Analysis of Fluid Suction Characteristics of Polyhedral Particles in Deep-Sea Hydraulic Collection Method
Abstract
:1. Introduction
2. The Characteristics of a Suction-Based Hydraulic Collection Method
2.1. The Hydraulic Collection Model
2.2. Control Equations
2.3. The Characters of Particles
2.4. Analysis of Dimensionless Parameters
3. Description of the Hydraulic Collection Experiment
3.1. The Experimental Platform
3.2. The Experimental Conditions
4. The Flow Characteristics of the Hydraulic Collection Flow Field
4.1. The Characteristics of the Time-Averaged Velocity of Flow Field
4.2. The Vortex at the Inlet of the Cone Hood
4.3. The Vertical Force of Central Particles Based on the Vortex
5. Results and Discussion
5.1. The Effect of Different Positions S and Different Particles on Suction Force Fd
5.2. The Effect of Parameters Φ and S/R on the Suction Coefficient Ratio
5.3. The Effect of Parameter H/dp and S/H on the Suction Coefficient Ratio
5.4. The Effect of Parameters R/H and S/R on the Suction Coefficient Ratio
6. Conclusions
- (1)
- As height H decreased, the pattern of the external flow field was observed, which showed that the fluid flow distributed along the wall of the hood and the flow velocity distribution at the center bottom were relatively low. The occurrence and movement of the suction vortex and coherent vortex were found in the central region between 0.1R and 0.2R, which can be attributed to the height H, the flow rate , and the structural characteristics of the cone-shaped collecting hood. The suction and coherent vortex can provide favorable conditions for particles collection.
- (2)
- The suction force (Fd) generally decreased with the increase in the Φ, and the downward trend of the Fd in the flow field with the high velocity was more obvious compared to the low-velocity flow fields. Notably, there were two peaks on the curve, at S = 0.010–0.020 m and S = 0.140–0.160 m, respectively. The positions favorable for particle collection were mainly distributed within the range of 0.1–0.2R and 0.8–1R, while the weakest collection occurred between 0.4R and 0.6R, which is not conducive to ore collection.
- (3)
- The ratio generally increased with the decreasing sphericity Φ at the same hydraulic collection location, while the fluctuation of became more stable as the Φ increased. The regular icosahedral shape (Φ = 0.940) exhibited a value of approximately 1.1, which indicates its superior overall stability and similarity to a spherical shape, so the suction coefficient (Cd) of the icosahedra was close to the sphere. Moreover, it was observed that the was highly sensitive to the high-speed field, and the maximum of FV and the maximum of FL appeared at the peak points of their force values, S/R = 0.875 (S = 0.140 m) and S/R = 1(S = 0.160 m), respectively, where is significantly larger. The decreases as the parameter H/dp increases, and the decreasing trend of significantly slows down when H/dp exceeds 3.5.
- (4)
- In terms of suction force, polyhedral particles exhibit greater hydraulic collection efficiency compared to spherical particles of the same weight, which is more obvious in high-speed flow fields. However, due to their complex surface structures and larger geometric shapes, polyhedral particles may undergo more intricate motion. Therefore, our future research will focus on investigating the dynamics of polyhedral particle motion.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
D | inlet diameter of cone hood |
H | distance from the hood inlet to the seabed |
Vl | water velocity |
Fv | vertical force |
Fl | horizontal force |
actual volume of the non-spherical particle | |
equivalent diameter | |
du | circumcircle diameter |
suction flow rate | |
sphericity of particle | |
sphericity of polyhedron particle | |
horizontal distance between particles and the collecting center | |
A | incoming flow area of particles |
inlet radius of cone collecting hood | |
Fd | suction force |
Cd | suction force coefficient |
fluid density | |
fluid mean velocity | |
Re | Reynolds number |
viscosity coefficient of fluid | |
vertical force coefficient ratio | |
horizontal force coefficient ratio | |
V | normal water velocity |
Vm | mean suction velocity |
U | horizontal water velocity |
e | elongation factor of particle |
f | flatness factor of particle |
Subscripts: | |
n | face number of polyhedron particle |
l | horizontal direction |
v | vertical direction |
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e | f | ||
---|---|---|---|
Value Range | Quantity | Value Range | Quantity |
0.9–1 | 18 | 0.9–1 | 7 |
0.7–0.9 | 55 | 0.7–0.9 | 19 |
0.5–0.7 | 34 | 0.5–0.7 | 42 |
0.3–0.5 | 11 | 0.3–0.5 | 31 |
<0.3 | 1 | <0.3 | 20 |
total | 119 | 119 |
Approximate Shape | Geometric Figure | Range of Form Factors | Quantity | Weight/g |
---|---|---|---|---|
convex polyhedron shape | e > 0.4 and f ≥ 0.4 | 72 | 47.8 | |
flat shape | e > 0.4 and f < 0.4 | 31 | 20.6 | |
belt shape | e ≤ 0.4 and f ≤ 0.4 | 12 | 8.9 | |
other | irregular shape | 4 | 2.7 | |
total | 119 | 80 |
Polyhedron | Regular Tetrahedron | Regular Hexahedron | Regular Octahedron | Regular Dodecahedron | Regular Icosahedron | Sphere |
---|---|---|---|---|---|---|
equivalent grain/dp | 0.61L4 | 1.24L6 | 0.97L8 | 2.45L12 | 1.61L20 | dpb |
sphericity/ | 0.675 | 0.805 | 0.853 | 0.913 | 0.940 | 1.000 |
circumcircle/du | 2.012dp4 | 1.397dp6 | 1.464dp8 | 1.146dp12 | 1.182dp20 | dps |
Order Number | Horizontal Position/S (m) | Height of Hood to Bottom/H (m) | Equivalent Diameter/dp (m) | (m3/h) | Cone-Shaped Hood/R (m) | Remarks | |
---|---|---|---|---|---|---|---|
1 | 0.805, 1 | 0 | 0.02, 0.04, 0.06 | 0.008 | 35 | 0.05 | Section 4.1 |
2 | 1 | 0 | 0.035 | 0.015 | 105, 115 | 0.16 | Section 4.3 |
3 | 0.940 | 0, 0.01, 0.02, 0.04 | 0.035 | 0.015 | 95, 110 | 0.16 | Section 4.3 Figure 13 |
4 | 1 | 0 | 0.045 | 0.025 | 95, 105, 115 | 0.16 | Section 4.3 Figure 14 |
5 | 0.675, 0.805, 0.853, 0.913, 0.940, 1 | 0, 0.01, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.17, 0.18 | 0.035 | 0.015 | 110 | 0.16 | Section 5.1 |
6 | 0.675, 0.805, 0.853, 0.913, 0.940, 1 | 0, 0.02, 0.08, 0.14, 0.16 | 0.035 | Section 5.2 | |||
7 | 0.853, 1 | 0, 0.02, 0.08, 0.14, 0.16 | 0.035 | Section 5.3 | |||
8 | 0.853, 1 | 0, 0.02, 0.08, 0.14, 0.16 | 0.035, 0.045, 0.055, 0.065 | 0.16 | Section 5.4 |
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Jiang, M.; Chen, B.; Li, K. Analysis of Fluid Suction Characteristics of Polyhedral Particles in Deep-Sea Hydraulic Collection Method. J. Mar. Sci. Eng. 2024, 12, 1543. https://doi.org/10.3390/jmse12091543
Jiang M, Chen B, Li K. Analysis of Fluid Suction Characteristics of Polyhedral Particles in Deep-Sea Hydraulic Collection Method. Journal of Marine Science and Engineering. 2024; 12(9):1543. https://doi.org/10.3390/jmse12091543
Chicago/Turabian StyleJiang, Min, Bingzheng Chen, and Kaihui Li. 2024. "Analysis of Fluid Suction Characteristics of Polyhedral Particles in Deep-Sea Hydraulic Collection Method" Journal of Marine Science and Engineering 12, no. 9: 1543. https://doi.org/10.3390/jmse12091543