A theoretical study on drop breakup modeling in turbulent flows: The inertial subrange versus the entire spectrum of isotropic turbulence

Chemical Engineering Science

Volumn 149, Issue , 2016, Pages 249-265

  Solsvik, Jannike ^a   Skjervold, Vidar T ^a   Han, Luchang ^b   Luo, He'an ^b   Jakobsen, Hugo A ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b XIANGTAN UNIVERSITY   (China)

Author keywords

Breakage; Dispersed multiphase flow; Mathematical modeling; Model energy spectrum; Structure function; Turbulence

Indexed keywords

COAL BREAKAGE; DISTRIBUTION FUNCTIONS; DROP BREAKUP; DROPS; MATHEMATICAL MODELS; REYNOLDS NUMBER; SPECTROSCOPY; TURBULENCE; TURBULENT FLOW;

CAMBRIDGE UNIVERSITY; ENERGY SPECTRA; FUNCTION DEFINITIONS; HIGH REYNOLDS NUMBER; ISOTROPIC TURBULENCE; LOW REYNOLDS NUMBER; STRUCTURE FUNCTIONS; VOLUME CONSERVATION;

FUNCTIONS;

EID: 84968895077     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2016.04.037     Document Type: Article

References (38)

1. Andersson, B., Andersson, R., Håkanson, L., Mortensen, M., Sudiyo, R., van Wachem, B., 2015. Computational Fluid Dynamics for Engineers, 11th edition. Chalmers University of Technology, Gothenburg.
2. Becker P.J., Puel F., Jakobsen H.A., Sheibat-Othman N. Development of an improved breakage kernel for high dispersed viscosity phase emulsification. Chem. Eng. Sci. 2014, 109:326-338.
3. Coulaloglou C.A., Tavlarides L.L. Description of interaction processes in agitated liquid-liquid dispersions. Chem. Eng. Sci. 1977, 32:1289-1297.
4. Davidson P.A. Turbulence. An Introduction for Scientists and Engineers 2004, Oxford University Press, Oxford.
5. Ghasempour, F., 2015. Structures, properties and dynamics of turbulent vortices (Ph.D. thesis), Chalmers University of Technology, Gothenburg, Sweden.
6. Ghasempour F., Andersson R., Andersson B. Multidimensional turbulence spectra-statistical analysis of turbulent vortices. Appl. Math. Model. 2014, 38:4226-4237.
7. Ghasempour F., Andersson R., Andersson B. Number density of turbulent vortices in the entire energy spectrum. AIChE J. 2014, 60:3989-3995.
8. Golub G.H., Welsch J.H. Calculation of Gauss quadrature rules. Math. Comput. 1969, 23:221-230.
9. Gotoh T., Fukayama D. Pressure spectrum in homogeneous turbulence. Phys. Rev. Lett. 2001, 86:3775-3778.
10. Han L., Gong S., Ding Y., Fu J., Gao N., Luo H. Consideration of low viscous droplet breakage in the framework of the wide energy spectrum and the multiple fragments. AIChE J. 2015, 61:2147-2168.
11. Han L., Gong S., Li Y., Ai Q., Luo H., Liu Z., Liu Y. A novel theoretical model of breakage rate and daughter size distribution for droplet in turbulent flows. Chem. Eng. Sci. 2013, 102:186-199.
12. Han L., Gong S., Li Y., Gao N., Fu J., Luo H., Liu Z. Influence of energy spectrum distribution on drop breakage in turbulent flows. Chem. Eng. Sci. 2014, 117:55-70.
13. Han L., Luo H., Liu Y. A theoretical model for droplet breakup in turbulent dispersions. Chem. Eng. Sci. 2011, 66:766-776.
14. Kolmogorov A.N. Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk. SSSR 1941, 32(1):16-18. (English translation in Proc. R. Soc. Lond. Ser. A 434: 15-17, 1991).
15. Kolmogorov A.N. The local structure of turbulence in an incompressible fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 1941, 30(4):299-303. (English translation in Proc. R. Soc. Lond. Ser. A 434: 9-13, 1991).
16. Kreyszig E. Advanced Engineering Mathematics 1999, John Wiley & Sons, Inc., New York. 8th edition.
17. Lamont J.C., Scott D.S. An eddy cell model of mass transfer into the surface of a turbulent liquid. AIChE J. 1970, 16:513-519.
18. Liao Y., Lucas D. A literature review of theoretical models for drop and bubble breakup in turbulent dispersions. Chem. Eng. Sci. 2009, 64:3389-3406.
19. Liao Y., Lucas D. A literature review on mechanisms and models for the coalescence process of fluid particles. Chem. Eng. Sci. 2010, 65:2851-2864.
20. Luo H., Svendsen H.F. Theoretical model for drop and bubble breakup in turbulent dispersions. AIChE J. 1996, 42:1225-1233.
21. Maaß S., Buscher S., Hermann S., Kraume M. Analysis of particle strain in stirred bioreactors by drop breakage investigations. Biotechnol. J. 2011, 6:1-14.
22. Maaß S., Kraume M. Determination of breakage rates using single drop experiments. Chem. Eng. Sci. 2012, 70:146-164.
23. Nachtigall, S., Zedel, D., Kraume, M., 2016. Analysis of drop deformation dynamics in turbulent flow. Chin. J. Chem. Eng. 24, 264-277.
24. Orvalho S., Ruzicka M.C., Olivieri G., Marzocchella A. Bubble coalescence. effect of bubble approach velocity and liquid viscosity. Chem. Eng. Sci. 2015, 134:205-216.
25. Pope S.B. Turbulent Flows 2000, Cambridge University Press, Cambridge, UK.
26. Prince M.J., Blanch H.W. Bubble coalescence and break-up in air-sparged bubble columns. AIChE J. 1990, 36:1485-1499.
27. Ramkrishna D. Population Balances. Theory and Applications to Particulate Systems in Engineering 2000, Academic Press, San Diego.
28. Solsvik J., Jakobsen H.A. Single drop breakage experiments in stirred liquid-liquid tank. Chem. Eng. Sci. 2015, 131:219-234.
29. Solsvik J., Jakobsen H.A. Development of fluid particle breakup and coalescence closure models for the complete energy spectrum of isotropic turbulence. Ind. Eng. Chem. Res. 2016, 55:1449-1460.
30. Solsvik, J., Jakobsen, H.A., 2016b. A review of the statistical turbulence theory required extending the population balance closure models to the entire spectrum of turbulence. AIChE J. 62(5), 1795-1820.
31. Solsvik J., Becker P.J., Sheibat-Othman N., Mohallick I., Farzad R., Jakobsen H.A. Viscous drop breakage in liquid-liquid stirred dispersions. population balance modeling. J. Dispers. Sci. Technol. 2015, 36:577-594.
32. Solsvik J., Nystrand S., Gawel B., Øye G., Jakobsen H.A. Theoretical and experimental investigation of film drainage time. Energy Proc. 2015, 64:33-42.
33. Solsvik J., Tangen S., Jakobsen H.A. On the constitutive equations for fluid particle breakage. Rev. Chem. Eng. 2013, 29:241-356.
34. Szegö G. Orthogonal Polynomials 1939, American Mathematical Society, New York.
35. Tennekes H., Lumley J.L. A First Course in Turbulence 1972, The MIT Press, Cambridge.
36. Villwock J., Gebauer F., Bart H.-J., Kraume M. Systematic analysis of single droplet coalescence. Chem. Eng. Technol. 2014, 37:1103-1111.
37. Yeoh G.H., Cheung C.P., Tu J. Multiphase Flow Analysis using Population Balance Modeling: Bubbles, Drops and Particles 2014, Butterworth-Heinemann, Amsterdam.
38. Zaccone A., Gäbler A., Maaß S., Marchisio D., Kraume M. Drop breakage in liquid-liquid stirred dispersions. modeling of single drop breakage. Chem. Eng. Sci. 2007, 62:6297-6307.