# The Simulation of Different Combustion Stages of Micron-Sized Aluminum Particles
###### Abstract  
In this study, a quasi-steady combustion model of an aluminum particle is established, which is more accurate to simulate the physical combustion process. Detailed gas-phase reaction mechanism and surface reaction mechanism are considered. Moreover, the particle temperature is not constant in this work, which is calculated in different combustion stages. The judgement standard of each combustion stage is from observational data in the experiment and the simulation results of combustion durations of each stage, and distribution of ambient temperature and gas-phase species profiles are in good agreement with experimental results. The calculation results show that in the first stage, burning rate of the particle is the fastest, and in the second stage, particle temperature can drop to more than 100 K below the boiling point for the large particles, which is slightly below the boiling point for small ones. As the combustion stage changes, \(Da\) number is going to keep going down, which will lead to the transition of combustion method from diffusion-limited control to kinetic-limited control for an aluminum particle. aluminum particle; combustion stages; combustion mechanism +
Footnote †: journal:  
summarized a large number of experimental studies and proposed an empirical correlation for burning time as:  
\[t=\frac{D^{1.8}}{6.27\times 10^{-7}(X_{O_{2}}+0.6X_{H_{2}O}+0.22X_{CO_{2}})p^{0.1}T^{0.2}} \tag{1}\]  
Though this empirical correlation is widely used, [PERSON], et al. [10] has reported it to be unsuitable for small particle sizes and has proposed another correlation for burning time for small particle sizes. [PERSON], et al. [11; 12] accurately observed a single aluminum particle and obtained the burning time of a large number of micron aluminum particles in a complex high-temperature gas. [PERSON], et al. [13] measured the distribution of ambient temperature and gas phase composition during the combustion process and suggested that the position of the peak of the AlO concentration represented the position of the flame. [PERSON] [14] measured the changes in the aluminum particle temperature and divided the combustion process of the aluminum particles in air into three stages just as Figure 1 shows. Recently, [PERSON], et al. [15] observed a similar phenomenon by the holography technique. [PERSON] and [PERSON] [16] proposed that the combustion of aluminum particles was similar to the hydrocarbon fuels. [PERSON] and [PERSON] [17; 18] proposed a two-dimensional unsteady state/quasi-steady state aluminum combustion model, including the finite rate chemical reactions and oxide cap. Further, [PERSON], et al. [19] improved the model by changing the ambient atmosphere to the rocket environment and subsequently calculated the burning time based on the assumption that the mass consumption rate decreased linearly. [PERSON], et al. [20; 21] incorporated the detailed mechanism of the gas phase chemical reactions and studied the transition from diffusion-limited to kinetic-limited combustion control. [PERSON], et al. [22] further supplemented the detailed mechanism of the surface reactions and regarded the evaporation process as a surface reaction. [PERSON], et al. [23; 24] suggested that the conversion rate of AlO and Al\({}_{2}\)O at the particle surface determined the combustion control method. Most of the previous aluminum combustion models are quasi-steady, but it is incorrect to use a quasi-steady state result to represent the entire combustion process. In the actual combustion process, the temperature of the particles is constantly changing, accompanied by the growth of oxidation caps, and sometimes the particles will rotate and micro-explode.