Effect of Different Acoustic Parameters on NOx Emissions of Partially Premixed Flame

The effects of acoustic frequency (f)/0–400 Hz and amplitude (A)/0–1400 Pa on nitrogen oxides (NOx) emissions of a partially premixed flame were investigated experimentally. The mechanism of NOx emissions was analyzed by the evolution of the vortex, which was shown by particle image velocimetry (PIV). From the relationship of NOx emission index (EINOx) and acoustic parameters, it was concluded that a critical frequency (fc) from 170 Hz to 190 Hz appeared. When the frequency was less than fc, EINOx decreased linearly with an increase in amplitude. The flame length became shorter, which led to a decrease in the global residence time, and hence, a reduction in reaction time for NOx. However, a direct proportional relationship between EINOx and amplitude was not found when the frequency was larger than fc. Based on PIV particle scattering images, with an increase of the acoustic frequency, the effects of the acoustic field on the flame base became less significant, but the flame length and reaction space of NOx were gradually increased.


Introduction
There is a growing interest in alternative technologies for energy generation applications, which can range from the emerging of hybrid solar receiver-combustor (HRC) technologies [1,2] to simpler fuel blending approaches, such as the co-firing of biomass feed stocks with coal for power generation purposes [3,4], because of increasing pressure to conserve ever diminishing fossil fuel resources and to reduce pollutant emissions. Excessive emissions of nitrogen oxide (NOx) from power generation applications is a severe problem that can lead to increased occurrences of acid rain and photochemical smog pollution. This has also led to research and investment into low NOx combustion technology [5][6][7], such as pulsed combustion technology. Pulse combustion technology is one of the highly combustion efficient and low NOx combustion technologies that have been demonstrated in engineering application. Pulse/pulsating combustion refers to the unstable combustion process under the effects of sound field or pulsating flow, while the steady-state variables such as temperature, pressure, air velocity, and heat release rate fluctuate periodically with time in the combustion zone. This phenomenon about heat excited acoustic oscillations was firstly observed by Rijke, who discovered that strong acoustic oscillations occurred when a heated metallic grid was positioned in the lower half of a vertical tube opened at both ends [8]. Rayleigh stated that the sound could be excited in a closed volume only if the pressure oscillation is in phase with the heat-release oscillation [9]. Based on Rayleigh's criterion, different kinds of pulse combustors, including the Rijke, Hemholtz, Schmidt

Experimental Setup
The experimental system consisted of the combustor and a sound generating device, as seen in Figure 1. It is an atmospheric, partially premixed combustor, consisting of an annular jet burner with a coflow tube and an optically accessible quartz combustion chamber. The improved Burke-Schumann burner, which was referenced in Hassan et al. [21] and Illingworth et al. [30], was designed. This Bunsen burner was installed in the center of a coflow tube (1600 mm × Φ140 mm) with two rectangular-shaped quartz windows (90 mm × 400 mm). The burner had an inner diameter, d F , of 18.0 mm and a lip thickness of 2.0 mm. The inner diameter of the coflow tube, d C , was 150 mm. The coflow air jet was injected parallel to the central jet of the methane mixture to provide enough oxygen for the combustor. The coflow air was maintained at a sufficiently low velocity, less than 0.1 m/s, so as not to disturb the flow field in the combustion area. Porous medium plates were set in the coflow tube to ensure a uniform airflow. A loud speaker (A0208A, JBL, Northridge, CA, USA) with a signal generator (AFG-2225, GW-INSTEK, Taiwan, China) and amplifier (E-470, Accuphase, Yokohama, Japan) were placed at the bottom of the combustor as a forced acoustic source to provide adjustable acoustic frequencies and amplitudes (see Figure 1). Appl. Sci. 2019, 9,

Instrumentation and Acquisition
A pressure sensor (CYG1409T, Shuang Qiao, Kun Shan, China), which was installed at the flame location and perpendicular to the cylinder's axis, was employed to measure the acoustic frequency and amplitude in the cylinder. The pressure sensor had a measuring range of 0-3000 Pa and a measuring accuracy of 1%. The results were obtained after fast Fourier transform (FFT) by a data acquisition system (PXI-1033, NI-DAQ).
As shown in Figure 2, the flame length was measured by processing the images taken by a highspeed digital camera (MVC1000DAF-GE1000, Microview, Beijing, China). A digital single-lens reflex (DSLR) camera (Canon, EOS 550d, Tokyo, Japan) was used to observe flame structures and flame surface wrinkling. The exposure time for the high-speed camera was set at 1/1000 s. To visualize the flow field, a particle image velocimetry (PIV) system (Dantec dynamics, Copenhagen, Denmark) was utilized to describe the flame response under acoustic excitation. The PIV system consists of a YAG laser generator with double 200 mJ pulses at 532 nm and a Dantec Dynamics Flow Sense 4 M digital camera with 2048 × 2048 pixels. Al2O3 seeding particles about 2.5 μm in diameter were used to seed the coflow air tube.
A 2D cross-correlation FFT algorithm incorporating a multi-pass approach was used to analyze corresponding particle image pairs. The initial pass of the routine analyzed the images using 32 by 32 pixel interrogation regions, and the final pass used interrogation regions of 16 by 16 pixels. A 3point Gaussian peak search algorithm was used to calculate sub-pixel displacement and a 50% Nyquist overlap of the regions was incorporated.
Phase-resolved PIV measurement was triggered by the signal from the pressure sensor. A compromise on the number of PIV image pairs was made for the phase-resolved PIV experiments. This was because the sampling rate was low due to phase jitter and a longer duration of the experiments would exacerbate the problem associated with deposition of seed particle on the enclosure wall. The 100 image pairs collected were deemed sufficient to produce stable mean velocities for examining the evolution of the flow field structures of partially premixed flame.

Instrumentation and Acquisition
A pressure sensor (CYG1409T, Shuang Qiao, Kunshan, China), which was installed at the flame location and perpendicular to the cylinder's axis, was employed to measure the acoustic frequency and amplitude in the cylinder. The pressure sensor had a measuring range of 0-3000 Pa and a measuring accuracy of 1%. The results were obtained after fast Fourier transform (FFT) by a data acquisition system (PXI-1033, NI-DAQ).
As shown in Figure 2, the flame length was measured by processing the images taken by a high-speed digital camera (MVC1000DAF-GE1000, Microview, Beijing, China). A digital single-lens reflex (DSLR) camera (Canon, EOS 550d, Tokyo, Japan) was used to observe flame structures and flame surface wrinkling. The exposure time for the high-speed camera was set at 1/1000 s. To visualize the flow field, a particle image velocimetry (PIV) system (Dantec Dynamics, Copenhagen, Denmark) was utilized to describe the flame response under acoustic excitation. The PIV system consists of a YAG laser generator with double 200 mJ pulses at 532 nm and a Dantec Dynamics Flow Sense 4 M digital camera with 2048 × 2048 pixels. Al 2 O 3 seeding particles about 2.5 µm in diameter were used to seed the coflow air tube.
A 2D cross-correlation FFT algorithm incorporating a multi-pass approach was used to analyze corresponding particle image pairs. The initial pass of the routine analyzed the images using 32 by 32 pixel interrogation regions, and the final pass used interrogation regions of 16 by 16 pixels. A 3-point Gaussian peak search algorithm was used to calculate sub-pixel displacement and a 50% Nyquist overlap of the regions was incorporated.
Phase-resolved PIV measurement was triggered by the signal from the pressure sensor. A compromise on the number of PIV image pairs was made for the phase-resolved PIV experiments. This was because the sampling rate was low due to phase jitter and a longer duration of the experiments would exacerbate the problem associated with deposition of seed particle on the enclosure wall. The The flame length was obtained by flame area image processing [31][32][33]. The flame contour and flame length were obtained by selecting the threshold value in the flame area image, which was captured by high-speed camera. The average flame length was calculated based on every 2000 photos. An electrochemical NOx sensor (CLD64, ECO Physics, Duernten, Switzerland) was located after the flue gas collection device, and the collection device used was made with reference to Costa's work but with slight modifications for adapting the size of the combustor [34]. Another infrared fuel gas analyzer (Photon, Madur, Vienna, Austria) was used to measure components of the exhaust gas. Measurement precision of components are shown in Table 1.  The NOx emission index (EINOx) was employed to characterize NOx emissions, which were defined as NOx per unit mass fuel. Assuming that all the carbons in the fuel are completely converted into CO2 and CO, EINOx is defined as: Here, is the mole fraction， is the number of carbon atoms in the fuel， and is molar mass.
According to the measurement error transfer formula, the arithmetic average error of EINOx is: The EINOx deviation was 0.001-0.005 g/kg, which was less than 1% of experimental values, which means the experimental data was accurate. The flame length was obtained by flame area image processing [31][32][33]. The flame contour and flame length were obtained by selecting the threshold value in the flame area image, which was captured by high-speed camera. The average flame length was calculated based on every 2000 photos. An electrochemical NOx sensor (CLD64, ECO Physics, Duernten, Switzerland) was located after the flue gas collection device, and the collection device used was made with reference to Costa's work but with slight modifications for adapting the size of the combustor [34]. Another infrared fuel gas analyzer (Photon, Madur, Vienna, Austria) was used to measure components of the exhaust gas. Measurement precision of components are shown in Table 1. The NOx emission index (EINOx) was employed to characterize NOx emissions, which were defined as NOx per unit mass fuel. Assuming that all the carbons in the fuel are completely converted into CO 2 and CO, EINOx is defined as: Here, x i is the mole fraction, m is the number of carbon atoms in the fuel, and MW i is molar mass.
According to the measurement error transfer formula, the arithmetic average error of EINOx is: Appl. Sci. 2019, 9, 1490 5 of 12 The EINOx deviation was 0.001-0.005 g/kg, which was less than 1% of experimental values, which means the experimental data was accurate.

Experimental Conditions
The primary equivalence ratios (Φ) of 2 and 3 were selected for comparison because the partially premixed flame would not flash back or blow off under acoustic excitation at these equivalence ratios. Methane and air flow rates were controlled by the mass flow controller (Sheng Ye, SY-93) with precision of approximately 1%. Experimental conditions are summarized in Table 2. The mean velocities of premixed fuel in the combustor were 0.393 m/s, 0.5895 m/s, and 0.426 m/s corresponding to case 1, case 2, and case 3, respectively. The average velocity of coflow air was 0.00964 m/s; therefore, the influence of the coflow air on the flame structures and flame surface wrinkling could be ignored. The Reynolds number ranged from 422.1 to 663.1, which belonged to laminar combustion without acoustic excitation. For laminar flame, the relationship between NOx and the flow field induced by acoustic excitation was more clearly. Comparison of NOx emission characteristics with equivalence ratios and Reynolds numbers were conducted.
The ranges of acoustic frequency and acoustic amplitude were selected between 0-400 Hz and 0-1400 Pa. Firstly, pulsed combustors tend to operate at low frequencies, usually around 100 Hz [17]. Secondly, based on the experimental results of the premixed flame under acoustic excitation, Bourehla [35] found the flame shape changed significantly within the frequency range of 100 Hz to 220 Hz. In addition, the flame structure also changed significantly following an increase in the amplitude. Furthermore, the acoustic response of the speaker had a good behavior between 0-400 Hz and 0-1400 Pa. The maximum of acoustic amplitude was 1400 Pa, and pressure amplitude p n could be converted to velocity amplitude u n by conversion relations [36,37]: Herein n is acoustic mode; ρ m is density (=0.946 kg/m 3 ); c is sonic speed (=387.23 m/s). As a result, the maximum of acoustic velocity amplitude was 3.8218 m/s.

Acoustic Characteristics of Experimental System
Acoustic amplitude and frequency were adjustable in this experiment. The measured results of 180 Hz with 579.04 Pa acoustic are shown in Figure 3; no obvious signal noise was apparant. Therefore, reliability of the acoustic excitation was verified.
Herein n is acoustic mode; is density (= 0.946 kg/m ); is sonic speed (=387.23 m/s). As a result, the maximum of acoustic velocity amplitude was 3.8218 m/s.

The Relationship between EINOx with Acoustic Amplitude
The NOx emissions for partially premixed flame under acoustic excitation are plotted in Figure 4. The linear relationship between acoustic amplitude and EINOx were presented at a fixed frequency. Under three different premixed gas parameters, the lines displayed a negative slope when the frequency was less than 180 Hz, while a positive slope appeared when the frequency was more than 190 Hz. Therefore, a critical frequency ( f c ) was defined between 170 Hz and 190 Hz, which was consistent with Delabroy's results from a liquid boiler [20].
Appl. Sci. 2019, 9, x 6 of 12 Acoustic amplitude and frequency were adjustable in this experiment. The measured results of 180 Hz with 579.04 Pa acoustic are shown in Figure 3; no obvious signal noise was apparant. Therefore, reliability of the acoustic excitation was verified.

The Relationship between EINOx with Acoustic Amplitude
The NOx emissions for partially premixed flame under acoustic excitation are plotted in Figure  4. The linear relationship between acoustic amplitude and EINOx were presented at a fixed frequency. Under three different premixed gas parameters, the lines displayed a negative slope when the frequency was less than 180 Hz, while a positive slope appeared when the frequency was more than 190Hz. Therefore, a critical frequency ( ) was defined between 170 Hz and 190 Hz, which was consistent with Delabroy's results from a liquid boiler [20].
EINOx and amplitude had linear relationships in each case. EINOx reduced 15% to 30% with the increase of amplitude by every 100 Pa when frequency was less than . Furthermore, the slope in this region ranged from -0.009 to -0.003. In contrast, the linear relationships were reversed when the frequency was greater than ; the positive slopes were also observed to range from 0.001 to 0.006. In a word, EINOx decreased with the increase of acoustic amplitudes while frequency was less than , and increased while the frequency was greater than .   EINOx and amplitude had linear relationships in each case. EINOx reduced 15% to 30% with the increase of amplitude by every 100 Pa when frequency was less than f c . Furthermore, the slope in this region ranged from −0.009 to −0.003. In contrast, the linear relationships were reversed when the frequency was greater than f c ; the positive slopes were also observed to range from 0.001 to 0.006. In a word, EINOx decreased with the increase of acoustic amplitudes while frequency was less than f c , and increased while the frequency was greater than f c .

The Relationship between EINOx and Acoustic Frequency
The effects of acoustic frequency on NOx emissions are shown in Figure 5. There was a clear linear relationship between EINOx and frequency when frequency was less than f c , as seen in Figure 5. The positive slope of the linear relationship between EINOx and acoustic frequency ranges from 0.001 to 0.003. However, the relationship between the frequency and EINOx is not clear when f > f c . This is related to the flame response to acoustic excitation at different frequencies.

The Relationship between EINOx and Acoustic Frequency
The effects of acoustic frequency on NOx emissions are shown in Figure 5. There was a clear linear relationship between EINOx and frequency when frequency was less than , as seen in Figure  5. The positive slope of the linear relationship between EINOx and acoustic frequency ranges from 0.001 to 0.003. However, the relationship between the frequency and EINOx is not clear when > . This is related to the flame response to acoustic excitation at different frequencies.

Flame Length and Flame Surface Wrinkling
The flame images were taken by a Canon CMOS(Complementary Metal Oxide Semiconductor ) camera to show the flame structures under the different frequencies. In Figure 6, the images are illustrated for case two of partially premixed flames with a range of acoustic frequency from 80 Hz to 280 Hz based on time-average images. Flame surface wrinkles were quite different with acoustic frequencies at a fixed acoustic amplitude of 345 ± 10 Pa. The effects of acoustic forcing on flame wrinkling at 80 Hz to 150 Hz were much stronger than 200 Hz to 280 Hz, which was in good agreement with the results in the change of NOx emissions with acoustic frequency.

Flame Length and Flame Surface Wrinkling
The flame images were taken by a Canon CMOS (Complementary Metal Oxide Semiconductor) camera to show the flame structures under the different frequencies. In Figure 6, the images are illustrated for case two of partially premixed flames with a range of acoustic frequency from 80 Hz to 280 Hz based on time-average images. Flame surface wrinkles were quite different with acoustic frequencies at a fixed acoustic amplitude of 345 ± 10 Pa. The effects of acoustic forcing on flame wrinkling at 80 Hz to 150 Hz were much stronger than 200 Hz to 280 Hz, which was in good agreement with the results in the change of NOx emissions with acoustic frequency. Flame length (L ) can quantitatively describe the relationship between acoustic parameters and EINOx for jet flame. Compared with Figure 4 and Figure 7, this was consistent with the relationship between acoustic amplitude and NOx. Flame length decreased visibly with a gradually increase of acoustic amplitude when the frequency was less than 170 Hz. There was also a good linear correlation between the flame length and the acoustic amplitude when the frequency was less than 170 Hz. However, there was no obvious regularity between flame length and acoustic amplitude when the frequency was larger than 170 Hz.

Mechanism for Interaction between EINOx and Vortex
To visualize the interaction between flame and vortex, Mie scattering images and velocity fields were obtained by the PIV system to display vortex structure in the partially premixed flame with acoustic parameters of 110 Hz and 321 Pa for case two. In Figure 8, the white circular scattering image indicated that a vortex shape was generated near the exit of the nozzle by acoustic excitation. The vortex grew, left the flame root, and then moved to the downstream zone of the partially premixed flame, which could be observed from the velocity contour. It was thought that the periodic acoustic Flame length (L f ) can quantitatively describe the relationship between acoustic parameters and EINOx for jet flame. Compared with Figures 4 and 7, this was consistent with the relationship between acoustic amplitude and NOx. Flame length decreased visibly with a gradually increase of acoustic amplitude when the frequency was less than 170 Hz. There was also a good linear correlation between the flame length and the acoustic amplitude when the frequency was less than 170 Hz. However, there was no obvious regularity between flame length and acoustic amplitude when the frequency was larger than 170 Hz. Flame length (L ) can quantitatively describe the relationship between acoustic parameters and EINOx for jet flame. Compared with Figure 4 and Figure 7, this was consistent with the relationship between acoustic amplitude and NOx. Flame length decreased visibly with a gradually increase of acoustic amplitude when the frequency was less than 170 Hz. There was also a good linear correlation between the flame length and the acoustic amplitude when the frequency was less than 170 Hz. However, there was no obvious regularity between flame length and acoustic amplitude when the frequency was larger than 170 Hz.

Mechanism for Interaction between EINOx and Vortex
To visualize the interaction between flame and vortex, Mie scattering images and velocity fields were obtained by the PIV system to display vortex structure in the partially premixed flame with acoustic parameters of 110 Hz and 321 Pa for case two. In Figure 8, the white circular scattering image indicated that a vortex shape was generated near the exit of the nozzle by acoustic excitation. The vortex grew, left the flame root, and then moved to the downstream zone of the partially premixed flame, which could be observed from the velocity contour. It was thought that the periodic acoustic

Mechanism for Interaction between EINOx and Vortex
To visualize the interaction between flame and vortex, Mie scattering images and velocity fields were obtained by the PIV system to display vortex structure in the partially premixed flame with acoustic parameters of 110 Hz and 321 Pa for case two. In Figure 8, the white circular scattering image indicated that a vortex shape was generated near the exit of the nozzle by acoustic excitation. The vortex grew, left the flame root, and then moved to the downstream zone of the partially premixed flame, which could be observed from the velocity contour. It was thought that the periodic acoustic excitation enhanced the mixing of fuel and air, and reduced the flame length. Research results showed that when the flame length reduced, the reaction region of NOx shortened, reaction rate strengthened, and NOx emission decreased [23,38].
Appl. Sci. 2019, 9, x 9 of 12 excitation enhanced the mixing of fuel and air, and reduced the flame length. Research results showed that when the flame length reduced, the reaction region of NOx shortened, reaction rate strengthened, and NOx emission decreased [23,38]. The interaction between vortex and flame was the important mechanism for reduction of NOx in partially premixed flame with acoustic excitation. Figure 9 shows the interaction of flame-vortex under the acoustic frequency range from 80 Hz to 280 Hz in a fixed amplitude at 241 ± 10 Pa. It can be observed that the intensity and position of the vortex showed different characteristics with acoustic frequency. The vortex changed from upstream to downstream with an increase in frequency from 80 Hz to 200 Hz at the same phase. Vortex diameter became larger and the vortex rolled up with surrounding air to the downstream when the acoustic frequency increased. The flame-vortex The interaction between vortex and flame was the important mechanism for reduction of NOx in partially premixed flame with acoustic excitation. Figure 9 shows the interaction of flame-vortex under the acoustic frequency range from 80 Hz to 280 Hz in a fixed amplitude at 241 ± 10 Pa. It can be observed that the intensity and position of the vortex showed different characteristics with acoustic frequency. The vortex changed from upstream to downstream with an increase in frequency from 80 Hz to 200 Hz at the same phase. Vortex diameter became larger and the vortex rolled up with surrounding air to the downstream when the acoustic frequency increased. The flame-vortex interaction caused the flame base to broaden when the frequency was less than f c ( f c − ), although this broadening effect did not reappear when the frequency was greater than f c ( f c + ). This corresponded to an increase of NOx emissions induced by the weakness of the mixing effect. This was the reason that EINOx for f c − was much less than for f c + .
Appl. Sci. 2019, 9, x 10 of 12 interaction caused the flame base to broaden when the frequency was less than , although this broadening effect did not reappear when the frequency was greater than . This corresponded to an increase of NOx emissions induced by the weakness of the mixing effect. This was the reason that EINOx for -was much less than for +. As Figure 10 shows, the vortex moved upstream and enhanced the interaction at the base of the flame with an increase of amplitude at 110 Hz, but the influence of amplitude on the length of flame was not obvious at 280 Hz. These changes in flame structure with amplitude variation at different frequencies were well matched with changes of flame length shown in Figure 6. Therefore, NOx emission and flame length both shortened observably with increased acoustic amplitude at 110 Hz; however, it was opposite when the frequency was at 280 Hz.

Conclusions
The NOx emission of partially premixed flames under acoustic parameters of 0-400 Hz/0-1400 Pa were investigated experimentally. The relationship between frequency, amplitude, and EINOx was discussed based on flame length, flame shape, and vortex. The main conclusions are as follows: (1) The critical frequency , ∈ 170,190 , occurs in the changing EINOx of partially premixed flame with the increase of amplitude and frequency. A similar phenomenon is also observed in the change of flame length with acoustic parameters. EINOx decreases with the increase of amplitude when < ; there is a linear relationship between EINOx and amplitude, and the slope range is from -0.009 to -0.003; EINOx increases with the increase of frequency in a fixed amplitude, and there is also a linear relationship between EINOx and frequency, where the slope range is from 0.01 to 0.03. However, EINOx increases with an increase of amplitude when > , and there is a linear relationship between EINOx and amplitude, where the slope ranges from 0.001 to 0.006.
(2) The flame length decreases with the increase of amplitude when < ; the reason is that an increasing acoustic effect makes the flame wrinkle and deform, and the mixing effect of the flow field As Figure 10 shows, the vortex moved upstream and enhanced the interaction at the base of the flame with an increase of amplitude at 110 Hz, but the influence of amplitude on the length of flame was not obvious at 280 Hz. These changes in flame structure with amplitude variation at different frequencies were well matched with changes of flame length shown in Figure 6. Therefore, NOx emission and flame length both shortened observably with increased acoustic amplitude at 110 Hz; however, it was opposite when the frequency was at 280 Hz.
Appl. Sci. 2019, 9, x 10 of 12 interaction caused the flame base to broaden when the frequency was less than , although this broadening effect did not reappear when the frequency was greater than . This corresponded to an increase of NOx emissions induced by the weakness of the mixing effect. This was the reason that EINOx for -was much less than for +. As Figure 10 shows, the vortex moved upstream and enhanced the interaction at the base of the flame with an increase of amplitude at 110 Hz, but the influence of amplitude on the length of flame was not obvious at 280 Hz. These changes in flame structure with amplitude variation at different frequencies were well matched with changes of flame length shown in Figure 6. Therefore, NOx emission and flame length both shortened observably with increased acoustic amplitude at 110 Hz; however, it was opposite when the frequency was at 280 Hz.

Conclusions
The NOx emission of partially premixed flames under acoustic parameters of 0-400 Hz/0-1400 Pa were investigated experimentally. The relationship between frequency, amplitude, and EINOx was discussed based on flame length, flame shape, and vortex. The main conclusions are as follows: (1) The critical frequency , ∈ 170,190 , occurs in the changing EINOx of partially premixed flame with the increase of amplitude and frequency. A similar phenomenon is also observed in the change of flame length with acoustic parameters. EINOx decreases with the increase of amplitude when < ; there is a linear relationship between EINOx and amplitude, and the slope range is from -0.009 to -0.003; EINOx increases with the increase of frequency in a fixed amplitude, and there is also a linear relationship between EINOx and frequency, where the slope range is from 0.01 to 0.03. However, EINOx increases with an increase of amplitude when > , and there is a linear relationship between EINOx and amplitude, where the slope ranges from 0.001 to 0.006.
(2) The flame length decreases with the increase of amplitude when < ; the reason is that an increasing acoustic effect makes the flame wrinkle and deform, and the mixing effect of the flow field

Conclusions
The NOx emission of partially premixed flames under acoustic parameters of 0-400 Hz/0-1400 Pa were investigated experimentally. The relationship between frequency, amplitude, and EINOx was discussed based on flame length, flame shape, and vortex. The main conclusions are as follows: (1) The critical frequency f c , f c ∈ [170,190], occurs in the changing EINOx of partially premixed flame with the increase of amplitude and frequency. A similar phenomenon is also observed in the change of flame length with acoustic parameters. EINOx decreases with the increase of amplitude when f < f c ; there is a linear relationship between EINOx and amplitude, and the slope range is from −0.009 to −0.003; EINOx increases with the increase of frequency in a fixed amplitude, and there is also a linear relationship between EINOx and frequency, where the slope range is from 0.01 to 0.03. However, EINOx increases with an increase of amplitude when f > f c , and there is a linear relationship between EINOx and amplitude, where the slope ranges from 0.001 to 0.006.
(2) The flame length decreases with the increase of amplitude when f < f c ; the reason is that an increasing acoustic effect makes the flame wrinkle and deform, and the mixing effect of the flow field is enhanced. The flame length increases with the increase of amplitude when f > f c ; the reason is that the influence of acoustics on the flame becomes weakened in this frequency range; flame diameter is decreased, and fuel gas velocity is increased with the increase of amplitude. This is the dominant factor for the decrease of EINOx.
(3) Interaction between flame and vortex influences the NOx emission. When acoustic amplitude increases at f > f c , the vortex moves to the upstream zone of the partially premixed flame, there is enhanced interaction at the flame base, and shortened flame length; therefore, NOx emissions decrease.