Experiments performed with bubbly flow in vertical pipes at different flow conditions covering the transition region: simulation by coupling Eulerian, Lagrangian and 3D random walks models
Two phase flow experiments with different superficial velocities of gas and water were performed in a vertical upward isothermal cocurrent air-water flow column with conditions ranging from bubbly flow, with very low void fraction, to transition flow with some cap and slug bubbles and void fractions around 25%. The superficial velocities of the liquid and the gas phases were varied from 0.5 to 3 m/s and from 0 to 0.6 m/s, respectively. Also to check the effect of changing the surface tension on the previous experiments small amounts of 1-butanol were added to the water. These amounts range from 9 to 75 ppm and change the surface tension. This study is interesting because in real cases the surface tension of the water diminishes with temperature, and with this kind of experiments we can study indirectly the effect of changing the temperature on the void fraction distribution. The following axial and radial distributions were measured in all these experiments: void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter and turbulence intensity. The range of values of the gas superficial velocities in these experiments covered the range from bubbly flow to the transition to cap/slug flow. Also with transition flow conditions we distinguish two groups of bubbles in the experiments, the small spherical bubbles and the cap/slug bubbles. Special interest was devoted to the transition region from bubbly to cap/slug flow; the goal was to understand the physical phenomena that take place during this transition A set of numerical simulations of some of these experiments for bubbly flow conditions has been performed by coupling a Lagrangian code, that tracks the three dimensional motion of the individual bubbles in cylindrical coordinates inside the field of the carrier liquid, to an Eulerian model that computes the magnitudes of continuous phase and to a 3D random walk model that takes on account the fluctuation in the velocity field of the carrier fluid that are seen by the bubbles due to turbulence fluctuations. Also we have included in the model the deformation that suffers the bubble when it touches the wall and it is compressed by the forces that pushes it toward the wall, provoking that the bubble rebound like a ball.
Kleinstreuer C. Ed: Two Phase Flow: Theory and Applications. Taylor and Francis, New York 1993.
Zaruba A., Lucas D., Prasser H. M., Höhne T.: Bubble-wall interaction in a vertical gas-liquid flow: Bouncing, sliding and bubble deformations. Chem. Eng. Sci. 62(2007), 1591-1605.
Zun I., Kljenak I., Moze S.: Space-time evolution of the non-homogeneous bubble distribution in upward flow. Int. J. Multiphase Flow 19(1993), 1, 151-172.
Prasser H. M., Krepper E., Lucas D.: Evolution of the two phase flow in a vertical tube, decomposition of gas fraction profiles according to bubble size classes using wire-mesh sensors. Int. J. Thermal Sci. 41(2002), 17-28,.
Tomiyama A., Zun I., Higaki H., Makino Y., Sakaguchi T.: A three-dimensional particle tracking method for bubbly flow simulation. Nucl. Eng. Des. 175(1997), 77-86.
Lucas D., Krepper E., Prasser H. M.: Development of co-current air-water flow in a vertical pipe. Int. J. Multiphase Flow 31(2005), 1304-1328.
Krepper E., Lucas D., Prasser, H. M.: On the modelling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235(2005), 597-611.
Bocksell T. L., Loth E.: Stochastic modelling of particle diffusion in a turbulent boundary layer. Int. J. Multiphase Flow 32(2006), 1234-1253.
Dehbi A.: Turbulent particle dispersion in arbitrary wall-bounded geometries: A coupled CFD-Langevin-equation based approach. Int. J. Multiphase Flow 34(2008), 819-828.
Haworth D. C., Pope S. B.: Generalized Langevin model for turbulent flows. Physics Fluids 29(1986), 2, 387-405.
Muñoz-Cobo J. L., Chiva S., Abdelazziz M., Méndez S.: Coupled Lagrangian and Eulerian simulation of bubbly flows in vertical pipes, validation with experimental data using multisensory conductivity probes and laser Doppler anemometry. Nucl. Eng. Des. 242(2012), 285-299.
Tomiyama A.: Struggle with computational Dynamics. In: Proc. Third Int. Conf. Multiphase Flow. ICMF-98, Lyon, France, 1998.
Auton T. R.: The Lift Force on a Spherical Body in a Rotational Flow. J. Fluid Mech., 183, 199-218, (1987).
Tomiyama A., Tamai H., Zun I., Hosokawa S.: Transverse migration of single bubbles in simple shear flows. Chem. Eng. Sci. 57(2002), 1849-1858.
Antal S. P., Lahey R. T. Jr., and Flaherty, J. E.: Analysis of two phase flow distribution in fully developped daminar bubbly two-phase flow, Int. J. Multiphase Flow 17(1991), 635-652.
Pope S. B.: Stochastic Lagrangian models of velocitiy in homogeneous turbulent shear flow. Phys. Fluids 14(2002), 5, 1696-1702.
Haworth D. C., Pope S. B.: A generalized Langevin model for turbulent flow. Phys. Fluids 29(1986), 2, 387-405.
Veenman, M. P. B.: Statistical Analysis of Turbulent Flow". PhD thesis, University of Eindhoven, Eindhoven 2004.
Dehbi A.: Turbulent particle dispersion in arbitrary wall-bounded geometries: a coupled CFD-Langevin-equation based approach. Int. J. Multiphase Flow 34(2008), 819-828.
Oesterlé B., Zaichik L. I.: On Lagrangian time scales and particle dispersion modeling in equilibrium shear flows. Phys. Fluids 16(2004), 9, 3374-3384.
Kallio G. A., Reeks M. W.: A numerical simulation of particle deposition in turbulent boundary layers. Int. J. Multiphase Flow 3(1989), 433-446.
Pozorski J., Minier J. P.: On the Lagrangian turbulent dispersion models based on the Langevin equation. Int. J. Multiphase Flow 24(1998), 913-945.
Kloeden P. E., Platen E. Eds.: Numerical Solution of Stochastic Differential Equations. Springer Verlag, Berlin 1995.
Kloeden P. E., Platen, E., Schurz, H. Eds.: Numerical Solution of Stochastic Differential Equations Through Computer Experiments. Springer Verlag, Berlin 1994.
Muñoz-Cobo J. L., Montesinos M. E., Peña J., Escrivá A., González G., Melara J.: Validation of reactor noise linear stability methods by means of advanced stochastic differential equations models. Ann. Nucl. Energy 38(2011), 1473-1488.
Launder B. E., Spalding B.: Mathematical Models of Turbulence. Academic Press, New York 1972.
Dhotre M. T., Smith B. L., Niceno B: CFD simulation of bubbly flows: Random dispersion model. Chem. Eng. Sci. 62(2007), 7140-7150.
Kim S.; Fu Y.; Ishii M.: Study on interfacial structures in slug flows using a miniaturized four-sensor conductivity probe. Nucl. Eng. Des. 204(2001), 45-55.
Mendez-Diaz S.: Experimental Measurement of the Interfacial Area Concentration. PhD thesis, Universidad Politécnica de Valencia, Valencia 2008 (in Spain).
Shen X. Y., Saito K., Nakamura M. H.: Methodological improvement of an intrusive four-sensor probe for the multi-dimensional two-phase flow measurement. Int. J. Multiphase Flow 31(2005), 593-617.
Delhaye J. P., Bricard P.: Interfacial area in bubbly flow: experimental data and correlations. J. Nucl. Eng. Des. 151(1994), 65-77.
Ishii M.: Thermo-Fluid Dynamic Theory of Two-Phase Fflow. Eyrolles, Paris 1975.
Hibiki T., Ishi M., Xiao Z.: Axial interfacial area transport of vertical bubbly flows. Int. J. Heat Mass Transfer 44(2001), 1869-1888.
Ferziger J. H., Peric M.: Computational methods for fluid dynamics, Springer, ISBN 3-540-42074-6, 2002.