Abstract
Bubbles with different sizes have different dynamic and kinetic behavior in a two-phase bubbly flow. A common two-fluid model based on the uniform bubble size assumption is not suitable for a bubbly flow with non-uniform bubble sizes. To deal with non-uniform bubbly flows, a multi-fluid model is established, with which bubbles are divided into several groups according to their sizes and a set of basic equations is derived for each group of bubbles with almost the same size. Through analyzing the bubble-bubble and bubble-pipe wall interactions, two new constitutive laws for the wall-force and pressure difference between the liquid phase and interface are developed to close the averaged basic equations. The respective phase distributions for each group of bubbles measured by a specially designed three-dimensional photographic method are used to check the model. Comparison between model-predicted values and experimental data shows that the model can describe laminar bubbly flow with non-uniform bubble sizes.
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References
Antal, S. P., Lahey, R. T. Jr. Flaherty, J. E., Analysis of phase distribution in fully developed laminar bubbly two-phase flow, Int. J. Multiphase Flow, 1991, 17: 635.
Nakoryakov, V. E., Kashinsky, O. N., Randin, V. V. et al., Gas-liquid bubbly flow in vertical pipes, Journal of Fluid Engineering, 1996, 118: 377.
Kashinsky, O. N., Timkin, L. S., Cartellier, A., Experimental study of “laminar” bubbly flows in a vertical pipe, Experiments in Fluids, 1993, 14: 308.
Song, Q., Theoretical and experimental research on bubbly flow in a vertical pipe, Ph. D. Thesis, Tsinghua University, 1999 Beijing, China.
Kataoka, M., Ishii, M., Serizawa, A., Local formulation of interfacial area concentration, Int. J. Multiphase Flow, 1986, 12: 505.
Drew, D. A., Mathematical modeling of two-phase flow, Annual Review of Fluid Mechanics, 1983, 15: 261.
Nigmatulin, R. I., Spatial averaging in the mechanics of heterogeneous and dispersed systems, Int. J. Multiphase Flow, 1979 5: 353.
Sato, Y., Sadatomi, M., Sekoguchi, K., Momentum and heat transfer in two-phase bubbly flow-I, Int. J. Multiphase Flow, 1981, 7: 167.
Ishii, M., Mishima, K., Two-fluid modeling and hydrodynamic constitutive relations, Nucl. Engng. Des., 1984, 82: 107.
Drew, D. A., Lahey, R. T. Jr., The virtual mass and lift force on a sphere in rotating and straining invicid flow, Int. J. Multiphase Flow, 1987, 13: 113.
Cherkutat, P., McLaughlin, J. B., Wall-induced lift on a sphere, Int. J. Multiphase Flow, 1990, 16: 899.
Tomiyama, A., Zun, I., Higaki, H. et al., A three-dimensional particle tracking method for bubbly flow simulation, Nucl. Engng. Des., 1997, 175: 77.
Van Wijingaarden, L., The mean rise velocity of pairwise-interacting bubbles in liquid, J. Fluid Mech., 1993, 251: 55.
Stuhmiller, J. H., The influence of interfacial pressure on the character of two-phase flow model equations, Int. J. Multiphase Flow, 1977, 3: 551.
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Luo, R., Song, Q., Yang, X. et al. Developed ‘laminar’ bubbly flow with non-uniform bubble sizes. Sci. China Ser. E-Technol. Sci. 44, 47–54 (2001). https://doi.org/10.1007/BF02916725
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DOI: https://doi.org/10.1007/BF02916725