Experimental and theoretical bubble growth comparison at the initial stages of horizontal injection
DOI:
https://doi.org/10.15587/1729-4061.2020.204102Keywords:
injection, deformation, bubble shape, frontal areaAbstract
Two-phase liquid-gas injection constitutes an important industrial process that is used in most separators. At the early step of injection, a cylindrical bubble is formed. As time elapses, the bubble shape becomes more complex and very difficult to analyze. In this study, a simple analytical model is developed to explain bubble shape changes. The analytical model was developed based on water flow inertia that continually pushes the bubble while the drag force resists it so that the frontal area of the bubble increases. The bubble size and frontal area were estimated using the assumption of the equilibrium between inertia force and drag force neglecting viscous force. From the estimation, the role of the vortex ring from the difference between theoretical and experimental results can be identified. The analytical model was verified through experimental data collected on the shape deformation induced by bubble motion at the beginning of injection. The experimental data used as verification were measured from the bubble nose image with ten times repetition having the uncertainty of ±6 %. The experimental method is conducted by injecting a bubble along the horizontal direction into a water pool. The inertial force of the water flow in front of the bubble nose generates the bubble. The bubble suddenly changes its shape, moves in the form of a bubble jet, and undergoes gradual shape changes. The frontal area of the bubble increases and reaches a maximum at the terminal velocity point. The bubble shape deformation is affected by the inertial force of the water flow that pushes the bubble forward. Accordingly, the bubble changes its shape from cylindrical to spherical, and then to an ellipsoidal disk. When the bubble attains terminal velocity, the inertial force becomes equal to the drag force. The edge of the ellipsoidal disk bubble exhibits increased surface tension. The difference between experimental data and the analytical model is due to the complex fluid and dynamic flow surrounding the bubble. The mathematical framework proposed in this work is envisaged to be an important tool for the prediction of the bubble frontal areaReferences
- Chu, P., Waters, K. E., Finch, J. A. (2016). Break-up in formation of small bubbles: Break-up in a confined volume. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 503, 88–93. doi: https://doi.org/10.1016/j.colsurfa.2016.05.037
- Movafaghian, S., Jaua-Marturet, J. A., Mohan, R. S., Shoham, O., Kouba, G. E. (2000). The effects of geometry, fluid properties and pressure on the hydrodynamics of gas–liquid cylindrical cyclone separators. International Journal of Multiphase Flow, 26 (6), 999–1018. doi: https://doi.org/10.1016/s0301-9322(99)00076-2
- Rosa, E. S., França, F. A., Ribeiro, G. S. (2001). The cyclone gas–liquid separator: operation and mechanistic modeling. Journal of Petroleum Science and Engineering, 32 (2-4), 87–101. doi: https://doi.org/10.1016/s0920-4105(01)00152-8
- Bozzano, G., Dente, M. (2001). Shape and terminal velocity of single bubble motion: a novel approach. Computers & Chemical Engineering, 25 (4-6), 571–576. doi: https://doi.org/10.1016/s0098-1354(01)00636-6
- Emami, A., Briens, C. (2008). Study of downward gas jets into a liquid. AIChE Journal, 54 (9), 2269–2280. doi: https://doi.org/10.1002/aic.11524
- Tomiyama, A., Celata, G. P., Hosokawa, S., Yoshida, S. (2002). Terminal velocity of single bubbles in surface tension force dominant regime. International Journal of Multiphase Flow, 28 (9), 1497–1519. doi: https://doi.org/10.1016/s0301-9322(02)00032-0
- Bari, S. D., Robinson, A. J. (2013). Experimental study of gas injected bubble growth from submerged orifices. Experimental Thermal and Fluid Science, 44, 124–137. doi: https://doi.org/10.1016/j.expthermflusci.2012.06.005
- Rassame, S., Hibiki, T., Ishii, M. (2016). Void penetration length from air injection through a downward large diameter submerged pipe in water pool. Annals of Nuclear Energy, 94, 832–840. doi: https://doi.org/10.1016/j.anucene.2016.04.046
- Bai, H., Thomas, B. G. (2001). Bubble formation during horizontal gas injection into downward-flowing liquid. Metallurgical and Materials Transactions B, 32 (6), 1143–1159. doi: https://doi.org/10.1007/s11663-001-0102-y
- Mandal, A. (2010). Characterization of gas-liquid parameters in a down-flow jet loop bubble column. Brazilian Journal of Chemical Engineering, 27 (2), 253–264. doi: https://doi.org/10.1590/s0104-66322010000200004
- Liu, Z., Reitz, R. D. (1997). An analysis of the distortion and breakup mechanisms of high speed liquid drops. International Journal of Multiphase Flow, 23 (4), 631–650. doi: https://doi.org/10.1016/s0301-9322(96)00086-9
- Liu, L., Yan, H., Zhao, G. (2015). Experimental studies on the shape and motion of air bubbles in viscous liquids. Experimental Thermal and Fluid Science, 62, 109–121. doi: https://doi.org/10.1016/j.expthermflusci.2014.11.018
- Hinze, J. O. (1955). Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE Journal, 1 (3), 289–295. doi: https://doi.org/10.1002/aic.690010303
- Han, L., Luo, H., Liu, Y. (2011). A theoretical model for droplet breakup in turbulent dispersions. Chemical Engineering Science, 66 (4), 766–776. doi: https://doi.org/10.1016/j.ces.2010.11.041
- Cihonski, A. J., Finn, J. R., Apte, S. V. (2013). Volume displacement effects during bubble entrainment in a travelling vortex ring. Journal of Fluid Mechanics, 721, 225–267. doi: https://doi.org/10.1017/jfm.2013.32
- Gao, L., Yu, S. C. M. (2010). A model for the pinch-off process of the leading vortex ring in a starting jet. Journal of Fluid Mechanics, 656, 205–222. doi: https://doi.org/10.1017/s0022112010001138
- Jiang, X. F., Zhu, C., Li, H. Z. (2017). Bubble pinch-off in Newtonian and non-Newtonian fluids. Chemical Engineering Science, 170, 98–104. doi: https://doi.org/10.1016/j.ces.2016.12.057
- Tomiyama, A., Kataoka, I., Zun, I., Sakaguchi, T. (1998). Drag Coefficients of Single Bubbles under Normal and Micro Gravity Conditions. JSME International Journal Series B, 41 (2), 472–479. doi: https://doi.org/10.1299/jsmeb.41.472
- Vincent, F., Le Goff, A., Lagubeau, G., Quéré, D. (2007). Bouncing Bubbles. The Journal of Adhesion, 83 (10), 897–906. doi: https://doi.org/10.1080/00218460701699765
- Walter, J. F., Blanch, H. W. (1986). Bubble break-up in gas – liquid bioreactors: Break-up in turbulent flows. The Chemical Engineering Journal, 32 (1), B7–B17. doi: https://doi.org/10.1016/0300-9467(86)85011-0
- Moore, D. W. (1965). The velocity of rise of distorted gas bubbles in a liquid of small viscosity. Journal of Fluid Mechanics, 23 (4), 749–766. doi: https://doi.org/10.1017/s0022112065001660
- Aoyama, S., Hayashi, K., Hosokawa, S., Tomiyama, A. (2016). Shapes of ellipsoidal bubbles in infinite stagnant liquids. International Journal of Multiphase Flow, 79, 23–30. doi: https://doi.org/10.1016/j.ijmultiphaseflow.2015.10.003
- Hreiz, R., Lainé, R., Wu, J., Lemaitre, C., Gentric, C., Fünfschilling, D. (2014). On the effect of the nozzle design on the performances of gas–liquid cylindrical cyclone separators. International Journal of Multiphase Flow, 58, 15–26. doi: https://doi.org/10.1016/j.ijmultiphaseflow.2013.08.006
- Tomita, Y., Robinson, P. B., Tong, R. P., Blake, J. R. (2002). Growth and collapse of cavitation bubbles near a curved rigid boundary. Journal of Fluid Mechanics, 466, 259–283. doi: https://doi.org/10.1017/s0022112002001209
- Fei, Y., Pang, M. (2019). A treatment for contaminated interfaces and its application to study the hydrodynamics of a spherical bubble contaminated by surfactants. Chemical Engineering Science, 200, 87–102. doi: https://doi.org/10.1016/j.ces.2019.01.052
- Chen, Y., Groll, M. (2006). Dynamics and shape of bubbles on heating surfaces: A simulation study. International Journal of Heat and Mass Transfer, 49 (5-6), 1115–1128. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2005.07.053
- Gharib, M., Rambod, E., Shariff, K. (1998). A universal time scale for vortex ring formation. Journal of Fluid Mechanics, 360, 121–140. doi: https://doi.org/10.1017/s0022112097008410
- Canedo, E. L., Favelukis, M., Tadmor, Z., Talmon, Y. (1993). An experimental study of bubble deformation in viscous liquids in simple shear flow. AIChE Journal, 39 (4), 553–559. doi: https://doi.org/10.1002/aic.690390403
- Uchiyama, T., Sasaki, S. (2014). Experimental Investigation of the Interaction between Rising Bubbles and Swirling Water Flow. International Journal of Chemical Engineering, 2014, 1–10. doi: https://doi.org/10.1155/2014/358241
- Yuan, D., Xiao, Z., Chen, D., Zhong, Y., Yan, X., Xu, J., Huang, Y. (2016). Numerical Investigation on Bubble Growth and Sliding Process of Subcooled Flow Boiling in Narrow Rectangular Channel. Science and Technology of Nuclear Installations, 2016, 1–12. doi: https://doi.org/10.1155/2016/7253907
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