# Analysis of Flame Evolution Generated from Methyl Laurate Droplet Using Deep Learning
## 3 Results and Discussion
### Temperature Profile and Evolutionary Dynamics of Flame and Droplet Combustion  
The change in droplet diameter during one individual test is shown during the ignition delay period until the end of the droplet's lifespan in Figure 10. The combustion period is segmented into three stages: t\({}_{1}\) represents the heating phase, t\({}_{2}\) signifies the unsteady combustion phase, and t\({}_{3}\) denotes the quasi-steady combustion phase. All fuel droplets gradually increase in size due to the expansion of bubbles, thermal expansion during the heating phase, and movement of bubbles to the surface of the droplet. The parameter D\({}^{2}\)/D\({}_{0}\)\({}^{2}\) represents the normalized square of the droplet diameter, where D\({}_{0}\) corresponds to the initial diameter and D denotes the diameter during the evaporation and combustion processes. This ratio provides a dimensionless measure of droplet size evolution over time. The increase in the ratio of D\({}^{2}\)/D\({}_{0}\)\({}^{2}\) in methyl laurate occurs gradually because the homogeneous fuel produces few bubbles. This contrasts with non-homogeneous fuels, which have varying boiling points and generate many bubbles, resulting in fluctuating D\({}^{2}\)/D\({}_{0}\)\({}^{2}\) values [7]. During stage t\({}_{2}\), fluctuations in droplet diameter were caused by the large size of the droplet. The heat transfer from the flame to the droplet occurred at a significantly faster rate than the mass transfer of fuel vapor to the surface  
Figure 8: Visualization of automatic image segmentation of methyl laurate flame. Figure 10: Droplet diameter and temperature during combustion of methyl laurate. Figure 9: Droplet auto-segmentation visualization of methyl laurate. of the droplet. Therefore, internal circulation existed between the fuel vapor contained within the droplet and the liquid phase of the fuel. When the fuel in the gaseous phase was trapped within the droplet, it resulted in an increase in the square of the droplet's diameter. This value subsequently decreased as the gas phase reached the surface of the droplet and started to diffuse into the surrounding air. Combustion concludes at stage t3 when the size of the droplet becomes quite small. This results in a rapid decrease in the droplet diameter squared, with no further fluctuations in size observed at this stage. There are several factors that affect droplet temperature, such as the flash point, heat loss through radiation from gas and soot within the flame, burning rate, and the fuel's heating value [60; 61]. Figure 10 depicts the correlation between droplet temperature and time throughout the combustion process. Initially, the temperature curve remains constant just before reaching the ignition temperature, marking the end of the evaporation stage. The highest droplet temperature is observed towards the end of combustion, where the flame persists even after the droplet has completely burned. At this point, the thermocouple junction is fully exposed to the flame. The peak temperature for the methyl laurate droplets is recorded at 382.6 \({}^{\circ}\)C. Figure 10 also illustrates the temperature history of the droplet throughout the evaporation stage until it reaches the ignition temperature. During this phase, the droplet temperature is influenced by the efficiency with which molecules absorb heat. This phenomenon occurs through the evaporation of methyl laurate once it reaches its boiling point. The process comes to a halt once the vapor-air mixture reaches the ignition point. Within 1.05 s, the droplet temperature shows a rapid increase until the delay time concludes. The observed fluctuations in droplet diameter during the quasi-steady combustion phase (Figure 10) may partially arise from limitations in thermocouple response time (\(\pm\)2.5 \({}^{\circ}\)C error) and transient environmental factors. However, the high segmentation accuracy of YOLOv9 (mAP 0.974 for flame detection) ensures that these variations primarily reflect physical combustion dynamics rather than measurement artifacts.