In relation to the modeling of the interfacial transfer terms in the two-fluid model, the concept of the interfacial area transport equation has been proposed to develop a constitutive relation for the interfacial area concentration. The interfacial area transport equation can replace the traditional flow regime maps and regime transition criteria. The changes in the two-phase flow structure can be predicted mechanistically and the effects of the boundary conditions and flow development are efficiently modeled by this transport equation. A successful development of the interfacial area transport equation can make a significant improvement in the two-fluid model formulation and the prediction accuracy of three-dimensional two-phase flow simulations. In this paper, the basic concept of the interfacial area transport equation and its formulation have been briefly described. Available models of the interfacial area sink and source terms and existing databases have been reviewed and the interfacial area transport equation has been benchmarked using adiabatic bubbly flow and condensation bubbly flow data. Future direction for this research has been suggested.
BartelM. D.IshiiM.MasukawaT.MiY. and SituR., Interfacial area measurements in subcooled flow boiling, Nuc. Eng. Des., 210, 2001, 135–155.
2.
ChenJ. C., Correlation for boiling heat transfer to saturated fluids in convective flow, Ind. Eng. Chem. Proc. Des. Dev., 5, 1966, 322–329.
3.
FuX. Y. and IshiiM., Two-group interfacial area transport in vertical air-water flow. I. Mechanistic model, Nuc. Eng. Des., 210, 2003a, 143–168.
4.
FuX. Y. and IshiiM., Two-group interfacial area transport in vertical air-water flow. II. Model evaluation, Nuc. Eng. Des., 210, 2003b, 169–190.
5.
GrosseteteC., Caracterisation experimentale et simulations de l'evolution d'un ecoulement diphasique a bulles ascendant dans une conduit vertical, PhD Thesis, Ecole Centrale Paris, France, 1995.
6.
HazukuT.TakamasaT.HibikiT. and IshiiM., Interfacial area concentration in annular two-phase flow, Int. J. Heat Mass Transfer, 50, 2007, 2986–2995.
7.
HibikiT.HogsettS. and IshiiM., Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow, Nuc. Eng. Des., 184, 1998, 287–304.
8.
HibikiT. and IshiiM., Experimental study on interfacial area transport in bubbly two-phase flows, Int. J. Heat Mass Transfer, 42, 1999, 3019–3035.
9.
HibikiT. and IshiiM., One-group interfacial area transport of bubbly flows in vertical round tubes, Int. J. Heat Mass Transfer, 43, 2000a, 2711–2726.
10.
HibikiT. and IshiiM., Two-group interfacial area transport equations at bubbly-to-slug flow transition, Nuc. Eng. Des., 202, 2000b, 39–76.
11.
HibikiT.IshiiM. and XiaoZ., Axial interfacial area transport of vertical bubbly flows, Int. J. Heat Mass Transfer, 44, 2001a, 1869–1888.
12.
HibikiT.TakamasaT. and IshiiM., Interfacial area transport of bubbly flow in a small diameter pipe, J. Nuc. Sci. Tech., 38, 2001b, 614–620.
13.
HibikiT. and IshiiM., Interfacial area concentration of bubbly flow systems, Chem. Eng. Sci., 57, 2002a, 3967–3977.
14.
HibikiT. and IshiiM., Development of one-group interfacial area transport equation in bubbly flow systems, Int. J. Heat Mass Transfer, 45, 2002b, 2351–2372.
15.
HibikiT. and IshiiM., Active nucleation site density in boiling systems, Int. J. Heat Mass Transfer, 46, 2003, 2587–2601.
16.
HibikiT.GodaH.KimS. J.IshiiM. and UhleJ., Experimental study on interfacial area transport of a vertical downward bubbly flow, Exp. Fluids, 35, 2003a, 100–111.
17.
HibikiT.SituR.MiY. and IshiiM., Experimental study on interfacial area transport in vertical upward bubbly two-phase flow in an annulus, Int. J. Heat Mass Transfer, 46, 2003b, 427–441.
18.
HibikiT.SituR.MiY. and IshiiM., Modeling of bubble-layer thickness for formulation of one-dimensional interfacial area transport equation in subcooled boiling two-phase flow, Int. J. Heat Mass Transfer, 46, 2003c, 1409–1423.
19.
HibikiT.GodaH.KimS. J.IshiiM. and UhleJ., Axial development of interfacial structure of vertical downward bubbly flow, Int. J. Heat Mass Transfer, 48, 2005, 749–764.
20.
HibikiT.LeeT. H.LeeJ. Y. and IshiiM., Interfacial area concentration in boiling bubbly flow systems, Chem. Eng. Sci., 61, 2–006, 7979–7990.
21.
HibikiT. and IshiiM., Lift force in bubbly flow systems, Chem. Eng. Sci., 62, 2007, 6457–6474.
22.
HibikiT.HazukuT.TakamasaT. and IshiiM., Some characteristics of developing bubbly flow in a vertical mini pipe, Int. J. Heat Mass Transfer, 28, 2007, 1034–1048.
23.
IshiiM., Thermo-fluid Dynamic Theory of Two-Phase Flow, Eyrolles, 1975.
24.
IshiiM. and ZuberN., Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE J., 25, 1979, 843–855.
25.
IshiiM. and KimS. J., Development of one-group and two-group interfacial area transport equation, Nuc. Sci. Eng., 146, 2004, 257–273.
26.
IshiiM. and HibikiT., Thermo-fluid Dynamics of Two-Phase Flow, Springer, 2005.
27.
JeongJ. J.OzarB.DixitA.JuliaJ. E.HibikiT. and IshiiM., Interfacial area transport of vertical upward air-water two-phase flow in an annulus channel, Int. J. Heat Fluid flow, 29, 2008, 178–193.
28.
KataokaI.IshiiM. and SerizawaA., Local formulation and measurements of interfacial area concentration in two-phase flow, Int. J. Multiphase Flow, 12, 1986, 505–529.
29.
KimS. J.FuX. Y.WangX. and IshiiM., Development of the miniaturized four-sensor conductivity probe and the signal processing scheme, Int. J. Heat Mass Transfer, 43, 2000, 4101–4118.
30.
KimS.SunX. D.IshiiM.BeusS. G. and LincolnF., Interfacial area transport and evaluation of source and sink terms for confined air-water bubbly flow, Nuc. Eng. Des., 219, 2003, 61–75.
31.
KlausnerJ. F.MeiR.BernhardD. M. and ZengL. Z., Vapor bubble departure in forced convection boiling, Int. J. Heat Mass Transfer, 36, 1993, 651–662.
32.
KocamustafaogullariG. and IshiiM., Interfacial area and nucleation site density in boiling systems, Int. J. Heat Mass Transfer, 26, 1983, 1377–1387.
33.
KocamustafaogullariG. and IshiiM., Foundation of the interfacial area transport equation and its closure relations, Int. J. Heat Mass Transfer, 38, 1995, 481–493.
34.
LeeT. H.SituR.HibikiT.ParkH. S.IshiiM. and MoriM., Axial developments of interfacial area and void concentration profiles in subcooled boiling flow of water, Int. J. Heat Mass Transfer, 2008, (in press).
35.
ParkH. S.LeeT. H.HibikiT.BaekW. P. and IshiiM., Modeling of the condensation sink term in an interfacial area transport equation, Int. J. Heat Mass Transfer, 50, 2007, 5041–5053.
36.
RevankarS. T. and IshiiM., Local interfacial area measurement in bubbly flow, Int. J. Heat Mass Transfer, 35, 1992, 913–925.
37.
RevankarS. T. and IshiiM., Theory and measurement of local interfacial area using a four sensor probe in two-phase flow, Int. J. Heat Mass Transfer, 36, 1993, 2997–3007.
38.
RiznicJ. R. and IshiiM., Bubble number density and vapor generation in flashing flow, 32, 1989, 1821–1833.
39.
SituR.HibikiT.SunX. D.MiY. and IshiiM., Axial development of subcooled boiling flow in an internally heated annulus, Exp. Fluids, 37, 2004, 589–603.
40.
SituR.HibikiT.IshiiM. and MoriM., Bubble lift-off size in forced convective subcooled boiling flow, Int. J. Heat Mass Transfer, 48, 2005, 5536–5548.
41.
SituR.IshiiM.HibikiT.TuJ. Y.YeohG. H. and MoriM., Bubble departure frequency in forced convective subcooled boiling flow, Int. J. Heat Mass Transfer, 51, 2008, 6268–6282.
42.
SunX. D.SmithT. R.KimS. J.IshiiM. and UhleJ., Interfacial area of bubbly flow in a relatively large diameter pipe, Exp. Thermal Fluids Sci., 27, 2002, 97–109.
43.
SunX. D.IshiiM. and KellyJ. M., Modified two-fluid model for the two-group interfacial area transport equation, Annals Nuc. Eng., 30, 2003a, 1601–1622.
44.
SunX. D.SmithT. R.KimS. J.IshiiM. and UhleJ., Interfacial structure of air-water two-phase flow in a relatively large pipe, Exp. Fluids, 34, 2003b, 206–219.
45.
SunX. D.KimS. J.ChengL.IshiiM. and BeusS. G., Interfacial structures in confined cap-turbulent and churn-turbulent flows, Int. J. Heat Mass Transfer, 25, 2004a, 44–57.
46.
SunX. D.KimS. J.IshiiM. and BeusS. G., Modeling of bubble coalescence and disintegration in confined upward two-phase flow, Nuc. Eng. Des., 230, 2004b, 3–26.
47.
SunX. D.ParanjapeSIshiiM. and UhleJ., LDA measurement in air-water downward flow, Exp. Thermal Fluids Sci., 28, 2004c, 317–328.
48.
TakamasaT.IguchiT.HazukuT.HibikiT. and IshiiM., Interfacial area transport of bubbly flow under microgravity environment, Int. J. Multiphase Flow, 29, 2003a, 291–304.
49.
TakamasaT.GotoT.HibikiT. and IshiiM., Experimental study of interfacial area transport of bubbly flow in small-diameter tube, Int. J. Multiphase Flow, 29, 2003b, 395–409.
50.
TakamasaT.HazukuT.FukamachiN.TamuraN.HibikiT. and IshiiM., Effect of gravity on axial development of bubbly flow at low liquid Reynolds number, Exp. Fluids, 37, 2004, 631–644.
51.
VasavadaS.SunX. D.IshiiM. and DuvalW., Study of two-phase flows in reduced gravity using ground based experiments, Exp. Fluids, 43, 2007, 53–75.
52.
WuQ.KimS. J.IshiiM. and BeusS. G., One-group interfacial area transport in vertical bubbly flow, Int. J. Heat Mass Transfer, 41, 1998, 1103–1112.
53.
WuQ. and IshiiM., Sensitivity study on double-sensor conductivity probe for the measurement of interfacial area concentration in bubbly flow, Int. J. Multiphase Flow, 25, 1999, 155–173.
54.
ZeitounO. M., Subcooled flow boiling and condensation, PhD Thesis, McMaster University, Canada, 1994.
55.
ZuberN., The dynamics of vapor bubbles in nonuniform temperature fields, Int. J. Heat Mass Transfer, 2, 1961, 83–98.
