## THERMAL SCIENCE

International Scientific Journal

### MODELING OF BUBBLE BREAK-UP IN STIRRED TANKS

**ABSTRACT**

The Lagrangian code LAG3D for dispersed phase flow modeling was implemented with the introduction of bubble break-up model. The research was restricted on bubbles with diameter less than 2 mm, i.e. bubbles which could be treated as spheres. The model was developed according to the approach of Martinez-Bazan model. It was rearranged and adjusted for the use in the particular problem of flow in stirred tanks. Developed model is stochastic one, based on the assumption that shear in the flow induces the break of the bubble. As a dominant parameter a dissipation of the turbulent kinetic energy was used. Computations were performed for two different types of the stirrer: Rushton turbine, and Pitch blade turbine. The geometry of the tank was kept constant (four blades). Two different types of liquids with very big difference in viscosity were used, i.e. silicon oil and dimethylsulfoxide, in order to enable computation of the flow in turbulent regime as well. As a parameter of the flow, the number of rotations of the stirrer was varying. As a result of the computation the fields of velocity of both phases were got, as well as the fields of bubble concentration bubble mean diameter and bubble Sauter diameter. To estimate the influence of the break-up model on the processes in the stirred tank a computations with and without this model were performed and compared. A considerable differences were found not only in the field of bubble diameter, but also in the field of bubble concentration. That confirmed a necessity of the introduction of such model. A comparison with the experiments performed with phase Doppler anemometry technique showed very good agreement in velocity and concentration profiles of the gas phase. The results for the average bubble diameter are qualitatively the same, but in almost all computations about 20% smaller bubble diameter was got than in the measurements.

**KEYWORDS**

PAPER SUBMITTED: 2004-02-05

PAPER REVISED: 2004-03-18

PAPER ACCEPTED: 2004-04-23

**THERMAL SCIENCE** YEAR

**2004**, VOLUME

**8**, ISSUE

**Issue 1**, PAGES [29 - 49]

- Batchelor, G. K., The Theory of Homogenous Turbulence, Cambridge University Press, Cambridge, UK, 1956
- Brenn, G., Braeske, H., ?ivkovic, G., Durst, F., Experimental and Numerical Investigation of Liquid Channel Flows with Dispersed Gas and Solid Particles, Int. J. Multiphase Flow, 29 (2003), pp. 219-247
- Crowe, C. T., Sharma, M. P., Stock, D. E., The Particle-Source-in-Cell (PSI-CELL) Model for gas-droplet flows, J. Fluids Eng, 99 (1977), 99, pp. 325-332
- Martinez-Bazan C., Montanes, J. L., Lasheras, J. C., On the Breakup of an air Bubble Injected into a Fully Developed Turbulent Flow, Part 1, Breakup Frequency, J. Fluid Mech, 401 (1999), pp. 157-182
- Martinez-Bazan C., Montanes, J. L., Lasheras, J. C., On the Breakup of an Air Bubble Injected into a Fully Developed Turbulent Flow, Part 2, Size PDF on the resulting daughter bubbles, J. Fluid Mech, 401 (1999), pp. 183-207
- Matsumoto, S., Saito, S., Monte Carlo Simulation of Horizontal Pneumatic Conveying Based on the Rough Wall Model, J. Chem. Engng. Japan, 3 (1970), pp. 223-230
- Migdal, D., Agosta, V. D., A Source Flow Model for Continuum Gas-Particle Flow, Trans. ASME, 34 (1967), pp. 860-865
- Milojevic, D., Lagrangian Stochastic-Deterministic (LSD) Prediction of Particle Dispersion in Turbulence, Part. Part. Syst. Charact. 7 (1990), pp. 181-190
- Mostafa, A. A., Elghobashi, S. E., A Two-Equation Turbulence Model for JET Flows Laden with Vaporising Droplets, Int. J. Multiphase Flow, 11 (1985), pp. 515-533
- Oesterle, B., Petitjean, A., Simulation of Particle-to-Particle Interaction in Gas-Solid Flows, Int. J. Multiphase Flow, 19 (1993), pp. 199-211
- Rubinow, S. I., Keller, B., The Transverse force on a Spinning Sphere Moving in a Viscous Fluid, J. Fluid Mech., 11 (1961), pp. 447-459
- Saffman, P. G., The Lift on a Small Sphere in a Shear Flow. J. Fluid Mech., 22 (1965), pp. 385-400
- Sch䦥r, M., H?fken, M., Durst, F., Detailed LDV Measurements for Visualization of the Flow Field within a Stirred-Tank Reactor Equipped with a Rushton Turbine, Trans. IChemE, 75(A) (1997), pp. 729-736
- Sommerfeld, M., Zivkovic, G., Recent Advances in the Numerical Simulation of Pneumatic Conveying through Pipe Systems, Computational Methods in Applied Science, Invited Lectures and Special Technological Sessions of the 1st European Computational Fluid Dynamics Conference, Brussels, 1992, pp. 201-212
- Tsuji, Y., Oshima, T., Morikawa, Y., Numerical Simulation of Pneumatical Conveying in a Horizontal Pipe, KONA, 3 (1985), pp. 38-51
- Wechsler, K., Breuer, M., Durst, F., Steady and Unsteady Computations of Turbulent Flows Induced by a 4/45o Pitched Blade Impeller, Journal of Fluids Engineering 121 (1999), pp .318-329