Novel Efficiency Calculation Model Based on Fine Particle Tracking Behavior
Abstract
:1. Introduction
2. Materials and Methods
3. Experimental Results
4. Model Analysis and Correction Methods
4.1. Tracking Coefficient
4.2. Entrainment Coefficient
4.3. Cut Size d50c
4.4. Model Formulation
5. Validation of Proposed Model
5.1. Comparison and Verification with Experimental Results
5.2. Verification of Proposed Model
6. Conclusions
- (1)
- The proposed model leverages changes in centrifugal settling velocity to describe how underflow entrainment affects the separation performance of particles. Specifically, large particles experience a decrease in velocity due to the entrainment effect while small particles increase in velocity due to the tracking effect. These effects on particle velocity can be quantified using tracking and entrainment coefficients. The relationship between these coefficients and factors such as the structure of the hydrocyclone, operating conditions, and particle properties was successfully expressed through theoretical analysis and mathematical fitting.
- (2)
- Experimental results showed that, compared to the original model, the proposed model’s efficiency calculations aligned more closely with experimental values and could accurately compute grade efficiency curves, including their fishhook segments. The model was validated based on experimental data from previous studies, demonstrating that despite variations in hydrocyclone structures, particle types, and particle concentrations, the proposed model captured the influence of various parameters and delivered consistently accurate calculation results.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Particles | D50 | Density | Sphericity |
---|---|---|---|
Quartz | 35.76 μm | 2.7 g/cm3 | 0.74 |
Glass frit | 40.52 μm | 2.56 g/cm3 | 0.98 |
Structure Parameters | Abdollahzadeh (mm) | Jiang (mm) |
---|---|---|
D | 15 | 75 |
Din | 4.2 | 18 |
Do | 5.1 | 25 |
H1 | 5 | 120 |
H2 | 79 | 97 |
Du | 3 | 15 |
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Liu, X.; Chen, J.; Cui, H.; Ma, X.; Zhang, H.; Shan, Y. Novel Efficiency Calculation Model Based on Fine Particle Tracking Behavior. Processes 2024, 12, 1710. https://doi.org/10.3390/pr12081710
Liu X, Chen J, Cui H, Ma X, Zhang H, Shan Y. Novel Efficiency Calculation Model Based on Fine Particle Tracking Behavior. Processes. 2024; 12(8):1710. https://doi.org/10.3390/pr12081710
Chicago/Turabian StyleLiu, Xiulin, Jianyi Chen, Hao Cui, Xiao Ma, Hongbin Zhang, and Yongrui Shan. 2024. "Novel Efficiency Calculation Model Based on Fine Particle Tracking Behavior" Processes 12, no. 8: 1710. https://doi.org/10.3390/pr12081710