# A Study on the Movement Characteristics of Fuel in the Fuel Tank during the Maneuvering Process
## 4 Conclusions  
Based on simulation analysis of the fuel motion characteristics of a typical flat fuel tank during aircraft maneuvering, the following conclusions are drawn: the simulation reveals complex phenomena such as fluctuation, surge, rolling, and fragmentation of the free liquid surface of the fuel, as well as the resulting shift in the fuel center of gravity. During the maneuvering process of the aircraft, there is little change in the longitudinal center of gravity, but the aerodynamic center of gravity shows significant fluctuations, with a range reaching 0.47 m. The longitudinal center of gravity continues to move backward with a displacement of 0.41 m. The maximum height of the free surface of the liquid during aircraft maneuvering is approximately 0.22 m, reaching the height of the upper panel of the  
Figure 8: Variation of fuel velocity field in the fuel tank. (**a**) \(t=0.24\) s; (**b**) \(t=0.51\) s; (**c**) \(t=0.99\) s; (**d**) \(t=1.50\) s; (**e**) \(t=2.52\) s; (**f**) \(t=2.97\) s. \begin{table}
\begin{tabular}{c c} \hline \hline
**Time** & **Fuel Motion Characteristics** \\ \hline \(t=0.24\) s & The fuel surface is shaking and tilting towards one side. \\  & The free surface phenomenon becomes more complex, with \\ \(t=0.51\) s & significant surface fragmentation; the fuel at the circular marker \\  & inside the compartment moves backward and fills the tail, \\  & forming an fuel-free zone. \\ \(t=0.99\) s & The fuel-free zone expands, and almost all the fuel in the front \\  & moves backward. \\ \(t\geq 1.5\) s & The fuel free surface exhibits significant fragmentation \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Temporal variations of fuel motion characteristics inside the tank. wing fuel tank, resulting in a certain impact on the upper panel. The maximum impact force generated during the aircraft maneuvering process is 2.3 \(\times\) 10\({}^{5}\) pascals, with the action location at the junction of the transverse frame and the upper panel. This data provides a reference for the design of the tank's strength. The findings of this study provide support for the safe design of aircraft fuel tank systems. The innovations of the paper are as follows:  
1. Compared to other studies related to the free surface of fluids, the object of this paper is not an idealized and simplified model, but an aircraft wing fuel tank model that encompasses all structural elements. The fuel tank structure considered here includes not only the surrounding walls but also internal transverse frames, longitudinal walls, and flow holes. These structures are carefully designed according to the fuel tank design standards. The presented results reflect the comprehensive damping effect of the fuel tank structure on fuel motion, thereby providing a more realistic representation of the fuel's movement characteristics during aircraft maneuvering. 2. Compared with our previous work [22], the flow characteristics of fuel in a flat tank are different from those of an approximate cube tank, and the size and shape of the movement space of the fuel have a significant influence on the movement of the free liquid level. This study only analyzes the influence of aircraft heading acceleration and pitch angle on fuel motion characteristics. However, actual maneuvering processes may also include parameters such as roll acceleration and angular acceleration, which affect the motion of fuel within the fuel tank. Therefore, future research will consider the effects of roll acceleration and angular acceleration, comprehensively analyzing the role of various excitation factors on fuel motion characteristics. Conceptualization, Y.W. and S.L. ; methodology, Y.W. ; software, Y.W. ; validation, Y.W. ; formal analysis, Y.W. and C.R. ; resources, Z.L. ; writing--original draft preparation, Y.W. ; writing--review and editing, C.R. ; visualization, C.R. ; supervision, S.L. ; project administration, Z.L. ; funding acquisition, S.L. All authors have read and agreed to the published version of the manuscript.