diameter of injector but also relies on the mass flow rate of primary air, that is to say, it was much more sensitive to the variation inṁ pri than the frequency of non-swirl flame. In addition, an accurate scaling of the puffing frequency with the mass flow rate of primary air may not be acquired at present as the current data is not much, while we will measure more experimental data to develop the scaling in the future.

Puffing Mean Value
To calculate the normalized puffing amplitude in the next section, the time-mean value of flame properties was first determined. Each time-mean value can be obtained as the ratio between the integration of the corresponding property to time and the time length (1.28 s). The results are shown in Figure 9; one can see that all flame properties except the correlation coefficient have an overall decreasing trend with the increment of the mass flow rate of primary air. The decreasing flame area, flame length, and flame equivalent width are attributed to the declined air entrainment needed for dilution of the fuel to stoichiometric levels asṁ pri increased. Which resulted in the reduction of the heat-release rate because it is proportional to the flame area as stated before. Moreover, the decreased flame center length indicates that the flame moves upstream at higherṁ pri . The correlation coefficient exhibits unusual behavior, which firstly diminished and then increased whenṁ pri increased. It can also be observed that the flame heat-release rate, flame area, and flame equivalent width almost have an identical variation trend, i.e., asṁ pri increased, they initially dropped and then remained nearly unchanged. The flame length and flame center length have a similar variation trend, i.e., they approximately uniformly descended with the increase inṁ pri . These time-averaged values were used to obtain the normalized amplitude. heat-release rate because it is proportional to the flame area as stated before. Moreover, the decreased flame center length indicates that the flame moves upstream at higher ṁpri. The correlation coefficient exhibits unusual behavior, which firstly diminished and then increased when ṁpri increased. It can also be observed that the flame heat-release rate, flame area, and flame equivalent width almost have an identical variation trend, i.e., as ṁpri increased, they initially dropped and then remained nearly unchanged. The flame length and flame center length have a similar variation trend, i.e., they approximately uniformly descended with the increase in ṁpri. These time-averaged values were used to obtain the normalized amplitude.

Puffing Amplitude
The peak-to-peak amplitude of flame puffing was normalized by the time-mean value obtained in Section 3.4; the results are presented in Figure 10. It can be found that the amplitude behaviors of flame properties are diverse, which can be summarized as the following. The normalized amplitude of flame heat-release rate, flame area, and flame center length have similar behavior, i.e., as ṁpri increased, the amplitude initially enlarged and then slightly decreased. While the amplitude of flame equivalent width increased with the increment of ṁpri (sharply at the beginning and mildly at the end). However, under increasing ṁpri, the amplitude of flame length evenly expanded but the amplitude of correction coefficient remained unchanged. One can also observe that the amplitude of flame length is the smallest in all properties, this indicates that the oscillating intensity of flame length is the most weakened. While the amplitude of the flame area and flame equivalent width are

Puffing Amplitude
The peak-to-peak amplitude of flame puffing was normalized by the time-mean value obtained in Section 3.4; the results are presented in Figure 10. It can be found that the amplitude behaviors of flame properties are diverse, which can be summarized as the following. The normalized amplitude of flame heat-release rate, flame area, and flame center length have similar behavior, i.e., asṁ pri increased, the amplitude initially enlarged and then slightly decreased. While the amplitude of flame equivalent width increased with the increment ofṁ pri (sharply at the beginning and mildly at the end). However, under increasingṁ pri , the amplitude of flame length evenly expanded but the amplitude of correction coefficient remained unchanged. One can also observe that the amplitude of flame length is the smallest in all properties, this indicates that the oscillating intensity of flame length is the most weakened. While the amplitude of the flame area and flame equivalent width are the largest, this implies both properties have the strongest oscillating level. Consequently, it can be inferred that the flame oscillation in width direction is much more intense than the oscillation in length direction; the flame puffing is mainly attributed to the oscillation in width direction.
Energies 2018, 11, x 12 of 14 the largest, this implies both properties have the strongest oscillating level. Consequently, it can be inferred that the flame oscillation in width direction is much more intense than the oscillation in length direction; the flame puffing is mainly attributed to the oscillation in width direction. Figure 10. The normalized peak-to-peak amplitude of flame puffing.

Conclusions
The puffing behavior of a swirl partially premixed flame under varying mass flow rate of primary air ṁpri was explored by performing an experiment. The puffing dynamics were analyzed, and the puffing frequency and amplitude were obtained. The main findings of this study are listed as follows: (1) Flame puffing was caused by the movements of large vortices around the flame surface due to the buoyancy. During the puffing process, some instability phenomena were also observed which gave a deeper insight into the understanding about the puffing. The observed phenomena include the local auto-ignition around the flame base, the variation in the height of flame liftoff, local extinction around the flame tip, and the production of isolated small flame regions. (2) Almost each spectrum had two fundamental frequencies: dominant frequency and sub-dominant frequency, other frequencies in the same spectrum are found to be their harmonic frequencies. This is different with the amplitude-frequency characteristic of non-swirl flame, which always has a single-peak spectrum. The appearance of multiple frequencies may be due to the occurrence of the spiral flow field in swirl flame, which leads to the complex flame oscillation behavior.

Conclusions
The puffing behavior of a swirl partially premixed flame under varying mass flow rate of primary airṁ pri was explored by performing an experiment. The puffing dynamics were analyzed, and the puffing frequency and amplitude were obtained. The main findings of this study are listed as follows: (1) Flame puffing was caused by the movements of large vortices around the flame surface due to the buoyancy. During the puffing process, some instability phenomena were also observed which gave a deeper insight into the understanding about the puffing. The observed phenomena include the local auto-ignition around the flame base, the variation in the height of flame liftoff, local extinction around the flame tip, and the production of isolated small flame regions. (2) Almost each spectrum had two fundamental frequencies: dominant frequency and sub-dominant frequency, other frequencies in the same spectrum are found to be their harmonic frequencies. This is different with the amplitude-frequency characteristic of non-swirl flame, which always has a single-peak spectrum. The appearance of multiple frequencies may be due to the occurrence of the spiral flow field in swirl flame, which leads to the complex flame oscillation behavior. (3) The flame heat-release rate, flame area, and flame equivalent width had identical dominant frequency and sub-dominant frequency, both of which decreased with the increase inṁ pri . This was attributed to the decreased overall flame temperature caused by the improved mixing of fuel and primary air. Although other properties exhibit different frequency behaviors, all frequencies are in the range of 3-14 Hz. (4) The predicted frequencies from the theoretical models based on non-swirl flame are larger than the present measurement of swirl flame. Which indicates that the puffing frequency of swirl flame not only depends on the diameter of injector but also relies on the mass flow rate of primary air. Alternatively, it was much more sensitive to the variation inṁ pri than the frequency of non-swirl flame.
Energies 2018, 11,1916 13 of 14 (5) The time-mean values of all flame properties, except the correlation coefficient, have an overall decreasing trend with the increment ofṁ pri . The decreasing flame area, flame length, and flame equivalent width were attributed to the declined air entrainment requirement for dilution of the fuel to the stoichiometric ratio asṁ pri increased. Which resulted in the reduction of the heat-release rate, since it is proportional to the flame area. (6) The normalized peak-to-peak amplitude behavior of flame properties is diverse. In all properties, the amplitude of flame length is the smallest with the most weakened oscillating intensity. While the amplitude of the flame area and flame equivalent width are the largest two, with the strongest oscillating level. Consequently, it can be inferred that the flame oscillation in width direction is more intensified than the oscillation in length direction, so the flame puffing is mainly attributed to the oscillation in width direction.