## 3 Results and Discussion
### Zoned Washcot
#### 3.2.2 Different Length Proportion and Porosity Configuration  
To further enhance flow consistency, the lengths of the two regions are adjusted based on the above research findings (as shown in Figure 4), while the porosity of the low coated region is fixed at 0.503 or the porosity of the high coated region is fixed at 0.497. Two sets of simulations are established at \(X\) = 0.4 and \(X\) = 0.6 to investigate the impact of the high length ratio of the first or second part on flow characteristics. The results are depicted in Figure 5.  
When X = 0.4, with a fixed porosity of the low coated zone (\(\epsilon_{front}\) = 0.503), ensuring an average porosity of 0.5 requires the porosity of the high coated zone (0.498) to be slightly higher than 0.497. The permeation velocity aligns with the curve of average partition in the first part but slightly surpasses the curve for a porosity of 0.497 in the second part. Conversely, with a fixed porosity of the high coated zone (\(\epsilon_{rear}\) = 0.497), the porosity of the low coated zone (0.5045) should be slightly higher than 0.503. The permeation velocity curve for the first part will be marginally higher than the curve for a porosity of 0.503, and there will be an overlap between the two curves in the second part compared to the average partition. When the length of the first part is longer (\(X\) = 0.6) compared to the average partition condition, a fixed porosity (\(\epsilon_{front}\) = 0.503) results in a coincident curve for the first part. Figure 5: (a) Curve of axial permeation velocity distribution, and (b) velocity variance corresponding to different X and fixed coated zones. However, if the porosity of the high coated zone is fixed (\(\varepsilon_{rear}=0.497\)), the coincident curve corresponds to the second part. In other words, the permeation velocity of a certain part remains constant as long as its porosity is fixed, regardless of changes in \(X\). Moreover, maintaining a constant value for the porosity of the first part results in a more pronounced disparity in permeation velocities compared to that of the second part with fixed porosity. The variance of axial velocity in the porous medium is calculated under four different conditions, as depicted in Figure 5b. Compared to the variance observed under the average partition, a larger variance and heterogeneity are found under \(X=0.4\). Fixing the porosity of the second part results in a greater variance compared to fixing the porosity of the first part. Conversely, a smaller variance and further improved uniformity are observed under \(X=0.6\). Fixing the porosity of the first part results in a greater variance compared to fixing the porosity of the second part. Consequently, it can be inferred that increasing the proportion of the length of the low coated zone and specifying the porosity of the high coated part appropriately enhances axial permeation velocity distribution uniformity. As the proportion of the length of the first part is further increased, with the porosity of the second part remaining fixed, the porosity of the first part gradually decreases and approaches 0.5 as X increases, as depicted in Figure 6b. Consequently, the permeation velocity of the first part gradually decreases and approaches the original curve (without partitioning), while the curves of the second part remain almost the same. The variations between adjacent working conditions also gradually decrease. Figure 6: (**a**) Contour and curve of axial permeation velocity distribution, (**b**) variance (solid line, variance) and \(\varepsilon_{front}\) corresponding to different X when \(\varepsilon_{rear}\) is fixed. The variances of axial permeability velocity for different \(X\) are calculated and compared in Figure 6b. It is observed that with an increase in \(X\), variance initially decreases before increasing again.