## 5 Analysis of Results
### Flow Field Analysis  
Figure 10 shows the velocity contour in the Y-direction on the YZ cross-section, illustrating a significant phenomenon. Before data assimilation, the positive and negative flows in the Y-direction are dispersed. After DA, a large-scale circumferential flow emerges in the slot. Figure 8: Comparison of predicted and experimental flows from the rectangular slot plunger RNG k-\(\varepsilon\) model and the ENKF+RNG k-\(\varepsilon\) model. Figure 9: Comparison of predicted and experimental flow rates of circular grooved plunger RNG k-\(\varepsilon\) model and ENKF+RNG k-\(\varepsilon\) model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Plunger Type** & **RNG k-\(\varepsilon\)** & **ENKF+RNG k-\(\varepsilon\)** \\ \hline Rectangular slot & 60.67 & 7.12 \\ Circular slot & 61.48 & 7.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean square Error (MSE) before and after data assimilation. Figure 11 depicts the significant changes in the 3D flow trajectories within the plunger groove before and after DA. Initially, as shown in Figure 11a, the flow trajectories exhibit clustered vortices, with adjacent vortices displaying opposing velocities in the Y-direction and minimal radial flow. After assimilation, Figure 11b shows that, while the original vortex structures are retained, these vortices transform into structures with extensive radial flow. The circumferential motion of the fluid in the axial cross-section is perpendicular to the inflow direction and is significantly influenced by the circumferential velocity. This interaction results in a more complex airflow pattern within the plunger gap. Specifically, the circumferential motion of the fluid combines with the axial inflow velocity, generating intricate vortex structures. This complex flow pattern may influence the sealing performance of the plunger. The increased flow complexity could lead to variations in turbulence intensity within the plunger gap, thereby affecting the sealing effectiveness. Whether this impact enhances or diminishes the plunger's sealing effectiveness requires further detailed analysis. As shown in Figure 12, this phenomenon is not limited to the second groove but is observed in all grooves of the plunger, ruling out the possibility of chance. The consistency  
Figure 11: (**a**) Streamlines before data assimilation. (**b**) Streamlines after data assimilation. Figure 10: (**a**) Y-direction velocity cloud before data assimilation. (**b**) Y-direction velocity cloud after data assimilation. of this phenomenon indicates that the flow changes induced by data assimilation follow a general rule rather than being isolated events. This further demonstrates the effectiveness and stability of data assimilation in improving fluid flow characteristics. Since this phenomenon occurs in all grooves, it suggests that data assimilation can produce significant flow optimization effects across different structural regions. This consistent flow pattern contributes to enhancing the overall performance and reliability of the system. Figure 13 illustrates the distribution of vortex magnitude on the surface before and after DA. The vortex magnitude reflects the rotational curl of the vortex velocity vector, enabling the assessment of the vortex's intensity and directional orientation. A larger vortex magnitude indicates higher fluid velocities, increased energy consumption, and greater fluid dissipation, all of which positively influence the sealing performance of the plunger. The figure shows that post-DA, the vortex magnitude is reduced compared to pre-DA levels. Analysis of the flow diagram reveals smaller vortex magnitudes in regions with circumferential flow of the flow slugs and larger magnitudes in areas opposing the vortex rotation. Figure 14 illustrates the distribution of turbulent kinetic energy, which aligns with the vortex magnitude distribution. Turbulent kinetic energy, an indicator of turbulence intensity within the fluid, is typically directly related to the fluid's dynamic activity and energy exchange.