Entrainment at T-junction: A review work

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Progress in Nuclear Energy 70 (2014) 221e241

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Progress in Nuclear Energy

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Review

Entrainment at T-junction: A review work

Zhaoming Meng, Laishun Wang, Wenxi Tian*, Suizheng Qiu, Guanghui SuSchool of Nuclear Science and Technology, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, No. 28, Xianning WestRoad, Xi’an 710049, China

a r t i c l e i n f o

Article history:Received 15 March 2013Received in revised form31 August 2013Accepted 7 October 2013

Keywords:T-junctionEntrainment phenomenaOnset entrainmentBranch qualityScaling analysis

* Corresponding author. Tel./fax: þ86 (0)29 826634E-mail addresses: mengzhaoming1987511@126

mail.xjtu.edu.cn (W. Tian).

0149-1970/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.pnucene.2013.10.005

a b s t r a c t

The T-junctions are widely used in industry, such as the joint between hot leg and Automatic Depres-surization System Stage Four (ADS-4)/Passive Residual Heat Removal (PRHR)/surge pipeline in AP1000plant, header-feeder geometry of CANDU reactor, complex piping systems in the water and petroleumprocessing and so on. In the nuclear plant accident analysis, the T-junction entrainment is fairly closelylinked with the water volume of reactor and reactor safety. Many researchers have conducted theexperimental and theoretical research on the generation process, mechanism, influencing factors andmodeling of entrainment. Research directions of entrainment at T-junction are multifarious, so a reviewwork is necessary. This paper describes a comprehensive literature review of entrainment at T-junction.Based on different geometric structures of T-junction, detailed summarizations and reviews on thepresent entrainment phenomena, entrainment models and scaling analysis are performed. Conclusionsand further research directions on entrainment at T-junction are proposed.

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1. Introduction

The T-junctions consisting of one or more branches mounted ona main pipe are widely used in industry, such as the joint betweenhot leg and Automatic Depressurization System Stage Four (ADS-4)/Passive Residual Heat Removal (PRHR)/surge pipeline in AP1000plant (Lin, 2008a,b), header-feeder geometry of CANDU reactor(Kowalski et al., 1989) and complex piping systems in thewater andpetroleum processing. Also, the T-junction can consist of the breakand the hot/cold leg during Loss of Coolant Accident (LOCA) innuclear power plants. Two-phase flow phenomena may occur inhorizontal pipes during LOCA, the liquid and vapor entrainmentphenomena at T-junction included (Zuber, 1980). Liquid entrain-ment relates to the water volume of reactor and reactor coreuncovering during LOCA. Gas entrainment may lead to ResidualHeat Removal pump failure in Pressurized Water Reactor (PWR).Also, entrainment phenomenonmay even affect evaluation of someother phenomena (Guide, 1989). Thus, entrainment at T-junction isvery significant.

In RELAP5/CATHARE code, the current entrainment model isable to be treated only 3 branch directions: bottom, top, and sidebranches, and be applied only to a single branch whose diameter is

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far smaller than the diameter of the main pipe (Division, 2001;Maciaszek and Micaelli, 1990). Also, no prevailing model is suit-able for simulations of entrainment through any angled branch andmultiple branches located in a main pipe so far, like entrainmentsimulation of header-feeder system of CANDU reactor during LOCA(Cho et al., 2010; Chung et al., 2010). In Advanced Plant Experimenttest facility, RELAP5 simulation failure to predict core uncoveringwas attributed to inappropriate and inaccurate liquid entrainmentcorrelations (Reyes et al., 1999). A RELAP5-3D simulation of a VVERplant for a Small Break Loss of Coolant Accident (SB-LOCA) achievesan incorrect result due to inappropriate vapor/gas entrainmentmodel (Riemke et al., 2006). Thus research of entrainment at T-junction is quite remarkable and incomplete.

T-junctions all consist of a horizontal main pipe and single ormultiple branches in entrainment research. But different branch an-gles and branch geometric shapesmake the structure of T-junction inentrainment research diversity. Also, flow regime in the main pipe ismostly stratified flow for research of entrainment at T-junction, butthere are other flow regimes (e.g. wavy flow and slug flow) whichhave been also included in this article. But research of some flow re-gimes (Azzopardi,1999;Wren and Azzopardi, 2004) approaching theT-junction mainly focuses on phase separation capabilities andpressure drops for the design of separators, which do not match thispaper topic and not reviewed in the paper. In addition, research di-rections of entrainment at T-junction are comprehensive and abun-dant. Effects of various influencing factors on entrainment areimportant besides the studies of basic entrainment phenomena and

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mechanism, such as effect of crossflow, geometry, variousparametersand so on. Modeling studies of onset entrainment and stableentrainment at T-junction have been ongoing for decades, but theystill have some demerits. In a word, research directions of entrain-ment at T-junction are multifarious and have different emphasispoints and analysis angles, a review work on the entrainment at T-junction is necessary. Hence, this paper presents a comprehensiveliterature review of liquid entrainment and gas entrainment at T-junction. Based on different geometry shapes of T-junction, thedetailed summarizations and reviews on the present entrainmentphenomena, modeling of the beginning/onset of entrainment (b.e./OE) and branch quality and scaling analysis are performed. Theobjective is to gain a comprehensive understanding, realize shortagesof studies and propose future work.

2. Entrainment phenomena

Based on the different geometry structures of T-junction, reviewof entrainment phenomena is divided into five sub-problems:bottom branch, top branch, side branch, arbitrary orientationbranch and multiple branches. Firstly, in each sub-problem, thebasic entrainment mechanism is first summarized to make us acomprehensive grasp and will definitely help us understand thefurther discussions. Secondly mainly research direction of eachsub-problem is introduced: Similar viewpoints are integrated as awhole, while different viewpoints are compared. Discrete researchconclusions are summarized to highlight a unified body of principalresearch concerns. Thirdly, comments on each sub-problem aremade: The shortage and future work is pointed out. It is worthmentioning that research of basic influencing factors are unnec-essary to go into details in this section, such as effects of pressure,branch diameter and flow rate, since entrainment models in Sec-tions 3 and 4 can reflect effects of the above variable.

2.1. Bottom branch

When two-phase flow approaches T-junction, entrainment maynot generate until certain conditions are met. For sufficiently smalldistance h between two-phase interface and branch entrance (or asincreased branch liquid mass flowW3L), the beginning/onset of gasentrainment (b.g.e./OGE) can occur, and then the interface level islowered still further (or W3L is increased further), a continuous/stable gas entrainment occur (Bowden and Hassan, 2011; Reimannand Khan, 1984; Smoglie and Reimann, 1986; Smoglie et al., 1987;Yonomoto and Tasaka, 1991). Hence, the basic entrainment

Fig. 1. Development of vortex gas entrainment at a bot

mechanism is clear, and neural network could predict it success-fully (Liang et al., 2008).

Two types of flow structure may exist during gas entrainment,such as vortex and vortex-free flow. For no crossflow W2L (i.e. nosuperimposed liquid flow or no resultant liquid flow in the down-streammain pipe) perpendicular to the branch axis, unstable vortexmay exist during gas entrainment. Gas entrainment begins when athin gas tube arrives at the branch inlet. This first gas tube is notstable and is swept awayafter several seconds, and another gas tubeis formed for a long time. By shortening the distance h (or increasingW3L), the gas tube becomes more stable and thicker (see Fig. 1)(Reimann and Khan, 1984; Smoglie and Reimann, 1986; Smoglieet al., 1987). However, when the distance h is decreased further af-ter b.g.e. or the crossflowW2L exist in the main pipe, the vortex-freeflow always occurs (Reimann and Khan, 1984). But Smoglie et al.(Smoglie and Reimann, 1986; Smoglie et al., 1987) later found thatfor a small value (v2L� 0.06m/s) the vortex is unstable and for a highvalue (v2L > 0.06 m/s) the flow field is always vortex-free.

In a word, we can roughly summarize the prevailing entrain-ment research at a bottom branch into three possible flow geom-etries, as shown in Fig. 2.

a) This geometry may exist on condition that a large liquid volumeexists at both sides of the branch in the nuclear power station.Axisymmetric flow at both sides of the branch can be assumed.

b) This geometry may exist on condition that the downstreamhorizontal pipe goes upward or is closed. One side of horizontalpipe is flow inlet, and the branch is flow outlet.

c) This geometry may exist on condition that the downstreamhorizontal pipe goes downward or is very long. One side ofhorizontal pipe is flow inlet, and the other side of the main pipeand the branch are flow outlet.

In conclusion, for the entrainment at a bottom branch, theentrainment mechanism is clarified basically, but the existing de-scriptions of entrainment generation process are not very clear. Forexample, relationshipsamongthecontinuousentrainment, thevortexflow and vortex-free flow are not definite. The occurrence sequenceand condition for the vortex and vortex-freefloware not veryexplicit.Thus, further studies on these phenomena should be conducted.

2.2. Top branch

The basic mechanism of entrainment through a top branch is asfollows: When the distance h between two-phase interface and

tom branch, W2L ¼ 0, increasing W3L from a) to c).

h }}

vortex flow

vortex-freeflow

W1L

W1GW1G

W3L

a)

h }}

W3L

vortex flow

vortex-freeflow

W1G

W1L

b)

h }W3L

vortex-freeflow

W2G

W2L

W1G

W1L

c)

Fig. 2. Gas entrainment schematic in different flow geometries, a) Symmetrical inflow,b) Inflow from one side c) Outflow from two sides.

Z. Meng et al. / Progress in Nuclear Energy 70 (2014) 221e241 223

branch entrance is large enough, only gas can enter the branch, andthe interface is a virtually ideal horizontal plane. For a furtherdecreased distance h, a great amount of liquid could be torn awayfrom the interface owing to the pressure drop in the main gas flowtowards the branch. However, the gas flow forms a vorticity toaccelerate the droplets in the radial direction. Thus, only a smallportion of droplets can enter the branch. Then most of liquid filmformed by accumulation of droplets in the branch wall runs offowing to gravity. Therefore, we can say that only a small fraction ofdroplets near the branch inlet can be sucked into the branch (seeFig. 3) (Smoglie and Reimann, 1986; Smoglie et al., 1987).

Research of entrainment at a top branch (Smoglie and Reimann,1986; Yonomoto and Tasaka, 1991) indicated that entrainmentbehavior was affected significantly by the occurrence of vorticesand waves. Vortex flow generally induces intermittent entrain-ment, and disappears as the gas flow increases (Lee et al., 2007;Yonomoto and Tasaka, 1991). Also, for high inlet gas velocity, theflow regime in the main pipe transforms from stratified flow towavy flow, and liquid entrainment can be enhanced (Maciaszekand Micaelli, 1990; Yonomoto and Tasaka, 1991). However,Smoglie and Reimann (1986) indicated that a high inlet gas flowinduced surface waves in the main line, which disturbed theentrainment process causing a slight decrease of liquid entrained.When the flow regime changed from stratified flow to slug flow in ahigher gas flow, the liquid entrained was then increased.

Therefore, according to the analysis of present studies, only thebasic entrainment mechanism makes no difference to studies ofdifferent people, but some detailed studies on the effect of wavyflow inmain pipemay have conflicting conclusions and still need tobe performed with the help of sophisticated instruments andvisualization method.

2.3. Side branch

On the basis of different relative position between water leveland branch, two different entrainment mechanisms could exist forentrainment through a side branch:

For two-phase interface below the side branch axis, entrain-ment generating process obviously indicates the Bernoulli’s effect.As gas flowW3G increases (or the distance h between interface andbranch axis decreases), a rising thin liquid film, determining b.l.e.and not influenced by vorticity, can be observed (see Fig. 4a) (Leeet al., 2007; Smoglie and Reimann, 1986). For a further higherW3G (see Fig. 4b and c), the liquid is dispersed into small dropletsowing to the strong acceleration in the vicinity of the branchentrance (Smoglie and Reimann, 1986).

For the two-phase interface above the side branch axis, b.g.e. isgenerated when the water (or heavier liquid) is given a biggishaccelerationmore than that of gravity and gives rise to instability inthe flow (Taylor, 1950). A thin gas tube reaches the branch entrance,which determines b.g.e. (Hassan et al., 1998; Lee et al., 2007;Smoglie and Reimann, 1986). For further increased liquid flow,initial gas tube rapidly approaches the main pipe wall, and thedeveloping of vortex is prevented due to the wall friction (Smoglieand Reimann, 1986). Also, when gas is directly contact with themain pipe wall. Thus, vortex gas is completely suppressed and avortex-free flow is formed between main pipe wall and liquid.Yonomoto and Tasaka (1991) indicated that vortex flow existedonly when gas entrainment was very small. In addition, Lee et al.(2007)’s discovery on the gas tube development process is notmore detailed than that of Smoglie, except that Lee et al. (2007)observed that small bubbles are strongly discharged through thebranch.

Moreover, research of various influencing factors is importantfocus. For the influence of crossflow on liquid entrainment, Smoglieand Reimann (1986) indicated that gas crossflow and liquid cross-flowmade no essential influence on the rising water film since wallfriction forces dominated. But then Yonomoto and Tasaka (1991)found the airewater interface distorting owing to the liquidcrossflow (see Fig. 5). For research of curvature affect, Hassan et al.(1997) found the effect of main pipe curvature on entrainmentthrough the side branch was insignificant in the 1990s. Two de-cades later, as research continues, Bowden and Hassan (2008)demonstrated that the curved wall could provide a more smoothliquid transition from the horizontal to the vertical than the flatwall did for b.l.e., which resulted in a lower loss of liquid mo-mentum and consequently a higher critical height.

Also, as shown in Fig. 6, when the tip of meniscus formed bysurface tension exceeds the top edge of the branch, and the lowwater level associates with small branch discharge rate, hm isprobably moremeaningful to description of gas entrainment than hdo. However, for the description of gas entrainment at largedischarge rate, there is relatively small difference between h and hm(Ahmad and Hassan, 2006; Ahmed et al., 2003; Parrott et al., 1991).In the existing research, the meniscus height (i.e. hmeh) is esti-mated to be 2.23mm (Ahmad and Hassan, 2006) or 3.3mm (Parrottet al., 1991).

Thus it can be seen that the same studies of different people onentrainment at the side branch/break did not observe a completelyidentical phenomena such as effect of liquid crossflow on liquid

Fig. 4. Liquid entrainment at a side branch, increasing W3G from a) to c).

Fig. 3. Liquid entrainment at a top branch.


Fig. 5. Influence of the liquid crossflow at a side branch, a) Liquid entrainment, b) Gasentrainment.


entrainment, and even effects of some factors on entrainment, suchas pipe curvature, the wetting of test section surface, surface ten-sion, etc., are a shortage of research, particularly the research ofvarious factors on gas entrainment is more insufficient than that onliquid entrainment. Further studies on quantifying the effects ofvarious factors are necessary to be performed.

2.4. Other angles branch

In industry field, branch orientation of T-junction can be arbi-trary except the above three directions, such as header-feeder ge-ometry of CANDU reactor. Branch orientation of T-junction

reservoir

upper branch

Frh hm

meniscus

Fig. 6. Definitions of h and hm.

consisting of break and hot leg/cold leg can also be arbitrary in thecase of the break of the primary loop during LOCA. Many modelingstudies for T-junction of arbitrary branch direction includingentrainment modeling (Cho et al., 2010; Chung et al., 2010) havebeen successfully implemented into RELAP5 code (Cho and Jeun,2003, 2007; Chung et al., 2000). Since it was hard to applyresearch results from specific branch angles of �90� or 0� to thecase of at an arbitrary branch direction, series of experiments andtheoretical studies were conducted on T-junction with an arbitrarybranch (see Fig. 7).

Two different entrainment mechanisms can be observed (seeTable 1) for b.e. (Lee et al., 2006, 2007), such as l.e. due to vortex(e.g. it occurs commonly for the top branch) or ascending liquid film(e.g. it occurs commonly for the incline branch and the side branch)and g.e. due to vortex (e.g. it occurs commonly for the bottombranch and the incline branch) or continuous gas film (e.g. it occurscommonly for the side branch). For the entire l.e. process throughan inclined branch, vortex entrainment is shown in Fig. 8aec. Theonset entrainment is determined when the droplets are found inthe branch. But the other entrainment phenomenon relates toascending liquid film without any formation of vortex. As the gasflow increases, this entrainment process is generated as shown inFig. 8def. Liquid vortex can be hardly observed due to the existenceof the inner wall friction. The whole entrainment process for theinclined branch is similar with that for the side branch. For theentire g.e. process through an inclined branch, as the liquid flowincreases, vortex and small bubbles are generated along with liquiddischarge at the proper water level (see Fig. 9a). With a furtherdecrease of water level, a gas tube is formed with a vortex andenters the branch (see Fig. 9b and c). But another gas entrainmentphenomenonmay come upwhen the vortex flow cannot be formedowing to the water level position or a very small vortex hard to beobserved is generated and then disappears again (see Fig. 9d). Withan increasing liquid flow, the thin tube of gas is formed between thewater level and the vicinity of the branch. As a liquid flow increasesfurther, the small bubbles are strongly discharged through thebranch (see Fig. 9e and f).

Moreover, more detailed research on entrainment phenomenaindicates (Lee et al., 2006): for l.e. at an incline branch (see Fig. 7),the entrainment phenomena at þ72�and top branches are similar,and those at �36� and side branches are almost the same. Also,

Fig. 7. Side view of T-junction.

Table 1Entrainment mechanisms for b.l.e. and b.g.e.

Object b.l.e. b.g.e.

Mechanism Vortex Ascending liquidfilm

Vortex Continuous gasfilm

Branch direction Top Incline, side Bottom, incline Side, incline


at þ36� branch the vorticity on the interface is difficult to beobserved due to inhibition of the inner wall (Lee et al., 2006); forthe g.e. at an incline branch (see Fig. 7), the entrainment phe-nomena at �36� and side branches are similar, and those at �72�

and bottom branches are almost the same. In addition, for the in-clined branch located in a flat wall (Bartley et al., 2008) as shown in

Fig. 8. Two kinds of developm

Fig. 9. Two kinds of developm

Fig. 10a (0��q � 90�), the b.l.e. is essentially independent of q, butfor b.g.e. this conclusion on q is not true. For the experimentalapparatus as shown in Fig. 10b, experimental results show the in-dependent effect of q on b.g.e. and the relevant effect of q on b.l.e..Moreover, by comparison, entrainment at an inclined branchlocated in a flat wall (Bartley et al., 2008) have a major differencewith those at an inclined branch located in a circular pipe (Lee et al.,2007). The wall curvature may result in an influence on the trendsand the magnitude of the data. More work is required to clarify themechanism and the characteristic of effect of wall curvature onentrainment. Also, the meniscus height may affect b.g.e. at lowFroude numbers, which is similar to the case of a side branch (i.e. atan angle of 0�). The meniscus height is estimated to be 2.03 mm fora branch mounted on the underpart of a curved surface at a specificangle of 45� (Ahmad and Hassan, 2006).

ent of liquid entrainment.

ent of gas entrainment.

Fig. 10. Schematic showing independent parameters, a) Example of positive h andpositive q; b) Example of negative h and negative q.


Fig. 10 Schematic showing independent parameters, a) exampleof positive h and positive q; b) example of negative h and negative q.

In a word, research of entrainment at an arbitrary branch hasbasically formed systemic theories as shown in Table 1, but thevisual image data of entrainment process at an inclined branchused to validate or study entrainment mechanism are facing a

Fig. 11. Geometry

serious shortage, since text descriptions easily influenced byartificial factor are the primary way to record phenomena. More-over, detailed experimental studies covering the full range of thebranch angle and ratio of branch and main pipe diameters areneeded. In addition, the effect of the wall curvature and meniscusheight cannot be accurately quantified with the existing experi-ments. Also, the effect of liquid crossflow on b.g.e. at the differentoriented branch is confirmed (Andreychek et al., 1988) just likeentrainment at a side branch but is not quantified, so more studiesare needed.

2.5. Multiple branches

Two different test apparatuses are generally used in the existingexperimental studies of entrainment at multiple branches, such asmultiple branches mounted on a curvature and multiple brancheslocated in an angled flat wall. For the dual horizontal side brancheswith centerlines falling in the same inclined plane (see Fig. 11)including the two branches with centerlines falling in the hori-zontal (a ¼ 0�) and the vertical (a ¼ 90�) planes, four distinguish-able g.e. modes may occur, such as Initial Vortex Entrainment (IVE)mode, Continuous Vortex Entrainment (CVE) mode, InitialDepression Entrainment (IDE) mode and Continuous DepressionEntrainment (CDE)mode (Maier,1998). IVE, characterized by a hair-thin vortex/gas tube formed between the flat interface (or thebottom of the depression) and branch inlet (see Fig. 12a), is alwaysintermittent entrainment. CVE, identical in appearance to IVE, al-ways originates from the bottom of the depression (see Fig. 12b).IDE is characterized by depression formed in the water level overthe branch and deepened with the decrease of the water level.Vortex cones, much like IVE, may occur before IDE. IDE is alwaysintermittent and is either vortex-free or vortex in nature (seeFig. 12c). CDE, identical in appearance to IDE, is continuous (seeFig. 12d). These four modes seem to summarize the flow phe-nomena of the gas entrainment for the dual side branches and arenormally observed with the decrease of the interface. But, the fourmodes do not always all occur in any experiment (Maier, 1998),even other modes except the four modes can be observed. Forexample, visible research of Parrott et al. (1991) showed the IVE andCVE models in sequence and presented the continuous vortex-freeentrainment at the lower level, much like the entrainment processof a single branch. However, for the l.e., the prevailing theory hasnot been developed yet. For the studies of flow phenomena, there is

parameter.

Fig. 12. Geometry parameter of four models, a) IVE entrainment model; b) CVE entrainment mode; c) IDE entrainment model; d) CDE entrainment mode.


not enough image data used to compare and integrate theentrainment theory, so a unified cognition of the detailed flowphenomena and the generating process of entrainment cannot beformed.

For b.g.e. and b.l.e. at dual branch (see Fig. 11), when the L/d isnot large enough, as Fr1 or Fr2 increases, the critical height increases(Maier, 1998; Maier et al., 2001a, 2001b). For b.l.e. through dualparallel slots, the similar conclusions that the critical height at thelower slot increases with the increase of Fr2 (i.e. Froude number ofthe upper slot) or the decrease of the distance between the twoslots can be found (Armstrong et al., 1992b). When the L/d is equalto 8 and entrainment is occurring at branch 2 as shown in Fig. 11,the critical height of branch 2 is relatively constant (Maier, 1998;Maier et al., 2001a, 2001b). In other words, by increasing L/d (i.e.increasing the distance between the two branches), the behavior ofthe two branches can be gradually regarded as two independentsingle branches. The similar conclusion on L/d ¼ 8 could be ob-tained during the studies of dual branch located in the same hori-zontal (Hassan et al., 1996a) and vertical (Hassan et al., 1996b)planes. Also, for dual branch with centerlines falling in the verticalplane, the influence of the lower branch on b.g.e. at the upperbranch became very little for L/d > 6 (Parrott et al., 1991) or L/d ¼ 8(Ahmed et al., 2004). Moreover, Armstrong et al. (1992a) found thatthe upper branch has a small effect on b.l.e. at the lower branch forL/d > 4. In addition, for b.g.e. and b.l.e. at dual branch (see Fig. 13),the critical height h decreases with the increase of the angularalignment of branches a (Maier, 1998; Maier et al., 2001a, 2001b) as

shown in Fig. 11. Also, the effect of wall curvature is a main researchdirection. For dual branch (see Fig. 14a), the wall/pipe curvature hasan effect on the entrainment (Hassan et al., 1997): b.g.e. at the lowerbranch in the circular pipe occurs at a higher water level than thatin the flat vertical wall, and the lower branch in the curvature wallcontinues to obtain higher quality than the lower branch in thevertical flat-wall case all the way until b.l.e. However, for entrain-ment at the upper branch, the effect of wall curvatures seems to besmall.

Hassan et al. (1997) investigated single, dual and tripledischarge from a smooth stratified region through side branchesconnected to a semicircular wall at angles of 90�, 45� and 0� fromthe horizontal, as shown in Fig. 14b. For the branch A, the mass flowrate and the branch quality are influenced by the flow from branchB and/or C, and the flow from branch B has a stronger influence onthe flow from branch A than the flow from branch C does. Inaddition, for the branch B, the flow from branch A pulls the gasaway from branch B, while the flow from branch C brings more gasinto branch B. The opposite is true for the liquid (Bowden andHassan, 2008). Similar trends were observed for flat walls(Hassan et al., 1996b). Recently, for the effect of a secondary branchon b.l.e. at the primary branch in the case of secondary branchbelow the primary branch (Bowden and Hassan, 2008), furtherconclusion has been obtained that the secondary branch at low tomoderate values of Fr2 is found to slightly assist b.l.e. with Fr1 > 1.But at Fr1 <1, due to the effects of surface tension and wetness, thesame conclusion is not always valid with the different recording

Fig. 13. Relevant flow and geometrical parameters.


method, such as the decreasing liquid level (DLL) method and theincreasing liquid level (ILL) method. For example, DLL method re-sults showed that the effect of the secondary branch made thecritical height higher, whereas the increasing liquid method ach-ieved the opposite result.

half section pipe

upper branch

45°

Lower branch

hA

hB

a)header

feader

45°

45° B

C

A

b)

Fig. 14. Experiment apparatus of branches mounted on a circular pipe.

Therefore, the interaction among different branches can bebasically confirmed, but the detailed and quantitative research oninteraction effect is facing a serious shortage, such as the influenceof a secondary branch on g.e. at the primary branch and the effect ofan upper branch on entrainment at the lower branch etc. Also,research around the separation distance L/d, particularly theangular alignment of branches a and the effects of surface tension,wetness and wall curvature is still insufficient for quantifying theireffect on entrainment. So, further research on quantifying the ef-fects of various factors on entrainment is necessary for modelimprovement.

For the three branches as shown in Fig. 14b, the early researchsuggests (Hassan et al., 1997) that when branch A and branch Balready exist, adding branch C does not significantly affect the flowfrom A, and the flow from A and B has essentially no effect on theflow from C, which also indicates that the experimental apparatuslike Fig. 14b is absolutely representative of a full header-feedergeometry of CANDU. But then a further study on l.e. of the threebranches is conducted as follows (Bowden and Hassan, 2008): Fortwo secondary branches below the primary branch A (see Fig. 14b)and below the interface, comparing the triple with the singledischarge case, a decreased critical height of the primary branch isfound with the DLL method, and there is an opposite tendencywith the ILL method; in comparison with the dual branch case asshown in Fig. 14a, an increase of the critical height (i.e. assistingthe b.l.e.) is found with either the DLL or ILL methods. Also, itshould be noted that the secondary branches interaction effect iscaptured by image data as shown in Fig. 15. In addition, for thethree branches cases with secondary branches above (branch A)and below (branch C) the primary branch B, increased criticalheight for l.e. is observed with an increase of either of the sec-ondary branch discharges.

For three branches, experimental investigation into theentrainment at triple discharge is still shortage, particularly theresearch on g.e. The entrainment process and phenomena are notvery clear due to the complicated interaction effect of tripledischarge. As well, theoretical work quantifying the interrelation-ship of the flow among different oriented branches mounted on thesame semicircular wall and modifying present models is not yetperformed.

For dual and triple discharge, experimental investigation intothe effect of multiple branches on entrainment is still more insuf-ficient than that of single branch. As well, further work quantifying

Fig. 15. Image of triple discharge.


the interrelationship of the flow among different branches moun-ted on the same semicircular wall is still not performed, and theinvestigations into the effect of crossflow and stratified wavy floware necessary to be performed. In addition, Quantitative flow fieldmeasurements like Particle Image Velocimetry (PIV) are necessaryto further explain multiple discharge flow field.

3. Onset entrainment models

Onset entrainment and stable entrainment are two importantparts in the entrainment modeling. In this section, onset entrain-ment models are summarized on the basis of different T-junctionstructures: single branch, arbitrary angle branch and multiplebranches. In each sub-problem, Introduction of each modelgenerally consists of premise, detailed description and comment,and models owning inherent link among each other are introducedtogether.

3.1. Single branch

Smoglie et al. (Smoglie, 1984; Smoglie and Reimann, 1986)considered that the influence of surface tension and viscosity onthe b.e. could be neglected, and developed the critical height forb.g.e. and b.l.e. which was expressed generally in the followingform:

hb ¼ KW0:43b =½grbðrL � rGÞ�0:2 (1)

where the constant K is dependent on experiments, b refers to thecontinuous phase in the entrainment. The variable W3b is the massflow rate of continuous phase in the branch. This equation is ob-tained from a point mass sink assumption for liquid entrainmentat a top or side branch, and is used in follow-up studies forentrainment at top, bottom and side branches (Smoglie andReimann, 1986; Smoglie et al., 1987). The same equation wascorrelated by Lubin and Springer (1967) for b.g.e. in an initiallystationary liquid draining through an orifice at the bottom of atank and was used by Reimann and Khan (1984) to describe theb.e. from a stratified two-phase region through a small branch/

break. This equation has been included in RELAP5 (Ardron andBryce, 1990; Division, 2001) and CATHARE (Maciaszek andMicaelli, 1990) codes, and theoretical research of b.e. widelyadopts this equation until now.

The Eq. (1) does not depend explicitly on the branch diameter d,therefore the branch can be regarded as a punctual sink. The cor-relation works considerably well for the data gained for relativelysmall branch size, that is, for the small ratio of the branch diameterd to the height hb (or the diameter of main pipe). Furthermore,Moon and No (2003) indicated that the existing equation for b.l.e.was applicablewithin the range of 1e10 of hb/d. In fact, Eq. (1) couldbe derivate from:

hbd

¼ K*

"v23brb

gdðrL � rGÞ

#a(2)

where K* and a are constants and are dependent on experiments,and the variable v3b is the continuous phase velocity in the branch.The Eq. (2) is developed by many researchers for simulation of b.l.e.and b.g.e. For example, in 1956 some researchers (Davidian andGlover, 1956) found the value of K* ¼ 0.42 and a ¼ 0.25 for b.l.e.through a top branch. Actually when the value a ¼ 0.2, Eq. (2) canbe transformed into Eq. (1) without parameter d. On the basis of anassumption of identifying wave spacing with the branch diameter,Maciaszek’s semi-empirical correlation for b.l.e. at an upwardbranch is of the form (Maciaszek and Micaelli, 1989):

hb ¼ 0:88

"W2

3GgrGðrL � rGÞd2

#1=3(3)

The correlation works considerably well for large size branch,but is not applicable for small branch where hb is almost inde-pendent of the branch/break size d. However, Welter et al. (Welter,2003; Welter et al., 2004) obtained a new model by the theoreticalanalysis for b.l.e. at a top branch:

w23g

gd5rGðrL � rGÞ¼ K

�hbd

�3�0:22

�hbd

�þ 1�2�

1��hbd

�2��1

(4)

The model solving the disadvantages of the correlations devel-oped in previous studies considers the effect of branch size d, but anadjustable factor in the correlations existing in the reasoning ofmodel was just derived from the theoretical analysis for b.l.e. andno experimental data are used to fine tune the constant.

Furthermore, Ahmed et al. (2003) modeled b.g.e. through afinite-side branch located in a flat vertical wall. A three-dimensional finite-branch model and a simplified point-sinkmodel were developed and used for comparative analysis. The re-sults showed that no noticeable deviation between the two modelscan be observed at higher Froude numbers. However, at the lowerFroude numbers (Fr < 10), the finite-branch model is recom-mended to predict b.g.e. due to approaching the physical limits (i.e.the physical limit of h/HOGE ¼ 1.0 when Fr ¼ 0). The point-sinkmodel is given in the following form:

HOGE

d¼ Fr0:4

�12

�DrrL

�0:2

þ 18

�rLDr

�0:8�(5)

where Fr ¼ vd=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigdDr=rL

p, and the finite-branch model is given by

HOGE

d¼ h*

2þ Fr2

2

nI1hh*io2

(6)


I1hh*iI2hh*i¼ �

�1Fr

�2� rL2Dr

�(7)

where

I1hh*i¼ �2

Z N

0

Z N

0

cosbh*

p2l

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffil2 þ b2

q �

264Z 1

�1sin�lffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� y*2

q �cos�bh*�dy*

375dydb

þ 2Z N

0

Z N

0

sinbh*


q264Z 1


q �sin�bh*�dy*idldb (8)

and

I2hh*i¼ �2

Z N

0

Z N

0

cosbh*

p2l


q �

264Z 1


q �cos�bh*�dy*

375dydb

þ 2Z N

0

Z N

0

sinbh*


q264Z 1


q �sin�bh*�375dy*dldb (9)

Fig. 16. Schematic diagram of the flow situation.

Based on the values of a given dimensionless height h* andFroude number Fr first calculated from Eq. (7), the critical height ofb.g.e. can be obtained by Eq. (6). The values of I1[h*] and I2[h*] aredetermined by numerical integration techniques, which are indi-cated by Gradshteyn and Ryzhik (2000) and Stroud (1971).

However, it should be noted that the experimental data used tocompare with the finite-branch model all belong to the experi-ments at Fr> 1. Since the effect of surface tension and viscous forceis not expected to be neglected at Fr < 1, experimental data of b.g.e.at low Froude numbers are needed to validate the finite-branchmodel.

A model mainly including two equations suitable for hand cal-culations was established by Soliman and Sims (1992) for b.l.e. froma side orifice of finite diameter (see Fig. 16) in the following form:

hd� sd¼ 1

2Fr2hF�sd

�i2(10)

and

Fr2hF�sd

�ihF 0�sd

�i¼ �1 (11)

where the function F and the first derivative of F are given by:

FðxÞ ¼ 14px2

Z10

�1� yy

�0:5�1� y

4x2

��1:5

dy (12)

F 0�sd

�¼ � 1

2pðs=dÞ3Z10

�1� yy

�0:5 1� y

4ðs=dÞ2!�1:5

� 1� 3y

2y� 8ðs=dÞ2!dy

(13)

The model indicates that the ratio h/d only depends on theFroude number, irrespective of d. At low Fr, the model approaches acorrect physical limit. That is, the physics of the problem givesh ¼ s ¼ d/2 at Fr ¼ 0. The model curve shows the similar tendencywith Armstrong et al. (1992a)’s experimental data, particularly atFr < 10, although the prediction values are generally higher than

experimental data. Therefore, the model can be considered to beapplicable to the entire range of Fr, provided that surface tensionand viscous forces can be neglected.

In addition, almost all the existing research on the entrainmentthrough a single branch is on the base of the circular cross-sectionbranch. However, for possible longitudinal cracks in pipes, Solimanand Sims (1991)’s research on b.l.e. through a side slot of finitewidth d was performed and developed the following correlations:

hd� sd¼ 1

2

�Frp

�2�ln�s=d� 1=2s=dþ 1=2

��2(14)

and


ln�s=dþ 1=2s=d� 1=2

�¼ ðs=dÞ2 � 1=4

ðFr=pÞ2!

(15)

where important geometry parameters can refer to Fig. 16. Theratios s/d and h/d only depend on the Froude number. In addition,the model approaches the correct physical limits, that is, the modelgives h ¼ s ¼ d/2 at the limit Fr ¼ 0, and can be recommended forFr < 10. However, calculation values of the model are not yetcompared with any relative experimental data, and further work onmodel validation and verification is not carried out.

As mentioned previously, vortex flow and vortex-free flow mayexist in an entrainment experiment, which brings a little differenceof the judgment criterion of b.e. Some correlations may take theoccurrence of vortex-free flow as the criterion of b.e., the criterionof b.e. of some correlations is the occurrence of vortex flow. Thus,different onset entrainment criterion for the same experiment canmodel different onset correlations (Lee et al., 2006). Reimann andKhan (1984) got two different constant values K in Eq. (1) for thevortex-free b.g.e. and the vortex b.g.e. For the b.g.e. at a smallbranch mounted on an inclined wall, the vortex flow data pointscorrespond to significantly higher values of hb/d (Bartley et al.,2008). In addition, Reimann and Khan (1984) indicated that theflow field was always vortex-free, when only a part of liquid flowedthrough the downward branch and the rest remains flow in thehorizontal main pipe. However, according to the study of Smoglie(1984), Smoglie and Reimann (1986) for b.e. at top, bottom andside branches, a significant influence of superimposed velocitieswas observed only for the bottom branch, a small superimposedvelocity (i.e. rLv22L=rLv

23L > 10�5) could prevent vortex formation.

Using the bottom branch affected significantly by superimposedvelocities as example, crossflow may break the process of the gascore penetrating the liquid layer to build the gas entrainment. Thus,gas entrainment is controlled by the balance between vertical andhorizontal inertial forces. This balance is represented by thedimensionless number rLv22L=rLv

23L. This dimensionless number has

been applied to CATHARE code as a modification factor of Eq. (1)(Maciaszek and Micaelli, 1990).

When vortex flow does not occur, crossflow in the main pipesignificantly affects the entrainment. Yonomoto and Tasaka (1988,1991) considered the significantly effect of vortex flow and liquidcrossflow for a bottom branch in their theoretical model research. Amodification factor C was proposed to modify the correlation: forthe vortex flow condition, C ¼ 5:1ðh=hb � 1:08Þ1:3 þ 1:4; for thevortex-free flow condition,C ¼ 1:7 exp½�1:0ðW2L=W1L � 1:2Þ8� þ 0:4W2L=W1L þ 1:4.

In a word, vortex flow and crossflow conditions should beconcerned in the process of conducting the entrainment experi-ments and establishing the models. In addition, it is worthmentioning that the wetting of the test section surface could bringtiny difference of experimental data (Hassan et al., 1998), butfurther quantitative research is not yet preformed.

3.2. Arbitrary angle branch

At first, some scholars concluded that the modeling of entrain-ment for the branch where the angle from the horizontal directionwas more than �60� was the same with that of the top branch orthe bottom branch (Chung et al., 2010), but this theory was nottestified by experiment. For the better prediction of the entrain-ment in header-feeder configuration of CANDU, the RELAP5entrainment models have been modified and considered the effectof branch orientations in the following form (Cho et al., 2010; Choand Jeun, 2004, 2007):

hb ¼ C1ðcos qÞC2

�dD

�C3"

_mbffiffiffiffiffiffiffiffiffiffiffiffiffigrbDr

p#0:4!

(16)

Eq. (16) is derived from assumptions of a point sink for thebranch and potential flow in thewhole field, and considers the non-dimensional compensation factor d/D for large diameter ratio be-tween the branch pipe and the horizontal pipe. Theoretically, themodel is suited for the entrainment of branch angleat�90� < q< 90�. But in practice, the applicable range of the modelwas valid at the �60� < q < 0� (�60� means downward inclinedbranch and 0� means horizontal branch) by the experimentalvalidation. In the case of d/D, the applicable range was verified at0.0291 � d/D � 0.39 by the experiment (Cho and Jeun, 2004). Also,the new model can give more reasonable results than those ofRELAP5 for top, bottom and side branches. But, according to thecomparison between experimental data and model curve, the newmodel still needs to study further.

In addition, based on the balance of the inertia force and thegravity force at the bifurcation point on the interface, a semi-theoretical model considering the effects of the branch orienta-tion and diameter is developed by Lee et al. (2007). The beginningof the entrainment due to the vortex can be determined as:

FrGðrG=DrÞ0:5 ¼ COLEðqÞ½ðhOLE=dÞ þ 1=2ðD=dÞð1� sin qÞ�2:5

(17)

FrLðrL=DrÞ0:5 ¼ COGEðqÞ½ðhOGE=dÞ þ 1=2ðD=dÞð1� sin qÞ�2:5

(18)

where q is the branch angle from the horizontal direction and brepresents the continuous phase. For g.e., the branch angleis �90��q < 0�; For l.e., the branch angle is 0� < q � 90�. Also, thebeginning of the entrainment due to the ascending film is describedas:

FrGðrG=DrÞ0:5 ¼ COLEð0Þ½ðhOLE=dÞ�2:5 (19)

FrLðrL=DrÞ0:5 ¼ COGEð0Þ½ðhOGE=dÞ�2:5 (20)

for q ¼ 0�, it is to say, Eqs. (19) and (20) is suitable for the conditionof the side branch.

Although, the correlations established by lee et al. consider theeffects of the inclination angle and the ratio of main pipe diameterand liquid level to branch diameter, the best fit coefficients due toascending film and vortex have a certain relationship with theinclination angle q. Thus, we need more data to further study therelationship of the best fit coefficients and the inclination angle q. Inaddition, for b.l.e., the Eq. (17) is suitable for the simulation ofexperimental apparatus like Fig. 17a and not applies to experi-mental apparatus like Fig. 17b. However, for b.g.e., experimentalapparatus corresponding to Eq. (18) is as shown in Fig. 17b. Hence,improvement models of b.l.e. and b.g.e. for any branch angle stillneed more investigations.

Also, twomodels were built for b.l.e. and b.g.e., respectively, at asingle branch mounted on an inclined plane (see Fig. 18) in thefollowing forms (Bartley et al., 2008): for b.l.e. as shown in Fig. 18a,

jhbj=d ¼ �0:625ðcosÞa1�Fr0:4ðcos q

2Þa2G

0+ � q � 90+; Fr G < 45;(21)

for b.g.e. as shown in Fig. 18b,

FrG

h

+

a)

FrL

h

-

b)

Fig. 18. Example of a branch mounted on an inclined plane, a) b.l.e.; b) b.g.e.

branch

interface(l.e)

main pipe

interface(g.e)

a)

branch

main pipeinterface(g.e)

interface(l.e)

b)

Fig. 17. Experimental apparatuses.


jhbj=d ¼h0:475ðcosÞb1

iFr

0:444ðcos q2Þb2

L

�90+ � q � 0+; Fr L < 70;(22)

where a1, a2, b1 and b2 are determined by experiment. It should benoted that the models are developed on the base of a single branchmounted on an inclined plane, not on a circular pipe. The majordifference in the geometry may become a limiting factor of themodel application.

A new correlation for b.l.e. and b.g.e. from branches at 90�, 45�

and 0� angles, based on Smoglie’s model (i.e. Eq. (1)), is given in thefollowing form (Majumdar et al., 1999):

hb ¼ Kð2εAÞg0:2

�DP

r1 � r2

�(23)

where K is determined by experiment and DP is single phasepressure drop.

K ¼ 1:05 for q ¼ 90+;K ¼ 0:85 for q ¼ 45+;K ¼ 0:69ðh � 0:0Þ or 0:75ðh > 0:0Þ for q ¼ 0+

The empirical model was indirectly validated by comparingcalculated values of mass flow rate and quality with the test data ofHassan et al. (1997), and quality prediction agreed well with theexperimental data, but the maximum deviation of 17% wasobserved between prediction values of the two-phase flow rate andthe data. Also, themodel was not fully comparedwith other modelsand test data and then not widely used. Thus, the use of this modelneeds to be further discussed.

Andaleeb et al. (2006) conducted theoretical investigation intob.g.e. through a single branch mounted on the underpart of asemicircular wall at angles of 90, 45 and 0�. Following Ahmed et al.(2003), a simple point-sink model and a finite-branch model wereproposed in the following forms: for point-sink model,

HOGE

d¼ D

dh* þ Fr2gDh*3I1

h*

4v2d�h*2I1

h*� I2

h*� (24)

where the values of h*, I1 and I2 are numerically computed by acomputer code, the detailed explanation of the point-sink model isprovided in the relevant literature (Andaleeb et al., 2006); for two-dimensional finite-branch analysis,

HOGE

d¼ h

dþ rL2gdDr

�vF

vy

B

�2(25)

Knowing the input values, the critical height can be found. Thedetailed explanation and calculation procedure of the finite-branchmodel is found in the relevant literature (Andaleeb et al., 2006).

The two models were relatively good consistent with Ahmadand Hassan (2006)’s experimental data. But at low Froude num-ber, the results also showed a significant deviation between the twomodels and Ahmad and Hassan (2006)’s data probably due toneglect of the surface tension and viscous forces in the models.

To further modeling of b.g.e., Saleh et al. (2009) firstly consid-ered the effects of surface tension based on the assumption of thedip formation and provided a hybrid model to predict b.g.e. at onlya single bottom branch mounted on a circular pipe (see Fig. 19). Thecritical height HOGE can be found to be:

HOGE

d¼ h

dþ

v2L;brL

2gdDr� 2sROCbgdDr

(26)

Fig. 20. Schematic diagram of geometry parameter for two branches mounted on thesame vertical plane, a) Experiment apparatus of gas entrainment; b) Experimentapparatus of liquid entrainment.

Fig. 19. Geometry used in the analysis.


The last dimensionless group on the right represents a ratio ofsurface tension to gravitational forces commonly known as themodified Bond number. The solution of the liquid velocity vL,b andthe radius of curvature ROCb at the lowest point of the dip e can befound in the literature (Saleh et al., 2009).

It should be noted that the new model was found to be valid atthe beginning of vortex-free gas entrainment and can better predictthe critical height than the point-sink model at low Froudenumbers. However, the dip radius of curvature is an unknown inthemodel andwas determined by experimental correlation. Hence,the new model makes an improvement in the prediction, but withthe limitation that the geometry of the dip needed to be defined.


Kowalski and Krishnan (1987) found that the correlations cor-responding to a single branch could not predict well the b.l.e. andb.g.e. of multiple branches. Thus, entrainment research of multiplebranches is necessary.

In the case of dual branch (see Fig. 20a), the b.g.e. is found torelate to the separation distance of two vertical branches and theliquid flow rates from the two branches. Parrott et al. (1991)developed a purely empirical correlation:

hmd

¼ c1�Fr1 þ Fr2 exp

�� c3ðL=dÞc4Frc51 Frc62��c2 (27)

where hm (some researchers define the parameter as s) is the dis-tance between the tip of the meniscus and the centerline of thebranch.

Eq. (27) is recommended only under the conditions similar tothose in their investigation. Since Eq. (27) is a purely empiricalcorrelation, its use has great limitation.

Armstrong et al. (1992a) performed a study on b.l.e. from thedual branch test apparatus as shown in Fig. 20b and established thefollowing correlations:

H ¼ Sþ 14

266664Fr*1S2 þ Fr*2

ð1þSÞ2Fr*1S3 þ Fr*2

ð1þSÞ3

377775 (28)

and"Fr*1S2

þ Fr*2ð1þ SÞ2

#"Fr*1S3

þ Fr*2ð1þ SÞ3

#¼ 32 (29)

where

Fr* ¼4p

_mffiffiffiffiffiffiffiffiffiffiffiffiffi

g Drr L

5q ; H ¼ h

L; S ¼ s

L(30)

and Fr* is related to Fr and H to h/d by

Fr ¼ Fr*�Ld

�2:5

&hd

¼�Ld

�H (31)


Good agreement can be found between the theoretical pre-dictions of the critical height and the experimental values, andexperimental evidence supports the contention that Fr* and H canbe relevant dimensionless groups.

Also, empirical correlations obtained by least-square fittingwere developed by Hassan et al. (1996b) for two side branches withcenterlines falling in the same vertical plane. As well, Hassan’s dataof b.g.e. agreed well with the data of Parrott et al. (1991), andHassan’s data of b.l.e. were reasonably consistent with the modeldeveloped by Armstrong et al. (1992a). These correlations are givenby the following relations: for the upper branch,

hOGEd

¼ 0:57ðA1FrOGEÞ0:4 (32)

jhOLEjd

¼ 0:87 FrA2OLE (33)

for the lower branch,

hOGEd

¼ 0:57FrA3OGE (34)

jhOLEjd

¼ 0:87ðA4FrOLEÞ0:31 (35)

where,

A1 ¼ 1:0þ exph� 1:96ðL=dÞ1:2=Fr0:32BGE

iA2 ¼ 0:31� 0:13 exp

h� 0:209ðL=dÞ1:5=Fr0:20BLE

iA3 ¼ 0:4� 0:223exp

h� 0:415ðL=dÞ1:5=Fr0:20BGE

iA4 ¼ 1:0þ exp

h� 2:27ðL=dÞ1:2=Fr0:32BLE

iHowever, the above empirical correlations are purely empirical

and are suitable for the conditions under which their experimentaldata were gathered.

For b.g.e. through dual side branches mounted on the samevertical plane, Ahmed et al. (2004) extended the finite-branchanalysis and the point-sink analysis carried out for single branch(Ahmed et al., 2003) to predict the critical heights at the upperbranch (branch 1) in the following forms: for finite-branch model,

HOGE

d¼ h*

2þ 12

hFr22I1

�h*�2 þ Fr21I2

�h*�2

þ 2Fr1Fr2I1�h*�I2�h*�i

(36)

for point-sink model,

HOGE

d¼ h*

2þ 18

"Fr1h*2

þ Fr2h* þ L*

2#2

(37)

The similar conclusion can be gained. That is, at higher Froudenumbers, the two models have no noticeable deviation for thepredicted critical heights. At lower Froude numbers, the finite-branch model can obtain a more accurate analysis. In addition,the procedures to solve the critical height and the solutions of in-termediate variables can be found in the literature (Ahmed et al.,2004).

Hassan (1995), Hassan et al. (1996a) performed an experimenton b.l.e. and b.g.e. from dual branch with centerlines falling in thesame horizontal planes located in the side of a reservoir. It shouldbe noted that the Froude numbers of two branches were equal in

the experiment. Empirical correlations for b.g.e. and b.l.e. wereproposed, respectively, in the following forms:

hOGEd

¼ 0:57ðAFrOGEÞ0:4 (38)

hOLEd

¼ 0:87ðBFrOLEÞ0:31 (39)

where

A ¼ 1:0þ e��0:613 l

d1:5

Fr�0:4OGE

�; B ¼ 1:0þ e

��2:06 l

d2:54

Fr�1:2OLE

�So far, entrainment models and test data for dual branch

mounted on the same horizontal plane are rarely seen, and thesemodels are able to converge to correct limits at L/d ¼ N and 0. So,further study on the commonality of models and complementarydata corresponding to the different Froude numbers in the twobranches is necessary.

For b.g.e through dual side branches mounted on a vertical wall(see Fig. 21), considering the factor of angular angle of branches a,Ahmed (2006) performed a point-sink analysis, the dimensionlesscritical height HOGE/d at point A and B could be respectivelyexpressed as follows:

HOGE

d

A¼ h*A

2

þ 18

("Fr1h*2A

þ

Fr2�h*A � L* sin q

�hL* cos q

2 þ �h*A � L* sin q�2i3=2

!#2

þ

Fr2L* cos qhL* cos q

2 þ �h*A � L* sin q�2i3=2

!2)

(40)

and

HOGE

d

B¼ h*B þ L* sin q

2

þ 18

("Fr2h*2B

þ

Fr1�h*B � L* sin q

�hL* cos q

2 þ �h*B � L* sin q�2i3=2

!#2

þ

Fr1L* cos qhL* cos q

2 þ �h*B � L* sin q�2i3=2

!2)

(41)

where hB* and hA

* can be calculated by their equations. For a specificvalue of q, L/d, Fr1 and Fr2, the two critical heights for two branchescan be obtained by their equations. Then, if (HOGE/d)jA > (HOGE/d)jB,it means that b.g.e. occurs at branch A, and the critical height HOGE

will be HOGEjA. If (HOGE/d)jA < (HOGE/d)jB, it means that b.g.e. occursat branch B, and the critical height HOGE will be HOGEjB. Also, if(HOGE/d)jA¼ (HOGE/d)jB, it means that b.g.e. occurs at both branches.Furthermore, for limiting case Fr1 ¼ Fr2 ¼ 0.0, the calculated valuesof the above equations approaches zero. However, the correct limitshould be d/2. This means that the point sink analysis is not suitablefor low Froude numbers. Therefore, a more accurate three-dimensional analysis named finite-branch analysis is presented inthe following forms:

Fig. 21. Geometry parameter for theoretical analysis.


HOGE

d

A¼ h*A

2þ 12p4

�nFr1hI1�h*A�i

þ Fr2hI2�h*A�io2

þnFr2hI5�h*A�io2�

(42)

and

HOGE

d

B¼ h*B þ L* sin q

2

!

þ 12p4

�nFr2hJ1�h*B�i

þ Fr1hJ2�h*B�io2

þnFr1hJ5�h*B�io2�

(43)

For a specific value of q, L/d, Fr1 and Fr2, the two critical heightsfor two branches can be obtained by their equations. The pro-cedures to solve the critical height and the solutions of interme-diate variables can be found in the relevant literature (Ahmed,2006). Then, if HOGE/djA ¼ HOGE/djB, it means that b.g.e. occurs atboth branches. Also, HOGE/d is selected as the largest one asmentioned previously. The predicted results agree well with theexperimental data within the percentage deviation of 12% atFr1 > 10. In addition, based on these models, the function re-lationships between various factors, including Fr1, Fr2, L/d, and q,and the critical height of b.g.e. can be clear.

Also, for b.l.e. through two side branches with centerlines fallingin a common inclined plane (see Fig. 11), a more-accurate finite-branch model (Maier et al., 2001b), which assumed the branches tobe square cross-section, yielded a closed-form solution and wasable to be solved by the use of iterative technique, fits the experi-mental data obtained by Maier’s investigation (Maier, 1998) andtheory model developed by Soliman and Sims (1992) for the cir-cular cross-section branch well. In addition, for b.g.e. at the upperbranch A (see Fig. 14) during two and three branches mounted on acurved wall resembling header-feeder configuration of CANDU,Saleh et al. (2011) developed a point sink model including fourmain equations to predict the critical height HOGE and to map theacceleration and velocities flow fields. The four main equations arefunctions of the gaseliquid interface height, the branch mass flowrates, the location of the b.g.e. dip, and the simulated header ge-ometry. The critical height HOGE can be solved by an in-housecomputer code. The predicted HOGE is within 25% of experimentsconducted by Ahmad and Hassan (2006) for moderate to high FrA

(FrA > 10). The details of the above two models are beyond thescope of this paper due to their complexity, the detailed indicationabout the models can refer to relevant literature.

In the present investigations, the research on entrainmentthrough the multiple branches is all base on the circular branchesexcept square branches. However, in view of the possible longitu-dinal cracks in pipes, Armstrong et al. (1992b) investigated intob.l.e. during simultaneous discharge through the two side slots ofsmall width d mounted on a vertical plane and obtained thefollowing correlations with the line-sink assumption:"Frþ1s=L

þ Frþ2ð1þ s=LÞ

#"Frþ1s=L

þ Frþ2ð1þ s=LÞ

#¼ p2 (44)

and

hL¼ s

Lþ 12

26664

Frþ1ðs=LÞ þ

Frþ2ð1þs=LÞ

Frþ1ðs=LÞ2 þ

Frþ2ð1þs=LÞ2

37775 (45)

Frþi ¼ QiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigL3Dr=r

p ¼ Friðd=LÞ1:5; i ¼ 1;2 (46)

where the geometry parameters can refer to Fig. 19b. This modelincluding two simple algebraic equations fits for hand calculations.But the model was not compared with experimental data andfurther validated. In addition, the experiment through the twoparallel slots is not yet conducted.

4. Branch quality models

Branch quality models are applied to the simulation of stableentrainment. Branch quality models are developed for the predic-tion of gas-phase quality through the branch. In the section,existing correlations are reviewed for different T-junctions geom-etries and introduction of eachmodel generally consists of premise,detailed description and comment.

4.1. Single branch

In RELAP5/MOD3.3, the following relationship developed bySmoglie (1984), Smoglie and Reimann (1986) and Smoglie et al.(1987) is adopted: for the flow quality at a bottom branch,


x ¼ x2:5Ro

h1� 0:5ð1þ RÞxð1�RÞ

o

i0:5(47)

where

R ¼ hhb

; xo ¼ 1:151þ ðrL=rGÞ

for the flow quality at a side branch,

x ¼ x1þCRo


o

i0:5(48)

where

C ¼ 1:09 for g:e:C ¼ 1:00 for l:e:

Also, for the flow quality at a top branch, Smoglie (1984)developed the following model:

x ¼ 1� x2Roh1� 0:5ð1þ RÞxð1�RÞ

o

i0:5(49)

However, in RELAP5 the following correlation developed bySchrock is finally adopted:

x ¼ R3:25ð1�RÞ2 (50)

In addition, for a branch mounted on the underpart of the mainpipe at 45� angle, a correlation for determining the branch quality isgiven by Majumdar et al. (1999):

x ¼ xð0:5þ1:25RÞo


o

i0:5(51)

It’s worthmentioning that the form of abovemodels is functionsof the dimensionless interface level and density ratio. Therefore, inprinciple, application of these models is not limited by flow ge-ometries downstream of branch inlet and fluids. Also, these modelscan agree well with the experimental data, but some detailedtrends still cannot be captured by these models (Division, 2001).

In CATHARE, branch quality models are given by Maciaszek andMicaelli (1990): for the flow quality at a bottom branch,

x ¼ aihai þ

ffiffiffiffiffiffiffiffiffiffiffiffirL=rG

p ð1� aiÞi (52)

where the void fraction ai at the branch entrance is a function of h/hOGE. The following form is assumed:

ai ¼ ð1� h=hOGEÞn1

where n1 is equal to 1 in accordance with test data; for the flowquality at a side branch, the similar model is proposed:

x ¼ aihai þ


p ð1� aiÞi (53)

where the void fraction ai at the branch entrance is a function of h/hOGE or h/hOLE and has been adjusted by steam-water data. Its formis divided into four domains:

ai ¼ 0:0 for h � hOGEai ¼ 1:0 for ð � hÞ � hOLEai ¼ 0:5 when h is at the branch centerline

ai

changes continuously when h movesbetween the top and the bottom ofthe main pipe

In this respect a proposal is: for �h < hb,

ai ¼ 1� 0:5ð1þ h=hbÞn2

for h < hb,

ai ¼ 0:5ð1þ h=hbÞn2

and

hb ¼ 0:69½W3t=gr3mðrL � rGÞ�

where n2 is equal to 2 in accordance with test data, and h is positivewhen the interface level h is higher than the centerline of the sidebranch. Also, r3m represents homogenous density in the branch andW3t is total branch mass flow rate.for the flow quality at a topbranch, three domains are distinguished: when h > hOLE (i.e. noentrainment)

x ¼ 0 (54)

when hlim < h < hOLE, the entrainment rate is low. Branch quality xis assumed to vary linearly between x0¼ 0.98 to 1 when h increasesfrom hlim to hOLE.when h< hlim, the entrainment rate is high. Branchquality x is given by:

x ¼ x0aihai þ


p ð1� aiÞi (55)

where

ai ¼ h=hlim

hlim ¼ 2:5ðd=DÞ0:666hOLE�1� R0:15

�

when h is decreased below a critical height called hlim, the interfacewave reaches the branch inlet and liquid entrainment increasesdrastically. Furthermore, any further decrease of h results in aconsiderable decrease of branch quality.

It should be noted that the entrainment models in CATHAREconsider the effect of crossflow, which brings a considerableimprovement to entrainment models. In addition, the detailedexplanation and definition of various parameters can refer to therelevant literature (Maciaszek and Micaelli, 1990).

Stable liquid entrainment through a top branch is hard to modelacross multiple flow regimes, since above models available topredict branch quality are empirical. Welter et al. (2004) built thefollowing model by considering time-averaged values in intermit-tent flow:

x ¼ 11þW3L=W3G

(56)

where


W3L

W3G¼ 3:0

�1� h

hb

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�rLhrGhb

��1�

�hhb

�2�r h�hbh

��v1bv1

�2 � 1i

�hhb

��0:22 h

hbþ 1�

v1b ¼ 1� 1pcos�1

�2hbD

� 1�þ 2p

�2hbD

� 1��

hbD

�1� hb

D

��1=2

The critical height hb can be obtained from Eq. (4) for a givenmass flow rate. In the process of modeling, a steady-state first-or-der approximation is used by averaging effects of two-phase flowintermittency over time domain. In the future, to improve accuracy,higher order terms can be added to include effects of large devia-tion in water level. It’s worth noting that the branch quality modeldoes not only depend on h/hb. Other parameters like fluid densities,branch size d and main pipe diameter D are also necessary indetermining branch quality x.

For the flow quality at a side branch, Hassan et al. (1998)developed the following relationship:

x ¼ 0:2 exp½6Hð1� 11:67HÞ=ð1� HÞ�

þ 0:8�1� H2

�1:3h� 0:0122þ 0:42=�1þ


p �iH(57)

where

H ¼ h� hOLEhOGE � hOLE

It should be emphasized that the model are empirical and onlyis recommended within the range of specific conditions covered inHassan et al. (1998)’s investigation. Also it should be noted thatnew normalized parameters presented in this model could perhapsbe used for developing universal model when the influences ofmeasuring techniques and different geometries are determined.


For the flow quality through two side branches (i.e. branch A andbranch B) mounted on the same vertical plane, empirical correla-tions for the prediction of x were developed in the following forms(Hassan et al., 1996b):

xA ¼ 0:2exp½6HAð1�B1HAÞ=ð1�HAÞ�

þ0:8�1�H2

A

�1:3nB2h�0:0122þ0:42=

�1þ


p �ioHA

(58)

xB ¼ 0:2exp½6HBð1�C1HBÞ=ð1�HBÞ�

þ0:8�1�H2

B

�1:3nC2h�0:0122þ0:42=

�1þ


p �ioHB

(59)

where

Hi ¼hi � hOLE;i

hOGE;i � hOLE;i; i ¼ A or B

B1 ¼ 11:67� 9:67 exph� 0:01ðL=dÞ3

i

B2 ¼ 1þ 0:92 exph� 0:75ðL=dÞ3

i

C1 ¼ 11:67� 3:03 exph� 0:016ðL=dÞ3

i

C2 ¼ 1� 0:71 exph� 0:03ðL=dÞ4

iAt the limit L/d ¼ N, the above models converge to the single-

branch model for x represented by Eq. (57). Moreover, the qualityx at the branch A or B can be predicted with a smaller root-mean-square error when the experimental data corresponding to thesmallest values of branch quality is ignored. However, the modelsare empirical and only are recommended within the range ofspecific conditions covered in Hassan et al. (1996b)’sinvestigation.

Also, for the flow quality through dual side branch mounted onthe same horizontal plane, Hassan et al. (1996a) developed thefollowing model for x in terms of the above normalized parameterH:

x ¼ 0:2exp½6Hð1� 11:67HÞ=ð1� HÞ�

þ 0:8�1� H2

�1:3h� 0:0122þ 0:42=�1þ


p �iH(60)

Themodel is apparently the same formwith themodel for a sidebranch (i.e. Eq. (57)), but solving models of hOGE and hOLE (i.e. Eqs.(38) and (39)) in normalized parameter H is based on dual branchand consider the effect of L/d. In addition, thismodel only is suitablefor the prediction of x through the dual branch possessing the sameFroude numbers. For the quality through dual branch possessingthe different Froude numbers, the model is necessary to bedeveloped.

In aword, the research on branch quality at multiple branches isgrossly inadequate, particularly for the dual branch mounted on anincline plane (i.e. considering angular alignment of branches a), thebranch quality models have not yet been developed.

5. Scaling analysis

When an experiment may not be conducted due to the limita-tion of experiment conditions and funds, scaling analysis can pro-vide a theory foundation for the design of scale-down test facilitieswhich is easy to be performed on the basis of the same investigatedphenomena between engineering practice and test apparatus. Inthis section, the dimensionless groups used for a scaling analysisare summarized for entrainment through a single branch andmultiple branches, and scaling analyses of onset entrainment andstable entrainment (i.e. branch quality) are two main discussionpoints in each sub-problem.

5.1. Single branch

In both plants and existing test, liquid viscosity and surfacetension commonly do not significantly affect vortex formation dueto the larger Fr, but the Froude number usually plays a significantrole in vortex formation. The conclusion is also valid on conditionthat the geometric scale ratio between plant and test exceeds a 4:1ratio (Andreychek et al., 1988). For onset entrainment through asingle branch in a horizontal main pipewith stratified flow, Smoglieand Reimann (1986) pointed out that dimensionless groups wereproposed under the premise of neglecting the effects of surfacetension and viscosity in the following forms:

hbd; Fr ¼ rbv

23b

gdðrL � rGÞ;rGv

22G

rbv23b

;rLv

22L

rbv23b

;dD

(61)


The first group represents the effect of the branch/break size onthe onset entrainment; the second group is the Froude number andrepresents the ratio of inertial force to gravitational force; the lastgroup represents a geometrical parameter showing the relative sizeof branch; the rest two groups represent the effect of crossflow onthe onset entrainment, and the two terms are usually too small tobe neglected due to larger denominator (i.e. the momentum flux inthe branch is far larger than the momentum flux in the down-stream of main pipe).

Therefore, once working medium and a scaling factor, such asscaling factor of flow rate, main pipe diameter or branch diameter,are confirmed, the other parameters in the experimental apparatuscorresponding to the engineering practice are uniquely defined byabovedimensionless groups. These dimensionless groupshavebeenused for entrainment theoretical research and appear in the onsetentrainment models which have been summarized in Section 3.

In addition, based on the Eq. (61), we can know that the equaldimensionless groups indicate the similarity between the model(e.g. the experimental apparatus) and the prototype (e.g. the plant).Thus, the following correlation can be obtained:

hFr ¼ rbv

23b

gdðrL�rGÞiR¼ 1

½d=D�R ¼ 1

Qb ¼ p4d

2

/½D�R ¼hQ2=5b

iR

(62)

where subscript R is the ratio of the dimensionless number in themodel to that in the prototype, and the ratio is equal to 1 whichrepresents the similarity (i.e. the dimensionless number in themodel is equal to that in the prototype). However, for the branchquality, the existing correlations are generally a function of h/hb,where the relation of ½hb�R ¼ ½Q2=5

b �R is ubiquity in the correlation.For example, this relation can be found in onset entrainment modelof RELAP5. Thus, for the branch quality x similarity, the followingcorrelation can be derived:

½x�R ¼ 1/�hhb

�R¼ 1/

"h

Q2=5b

#¼

264 d h

d

Q2=5b

375 ¼ 1/½D�R

¼hQ2=5b

iR

(63)

So, the conclusion proves that the similarity of branch quality xalso can be satisfied on the basis of onset entrainment similarity.

However, through the above analysis, the geometric scalingfactor may seem to get arbitrarily small value, and if so, based onthe equal Froude number, the experimental flow can get a smallvalue so that maximum load of the test can be reduced. However,this may not be true, because larger geometric scale-down factormay result in the distortion of investigated phenomena. For thelarger geometric scale-down factor, although the similarity of theonset entrainment and branch quality is theoretically satisfied, theexperimental phenomena from the onset entrainment to contin-uous entrainment may not be same with the engineering practice.Just like the flow of microchannels could be different from that ofconventional channels (Liang et al., 2012; Peng and Peterson, 1995;Wang and Peng, 1994). Thus, the study of the optimal geometricscale-down factor needs to be concerned in the stage of experi-mental design.


For the dual branch, following Parrott et al. (1991) andArmstrong et al. (1992a,b)and neglecting the effects of surface

tension and viscosity, the relevant physical parameters include QA,QB, gDr/r, d, L and h. Four dimensionless groups are developed by adimensional analysis in the following forms: Fr1, Fr2, L/d and h/d.Moreover, the correlation for b.g.e. and b.l.e. is expected to take thefollowing form:

hbd

¼ f�Fr1; Fr2;

Ld

�(64)

In addition, for the triple discharge, a dimensional analysis usingrelevant physical parameters, neglecting surface tension andviscous effects, finds the following relationship:

hbd

¼ f�Fr1; Fr2; Fr3;

Ld

�(65)

The design of entrainment experiments through multiplebranches mainly based on the header-feeder configuration ofCANDU reactor is guided by the above dimensionless groups.However, scaling research for entrainment at multiple branches ismore shortage than that at single branch, and scaling analysis ofbranch quality x is particularly needed.

6. Conclusions and prospects

In this paper, mainly based on the entrainment phenomena, theonset entrainment model and branch quality model and scalinganalysis, detailed literature review is performed, and comments aremadeafterdescriptionof each sub-problemormodel. In this section,the main conclusions and further work are summarized as follows:

Many entrainment experiments are conducted in the case of thesmall ratio of the diameter of the branch to the diameter of themain pipe (i.e. d/D < 0.2). However, few experimental data seem tobe available when d/D is a larger value. For example, based on theratio of the diameter of ADS-4 pipe to the diameter of main pipe inAP1000 plant (i.e. d/D ¼ 0.62), experiment and theoretical work onentrainment is not yet performed.

Most of entrainment studies are performed in the case ofstratified flow existing in a horizontal main pipe of T-junction. Also,Moon and No (2003) found a strong influence on the dischargequality and developed a new correlation for discharge quality onthe basis of slug flow approaching to T-junction. Moreover, the ef-fects of other flow regimes and flow-regimes in transition region onentrainment at T-junction, such as wavy-stratified flow, shouldperform a study on entrainment mechanism and theoreticalsimulation.

The flow phenomena presenting in the entrainment at T-junc-tion generally include vortex or vortex-free flow, intermittent orcontinuous entrainment and initial depression entrainment orcontinuous depression entrainment. Moreover, these flow phe-nomena are deeply connected to entrainment modeling, forexample, vortex flow or vortex-free flow being the onset criterionshould develop different models of onset entrainment. But the re-lationships among different phenomena do not have a full under-standing yet. Much phenomena research is just verbal descriptioncontaining personal understanding, and images for entrainmentphenomena have a serious shortage. That is a major reason why aunified theory of the same research object cannot be formed.

The literature review indicates that limited information is ob-tained for dual branch with centerlines falling in a vertical, hori-zontal and inclined planes. For a unified cognition of entrainmentphenomena and process and quantifying the effects of variousfactors (i.e. geometry, crossflow, surface tension, wetness, wallcurvature etc.), experimental data and theoretical models urgentlyneed to be augmented, which also has a significant benefit for thedesign of piping networks.


For entrainment at triple discharge, few studies on the inter-action of multiple branches are carried out. Although the interac-tion effect of three branches is basically clear, the existing researchis not enough to quantify the entrainment phenomena and noteven clearly describes entrainment phenomena and generationprogress at triple discharge. In addition, the research of variousfactors such as the effect of crossflow, wall curvature wavy-stratified etc. is not performed yet.

Many onset entrainment models have been develop so far, butthe existing models are not perfect, improvement or developmentwork of models still need to be carried out: for the entrainment at asingle branch, no model not only takes into account the differentangle of branch orientation, but also considers the effect of surfacetension at lower Fr and the modification of various factor such ascrossflow and vortex etc.; for the entrainment at multiple branches,the verification and validation work need to be further performedon the multitudinous models.

The existing investigations show that the airewater two-phaseexperiments are given priority, because it is easy to perform. Rarelysteam-water experiments are found, since steam condensation maybe a big problem and hard to be eliminated, which can result in aseriousdistortionof entrainmentmeasurement.Alsothe steam-waterexperiments demand for steam and water at saturation, which makethe experiment complex and hard to be performed. But it cannot bedenied that the steam-water experiments have a great engineeringsignificance for power stations. In addition, the liquid existing in thenuclearplant isboricacid solution,notpurewater, but any researchersnever perform on the gas-boric acid entrainment experiments. Theeffect of boric acid concentration on the entrainment at T-junction,which is approximate to engineering practice, is unclear yet.

As the technology improves, advanced measuring means suchas the Particle Image Velocimetry (PIV) system etc. should beencouraged in the entrainment research, which contributes toexperimental research. For example, Bowden and Hassan (2006,2007) and Saleh (2008) recommended the PIV for quantitativemeasurement of the flow field, which is practically helpful to un-derstand the phenomena and validate entrainment models.

Studies on models for the prediction of x are insufficientcompared to the research on models for onset entrainment. Also,branch quality models through a single branch at an arbitrary angleand through dual branch mounted on an incline plane are seriouslyinsufficient. In addition, the most existing quality model just canensure accuracy within the range of specific conditions underwhich their experiments are performed, thus the commonality ofthese models is weak and can still be improved.

For the designs of scale-down entrainment experiment, thesimilarities of the Froude number and geometric dimensionlessnumbers are the most important considerations under the premiseof neglecting the effects of surface tension and viscosity. However,it should be noted that the larger geometric scale-down may resultin the serious distortion of the investigated phenomena, even if allthe dimensionless numbers are fulfilled, so the optimal geometricscaling factor is necessary to be considered in the experimentaldesign. In addition, scaling research for entrainment at multiplebranches is more shortage than that at single branch, and scalinganalysis of branch quality x is particularly needed.

Nomenclature

d branch diameter/slot widthD main pipe diametere point on the interface located at the lowest point of the

dipFr Fround numbeFrþ modified Froude numbe

g gravitational accelerationh distance between interface and branch centerlineh*(H) dimensionless heighthlim critical height when the wavy reaches branch inletHOGE critical height at the onset of gas entrainmenthOLE critical height at the onset of liquid entrainmentL separation distance of branches_m volumetric discharge rate per unit lengthq volumetric discharge rate per unit lengthQ volume flow rateROCb dip radius of curvatures(hm) distance between the tip of the meniscus and the branch

centerlinev velocityvd velocity at the entrance of the branchvL,b liquid velocityW mass flow rateDP pressure drop

Greek symbolsq branch inclination anglea angular alignment of branchesai void fractionDr density differencer densitys surface tension coefficientF potential function

Subscripts1 main pipe upstream2 main pipe downstream3 branchA branch 1 corresponding to multiple branchesB branch 2 corresponding to multiple branchesb continuous phaseC branch 3 corresponding to multiple branchesG gasL liquidm meanR ratio of the model to the prototypet total

AbbreviationsADS-4 Automatic Depressurization System Stage Fourb.g.e. (OGE) onset of gas entrainmentb.l.e. (OLE) onset of liquid entrainmentCDE Continuous Depression EntrainmentCVE Continuous Vortex Entrainmentg.e. gas entrainmentIDE Initial Depression EntrainmentIVE Initial Vortex Entrainmentl.e. liquid entrainmentLOCA Loss of Coolant AccidentPRHR Passive Residual Heat RemovalPWR Pressured Water ReactorSB-LOCA Small Break Loss of Coolant Accident

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Entrainment at T-junction: A review work