# Analysis of Flame Evolution Generated from Methyl Laurate Droplet Using Deep Learning
## 3 Results and Discussion  
### Ignition Delay Time and Droplet Lifetime  
In droplet combustion, the heating process results in an increase in the droplet's surface temperature as it absorbs heat from the surrounding environment and undergoes evaporation. There is a phase called ignition delay time, which is the interval between the  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Batch & 16 & Learning rate & 0.001 \\ Subdivision & 4 & Burn\_in & 1000 \\ Width & 640 & Max\_batches & 5000 \\ Height & 640 & Policy & Steps \\ Channels & 3 & Steps & 4000 \\ Momentum & 0.937 & Scales & 0.1 \\ Decay & 0.0005 & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Model configuration of YOLOv9.  
Figure 3: (**a**) Example image of flame, and (**b**) Image of droplet with backlight.  
droplet being subjected to high temperatures and the appearance of the flame [47]. The measurement of the total ignition delay time encompassed the entire process, starting from the initial heating of the droplet, its surface evaporation, the diffusion of gas-phase fuel into the surrounding environment, and the associated chemical reactions. The ignition delay time is separated into two phases: the physical ignition delay and the chemical ignition delay [48]. The physical ignition delay time is the duration needed to establish a uniform reactive mixture of fuel and air. In this stage, the fuel evaporates, mixes with air, and heats up to reach the ignition temperature. Viscosity plays a key role during this period, with lower-viscosity fuels experiencing a shorter ignition delay. The chemical ignition delay time refers to the period required for the formation of reactive radicals that trigger thermal explosions in a uniform mixture. This duration is affected by the chemical composition of the fuel, particularly the concentration of low-volatility species.  
In this study, the average ignition delay time value of methyl laurate was 0.28 s. The ignition delay time is also impacted by the diffusivity of fuel vapor into the air, which serves as the oxidizer [49]. Fuel vapor diffusivity plays a crucial role in the physical ignition delay stage. Higher vapor diffusivity means that the fuel vaporizes more quickly, which can reduce the physical ignition delay time. Conversely, fuels with low vapor diffusivity may take longer to vaporize, leading to a longer physical ignition delay [47]. The fuel vapor diffusivity is determined by the molecular weight of the fuel. Methyl laurate has a molecular weight of 214.34 g/mol (Table 1). Since methyl laurate has a relatively high molecular weight [47; 47], its vapor diffusivity would be lower compared to lighter fuels. This means it would take longer for methyl laurate to vaporize and mix with air. Regarding ignition delay time, methyl laurate tends to have a higher ignition delay time compared to some other fuels [50]. This is due to its lower vapor diffusivity and higher molecular weight, which results in slower vaporization and mixing with the oxidizer. With a prolonged ignition delay, a greater proportion of the fuel combusts in premix mode rather than diffusion mode, consequently reducing the droplet's lifetime [51].  
Another important factor that affects ignition delay time is viscosity. Methyl laurate is a fatty acid ester, and it exhibits a notable relationship between its viscosity and ignition delay time. A higher viscosity of methyl laurate (Table 1) leads to increased ignition delay time due to slower fuel atomization and vaporization rates [52]. This results in larger fuel droplets that take longer to evaporate and mix with air, delaying the formation of a combustible mixture. Consequently, the ignition process is postponed until the fuel vapor concentration reaches a critical level. Conversely, lower-viscosity fuel vaporizes more rapidly, promoting quicker and more uniform mixing with air, thereby reducing the ignition delay time.