## 3 Results and Discussion
### Variation of Pressures under the Influence of NSSs
\[Rp_{\max}=\frac{P_{\max}^{0}-P_{\max}^{1}}{P_{\max}^{0}}\times 100\%, \tag{2}\]  
\[\Phi=\frac{\Delta P}{\Delta t}=\frac{\Delta P}{t_{\rm e}-t_{\rm e}} \tag{3}\]  
\[\Phi_{e\_\max}=\frac{\Delta P}{\Delta t}=\frac{R_{\max}-P_{e}}{t_{\rm max}-t_ {e}}\]  
where \(p_{\max}\) is overpressure in the filled CVCB, \(P_{\max}^{0}\) is overpressure in the unfilled CVCB, \(\Phi_{0,e}\) is the rate of average pressure rise when propane and air occurred reaction early, the time is 0 to \(t_{\rm e}\). \(\Phi_{e\_\max}\) is the rate of average pressure rise when NSSs retarded effective energy release, the time is \(t_{\rm e}\) to \(t_{\rm max}\). \(P_{\rm e}\) is pressure when the time is \(t_{\rm e}\). Corresponding overpressure \(P_{\max}\) of in-cylinder and some important features from Figure 4 are summarized in Table 3. When the filling density is 21.9 kg/m\({}^{3}\) and the initial pressures are 0.2 MPa, 0.3 MPa and 0.4 MPa, the corresponding decay rates of overpressures \(Rp_{\max}\) are 11.10%, 11.54% and 18.10%, respectively. When the filling density is 38.7 kg/m\({}^{3}\) and the initial pressures are 0.2 MPa, 0.3 MPa and 0.4 MPa, the corresponding decay rates of overpressures \(Rp_{\max}\) are 21.12%, 28.88% and 35.80%, respectively. When the filling density is 45.1 kg/m\({}^{3}\) and the initial pressures are 0.2 MPa, 0.3 MPa and 0.4 MPa, the corresponding decay rates of overpressures \(Rp_{\max}\) are 28.16%, 34.01% and 43.72%, respectively. Under different filling densities, the decay rates of overpressures \(Rp_{\max}\) increase with increasing initial pressures which is an interesting phenomenon that deserves further investigation. It is obvious that the time histories of in-cylinder pressures in the unfilled CVCB are approximately straight line, there is no obvious inflection point, thus we believe that \(\Phi_{0,e}\) is approximately equal to \(\Phi_{e\_\max}\). The time histories of in-cylinder  
Figure 4: Time history of in-cylinder pressures at initial pressures of 0.2 MPa, 0.3 MPa and 0.4 MPa. pressures in the filled CVCB have an inflection point, \(t_{\text{e}}\) is the moment corresponding to the inflection point \(P_{\text{e}}\). From 0 to \(t_{\text{e}}\), propane and air occur reaction early, the beginning of the flame propagation process, flame propagation has less contact surface with NSSs. Rates of average pressures rise \(\Phi_{0\_\_\text{e}}\) are much greater than that without filling due to the presence of obstacles. A possible explanation for this might be that NSSs are playing roles as multiple obstacles. These obstacles promote the formation of turbulence, resulted in flame acceleration, and induce earlier rise of dP/dt [36]. NSSs acts as a turbulence generator, which plays positive roles in affecting the explosion [37]. As flame continues to spread from \(t_{\text{e}}\) to \(t_{\text{max}}\), NSSs retard effective energy release. Rates of average pressures rise \(\Phi_{0\_\_\text{e}}\) are reduced rapidly. Compared with unfilled CVCB, rates of average pressures rise \(\Phi_{0\_\_\text{e}}\) become smaller after filling NSSs in CVCB. As described by [PERSON] [38] and [PERSON] [14], a very high surface efficiency is formed in a unit volume by structure of NSSs with excellent thermal conductivity, and absorbed a good deal of heat. Thus, it could form significantly reduce reaction rate. At the same time, the time \(t_{\text{max}}\) to reach explosion overpressure is smaller than that with unfilled CVCB, and overpressures appear earlier than that with unfilled CVCB. A possible explanation for this might be that the reaction has been effectively reduced by NSSs including increasing residual reactant. The skeleton structure suppresses propane from cracking into more radicals, and thus leads to a higher amount of residual propane. To sum up, NSSs play both positive and negative roles in affecting the explosion. On one hand, when flame propagation has less contact surface with NSSs, they act as turbulence generator and facilitate explosion process, causing the rate of pressure rise increase.