## 3 LBV of Conventional Aviation Fuel
### LBV of JP-8  
JP-8 is a Jet-A-derivative fuel formulated with additives for thermal stability, giving it a chemical composition very similar to that of Jet A-1. Due to its lower freezing point, JP-8 can serve both as both coolant and fuel within fuel systems, making it widely utilized by the US military in aircraft engines. [PERSON] et al., employing a combination of a spherical vessel and a shadowgraph system, observed that the LBV of JP-8 increases with temperature and decreases with pressure [44]. The LBV data were fitted to the following power law correlation:  
\[S_{L}=S_{L0}\Big{[}1+a_{1}(1-\varphi)+a_{2}(1-\varphi)^{2}\Big{]}\left(\frac{T}{ T_{0}}\right)^{\alpha}\left(\frac{P}{P_{0}}\right)^{\beta} \tag{6}\]  
In the equation, S\({}_{L0}\) denotes the LBV at P\({}_{0}\) = 1 atm, T\({}_{0}\) = 500 K, and \(\Phi\) = 1, where a\({}_{1}\), a\({}_{2}\), \(\alpha\), and \(\beta\) are constants. This correlation is specifically applicable to the LBV of JP-8/air flames. It is valid within the pressure range of 1 atm < P \(<\) P\({}_{\rm cr}\), temperature range of 500 K < Tu < T\({}_{\rm cr}\), and equivalence ratio range of 0.8 < \(\Phi\) < 1.0. Here, T\({}_{\rm cr}\) and P\({}_{\rm cr}\) represent  
Figure 3: Illustration of the LBV of RP-3 at different initial pressures (P\({}_{0}\) = 1/2/3/5 atm) under conditions where (**a**) T\({}_{0}\)\(\approx\) 420 K, (**b**) T\({}_{0}\)\(\approx\) 450 K, and (**c**) T\({}_{0}\)\(\approx\) 480 K. Reference cited from [PERSON] (2022) [42], [PERSON] (2023) [43].  
the critical temperature and pressure at which cell formation initiates. P\({}_{\rm cr}\) can be obtained from empirical tables in the text, while T\({}_{\rm cr}\) can be calculated from the following equation:  
\[T_{cr}=T_{i}\left(\frac{P_{\rm cr}}{P_{i}}\right)^{\frac{\gamma-1}{\gamma}} \tag{7}\]  
where T\({}_{\rm i}\) and P\({}_{\rm i}\) denote the initial temperature and pressure, respectively, while \(\gamma\) represents the ratio of specific heat at constant pressure to that at constant volume.  
During the actual flight of an aircraft, the occurrence of in-flight shutdown may subject the combustion chamber of aviation engines to extremely low pressures, necessitating a comprehensive understanding of the flame propagation characteristics of aviation fuel under low-pressure conditions. [PERSON] et al. innovatively incorporated a fan-stirred device into the constant-volume bomb apparatus to homogenize the gas-phase mixture within the chamber [1]. Additionally, with 6.5 kW band heaters, they were integrated into the cylindrical stainless steel combustion chamber to achieve a maximum temperature of 573 K and facilitate experiments at varying initial pressures. The LBV also increases with increasing initial temperature and decreasing initial pressure. Across all temperatures and pressures, the LBV\({}_{\rm max}\) of aviation kerosene occurs at an equivalence ratio of 1.1. Based on experimental findings, Formula 6 is fitted and is applicable within the pressure range of 25-100 kPa, temperature range of 400-480 K, and equivalence ratio range of 0.7-1.5. The reference conditions for the formula are T\({}_{0}\) = 450 K and P\({}_{0}\) = 100 kPa.  
\[{S_{L}}^{0}=\left[199\varphi^{4}-878\varphi^{3}+1242\varphi^{2}-613\varphi+117 \right]\left(\frac{T}{T_{0}}\right)^{1.76}\left(\frac{P}{P_{0}}\right)^{-0.15} \tag{8}\]  
With the exception of occasional data points under rich fuel conditions, the formula demonstrates good consistency with experimental test values (within 5% error). In conditions where there is significant deviation between the two sets of results, due to the instability of flame propagation, the uncertainty in data testing outweighs the deviation in fitting results. The fitted temperature exponent (\(\alpha\) = 1.76) is positive, attributed to faster reaction rates and mass diffusion at higher temperatures, which enhance flame propagation. The pressure exponent (\(\beta\) = \(-\)0.15) is negative, because lower pressure suppresses hydrodynamic and diffusive-thermal flame instabilities.