Numerical Study of Internal Flow Field in a Disc Stack Centrifuge Based on Mixture-PBM Model
Abstract
:1. Introduction
2. Physical Models and Numerical Simulation
2.1. Model and Meshing
2.2. Numerical Methods and Boundary Conditions
3. Results and Discussion
3.1. Comparison of Experimental and Numerical Simulation Results
3.2. Effect of Ribs on the Distribution of Flow Field Parameters
3.3. Coalescence and Breakup of Water Droplets
3.4. Three-Dimensional Flow Characteristics of the Internal Flow Field
4. Conclusions
- The error between the numerical simulation results and the separation efficiency of the test results is less than 1%. When Nd = 1~1.06, the separation efficiency of the disc stack centrifuge increases with the increase in rotational speed. When Nd = 1.06, the separation efficiency η = 99.99%.
- Considering the ribs of the disc, the hysteresis phenomenon of the liquid flow in the disc stack centrifuge is significantly reduced, and the results of numerical simulation (parameter distribution of the flow field) can reach 98% of the theoretical results, which verifies the reliability of the numerical simulation results. The ribs of the disc have an indispensable role.
- A total of 90% of the water droplets in the oil–water mixture complete coalescence and precipitation in the distributor and do not pass through the rising channel but enter the heavy liquid area of the bowl through the rectangular channel and are discharged to the disc stack centrifuge through the water-phase outlet. The coalescence phenomenon of the water droplets entering the separation channel is greater than the breakup phenomenon.
- The water content in the rising channel gradually decreases, and 95% of the water enters the bottom separation channel of the bowl component. The processing capacity of each layer of the separation channel gradually increases, showing the law of having a small bottom layer, large top layer, and uniform middle layer.
- After the oil–water mixture enters the separation channel from the neutral pore, under the action of Coriolis force, the motion trajectory is not parallel to the generatrix of the disc but forms a vortex near the neutral pore, and the area of the vortex is small at the bottom and large at the top. The coalescence phenomenon and the water content of the water droplets affect the vortex scale, which is different from the classical two-dimensional simplified model with obvious three-dimensional characteristics. With the increase in λ, the motion trajectory of the liquid is more and more deviating from the generatrix direction of the disc. In addition, the circumferential and radial velocities in the separation channel show a law of being large in the middle and small near the wall.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
η | Separation efficiency of disc stack centrifuge |
c0 | Volume fraction of the water phase at the inlet of the computational domain |
c1 | Volume fraction of the water phase at the outlet of the oil phase of the computational domain |
Qd | Design flow of the disc stack centrifuge (m3/h) |
Q | Actual flow of the disc stack centrifuge (m3/h) |
Qd | Design flow of the disc stack centrifuge (m3/h) |
Nh | Rotational speed coefficient of the disc stack centrifuge |
N | Actual rotational speed of the disc stack centrifuge (rpm) |
Nd | Design rotational speed of the disc stack centrifuge (rpm) |
D | Maximum radius of the disc stack centrifuge (m) |
P | Centrifugal hydraulic pressure difference at the free liquid surface and the inlet of the flow channel (Pa) |
Vc | Circumferential velocity (m/s) |
Density of the liquid (kg/m3) | |
Rotational angular speed of the liquid (rad/s) | |
r | Radius at any position in the computational domain (m) |
rf | Radius of the free liquid surface at the outlet of the oil phase or water phase (m) |
rf,l | Radius of the free liquid surface at the outlet of the oil phase (m) |
rf,h | Radius of the free liquid surface at the outlet of the water phase (m) |
PS | Represents the pressure surface |
SS | Represents the suction surface |
λ | Dimensionless number that describes the regularity of the flow of a liquid in a separation channel |
h | Height of the separation channel (m) |
α | Angle between the generatrix of the disc and the rotation axis (°) |
ν | Kinematic viscosity of the liquid (m2/s2) |
CFD | Computational Fluid Dynamics |
PBM | Population Balance Model |
VOF | Volume of Fluid |
SIMPLE | Semi-Implicit Method for Pressure-Linked Equations |
RNG | Re-Normalization Group |
u | Rotational velocity of the liquid (m/s) |
c | Absolute velocity of the liquid (m/s) |
w | Relative velocity of the liquid (m/s) |
k | Turbulence kinetic energy |
ε | Turbulence dissipation rate |
Gk | Generation of turbulence kinetic energy due to the mean velocity gradients |
Gb | Generation of turbulence kinetic energy due to buoyancy |
YM | Contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate |
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Material | Density (kg/m3) | Dynamic Viscosity (Pa·s) |
---|---|---|
Oil | 814 | 0.0031 |
Water | 998 | 0.0010 |
Scheme | Number of Grids in the Circumferential Direction | Number of Grids in the Direction of the Generatrix | Number of Grids in The NORMAL Direction | Total Number of Grids |
---|---|---|---|---|
1 | 24 | 61 | 2 | 6088 |
2 | 29 | 73 | 3 | 11,249 |
3 | 37 | 88 | 4 | 20,130 |
4 | 44 | 106 | 5 | 35,800 |
5 | 53 | 127 | 6 | 64,652 |
6 | 60 | 147 | 7 | 123,480 |
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Dong, H.; Wan, R.; Huang, C.; Liu, S.; Luo, S.; Chen, L.; Li, S.; Song, X. Numerical Study of Internal Flow Field in a Disc Stack Centrifuge Based on Mixture-PBM Model. Appl. Sci. 2024, 14, 8070. https://doi.org/10.3390/app14178070
Dong H, Wan R, Huang C, Liu S, Luo S, Chen L, Li S, Song X. Numerical Study of Internal Flow Field in a Disc Stack Centrifuge Based on Mixture-PBM Model. Applied Sciences. 2024; 14(17):8070. https://doi.org/10.3390/app14178070
Chicago/Turabian StyleDong, Hefeng, Ran Wan, Changan Huang, Shoulie Liu, Shamiao Luo, Liangbin Chen, Shaobin Li, and Xizhen Song. 2024. "Numerical Study of Internal Flow Field in a Disc Stack Centrifuge Based on Mixture-PBM Model" Applied Sciences 14, no. 17: 8070. https://doi.org/10.3390/app14178070