**1. Introduction**

A single-channel pump is one type of sewage pump with a specially designed impeller. For the transport of various foreign objects in sewage, such as solids and fibers, it is intended that there is only one blade in the impeller. With the advantage of anti-clogging, a single-channel pump has been widely used for domestic and industrial sewage transport systems. However, compared with conventional centrifugal pumps, this particular design also brings some problems that cannot be ignored, such as hydrodynamic unbalance and relatively lower efficiency [1]. In order to improve the hydraulic performance of a single-channel pump, many numerical and experimental studies have focused on the inner flow field in the pump. Benra et al. [2,3] used PIV (Particle Image Velocimetry) technology to measure the periodic unsteady flow field in the impeller of a single-channel pump and compared the experimental results with numerical ones. The velocity field inside the pump investigated by PIV showed a good agreemen<sup>t</sup> with numerical one, which validated that using commercial Navier–Stokes solvers appears to be reliable. Nishi et al. [4] adopted LDV (Laser Doppler Velocimetry) and CFD (Computational Fluid Dynamics) methods to study the internal flow field of a single-channel pump. The results showed that the flow stagnation point on the work surface of the blade is far away from the inlet edge of the blade, resulting in a flow separation zone near the inlet edge. Auvinen et al. [5] used the OpenFOAM software to research the velocity field in a single-channel pump, and the results indicated that on the premise of high grid quality, the grid resolution had a

slight influence on the pump performance prediction. Generally, these CFD methods above treated the fluid in a single-channel pump as a single-phase flow and obtained the flow characteristics of a liquid. However, those solid particles and fibers in sewage systems in fact have an essential effect on the pump performance. The particle features, material properties, shapes, and sizes can not ge<sup>t</sup> an accurate assessment in this way. Moreover, these CFD methods cannot provide a reliable estimate for the behaviors of particle-particle and particle-wall, such as collision, which may damage the pump.

Alternatively, the Discrete Element Method (DEM), a professional numerical method for processing discrete phases, has been widely applied in the calculation of particle systems. DEM can provide an accurate description of the particle property and calculate its dynamic motions in accordance with Newton's second law. Given this, the DEM coupled with the CFD method was proposed to improve the computational efficiency and numerical accuracy in two-phase flow by Tsuji et al. [6] and Kafui et al. [7]. On the other hand, with an increasing realization of the relevance of particle shapes in soil behavior and flow patterns [8–10], the modeling of particle shapes has been developed into various constructs instead of a single sphere in the DEM. Cleary et al. [8] compared the effect of particle shapes on granular flows in hopper discharge. Santamarina et al. [9] concluded that particle shape emerges as a significant parameter needing to be properly characterized and documented as part of every soil characterization exercise. Pena et al. [10] studied the influence of particle shape on the global mechanical behavior of dense granular media.

Although the CFD-DEM coupling method has incomparable superiority, it was seldom applied to study solid-liquid two-phase flow in a centrifugal pump. Taking specific particle features, including size and material property into consideration, Huang et al. [11] used the CFD-DEM coupling method to calculate the unsteady solid-liquid two-phase flow in a centrifugal pump and obtained the solid phase distribution. Liu et al. [12] studied the crystal particles' behavior in a centrifugal pump with the CFD-DEM coupling method, and the results showed that some crystal particles begin to ge<sup>t</sup> aggregation near the inlet edges of blades, forming the larger particles. Li et al. [13] used this method to simulate the reflux of different-diameter particles with the same volume concentration in a mixed pump. The results indicated that particles with a diameter of 50 mm cannot be refluxed, and they are likely to accumulate at the junction of the impeller and vanes.

Based on the above, in consideration of the particle features, the CFD-DEM coupling method was employed for the first time to study the distribution and motion of solid particles in a single-channel pump. The distribution and motion of the particles were analyzed by a DEM code inside the commercial CFD tool STAR-CCM+. The calculation factors in the shape and size with the material properties of the particles and the interactions of particle–particle, particle-wall, and particle-liquid. These results could be used to highlight some design guidance for designing a single-channel pump by obtaining the flow characteristics of solid particles.
