Modeling strategy of the source and sink terms in the two-group interfacial area transport equation

Annals of Nuclear Energy

Volumn 30, Issue 13, 2003, Pages 1309-1331

  Ishii, Mamoru ^a   Sun, Xiaodong ^a   Kim, Seungjin ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BUBBLES (IN FLUIDS); COALESCENCE; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; TURBULENCE; TURBULENT FLOW;

TWO-PHASE FLOW;

HEAT SINKS;

GASTROPODA;

EID: 0038237516     PISSN: 03064549     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0306-4549(03)00075-6     Document Type: Article

References (44)

1. Batchelor G.K. Pressure fluctuation in isotropic turbulence. Proc. Cambridge Phil. Soc. 47:1951;359-371.
2. Calderbank, P.H., Moo-Young, M.B., Bibbly, R. 1964. Coalescence in bubble reactors and absorbers. Proc. Euro. Symp. On Chem. Reaction Eng., 91.
3. Chatzi E., Lee J.M. Analysis of interactions for liquid-liquid dispersions in agitated vessels. Ind. Eng. Chem. Res. 26:1987;2263-2267.
4. Clift R., Grace J.R., Weber M.E. Bubbles, Drops, and Particles. 1978;Academic Press, New York.
5. Coulaloglou C.A., Tavlarides L.L. Description of interaction processes in agitated liquid-liquid dispersions. Chem. Eng. Sci. 32:1977;1289-1297.
6. Crabtree J.R., Bridgwater J. Bubble coalescence in viscous liquids. Chem. Eng. Sci. 26:1971;839-851.
7. de Nevers N., Wu J.L. Bubble coalescence in viscous fluids. AIChE J. 17:1971;182-186.
8. Grand, D. 1997. Thermal-hydraulic modeling requirements for next generation reactor safety analysis codes. In: Eltawila, F., Ishii, M. (Eds.), Proc. of the OECD/CSNI Specialist Meeting on Advanced Instrumentation and Measurement Techniques, NUREG/CP-0160. Santa Barbara, pp. 31-41.
9. Hamaguchi, H., Sakaguchi, T. 1996. Velocity of a large bubble in a moving liquid in a vertical tube. Proc. US-Japan Seminar, Fukuoka, Japan.
10. Hibiki T., Ishii M. One-group interfacial area transport of bubbly flows in vertical round tubes. Int. J. Heat Mass Transfer. 43(15):2000;2711-2726.
11. Hinze J.O. Fundamentals of the hydrodynamics of mechanics of splitting in dispersion process. AIChE J. 1(3):1955;289-295.
12. Howarth W.J. Coalescence of drops in a turbulent flow field. Chem. Eng. Sci. 19:1964;33-38.
13. Ishii M. Thermo-fluid Dynamic Theory of Two-phase Flow. 1975;Eyrolles, Paris.
14. Ishii, M., Kim, S. 2003. Development of one-group and two-group interfacial area transport equation. Nucl. Sci. Eng. (in preparation).
15. Ishii, M., Kojasoy, G. 1993. Interfacial Area Transport Equation and Preliminary Considerations on Closure Relations. PU/NE-93-6, Purdue University, West Lafayette, IN, USA.
16. Kelly, J.M., 1997. Constitutive model development needs for reactor safety thermal-hydraulic codes. In: Eltawila, F., Ishii, M. (Eds.), Proc. of the OECD/CSNI Specialist Meeting on Advanced Instrumentation and Measurement Techniques, NUREG/CP-0160. Santa Barbara, pp. 3-29.
17. Kim, S. 1999. Interfacial Area Transport Equation and Measurement of Local Interfacial Characteristics. PhD thesis, Purdue University, West Lafayette, IN, USA.
18. Kim W.K., Lee K.L. Coalescence behavior of two bubbles in stagnant liquids. J. Chem. Eng. Japan. 20:1987;449.
19. Kirkpatrick R.D., Lockett M.J. The influence of approach velocity on bubble coalescence. Chem. Eng. Sci. 29(12):1974;2363-2373.
20. Kocamustafaogullari G., Ishii M. Foundation of the interfacial area transport equation and its closure relations. Int. J. Heat Mass Transfer. 38(3):1995;481-493.
21. Kocamustafaogullari, G., Chen, I.Y, Ishii, M. 1984. Unified Theory for Predicting Maximum Fluid Particle Size for Drops and Bubbles. NUREG/CR-4028.
22. Kolmogorov, N. 1949. On the disintegration of drops in a turbulent flow. Doklady Akad. Nauk., SSSR 66, 825.
23. Lafi, A.Y., Reyes Jr., J.N. 1991. Phenomenological Models for Fluid Particle Coalescence and Breakage. OSU-NE-9120, Oregon State University, Corvallis, OR, USA.
24. Marrucci G. A theory of coalescence. Chem. Eng. Sci. 24:1969;975.
25. 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;157-182.
26. 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 of the resulting daughter bubbles. J. Fluid Mech. 401:1999;183-207.
27. Millies M., Drew D.A., Lahey R.T. Jr. A first order relaxation model for the prediction of the local interfacial area density in two-phase flows. Int. J. Multiphase Flow. 22(6):1996;1073-1104.
28. Morel C., Goreaud N., Delhaye J.-M. The local volumetric interfacial area transport equation: derivation and physical significance. Int. J. Multiphase Flow. 25(6-7):1999;1099-1128.
29. Otake T., Tone S., Nakao K., Mitsuhashi Y. Coalescence and breakup of bubbles in liquid. Chem. Eng. Sci. 32:1977;377-383.
30. Prince M.J., Blanch H.W. Bubble coalescence and break-up in air-sparged bubble columns. AIChE J. 36(10):1990;1485-1499.
31. Reyes, J.N. 1989. Statistically derived conservation equations for fluid particle flows. Proc. of ANS-THD, Vol. 5, ANS Winter Meeting, San Francisco, CA, pp. 12-19.
32. Reyleigh Lord On the instability of jets. Lond. Math. Soc. Proc. 10(4):1878;4-18.
33. Riznic J.R., Ishii M. Bubble number density and vapor generation in flashing flow. Int. J. Heat Mass Transfer. 32(10):1989;1821-1833.
34. Ross S.L., Verhoff F.H., Curl R.L. Droplet breakage and coalescence processes in an agitated dispersion: II. Measurement and interpretation of mixing experiments. Ind. and Eng. Chem. Fund. 17(2):1978;101-108.
35. Sevik M., Park S.H. The splitting of drops and bubbles by turbulent fluid flow. J. Fluids Eng. 95(1):1973;53-60.
36. Städtke, H., 1996. Thermal-hydraulic codes for LWR safety analysis - present status and future perspective. In: Ebert, D. (Ed.), Proc. of OECD/CSNI Workshop on Transient Thermal-hydraulic and Neutronic Codes Requirements, NUREG/CP-0159. Annapolis, Maryland, pp. 732-750.
37. Stewart C.W. Bubble interaction in low-viscosity liquids. Int. J. Multiphase Flow. 21(6):1995;1037-1046.
38. Sun, X. 2001. Two-group Interfacial Area Transport Equation for a Confined Test Section. PhD thesis, Purdue University, West Lafayette, IN, USA.
39. Tsuchiya K., Miyahara T., Fan L.S. Visualization of bubble-wake interactions for a stream of bubbles in a two-dimensional liquid-solid fluidized bed. Int. J. Multiphase Flow. 15(1):1989;35-49.
40. Tsuchiya K., Shsaki K., Taguchi K. Large and small bubble interaction pattern in a bubble column. Int. J. Multiphase Flow. 22(1):1996;121-132.
41. Valentas K.J., Amundson N.R. Breakage and coalescence in dispersed phase systems. Ind. and Eng. Chem. Fund. 5:1966;533.
42. Vernier P., Delhaye J.-M. General two-phase flow equations applied to the thermohydrodynamics of boiling nuclear reactors. Energie Primaire. 4(1):1968;3-43.
43. Wu Q., Ishii M., Uhle J. Framework of two-group model for interfacial area transport in vertical two-phase flows. Trans. of ANS. 79:1998;351-352.
44. Wu Q., Kim S., Ishii M., Beus S.G. One-group interfacial area transport in vertical bubbly flow. Int. J. Heat Mass Transfer. 41(8-9):1998;1103-1112.