On the numerical study of isothermal vertical bubbly flow using two population balance approaches

Chemical Engineering Science

Volumn 62, Issue 17, 2007, Pages 4659-4674

  Cheung, Sherman C P ^a   Yeoh, G H ^b   Tu, J Y ^a  

^a RMIT UNIVERSITY   (Australia)

^b AUSTRALIAN NUCLEAR SCIENCE AND TECHNOLOGY ORGANISATION   (Australia)

Author keywords

Average bubble number density; Bubbly flow; CFD; Population balance

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL METHODS; HEAT TRANSFER; MASS TRANSFER; TURBULENT FLOW; TWO PHASE FLOW;

AVERAGE BUBBLE NUMBER DENSITY; BUBBLE NUMBER; BUBBLE SIZE DISTRIBUTION; ISOTHERMAL CONDITIONS; LIQUID VELOCITIES;

BUBBLE COLUMNS;

BUBBLE COLUMNS; COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL METHODS; HEAT TRANSFER; MASS TRANSFER; TURBULENT FLOW; TWO PHASE FLOW;

EID: 34547472135     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2007.05.030     Document Type: Article

References (58)

1. ANSYS, 2005. CFX-10 User Manual. ANSYS CFX.
2. Antal S.P., Lahey Jr. R.T., and Flaherty J.E. Analysis of phase distribution in fully developed laminar bubbly two-phase flow. International Journal of Multiphase Flow 17 (1991) 635-652
3. Bertola, F., Grundseth, J., Hagesaether, L., Dorao, C., Luo, H., Hjarbo, K.W., Svendsen, H.F., Vanni, M.B., Jakobsen, H.A., 2003. Numerical analysis and experimental validation of bubble size distributions in two phase bubble column reactors. In: Proceedings of the Third European-Japanese Two Phase Flow Group Meeting, Certosa di Pontignano.
4. Bove S., Solberg T., and Hjertager B.H. A novel algorithm for solving population balance equations: the parallel parent and daughter classes. Derivation, analysis and testing. Chemical Engineering Science 60 (2005) 1449-1464
5. Bukur D.B., Daly J.G., and Patel S.A. Application of γ-ray attenuation for measurement of gas hold-ups and flow regime transitions in bubble columns. Industrial and Engineering Chemical Research 35 (1996) 70-80
6. Burns, A.D., Frank, T., Hamill, I., Shi, J., 2004. The Farve averaged drag model for turbulent dispersion in Eulerian multi-phase flows. In: Proceeding of the Fifth International Conference on Multiphase flow, Yokohama, Japan.
7. Chen P., Sanyal J., and Duduković M.P. Numerical simulation of bubble columns flows: effect of different breakup and coalescence closures. Chemical Engineering Science 60 (2005) 1085-1101
8. Chesters A.K., and Hoffman G. Bubble coalescence in pure liquids. Applied Scientific Research 38 (1982) 353-361
9. Cheung, S.C.P., Yeoh, G.H., Tu, J.Y., 2006. On the modelling of population balance in isothermal vertical bubbly flows-average bubble number density approach. Chemical Engineering Processing 46, 742-756.
10. Coulaloglou C.A., and Tavlarides L.L. Description of interaction processes in agitated liquid-liquid dispersions. Chemical Engineering Science 32 (1977) 1289
11. Drew D.A., and Lahey Jr. R.T. Application of general constitutive principles to the derivation of multidimensional two-phase flow equation. International Journal of Multiphase Flow 5 (1979) 243-264
12. Dorao C.A., and Jakobsen H.A. A least squares method for the solution of population balance problems. Computer and Chemical Engineering 30 (2006) 535-547
13. Dorao C.A., and Jakobsen H.A. Time-space-property least square spectral method for population balance problems. Chemical Engineering Science 62 (2007) 1323-1333
14. Frank, T., Shi, J., Burns, A.D., 2004. Validation of Eulerian multiphase flow models for nuclear safety application. In: Proceeding of the Third International Symposium on Two-Phase Modelling and Experimentation, Pisa, Italy.
15. Frank, T., Zwart, P.J., Shi, J., Krepper, E., Lucas, D., Rohde, U., 2005. Inhomogeneous MUSIG model-a population balance approach for polydispersed bubbly flow. In: Proceeding of International Conference for Nuclear Energy for New Europe, Bled, Slovenia.
16. Fu X.Y., and Ishii M. Two-group interfacial area transport in vertical air-water flow I. Mechanistic model. Nuclear Engineering and Design 219 (2002) 143-168
17. Fu X.Y., and Ishii M. Two-group interfacial area transport in vertical air-water flow II. Model evaluation. Nuclear Engineering and Design 219 (2002) 169-190
18. George, D.L., Shollenberger, K.A., Torczynski, J.R., 2000. Sparger effect on gas volume fraction distributions in vertical bubble-column flows as measured by gamma-densitometry tomography. In: ASME 2000 Fluid Engineering Division Summer Meeting, Boston, USA.
19. Hibiki T., and Ishii M. One-group interfacial area transport of bubbly flows in vertical round tubes. International Journal of Heat Mass Transfer 43 (2000) 2711-2726
20. Hibiki T., and Ishii M. Two-group interfacial area transport equations at bubbly-to-slug flow transition. Nuclear Engineering and Design 202 (2000) 39-76
21. Hibiki T., and Ishii M. Development of one-group interfacial area transport equation in bubbly flow systems. International Journal of Heat Mass Transfer 45 (2002) 2351-2372
22. Hibiki T., Ishii M., and Xiao Z. Axial interfacial area transport of vertical bubble flows. International Journal of Heat Mass Transfer 44 (2001) 1869-1888
23. Ho M.K., and Yeoh G.H. Phenomenological investigation of gas-liquid flows. Transaction of the American Nuclear Society 93 (2005) 408-409
24. Ishii M. Thermo-fluid Dynamic Theory of Two-phase Flow (1975), Eyrolles, Paris
25. Ishii M., and Zuber N. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. A.I.Ch.E. Journal 5 (1979) 843-855
26. Kocamustafaogullari G., and Ishii M. Foundation of the interfacial area transport equation and its closure relations. International Journal of Heat Mass Transfer 38 (1995) 481-493
27. Krepper E., Lucas D., and Prasser H. On the modelling of bubbly flow in vertical pipes. Nuclear Engineering and Design 235 (2005) 597-611
28. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretisation-I. A fixed pivot technique. Chemical Engineering Science 51 (1996) 1311-1332
29. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretisation-II. A moving pivot technique. Chemical Engineering Science 51 (1996) 1333-1342
30. Levich V.G. Physicochemical Hydrodynamics (1962), Prentice-Hall, Englewood Cliffs, NJ, USA
31. Liu T.J., and Bankoff S.G. Structure of air-water bubbly flow in a vertical pipe-I. Liquid mean velocity and turbulence measurements. International Journal of Heat Mass Transfer 36 (1993) 1049-1060
32. Liu T.J., and Bankoff S.G. Structure of air-water bubbly flow in a vertical pipe-II. Void fraction, bubble velocity and bubble size distribution. International Journal of Heat Mass Transfer 36 (1993) 1061-1072
33. Luo H., and Svendsen H. Theoretical model for drop and bubble break-up in turbulent dispersions. A.I.Ch.E. Journal 42 (1996) 1225-1233
34. Marchisio D.L., and Fox P.O. Solution of population balance equations using the direct quadrature method of moments. Journal of Aerosol Science 36 (2005) 43-73
35. Marchisio D.L., Vigil R.D., and Fox R.O. Quadrature method of moments for aggregation-breakage processes. Journal of Colloid and Interface Science 258 (2003) 322-334
36. Marchisio D.L., Pikturna J.T., Fox R.O., and Vigil R.D. Quadrature method for moments for population-balance equations. A.I.Ch.E. Journal 49 (2003) 1266-1276
37. Menter F.R. Two-equation eddy viscosity turbulence models for engineering applications. AIAA Journal 32 (1994) 1598-1605
38. Olmos E., Gentric C., Vial Ch., Wild G., and Midoux N. Numerical simulation of multiphase flow in bubble column. Influence of bubble coalescence and break-up. Chemical Engineering Science 56 (2001) 6359-6365
39. Oolman T., and Blanch H.W. Bubble coalescence in air-sparged bioreactor. Biotechnology and Bioengineering 28 (1986) 578-584
40. Oolman T., and Blanch H.W. Bubble coalescence stagnant liquids. Chemical Engineering Communications 43 (1986) 237-261
41. Pohorecki R., Moniuk W., Bielski P., and Zdrojkwoski A. Modelling of the coalescence/redisperison processes in bubble columns. Chemical Engineering Science 56 (2001) 6157-6164
42. Politano M.S., Carrica P.M., and Converti J. A model for turbulent polydisperse two-phase flow in vertical channels. International Journal of Multiphase Flow 29 (2003) 1153-1182
43. Prince M.J., and Blanch H.W. Bubble coalescence and break-up in air sparged bubble columns. A.I.Ch.E. Journal 36 (1990) 1485-1499
44. Ramkrishna D. Population Balance (2000), Academic Press, San Diego
45. Ramkrishna D., and Mahoney A.W. Population balance modeling. Promise for the future. Chemical Engineering Science 57 (2002) 595-606
46. Rotta, J.C., 1972. Turbulente Stromungen. B.G. Teubner, Stuttgart.
47. Sato Y., Sadatomi M., and Sekoguchi K. Momentum and heat transfer in two-phase bubbly flow-I. International Journal of Multiphase Flow 7 (1981) 167-178
48. Serizawa, A., Kataoka, I., 1988. Phase distribution in two-phase flow. In: Afgan, N.H. (Ed.), Transient Phenomena in Multiphase Flow. Washington, DC, pp. 179-224.
49. Serizawa A., and Kataoka I. Turbulence suppression in bubbly two-phase flow. Nuclear Engineering Design 122 (1990) 1-16
50. Sevik M., and Park S.H. The splitting of drops and bubbles by turbulent fluid flow. Journal of Fluid Engineering Transactions of ASME 95 (1973) 53-60
51. Taitel Y., Bornea D., and Dukler E.A. Modelling flow pattern transition for steady upward gas-liquid flow in vertical tubes. A.I.Ch.E. Journal 26 (1980) 345-354
52. Tomiyama, A., 1998. Struggle with computational bubble dynamics. In: Proceeding of the Third International Conference on Multiphase Flow. Lyon, France.
53. Wellek R.M., Agrawal A.K., and Skelland A.H.P. Shapes of liquid drops moving in liquid media. A.I.Ch.E. Journal 12 (1966) 854
54. Wu Q., Kim S., Ishii M., and Beus S.G. One-group interfacial area transport in vertical bubbly flow. International Journal of Heat Mass Transfer 41 (1998) 1103-1112
55. Yao W., and Morel C. Volumetric interfacial area prediction in upwards bubbly two-phase flow. International Journal of Heat Mass Transfer 47 (2004) 307-328
56. Yeoh G.H., and Tu J.Y. Population balance modelling for bubbly flows with heat and mass transfer. Chemical Engineering Science 59 (2004) 3125-3139
57. Yeoh G.H., and Tu J.Y. Thermal-hydrodynamic modelling of bubbly flows with heat and mass transfer. A.I.Ch.E. Journal 51 (2005) 8-27
58. Yeoh G.H., and Tu J.Y. Numerical modelling of bubbly flows with and without heat and mass transfer. Applied Mathematical Model 30 (2006) 1067-1095