## 3 Results and Discussion
### Effect of Filling Density on Flame Tip Velocity  
The average flame tip velocities at different initial pressures and different filling densities in CVCB are obtained, as show in Table 4. The average flame tip velocities filled with NSSs are greater than that of unfilled NSSs in CVCB. The average flame tip velocity reaches maximum when the filling density was 21.9 kg/m\({}^{3}\), and initial pressure has little effect on average of flame tip velocity. The average flame tip velocities of 38.7 kg/m\({}^{3}\) and 45.1 kg/m\({}^{3}\) are significantly lower than that of 21.9 kg/m\({}^{3}\). With the increase of initial pressure, the average flame tip velocity decreases. This is positively correlated with the decay rates of the propane explosion overpressures which was increasing as the initial pressure increased. The average flame tip velocity is maximum when the filling density is 21.9 kg/m\({}^{3}\), a possible explanation for this might be that less NSSs are stacked together to form the larger gaps and spaces, which enhances the turbulence of flame combustion. During the process, as [PERSON]' work [44], the mixture would be involved in the eddy turbulence, and the flame had a higher velocity.  
Compared with the filling density of 21.9 kg/m\({}^{3}\), the average flame tip velocities of 38.1 kg/m\({}^{3}\) and 45.1 kg/m\({}^{3}\) decrease. It is well explained that when the filling density of NSSs are large, there is less space for the flame vortex to be broken and the flame front to stretch, and the flame existed behind the skeleton structures of NSSs, led to the flame velocity decrease. Similar to [PERSON]'s [45] study, the flame velocity would decrease just behind the plate obstacle because of the obstacle-induced eddy momentum.  
In Figure 7, NSSs have the same influence on flame propagation, so after filling NSSs, the flame tip velocities have different oscillation degree in the cylinder. When the filling density is 21.9 kg/m\({}^{3}\), the maximum flame tip velocity is larger and the oscillation degree of the flame tip velocity is greater than that when the filling density are 38.7 kg/m\({}^{3}\) and 45.1 kg/m\({}^{3}\). This was related to the distribution state of NSSs. Thus, it is also verified that the average flame tip velocities because of filling NSSs are greater than that of unfilled NSSs in CVCB. However, the average flame tip velocity decreases with increasing filling density of NSSs.  
\begin{table}
\begin{tabular}{c c c} \hline \(\rho\)/kg/m\({}^{3}\) & \(P_{0}\)/MPa & v/m/s \\ \hline  & 0.2 & 2.17 \\
0 & 0.3 & 0.81 \\  & 0.4 & 1.85 \\ \hline  & 0.2 & 22.38 \\
21.9 & 0.3 & 25.84 \\  & 0.4 & 22.56 \\ \hline  & 0.2 & 14.49 \\
38.7 & 0.3 & 9.11 \\  & 0.4 & 6.73 \\ \hline  & 0.2 & 15.34 \\
45.1 & 0.3 & 12.56 \\  & 0.4 & 11.49 \\ \hline \end{tabular}
\end{table}
Table 4: Average flame tip velocities at different filling densities.  
To sum up, by combining overpressure and flame velocity, NSSs had promotion/suppressing double functions on the explosion of propane-air mixtures. NSSs showed a better suppressing effect on overpressure, but NSSs had a positive effect on the flame propagation. Thus, the suppression effect of NSSs was influenced by its suppression and promotion effect on explosion of propane-air mixtures. With the increase of filling density, the stronger the suppressing effect of overpressure was, the weaker the promoting effect on the velocity was, and the better the comprehensive suppressing effect was. The results of this work might provide a new insight for the explosion-suppression mechanism of NSSs in confined space such as gas tank, and provide a new scientific basis for application of NSSs explosion-suppression.