Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 532638, 6 pages
http://dx.doi.org/10.1155/2013/532638
Research Article

A Fractal Model for the Maximum Droplet Diameter in Gas-Liquid Mist Flow

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China

Received 17 June 2013; Revised 18 September 2013; Accepted 22 September 2013

Academic Editor: Tirivanhu Chinyoka

Copyright © 2013 Xiao-Hua Tan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. T. Vladisavljević, I. Kobayashi, and M. Nakajima, “Effect of dispersed phase viscosity on maximum droplet generation frequency in microchannel emulsification using asymmetric straight-through channels,” Microfluidics and Nanofluidics, vol. 10, no. 6, pp. 1199–1209, 2011. View at Publisher · View at Google Scholar · View at Scopus
  2. T. S. H. Leong, T. J. Wooster, S. E. Kentish, and M. Ashokkumar, “Minimising oil droplet size using ultrasonic emulsification,” Ultrasonics Sonochemistry, vol. 16, no. 6, pp. 721–727, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. N. Vankova, S. Tcholakova, N. D. Denkov, I. B. Ivanov, V. D. Vulchev, and T. Danner, “Emulsification in turbulent flow. 1. Mean and maximum drop diameters in inertial and viscous regimes,” Journal of Colloid and Interface Science, vol. 312, no. 2, pp. 363–380, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. J.-L. Liu, R. Xia, B.-W. Li, and X.-Q. Feng, “Directional motion of droplets in a conical tube or on a conical fibre,” Chinese Physics Letters, vol. 24, no. 11, pp. 3210–3213, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. X.-Y. Peng, J. Zhang, T.-J. Liang et al., “Double jet emission of hot electrons from a micro-droplet spray,” Chinese Physics Letters, vol. 21, no. 4, pp. 693–696, 2004. View at Publisher · View at Google Scholar · View at Scopus
  6. D. E. Woodmansee and T. J. Hanratty, “Mechanism for the removal of droplets from a liquid surface by a parallel air flow,” Chemical Engineering Science, vol. 24, no. 2, pp. 299–307, 1969. View at Google Scholar · View at Scopus
  7. D. F. Tatterson, J. C. Dallman, and T. J. Hanratty, “Drop sizes in annular gas-liquid flows,” AIChE Journal, vol. 23, no. 1, pp. 68–76, 1977. View at Google Scholar · View at Scopus
  8. P. Andreussi, G. Romano, and S. Zanelli, “Drop size distribution in annular mist flow,” in Proceedings of the 1st Conference on Liquid Atomisation and Spray Systems, Tokyo, Japan, 1978.
  9. T. Ueda, “Entrainment rate and size of entrained droplets in annular two-phase flow,” Bulletin of the JSME, vol. 22, no. 171, pp. 1258–1265, 1979. View at Google Scholar · View at Scopus
  10. M. Sevik and S. H. Park, “The splitting of drops and bubbles by turbulent fluid flow,” Journal of Fluids Engineering, vol. 95, no. 1, pp. 53–60, 1973. View at Google Scholar · View at Scopus
  11. B. Azzopardi, G. Freeman, and D. King, “Drop sizes and deposition in annular two-phase flow,” UKAEA Report AERE-R9634, 1980. View at Google Scholar
  12. J. C. B. Lopes and A. E. Dukler, Droplet Sizes, Dynamics and Deposition in Vertical Annular Flow, 1985.
  13. G. Kocamustafaogullari, S. Smits, J. Razi, and W. Huang, “Droplet size modelling in annular flow,” in Proceedings of the 6th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, 1993.
  14. B. J. Azzopardi, A. Piearcey, and D. M. Jepson, “Drop size measurements for annular two-phase flow in a 20 mm diameter vertical tube,” Experiments in Fluids, vol. 11, no. 2-3, pp. 191–197, 1991. View at Publisher · View at Google Scholar · View at Scopus
  15. U. Shavit and N. Chigier, “fractal dimensions of liquid jet interface under breakup,” Atomization and Sprays, vol. 5, no. 6, pp. 525–543, 1995. View at Google Scholar
  16. Z. Weixing, Z. Tiejun, W. Tao, and Y. Zunhong, “Application of fractal geometry to atomization process,” Chemical Engineering Journal, vol. 78, no. 2-3, pp. 193–197, 2000. View at Publisher · View at Google Scholar · View at Scopus
  17. W.-X. Zhou and Z.-H. Yu, “Multifractality of drop breakup in the air-blast nozzle atomization process,” Physical Review E, vol. 63, no. 1, Article ID 016302, 6 pages, 2001. View at Publisher · View at Google Scholar
  18. S. V. Apte, M. Gorokhovski, and P. Moin, “LES of atomizing spray with stochastic modeling of secondary breakup,” International Journal of Multiphase Flow, vol. 29, no. 9, pp. 1503–1522, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. M. A. Gorokhovski and V. L. Saveliev, “Analyses of Kolmogorov's model of breakup and its application into Lagrangian computation of liquid sprays under air-blast atomization,” Physics of Fluids, vol. 15, no. 1, pp. 184–192, 2003. View at Publisher · View at Google Scholar · View at Scopus
  20. H.-F. Liu, X. Gong, W.-F. Li, F.-C. Wang, and Z.-H. Yu, “Prediction of droplet size distribution in sprays of prefilming air-blast atomizers,” Chemical Engineering Science, vol. 61, no. 6, pp. 1741–1747, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. D.-J. Jiang, H.-F. Liu, W.-F. Li, J.-L. Xu, F.-C. Wang, and X. Gong, “Modeling atomization of a round water jet by a high-speed annular air jet based on the self-similarity of droplet breakup,” Chemical Engineering Research and Design, vol. 90, no. 2, pp. 185–192, 2012. View at Publisher · View at Google Scholar · View at Scopus
  22. M.-J. Yun, B.-M. Yu, P. Xu, and J.-C. Cai, “Fractal analysis of power-law fluid in a single capillary,” Chinese Physics Letters, vol. 25, no. 2, pp. 616–619, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. Y. Mei-Juan and Z. Wei, “Fractal analysis of Robertson-Stiff fluid flow in porous media,” Chinese Physics Letters, vol. 29, no. 6, Article ID 064706, 2012. View at Google Scholar
  24. M. Yun, B. Yu, and J. Cai, “Analysis of seepage characters in fractal porous media,” International Journal of Heat and Mass Transfer, vol. 52, no. 13-14, pp. 3272–3278, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  25. Y. Mei-Juan, Z. Wei, L. Yun-Bao, and L. Yu, “Fractal analysis of Herschel-Bulkley fluid flow in a capillary,” Acta Physica Sinica, vol. 61, no. 16, Article ID 164701, 2012. View at Google Scholar
  26. M. Yun, B. Yu, and J. Cai, “A fractal model for the starting pressure gradient for Bingham fluids in porous media,” International Journal of Heat and Mass Transfer, vol. 51, no. 5-6, pp. 1402–1408, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  27. M.-J. Yuan, B.-M. Yu, W. Zheng, and J. Yuan, “Fractal analysis of Casson fluid flow in porous media,” Acta Physica Sinica, vol. 60, no. 2, Article ID 024703, 2011. View at Google Scholar · View at Scopus
  28. B. J. Azzopardi and J. C. F. Teixeira, “Detailed measurements of vertical annular two-phase flow—part I: drop velocities and sizes,” Journal of Fluids Engineering, vol. 116, no. 4, pp. 792–795, 1994. View at Google Scholar · View at Scopus
  29. L. B. Fore and A. E. Dukler, “The distribution of drop size and velocity in gas-liquid annular flow,” International Journal of Multiphase Flow, vol. 21, no. 2, pp. 137–149, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  30. J. O. Hinze, “Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes,” AIChE Journal, vol. 1, no. 3, pp. 289–295, 1955. View at Publisher · View at Google Scholar
  31. A. W. Adamson, Physical Chemistry of Surfaces, John Wiley & Sons, New York, NY, USA, 5th edition, 1990.
  32. F. M. White, Viscous Fluid Flow, McGraw-Hill, New York, NY, USA, 2nd edition, 1991.
  33. H.-Q. Zhang, W. Qian, C. Sarica, and J. P. Brill, “A unified mechanistic model for slug liquid holdup and transition between slug and dispersed bubble flows,” International Journal of Multiphase Flow, vol. 29, no. 1, pp. 97–107, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  34. Y. Taitel, D. Bornea, and A. E. Dukler, “Modelling flow pattern transitions for steady upward gas-liquid flow in vertical tubes,” AIChE Journal, vol. 26, no. 3, pp. 345–354, 1980. View at Google Scholar · View at Scopus
  35. X. T. Chen, X. D. Cai, and J. P. Brill, “A general model for transition to dispersed bubble flow,” Chemical Engineering Science, vol. 52, no. 23, pp. 4373–4380, 1997. View at Google Scholar · View at Scopus
  36. X.-H. Tan, X.-P. Li, and J.-Y. Liu, “Model of continuous liquid removal from gas wells by droplet diameter estimation,” Journal of Natural Gas Science and Engineering, vol. 15, pp. 8–13, 2013. View at Publisher · View at Google Scholar