## 5 Conclusions  
In this paper, a simulation model featuring a front-1-rear-3 configuration and a rear nozzle inclination ranging from 25\({}^{\circ}\) to 40\({}^{\circ}\) has been established. Additionally, a nozzle model with varying aperture sizes has been developed. By utilizing 2023 version of Fluent  
Figure 14: (**a**), the scheme with an inclination angle of 35\({}^{\circ}\), and the pore sizes are 2 mm and 3.5 mm, respectively. The velocity and displacement relationship of the fluid near the pipe wall is shown in Figure (**a**); (**b**), the scheme with an inclination angle of 35\({}^{\circ}\), and the apertures are 2 mm and 3.5 mm, respectively. The relationship between the velocity and displacement of the fluid at the outlet of the front nozzle is plotted.  
simulation software, the flow field simulation of the nozzle jet within the pipeline has been conducted, yielding the following conclusions:  
1. The rear nozzle's varying inclination angles significantly influence the internal flow field of the pipeline. Specifically, when the inclination angle is set at 35\({}^{\circ}\), further increasing the angle leads to a shortened stroke from the outlet to the wall surface, resulting in an elevated instantaneous velocity of the rear jet upon contact with the wall. However, this does not translate to a continual increase in the overall wall velocity.
2. The interplay between the rear and front jets creates vortex zones and wall backflow within the pipeline, subsequently affecting the jet velocity of the front nozzle. Notably, at an inclination angle of 35\({}^{\circ}\) for the rear nozzle, the impact on the flow velocity within the front jet pipe is minimized. Taking the 35\({}^{\circ}\) inclined rear nozzle scheme as an example, the jet velocity of the 2 mm aperture front nozzle experiences an attenuation of 77.2%, while the jet velocity of the 3.5 mm aperture front nozzle undergoes an attenuation of 67.7%.
3. When the inclination angle of the rear nozzle remains constant, augmenting the nozzle aperture from 2 mm to 3.5 mm effectively decreases the size of the vortex area. The vortex area of the 3.5 mm aperture nozzle comprises 63% of that of the 2 mm aperture nozzle. The reduction in this vortex can improve the dredging efficiency and reduce the damage to the workpiece.  
[PERSON] conceived and designed the methodology; [PERSON] performed the experiment and wrote the manuscript; [PERSON] was responsible for software; [PERSON] performed validation; [PERSON] carried out formal analysis. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Natural Science Foundation of Hebei Province Ecological Intelligent Mine Joint Fund (E2022402102). Data Availability Statement: Data is contained within the article.  
I sincerely thank all the teachers, classmates, family members, and friends who have given me help and support in the process of completing this thesis. Without your understanding, encouragement, patient guidance, and selfless help, I would not be able to successfully complete this paper. Finally, thanks to the review experts and editors, thanks to your criticism and suggestions to make this paper can be constantly improved, let me in the academic research progress. Thank you again to all those who have given me help and support. May we grow together and make progress together in the future academic journey.  
The authors declare no conflicts of Interest.