Numerical Simulation of a Single Air Bubble Rising in Water with Various Models of Surface Tension Force
Different numerical methods are employed and developed for simulating interfacial flows. A large range of applications belong to this group, e.g. two-phase flows of air bubbles in water or water drops in air. In such problems surface tension effects often play a dominant role. In this paper, various models of surface tension force for interfacial flows, the CSF, CSS, PCIL and SGIP models have been applied to simulate the motion of small air bubbles in water and the results were compared and reviewed. It has been pointed out that by using SGIP or PCIL models, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.
[1] Youngs, D.L. "Time-dependent multi-material flow with large fluid
distribution", in Numerical methods for fluid dynamics, Morton and
Norman,Editor,187-221,1996
[2] D. Jamet, D. Torres, J.U. Brackbill, On the theory and computation of
surface tension: the elimination of parasitic currents through energy
conservation in the second-gradient method, J. Comp. Phys. 182 (2002)
262-276.
[3] J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for
modeling surface tension, J. Comp. Phys. 100 (1992) 335-354.
[4] Landau, L. D. and Lifshitz, E. M., "Fluid Mechanics", Pergoman Press,
New York, 1959
[5] Kothe, D.B., W.J. Rider, S.J. Mosso, and J.S. Brock, "Volume tracking
of interfaces having surface tension in two and three dimensions" AIAA
96-0859, 1996.
[6] Aleinov, I., and Puckett, E.G., "Computing surface tension with highorder
kernels", in Dwyer, H.A., ed., Proceedings of the Sixth
International Symposium on Computational Fluid dynamics, pp. 13-18,
Lake Tahoe, NV, 1995.
[7] B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, G. Zanetti,
Modeling merging and fragmentation in multiphase .ows with SURFER,
J. Comp. Phys. 113 (1994) 134-147.
[8] Meier, M., Yadigaroglu, H. and Smith, B.L., "A novel technique for
including surface tension in PLIC-VOF methods", Eur. J. B/fluids, 21,
61-73, 2002.
[9] Shirani, E., Ashgriz, N. and Mostaghimi, J.," Interface pressure
calculation based on conservative of momentum for front tracking
methods", J. Comp. Phys., 203, 153-175, 2005.
[10] Seifollahi, M., Shirani, E. and Ashgriz, N., "An Improved Method for
Calculation of Interface Pressure Force in PLIC-VOF Methods",
European Journal of Mechanics- B/Fluids, 27, 1-23, 2008.
[11] Ahmadi nadooshan, A. and Shirani, E., "Interface Pressure Model for
Surface Tension Force for VOF-Based Methods in Interfacial Flows",
Submitted for Publication, Engineering Applications of Computational
Fluid Mechanics journal, January 2008.
[12] Chen L, Garimella SV, Reizes JA, Leonardi E., The development of a
bubble rising in a viscous liquid.", J Fluid Mech. 1999, 387:61-96.
[13] van Wachem BGM, Schouten JC., "Experimental validation of 3-D
Lagrangian VOF model: bubble shape and rise velocity.", AIChE J,
2002, 48(12):2744-2753.
[14] Tomiyama A, Zun I, Sou A, Sakaguchi T., "Numerical analysis of
bubble motion with the VOF method." , Nuclear Eng Design
,1993;141:69-82.
[15] Meier M., "Numerical and experimental study of large steam-air bubbles
injected in a water pool," Dissertation no. 13091, Swiss Federal Institute
of Technology, Zurich, Switzerland, 1999.
[16] Clift R, Grace JR, "Weber ME. Bubbles, Drops and Particles," Academic
Press, London,1st edition, 1978.
[17] Martin W. and Chandler GM.," The local measurement of the size and
velocity of bubbles rising in liquids.", in Mechanics and Physics of
Bubbles in Liquids, L. van Wijngaarden, Ed., Nijhoff Pub., 1982.
[1] Youngs, D.L. "Time-dependent multi-material flow with large fluid
distribution", in Numerical methods for fluid dynamics, Morton and
Norman,Editor,187-221,1996
[2] D. Jamet, D. Torres, J.U. Brackbill, On the theory and computation of
surface tension: the elimination of parasitic currents through energy
conservation in the second-gradient method, J. Comp. Phys. 182 (2002)
262-276.
[3] J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for
modeling surface tension, J. Comp. Phys. 100 (1992) 335-354.
[4] Landau, L. D. and Lifshitz, E. M., "Fluid Mechanics", Pergoman Press,
New York, 1959
[5] Kothe, D.B., W.J. Rider, S.J. Mosso, and J.S. Brock, "Volume tracking
of interfaces having surface tension in two and three dimensions" AIAA
96-0859, 1996.
[6] Aleinov, I., and Puckett, E.G., "Computing surface tension with highorder
kernels", in Dwyer, H.A., ed., Proceedings of the Sixth
International Symposium on Computational Fluid dynamics, pp. 13-18,
Lake Tahoe, NV, 1995.
[7] B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, G. Zanetti,
Modeling merging and fragmentation in multiphase .ows with SURFER,
J. Comp. Phys. 113 (1994) 134-147.
[8] Meier, M., Yadigaroglu, H. and Smith, B.L., "A novel technique for
including surface tension in PLIC-VOF methods", Eur. J. B/fluids, 21,
61-73, 2002.
[9] Shirani, E., Ashgriz, N. and Mostaghimi, J.," Interface pressure
calculation based on conservative of momentum for front tracking
methods", J. Comp. Phys., 203, 153-175, 2005.
[10] Seifollahi, M., Shirani, E. and Ashgriz, N., "An Improved Method for
Calculation of Interface Pressure Force in PLIC-VOF Methods",
European Journal of Mechanics- B/Fluids, 27, 1-23, 2008.
[11] Ahmadi nadooshan, A. and Shirani, E., "Interface Pressure Model for
Surface Tension Force for VOF-Based Methods in Interfacial Flows",
Submitted for Publication, Engineering Applications of Computational
Fluid Mechanics journal, January 2008.
[12] Chen L, Garimella SV, Reizes JA, Leonardi E., The development of a
bubble rising in a viscous liquid.", J Fluid Mech. 1999, 387:61-96.
[13] van Wachem BGM, Schouten JC., "Experimental validation of 3-D
Lagrangian VOF model: bubble shape and rise velocity.", AIChE J,
2002, 48(12):2744-2753.
[14] Tomiyama A, Zun I, Sou A, Sakaguchi T., "Numerical analysis of
bubble motion with the VOF method." , Nuclear Eng Design
,1993;141:69-82.
[15] Meier M., "Numerical and experimental study of large steam-air bubbles
injected in a water pool," Dissertation no. 13091, Swiss Federal Institute
of Technology, Zurich, Switzerland, 1999.
[16] Clift R, Grace JR, "Weber ME. Bubbles, Drops and Particles," Academic
Press, London,1st edition, 1978.
[17] Martin W. and Chandler GM.," The local measurement of the size and
velocity of bubbles rising in liquids.", in Mechanics and Physics of
Bubbles in Liquids, L. van Wijngaarden, Ed., Nijhoff Pub., 1982.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:54808", author = "Afshin Ahmadi Nadooshan and Ebrahim Shirani", title = "Numerical Simulation of a Single Air Bubble Rising in Water with Various Models of Surface Tension Force", abstract = "Different numerical methods are employed and developed for simulating interfacial flows. A large range of applications belong to this group, e.g. two-phase flows of air bubbles in water or water drops in air. In such problems surface tension effects often play a dominant role. In this paper, various models of surface tension force for interfacial flows, the CSF, CSS, PCIL and SGIP models have been applied to simulate the motion of small air bubbles in water and the results were compared and reviewed. It has been pointed out that by using SGIP or PCIL models, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.
", keywords = "Volume-of-Fluid, Bubble Rising, SGIP model, CSS model, CSF model, PCIL model, interface, surface tension force.", volume = "2", number = "3", pages = "295-5", }
