Bibliography [Alves et al. (2004)]S.S. Alves, S.P. Orvalho, J.M.T. Vasconcelos. Effect of bubble contamination on rise velocity and mass transfer. Department of Chemical Engineering, Instituto Superior Técnico, Centro de Eng. Biológica y Química, 1049-001 Lisboa, Portugal. 2004 [Ansys (2009)] Ansys, inc., Ansys cfx reference guide 12.0, 2009. [Ansys2(2009)]Ansys CFX,heat transfer validation report [Antal, Lahey et al. (2001)]Antal, S.P., Lahey, R.T., Flaherty, J.E. Analysis of Phase Distribution in Fully Developed Laminar Bubbly Two-Phase Flow, Int. Journal of Multiphase Flow, Vol 17, 635-652, 1991 [Auton (1987)]. Auton, T.R. The lift force on a spherical body in a rotational flow. Journal of Fluid Mechanics. 183 (1987) 199 218. [Azbel and Athanasios (1983)] D. Azbel, I.L. Athanasios, A mechanism of liquid entrainment, in: N. Cheremisinoff (Ed.), Handbook of Fluids in Motion, Ann Arbor Science Publishers, Ann Arbor, USA, 1983, p. 473. [Best Guidelines (2007)] Best Practice Guidelines for the use of CFD in Nuclear Reactor Safety Applications [Burns et al. (2004)]Burns, A.D., et al... The Favre averaged drag model for turbulence dispersion in Eulerian multi-phase flows. 5th Int. Conf. on Multiphase Flow, ICMF 2004, Yokohama, Japan. [Carrica et al. (1999)] Carrica, P. M., et al.. A polydispersed model for bubbly two-phase flow around a surface shipe. Int. J. Multiphase Flow, 25, pp.257-305, 1999 [Celata and Tomiyama (2001)] G.P. Celata, M. Cumo, F. D Annibale, A.Tomiyama (2001). Bubble Rising Velocity in Saturated Liquid up to Critical Pressure. Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics, pp. 1319-1328. [Chen et al. (2005)] Chen, P., Dudukovic, M.P., Sanyal, J., 2005. Three-dimensional simulation of bubble column flows with bubble coalescence and break-up. AIChE J. 51, 696 712. [Cheng (2006)]. Cheng, Simon, Alvin. Modeling particle distribution and deposition in indoor environments with a new drift flux model. Atmospheric Environment, 40 (2006) 357-367. [Cheung et al. (2007a)]. Sherman C.P. Cheung, G.H. Yeoh, J.Y. Tu, On the numerical study of isothermal vertical bubbly flow using two population balance approaches, Chemical Engineering Science, Volume 62, Issue 17, September 2007, Pages 4659-4674 [Cheung et al. (2007b)] Sherman, C.P. Cheung, G.H. Yeoh, J.Y. Tu, On the modeling of population balance in isothermal vertical bubbly flows Average bubble number density approach, Chemical Engineering and Processing: Process Intensification, Volume 46, Issue 8, August 2007, Pages 742-756 [Collier and Thome (1994)]Collier and Thome (1994). Convective Boiling and Condensation. Oxford University Press, Ney York. [Coulaloglou and Tavlaridès (1977)] C.A. Coulaloglou, L.L. Tavlaridès, Description of interaction processes in agitated liquid liquid dispersions, Chem. Eng. Sci. 32 (1977) 1289 1297. [Crowe et al. (1996)] Crowe, C. T., Troutt, T. & J.N.Chung 1996 Numerical models for twophase turbulent flows. Ann. Rev. Fluid Mech. 28, 11 43. CSANADY, G. 149
[Delhaye (2001)] J.M. Delhaye, Some issues related to the modeling of interfacial areas in gas liquid flows, Part II: modeling the source terms for dispersed flows, C.R. Acad. Sci. Paris, Ser. IIb t. 329 (2001) 473 486. [Descamps (2008)]. Descamps M.N., Oliemans R.V.A., Ooms G., Mudde R.F. Air-Water Flow in a Vertical Pipe: Experimental Study of Air Bubble in the Vicinity of the Wall. Experiments in Fluids. 45 (2008) 357-379. [Drew (2001)] Drew, D. A.. A turbulent dispersion model for particles or bubbles. J. of Engineering Drew, D. A.. A turbulent dispersion model for particles or bubbles. J. of Engineering Mathematics, 41, pp.259-274, 2001 [Drew and Lahey (1979)] D.A. Drew and R.T. Lahey Jr., Application of general constitutive principles to the derivation of multidimensional two-phase flow equation, International Journal of Multiphase Flow 5, 1979, pp. 243-264 [Drew(1987)]. Drew, D.A., Lahey Jr., R.T. The virtual mass and lift force on a sphere in rotating and straining inviscid flow. International Journal of Multiphase Flow. 13 (1987) 113 121. [Ervin and Tryggvason(1997)] Ervin, E.A., Tryggvason, G., 1997. The rise of bubbles in a vertical shear flow. J. Fluids Eng. 119, 443 449. [Frank et al. (2004)] Frank, Th., Shi, J. M. and Burns, A. D., Validation of Eulerian Multiphase Flow Models for Nuclear Safety Applications, 3rd International Symposium on Two- Phase Flow Modeling and Experimentation, Pisa, Italy, 22-24, Sept. 2004. [Frank et al.(2005)]frank, T., Zwart, P.J., Shi, J.-M., Krepper, E., Rohde, U., 2005. Inhomogeneous MUSIG Model a population balance approach for polydispersed bubbly flows. In: International Conference Nuclear Energy for New Europe 2005, Bled, Slovenia, September 5 8, 2005. [Frank et al.(2008)] Frank Th., Zwart P.J., Krepper E., Prasser H.-M., Lucas D., Validation of CFD models for mono- and polydispersed air water two-phase flows in pipes, Nuclear Engineering and Design 238 (2008) 647 659 [Gillard (2007)]. Guillar, Duval. A Darcy law for the drift velocity in a two phase flow model. Journal of Computational Physics. 224 (2007) 288-313. [Gosman (1992)] Gosman, A.D., et al.. Multidimensional modeling of turbulent two-phase flows in stirred vessels. AIChE Journal, 38, pp. 1946-1956, 1992 [Grace (1982)] Grace, H. P.. Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Chem. Eng.Commun., 14, pp.225-277, 1982 [Grace(1967)] Grace, D. Harrison (1967). The Influence of Bubble Shape on Rising Velocities of Large Bubbles. Chemical Engineering Science, Vol 22, pp. 1337-1347. [Grace, Clift et al(1978)] Grace J.R., Clift R., Weber M.E., Bubbles, Drops and Particles, Academic Press, 1978. [Hibiki and Ishii (1999)] One-group interfacial area transport of bubbly flows in vertical round tubes T. Hibiki, Research Reactor Institute, Kyoto University, Kumatori, Sennan, Osaka, M. Ishii, School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907-1290, USA(1999) [Hibiki2007]. Hibiki T., Ishii M. Lift force in bubbly flow systems. Chemical Engineering Science. 62 (2007) 6457 6474. [Ishii (1975)] M. Ishii, Thermo-fluid Dynamic Theory of Two-phase Flow, Eyrolles, Paris,1975 [Ishii (1990)] M. Ishii, Two-fluid model for two-phase flow, Multiphase Sci. Technol. 5 (1990) 1 58. 150
[Ishii and Chawla (1979)] Ishii, M. and Chawla, T. C., Local drag laws in dispersed two-phase flow. Technical report, ANL-79-105, Argonne National Laboratory, Chicago, 1979. [Ishii and Hibiki(2006)] Thermo-fluid dynamics of two phase flow. Mamom Ishii,School of Nuclear Engineering Purdue University ;Takashi Hibiki, Research Reactor Institute, Kyoto University(2006) [Ishii and Kim (2004)] Ishii, M. and Kim, S., (2004). Development of One group and Twogroup Interfacial Area Transport Equation, Nucl. Sci. Eng. 146: 257-273. [Ishii and Kim(2000)] Ishii,M.,Kim et al. Micro four-sensor probe measurement of interfacial area transport for bubbly flow in round pipes M. Ishii, S. Kim ; School of Nuclear Engineering, 1290 NE Purdue Uni6ersity, West Lafayette, (2000) [Ishii and Kojasoy (1993)] Ishii, M. and Kojasoy, G., Interfacial area transport equation and preliminary considerations for closure relations. Technical report, PU-NE-93/6, Nuclear Engineering Department, Purdue University, West Lafayette, IN, 1993. [Ishii and Mishima(1981)] Ishii, M., Mishima, K.. Study of two-fluid model and interfacial area, Argonne National Lab Report ANL-80-111, 1981 [Ishii and Zuber (1979)] Ishii, M., Zuber, N.. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J., 25, pp.843-855, 1979 [Ishii et al. (1998)] Ishii, M. Mishima.K et al.. Interfacial area transport equation for two-fluid model formulation. Proceedings of IMuST Meeting, Santa Barbara, pp.35-42, 1998 [Ishii et al.(2002)] Ishii, M., Kim, S., and Uhle, J., 2002. Interfacial area transport equation: model development and benchmark experiments. International Journal of Heat and Mass Transfer 45(15), 3111-3123. [John R. Thome(2007)] John R. Thome, Professor (2004-2010). Wolverine tube Inc. Engineering data book III. Faculty of Engineering Science and Technology Swiss Federal Institute of Technology Lausanne (EPFL). [Jones et al. (2003)]Jones, I.P., Guilbert, P.W., Owens, M.P., Hamill, I.S., Montavon, C.A., Penrose, J.M.T., Prast, B., 2003. The use of coupled solvers for complex multi-phase and reacting flows. In: Third International Conference on CFD in the Minerals and Process Industries, CSIRO, Melbourne, Australia, 10 12 December. [Kataoka and Sherizawa(1997)] Kataoka, I., Serizawa, A., 1997. Turbulence characteristics and their application to multi-dimensional analysis of two-phase flow. Proceedings of the 8th International TopicalMeeting onnuclear Reactor Thermal-Hydraulics,Kyoto, Japan, Vol. 3, 1677 1683. [Kawamura et al(2002)] Kawamura, T., Kodama, Y.. Numerical simulation method to resolve interactions between bubbles and turbulence. International Journal of Heat and Fluid Flow, 23, pp.627-638, 2002 [Kim et al.(1987)] W.K. Kim, K.L. Lee, Coalescence behavior of two bubbles in stagnant liquids, J. Chem. Eng., Jpn. 20 (1987) 449. [Kim(1999)]. S. Kim. Interfacial Area Transport Equation and Measurement of local interfacial Characteristics. PhD Thesis, Purdue University, West Lafayette, IN, USA. (1999). [Kirkpatrick and Lockett(1974)] R.D. Kirkpatrick, M.J. Lockett, The influence of approach velocity on bubble coalescence, Chem. Eng. Sci. 29 (1974) 2363. [Kocamustafaogullari and Ishii (1983)] G. Kocamustafaogullari, M. Ishii, Interfacial area and nucleation site density in boiling systems, Int. J. Heat Mass Transfer 26 (9) (1983) 1377 1387. [Kocamustafaogullari et al (1995)] Kocamustafaogullari, G., Ishii, M.. Foundation of the interfacial area transport equation and its closure relations. International Journal of Heat and Mass Transfer, 38, pp.481-493, 1995 151
[Kolmogorov (1949)] A.N. Kolmogorov, On the disintegration of drops in a turbulent flow, Doklady Akad. Nauk., SSSR 66 (1949) 825. [Krepper et al.(2007)] Krepper E., Končar B., Egorov Y., CFD modeling of subcooled boiling Concept, validation and application to fuel assembly design,nuclear Engineering and Design 237 (2007) 716 731 [Krepper et al.(2008)] Krepper, E., Frank, Th., Lucas, D., Prasser, H.-M., Zwart, P.J., 2008. The Inhomogeneous MUSIG model for the simulation of polydispersed flows. Nucl. Eng. Des. 238, 1690 1702. [Krepper, Lucas et al.(2005)] E. Krepper, Lucas D., Prasser H.-M., On the modeling of bubbly flow in vertical pipes, Nuclear Engineering and Design 235 (2005) 597 611 [Lahey(1993)]. Lahey, R.T., Lopez de Bertodano, M., Jones, O.C. Phase distribution in complex geometry conduits. Nuclear Engineering and Design 141 (1993) 177 201. [Legendre and Magnaudet (1998)]Legendre, D. and Magnaudet, J., The lift force on a spherical bubble in a viscous linear shear flow, J. Fluid Mech., 368, pp. 81 126, 1998. [Liao et al(2010)] Development of a generalized coalescence and breakup closure for the inhomogeneous MUSIG model Yixiang Liao, Dirk Lucas, Eckhard Krepper, Martin Schmidtke Forschungszentrum Dresden-Rossendorf e.v., Institute of Safety Research, Dresden, Germany [Lo (1996)] Lo, S.M., 1996. Application of the MUSIG model to bubbly flows, AEAT-1096, AEA Technology. [Loeb (1927)] L.B. Loeb, The Kinetic Theory of Gases, Dover, New York, USA, 1927. [Lopez de Bertodano (1991)] Lopez de Bertodano, M., Turbulent Bubbly Flow in a Triangular Duct, Ph. D. Thesis, Rensselaer Polytechnic Institute, Troy New York, 1991 [Lopez de Bertodano (1998)] Lopez de Bertodano, M., Two Fluid Model for Two-Phase Turbulent Jet, Nucl. Eng. Des. 179, 65-74, 1998. [Lopez et al.(2010)] CFD Two Fluid Model for Adiabatic and Boiling Bubbly Flows in Ducts. Martin Lopez de Bertodano and Deoras Prabhudharwadkar; School of Nuclear Engineering, Purdue University(2010) [Lucas and Krepper (2007)] Lucas, D., Krepper, E., Prasser, H.-M., 2007. Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows. Chem. Sci. Eng. 62, 4146 4157. [Lucas et al. (2001a)] Lucas, D., et al.. Prediction of radial gas profiles in vertical pipe flow on the basis of bubble size distribution. International Journal of Thermal Sciences, 40, pp.217-225, 2001a [Lucas et al.(2004)] Lucas, D., Shi, J.-M., Krepper, E., Prasser, H.-M., Models for the forces acting on bubbles in comparison with experimental data for vertical pipe flow. In: 3 rd International Symposium on Two-Phase Flow Modeling and Experimentation, Pisa, Italy, 2004. [Lucas et al.(2011)] D.Lucas,A.Tomiyama.On the role of the lateral lift force in polydisperse bubbly flow(2011) [Lucas(2005)] Lucas, D., Krepper, E. Prasser, H.-M.,. Development of co-current air-water flow in a vertical pipe. International Journal of Multiphase Flow. 31 (2005) 1304 1328. [Lucas,Krepper et al.(2001b)]lucas, D., Krepper, E., Prasser, H.M., 2001. Modeling of radial gas fraction profiles for bubble flow in vertical pipes. In: Ninth International Conference on Nuclear Engineering (ICONE-9), Nice, France, April 2001. [Lunde and Perkins(1998)] Lunde, K., Perkins, R., 1998. Shape oscillations of rising bubbles. Appl. Sci. Res. 58, 387 408. 152
[Luo and Svendsen(1996)] Luo, H., Svendsen, H.F., 1996. Theoretical model for drop and bubble break-up in turbulent flows. AIChE J. 42 (5), 1225 1233 [Magnaudet and Eames(2000)]Magnaudet, J., Eames, I., 2000. The motion of high-reynoldsnumber bubbles in inhomogeneous flows. Ann. Rev. Fluid Mech. 32, 659 708. [Martinez Bazan1999a]. C. Martinez-Bazan, J. L. Montanes, J. C. Lasheras. On the breakup o fan air bubble injected into a fully developed turbulent flow. Part 1: Breakup frecuency. Journal of Fluids Mechanics 401 (1999) 157-182. [Menter (1994)] Menter, F., 1994. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32. [Moraga et al. (2003)] Moraga, J.F., Larreteguy, A.E., Drew, D.A., and Lahey, R.T., Assessment of turbulent dispersion models for bubbly flows in the low Stokes number limit, Int. J. Multiphase Flow, 29, p. 655, 2003. [Moraga(1999)]. F. J. Moraga, F. J. Bonetto, R. T. Lahey. Lateral forces on spheres in turbulent uniform shear flow. International Journal of Multiphase Flow, 25, Issues 6-7, 11, pp 1321-1372, 1999 [Mougin(2002)]. Mouigin, G., Magnaudet J. The generalized Kirchoff Equations and their Aplication to the Interaction between a Rigid Body and an Arbitrary Time Dependent Viscous Flow. Int. J. Multiphase Flow, 28, pp 1837-1851, 2002 [Otake et al.(1977)] T. Otake, S. Tone, K. Nakao, Y. Mitsuhashi, Coalescence and breakup of bubbles in liquids, Chem. Eng. Sci. 32 (1977) 377 383. [Pfleger and Becker(2001)] Pfleger, D., Becker, S.. Modeling and Simulation of the Dynamic Flow Behaviour in a Bubble Column. Chem. Eng. Sci., 56, pp.1737-1747, 2001 [Politano et al (2003)] Politano, M. S., et al.. A Model for Turbulent Polydisperse Two-Phase Flow in Vertical Channels. Int. J. Multiphase Flow, 29, pp.1153-1182, 2003 [Prabhudharwakar et al(2009)]d. Prabhudharwadkar, C Bailey, M. L. de Bertodano, J. R. Buchanan Jr.,Two-fluid cfd model of adiabatic air-water upward bubbly flow Through a vertical pipe with a one-group interfacial area transport equation, FEDSM2009, August 2 6, 2009, Vail, Colorado, USA [Prasser et al. (2007)] Prasser, H.-M., Beyer, M., Carl, H., Gregor, S., Lucas, D., Pietruske, H., Schutz, P.,Weiss, F.-P., 2007. Evolution of the structure of a gas liquid two-phase flow in a large vertical pipe. Nucl. Eng. Des. 237, 1848 1861. [Prasser(2002)] Prasser, H.-M., Krepper, E., Lucas, D. Evolution of the two-phase flow in a vertical tube-decomposition of gas fraction profiles according to bubble size classes using wire-mesh sensors. International Journal of Thermal Science. 41 (2002) 17 28. [Prasser(2008)]. H. M. Prasser. Novel experimental measuring techniques required to provide data for cfd validation. Nuclear Engineering and Design 238 (2008) 744-770. [Prince and Blanch(1990)] Prince, M.J., Blanch, H.W., 1990. Bubble coalescence and break-up in air-sparged bubble columns. AIChE J. 36 (10), 1485 1499. [R.Clift(1978)] R. Clift, J.R. Grace, M.E. Weber (1978). Bubbles, Drops, and Particles. Academic Press, London. [Risso(2000)] F. Risso, The mechanisms of deformation and breakup of drops and bubbles, Multiphase Sci. Technol. 12(2000) 1 50. [Santos Méndez (2008)] Santos Méndez Díaz,2008,Medida experimental de la concentración del área interfacial en flujos bifásicos finamente dispersos y en transición.programa Doctoral en Tecnología Energética.Universidad Politénica de Valencia [Sari et al.(2009)]s.sarı, S. Ergün, M. Barık, C. Kocar, C. N. Sokmen Modeling of isothermal bubbly flow with interfacial area transport equation and bubble number density approach, Annals of Nuclear Energy 36 (2009) 222 232 153
[Sato et al. (1975)] Sato, Y., Sekoguchi, K., 1975. Liquid velocity distribution in two phase bubble flow. Int. J. Multiphase Flow 2, 79 95. [Sato et al. (1981)] Sato, Y., et al.. Momentum and heat transfer in two-phase bubble flow. International Journal of Multiphase Flow, 7, pp.167-177, 1981 [Schiller and Naumann (1933)]Schiller, L., Naumann, A. Über die grundlegenden Berechungen beider Schwerkraftaufbereitung. Duetscher Ingenieure, 77, pp.318, 1933 [Serizawa(1994)]. Serizawa, A., Kataoka, I. Dispersed flow I. Multiphase Science and Technology, vol. 8. Begell House Inc., New York. pp. 125 194, 1994. [Serzawa(1988)]. Serizawa, A., Kataoka, I. Phase Distribution in Twophase Flow. Transient Phenomena in Multiphase Flow. Hemisphere, Washington, DC. pp. pp. 179 224. 1988. [Shi et al.(2004)]shi, J.-M., Zwart, P.-J., Frank, T., Rohde U., Prasser, H.-M, 2004. Development of a multiple velocity multiple size group model for poly-dispersed multiphase flows. Annual Report of Institute of Safety Research. Forschungszentrum Rossendorf, Germany. [Stewart (1995)] C.W. Stewart, Bubble interaction in low-viscosity liquids, Int. J. Multiphase Flow 21 (6) (1995) 1037 1046. [Taitel et al.(1980)] Y. Taitel, D. Bornea, A.E. Dukler, Modeling flow pattern transitions for steady upward gas-liquid flow in vertical tubes, AIChE Journal 26 (1980) 345-354 [Tomiyama (2001)]Terminal velocity of single bubbles in surface tension force dominant regime Tomiyama, G.P. Celata, S. Hosokawa, S. Yoshida [Tomiyama and Shimada (1998)] Tomiyama, A., Shimada, N., 1998. Numerical simulations of bubble columns using a 3D multi-fluid model. In: Third International Conference Multiphase Flow ICMF 98, Lyon, France, June 8 12. [Tomiyama et al. (1995)] Tomiyama, A., Sou, I., Zun, I., Kanami, N., Sakaguchi, T., 1995. Effects of Eotvos number and dimensionless liquid volumetric flux on lateral motion of a bubble in a laminar duct flow. Adv. Multiphase Flow, 3 15. [Tomiyama et al.(1998a)] Tomiyama, A., et al.. Drag coefficients of single bubbles under normal and micro gravity conditions.. JSME International Journal, Series B, 41, pp.472-479, 1998a [Tomiyama et al.(1998b)] Tomiyama, A., 1998. Struggle with computational bubble dynamics. In: ICMF 98, 3rd Int. Conf. Multiphase Flow, Lyon, France, June 8 12, 1998, pp. 1 18. [Tomiyama(2002)]. Tomiyama, A., Tamai, H., Zun, I., Hosokawa, S.,. Transverse migration of single bubbles in simple shear flows. Chemical Engineering Science. 57 (2002) 1849 1858. [Tomiyama(2004)]. Tomiyama A. Drag, Lift and Virtual Mass Forces Acting on a Sigle Bubble. 3rd International Symposium on Two-Phase Flow Modeling and Experimentation, Pisa, 2004 [Troshko et al.(2001)] Troshko, A. A., Hassan, Y. A.. A Two-Equation Model of Turbulent Bubbly Flows. Int. J. Multiphase Flow, 27, pp.1965-2000, 2001 [Uhle et al. (1998)]Uhle, J. et al. Dynamic flow regime modeling. Proceedings of 6th International Conference on Nuclear Engineering, ICONE 6, San Diego, California, May 10-15, 1998 [Wallis (1969)] Wallis, G. B., One-dimensional Two-phase Flow. McGraw-Hill, New York, 1969. [Wang (2010)] Wang.Dissertation for the Degree Doctor in the Graduate School of The Ohio State University By Xia Wang Graduate Program in Nuclear Engineering The Ohio State University;2010 154
[Wang et al.(2003)]wang, T., Wang, J., Jin, Y., 2003. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chem. Eng. Sci. 58, 4629 4637. [Wellek et al. (1966)] Wellek, R.M., Agrawal, A.K., Skelland, A.H.P., 1966. Shapes of liquid drops moving in liquid media. AIChE J. 12, 854 860. [Wieringa et al(1996)] Wieringa, J. A., et al.. Droplet breakup mechanisms during emulsification in colloid mills at high dispersed phase volume fraction. Trans. Inst. Chem. Eng., 74-!, pp.554-562, 1996 [Wilcox(1998)] D.C. Wilcox. Turbulence modeling for CFD. DCW Industries Inc., 1998. [Wörner et al.(2004)] Wörner,M., Ghidersa, B.E., Ili c, M., Cacuci, D.G., 2004. Volume-offluidmethod based numerical simulations of gas-liquid two phase flow in confined geometries, Advances in the modeling methodologies of two-phase flows, Lyons, France, November 24 26, paper no. 04. [Wu et al.(1997)] One-group interfacial area transport in vertical bubbly flow Q. Wu, S. Kim and M. Ishii Thermal Hydraulics and Reactor Safety Laboratory, Purdue University,, and S. G. BEUS Bettis Atomic Power Laboratory, Westinghouse Electric Corporation, [Wu et al.(1998b)] Wu, Q. et al. Framework of two-group model for interfacial area transport in vertical two-phase flows. Transactions of the American Nuclear Society, 79, pp. 351 352, 1998b [Wu et al.(2002)]s Kim, M Ishii, Q Wu, D McCreary, S.G Beus, Interfacial structures of confined air water two-phase bubbly flow, Experimental Thermal and Fluid Science, Volume 26, Issue 5 [Yao and Morel(2004)]Yao, W., Morel, C.. Volumetric Interfacial Area Prediction in Upward Bubbly Two- Phase Flow. International Journal of Heat and Mass Transfer, 47, pp.307 328, 2003 [Zaruba(2007)]. Zaruba A., Lucas D., Prasser H., Hohne T. Bubble-wall interactions in a vertical gas liquid flow: Bouncing, sliding and bubble deformations. Chemical Engineering Science. 62 (2007) 1591 1605. [Zhang et al(2001)]zhang, Y., Finch, J., 2001. A note on single bubble motion in surfactant solutions. J. Fluid Mech. 429, 63 66. [Zuber(1965)]. N. Zuber, J. A. Findlay. Average volumetric concentration in two-phase flow systems. J. Heat Trans. 87 (1965) 453. [Zwart et al.(2003)] Zwart, P., Burns,A.,Montavon, C., 2003. Multiple size group models. TechnicalReport. AEA Technology plc, November, 2003. CFX-5.7 155
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