## 3 Results and Discussions
### Effects of inlet Structure on Mixing Characteristics  
Figure 6 shows the equivalence ratio contours of various inlet structures within the combustor region. According to the different equivalence ratio distributions, it can be found that the inlet structure of RDC influences the mixing characteristic of CH4 and air obviously under various mass flow rates. The equivalence ratio is around 1 all over the combustor in Cases 1 and 2 comparatively except for Structures 1 and 2 in Case 3 (higher than 1). To gain a deep understanding of the mixing characteristics in the combustor, the parameter of unmixedness (s) is employed here to reflect the mixing quality of reactant, which is defined as the following [33]:  
\[s=\frac{Y_{max}-Y_{ave}}{Y_{max}} \tag{1}\]  
where \(Y_{max}\) is the maximal mass fraction of CH4 on the planes perpendicular to \(x\) axis, \(Y_{ave}\) is the average mass fraction of CH4 on the same plane. Lower \(s\) indicates higher uniformity. A clear comparison of unmixedness variations under different inlet structures with axial length of combustor are displayed in Figure 7. The unmixedness drops monotonically with the increase of axial length, which indicates the mixing degree of CH4 and air is gradually uniform. In the initial stage where CH4 and air begin to interact with each other near the entrance of combustor, unmixedness drops rapidly compared to the following stage of slow decrease when close to outlet. A certain sequence of \(s\) is observed in Figure 7 when axial location is over 200 mm, Structure 3 \(<\) Structure 4 \(<\) Structure 1 \(<\) Structure 2, meaning Structure 3 has superior mixing quality and Structure 2 has poor mixing quality. Please note that unmixedness approaches to the same value and the difference of \(s\) almost disappears when the reactant close to the combustor outlet. Besides, as the total mass flow rate decreases (from Case 1 to 3), unmixedness rises up at the same axial location for every case. Large total mass flow rate in Case 1 produces higher inlet velocity of reactants. This causes excellent penetration ability of gas flow compared to the rest cases, which makes the violent interactions between CH4 and air, the mixing quality is also enhanced correspondingly. Figure 8 shows the stream lines and stream function contours of different inlet structures. To display the whole recirculation zone of each case, the axial length is extended to 600 mm in Figure 8. Based on the stream lines within combustor, the flow of reactant presents different trend when air axially or radially injected. As the air stream axially enters into the combustor, it keeps the axial direction all the time and exit straightly. When the air radially injected into the combustor, it flows along the inlet wall firstly and turns suddenly towards axial direction when encountering the corner of inner wall and inlet wall. This sudden change of flow direction might cause more drastic interaction of CH4 and air compared to air axial injection scheme. The recirculation zone appears in every case based on the distribution of stream lines, but the shape of them possesses slight difference for various structures. According to the theory quality of stream function, the volume flow rate of fluid passing through arbitrary curve (unit thickness) of two stream lines is equal to the difference of the two stream functions corresponding to the two steam lines. This means the difference of the stream lines is greater, larger reactant will flow past between them. For air axial injection (Structures 1 and 2), the maximal difference of stream function is observed at the zone close to the outer wall indicating the majority of reactant flow through this passage. Unlike air axial injection, for air radial injection (Structures 3 and 4), the maximal difference of stream function occurs at the region near the inlet and inner wall. That demonstrates most of the reactant passes through theway where gas flows along the inlet wall and turns direction towards inner wall.