# Effect of Different Acoustic Parameters on NOx Emissions of Partially Premixed Flame
## Materials and Methods
### Instrumentation and Acquisition  
A pressure sensor (CYG1409T, [PERSON], 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 (MVC1000 DAF-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 \(\times\) 2048 pixels. Al\({}_{2}\)O\({}_{3}\) seeding particles about 2.5 \(\upmu\)m 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  
Figure 1: Experimental system. 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. 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 [PERSON]'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:  
\[\text{EINOx}=(\frac{x_{NO_{x}}}{x_{CO}+x_{CO_{2}}})\cdot(\frac{mMW_{NOx}}{MW_{F }}). \tag{1}\]  
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:  
\[\text{\Delta EINOx}=(\frac{\Delta x_{NOx}}{x_{CO}+x_{CO_{2}}}+\left(-\frac{ \Delta x_{CO}\cdot x_{NOx}}{\left(x_{CO}+x_{CO_{2}}\right)^{2}}\right)+(-\frac {\Delta x_{CO_{2}}\cdot x_{NOx}}{\left(x_{CO}+x_{CO_{2}}\right)^{2}}))(\frac{ xMW_{NOx}}{MW_{F}}). \tag{2}\]