The effect of bubbles on the structure of flow and the friction in upward turbulent gas–liquid flow

B. A. Snigerev

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 19 (2019) no. 2, pp. 182-195.

Résumé

This paper presents the computational study results of the ascending gas-liquid flow local structure in a vertical pipe. The mathematical model is based on the use of two-fluid Eulerian approach taking into account the inverse influence of bubbles on averaged characteristics and turbulence of the carrying phase. The equations conservation of mass and momentum quantity of motion in the form of Navier – Stokes equations averaged over Reynolds for each phase are written down. For turbulent stresses the relations under the assumption of the Boussinesq hypothesis are written. Turbulent viscosity for the carrier liquid phase is determined using a two-parameter turbulence model modified for two-phase media. In the equations for transferring the kinetic energy of turbulence and its dissipation, additional terms for the kinetic energy, caused by pulsations of bubbles are introduced. As the main forces, the following components are considered: Archimedes force, resistance force, attachment force, Magnus rotational force, near-wall frictional force. To describe the bubble size distribution in a two-phase flow, an equation for preservation of the number of particles, taking into account the processes of coalescence and breakup is written. To solve the number of bubbles conservation equation, an approach based on the method of fractions is applied. The particle size distribution spectrum is divided into a number of fractions with fixed boundaries. It is assumed that bubbles can be exchanged between different fractions as a result of coalescence and breakups. In the framework of this method, the bubble size distribution is approximated by a piecewise equiprobable. Thus, the problem of describing the spectrum of drops by size reduces to the solution of equations for the volume concentrations of individual fractions. The effect of changes in the degree of dispersion of the gas phase volumetric gas flow rate, the velocity of the dispersed phase to the local structure and surface friction in a two-phase flow are numerically investigated. Comparison of the simulation results with experimental data showed that the developed approach allows to adequately describe turbulent gas-liquid flows in a wide range of gas content and initial bubble sizes.

Bibliographie

[1] Brounchtein B. I., Chegolev B. B., Gydrogynamics, mass and heat transfer in bubble columns, Khimia, L., 1988, 336 pp. (in Russian)

[2] Butterworth D., Hewitt G. F., Two-phase flow and heat transfer, Oxford Press, 1977, 321 pp.

[3] Nigmatulin R. I., Fundamentals of multiphase media, Nauka, M., 1978, 336 pp. (in Russian) | MR

[4] Burdukov A. P., Valukina N. V., Nakoryakov V. E., “Special characteristics of the flow of a gas-liquid bubble-type mixture with small Reynolds number”, J. Appl. Mech. Tech. Phys., 16:4 (1975), 592–597 | DOI

[5] Tarasova N. V., Leontiev A. I., “Hydraulic resistance when the flow of steam-water mixture in a heated tube”, Teploviz. Vys. Temp., 3:1 (1965), 115–123 (in Russian)

[6] Ganchev B. G., Peresadko V. G., “Processes of hydrodynamics and heat exchange in descending bubble flows”, Journal of Engineering Physics, 49:2 (1985), 879–885 | DOI

[7] Gorelik P. C., Kashinsky O. N., Nakoryakov V. E., “Study of downward bubbly flow in a vertical pipe”, J. Appl. Mech. Tech. Phys., 28:1 (1987), 64–67 | DOI

[8] Kashinsky O. N., Lobanov P. D., Pakhomov M. A., “Experimental and numerical study of downward bubbly flow in a pipe”, Int. J. Heat Mass Transfer, 49 (2006), 3717–3722 | DOI

[9] Zaichik L. I., Mukin R. V., Strizhov V. F., “Development of a diffusion-inertia model for calculating bubble turbulent flows: isothermal polydispersed flow in a vertical pipe”, High Temperature, 50:5 (2012), 665–675 | DOI

[10] Paxomov M. A., Terexov V. I., “Modeling of the turbulent flow structure of an upward a polydisperse gas-liquid flow”, Fluid Dynamics, 50:2 (2015), 229–239 | DOI | MR

[11] Pfleger D., Gomes S., Wagner G. H., Gilbert N., “Hydrodynamics simulations of laboratory scale bubble columns: fundamentals studies on the eulerian-eulerian modeling approach”, Chem. Eng. Sci., 54:4 (1999), 5091–5095 | DOI

[12] Sato Y., Sadatomi M., Sekoguchi K., “Momentum and heat transfer in two-phase bubble flow-I. Theory”, Int. J. Multiphase Flow, 7 (1981), 167–177 | DOI | Zbl

[13] Luo H., Svendsen H., “Theoretical model for drop and bubble breakup in turbulent dispersions”, AIChE. J., 46 (1996), 1225–1231 | DOI

[14] Prince M. J., Blanch H. W., “Bubble coalescence and break-up in air sparged bubble columns”, AIChE. J, 36 (1990), 1485–1489 | DOI

[15] Muller-Steinhagen H., Heck K., “A simple friction pressure drop correlation for two-phase flow in pipes”, Chem. Eng. Prog., 26 (1986), 297–308 | DOI

[16] Weller N. G., Tabor G., Jasak H., “A tensorial approach to computational continuum mechanics using object oriented tecniques”, Computers in Physics, 12 (1998), 620–624 | DOI

[17] Hibiki T., Ishii M., Xiao Z., “Axial interfacial area transport of vertical bubble flows”, Int. J. Heat Mass Transfer, 44 (2001), 1869–1871 | DOI | MR