Study of the features of rising of air bubbles and solid spheres

The results of numerical modeling of rising of bubbles and solid spheres with a diameter of 1 to 20 mm in water are presented. The analysis is based on the numerical solution of the complete system of Navier—Stokes equations for a two-phase medium in a three-dimensional formulation in an implicit manner. The interface gas-water boundary is automatically monitored by the method of allocating the volume fraction. The motion of solid spheres is modeled using the method “Chimera”. Particular attention is paid to the study of local physical characteristics of motion process. Comparison of average calculated rising velocities with experimental data is carried out. The periodic (zigzag or spiral) character of the trajectory of moving bubbles associated with changing their shape and with the formation of a characteristic turbulent trace is shown. The correlation of the velocity of bubble rise with the forces acting on it is obtained. The tendency of change of a rise trajectory in process of increase of number of Galileo is revealed for solid spheres.

1. Veldhuis C., Biesheuvel A., Wijngaarden L. Shape oscillations on bubbles rising in clean and in tap water // Physics of fluids. 2008. V. 20. P. 1—12.

2. Hua J., Stene J., Lin P. Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method // J. Comp. Phys. 2008. V. 227, N 6. P. 3358—3382.

3. Horowitz M., Williamson C.H.K. The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres // J. Fluid Mech. 2010. V. 651. P. 251—294.

4. Букреев В. И., Костомаха В. А., Романов Е. М. Погружение шара в однородной жидкости // Труды Международной конференции RDAMM-2001. 2001. Т. 6, Ч. 2. C. 144—149.

5. Архипов В. А., Васенин И. М., Ткаченко А. С., Усанина А. С. О нестационарном всплытии пузырька в вязкой жидкости при малых числах Рейнольдса // Известия РАН. Механика жидкости и газа. 2015. № 1. С. 86—94.

6. Abbad M., Souhar M. Effects of the history force on an oscillating rigid sphere at low Reynolds number // Experiments Fluids. 2004. N 36. P. 775—782.

7. Stepanyants Y. A., Yeoh G. H. Particle and bubble dynamics in a creeping flow // Eur. J. Mech. – B/Fluids. 2009. V. 28. Р. 619—629.

8. Lovalenti P. M., Brady J. F. The force on a bubble, drop, or particle in arbitrary time-dependent motion at small Reynolds number

9. // Phys. Fluids A. 1993. V. 5. Р. 2104—2116.

10. Hassan H., Stepanyants Y. Dynamics of two charged particles in a creeping flow // J. Phys. Maths. 2015. V. 6, N 2. P. 1000145-1-7.

11. Rusche H. Computational Fluid Dynamics of Dispersed Two-Phase Flows at high phase fraction // PhD thesis, Imperial College of Science, Technology& Medicine, Dep. of Mech. Eng., London, 2002.

12. Jenny M., Dusek J., Bouchet G. Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid // J. Fluid Mech. 2004. V. 508. P. 201—239.

13. Preukschat A. W. Measurements of drag coefficients for falling and rising spheres in free motion // PhD thesis, California Institute of Technology, Pasadena,CA. 1964.

14. MacCready P. B., Jex Y. R. Study of sphere motion and balloon wind sensors. Tech. Rep. Tech. Mem., X53089, NASA, 1964.

15. Wu M., Gharib M. Experimental studies on the shape and path of small air bubbles rising in clean water // Phys. Fluid. 2002. V. 14, N 7. P. L49—L52.

16. Clift R., Grace J. R., Weber M. E. Bubbles, drops and particles. London: Academic Press, 1978.

17. Ellingsen K., Risso F. On the rise of an ellipsoidal bubble in water: oscillatory paths and liquid induced velocity // J. Fluid. Mech. 2001. V. 440. P. 235—268.

18. Козелков А. С., Куркин А. А., Пелиновский Е. Н., Курулин В. В., Тятюшкина Е. С. Моделирование возмущений в озере Чебаркуль при падении метеорита в 2013 году // Известия РАН. Механика жидкости и газа. 2015. № 6. С. 134—143.

19. Chen L., Garimella S. V., Reizes J. A., Leonardi E. The development of a bubble rising in a viscous liquid // J. Fluid Mech. 1999. V. 387. P. 61—96.

20. Brackbill J. U., Kothe D. B., Zemach C. A continuum method for modelling surface tension // J. Comp. Phys. 1992. V. 100. P. 335—354.

21. Kozelkov A. S., Kurkin A. A., Pelinovsky E. N., Tyatyushkina E. S., Kurulin V. V., Tarasova N. V. Landslide-type tsunami modelling based on the Navier-Stokes Equations // Science of tsunami Hazards. 2016. V. 35, N 3. P. 106—144.

22. Ferziger J. H., Peric M. Computational methods fluid dynamics. Berlin, Heidelberg, NewYork: Springer-Verlag. 2002. 423 p.

23. Benek J. A., Buning P. G., Steger J. L. A 3-D Chimera Grid Embedding Technique // AIAA Paper. 1985. No. 85—1523.

24. Волков К. Н., Дерюгин Ю. Н., Емельянов В. Н., Карпенко А. Г., Козелков А. С., Тетерина И. В. Методы ускорения газодинамических расчетов на неструктурированных сетках. Москва: Физматлит, 2013. 536 с.

25. Kozelkov A. S., Shagaliev R. M., Kurulin V. V., Yalozo A. V., Lashkin S. V. Investigation of Supercomputer Capabilities for the Scalable Numerical Simulation of Computational Fluid Dynamics Problems in Industrial Applications // Computational Mathematics and Mathematical Physics. 2016. V. 56, N 8. P. 1506—1516.

26. Talaia M.A.R. Terminal velocity of a bubble rise in a liquid column // International Journal of Physical and Mathematical Sciences. 2007. V. 1, N 4. P. 220—224.

27. Saffman P. G. On the rise of small air bubbles in water // J. Fluid. Mech. 1956. V. 1. P. 249—275.

28. Cuenot B., Magnaudet J., Speranto B. The effect of slightly soluble surfactants on the flow around a spherical bubble // J. Fluid Mech. 1997. V. 339. P. 25—29.

29. Esmaeeli A., Tryggvason G. Direct numerical simulation of bubbly flows. Part 2. Moderate Reynolds number array // J. Fluid Mech. 1999. V. 385. P. 325—358.

30. Baz-Rodriguez S., Aguilar-Corona A., Soria A. Rising velocity for single bubbles in pure liquids // Revista Mexicana de Ingenieria Quimica (Mexico). 2012. V. 11, N 2. P. 269—278.