## 5 Concluding Remarks  
(1) Dual functions are accomplished with the sand pump proposed. The lower and upper parts of the primary impeller are characterized by significantly different inner flow patterns. Intensified mixing occurs in the volute chamber, where the mediums discharged from the upper and lower parts of the primary impeller mix with each other, creating circumferentially uneven distributions of velocity and pressure.  
(2) The operating characteristics of the pump differ explicitly from general knowledge. The pump head increases with the rotational speed. However, the pump efficiency varies non-monotonically with the rotational speed and the feed rate of sand. At a rotational speed of 950 rpm, the lowest pump efficiency arises at a feed rate of sand of 2.10 m\({}^{3}\)/min. Such a pump efficiency is also lower than those obtained at the same feed rate of sand but at different rotational speeds.  
(3) The distributions of the solid volume fraction in the blade channels of the upper part of the primary impeller are considerably different. The distribution of the solid volume fraction in the volute chamber is uniformized with increasing rotational speed. With an increasing feed rate of sand, the risk of the blockage of the sand inlet segment increases.  
(4) Radial hydraulic forces acting on the primary impeller point toward the third and fourth quadrants. No monotonical relation is evidenced between the radial force and the rotational speed or the feed rate of sand. The largest radial force is produced at a rotational speed of 950 rpm and a feed rate of sand of 3.12 m\({}^{3}\)/min. The axial force increases continuously with the feed rate of sand and the rotational speed of the impeller.  
(5) The pump studied is special in terms of both the pump structure and the two-phase flow field. Furthermore, the attainable solid volume fraction is much higher than those generally adopted. Future studies aiming to elucidate the effects of geometric parameters of the impeller and other operating parameters, such as particle size, on pump performance are expected. Attention should focus on how to mitigate the suction of air by deploying an auxiliary device at the sand inlet. Moreover, the relationship between the water flow rate and pump performance is expected to be comparatively investigated with different impeller schemes.  
Conceptualization, C.K.; methodology, C.K. and C.L.; software, Y.Z. ([PERSON]); validation, Y.Z. ([PERSON]) and C.L.; formal analysis, Y.Z. ([PERSON]) and H.W.; investigation, C.K., Y.Z. ([PERSON]) and H.W.; data curation, Y.Z. ([PERSON]); writing--original draft preparation, Y.Z. ([PERSON]); writing--review and editing, C.K.; visualization, Y.Z. ([PERSON]) and C.L.; supervision, C.K.; funding acquisition, C.K. and C.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Program of China (Grant No. 2021 YFC2801600) and the Foreign Expert Project of the Ministry of Science and Technology of China (Grant No. QN2023014002).  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available because of the fact that the dataset production is part of the innovation point of this paper. The dataset is not open-source at this time as we continue to explore new possibilities in subsequent experimental research. Then, the dataset will be made public along with the related code.  
The Computation Center of Jiangsu University provided the computer clusters for the numerical work.