## 3 Investigations Focusing on Flow Regime Characteristics
### Investigations with Single-Sized Spherical Particles
#### 3.1.2 Experimental Results and Discussion  
In light of experimental observations, pool convection and particle inertia were confirmed to be predominant in affecting flow regime characteristics during bed formation. As shown in Figure 12, due to their different predominance at varying parametric situations,  
Figure 11: Experimental Visualization system for investigations focusing on flow regime characteristics. (**a**) Schematic view of experimental system, and (**b**) detailed view of the main apparatus [24]. four types of flow regimes were found to form, including the particle-suspension regime (Regime I), pool-convection dominant regime (Regime II), transitional regime (Regime III), and particle-inertia dominant regime (Regime IV). In Figure 13, the characteristics and mechanisms of each flow regime are described together with the effect of the different parameters. In general, the DBF process can be divided into two stages. Stage 1 is the particle-releasing stage, during which the falling particles are released from the nozzle to the upper area of the forming bed. In Stage 1, the nozzle outlet size and the properties of the released particles can significantly affect the releasing rate of particles, which subsequently influences the pool-convection intensity triggered by the falling particles and bed formation behavior. While Stage 2 is the particle accumulating stage (around the bottom area of the tank), during which the effects of particle inertia and particle-flow-induced pool convection play competing roles in determining the final bed shape. As shown in the final photos in Figure 12, after the particles are released and accumulated, four bed shapes, including flat, concave, trapezoid, and convex shapes, can be identified as a result of the different flow regime characteristics. Figure 12: Typical flow-regime characteristics (glass spherical particles, \(H_{\text{n}}\) = 110 cm, \(d_{\text{n}}\) = 30 mm, \(H_{\text{w}}\) = 60 cm, and \(W_{\text{tank}}\) = 60 mm) (arrows represent the flow directions); (**a**) \(d_{\text{p}}\) = 0.25 mm; (**b**) \(d_{\text{p}}\) = 0.5 mm; (**c**) \(d_{\text{p}}\) = 2 mm; and (**d**) \(d_{\text{p}}\) = 8 mm [69]. As for the effect of experimental parameters, through qualitatively observing the particle bed formation process and quantitatively measuring the base angles and the vertex angles (see Figure 14), it was confirmed that, in general, a larger particle density and size could contribute to the particle inertia, thus resulting in the formation of greater-numbered flow regimes, consistent with the observations from above-mentioned 3D experiments focusing on accumulated-bed characteristics and resulting in more convex beds. Additionally, increasing the water depth would effectively facilitate the formation of pool convection (or enhance the intensity), resulting in the transition of greater-numbered regimes to lower-numbered ones, which indicates a tendency towards forming a more concave or flatter particle bed. Meanwhile, decreasing the nozzle size was expected to lead from a lower-numbered flow regime transit to a greater-numbered one because, in such a case, the resistance for discharging particles (such as frictions and collisions) was significantly strengthened, thus decreasing the particle discharging rate along with the predominance of pool convection. Moreover, similar to the observations of the experiments focusing on accumulated-bed characteristics, a slight tendency for particle bed to become flatter when the nozzle height increased was found because of more violent pool convections resulting from more remarkable differences in the velocity between the fluid flow and particle jet, although the flow regime transition did not emerge due to the rather limited range of parameters. Further, by varying the tank thickness, it was inferred that no remarkable variation in flow regime characteristics or bed geometry was observable, although the bed heights were changed due to the different cross-sectional areas.