Numerical investigation on the influencing interphase forces on bubble size distribution around NACA0015 hydrofoil

Abstract

Two-phase bubbly flows are prevalent in many industries and in nature. The aeration process that happens in the auto-venting turbine (AVT) is involved with two-phase bubbly flow downstream the turbine. The quality of the water in the turbine downstream is directly impacted by the bubble size distribution in the wake of turbine hydrofoils. In order to be able to accurately capture the physics associated with this process numerically, the interphase forces need to be considered carefully. Therefore, in this paper, the influence of interphase forces on the bubble size distribution around an NACA0015 hydrofoil is investigated. The numerical simulations require the consideration of the dynamic behaviors of two-phase flow and bubbles undergoing coalescence and breakup. For this purpose, the ensemble-averaged mass and momentum transport equations for continuous and dispersed phases are modeled within the two-fluid modelling framework. These equations are coupled with population balance equations (PBEs) to aptly account for the coalescence and breakup of the bubbles. The influence of the interphase forces: drag, lift, wall lubrication, virtual mass, turbulent dispersion forces, and turbulence transfer models, on the resulting bubble size distribution, is investigated and compared to existing experimental data.

This is a preview of subscription content, access via your institution.

References

  1. Anglart, H., Nylund, O. 1996. CFD application to prediction of void distribution in two-phase bubbly flows in rod bundles. Nucl Eng Des, 163: 81–98.

    Article  Google Scholar 

  2. Antal, S., Lahey, R. T. Jr., Flaherty, J. 1991. Analysis of phase distribution and turbulence in dispersed particle/liquid flows. Chem Eng Commun, 174: 85–113.

    Google Scholar 

  3. Bohac, C. E., Shane, R. M., Harshbarger, E. D., Goranflo, H. M. 1986. Recent progress on improving reservoir releases. Lake Reserv Manage, 2: 187–190.

    Article  Google Scholar 

  4. Bolotnov, I. A., Jansen, K. E., Drew, D. A., Oberai, A. A., Lahey, R. T. Jr., Podowski, M. Z. 2011. Detached direct numerical simulations of turbulent two-phase bubbly channel flow. Int J Multiphase Flow, 37: 647–659.

    Article  Google Scholar 

  5. Bunea, F., Ciocan, G. D., Oprina, G., Băran, G., Băbutanu, C. A. 2010. Hydropower impact on water quality. Environ Eng Manag J, 9: 1459–1464.

    Article  Google Scholar 

  6. Burns, A. D., Frank, T., Hamill, I., Shi, J.-M. 2004. The Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows. In: Proceedings of the 5th International Conference on Multiphase Flow, Paper No. 392.

  7. Chesters, A. K., Hofman, G. 1982. Bubble coalescence in pure liquids. In: Mechanics and Physics of Bubbles in Liquids. Van Wijngaarden, L. Ed. Springer Dordrecht, 353–361.

    Google Scholar 

  8. Cheung, S. C. P., Yeoh, G. H., Tu, J. Y. 2007a. On the modelling of population balance in isothermal vertical bubbly flows: Average bubble number density approach. Chem Eng Process, 46: 742–756.

    Article  Google Scholar 

  9. Cheung, S. C. P., Yeoh, G. H., Tu, J. Y. 2007b. On the numerical study of isothermal vertical bubbly flow using two population balance approaches. Chem Eng Sci, 62: 4659–4674.

    Article  Google Scholar 

  10. Cheung, S. C. P., Yeoh, G. H., Tu, J. Y. 2008. Population balance modeling of bubbly flows considering the hydrodynamics and thermomechanical processes. AIChE J, 54: 1689–1710.

    Article  Google Scholar 

  11. Ekambara, K., Sanders, R. S., Nandakumar, K., Masliyah, J. H. 2008. CFD simulation of bubbly two-phase flow in horizontal pipes. Chem Eng J, 144: 277–288.

    Article  Google Scholar 

  12. Ellis, C., Karn, A., Hong, J., Lee, S. J., Kawakami, E., Scott, D., Gulliver, J., Arndt, R. E. A. 2014. Measurements in the wake of a ventilated hydrofoil: A step towards improved turbine aeration techniques. IOP C Ser Earth Env, 22: 062009.

    Article  Google Scholar 

  13. Frank, T., Shi, J., Burns, A. D. 2004. Validation of Eulerian multiphase flow models for nuclear safety application. In: Proceedings of the 3rd International Symposium on Two-Phase Modelling and Experimentation.

  14. Hayes, D. F., Labadie, J. W., Sanders, T. G., Brown, J. K. 1998. Enhancing water quality in hydropower system operations. Water Resour Res, 34: 471–483.

    Article  Google Scholar 

  15. Ishii, M., Zuber, N. 1979. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J, 25: 843–855.

    Article  Google Scholar 

  16. Karn, A., Ellis, C. R., Hong, J. R., Arndt, R. E. A. 2015a. Investigations into the turbulent bubbly wake of a ventilated hydrofoil: Moving toward improved turbine aeration techniques. Exp Therm Fluid Sci, 64: 186–195.

    Article  Google Scholar 

  17. Karn, A., Ellis, C. R., Milliren, C., Hong, J. R., Scott, D., Arndt, R. E., Gulliver, J. S. 2015b. Bubble size characteristics in the wake of ventilated hydrofoils with two aeration configurations. International Journal of Fluid Machinery and Systems, 8: 73–84.

    Article  Google Scholar 

  18. Karn, A., Monson, G. M., Ellis, C. R., Hong, J. R., Arndt, R. E. A., Gulliver, J. S. 2015c. Mass transfer studies across ventilated hydrofoils: A step towards hydroturbine aeration. Int J Heat Mass Transfer, 87: 512–520.

    Article  Google Scholar 

  19. Karn, A., Shao, S. Y., Arndt, R. E. A., Hong, J. R. 2016. Bubble coalescence and breakup in turbulent bubbly wake of a ventilated hydrofoil. Exp Therm Fluid Sci, 70: 397–407.

    Article  Google Scholar 

  20. Kurul, N., Podowski, M. Z. 1990. Multidimensional effects in forced convection subcooled boiling. In: Proceedings of the 9th Heat Transfer Conference, 19–24.

  21. Lahey, R. T. Jr., Drew, D. A. 2001. The analysis of two-phase flow and heat transfer using a multidimensional, four field, two-fluid model. Nucl Eng Des, 204: 29–44.

    Article  Google Scholar 

  22. Liao, Y. X., Lucas, D. 2010. A literature review on mechanisms and models for the coalescence process of fluid particles. Chem Eng Sci, 65: 2851–2864.

    Article  Google Scholar 

  23. Luo, H. A., Svendsen, H. F. 1996. Theoretical model for drop and bubble breakup in turbulent dispersions. AIChE J, 42: 1225–1233.

    Article  Google Scholar 

  24. March, P. A., Brice, T. A., Mobley, M. H. 1992. Turbines for solving the DO dilemma. Hydro Review, 11: 30–36.

    Google Scholar 

  25. Olmos, E., Gentric, C., Vial, C., Wild, G., Midoux, N. 2001. Numerical simulation of multiphase flow in bubble column reactors. Influence of bubble coalescence and breakup. Chem Eng Sci, 56: 6359–6365.

    Article  Google Scholar 

  26. Pohorecki, R., Moniuk, W., Bielski, P., Zdrójkowski, A. 2001. Modelling of the coalescence/redispersion processes in bubble columns. Chem Eng Sci, 56: 6157–6164.

    Article  Google Scholar 

  27. Pourtousi, M., Sahu, J. N., Ganesan, P. 2014. Effect of interfacial forces and turbulence models on predicting flow pattern inside the bubble column. Chem Eng Process, 75: 38–47.

    Article  Google Scholar 

  28. Prince, M. J., Blanch, H. W. 1990. Bubble coalescence and breakup in air-sparged bubble columns. AIChE J, 36: 1485–1499.

    Article  Google Scholar 

  29. Rotta, J. C. 1972. Turbulente Strömungen. Teubner, Stuttgart.

    Google Scholar 

  30. Rzehak, R., Krepper, E., Lifante, C. 2012. Comparative study of wall-force models for the simulation of bubbly flows. Nucl Eng Des, 253: 41–49.

    Article  Google Scholar 

  31. Tabib, M. V., Roy, S. A., Joshi, J. B. 2008. CFD simulation of bubble column: An analysis of interphase forces and turbulence models. Chem Eng J, 139: 589–614.

    Article  Google Scholar 

  32. Wang, S. K., Lee, S. J., Jones, O. C. Jr., Lahey, R. T. Jr. 1987. 3-D turbulence structure and phase distribution measurements in bubbly two-phase flows. Int J Multiphase Flow, 13: 327–343.

    Article  Google Scholar 

  33. Yamoah, S., Martínez-Cuenca, R., Monrós, G., Chiva, S., MacIán-Juan, R. 2015. Numerical investigation of models for drag, lift, wall lubrication and turbulent dispersion forces for the simulation of gas-liquid two-phase flow. Chem Eng Res Des, 98: 17–35.

    Article  Google Scholar 

  34. Yeoh, G. H., Cheung, S. C. P., Tu, J. Y. 2012. On the prediction of the phase distribution of bubbly flow in a horizontal pipe. Chem Eng Res Des, 90: 40–51.

    Article  Google Scholar 

  35. Yeoh, G. H., Tu, J. Y. 2004. Population balance modelling for bubbly flows with heat and mass transfer. Chem Eng Sci, 59: 3125–3139.

    Article  Google Scholar 

  36. Yeoh, G. H., Tu, J. Y. 2005. Thermal-hydrodynamic modeling of bubbly flows with heat and mass transfer. AlChE J, 51: 8–27.

    Article  Google Scholar 

  37. Yu, Z. Y., Zhu, B. S., Cao, S. L. 2015. Interphase force analysis for air-water bubbly flow in a multiphase rotodynamic pump. Eng Comput, 32: 2166–2180.

    Article  Google Scholar 

  38. Zhang, D., Deen, N. G., Kuipers, J. A. M. 2006. Numerical simulation of the dynamic flow behavior in a bubble column: A study of closures for turbulence and interface forces. Chem Eng Sci, 61: 7593–7608.

    Article  Google Scholar 

  39. Zhu, B. H., Liu, Q. C., Kong, M., Yang, J., Li, D. H., Chattopadhyay, K. 2017. Effect of interphase forces on gas-liquid multiphase flow in RH degasser. Metall Mater Trans B, 48: 2620–2630.

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful for the support provided by Australia-China Joint Research Centre on Maritime Engineering, National Natural Science Foundation of China (No. 51436002), and the CSC Scholarship (No. 201506575024).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sara Vahaji.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Han, J., Vahaji, S. & Cheung, S.C.P. Numerical investigation on the influencing interphase forces on bubble size distribution around NACA0015 hydrofoil. Exp. Comput. Multiph. Flow 1, 145–157 (2019). https://doi.org/10.1007/s42757-019-0020-3

Download citation

Keywords

  • gas–liquid flow
  • bubble size distribution
  • hydrofoil
  • cavitation