Modeling Liquid Droplet Sizes in Gas–Liquid Annular Flow
Abstract
:1. Introduction
2. Review of Previous Experimental Studies
2.1. Droplet Entrainment Mechanism
2.2. Effect of Fluid Properties on Droplet Size
2.2.1. Effect of Fluid Viscosity on Droplet Size
2.2.2. Effect of Fluid Density on Droplet Size
2.2.3. Effect of Surface Tension on Droplet Size
2.3. Effect of Flowing Conditions on Droplet Size
2.3.1. Effect of Superficial Gas Velocity on Droplet Size
2.3.2. Effect of Superficial Liquid Velocity on Droplet Size
2.4. Effects of Pipe Internal Diameter and Inclination on Droplet Size
3. Droplet-Size Modeling
3.1. Modeling the Maximum Droplet Size
3.2. Modeling the Sauter Mean Diameter
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
Authors | dmax/d32 Based on Experimental Data | dmax/d32 Based on New Model Predictions |
---|---|---|
Lopes and Dukler (1985) [40] | 2.30 | 2.37 |
Hurlburt and Hanratty (2002) [61] | 3.10 | 4.66 |
Al-Sarkhi and Hanratty (2002) [58]; data analysis | 4.37 | 5.43 |
Fore et al. (2002) [48]; data analysis | 2.65 | 3.41 |
Gawas et al. (2015) [55]; data analysis | 2.74 | 1.89 |
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Authors | Fluids and Flow Geometry | Operational Conditions | Measurement Technique | ||
---|---|---|---|---|---|
Lopes and Dukler (1985) [40] | Air–water; vertical upflow pipe ID = 0.051 m | 833 | 53 | 1 atm, 20 °C; | Phase Doppler Anemometry |
Fore and Dukler (1995a) [11] | Air–water; vertical upflow pipe ID = 0.051 m | 760 | 53 | 1 atm, 20 °C; | Laser Grating |
Fore and Dukler (1995a) [11] | Air–water/glycerin Vertical upflow pipe ID = 0.051 m | 870 | 303 | 1 atm, 20 °C; | Laser Grating |
Hay et al. (1996) [64] | Air–water; vertical upflow pipe ID = 0.042 m | 816 | 45 | 1 atm, 20 °C; | Direct In Situ Photography |
Al-Sarkhi and Hanratty (2002) [58] | Air–water; horizontal flow pipe ID = 0.025 m | 816 | 45 | 1 atm, 20 °C; | Laser Diffraction |
Fore et al. (2002) [48] | Nitrogen–water; vertical upflow 101.6 × 5.08 mm rectangular duct | 250 | 37 | 3.4 atm, 38 °C; | Video Images |
Fore et al. (2002) [48] | Nitrogen–water; vertical upflow 101.6 × 5.08 mm rectangular duct | 50 | 37 | 17 atm, 38 °C; | Video Images |
Hurlburt and Hanratty (2002) [61] | Air–water; horizontal flow pipe ID = 0.095 m | 816 | 45 | 1 atm, 20 °C; | Immersion Method |
Gawas et al. (2015) [55] | Air–mineral oil; horizontal flow pipe ID = 0.152 m | 360 | 78 | 1 atm, 20 °C; | Backlit High-Speed Visualization |
Authors | Fluids and Flow Geometry | Operational Conditions | Measurement Technique | ||
---|---|---|---|---|---|
Azzopardi (1985) [6] | Air–water, vertical upward ID = 0.032 m | 816 | 50 | 1 atm; 20 °C; ReSL = 500–5000 ReSG = 69,500–164,000 | Laser Diffraction |
Azzopardi (1985) [6] | Air–water, vertical upward ID = 0.125 m | 816 | 50 | 1 atm; 20 °C; ReSL = 1000–3200 ReSG = 224,000–320,600 | Laser Diffraction |
Lopes and Dukler (1985) [40] | Air–water, vertical upward ID = 0.051 m | 833 | 53 | 1 atm, 20 °C ReSL = 1600–5800 ReSG = 42,600–75,200 | Phase Doppler Anemometry |
Teixeira (1988) [10] | Air–water, vertical upward ID = 0.032 m | 555 | 64 | 1.5 atm, 15 °C ReSL = 450–3500 ReSG = 78,250–163,300 | Laser Diffraction and Phase Doppler Anemometry |
Jepson et al. (1989) [50] | Air–water, vertical upward ID = 0.010 m | 544 | 53 | 1.5 atm, 20 °C ReSL = 400–1400 ReSG = 20,900–62,800 | Laser Diffraction |
Jepson et al. (1989) [50] | Helium–water, vertical upward ID = 0.010 m | 3733 | 56 | 1.5 atm, 20 °C ReSL = 400–1400 ReSG = 6500–11,100 | Laser Diffraction |
Ribeiro (1993) [56] | Air–water, horizontal ID = 0.032 m | 591–640 | 64 | 1 atm, 20 °C ReSL = 500–3000 ReSG = 71,500–125,100 | Laser Diffraction |
Azzopardi and Teixeira (1994) [44] | Air–water, vertical upward ID = 0.032 m | 833 | 53 | 1 atm, 20 °C ReSL = 500–1400 ReSG = 39,200–89,000 | Laser Diffraction |
Fore and Dukler (1995a) [11] | Air–water, vertical upward ID = 0.051 m | 694–847 | 53 | 1 atm, 20 °C ReSL = 750–3000 ReSG = 51,800–120,700 | Laser Grating |
Fore and Dukler (1995a) [11] | Air–water/glycerin vertical upward; ID = 0.051 m | 794–956 | 303 | 1 atm, 20 °C ReSL = 140–560 ReSG = 48,800–114,000 | Laser Grating |
Hay et al. (1996) [64] | Air–water, vertical upward ID = 0.042 m | 816 | 45 | 1 atm, 20 °C ReSL = 1000–5700 ReSG = 92,600 | Direct In Situ Photography |
Simmons and Hanratty (2001) [59] | Air–water, horizontal ID = 0.095 m | 816 | 45 | 1 atm, 20 °C ReSL = 1700–13,000 ReSG = 175,000–292,000 | Laser Diffraction |
Al-Sarkhi and Hanratty (2002) [58] | Air–water, horizontal ID = 0.025 m | 816 | 45 | 1 atm, 20 °C ReSL = 1100–3500 ReSG = 46,700–77,800 | Laser Diffraction |
Fore et al. (2002) [48] | Nitrogen–water; vertical upward 101.6 × 5.08 mm rectangular duct | 250 | 37 | 3.4 atm, 38 °C ReSL = 300–2600 ReSG = 10,800–35,700 | Photographic |
Fore et al. (2002) [48] | Nitrogen–water, vertical upflow 101.6 × 5.08 mm rectangular duct | 50 | 37 | 17 atm, 38 °C ReSL = 300–1300 ReSG = 35,700–90,500 | Photographic |
Hurlburt and Hanratty (2002) [61] | Air–water, horizontal ID = 0.095 m | 816 | 45 | 1 atm, 20 °C ReSL = 1600–7400 ReSG = 117,000–210,000 | Oil Immersion |
Alamu (2010) [65] | Air–water, vertical upward ID = 0.019 m | 714 | 56 | 1.4 atm, 20 °C ReSL = 950–3700 ReSG = 19,400–63,400 | Light Scattering |
Gawas et al. (2015) [55] | Air–mineral oil, horizontal ID = 0.152 m | 360 | 78 | 1 atm, 20 °C ReSL = 800–8200 ReSG = 296,000–408,000 | Backlit High-Speed Visualization |
Wang et al. (2020) [49] | Air–water, vertical upward ID = 0.050 m | 816–955 | 50–1500 | 1 atm, 20 °C ReSL = 100–4000 ReSG = 76,500–177,600 | Particle Dynamic Analyzer |
Zhu et al. (2021) [66] | Air–water, vertical upward 70 × 2 mm narrow rectangular channel | 816 | 50 | 1 atm, 20 °C ReSL = 580–1170 ReSG = 4760–9530 | Laser Diffraction |
Models | Hinze (1955) [14] | Kataoka et al. (1983) [46] | Lopes and Dukler (1985) [40] | Kocamustafaogullari et al. (1994) [41] | Pereyra et al. (2015) [78] | New Model |
---|---|---|---|---|---|---|
AARE (%) | 417 | 154 | 185 | 71 | 84 | 14.8 |
Models | Correlations |
---|---|
Azzopardi et al. (1980) [62] | |
Kataoka et al. (1983) [46] | |
Azzopardi (1985) [6] | |
Gibbons (1985) [47] | |
Lopes and Dukler (1985) [40] | |
Azzopardi et al. (1989) [80] | |
Ambrosini et al. (1991) [81] | |
Kim et al. (1993) [82] | |
Kocamustafaogullari et al. (1994) [41] | |
Simmons and Hanratty (2001) [59] | |
Al-Sarkhi and Hanratty (2002) [58] | |
Fore et al. (2002) [48] | |
Pan and Hanratty (2002b) [51] | |
Azzopardi (2006) [83] | |
Caraghiaur and Anglart (2013) [13] | |
Wang et al. (2020) [49] | |
Zhu et al. (2021) [66] |
Models | AARE (%) | Models | AARE (%) |
---|---|---|---|
Azzopardi et al. (1980) [62] | 49 | Simmons and Hanratty (2001) [59] | 63 |
Kataoka et al. (1983) [46] | 228 | Al-Sarkhi and Hanratty (2002) [58] | 53 |
Azzopardi (1985) [6] | 49 | Fore et al. (2002) [48] | 259 |
Gibbons (1985) [47] | 55 | Pan and Hanratty (2002b) [51] | 59 |
Lopes and Dukler (1985) [40] | 214 | Azzopardi (2006) [83] | 116 |
Azzopardi et al. (1989) [80] | 44 | Caraghiaur and Anglart (2013) [13] | 67 |
Ambrosini et al. (1991) [81] | 120 | Wang et al. (2020) [49] | 62 |
Kim et al. (1993) [82] | 293 | Zhu et al. (2021) [66] | 67 |
Kocamustafaogullari et al. (1994) [41] | 107 | New Model | 29 |
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Karatayev, K.; Fan, Y. Modeling Liquid Droplet Sizes in Gas–Liquid Annular Flow. Energies 2024, 17, 3094. https://doi.org/10.3390/en17133094
Karatayev K, Fan Y. Modeling Liquid Droplet Sizes in Gas–Liquid Annular Flow. Energies. 2024; 17(13):3094. https://doi.org/10.3390/en17133094
Chicago/Turabian StyleKaratayev, Kanat, and Yilin Fan. 2024. "Modeling Liquid Droplet Sizes in Gas–Liquid Annular Flow" Energies 17, no. 13: 3094. https://doi.org/10.3390/en17133094