## 4 Conclusions  
In this paper, the accuracy of the numerical model in predicting the entrainment behavior of the Venturi injector was validated through experimental measurements of the entrainment rate. Additionally, the effect of the gas-liquid interface structure within the mixing section on entrainment behavior was investigated by varying the mixing section geometry. The parameters \(D_{M}/D_{N}\) and \(L_{M}/D_{M}\) were used to characterize the mixing section structure, minimizing the influence of structural changes in the suction chamber and diffuser section. The main conclusions are as follows:  
1. Along the jet flow direction, the gas-liquid interface gradually transitions from a smooth cylindrical shape to a lobed pattern. The smooth interface predominantly occurs at low \(D_{M}/D_{N}\) or \(L_{M}/D_{M}\). The slug interface primarily appears when \(D_{M}/D_{N}\leq 2.25\) and \(L_{M}/D_{M}\) exceeds a certain critical value, while the punctiform interface only emerges when \(D_{M}/D_{N}\geq 25\) and \(L_{M}/D_{M}\geq 10\).
2. The presence of lobed and surface wave structures can reduce the radial flow near the gas-liquid interface, thereby decreasing gas-phase pressure losses. When the gas flow resistance is low (i.e., \(D_{M}/D_{N}\) = 2 and \(L_{M}/D_{M}\leq 7.5\) or \(D_{M}/D_{N}>1.75\)), the lobed interface and surface waves cause the gas-phase axial velocity to increase with \(L_{M}/D_{M}\), subsequently enhancing the gas-liquid volumetric ratio.
3. The lobed and surface wave structures can increase the axial flow near the gas-liquid interface. However, as \(D_{M}/D_{N}\) increases from 2.25 to 2.5, the slug interface transitions to a punctiform interface. This transition significantly reduces the surface area of the interface, thereby decreasing the axial velocity at the interface. This phenomenon reduces the axial flow near the interface, leading to a slower rate of increase in the gas-liquid volumetric ratio as \(D_{M}/D_{N}\) increases.  
Figure 13: Radial and axial velocity contours of three instantaneous gas–liquid interfaces (a) \(D_{M}/D_{N}\) = 2.75, \(L_{M}/D_{M}\) = 7.5; (b) \(D_{M}/D_{N}\) = 1.75, \(L_{M}/D_{M}\) = 17.5; and (c) \(D_{M}/D_{N}\) = 2.5, \(L_{M}/D_{M}\) = 17.5.  
To accurately capture the annular-mist flow regime, future simulations should incorporate novel grid refinement techniques. Further investigation is required into the effects of temperature variations, external disturbances, and excitations on the gas-liquid interface. Moreover, the integration of advanced multiphase flow detection techniques in subsequent studies could provide more precise insights into interface dynamics, thereby improving the accuracy of CFD predictions.  
Conceptualization, E.X. and Z.M.; methodology, Y.Z., W.Z., E.X. and Z.M.; formal analysis, Y.Z. and W.Z.; resources, E.X. and Z.M.; data curation, Y.Z. and W.Z.; writing--original draft preparation, Y.Z.; writing--review and editing, Y.Z., W.Z., E.X. and Z.M.; visualization, Y.Z.; funding acquisition, E.X. and Z.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China under grant numbers 52104275 and 52104279.  
Not applicable.  
The data presented in this study are available upon request from the corresponding authors.  
The authors acknowledge the contributions of [PERSON] to the conceptualization, methodology, and validation of this study and [PERSON] to the methodology and validation.  
The authors declare no conflict of interest.