## 4 Conclusions  
A mixing process of CH\({}_{4}\) and air in RDC is simulated accompanied with the evaluation of mixing quality and total pressure loss evaluation under different inlet structures. According to the numerical results, inlet structure has significant effect on the mixing characteristic, total pressure loss of the reactant and critical ignition energy. The primary conclusions from this work include the following:  
1. The initial mixing process of reactant is very quick in a relative short distance at the head end of combustor owing to the first interaction of CH\({}_{4}\) and air. Compared to initial stage, the mixing process gradually slow down downstream. Because the majority of reactant interacts sufficiently with recirculation zone when air radial injection, so air radial injection scheme possesses superior mixing quality to air axial injection scheme. Based on mixing quality to identify the sequence of various structures, Structure 3 \(>\) Structure 4 \(>\) Structure 1 \(>\) Structure 2.
2. Within the scope of air axial injection scheme, the structure of CH\({}_{4}\) injecting towards outer wall has the longest mixing length due to the main diffusion peak is restricted by the outer wall, which limits the ability of CH\({}_{4}\) diffusion.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Structure 1** & **Structure 2** & **Structure 3** & **Structure 4** \\ \hline Case 1 & 2.859 & 2.866 & 2.846 & 2.861 \\ Case 2 & 2.752 & 2.798 & 2.715 & 2.724 \\ Case 3 & 3.248 & 3.412 & 2.728 & 2.732 \\ \hline \end{tabular}
\end{table}
Table 4: Critical ignition energy (MJ) in ignition position.  
Figure 12: Schematic of ignition location.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Structure 1** & **Structure 2** & **Structure 3** & **Structure 4** \\ \hline Case 1 & 0.094/1.06 & 0.096/1.07 & 0.093/0.96 & 0.091/0.96 \\ Case 2 & 0.097/1.14 & 0.097/1.20 & 0.096/1.01 & 0.095/1.04 \\ Case 3 & 0.101/1.55 & 0.101/1.58 & 0.100/1.03 & 0.100/1.11 \\ \hline \end{tabular}
\end{table}
Table 3: Static pressure (MPa)/ equivalence ratio in ignition position.  
3. As the mass flow rate increase, the total pressure loss of reactant in combustor increases correspondingly owing to violently turbulent intensity. When the total mass flow rate is 12.71 kg/s, total pressure recovery parameter is around 0.3. As the total mass flow rate decrease to 1.82 kg/s, total pressure recovery parameter rises to above 0.96.
4. At the ignition position in our study, pressure has little effect on the critical ignition energy. The equivalence ratio determines the critical ignition energy, meaning mixing quality plays a crucial role for the ignition process. Comparing four inlet structures, Structure 2 needs the highest critical ignition energy. Owing to the superior mixing quality of Structure 3, its critical ignition energy is the lowest.  
Conceptualization, Z.L.; methodology, S.J.; software and validation, Q.M.; investigation, S.J. and N.Z.; writing--original draft preparation, S.J. and H.Z.; writing--review and editing, N.Z. and J.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Nature Science Foundation of China (Grant No. 51709059), the Province Nature Science Foundation of Heilongjiang (Grant No. QC2017045) and the Fundamental Research Funds for the Central Universities (Grant No. HEUCFJ170304, Grant No. HEUCFP201719).  
We declare that we have no conflict of interest.