*2.3. Experiment*

The Faculty of Civil Engineering of the University of Rijeka is home to the GUNT HM 162 experimental flume (shown on Figure 3), which is an open-channel flow physical model with a test section with a length of 12,500 mm and a rectangular cross section measuring 309 mm in width and 450 mm in height. This experimental flume is also fitted with a separate particle inlet.

**Figure 3.** HM 162 experimental flume: 1—water tank, 2—water outlet element, 3—sediment screen basket, 4—sediment pump, 5—PLC (switch box), 6—centrifugal pump, 7—flow rate sensor, 8—openchannel test section, 9—particle (sediment) inlet, 10—inclination adjustment element, 11—water inlet element.

The HM 162 experimental flume consists of an open-channel test section that is a part of a closed water circuit. The water is circulated from a water tank into the pipe and through the water inlet element into the experimental section by a Lowara SHS4 centrifugal pump, which can provide a maximum head of 16.1 m and has an operating flow rate in the range of 5.4 to 130 m<sup>3</sup> h−1. The water flows back into the water tank through the outlet element at the end of the experimental section. The water pump is controlled by the PLC (switch box) to adjust the flow rate. The actual flow rate is reported by the Endress+Hauser Promag 10L electromagnetic flow rate sensor, which is built into the pipe between the water pump and inlet section and has a measuring range of 5.4 to 180 m3 h−1. The water level and the tilt of the open-channel section are also adjustable via the adjustable overflow edge and the inclination adjustment element, respectively.

The particle inlet that is supplied by GUNT (as shown in Figure 3) is intended for dense sediment flows, with high sediment flow rates achieved by means of a separate GUNT-manufactured sediment pump. The pump is designed for fine-grained sand with a granulation of up to 2 mm and can achieve a maximum flow rate of 36 m3 h<sup>−</sup>1. Because this work is focused on small batches of particles that are passively introduced into the water and are larger than 2 mm, a new particle inlet was constructed at the hydraulic laboratory of the Faculty of Civil Engineering, University of Rijeka.

A metal funnel was fitted with a 3D-printed opening mechanism and fixed inside a 3D-printed holding plate. The holding plate was attached to four steel wires, which were attached to the base plate. When the base plate was placed on top of the experimental section side walls, the funnel was positioned as shown in Figure 4.

**Figure 4.** Detailed view of the particle inlet funnel.

We investigated the settling and particle size distribution of 3D-printed spherical plastic particles with a density of 1140 kg m<sup>−</sup>3. The particle size distribution is presented in Table 1; each particle was colored according to its size for size identification.

**Table 1.** Particle sizes used in the settling experiment.


The volumetric flow rate was set to 27 m<sup>3</sup> h<sup>−</sup>1, and the water level was set to 350 mm. The tilt of the channel was horizontal (no tilt). As shown in Figure 4, the particle inlet was positioned in the middle of the width of the test section and 5450 mm downstream of the beginning of the test section. The bottom of the funnel where particles enter the water was positioned 80 mm below the free surface.

Particle release and settling were filmed with two cameras: one obtaining a top view and one capturing a side view of the channel. Settling times and downstream settling distances were determined from the videos.

#### **3. Computational Setup**

For the purpose of conducting a mesh study, three different structured, hexahedral computational meshes of the whole channel geometry were prepared with the ANSYS (Canonsburg, PA, USA) Meshing module. To reduce the number of cells and therefore the computational time, the computational domain was reduced only to the area of interest, where the domain was shortened to 5250 mm by moving the inlet 3550 mm downstream and moving the outlet 3700 mm upstream of the experimental open-channel test section. Three different meshes of this reduced domain were generated, with element sizes between corresponding mesh densities kept constant. The final mesh statistics are presented in Table 2.

A velocity inlet that matches the volumetric flow rate was used in the experiment, relative pressure at the outlet was set to 0 Pa and the operating pressure was set to 101,325 Pa. A no-slip condition was imposed on the walls of the flume, and a free-slip wall condition was imposed on the free surface of the flow. All walls were treated as smooth walls.

The continuous phase was water with constant density of 998.2 kg m−<sup>3</sup> and a constant viscosity of 0.001003 kg m−<sup>1</sup> s−1. The particles were made with VeroBlue RGD840 material with a density of 1140 kg m−3, Poisson's ratio of 0.49 and a Young's modulus of 2650 MPa. For the DEM approach, properties of the walls, particle–particle interaction and particle–wall interaction properties were further prescribed. For the bottom steel wall, a density of 7800 kg m−<sup>3</sup> was prescribed with a Poisson's ratio of 0.3 and a Young's modulus

of 210,000 MPa. The glass side walls were prescribed a density of 2500 kg m<sup>−</sup>3, a Poisson's ratio of 0.22 and a Young's modulus of 70,000 MPa. For both the particle–particle interaction and particle–wall interaction, the coefficient of restitution was 0.5, the coefficient of static friction was 0.5 and the coefficient of rolling friction was 0.01. Temperature dependence of material properties was not considered, and an isothermal simulation approach was adopted, with all material properties reported for 20 ◦C.

**Table 2.** Information about analyzed computational meshes: M1—coarse mesh, full domain; M2—medium mesh, full domain; M3—fine mesh, full domain; M1r—coarse mesh, reduced domain; M2r—medium mesh, reduced domain; M3r—fine mesh, reduced domain.


Pressure–velocity coupling of equations was achieved via the Coupled scheme, gradients were evaluated using the least squares cell-based method, pressure at the cell faces was interpolated using the PRESTO! method and the third-order accurate QUICK spatial discretization scheme was adopted for all equations. Temporal discretization of equations was achieved by the bounded second-order implicit time integration scheme. A time step of 0.05 s was chosen, which was shorter than the particle response time, resulting in a maximum Courant number of less than 1. The iterative solution of equations within each time step was limited to 100 iterations; however, a scaled residuals convergence criterion of 10–4 was achieved before this limitation.

For the particles, an inlet velocity of0ms−<sup>1</sup> was imposed, and a mass flow rate for each size fraction was determined to match the number of particles for a given size fraction within a time window of 1.1 s, which was determined in the experiment.

#### **4. Results and Discussion**

Vertical and horizontal fluid velocity profiles were plotted along the respective directions at the particle inlet location before particles were injected into domain. As shown in Figures 5 and 6, both in the case of a whole domain and in the case of a reduced domain, all three mesh densities predict a similar velocity profile. The main difference is observed near the channel walls, where the coarse mesh underpredicts both the velocity gradient and the velocity magnitude. In comparison to the whole domain, significantly different velocity profiles are obtained on the meshes of the reduced domain. However, this can be corrected by applying the calculated velocity profiles on the fine mesh from the whole-domain case as an inlet boundary condition in the reduced-domain case.

A comparison of calculated settling times obtained using three approaches and experimental values is presented in Figure 7. Satisfactory agreement was achieved for all three simulation approaches, except for the smallest particles with a diameter of 2 mm. A similar observation can be derived from the comparison of the downstream distance travelled by particles before settling on the bottom of the channel, as presented in Figure 8. Interaction between particles does not appear to be significant, as the DDPM approaches with and without inclusion of DEM produce similar results.

A more detailed comparison of the DPM and DDPM approaches is presented in Figures 9 and 10, showing a time evolution of settling velocity and horizontal particle velocity, respectively. Minor differences can be observed, indicating that the point particle assumption of DPM is sufficient for treatment of mesoplastic particles in an open-channel flow.

**Figure 5.** Vertical velocity profiles of water: (**a**) comparison between three mesh densities for the full domain and the fine mesh of the reduced domain; (**b**) comparison between three mesh densities of the reduced domain with a velocity profile boundary condition.

**Figure 6.** Horizontal velocity profiles of water: (**a**) comparison between three mesh densities for the full domain and the fine mesh of the reduced domain; (**b**) comparison between three mesh densities of the reduced domain with a velocity profile boundary condition.

Figure 11 presents the propagation of a particle cloud as observed in the DPM simulation and the experiment at three different times. The color of the largest 4 mm particles is changed from white to yellow in the visualization of the simulation results for improved visibility. Additional vertical lines are drawn in the photos from the experiment that correspond to vertical lines drawn in the pictures from the simulation due to the difference in perspective. As shown in Figure 11, general agreement can be observed between simulation and experimental results, although with a noticeably tighter grouping of particles by size in the case of the simulation.

From both the experiment and simulations, it is evident that larger plastic particles settle more quickly than smaller particles, as expected, with the larger particles reaching a higher settling velocity. As shown in Figure 9, all particles reach terminal velocity (flattening of all curves for time evolution of velocity). Similarly, all particles reach the maximum horizontal velocity of the flow; as expected, smaller particles reach this velocity quicker than larger particles. Because larger particles reach the bottom of the channel sooner than smaller particles, their horizontal velocity also drops sooner. As shown by the velocity profile presented in Figure 5, the velocity adheres to a no-slip law (boundary condition); therefore, when particles approach the bottom of the channel, their velocity reduces accordingly. Figure 10 shows that settled particles retain some horizontal velocity in the simulation; however, this behavior is not observed in the experiment because an accurate particle–wall interaction was outside the scope of this study, and only the settling motion in the fluid was analyzed.

**Figure 7.** Average settling times of plastic particles; error bars represent one standard deviation.

**Figure 8.** Average downstream settling distance of plastic particles; error bars represent one standard deviation.

**Figure 9.** Settling velocity of plastic particles; points represent average values, and error bars represent one standard deviation.

**Figure 10.** Horizontal velocity of plastic particles; points represent average values, and error bars represent one standard deviation.

**Figure 11.** Comparison of the particle cloud as observed in the experiment and the simulation using the DPM approach: (**a**) and (**b**) 0.5 s after the release of particles; (**c**) and (**d**) 1.5 s after the release of particles; (**e**) and (**f**) 2.5 s after the release of particles. Particles are colored by size as described in Table 1. Yellow color is used instead of white in the visualization of the simulation results.
