## 4 Conclusions  
This study experimentally investigated the suppression effect of the stratified jet-in-crossflow on thermoacoustic instability and \(\mathrm{NO_{x}}\) emissions in unstable premixed flames. This research would be used in the control scenario of combustion instability of heavy-duty gas turbines or gas-fired boilers. We explored the flame response characteristics at different jet flow rates and gas densities. The experimental results revealed that the Ar/He stratified jet can effectively reduce the thermoacoustic oscillation intensity and \(\mathrm{NO_{x}}\) emissions. The main conclusions are as follows:  
The Ar/He stratified jet reduces the intensity of thermoacoustic oscillations by up to 58%. The optimization of the jet flow rate and Ar/He volume ratio effectively reduces the amplitude of sound pressure in the combustion and premixed chambers. However, not all jet-in-crossflow conditions significantly reduce the amplitude of thermoacoustic instabilities. At a jet flow rate of 4 L/min, the suppression effect on thermoacoustic oscillations is minimal. The stratified jet-in-crossflow is influenced by several parameters. Therefore, more detailed primary and secondary analyses are required in the future to identify the key physical or chemical factors affecting thermoacoustic instabilities. As the flame oscillation intensity decreases, the oscillation mode shifts. These results indicate that the flame downstream of the jet shifts from an initial single-mode oscillation to the coexistence of multi-mode oscillations. The stratified jet-in-crossflow causes the flame to shift from an initial limit cycle state to a chaotic state. This indicates that the stratified jet-in-crossflow can suppress the intensity of combustion oscillations and promote the migration of oscillation modes, thereby disrupting the original balance of energy exchange in the limit cycle. After the jet introduction, the maximum \(\mathrm{NO_{x}}\) concentration of the flame decreases by 48.8%. During the experiment, the \(\mathrm{NO_{x}}\) concentration decreases linearly with the jet flow rate. Additionally, a higher Ar/He volume ratio contributes to a further reduction in \(\mathrm{NO_{x}}\) concentration. This reduction is mainly due to the stratified jet, which reduces the equivalence ratio of the flame and causes the flame to shift toward a leaner combustion mode, thereby reducing \(\mathrm{NO_{x}}\) emissions. The Ar/He stratified jet modifies the temperature field and flame shape in the combustion chamber, leading to a more uniform temperature distribution. This indicates a reduction in the flame residence time, which regulates the \(\mathrm{NO_{x}}\) generation process. It can be seen that this study only considers the thermoacoustic instability of combustion at atmospheric pressure. In the future, this study will further analyze the impact of stratified jet-in-cross-flow on flame stability in high-pressure combustion chambers through advanced flow field measurement methods. Figure 13: Momentum ratio of jet-in-crossflow at different flow rates and gas densities. **Author Contributions:** Conceptualization, R.S. and C.T. ; methodology, R.S. ; formal analysis, R.S. ; investigation, R.S. and C.T. ; writing--original draft preparation, R.S. ; writing--review and editing, R.S. ; supervision, C.T. ; funding acquisition, R.S. and C.T. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Qinglan Project of Jiangsu Province of China, the Innovation Fund of the Nanjing Institute of Technology (CKJA202202), the Natural Science Foundation of Jiangsu Province (No. BK20230699), and the China Postdoctoral Science Foundation (No. 2023M731492). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.