## 3 Results and Discussions
### Effects of inlet Structure on Mixing Characteristics
Compared with the stream path of the majority of reactant in two air injection schemes, we can find that the stream path of air radial injection is longer than air axial injection, resulting in the stream interacts with recirculation zone sufficiently and efficiently for air radical injection. This can enhance the mixing quality of reactant to some extent. To understand the overall mixing characteristics of CH4 and air in the combustor, the turbulent CH4 mass diffusion is calculated here and the formula is defined as following where \(G_{\text{CH4}}\) is the mass flux of CH4, \(\mu_{\text{t}}\) is the turbulent viscosity. Assuming gas momentum diffusivity is equal to species diffusivity, then, Schmidt number \(S_{\text{ct}}\) is a constant given by 0.7. \(Y_{\text{CH4}}\) is the mass fraction of CH4 [22]. \[M_{diff,\text{CH4}}=\frac{1}{G_{\text{CH4}}}\frac{\mu_{t}}{S_{\text{ct}}}\left[ \left(\frac{\partial Y_{\text{CH4}}}{\partial x}\right)^{2}+\left(\frac{ \partial Y_{\text{CH4}}}{\partial y}\right)^{2}\right]^{0.5} \tag{2}\]  
The contours of turbulent CH4 mass diffusion are shown in Figure 9. Diffusion peak of CH4 is observed close to inlet region due to the first interaction of CH4 and air. Besides, the diffusion  
Figure 6: Contours of equivalence ratio for various inlet structures. length of CH\({}_{4}\) is the longest in Structure 2 among all of the structures even though the total mass flow rate is changed. This can be explained by the different diffusion pattern affected by the injecting direction of CH\({}_{4}\). Taking Case 1 as an example, two diffusion peaks are observed for air axial injection (Structures 1 and 2) as shown in Figure 8(a). \(W_{1}\) means the diffusion peak which is close to outer wall and R means radial diffusion peak. The diffusivity of peak \(W_{1}\) is restricted by outer wall because it almost attaches to the outer wall and CH\({}_{4}\) fails to diffuse towards that direction. For inlet Structure 2, CH\({}_{4}\) is injected towards the outer wall, making an army of CH\({}_{4}\) flow adjoin to the wall tightly. As a result, \(W_{1}\) becomes the main diffusion peak in Structure 2. Recall that \(W_{1}\) is limited by wall and the diffusivity of it probably cannot support the transport of such a quantity of CH\({}_{4}\), resulting in the CH\({}_{4}\) has to diffuse continuously downstream of the combustor in Structure 2. Therefore, Structure 2 has the longest diffusion length. Similarly, two diffusion peaks are also obtained for air radial injection scheme (Structures 3 and 4). One is close to inlet wall (\(W_{2}\)) diffusing radially towards inner wall and limited by inlet wall. After encountering inner wall, peak \(W_{2}\) turns to diffuse axially and it is not restricted by inlet wall anymore. The other peak (\(A\)) diffuses axially towards the outlet of combustor and avoids being influenced by any wall. Therefore, two diffusion peaks both remain relatively high diffusion abilities, causing CH\({}_{4}\) diffuses faster compared to air radial injection. Figure 7: Effects of inlet structure on mixing no uniformity. Figure 8: Effects of inlet structures on stream function and stream lines. Figure 9: Contours of CH4 mass diffusion.