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Simulation of single- and two-phase naturalcirculation in the passive condensate cooling tankusing the CUPID codeHyoung Kyu Cho a b , Seung-Jun Lee a , Han Young Yoon a , Kyoung-Ho Kang a & Jae JunJeong ca Korea Atomic Energy Research Institute (KAERI), Yuseong , Daejeon , 305-600 , Koreab Department of Nuclear Engineering , Seoul National University , Seoul , 151-742 , Koreac School of Mechanical Engineering , Pusan National University , Busan , 609-735 , KoreaPublished online: 14 Jun 2013.

To cite this article: Hyoung Kyu Cho , Seung-Jun Lee , Han Young Yoon , Kyoung-Ho Kang & Jae Jun Jeong (2013):Simulation of single- and two-phase natural circulation in the passive condensate cooling tank using the CUPID code,Journal of Nuclear Science and Technology, 50:7, 709-722

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Journal of Nuclear Science and Technology, 2013Vol. 50, No. 7, 709–722, http://dx.doi.org/10.1080/00223131.2013.791891

ARTICLE

Simulation of single- and two-phase natural circulation in the passive condensate cooling tank usingthe CUPID code

Hyoung Kyu Choa,b, Seung-Jun Leea, Han Young Yoona, Kyoung-Ho Kanga and Jae Jun Jeongc∗

aKorea Atomic Energy Research Institute (KAERI), Yuseong, Daejeon 305-600, Korea; bDepartment of Nuclear Engineering, SeoulNational University, Seoul 151-742, Korea; cSchool of Mechanical Engineering, Pusan National University, Busan 609-735, Korea

(Received 7 January 2013; accepted final version for publication 22 March 2013)

For the analysis of transient two-phase flows in nuclear reactor components, a three-dimensional thermal-hydraulic code, named CUPID, has been developed. In the present study, the CUPID code was appliedfor the simulation of the PASCAL test facility constructed with an aim of validating the cooling and oper-ational performance of the passive auxiliary feedwater system (PAFS). The PAFS is one of the advancedsafety features adopted in the Advanced Power Reactor + (APR+ ), which is intended to completely re-place the conventional active auxiliary feedwater system. This paper introduces the simulation results forthe passive condensate cooling tank (PCCT) of the PASCAL facility performed with the CUPID code inorder to investigate the thermal-hydraulic phenomena in the PCCT. The simulation showed that the im-portant thermal-hydraulic characteristics in the PCCT, such as two-phase natural circulation and boil-offphenomena, can be successfully reproduced by CUPID. Two important validation parameters, collapsedwater level and local liquid temperature, were quantitatively well captured in the simulation. This paperpresents the description of the PASCAL test facility, the physical models of the CUPID code, and its sim-ulation result for the PCCT.

Keywords: thermal hydraulics; two-phase flow; two-fluid model; CUPID; PASCAL; passive cooling system

1. Introduction

Recently, greater attention has been paid to pas-sive safety features for advanced nuclear power plants.In order to improve the reliability and performance ofthe safety systems and to reduce their complexity, theyincorporate the use of passive, gravity-fed water sup-plies for an emergency core cooling and a natural cir-culation decay heat removal system from the primarysystem and containment. The passive auxiliary feedwa-ter system (PAFS) is one of the passive safety featuresadopted in the Advanced Power Reactor + (APR+ )which is intended to completely replace the conventionalactive auxiliary feedwater system [1]. In the PAFS, thesteam from steam generators condenses when it flowsthrough heat exchanger tubes submerged into a largewater pool. Inside the water pool, the hydraulic driv-ing force is very small compared with conventional ac-tive systems, and the fluid flow is multi-dimensional withsubcooled boiling and flashing. Thus, a sophisticatedtwo-phase thermal-hydraulic analysis is required to as-sess the test data and to evaluate the performance of

∗Corresponding author. Email: jjjeong@pusan.ac.kr

the passive safety system [2]. This technical need for themulti-dimensional analysis motivated the developmentof a three-dimensional component analysis code, namedCUPID [3], which is in progress at KAERI. The objec-tive of the development is to support a resolution for thethermal-hydraulic issues regarding the transient multi-dimensional two-phase phenomena which can arise inan advanced light water reactor.

The CUPID adopts the three-dimensional two-fluidthree-field model with unstructured grids for complexgeometry. It has been verified against standard concep-tual problems of single- and two-phase flows and vali-dated for thermal-hydraulic experiments in our previousstudies[4–6]. The assessment strategy for the future ver-ification and validation was outlined in Jeong et al [7].Recently, the CUPID code was coupled with a sys-tem analysis code, namedMARS[8], and a three-dimen-sional kinetics code, named MASTER [9], which is ex-pected to provide the advanced multi-scale and multi-physics calculations for many safety-related issues of thelight water reactors. The verification results for these

C© 2013 Atomic Energy Society of Japan. All rights reserved.

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Figure 1. Schematic diagram of the APR+ PAFS and the PCHX.

multi-scale and multi-physics calculations showed thata coupled thermal-hydraulic analysis using the CUPIDcode can be one of its major applications in the future.

A simulation of an advanced light water reactor thatincorporates a passive secondary cooling system, suchas the PAFS, is one of the applications that require themulti-scale thermal-hydraulic analysis. The PAFS coolsdown the steam generator secondary side by condens-

ing steam in nearly-horizontal U-tubes (passive conden-sation heat exchanger: PCHX) submerged into a largewater pool (passive condensate cooling tank: PCCT) asshown in Figure 1 [10,11] and, eventually, removes thedecay heat from the reactor core. The thermal-hydraulicphenomena inside the PCHX are expected to be repro-ducible by one-dimensional system analysis codes be-cause the condensation in a nearly horizontal tube has

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Journal of Nuclear Science and Technology, Volume 50, No. 7, July 2013 711

Figure 2. PASCAL test facility.

been modeled in many nuclear applications. Contraryto this, for the PCCT, a multi-dimensional analysis toolis required in order to reproduce the natural circulationand the boil-off of the inventory water precisely. There-fore, a coupled calculation between a one-dimensionalsystem analysis code and a multi-dimensional compo-nent analysis code is an attainable way to simulate thelong transient (longer than 8 hours) of the accident sce-nario with a reliable accuracy. In this approach, the sys-tem analysis code is supposed to simulate the overallsystem including the primary system of the reactor, thesteam generators, the PCHX, etc., while the componentcode covers the PCCT region solely.

In this study, the CUPID code was applied for thesimulation of the PCCT of the PASCAL test facility,which is constructed in a bid to validate the cooling andoperational performance of the PAFS. Prior to the cou-pled calculation between MARS and CUPID, a stand-alone calculation for the PCCT has been carried outby CUPID imposing a heat source boundary condi-tion for the heat transfer from the PCHX to investigatethe important thermal-hydraulic characteristics in thePCCT, such as natural circulation and boil-off phenom-ena. This paper presents the description of the PASCALtest facility, the physical models of the code, and its sim-ulation results for the PCCT.

2. PASCAL test facility

The PAFS is the auxiliary feedwater system which iscapable of condensing steam generated in a steam gen-erator passively and re-feeding the condensed water tothe stream generator by gravity as illustrated in Figure 1

[10,11]. It incorporates 240 horizontal U-tubes (PCHX)submerged into a large water pool (PCCT). The steamflows through the tubes and condenses due to the heattransfer from the PCHX to the PCCT. The water tem-perature inside the PCCT increases with the heat releaseuntil it reaches the saturation temperature, and then,consequently, boiling is activated. The water level de-creases with the boiling and the steam generator feedingcan be continued until the water level is decreased lowerthan the PCHX elevation. The system was designed toprovide the cooling capability for removing the wholedecay heat from the reactor core longer than 8 hoursduring accident transients.

With an aim of validating the cooling and opera-tional performance of the PAFS and investigating thecondensation heat transfer in the PCHX and the natu-ral convection in the PCCT, the PASCAL test facilitywas constructed [12]. A single nearly horizontal U-tube,of which dimension is the same as that of the prototypicU-tube of the APR+ PAFS, is simulated in the PAS-CAL. The fulfillment of the heat removal requirementvia the PAFS has been validated and the effect of non-condensable gas and the start-up transient of the PAFShave been investigated using the test facility. By perform-ing the test, the major thermal-hydraulic parameters,such as local/overall heat transfer coefficients, fluid tem-perature inside the tube, wall temperature of the tube,and pool temperature distribution in the PCCT, wereproduced.

Figure 2 shows the photos and the schematic dia-gram of the PASCAL test facility [12]. It is composedof a steam-supply line, the PCHX (a single tube), the

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712 H.K. Cho et al.

PCCT (a slab), and a return-water line for the condensedwater. The steam generator supplies saturated steam at7.4MPa. It is connected to the heat exchanger tube witha steam-supply line and a return-water line. The PCHXand the PCCT of the PASCAL facility were designed ac-cording to a volumetric scalingmethodology [13]. It sim-ulates a single tube among 240 tubes in the prototype,and its diameter and length are preserved with the pro-totype. Thus, the volumetric scaling ratio of the PCHXis 1/240. The volume of the PCCT was reduced to 1/240of the prototype as well. In order to preserve the natu-ral convection flow in the PCCT, the height of the pool,11.5 m, is determined to be the same as that of the pro-totype. The width of the PCCT in the PASCAL facilityis 6.7 m, which is a half of that of the prototype, con-sidering the symmetric geometry of the PCCT in thewidth direction. Consequently, the depth of the PCCTis 0.112 m, which is equivalent to 1/120 of the proto-type and the PCCT of the PASCAL facility has slabgeometry.

In the PASCAL test facility, a total of 328 instrumen-tations are installed for the measurement of thermal-hydraulic phenomena including thermocouples for thesteam and water temperature and differential pressuretransmitters for the water-level measurement. Details ofthe instrumentation were described in Bae et al [10].

3. Physical models of the CUPID code

The CUPID code adopts the two-fluid three-fieldmodel [2] for two-phase flows. It uses three momentumequations if the droplet behavior needs to be modeledseparately; otherwise it uses two momentum equations.In this analysis, the droplet field was deactivated sincedroplets exist only above the free surface and play a mi-nor role for the overall transient. It incorporates bothopen- and porous-medium models. In the present cal-culation, the porous-medium model was selected in or-der to save the computational cost for the long transientanalysis (8 hours), focusing on the overall two-phasephenomena inside the PCCT instead of the detailedflow behavior near the heat exchanger. Accordingly, thecomplicated geometry of the heat exchanger and itssupporting structures were considered using porosity,permeability, heat transfer area, etc. The slab geome-try of the PCCT was modeled in two dimensions by as-suming that the depth directional flow behavior is neg-ligible. The effect of the two planes confining the slabwas considered by implementing wall friction terms inthe momentum equations. This chapter introduces thesingle- and two-phase flow models in the porous mediaimplemented for the present simulation.

In the two-fluid model for the two-phase flow anal-ysis, the mass, energy, and momentum equations foreach field are established separately, and they are subse-quently linked by the interfacial mass, momentum, andenergy transfer models. For a mathematical closure ofthe governing equations, constitutive relations for the

Figure 3. Inter-phase surface topology map.

interfacial transfer terms are necessary, depending onthe flow patterns and their inter-phase shape. In thePCCT of the PAFS, various flow regimes may appearduring the transient including a single-phase liquid flow,bubbly flow, free surface, and single-phase steam/airflow. In order to consider these flow patterns, the inter-phase surface topology map [14] was applied as a flowregime map for the multi-dimensional two-phase flow.Since the heat flux on the PCHX outer surface is lowerthan the critical heat flux, simplified flow patterns weredefined, such as the bubble topology, drop topology,sharp interface topology, and the interpolation regionsamong them. Figure 3 shows the concept of the inter-phase topology map. The transition criteria of the voidfraction, the void fraction gradient, and the definition ofthe characteristic length (δ) are as follows:

{αg,bc = 0.3αg,cm = 0.9

,

{γ1 = 0.2γ2 = 0.45

, and

�δ = Vi∑f

|Sf,x|/Nfi + Vi∑

f|Sf,y|/Nf

j + Vi∑f

|Sf,z|/Nfk, (1)

respectively, where γ = 0.5 · �δ · [∣∣ ∂αg∂x

∣∣i + ∣∣ ∂αg∂y

∣∣j+∣∣ ∂αg∂z

∣∣k].

Once the local topology is determined for eachcell, the interfacial area and interfacial transfer mod-els, thereafter, are defined depending on the topology ofeach cell.

The interfacial area concentration is defined by

Ai = 6αkDk

, (2)

where k is the phase of the dispersed particle and Dk isthe particle diameter. Hibiki [15] and Kataoka [16] cor-relations were adopted for the bubble and droplet diam-eters, respectively. For bubble topology,

Db = 4.34 · Lo · N−0.335Lo · α0.170 · Re−0.239

b , (3)

where NLo = LoDH

, Reb = ε1/3Lo4/3

ν f, Lo =

√σgρ

,

ε = g| jg| exp(−0.0005839Re f ) + | j |ρm

(−dpdz

)F

× {1 − exp (−0.0005839)Re f

}, j = jg + j f ,

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Journal of Nuclear Science and Technology, Volume 50, No. 7, July 2013 713

Re f = j f DH

ν f, and

(− dp

dz

)Fis the frictional pressure

drop calculated with Lockhart–Martinelli’s correlation[17]. For mist topology,

Dd (P, αg) = 0.01σ

ρg j2gRe2/3g

(ρg

ρ f

)−1/3 (μg

μ f

)2/3

, (4)

where Reg = jg DH

νg. For interface topology, the interfa-

cial area is evaluated by

Ai = |∇αg| [18]. (5)

The interfacial momentum transfer term, Mik, in-cludes the interfacial drag, themomentum exchange dueto the phase change (bulk boiling/condensation andwallboiling) at the interface, and the virtual mass force. Mikis written as

Mig = −Fgl + �vugi + �wallugi + Fvm = −Mil . (6)

The interfacial drag force terms in the momentumequations can be expressed as follows: for dispersedtopology:

Fgl = 18AiρcCD|ug − ul |(ug − ul ), (7)

for interface topology:

Fgl = 12AiρmCi (ϕ)|ug − ul |(ug − ul ). (8)

Interfacial drag coefficientsCD andCi (ϕ) are definedby the following correlations: for bubble topology [19]:

Cb = 24Reb

(1 + 0.15Re0.687b

)for 0 < Reb ≤ 1000

Cb = 0.44 for Reb > 1000,(9)

for mist topology [19]:

Cd = 24Red

(1 + 0.15Re0.687d

)for 0 < Red ≤ 1000,

Cd = 0.44 for Red > 1000,(10)

for interface topology [14]:

Ci (ϕ) = Ci,tan + (Ci,ort − Ci,tan) |cosϕ| , (11)

where Ci,tan = 0.005, Ci,ort = 1, and

cosϕ = (ug − ul ) · ∇α∣∣∣(ug − ul )∣∣∣ |∇α|

.

The interfacial drag force in the transition topologywas calculated from the linear interpolation between two

values on the boundaries of the two different topolo-gies:

Fgl = χi (ug − ul ), (12)

where (χi )transition = w · (χi )1 + (1 − w) · (χi )2,

w = αg,cm − αg

αg,cm − αg,bcor w = γ2 − γ

γ2 − γ1,

(χi )1 = χi (αg,bc) or (χi )1 = χi (γ1),

(χi )2 = χi (αg,cm) or (χi )2 = χi (γ2).

For the virtual mass force, the followingmodel proposedby Drew et al. [20] was applied:

Fvm = Cvmg αgαlρm

∂(ul − ug)

∂t, (13)

where

Cvmg =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

(1 + 2αg

)2(1 − αg

) for αg < 0.5,(3 − 2αg

)2αg

for 0.5 ≤ αg ≤ 1.

The interfacial mass and the heat transfer terms arewritten as

�g = �v + �wall = −�l , (14)

Qig = Ps/P · Hig Ai (Tsat − Tg) + �vhgi + �wallhg,sat,(15)

Qil = Hil Ai (Tsat − Tl ) − �vhli − �wallhl , (16)

where (hgi , hli ) = (hg,sat, hl ) if � ≥ 0, and (hgi , hli ) =(hg, hl,sat) if � < 0.

Because the sum of Qig and Qil is zero, the volumet-ric vapor generation rate is represented as

�v = −PsP Hig Ai (Tsat − Tg) + Hil Ai (Tsat − Tl )

hgi − hli. (17)

The interfacial heat transfer coefficients for eachtopology adopted for the present solver are listed below.For bubble topology (Ranz and Marshall [21]),

Hik = kkNubDb

and Nub = 2 + 0.6Re0.5b Pr0.3l , (18)

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Table 1. Models for wall heat partitioning.

Variables Models References

Active nucleate site density N′′ = [185 (Tw − Tsat)]1.805 CFX4 [23]

Bubble departure frequency f =√

4g(ρl−ρg)3Db,departρl

Bubble departure diameter Db,depart = 0.0208 · θ ·√

σ

9.81(ρl−ρg)θ = 38◦

Fritz [24]

Bubble waiting time tw = 0.8f CFX4 [23]

Heat transfer coefficient hc,l = St · ρl · cpl · |�ul | ,hc,g = St · ρg · cpg · ∣∣�ug∣∣ , St = 0.0045

Single-phase heat transfer area A1 f = 1 − A2, f

Two-phase heat transfer area A2 f = N′′ πD2b,depart4 K

Bubble influence factor K = 4

for mist topology (Ranz and Marshall [21]),

Hik = kkNudDd

and Nud = 2 + 0.6Re0.5d Pr0.3g , (19)

and for interface topology (Tentner et al. [14]),

Hik = Stρkcp,k|ugτ − ulτ |, (20)

where St = 0.0045(ρg|ug|μl/ρl |ul |μg)1/3 and ugτ − ulτ= (ug − ul ) − [

(ug − ul ) · ∇α|∇α|

] ∇α|∇α| .

The interfacial heat transfer term in the transitiontopology was calculated from the following linear inter-polation as described in Equation (12):

(HikAi )transition = w · (HikAi )1 + (1 − w) · (HikAi )2 .

(21)During flashing, where Tl > Tsat, the minimum value

of the liquid to interface heat transfer rate is set by thefollowing approximation [22]:

(Hil Ai )flashing = αlρlCpl

δt, (22)

where δt = 0.05. The temperature of superheated liquidquickly dropped to the saturated temperature due to thelarge interfacial heat transfer rate of Equation (22).

Moreover, subcooled boiling occurs at the surfaceof the PCHX and on this account, a heat-partitioningmodel for the heating surface is required. The mecha-nisms of a heat transfer from the wall to a two-phaseflow consist of the surface quenching (qq), evaporation(qe), and single-phase convections (qwlc and qwgc). Thewall-to-liquid heat transfer (qwl) is the sum of the qq andqwlc. It is assumed that the direct contact heat transferbetween droplets and the wall is negligible so that a gasphase convective heat transfer is merely considered forthe mist topology (qwgc = qwg). An equation of the heatflux conservation on a heated surface is then:

qwall = w · (qq + qe + qwlc

) + (1 − w) · qwg, (23)

where

w = min[1,max

(0,

αg,cm − αg

αg,cm − αg,bc

)].

The closure relations for this heat flux partitioningare listed in Table 1. The wall vapor generation rate iscalculated by

�wall = qe(hg,sat − hl )

. (24)

In the present calculation for the PASCAL test facil-ity, the porous-medium model was selected and the slabgeometry of the PCCT was modeled in two dimensions.In order to consider the effect of the two planes confin-ing the slab and the pressure drop caused by the internalstructures, such as the heat exchanger and the support-ers, the wall friction and the form loss models were im-plemented as

�Mwk = −Fwk�uk, (25)

where

Fwk =(fwk2Dh

+ αkKL

)ρk|�uk|,

fk = A+ BRe1/m

: wall friction factor (Kakac et al. [25]),

A= 0, B = 16, m = 1 if Re < 2100;

A= 0.0054, B = 2.3 × 10−8,

m = −2/3, if 2100 ≤ Re < 4000;

A= 1.28 × 10−3, B = 0.1143,

m = 3.2154 if 4000 ≤ Re;

K: form loss coefficient.The wall friction term was activated for the con-

tinuous phase in the dispersed topologies and for both

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Table 2. Initial and boundary conditions.

Parameter Value

Initial pressure 0.1013 MPaInitial liquid temperature 40◦CInitial gas temperature 40◦CInitial water level 9.8 mOutlet pressure 0.1013 MPaPower Indicated in Figure 5

phases in the interface topology. The form loss coeffi-cient was obtained from the resistance coefficient of thecircular smooth cylinder in a plane-parallel flow [26].

The CUPID code incorporates two models for theturbulent viscosity: one is the mixing length model andthe other is the k–ε model. For this calculation, the for-mer proposed by Noto and Matsumoto [27] was used.

4. Calculation result

Among a series of the PASCAL experiment, testnumber SS/PL-540-P1 was selected in this analysis,which was performed with 540 kW of the steam gener-ator power and correspondent with the core decay heatin APR+ at 300 seconds [10]. A transient calculationfor 28,800 seconds was performed using the CUPIDin order to investigate the natural circulation and theboil-off phenomena in the PCCT of the PASCAL testfacility. It was modeled in two dimensions using theporous-medium model, where a total of 1815 (33× 55)meshes were used. Figure 4 shows the computational do-main of the calculation and the initial condition of thevoid fraction, and the initial and boundary conditionsare summarized in Table 2.

Figure 4. Computational domain and initial condition ofvoid fraction.

The initial PCCT water level was 9.8 m and the re-gion above the free surface was filled with air. The ini-tial liquid and gas temperatures were 40◦C. A pressureboundary condition was imposed at the top-right cellof the PCCT as indicated in Figure 4. The pressure atthe boundary was maintained at 0.1013MPa during thetransient. In two porous zones that include the PCHXand its supporting structures, the porosity and perme-ability were applied considering their geometries. Theheat released from the PCHX was simulated by impos-ing a volumetric heat source boundary condition on thesolid part of the porous zone, and the transient powervalues were obtained from the experimental measure-ment results [10]. Figure 5 shows the measurement re-

Figure 5. Imposed power transient and axial power distribution.

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716 H.K. Cho et al.

Figure 6. Mesh convergence test results (void fraction and liquid temperature).

sults on the total power released from the PCHX surface

and the local power ratio(q ′′local/q

′′average

). Themesh con-

vergencewas testedwith the defaultmesh and a finer one(66 × 110). Using the two different mesh types, the voidfraction distributions and the liquid temperature pro-files obtained at two different elevations are presentedin Figure 6. The temperature profile obtained with thefiner mesh has a slightly steeper inclination near the left-side wall, but a reasonable convergence was achieved be-tween the default mesh and a finer one in general.

The observed important phenomena in the experi-ment are illustrated in Figure 7 and are listed as fol-lows.

(1) Subcooled boiling on the PCHX surface and im-mediate condensation due to the high subcool-

Figure 7. Major T/H phenomena in the PCCT.

ing of the water for the early stage of the experi-ment.

(2) Single-phase natural circulation due to the heatrelease from the PCHX.

(3) Flashing near the free surface: The liquid tem-perature increases with time and at a certain mo-ment, it may exceed the 100◦C near the PCHX.But the hydraulic head ensures the liquid in asubcooled state (the saturation temperature nearthe PCHX is around 115 ◦C). When the heatedwater moves up, however, it becomes a super-heated liquid due to the pressure decrease alongthe elevation. Eventually, the superheated liquidturns into steam very rapidly by a flashing.

(4) Transition from a single-phase natural circula-tion to a two-phase natural circulation: With theinitiation of the flashing, a two-phase natural cir-culation can be established.

(5) Deviation of the free surface and droplet gener-ation: When the bubbles pass through the freesurface, droplets can be generated and the strongupward flow can cause surface deviations fromhorizontal.

(6) Boiling-off: The water level in the PCCT de-creases gradually with boil-off and the passivecooling capability of the PCCT can be contin-ued until the water level reaches the elevation ofthe PCHX.

The purpose of the present simulation was to verifywhether the CUPID code can reproduce these thermal-hydraulic phenomena in the PCCT and to validate rele-vant models.

Figure 8 indicates the liquid temperature distributionat 900 seconds. As the calculation started, the heat wasimposed on the PCHX and the water temperature nearthe PCHXwas subsequently increased.Due to the buoy-ancy, the heated water rose up and the natural circula-tion was activated in the clockwise direction. Figure 9presents the phase change rates on the PCHX in theporous region and in the bulk fluid at 900 seconds. Thewall evaporation rate was calculated by the subcooled

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Figure 8. Calculated liquid temperature at 900 seconds.

boiling model and the condensation rate was calculatedin the bulk fluid by the interfacial heat andmass transfermodel. It was shown that the evaporation and condensa-tion rates are almost identical at each cell, meaning thatthe subcooled boiling and the immediate condensationnear the PCHXobserved in the experiment as illustratedin Figure 7 were properly reproduced in this calculation.

Figure 10 shows the behavior of the void fractiondistribution until a flashing was initiated. As the watertemperature increased, the water level was elevated from

Figure 9. Calculation results: evaporation and condensationrates at 900 seconds.

9.8 to 10.4 m owing to swelling (Figure 10(a) and (b)).For initial 7000 seconds, the single-phase natural circu-lation was continued because the liquid subcooling hadbeen maintained, but after that, a two-phase region ap-peared near the free surface as presented in Figure 10(c).Note that this phase change was induced by the flash-ing of the water. Due to the hydraulic head of the wa-ter, the pressure at the top of the PCHX was 0.173 MPaand the saturation temperature was 115.7◦C. As a result,the liquid could be heated up to 107◦C and then it roseto the free surface along the left side wall as indicatedin Figure 11. Since the pressure near the free surfacewas close to the atmospheric pressure, the liquid becamesuperheated water as it flowed upward, and a flashingwas subsequently initiated. After the flashing, the water

Figure 10. Calculation results: void fraction. (a) 0 second, (b) 5000 seconds, (c) 7500 seconds.

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Figure 11. Liquid temperature and liquid superficial velocityat 7000 seconds.

temperature dropped to the saturation temperature andthe liquid flowed downward along the other side wall,and, eventually, the two-phase natural circulation wasestablished. The start of the two-phase natural circula-tion caused the acceleration of the liquid by bubbles andresulted in a remarkable increase of the liquid velocity asplotted in Figure 12. Due to a high velocity of the bub-bles while passing through the free surface, it was devi-ated from horizontal as shown in Figure 10(c). Qualita-tively, these are well correspondent with the experimen-tal observation result.

The void fraction distributions after the flashing areplotted in Figure 13. Due to the flashing near the freesurface, the water level decreased gradually and reachedthe PCHX elevation in the end. The heat removal bythe two-phase natural circulationwas then finished. Thisresult showed that the heat removal by the boil-off

Figure 12. Liquid velocity transient.

lasts longer than 8 hours (28,800 seconds) as designed.Figure 14 compares the liquid temperature distributionsin the experiment and the calculation in the case thatthey had the same water level. It shows that the over-all temperature contours were well preserved. The cal-culated andmeasured temperatures agree well especiallyat the high-temperature region caused by the movementof the heated liquid from the PCHX to the left side wall.Approximately 1◦C difference between the two cases ex-ists in the downward liquid near the right side wall andthe bottom wall. A quantitative comparison for thesetemperature contourswas not conducted considering thesmall difference (<4.4◦C) between the highest and low-est temperatures and the uncertainty of the temperaturemeasurement (± 1◦C).

Figure 13. Water-level decrease due to the boil-off: (a) 7000 seconds, (b) 18,000 seconds, and (c) 28,800 seconds.

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Figure 14. Liquid temperatures in the experiment and thecalculation (water level = 9.3 m).

The non-condensable gas quality (Xnc) at the exit ofthe PCCT is shown in Figure 15, which is expressed as

Xnc = mnc

mgas,mixture. (26)

Initially, the region above the water level was filledwith air. With time, the non-condensable gas qualitygradually decreased with the evaporation from the free

Figure 15. Non-condensable gas quality transient.

surface, although the single-phase natural circulationwas continued. After 5000 seconds, the evaporationrate increased with the liquid temperature and the non-condensable gas quality significantly decreased and be-came almost zero as the two-phase natural circulationinitiated. This implies that the steam–airmixture that ex-ists above the free surface was properly handled by thepresent solver.

In Figure 16, the liquid temperature transients attwo different positions were compared between the

Figure 16. Liquid temperatures transient in the experiment and the calculation: (a) positions for comparison and (b) liquid tem-perature transient.

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Figure 17. Collapsed water-level behavior.

experiment and the calculation: one is located 0.3 m be-low the initial free surface elevation and the other 0.1 mbelow the PCHX. The locations are indicated in Fig-ure 16(a). If the water level is below the position andthe void fraction becomes 1.0 in the calculation, the liq-uid is assumed to be saturated. In the case of Position1, therefore, the liquid temperature after the water levelbecame lower than the elevation (about 12,000 seconds)meant the saturation temperature. The liquid tempera-ture gradually increased from 40◦C with the heat releasefrom the PCHX and settled down as it reached the sat-uration temperature. The experimental result was wellcaptured by the calculation not only qualitatively butalso quantitatively.

Figure 17 shows the collapsed water-level behaviorin the boil-off simulation. The error in the water leveldecreasing rate is 6.4% for the whole transient. Despitethat the boiling-off was started, there existed a certainportion of the sensible heat transfer because the waternear the heat exchanger still remained in a subcooledstate due to the hydraulic head of the water. Therefore,the underestimated sensible heat transfer could result inthe error in the decreasing rate. On the other hand, theerror can be caused by the estimation of the heat lossduring the two-phase natural circulation. Since the ex-periment provides neither heat loss rate nor thewall tem-perature measurement data, the heat loss rate was esti-mated by comparing the liquid temperature increasingrate and the imposed power. But in the two-phase con-ditions, the error can be enlarged with the distorted andfluctuating water level. In spite of the error, the overallboil-off procedure was reasonably well reproduced bythe present solver. Thus, we concluded that the modelsand the constitutive relations implemented for this sim-ulation can be applied for the analysis of the PASCALfacility.

More validation works need to be performed to ex-tend this solver for the analysis of the PAFS in APR+since the PCCT is not a slab geometry; hence, a three-dimensional analysis is desired. Moreover, the APR+

PAFS has 240 heat exchangers in the PCCT and therecertainly exists the effect of the heat exchanger bundlefor the heat transfer and pressure drop. Therefore, theheat exchanger bundle models need to be implementedfor the porous-medium model of the present solver.

5. Conclusion

In the present study, the CUPID code was appliedfor the simulation of the PCCT of the PASCAL test fa-cility. It was modeled solely without the PCHX by im-posing a heat source boundary condition. The porous-medium model was applied in order to consider the ef-fect of the distributed structures that give resistance tothe natural circulating flow. The inter-phase topologymethod was employed for the various flow patterns thatmay appear during the transient of the PCCT. The longtransient (28,800 seconds) of the thermal-hydraulic phe-nomena inside the PCCTwas successfully simulated andthe important characteristics were qualitatively well re-produced by the CUPID code including the natural cir-culation and the water-level decrease by the boil-off. Theliquid temperature transients and the water level de-creasing rate calculated by CUPID were analyzed quan-titatively by comparing with the experimental results. Itwas shown that these parameters are in good agreementwith their values obtained from experiments.

In the future, the PASCAL test facility will be sim-ulated using the coupled MARS-CUPID code and thefeasibility of the multi-scale thermal-hydraulic analysisfor the passive cooling system will be tested. Afterward,more validation work and improvement required to ex-tend this solver for the full-scale PAFS analysis will becarried out, which include the validation for the three-dimensional natural circulation and the implementationof the heat exchanger bundle model.

AcknowledgementsThis work was supported by Nuclear Research & Devel-

opment Program of the NRF (National Research Foundationof Korea) grant funded by the MEST (Ministry of Education,Science and Technology) of the Korean government (Grantcode: M20702040003-08M0204-00310).

Nomenclature

Ai : Interfacial area concentrationC : Drag coefficientCpl : Specific heatD : Diameter

DH : Hydraulic diameterF : Interfacial force term

fwk : Wall friction factorh : EnthalpyH : Interfacial heat transfer coefficientH : Heightj : Superficial velocityK : Form loss coefficientL : Elevation or length

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m : MassM : Momentum transfer termN : Number of faces at a cellNu : Nusselt numberPr: Prandtl numberQ : Interfacial heat transfer termq : Wall heat transfer termq” : Wall heat fluxRe: Reynolds numberSt : Stanton numberSf : Face area between cellsδt : Time for flashingu : VelocityV : Cell volumew : Weighting factorXnc: Non-condensable gas quality

Greek letter

α : Volume fractionε : Energy dissipation rate per unit massδ : Characteristic lengthγ : Dimensionless void fraction gradient�: Bulk phase change rate

�wall: Wall evaporation rateχ : Interfacial friction coefficientμ : Dynamic viscosityν : Kinematic viscosityρ : Densityσ : Surface tension�: Total phase change rate

Superscripts

vm : Virtual mass

Subscripts

b : Bubblebc: Bubble-churn transitionc : Continuous phase

cell: Cellcm: Churn-mist transitiond : Dropletf : Cell facef : FluidF : Frictiong : Gasi : Interfacek : Gas, liquid or dropletl : Liquidm : Mixturenc: Non-condensableτ : Tangentialsat: Saturations : Steamv : Vapor

vm: Virtual masswall: Wall

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