Chapter 4. DEM Analysis on Jamming Probability
4.1 Effect of physical parameters on jamming
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The analysis results for each physical parameters were as below. Unless otherwise noted, each parameter defaulted to the following values reflecting actual physical quantities:
① Hopper outlet diameter (D) : 12 mm
② Ball diameter (d) : 2~6 mm
③ Friction coefficient between wall and particles (μ) : 0.158
④ Density (ρ) : 8000 kg/m3
⑤ Number of balls in the hopper (N0) : 1000
4.1.1 Effect of D/d
Jamming probabilities have been represented by the function of the hopper and ball diameter in various studies for jamming analysis (Angel Garcimartin et al., 2010; Kiwing To et al., 2001). In this study, jamming probability was arranged as a function of D/d like previous studies. As a result, it could be seen that the jamming probability tends to decrease as the hopper outlet diameter D increases and the ball diameter d decreases as shown in Fig. 4.1. If jamming occurs in the actual Ball-type SSS, it will lead to a severe accident. Therefore, D and d must be determined in the region where the jamming probability converges to zero. In particular, it was confirmed that balls were injected into the guide tube without jamming in the region of D/d> 4.5 regardless of the other
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conditions. In this study, a minimum D/d value with the jamming probability of less than 1% was found, and it was named as critical D/d. In this case, the effect of each parameter on jamming was confirmed by measuring the change of critical D/d value.
4.1.2 Effect of hopper angle (Ф)
The influence of the hopper angle (Φ) on the granular flow has been confirmed by various studies. A previous study using both experimental and numerical methods for the analyzing stresses of static granular media inside hopper show that the hopper angle has a strong influence on the spatial distribution of maximum shear stress distribution inside the hoppers (Saeed Albaraki et al. 2013). In this study, the variation of jamming probability was observed by changing the hopper angle to 40˚, 60˚, and 80˚ as shown in Fig. 4.2.
As a result, the jamming probability tended to decrease as the hopper angle increases as shown in Fig. 4.3. As the angle changed from 40˚ to 60˚ and 80˚ the critical D/d decreased to 3.967, 3.818, and 3.011. This phenomenon occurs because as the hopper angle increases, the frictional force acting on the particles decreases. Reduced frictional forces make arch formation difficult in the hopper.
From this results, it could be expected that Ball-type SSS operate with higher reliability when the hopper angle is larger. However, as the hopper angle increase, the hopper volume increased as shown in Fig. 4.2. Therefore, the hopper angle should be determined to the maximum within the space allowed in an actual Ball-type SSS.
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4.1.3 Effect of friction coefficient (μ)
The effect of friction coefficient (μ) between the wall and the particles on jamming was confirmed. As a result, the jamming probability increased as the coefficient of friction increased to 0.1, 0.2, and 0.4 as shown in Fig. 4.4. In this case, critical D/d increased to 3.701, 3.947, and 4.227. This phenomenon occurs because as the friction between the particle and the wall decreases, the particles form fewer arches, and it is more difficult to balance forces within the hopper.
From this results, it could be expected that Ball-type SSS operate with higher reliability when the surface treatment is performed to minimize the friction between the ball and the wall.
4.1.4 Effect of geometry size (D)
For the same D/d, the effect of the whole geometry size on jamming was confirmed. As a result, the jamming probability decreased when the geometry size doubles as shown in Fig. 4.5. In this case, critical D/d decreased 3.818 to 3.734. This was because of the average particle passing speed at the hopper outlet increased as shown in Fig. 4.6, 4.7. Beverloo correlation can explain the increase in passing velocity at the hopper exit when the scale increased.
According to Beverloo (1961), the mass flow rate of the ball passing through the 3-dimensional hopper satisfies the relation of Eq.4.1.
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( )2.5
Q g Wkd (4.1)
When both the size of the hopper and ball are doubled, the mass flow rate becomes 25/2 times. However, the passing area becomes 22 times larger, and velocities of the balls through the hopper exit is 21/2 times faster. Jamming occurs when a particle forms an arch through interaction with surrounding particles. If the velocity of the ball passes fast, the probability of exiting before interacting with the surrounding particles increases and the jamming probability decreases. According to this result, the actual Ball-type SSS should be designed to the largest size as long as space is allowed.
4.1.5 Effect of ball density (ρ)
The effect of particle density on jamming was confirmed. As a result, the simulation performed with increasing particle density to 4000 kg/m3, 8000 kg/m3, and 16000 kg/m3 showed that the same jamming probability is obtained within the error range as shown in Fig. 4.8. In this case, critical D/d changed to 3.737, 3.818, and 3.808. This phenomenon occurs because both the frictional force that maintains jamming and the gravitational force that breaks jamming are proportional to the particle density. From this result, it can be confirmed that the material of the neutron absorber can be selected without density restriction in an actual Ball-type SSS.
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4.1.6 Effect of number of particles (N0)
Finally, the effect of the number of particles on jamming was confirmed. As a result, the jamming probability increased as the number of particles increased to 500, 1000, and 2000 as shown in Fig. 4.9. In this case, critical D/d increased to 3.571, 3.818, and 3.860. This phenomenon occurs because as the number of balls increases, the number of attempts to pass through the hopper exit increases, and the jamming probability increases. As in previous studies, if the probability of one ball passing is constant, the probability of all balls passing must increase exponentially with regard to the number of balls. However, the results in Figure 4.9 did not satisfy this trend. The interpretation of this was explained in the next chapter.