Volume of Fluid Computations of Gas Entrainment and Void Fraction for Plunging Liquid Jets to Aerate Wastewater
Abstract
:1. Introduction
2. Methodology
2.1. Physical Parameters
2.2. Numerical Scheme
Turbulence Equations
2.3. Simulation Plan
Geometry, Mesh, and Boundary Conditions
3. Numerical Results
3.1. Gas Entrainment and Developing Bubbly Regime
3.2. Penetration Depth
3.3. Void Fraction
4. Conclusions
Funding
Conflicts of Interest
References
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Equation | |||
---|---|---|---|
Continuity | 0 | 0 | |
Radial momentum | v | μeff | |
Axial momentum | u | μeff | |
k Equation | k | ||
ε Equation | ε |
Case No. | Jet Velocity (m/s) | Mesh Size (Millions) | Element | Type | Mesh | Provision | Jet Penetration Length/Dia |
---|---|---|---|---|---|---|---|
01 | 1.7–15.7 | 0.31 | Hex | Cooper | Fine | More fine in upper region near the jet impingement zone up till the middle of the rig | 27.3–39.7/6.83–11.2 |
02 | 1.7–15.7 | 0.35 | Hex | Cooper | Fine | More fine in upper region near the jet impingement zone up till the middle of the rig | 31.8–41.2./7.9–13.2 |
03 | 1.7–15.7 | 0.37 | Hex | Cooper | Fine | More fine in upper region near the jet impingement zone up till the middle of the rig | 34.2–45.7/10.4–17.1 |
04 | 1.7–15.7 | 0.41 | Hex | Cooper | Fine | More fine in upper region near the jet impingement zone up till the middle of the rig | 37.88–49.12/12.7–20.41 |
05 | 1.7–15.7 | 0.43 | Hex | Cooper | Fine | More fine in upper region near the jet impingement zone up till the middle of the rig | 55.79–67–56/14.77–22.18 |
06 | 1.7–15.7 | 0.48 | Hex | Cooper | Fine | More fine in upper region near the jet impingement zone up till the middle of the rig | 74.58–89.18/18.79–24.87 |
07 | 1.7–15.7 | 0.57 | Hex | Cooper | Fine | More fine in upper region near the jet impingement zone up till the middle of the rig | 84.58–99.98/19.55–24.98 |
08 | 1.7–15.7 | 0.64 | Hex | Cooper | Fine | More fine in upper region near the jet impingement zone up till the middle of the rig | 85.58–99.99/19.55–24.99 |
09 | 1.7–15.7 | 0.69 | Hex | Cooper | Fine | More fine in upper region near the jet impingement zone up till the middle of the rig | 85.58–99.99/19.55–24.99 |
10 | 1.7–15.7 | 0.75 | Hex | Cooper | Fine | More fine in upper region near the jet impingement zone up till the middle of the rig | 85.58–99.99/19.55–24.99 |
(a) | ||||||||
SIM No. | Nozzle Dia (mm)-DN | Jet Dia (mm)-DJ | Jet Length (mm)-LJ | |||||
1 | 25 | 24 | 100 | |||||
2 | 12.5 | 12.5 | 50 | |||||
3 | 6.83 | 6.83 | 27.3 | |||||
4 | 0.3, 1.3, 2.4 | 0.3, 1.3, 2.4 | ||||||
(b) | ||||||||
SIM No. | Nozzle Dia (mm)-DN | Jet Dia (mm)-DJ | Jet Length (mm)–LJ | Jet Velocity (m/s) | Profile Locations (m) | Fluid Properties and Details | Frj | Rej |
1 | 25 | 24 | 100 | 3.5 | 0.8DJ, 1.2DJ, 2DJ | Tap water, μw = 1.015 × 10−3 Pa.s | 7.2 | 82,760 |
4.1 | ρw = 1000 kg.m−3 | 8.4 | 96,950 | |||||
4.4 | σ = 0.055 N/m | 9 | 104,040 | |||||
2 | 12.5 | 12.5 | 50 | 2.42 | 7.1 | 29,805 | ||
3.04 | 8.8 | 37,440 | ||||||
3.46 | 10 | 42,615 | ||||||
3 | 6.83 | 6.83 | 27.3 | 1.79 | 7.1 | 12,050 | ||
2.16 | 8.5 | 14,540 | ||||||
2.49 | 9.7 | 16,760 | ||||||
4 | 0.3, 1.3, 2.4 | 0.3, 1.3, 2.4 | 9.83–12.0, 1.86–15.7, 2.92–6.79 | Penetration Depth | 181.2–221.2, 16.47–139, 19–44.3 | 2949–3600, 2418–20410, 7008–16296 |
Dj(m) | uj (m/s) | Lj (m) | Fr | Qair/Qw | |
---|---|---|---|---|---|
Bin [13] Correlation | |||||
0.024 | 3.5 | 0.1 | 7.2 | 0.12 | |
0.005 | 2.54 | 0.01 | 11.47 | 0.104 | |
0.00683 | 2.49 | 0.027 | 9.62 | 0.131 | |
Chanson’s Values [39] | |||||
0.024 | 3.5 | 0.1 | 7.2 | 0.11 | |
0.00683 | 2.49 | 0.027 | 9.62 | 0.193 | |
Euler-Euler [25] | |||||
0.005 | 2.54 | 0.01 | 11.47 | 0.5 | |
VOF Simulations | |||||
0.024 | 3.5 | 0.1 | 7.2 | 0.19 | |
0.005 | 2.54 | 0.01 | 11.47 | 0.24 | |
0.00683 | 2.49 | 0.027 | 9.62 | 0.26 |
Experimental | Bin’s Correlation | Euler-Euler | VOF Simulation |
---|---|---|---|
0.23 | 0.131 | 0.10 | 0.3 |
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Bahadar, A. Volume of Fluid Computations of Gas Entrainment and Void Fraction for Plunging Liquid Jets to Aerate Wastewater. ChemEngineering 2020, 4, 56. https://0-doi-org.brum.beds.ac.uk/10.3390/chemengineering4040056
Bahadar A. Volume of Fluid Computations of Gas Entrainment and Void Fraction for Plunging Liquid Jets to Aerate Wastewater. ChemEngineering. 2020; 4(4):56. https://0-doi-org.brum.beds.ac.uk/10.3390/chemengineering4040056
Chicago/Turabian StyleBahadar, Ali. 2020. "Volume of Fluid Computations of Gas Entrainment and Void Fraction for Plunging Liquid Jets to Aerate Wastewater" ChemEngineering 4, no. 4: 56. https://0-doi-org.brum.beds.ac.uk/10.3390/chemengineering4040056