## 3 Results
### Multi-Channel Model Validation and Results  
It is well known that the conversion efficiency of nitrogen oxides is closely related to the ammonia uniformity coefficient [23]. The multi-channel model method (20 channels) was adopted to simulate the urea flow maldistribution. The local urea dose/average urea dose level was evaluated when the UI coefficients were 0.85, 0.9, and 0.95, respectively. Figure 6 shows the probability density distribution function of the maldistribution coefficient corresponding to the three UIs. The urea distribution at the SCR inlet was obtained by applying the UI factor to 20 inlet channels. The average value of the random distribution factor was maintained at 1 to ensure mass conservation. Parameters within the normal distribution function were tuned to obtain the desired UI. Afterwards, DOE calculations were performed with the urea dosing flow rate factor as a DOE parameter for 20 channels. Finally, the calculation results were multiplied by each corresponding probability density factor for each individual channel to obtain an average NOx emission or NH\({}_{3}\) slip.  
Figure 4: Simulated results of 1D model with uniform spatial urea distribution.  
Figure 5: Simulated results of 1D model with different urea dosing ratios: 0.95, 0.9, and 0.85.  
The simulated and experimental cumulative NOx emissions out of the ATS during the WHSC cycle are shown in Figure 7. And the traditional 1D model was equal to the model with UI = 1.0. Based on the predicted results comparison, relatively good agreement of the simulated and test results could be achieved by UI = 0.95, indicating that a relatively good mixer and urea dosing system leads to relatively uniform distribution of urea or ANR across the SCR inlet. The outlet NOx emissions were found to double when the UI dropped to 0.9 and they were found to triple with a UI of 0.85 compared to the uniform distribution condition. That is a 7% decrease in the overall deNOx efficiency (97% compared to 90%). At the same time, a higher NH\({}_{3}\) slip was observed due to the insufficient consumption of urea dosing flow. These results further proved that the improvement of the injected urea mixing system with exhaust flow can have an improving effect on both the enhancement of the deNOx conversion performance and the reduction of NH\({}_{3}\) slip. It means that the input amount of ammonia added must be controlled for an optimized urea injection dosing strategy with a higher UI level and must be compatible with the need to minimize the NOx emission, as well as to maintain the ammonia slip below the acceptable level.  
However, it is noticed that even with a UI = 0.95, there is still slight gap between the experimental and simulated results. This may result from the urea maldistribution fluctuation with the cycle time and flow condition. Therefore, an improved segment UI factor was applied for maldistribution description, with UI1 corresponding to a flowrate \(\geq\) 300 kg/h and UI2 corresponding to a flowrate \(<\) 300 kg/h. The final excellent transient simulated results were obtained as shown in Figure 7. And the corresponding calculated NOx efficiency is within 2% of the experimental data, similar to that in previous reports [16; 24; 25].  
Figure 6: Urea distribution of multi-channel modelling approach with normalized distribution of SCR inlet urea dosing.  
Figure 7: Simulated results with multi-channel modelling using different maldistribution factors.  
These results substantiate that, compared with the ideal perfect mixture with a UI equal to 1, the UI must exceed 0.95 to incur a minimum loss in conversion efficiency compared to the perfect mixture ideal (UI = 1.0), which is analogous to that suggested by [PERSON] [17].