## 4 Simulation Results Analysis
Figure 7: Variation diagram of total pressure with cross section along the mixer. The spatial non-uniformity of gas and air refers to the degree of non-uniformity of the gas concentration distribution on the cross-section of interest, often represented by SMD [22]. A larger SMD indicates worse mixing, while a smaller SMD indicates better mixing. There are many methods to evaluate spatial non-uniformity. In this paper, the method used by [PERSON] et al. [22] of Tsinghua University to study the mixing performance of the R0110 heavy-duty gas turbine combustor was used to evaluate the mixing performance. \[N_{s}=\overline{(\sigma_{f}/C_{f})} \tag{7}\]  
\[\sigma_{f}=\sqrt{\frac{1}{N-1}}\underset{i=1}{\overset{N}{\sum}}\left(C_{f,i}- \overline{C_{f}}\right)^{2} \tag{8}\]  
where \(\overline{C_{f}}\) represents the spatial average of the gas concentration on a certain cross-section, \(\sigma_{f}\) represents the corresponding concentration deviation, and \(N_{s}\) is the average spatial non-uniformity of the mixed gas and air. Figure 9 shows the spatial non-uniformity of the gas concentration on the cross-section of the mixer under the four blending structures. As shown in the figure, as the length of the mixing zone increased, the spatial non-uniformity generally decreased, with the most significant decrease observed in the structure where only gas rotated. When the mixing zone reached a certain length, the spatial non-uniformity under the structures where only air rotated and where air and gas rotated in the same direction stabilized, and further increasing the mixing zone length did not significantly improve the gas mixing effect. When the mixing zone length was short, the structure with the same rotation direction performed relatively better, but the spatial non-uniformity was still greater than 15%. The minimum mixing zone length required to achieve a spatial non-uniformity of less than 15% was 1.1 m. Comparing the structure where only gas rotated and the structure where air and gas rotated in opposite directions, it can be seen that the air rotation had little effect on the gas mixing effect, and as the mixing zone length increased, the difference in spatial non-uniformity gradually decreased. At 2 m, the spatial non-uniformity of the structure where only gas rotated and the structure where air and gas rotated in opposite directions reached the lowest, about 8%, which meets the requirement of less than 15% spatial non-uniformity in engineering requirement. Figure 10 shows the pressure loss at the inlet and outlet, and the spatial non-uniformity of the outlet gas for the four structures with clockwise or counterclockwise spiral blades added at the forefront of the mixing zone. The structure numbers are shown in Table 1. As shown in the figure, the a1 and a2 structures had similar effects. Compared to the a structure, the spatial non-uniformity of the outlet gas decreased by 60%, but the pressure loss increased significantly, from 30.8 Pa to 200-300 Pa. The b1 structure had the best gas mixing effect among all the structures with helical blades at the front end of the mixing  
Figure 8: Pressure distribution contours along the mixer axis plane and outlet surface. (c) Air–gas counter-rotating. (d) Air–gas co-rotating. zone, but its pressure loss far exceeded that of the other structures. According to the data, the b2 structure had a slightly higher pressure loss than the b structure, and the outlet spatial non-uniformity was slightly lower. The c1 structure had a 67.7% decrease in outlet non-uniformity compared to the c structure, while the c2 structure had a 54.4% decrease, but the pressure loss of the c1 structure increased from 359 Pa to 1135 Pa, and the c2 structure increased from 359 Pa to 605 Pa. The d1 structure had the worst mixing effect, and its pressure loss was also at a high level. The d2 structure had an 84% decrease in outlet non-uniformity compared to the d structure, but its pressure loss was still at a high level.