A first order relaxation model for the prediction of the local interfacial area density in two-phase flows

International Journal of Multiphase Flow

Volumn 22, Issue 6, 1996, Pages 1073-1104

  Millies, M ^a,b   Drew, D A ^a   Lahey, R T ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^b LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Bubble break up; Coalescence; Interfacial area

Indexed keywords

BUBBLE FORMATION; DENSITY (SPECIFIC GRAVITY); INTERFACES (MATERIALS); LIQUIDS; MATHEMATICAL MODELS; RELAXATION PROCESSES; VAPORS;

INTERFACIAL AREAS;

TWO PHASE FLOW;

INTERFACES; MODELLING-MATHEMATICAL; TWO-PHASE FLOW(GAS/LIQUID);

EID: 0030294526     PISSN: 03019322     EISSN: None     Source Type: Journal    
DOI: 10.1016/0301-9322(96)00031-6     Document Type: Article

References (40)

1. Akita, K. & Yoshida, F. 1974 Bubble size, interfacial area, and liquid-phase mass transfer coefficient in bubble columns. Ind. Eng. Chem. Process Des. Develop. 13, 84-91.
2. Bensler, H., Delhaye, J. M. & Favreau, C. 1991 Determination of the volumetric interfacial area, volumetric void fraction and Sauter mean diameter in bubbly flow by means of ultrasound attenuation. Proc. World Conf. on Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics, pp. 1096-1104.
3. Burgess, J. & Calderbank, P. H. 1975 The measurement of bubble parameters in two-phase dispersions-I. Chem. Eng. Sci. 30, 743-750.
4. Burgess, J. & Calderbank, P. H. 1975 The measurement of bubble parameters in two-phase dispersions-II. Chem. Eng. Sci. 30, 1107-1121.
5. Burgess, J. & Calderbank, P. H. 1975 The measurement of bubble parameters in two-phase dispersions-III. Chem. Eng. Sci. 30, 1511-1518.
6. Calderbank, P. 1967 Gas absorption from bubbles. The Chem. Eng. 43, CE209-CE233.
7. Chandrasekharan, K. & Calderbank, P. H. 1981 Further observations on the scale-up aerated mixing vessels. Chem. Eng. Sci. 36, 819-823.
8. Chang, J. & Harvel, G. D. 1992 Determination of gas-liquid bubble column instantaneous interfacial area and void fraction by a real-time neutron radiography method. Chem. Eng. Sci. 47, 13-14; 3639-3646.
9. Daly, J., Patel, S. A. & Bukur, D. B. 1992 Measurement of gas holdups and sauter mean bubble diameters in bubble column reactors by dynamic gas disengagement method. Chem. Eng. Sci 47, 13-14; 3647-3654.
10. Deckwer, W.-D. 1992 Bubble Columns. Otto Salle Verlag, Frankfurt, Germany.
11. de Figueiredo, M. L. & Calderbank, P. H. 1979 The scale-up of aerated mixing vessels for specified oxygen dissolution rates. Chem. Eng. Sci. 34, 1333-1338.
12. Garncarek, Z., Idzik, J. & Spisak, W. 1991 A new method in investigations of bubble cluster shapes in two-phase flow. Chem. Eng. Process. 30, 107-112.
13. Guido-Lavalle, G., Clausse, A. & Converti, J. 1993 A contribution to the kinetic formulation of gas-liquid flows. Chem. Eng. Communications 120, 99.
14. Guido-Lavalle, G., Garcia, P., Clausse, A. & Qazi, M. K. 1994 A bubble number density constitutive equation. Nuclear Eng. Design 152, 213-224.
15. Ishii, M. 1975 Thermo-fluid Dynamic Theory of Two-phase Flow. Eyrolles, Paris.
16. Ishii, M. & Mishima, K. 1984 Two-fluid model and hydrodynamic constitutive relations. Nucl. Eng. Des. 82, 107-126.
17. Ishii, M. 1992 Interfacial area in two-phase flow. HTD Vol. 197, pp. 1-5. Two-phase Flow and Heat Transfer, ASME.
18. Kalkach-Navarro, S. 1992 Two-fluid modeling of the bubbly/slug flow regime transition. Ph.D. Thesis, Rensselear Polytechnic Institute, Troy.
19. Kataoka, I., Ishii, M. & Serizawa, A. 1986 Local formulation and measurements of interfacial area concentration in two-phase flow. Int. J. Mult. Flow 12, 505-529.
20. Kelly, J. 1993 A four-field approach towards developing a mechanistic model for multiphase flow. Pacific Northwest Laboratory Report PNL-SA-18878, DE93 006572.
21. Lahey, R. T. & Lee, S. J. 1992 Phase distribution and two-phase turbulence for bubbly flows in pipe. In Multiphase Science and Technology, Vol. 6, pp. 303-349. Hemisphere Publishing Corp., Washington.
22. Levich, V. 1962 Physiochemical Hydrodynamics. Prentice Hall, Englewood Cliffs, NJ.
23. Lewis, D. A. & Davidson, J. F. 1983 Bubble sizes produced by shear and turbulence in a bubble column. Chem. Eng. Sci. 38, 161-167.
24. Marrucci, G. & Nicodemo, L. 1967 Coalescence of gas bubbles in aqueous solutions of inorganic electrolytes. Chem. Eng. Sci. 22, 1257-1265.
25. Mudde, R., Bakker, R. A. & van den Akker, H. E. A. 1992 Noise analysis of transmitted light beams for determining bubble velocity and gas holdup profiles in a bubble column. Chem. Eng. Sci. 47, 13-14; 3631-3638.
26. Nagel, O., Kürten, H. & Sinn, R. 1972 Stoffaustauschfläche und Energiedissipationsdichte als Auswahlkriterien für Gas/Flüssig-Reaktoren: Teil 1. Chem. Ing. Tech. 44, 367-373.
27. Nagel, O., Kürten, H. & Sinn, R. 1972 Stoffaustauschfläche und Energiedissipationsdichte als Auswahlkriterien für Gas/Flüssigkeits-Reaktoren: Teil 2. Chem. Ing. Tech. 44, 899-903.
28. Nagel, O., Kürten, H. & Hegner, B. 1973 Die Stoffaustauschfläche in Gas/Flüssigkeits-Kontaktapparaten Auswahlkriterien und Unterlagen zur Vergrößerung. Chem. Ing. Tech. 45, 913-920.
29. Nagel, O. & Kürten, H. 1976 Untersuchungen zum Dispergieren im turbulenten Scherfeld. Chem. Ing. Tech. 48, 513-519.
30. Nagel, O., Hegner, B. & Kürten, H. 1978 Kriterien für die Auswahl und die Auslegung von Gas/Flüssigkeits-Reaktoren. Chem. Ing. Tech. 50, 935-944.
31. Nagel, O., Kürten, H. & Hegner, B. 1978 Design of gas/liquid reactors: mass transfer area and input of energy. Proc. ICHMT, pp. 835-876. Hemisphere Publishing Corp., Washington.
32. Oolman, T. & Blanch, H. W. 1986 Bubble coalescence in air-sparged bioreactors. Chemical Engng J. 32, B7-B17.
33. Park, J. 1992 Void wave propagation in two-phase flow. Ph.D. Thesis, RPI, Troy.
34. Patel, S., Daly, J. G. & Bukur, D. B. 1989 holdup and interfacial area measurements using dynamic gas disengagements. AIChE J. 35, 931-942.
35. Prince, M. & Blanch, H. W. 1990 Transition electrolyte concentrations for bubble coalescence. AIChE J. 36, 1425-1429.
36. Prince, M. & Blanch, H. W. 1990b Bubble coalescence and break-up in air sparged bubble columns. AIChE J. 36, 1485-1499.
37. Schumpe, A. & Grund, G. 1986 The gas desengagement technique for studying gas holdup structure in bubble columns. Can J. Chem. Eng. 64, 891-896.
38. Serizawa, A. & Kataoka, I. 1990 Phase distribution in two-phase flow. Int. Conf. Heat Mass Transfer, Dubrovnik.
39. Stewart, C., Crowe, C. T. & Saunders, S. C. 1993 A model for simultaneous coalescence of bubble clusters. Chem. Eng. Sci. 48, 3347-3354.
40. Thomas, N., Auton, T. R., Sene, K. & Hunt, J. C. R. 1983 Physical modelling of multi-phase flow. BHRA Fluid Engng. 169-184.