# 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
In this study, the diameter linked to the volume was the controlled variable for droplet combustion. Thus, the heating value is represented as the volumetric higher heating value (\(HHV_{volumetric}\)) in kJ/cm\({}^{3}\) using Equation (3) below [8]. \(HHV_{graumetric}\) emphasizes the energy content of a fuel based on its weight, which is ideal for comparing dense or compact fuels, while \(HHV_{volumetric}\) focuses on energy per volume and is suited for analyzing the storage and distribution efficiency of liquid or gaseous fuels. \[HHV_{volumetric}=HHV_{graumetric}\;\rho \tag{3}\]  
The energy density of the methyl laurate was 32.34 kJ/cm\({}^{3}\). Previous works shows that methyl laurate, with its relatively lower viscosity and melting point, remains fluid and efficient for combustion even at lower temperatures, enhancing its application in various climates. Additionally, its derived thermodynamic properties, such as the coefficient of thermal expansion and bulk compressibility, further affirm methyl laurate's favorable characteristics for stable fuel performance and efficient combustion, especially compared to longer-chain esters like methyl istearate [62]. The flame length was derived through precise centerline extraction and processing based on the machine vision algorithm. Initially, the centerline was computed by identifying the middle pixel positions along the flame contour at each vertical axis level within the segmented flame image. This technique ensures that the centerline accurately represents the flame's structural symmetry. Figure 11 shows the extracted centerline data, which were then processed using the Savitzky-Golay filter to reduce noise and smooth their trajectory, providing a robust representation of the flame's progression [63]. Subsequently, the centerline was reoriented to align with the flame's horizontal axis, thereby transforming the conventional measured flame height into flame length. Flame height is the vertical distance from the flame base to its tip, primarily influenced by buoyancy, and it is visible in stationary flames. Flame length, in contrast, measures the entire flame axis, including its curvature, capturing both visible and reaction zones. It is commonly used for flames experiencing disturbances due to turbulence. This approach facilitates a more accurate analysis of flame evolution, ensuring compatibility with the horizontal plane typically used in combustion studies. The processed data, coupled with corresponding time-series information, enabled the precise measurement of the flame's dynamic length during the combustion process, as depicted in Figure 12.  
Figure 12 shows the flame dynamics and stability. After ignition, the flame length increases rapidly and shows a peak before stabilizing and eventually decreasing. The fluctuations in the flame length after the initial rise could indicate instabilities in the flame due to varying fuel availability, incomplete combustion, and changes in heat transfer [64; 65]. The decline in flame length as the combustion approaches completion suggests the depletion of available fuel. While this study provides valuable insights into the combustion dynamics of methyl laurate droplets at atmospheric pressure, it is important to acknowledge the limitations of  
Figure 11: The centerline of flame evolution (**a**) without process, (**b**) with Savitzky–[PERSON] filter. Figure 12: Flame evolution and temperature during combustion of methyl laurate. these conditions in relation to real-world applications, particularly in internal combustion engines where pressures are significantly higher. At elevated pressures, several factors could alter the combustion behavior of methyl laurate droplets, including:  
* Increased fuel vaporization rates, which may lead to faster ignition and shorter ignition delay times [49; 51]. * Altered flame propagation speeds due to changes in the density and reactivity of the fuel-air mixture [15; 55].