# Experimental Investigation in Drag Coefficient of Cubes
## 4 Results and Discussion
### Behavior of the Spliced Cube Drag Coefficient  
Then, the free settling experiment is performed by using the spliced cubes. The settling orientation angle of \(\alpha\) is defined as the angle of bottom edge of the cube, and the horizontal line on the high speed camera recorded the image, as shown in Figure 5. Therefore, the orientation angle of the cube is within a limit range of \(0^{\circ}\leq\alpha\leq 45^{\circ}\) during the settling process. When the orientation angle is \(0^{\circ}\), the cube has the minimum frontal area. When the orientation angle is \(45^{\circ}\), the cube reaches its maximum frontal area during the settling process. For the spliced cubes, the slight secondary motion still exists at a high Reynolds number during its settling process. However, compared with the uniformed cube, the secondary motion amplitude of the spliced cube is suppressed significantly. Figure 6 exhibits the experimental drag coefficient of the spliced cube with \(h/a=0.5\) and \(h/a=1.0\). The drag coefficient of the sphere is also shown in Figure 6 as a comparison. The experimental Reynolds number, which is in the range of \(0.45\leq Re\leq 4516\), covers the Creeping flow regime, Transition regime, and Newton regime as well. Under the effect of eccentric moments, the spliced cube with \(h/a=0.5\) and \(h/a=1.0\) can maintain the orientation angle around \(0^{\circ}\) and \(45^{\circ}\) in the settling process, respectively. Similarly to the uniform cube, the drag coefficient of the spliced cube is always higher than that of the sphere at the same Reynolds number. However, the drag coefficients of different spliced cubes show different variation trends, especially in the range of \(10\leq Re\leq 2.186\times 10^{3}\). This indicates that the angle factor has a significant impact on the resistance coefficient of the particles. For the spliced cube with \(h/a=1.0\) and \(\alpha=45^{\circ}\) the drag coefficient of the cube keeps decreasing as the Reynolds number increases. The decreasing ratio of the drag coefficient is also reduced as the Reynolds number increases. However, the decreasing ratio of the spliced cube with \(h/a=1.0\) is smaller than that of the sphere as Re > 10. As a result, the drag coefficient of the spliced cube with \(h/a=1.0\) is significantly higher than that of the sphere. The variation trend of the drag coefficient of the spliced cube with \(h/a=0.5\) and \(\alpha=0^{\circ}\) also shows different characteristics with the sphere. The drag coefficients of the cube with \(h/a=0.5\) keep decreasing as the Reynolds number increases in the range of \(1<Re<2.5\times 10^{2}\). Then, the drag coefficient shows an increasing trend in the range of \(2.50\times 10^{2}<Re<2.186\times 10^{3}\). The value of the drag coefficient of the spliced cube is close to that with \(h/a=1.0\) at the same Reynolds number when \(Re<10\). Then, the value of the drag coefficient of the spliced cube with \(h/a=0.5\) is smaller than that with \(h/a=1.0\) in the  
Figure 4: Relationship between drag coefficient and Reynolds number for uniformed cube [9]. range of \(10<Re<10^{3}\). Finally, the drag coefficient of the two spliced cubes is similar to each other again in the Newton regime. For the spliced cube with \(h/a=0.67\), the eccentric moment makes the cube drop in an unsymmetrical incline, which will be affected by the significant lateral force of the fluid. As a result, the orientation angle of the spliced cube with \(h/a=0.67\) is more easily changed compared to the two other cubes with \(h/a=0.5\) and \(1.0\) during the settling process. Figure 7 exhibits the relationship between the orientation angle and Reynolds number for the spliced cube with \(h/a=0.67\), obtained by the experimental data. As can be seen, the orientation angle of the cube varies along with the Reynolds number. The mean orientation angle of the cube is \(16.52^{\circ}\) and the standard deviation is \(6.076\).