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Nuclear Engineering and Design 249 (2012) 364– 378

Contents lists available at SciVerse ScienceDirect

Nuclear Engineering and Design

jo u r n al hom epage : www.elsev ier .com/ locate /nucengdes

evelopment of a thermal–hydraulic system code, TAPINS, for 10 MW regionalnergy reactor

eon-Gun Lee ∗, Jong-Won Kim, Goon-Cherl Parkepartment of Nuclear Engineering, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-744, Republic of Korea

r t i c l e i n f o

rticle history:eceived 11 February 2012eceived in revised form 22 April 2012ccepted 25 April 2012

a b s t r a c t

Small modular reactors (SMRs) with integral system layout have been drawing a great deal of attentionas alternative options to branch out the utilization of nuclear energy as well as to offer the inherent safetyfeatures. Serving to confirm the design basis and analyze the transient behavior of an integral reactorsuch as REX-10, a thermal–hydraulic system code named TAPINS (Thermal–hydraulic Analysis Programfor INtegral reactor System) is developed in this study. The TAPINS supports the simple pre-processingto build up the frameworks of node diagram for the typical integral reactor configuration. The TAPINSbasically consists of mathematical models for the reactor coolant system, the core, the once-throughhelical-coil steam generator, and the built-in steam–gas pressurizer. The hydrodynamic model of theTAPINS is formulated using the one-dimensional momentum integral model, which is based on the ana-lytical integration of the momentum equation around the closed loop in the system. As a key contributionof the study, a dynamic model for the steam–gas pressurizer with non-condensable gas present is newlyproposed and incorporated into the code. The TAPINS is validated by comparing against the experimental

data from the pressurizer insurge tests conducted at MIT (Massachusetts Institute of Technology) andnatural circulation tests in the RTF (REX-10 Test Facility) at RERI (Regional Energy Reactor Institute). Fromthe comparison results, it is demonstrated that, notwithstanding a few simplifying assumptions and theundemanding solution method to facilitate solutions for transients, the TAPINS can provide a reasonableprediction on the performances and the transients of an integral reactor system operating on naturalcirculation.

. Introduction

The substantial amount of R&D that has been carried out onmall modular reactors by research groups from around the globeeveals the rising worldwide expectation for an innovative andeliable nuclear system. The application range of these nuclear reac-ors is no longer restricted to electricity generation. As a flexiblend cost-effective energy alternative, SMRs have become one ofhe preferred options for non-electrical applications such as sea-ater desalination, ship propulsion, heat supply stations and so

orth. The most promising SMR candidates to be deployed include&W mPower (Spring, 2010), NuScale (NuScale Power, 2010), 4SIshii et al., 2011), and SMART (Zee et al., 2007). These upcomingMRs employ an integral layout for the major system components.esides its multi-purpose applicability, the integral reactor is favor-

ble in terms of safety as the possibility of system depressurizations lowered by localizing the radioactive coolant in one reactor vesselIAEA, 1995).

∗ Corresponding author. Tel.: +82 2 880 8339; fax: +82 2 889 2688.E-mail address: yeongun2@snu.ac.kr (Y.-G. Lee).

029-5493/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.nucengdes.2012.04.020

© 2012 Elsevier B.V. All rights reserved.

At Seoul National University (SNU), RERI undertook an exten-sive project in 2005 to develop a new SMR, REX-10, which has arated thermal output of 10 MW (Kim et al., 2009a). REX-10 is asmall-sized integral pressurized-water reactor (iPWR) that can pro-vide small-scale electricity generation and district heating either inthe vicinity of densely populated cities or in remote areas far frompower grids. Fig. 1 shows a schematic diagram of REX-10. Housedin the reactor pressure vessel are a thorium-fueled core, a built-insteam–gas pressurizer, a once-through steam generator (S/G), andso on. REX-10 is designed to operate at a low pressure of 2.0 MPaand its coolant flow is driven by natural circulation without a reac-tor coolant pump. For elaborated analyses of REX-10, therefore,the modeling of these components and the coolant conditions ofREX-10 have to be taken into account.

The objective of this study is to provide a reliablethermal–hydraulic system code for integral reactors such as REX-10. In describing the thermal–hydraulic behavior of REX-10, onemay use commercial system codes such as RELAP5 (Ransom et al.,

2001), RETRAN-3D (Paulsen et al., 1998), and CATHARE (Emonotet al., 2009), which have reached a high degree of maturity throughextensive qualifications. However, when unconventional systemsor reactor components, e.g. integral reactor systems, an in-vessel

Y.-G. Lee et al. / Nuclear Engineering and Design 249 (2012) 364– 378 365

Nomenclature

A cross-sectional area (m2)As heat transfer area of structural wall (m2)c specific heat (J kg−1 K−1)Ci neutron precursor concentration of group i (m−3)do outer diameter of helical tube (m)D diffusion coefficient (m2 s−1)Dh hydraulic diameter (m)Di inner diameter of annulus (m)Do outer diameter of annulus (m)Eu Euler numberf Darcy friction factor, condensation coefficientg gravitational acceleration (m s−2)G mass flux (kg m−2 s−1)Gr Grashof numberh enthalpy (J kg−1)K form loss coefficientL length (m)M mass (kg), molecular weight (kg mol−1)N neutron density (m−3)Ncol number of columns in tube bundlesNZ number of tube rowsNu Nusselt numberP pressure (Pa) or total input power (W)P time derivative of pressure (Pa s−1)Ph heated perimeter (m)Pr Prandtl numberq′′ heat flux (W m−2)q heat transfer rate (W)Q volumetric flow rate (m3 s−1)R overall flow resistances (m−4), universal gas con-

stant (J mol−1 K−1)Ra Rayleigh numberSc Schmidt numberSh Sherwood numbert time (s)T temperature (◦C)T core-averaged temperature (◦C)u velocity (m s−1)ub bubble terminal velocity (m s−1)ud liquid drop velocity (m s−1)v specific volume (m3 kg−1)w mass fractionW mass flow rate (kg s−1)z spatial coordinates (m)z elevation of midplane (m)

Greek letters˛ reactivity temperature coefficient (K−1), heat trans-

fer coefficient (W m−2 K−1) volumetric expansion coefficient (K−1), total

delayed neutron fractionˇi delayed neutron fraction of group i� neutron generation time (s)�i decay constant of precursor group i (s−1)� viscosity (Pa s)� node inclination angle (rad)� density (kg m−3)� core-averaged density of coolant (kg m−3)�0 reference density (kg m−3)� weighting parameter for flow direction

Subscriptsannu annulus between core barrel and reactor pressure

vesselb bulk propertiesext externally introducedf fuel, saturated liquidg saturated vaporG gaseous mixture in pressurizeri delayed neutron precursor group, interfaceIN insertion of non-condensable gas into pressurizerj index for minor lossk node indexL1 lower liquid region of pressurizerL2 upper liquid region of pressurizerL12 between lower and upper liquid regionsm moderatormax maximummin minimumnc natural circulationNC non-condensable gasRV relief of gaseous mixtures structural wall, saturated stateSTM steamw wallv vapor phase0 initial value∞ free stream condition

Fig. 1. Schematic diagram of REX-10.

gas pressurizer or a helically coiled S/G, and so on, are encountered,it is not easy for users to modify and supplement the required

physical models in the source codes due to their complex struc-tures. In addition, RERI intends to establish an autonomous analysissystem to assess the design decisions and simulate the transientbehaviors of the new reactor. To achieve this, it needs to develop a

3 ring and Design 249 (2012) 364– 378

tr

bcmakmeaeihbIcmctcitscTct

TiTmc

2

spitaoeos

liis(tww

ahtfu(tt

Table 1Main design parameters of REX-10.

Parameters Design value

General informationReactor type Integral PWRReactor power (MW) 10Service years (yr.) 20

Reactor coolant systemCooling mode Natural circulationOperating pressure (MPa) 2.0Design pressure (MPa) 3.0Core inlet/outlet Temp. (◦C) 165.0/200.0Mass flow rate (kg/s) 64.9

Fuel and reactor coreFuel type 9 × 9 square FAFuel material Heterogeneous Th/UO2

No. of fuel assembly 37No. of fuel rods (/FA) 72Effective height (m) 0.8

Steam generatorType Helical-coil HXFeedwater mass flow (kg/s) 4.47Feedwater temperature (◦C) 120.0Steam temperature (◦C) 142.0 (sat. steam)Steam pressure (MPa) 0.4

Reactor vessel and pressurizerVessel outer diameter (m) 2.272Core barrel diameter (m) 1.607Vessel height (m) 4.588 + 1.127 (PRZ)Pressurizer type Steam–gas PRZNon-condensable gas Nitrogen

66 Y.-G. Lee et al. / Nuclear Enginee

hermal–hydraulic system code with simple structures and aeal-time simulation capability for flexible utilization.

This paper presents the development of the TAPINS code, whichasically consists of models of the reactor coolant system (RCS),ore, helical-coil steam generator, and steam–gas pressurizer. Theomentum integral model is applied to the one-dimensional node

nd flow-path network for RCS thermal–hydraulics. The reactorinetics model, which includes feedback effects due to fuel andoderator temperature, and the heat transfer and frictional mod-

ls for helical tubes are incorporated into the TAPINS. In particular,n analytical model for the steam–gas pressurizer, where the pres-nce of non-condensable gas is coupled to the pressure behavior,s newly proposed and implemented in the TAPINS. The transienteat transport in the fuel elements and S/G tubes is calculatedy solving the heat conduction equation in the radial direction.n order to assure the numerical stability and computational effi-iency, implicit approaches are employed to numerically solve theomentum and energy equations. The validation of the TAPINS

ode is performed by comparing against experimental data fromhe pressurizer insurge tests conducted at MIT and the RTF testsarried out by RERI. The transient responses of the pressurizern the presence of non-condensable gas are simulated to assesshe distinctive pressurizer model in the TAPINS. Furthermore, theteady-state natural circulation and the transients induced by theore power and feedwater in a scaled-down IET (Integral Effectest) facility are predicted by using the TAPINS. The fast-runningapability of the code is confirmed by the measured computingime.

The design features of REX-10 and the code structure of theAPINS are described in Sections 2 and 3, respectively. Presentedn Section 4 are the mathematical models incorporated into theAPINS for integral reactors, followed by the numerical solutionethods in Section 5. The results simulated by the TAPINS are

ompared with experimental data in Section 6.

. Description of REX-10

The aim of the development of REX-10 is to achieve a moretable, efficient, area-independent system operation and energyroduction (Lee and Park, 2012). The design goals of REX-10 include

mplementing high levels of inherent safety into the reactor designo enhance the public acceptance of an innovative system, andttaining non-proliferation during all processes of construction andperation. Economic efficiency is also an inevitable criterion of anynergy generation method. In particular, much emphasis is placedn the assurance of passive safety features for REX-10 at the designtage.

REX-10 is designed to generate the rated output of 10 MW at aow pressure (2.0 MPa) compared to conventional reactors. It is anntegral-type small PWR which contains the primary componentsnside the reactor vessel. This layout eliminates the possibility ofystem depressurization by a large-break loss-of-coolant accidentLOCA) by virtue of the absence of large-diameter pipelines. In addi-ion, as the coolant circulates by gravity-driven free convectionithout a reactor coolant pump (RCP), all safety issues associatedith the failure of the RCP can be eliminated.

The major design parameters of REX-10 are listed in Table 1 (Leend Park, 2012). A cylindrical reactor vessel with a height of 5.715 mouses the core, CRDM, pressurizer, and steam generator. Placed athe bottom of the reactor vessel are the 9 × 9 heterogeneous Th/UO2uel assemblies that are used to achieve an ultra-long fuel cycle of

p to 20 years on the basis of the Seed-Blanket Unit (SBU) designPark et al., 2010). This thorium-based fuel has a major benefit inhe intrinsic proliferation resistance since 232U, formed along withhe bred 233U, and its daughter isotopes emit intensive alpha and

Fig. 2. Plan view of a quarter fuel assembly in REX-10.

gamma radiation, hindering the access to nuclear fuel. A total of37 assemblies with an active height of 0.8 m are composed of fuelbundles enriched to 20 w/o. The configuration of a quarter assemblyis depicted in Fig. 2. In REX-10, the intrinsic feedback capabilityis enhanced by refusal from soluble boron control, while excess

reactivity is dealt by burnable poison and control rods. The longriser region above the core provides sufficient head for the freeconvection of fluid.

Y.-G. Lee et al. / Nuclear Engineering and Design 249 (2012) 364– 378 367

afety

ap1ttfldcolprtssts

usfdiRtiset

3

3

t

Fig. 3. Engineered s

The gaseous mixture volume in the upper part of the reactorbove the coolant level is referred to as the built-in steam–gasressurizer. It is the most distinguishing component of the REX-0, and represents progress in incorporating passive features intohe integral reactor system (Lee et al., 2009). In normal operation,he saturation vapor corresponding to the temperature of the hotuid in RCS is maintained in the gas region by establishing theynamic equilibrium with liquid region, and mixed with the non-ondensable gas like nitrogen. The once-through steam generatorf REX-10 consists of helical tubes wrapped around the entire annu-us between the core barrel and the reactor pressure vessel. Therimary coolant flows downward across the tube bundles to evapo-ate the coolant on the tube-side. Flowing in the opposite direction,he secondary feedwater enters into the helical coil in a subcooledtate; by the time it leaves the coil, it has turned into saturatedteam. For ensuring the single-phase steam condition to protect theurbine from moistures, REX-10 has to be equipped with a moistureeparator and a steam dryer.

The containment of REX-10 is filled with water and buriednderground. The large amount of water in the containment canerve not only as a barrier against the release of radioactive materialrom the reactor system but also as a heat sink under accident con-itions (Lim, 2010). The engineered safety systems of REX-10 are

llustrated in Fig. 3. As a representative safety system prepared forEX-10, the passive residual heat removal system (PRHRS) removeshe decay heat in the event of reactor shutdown. Automatically putnto action by the trip signal, the PRHRS condenses vapor from theteam generator by means of natural circulation through a heatxchanger, which is located higher than the S/G and submerged inhe water of containment building.

. Features of TAPINS code

.1. Code structure

It has to be clarified that our prior mission is to develop an easy-o-use and fast-running system code for integral reactors. While

systems of REX-10.

the aforementioned commercial codes are highly generic analy-sis tools whose applications cover a broad range of nuclear andnon-nuclear systems (Ransom et al., 2001), one can define the TAP-INS as an integrated-system-specific analysis code with relativelyfinite subjects to be simulated. The principal analyses of this workare targeting to confirm the design basis of an integral reactor andinvestigate the RCS response to the non-LOCA transients on thenatural circulation.

In selecting the hydrodynamic model, the focus has to bedirected towards choosing the least sophisticated model that iscapable of embracing the phenomena of interest. It can be donewith clarifying the basic assumptions in developing the TAPINS asfollows:

(1) The coolant flow is driven by free convection around a com-pletely closed loop.

(2) Local pressure changes and corresponding variations of fluidproperties in the natural circulation loop are negligible.

(3) The LOCA by the pipe rupture can be excluded in an integralreactor.

(4) The feedwater flow rate is kept constant and considered uni-form along the whole channel.

Since our current issues do not encompass the complex two-phase flow phenomena, the field equations of the TAPINS areformulated on the basis of the three-equation homogeneous equi-librium model (HEM), employing a few simplifying assumptionsand the undemanding solution method to facilitate solution oftransient problems. Modeling of new integral components typifiedby the once-through steam generator and the built-in pressurizer,which serves as the main computational challenges in the analy-ses of an integral reactor, is also carried out. The TAPINS is writtenin FORTRAN 90 and easily executed on a PC. Its code architecture

supports the optimal calculation for reactor systems with integralconfigurations.

The block structure of the TAPINS is described in Fig. 4. The sub-routine InpReader reads all data from the input file and checks for

368 Y.-G. Lee et al. / Nuclear Engineering and Design 249 (2012) 364– 378

TAPINSCode

TAPINSCode

InpReaderInpReader

SetSysSetSys

IniCndtnIniCndtn

SolverSolver Reactor Kine�csReactor Kine�cs

HydrodynamicsHydrodynamics

Heat Conduc�onHeat Conduc�on

Correla�ons and Proper�esCorrela�ons and Proper�es

SGPModel

Data Reading from InputData Reading from Input

Define T/H variablesDefine T/H variables

SystemGeometrySystemGeometry

Ini�alize RCS TemperatureIni�alize RCS Temperature

Core & SG Steady-stateCore & SG Steady-state

cture

sSdcdsSmtsat

rpitiogtc

3

itimotden

rca

Fig. 4. Code stru

ome probable errors. From the stored data, the subroutine Set-ys prepares the pre-processors required to the computation byefining the fundamental variables for the core and S/G and allo-ating the geometric data to the dynamic arrays. The temperatureistribution of the primary circuit is initialized and the steady-tate heat conduction solution is found for the fuel rods and the/G tubes in the subroutine IniCndtn. The subroutine Solver is theain module of the TAPINS; it contains the subroutines to advance

he solutions for the reactor kinetics, the hydrodynamic model, theteam–gas pressurizer model, and the heat conduction equations,s well as those to call the empirical correlations and the requiredhermophysical properties.

The TAPINS is a specialized code for analysis of the integraleactors such as REX-10. Therefore, the component models incor-orated in the TAPINS are somewhat limited to those for the

ntegral reactors like REX-10. In addition, the TAPINS does not serveo the events associated with loss of fluid and the correspond-ng phenomena since it is developed on the assumption that theccurrence of LOCA is conceptually eliminated in the design of inte-ral reactors. Specifically, the TAPINS is capable of simulating up tohe level of condition II (Faults of Moderate Frequency) in the ANSlassification of plant conditions.

.2. Input file

Significant emphasis is placed on achieving user conveniencen preparing the input file for practical applications. It is intendedo minimize the engineering labor and time required to write thenput by reducing, if possible, the number of input data fields which

ust be filled in by the user. When simulating a nuclear system,ne can easily encounter a situation where a component or sec-ion is divided into a framework of equidistant nodes. In that case,epending on the kind of system code, the user may be required tonter the same figures repeatedly, as many times as the number ofodes.

On the other hand, the input module of the TAPINS divides theeactor coolant system of the integral reactor into six subsections:ore, riser, upper head, helical-coil steam generator, downcomer,nd lower plenum. By receiving only the number of nodes for

SGPModel

s of the TAPINS.

each subsection, the TAPINS can nodalize them with geometri-cally identical control volumes, if the user chooses this option forconvenience, and perform automatic node numbering. This meansthat the user can avoid unnecessary repetition in building up thenode diagram. Of course, it is possible to assign detailed input datacorresponding to individual nodes for elaborated analyses.

4. Hydrodynamic and component models

4.1. Field equations

The formulation of the hydrodynamic model used in the TAP-INS is based on the one-dimensional HEM, which consists of theconservation laws for mass, momentum, and energy (Todreas andKazimi, 1990b):

Continuity equation:

∂�

∂t+ ∂G

∂z= 0 (1)

Momentum conservation equation:

∂G

∂t+ ∂

∂z

(G2

�

)= −∂P

∂z− f

2Dh

G∣∣G∣∣�

− �g (2)

Energy conservation equation:

�∂h

∂t+ G

∂h

∂z= q"Ph

A(3)

Frictional dissipation and the work done by the pressure areneglected in the energy equation. Using the non-conservative formof the energy equation is plausible since the loss of accuracy isexpected to be insignificant due to the existence of large sources orsinks of heat in the RCS. It is also more convenient for the treatmentof the difference schemes.

A fundamental aspect of the momentum integral model (Meyer,1961) is that the fluid is considered incompressible but thermallyexpandable, as follows:

� = �(P∗, h) (4)

where P* is a reference pressure which is assumed to be constantduring transients. This means that the variation of fluid properties

ring a

dcecdbimo

lsttRaslo

�

tm(shtlZccoace2

pgpft

4

pitlf

e

Y.-G. Lee et al. / Nuclear Enginee

ue to the pressure change is ignored. This assumption is physi-ally acceptable for most operational transients in a nuclear reactor,xcept for events accompanied by a huge loss or bulk boiling of theoolant. In the TAPINS, instead of coming up with a local pressureistribution, a representative value of the system pressure updatedy a steam–gas pressurizer model is imposed as P*. From the fluid

ncompressibility, a further convenience is obtained as the volu-etric flow rate becomes uniform around the loop, depending only

n time.The principal point of the momentum integral model is the ana-

ytical integration of the momentum conservation equation overpace. This approach eliminates the pressure gradient term becausehe sum of the pressure drop around any closed circuit is zero. Fur-hermore, on account of the normal mode of coolant circulation inEX-10 being natural convection, the Boussinesq approximation ispplied to the momentum equation; the density is regarded as con-tant except for the gravitational term, in which the density variesinearly with temperature (Zvirin, 1981). Therefore, the final formf the integral momentum equation solved in the TAPINS is:

0

(∑k

Lk

Ak

)dQ

dt= −�0

2

⎛⎝∑

k

fkLk

DhkA2

k

+∑

j

Kj

A2j

⎞⎠Q 2

+ �0gˇ∑

k

TkLk cos �k (5)

The fluid properties are to be homogeneous in each node. Inhe closed circuit, the boundary condition is altered to the require-

ent that the coolant enthalpy is continuous around the loop. Eqs.3) and (5) are applied to the one-dimensional network. The con-titutive relations, e.g. the equation-of-state, friction coefficient,eat transfer correlation and so on, complete the definition ofhe system properties. In the TAPINS, the friction factor is calcu-ated by the theoretical relation, f = 64/Re, for laminar flow and theigrang–Sylvester equation (1985) for turbulent flow. The form lossoefficient for an abrupt area change is either given in the inputard by the user or calculated automatically by a simple modulef the TAPINS which compares the flow area of adjacent nodesnd computes the loss coefficients by sudden expansion or suddenontraction using the empirical formula. The thermophysical prop-rties of fluids are calculated by PROPATH 12.1 (PROPATH GROUP,001).

Solving just a single integral momentum equation, along withlacing less stringent requirements on the time-step, results inreat savings in the computational cost. This is the reason for incor-orating the above simplified hydrodynamic model formulatedrom the momentum integral model into the TAPINS, even thoughhere might be some loss of local information.

.2. Point reactor kinetics

To determine the time-dependent behavior of the fission power,oint kinetics equations with six delayed neutron groups are solved

n the TAPINS. By allowing the spatial dependence to be eliminated,he point reactor kinetics yields solutions for the neutron popu-ation density and the delayed neutron precursor concentrationsrom this set of coupled ordinary differential equations:

dN(t)dt

= �(t) − ˇ

�(t)N(t) +

∑i

�iCi(t) (6)

dCi(t)dt

= ˇi

�(t)N(t) − �iCi(t) (i = 1, 2, . . . , 6) (7)

The change in the reactivity induced by the negative feedbackffect is also taken into account. The reactivity feedbacks caused

nd Design 249 (2012) 364– 378 369

by the variation of the core-averaged fuel element and the coolanttemperatures as well as the externally introduced reactivity are ofgreat importance:

�(t) = �0 + ˛Tf

(Tf (t) − Tf 0

)+ ˛Tm

(Tm(t) − Tm0

)+ ı�ext(t) (8)

In the core kinetics model of the TAPINS, the neutron kineticsparameters, the reactivity temperature coefficients and the axialprofile of the core power are given in the input data. The user canalso include the reactivity feedback by the variation of the moder-ator density, if desired, for the abnormal accidents associated withthe coolant voiding.

The heat conduction equation is also solved in polar coordinatesso that the radial temperature distribution in the fuel rods is deter-mined. With the axial heat conduction neglected, the transient heattransport in the fuel elements is represented by a model of a typi-cal fuel rod to obtain the average fuel temperature and the claddingsurface temperature. The temperature dependence of the thermalconductivity is explicitly modeled. The boundary conditions for thefuel-cladding gap and the cladding–coolant interface are imple-mented by supposing a quadratic temperature profile in the vicinityof the boundaries and imposing heat flux continuity. In order toobtain the convective heat transfer rate into the coolant, a correla-tion suggested by Churchill and Chu (1975a), which is suitable forfree convection flows, is used as a default model:

Nu =

⎧⎪⎨⎪⎩0.825 + 0.387Ra1/6[

1 + (0.492/Pr)9/16]8/27

⎫⎪⎬⎪⎭

2

(9)

For turbulent flow in the range of Re > 10,000, the heat transfermodel is replaced by the Dittus–Boelter equation. As a CHF cor-relation, the empirical correlation proposed by Bowring (1972) isincorporated into the TAPINS. It is derived from the database cov-ering the pressure range of 2–190 bar, to which the operationalpressure of REX-10 belongs.

4.3. Helical-coil steam generator model

The precise prediction of heat transport in the steam genera-tor is of great importance, especially for free convection flow inan integral system such as REX-10, since the cooling capability ofthe S/G directly determines the stabilized temperature of the pri-mary coolant as well as the transient behavior of RCS. The steamgenerator model in the TAPINS calculates the shell-side and thetube-side heat transfer coefficients for helically wound tubes. Theheat transfer on the tube-side is estimated using a single helicalcoil and the effective heat transfer regions of both sides are com-posed of the same number of nodes. The heat transfer regions insidethe tubes are divided into three parts: economizer, evaporator andsuperheater sections. Similar heat transfer and friction factor mod-els to those used by Yoon et al. (2000), which are employed forthe thermal–hydraulic design of a once-through steam generatorin SMART, are used in the TAPINS with slight modifications. Theempirical correlations for the helical-coil S/G in the TAPINS aresummarized in Table 2.

While a number of investigations have been performed on theinternal heat transfer and flow characteristics inside the curved coil,including those reported by Mori and Nakayama (1967) and Kozekiet al. (1970), there is no generalized correlation for the shell-sidetube bundles in the helical-coil steam generator. One of the mostwidely used correlations was proposed by Zukauskas and Ulinskas

(1985), and it is associated with the cross flow across banks of tubesin the form:

Nu = CRemmaxPr0.36

(Pr

Prw

)0.25(10)

370 Y.-G. Lee et al. / Nuclear Engineering a

Table 2Empirical correlations for helical-coil S/G in the TAPINS.

Tube-side Shell-side

Friction factor Mori–Nakayama Zukauskas

Heat transfer coefficientSubcooled water Mori–Nakayama Max

[Zukauskas,Churchill-Chu]

Saturated boiling ChenDryout quality KozekiMist evaporation Linear interpolation

w

R

saomtma

cciCociocslc

atvgca

osdsfrfl

wf

E

c

The energy conservation equations are written in terms of the

Superheated steam Mori–Nakayama

here the maximum Reynolds number is defined as the following:

emax = �umaxdo

�(11)

The values of C and m are governed by the tube arrangement, i.e.taggered or aligned, and the Reynolds number. Note that the char-cteristic dimension of the Reynolds number on the shell-side is theuter diameter of the tube, and the Reynolds number is based on theaximum fluid velocity that occurs when the fluid passes through

he region of minimum inter-tube area. In the TAPINS, the mini-um flow area is computed by taking into account the fractional

rea occupied by tubes in the transverse plane, as follows:

Amin

Aannu= 1 − Ncol

2do

Do − Di(12)

The preliminary analyses revealed, however, that the Zukauskasorrelation quite underestimates the heat transfer rate to the heli-al coil when the fluid velocity is very low. The problem is overcomen the TAPINS by introducing another correlation recommended byhurchill and Chu (1975b) for external natural convection flowsn the horizontal cylinder. The maximum heat transfer coeffi-ient between the two is chosen to calculate the heat transportn the primary side, combined with the total heat transfer areaf the tube bundles. Generally, the value by Churchill and Chuorrelation is adopted on the low Reynolds number conditionsuch as the natural circulation mode while the Zukauskas corre-ation provides the larger heat transfer coefficient for the forcedonvection.

The flow rate of the secondary coolant is assumed to be constantnd Eq. (3) for the energy balance is solved in the same way as forhe primary side. Instead of solving the PDE for momentum conser-ation, the three components due to acceleration, friction loss andravity are summed to give the total pressure drop along the helicaloil. Moreover, the time-dependent heat conduction solutions aredvanced across the tubes, which are divided into several intervals.

Another issue associated with a helical-coil S/G is the predictionf shell-side pressure loss across the tube bundles. Notwith-tanding its crucial importance in sizing a heat exchanger andetermining the convective flow rate in a primary system, a univer-al method applicable to various designs of helical-coil S/G is rarelyound. In the TAPINS, the shell-side pressure loss is determined byeferring to the research of Zukauskas and Ulinskas (1998) on theows across banks of tubes. The pressure drop is expressed as:

P = Eu

(�u2

max

2

)NZ (13)

here the Euler number is obtained from the correlation in theorm:

u = c0 + c1

Re+ c2

Re2+ c3

Re3+ c4

Re4(14)

The coefficients of Eq. (14) depend on the Reynolds number, theonfiguration of tube bundles and the relative transverse pitch. The

nd Design 249 (2012) 364– 378

interpolated Euler number is reflected to calculate the total frictionloss term appearing in Eq. (5).

4.4. Steam–gas pressurizer model

In the steam–gas pressurizer, a certain content of non-condensable gas (nitrogen) is maintained in the gas phase. As thepresence of the non-condensable gas provides excess pressure inaddition to the partial pressure of steam, the subcooled state canbe retained at the core outlet. This excludes the use of active equip-ment such as a spray or heater for control of the primary systempressure. Located at the upper head region of the reactor vessel,the steam–gas pressurizer can hold a large volume of water andgaseous mixture compared to a conventional separate pressurizer.

In order to predict the dynamic behavior of the primary sys-tem pressure, an analytical model for the steam–gas pressurizeris newly proposed. The previous pressurizer models are advancedfrom the two-region model (Baron, 1973) to a three-region non-equilibrium model (Baek, 1986). However, these models deal witha pressurizer containing only steam in the upper gas region andthus the presence of non-condensable gas is not coupled with thepressure behavior. Since the non-condensable gas affects not onlythe intensity of mass diffusions occurring in the pressurizer butalso the total pressure responses to the transients, a new modelaccounting for the effect of non-condensable gas is indispensable.

The steam–gas pressurizer model of the TAPINS is the three-region non-equilibrium model based on the basic conservationprinciples of mass and energy. The pressurizer volume is separatedinto three distinct regions of a gaseous mixture and upper and lowerliquid regions, each establishing its own thermodynamic state. Bythermal stratification, the lower liquid region is immediately influ-enced by surge flow while the upper region floats to the top withlittle change in temperature. The following assumptions are madein this model:

(1) All regions in the pressurizer share the same pressure.(2) The Gibbs–Dalton law is valid for the gas phase.(3) The gaseous mixture establishes thermal equilibrium, i.e. the

temperatures of the steam and the non-condensable gas arethe same.

(4) Dissolution of the non-condensable gas in the liquid is negligi-ble.

With regard to mass and energy balance, the model takes intoaccount all the processes of heat and mass transfer that occurbetween the vapor and liquid phases inside the steam–gas pres-surizer, as well as the surge flow from the primary loop. Theconservation equations are applied to the steam, non-condensablegas and liquid water. Physical phenomena to be modeled includesurge (SU), rainout (RO), flashing (FL), inter-region heat and masstransfer (ITR), and wall condensation (WC), as illustrated in Fig. 5.The mass conservation equations are:

dML1

dt= WSU − WFL1 − WL12 (15)

dML2

dt= WFL1 − WFL2 + WL12 + WRO + WITR + WWC (16)

dMSTM

dt= WFL2 − WRO − WITR − WWC − WRVSTM

(17)

dMNC

dt= WIN − WRVNC

(18)

convective energy flows and the mechanical work done as follows:

d

dt(ML1hL1) = WSUhSU − WFL1hg − WL12hL12 + VL1

dP

dt(19)

Y.-G. Lee et al. / Nuclear Engineering and Design 249 (2012) 364– 378 371

tvpsa2eht

upfseW

P

Table 3Physical models of local phenomena in steam–gas pressurizer.

Type of masstransfer

Physical model Remarks

Flashing WFL = �gub˛lA ub: Wilson’s formula

Rainout WRO = �f ud(1 − ˛v)A ud =[

gLG

(v−f

)/vv

]1/2

Interfacialmass transfer

WITR = f1−0.5f

[M

2�R

]1/2(Pv

Tv1/2 − Ps

Ts1/2

)· A Gas kinetic theory

Equilibrium at saturationpressure

Wallcondensation

WWC = Sh �DL

wNC,i−wNC,bwNC,i

· A

where Sh = a (Gr · Sc)b

Heat and mass transferanalogyEffect of thenon-condensable gas onthe condensation heat

i · (∂v

,L2

(M

Fig. 5. Local mass diffusions in steam–gas pressurizer.

d

dt(ML2hL2) = WL12h12 + (WFL1 − WFL2 + WITR) hg + (WRO

WWC ) hf + VL2dP

dt(20)

d

dt(MSTMhSTM) = (WFL2 − WITR) hg − WROhf

−(

WWC + WRVSTM

)hSTM + VG

dPSTM

dt(21)

d

dt(MNChNC ) = WINhIN − WRVNC

hNC + VGdPNC

dt(22)

Contrary to the conventional pressurizer models, it is notedhat terms for the heater or spray do not appear in the conser-ation equations. Table 3 summarizes the physical models for localhenomena occurring in the steam–gas pressurizer. In particular,pecial emphasis is placed on the prediction of condensate ratet the wall in the presence of non-condensable gas (Kim et al.,009b) on the basis of the heat and mass transfer analogy, whichmploys the same functional dependence found in correlating theeat transfer to express the analogous relationships for predictinghe mass transfer.

The above conservation equations form a system in which thenknowns outnumber the equations by 11 (4 mass, 4 enthalpy, 3ressure) to 8. Thus one requires three more constitutive relationsor closure. One is the Gibbs–Dalton law for the gas phase, whichtates that the total pressure exerted by the gaseous mixture is

P = −

∑i=G,L1,L2

(vi · Wi) +∑

i=L1,L2

(M

∑i=L1

qual to the sum of the partial pressures of steam and nitrogen.ith respect to time, this can be expressed as:

˙ = PSTM + PNC (23)

transfer

Another constraint is the thermodynamic equilibrium conditionin the gas phase. The temperatures of steam and nitrogen, deter-mined by their respective partial pressure and enthalpy, are givenby the following:

TH2O(PSTM, hSTM) = TNC (PNC, hNC ) = TG (24)

The other relation is the time-dependent pressure equationderived from constraints on the invariant pressurizer volume withtime, which is expressed as:

VSGP = VG + VL =∑

i=G,L1,L2

d

dt(vi · Mi) = 0 (25)

where the specific volume of the gaseous mixture is defined by:

G = G(PSTM, PNC, hSTM) (26)

Note that the enthalpy of the non-condensable gas is notincluded in the above equation-of-state since it is determined fromthe thermal constraints of Eq. (24). Substituting the equation-of-states for the gas and the liquid into Eq. (25) and rearranging themwith respect to the time derivative of pressure yields:

i/∂hi) · (dhi/dt))

+ MG · (∂vG/∂hSTM) · (dhSTM/dt) + �G

i · ∂vi/∂P)

+ MG · ∂vG/∂PSTM

(27)

where

�G = MGPNC

(∂G

∂PNC− ∂G

∂PSTM

)(28)

The conservation equations are numerically solved in an iter-ative way in conjunction with these three closure relations. Thevariation of the water level is advanced from the time derivative ofthe total liquid volume.

5. Numerical solution methods

On the basis of the finite difference scheme, implicit approachesare employed as a numerical solution scheme so as to assure thenumerical stability and computational efficiency. Shown in Fig. 6is the flow chart of the transient calculation in the TAPINS. From

the initial conditions, the energy equation is solved for the primarycircuit to acquire a new enthalpy distribution over the whole loop.Using a staggered arrangement of variables, Eq. (3) is integratedover the mesh cells and discretized by the implicit Euler method

372 Y.-G. Lee et al. / Nuclear Engineering and Design 249 (2012) 364– 378

Read preprocessorsfrom input file

Initial guesses andsteady-state calculation

forcore and S/G

Update core powerby point kinetics

Solve energy Eq.forprimary circuit

Update enthalpy ofsecondary coolant

Calculate heat transferrates in core and S/G

Update primary pressureby pressurizermodel

Solve momentum Eq.to get new flow rate

Elapsed timeFinal time

END

RTime

advancement

START

Yes

No

R

Solve heat conductionmodel in helical tube

ient c

ft

�

w

h

�

EGtctapa

tgtmtcRn

aTtsesbsp

Fig. 6. Flow chart of trans

or the temporal derivative and the upwind difference scheme forhe spatial derivative in the form:

nk Vk

hn+1k

− hnk

t+ Wn

k

(hn+1

k+1/2 − hn+1k−1/2

)= [q]n (29)

here

k+1/2 =(

1 + �

2

)hk +

(1 − �

2

)hk+1 (30)

= Wnk∣∣Wnk

∣∣ (31)

The heat transfer rate which appears in the right hand side ofq. (29) is obtained from the old time variables at each time-step.aussian elimination is sufficient for solving the linear system since

he matrix size is just N × N, where N is the total number of meshells in the primary system. The energy equation is also solved forhe secondary side of the S/G, accounting for the pressure droplong the tube, and the heat conduction across the tube is com-uted simultaneously using the Crank–Nicholson method for timedvancement.

The updated temperature in the primary loop is used to calculatehe gravitational term in Eq. (5). The implicit scheme for the inte-rated momentum equation yields a nonlinear equation in terms ofhe loop flow rate, which is determined from the Newton–Raphson

ethod. From the average fuel and coolant temperatures, a nega-ive feedback effect in the core is predicted. The solutions for sevenoupled point kinetics equations are obtained via the fourth-orderunge–Kutta method. The above processes are repeated until theumerical time reaches the prescribed final time.

It is unnecessary to calculate the steam–gas pressurizer modulet every time-step unless an excessive transient is encountered.herefore the computation interval is controllable in the input ofhe TAPINS. Among the closure relations for the steam–gas pres-urizer, the thermal constraint represented by Eq. (24) cannot bexpressed in the form of an explicit function. Thus a linear matrix

ystem cannot be setup and a successive iteration method has toe employed to get the solutions. The detailed procedure of theolution scheme for the steam–gas pressurizer can be found in arevious work of the author (Lee et al., 2011).

alculation in the TAPINS.

6. Simulation results and discussions

6.1. Pressurizer insurge experiment

The first validation activity that is carried out for a comprehen-sive assessment of the TAPINS is concerned with the steam–gaspressurizer model. As it is not essential for the conventional pres-surizer used in nuclear power plants (NPPs), experimental dataon the transient response of the pressurizer in the presence ofnon-condensable gas is rarely found. However, Leonard (1983)conducted a series of experiments to investigate the responses ofa small-scale pressurized vessel to insurge transients with threenon-condensable gases: nitrogen, helium and argon. The pressurehistories caused by the rapid insurge were observed with differenttypes and concentrations of non-condensable gas.

The primary tank in the tests is 0.203 m in inner diameterand 1.143 m in height. The transient is initiated by injecting thesubcooled water into the primary tank from the storage tank pres-surized with nitrogen. The insurge is maintained for approximately35 s. The accuracy of the pressure behavior predicted by the newlyproposed dynamic model in the TAPINS is evaluated against thedata from the separate effect tests (SET) conducted by Leonard.Among the various test cases, two cases of the insurge transientin the presence of nitrogen are simulated with the TAPINS, sincenitrogen would constitute the gaseous mixture in the steam–gaspressurizer of REX-10.

Fig. 7 displays the transient calculation result when the initialmass fraction of nitrogen is 9.7%. During the insurge, the vesselpressure continuously rises by virtue of the reduction in the gasvolume. After termination of the insurge, however, the wall heattransfer from the gaseous mixture results in a moderate decrease ofthe pressure. The rate of decline slowly goes down as the naturallyconvective gaseous mixture becomes stagnant after the rise in thewater level ceases. Fig. 7 reveals that the steam–gas pressurizermodel in the TAPINS successfully predicts the pressure historiesarising from these mechanisms. The deviation of the calculated finalwater level from the measured one is at most 1.5 mm.

A notable simulation result is observed when the two-regionpressurizer model is employed, in which the thorough mixing ofthe insurge flow with the liquid phase is assumed by using a sin-gle integrated control volume for the liquid regions. While the

insurge of subcooled water immediately leads to a decrease inthe temperature of an overall liquid region in the simulation ofa two-region model, the hot liquid layer, keeping the temperaturenearly constant, floats to the top of the liquid region due to thermal

Y.-G. Lee et al. / Nuclear Engineering a

6040200

5

6

7

8

9

Pre

ssu

re (

ba

r)

Time (sec)

Experiment

TAPINS

Two-region model

Termination of insurge

Fig. 7. Pressure responses to insurge transients with nitrogen present (mass frac-tion: 10%).

0 10 20 30 40 50 60

5

6

7

8

9

10

11

Pre

ssu

re (

ba

r)

Time (sec)

Experi ment

TAPI NS

Fig. 8. Pressure responses to insurge transients with nitrogen present (mass frac-tion: 20%).

sfskem

usvgwdBtb

to the enormous flow resistance applied by the hot legs and theflowmeter where the fluid passes through a very narrow flowchannel. Inspection of Fig. 12 reveals that the steady-state flowrates predicted by the TAPINS show excellent agreement with the

tratification in the actual conditions. The net effect is that the inter-acial mass transfer at the interface into the liquid is over-predicted,o that the pressure response to the insurge is miscalculated. In thisind of SET apparatus, which has quite a small volume, slight differ-nces in the calculated mass transfer rates of the local phenomenaay give rise to considerable deviation in the simulation results.The simulation result when the mass fraction of nitrogen goes

p to 20.1% is plotted in Fig. 8. Compared to Fig. 7, the pressure tran-ient exhibits a steeper slope during the insurge and a higher peakalue. It is widely reported that the accumulated non-condensableas along the wall provides resistance against heat transfer to theall by condensation. Therefore, the rate of wall condensation isegraded as the concentration of non-condensable gas increases.y incorporating the condensation model with the heat and massransfer analogy, the TAPINS predicts the pressure response causedy insurge transients with reasonable accuracy.

nd Design 249 (2012) 364– 378 373

6.2. RTF tests

The aforementioned mathematical models and solution schemeare applied to the REX-10 Test Facility for quantitative validationof the TAPINS. The RTF is intended to experimentally evaluatethe natural circulation capability of REX-10 and understand thethermal–hydraulic behavior of the RCS (Jang et al., 2011). Con-structed in SNU, the RTF is a scaled-down facility designed by Ishii’sscaling law with a volume ratio of 1:50, but the length scale is pre-served so that the system can provide an identical hydrostatic headto that of REX-10 for natural circulation.

The primary system of the RTF consists of electrical heaters, ariser, four hot legs, and a helical-coil heat exchanger as shown inFig. 9. It is designed to operate at full pressure (20 bar) and temper-ature (200 ◦C) with a maximum heater power of 200 kW.

Fig. 10 illustrates the integral configuration of the system com-ponents housed in the reactor vessel which has a height of 4.76 m.The core region, which consists of 60 electrical heaters, has an effec-tive length of 1.0 m and an outer diameter of 12.0 mm. The primarycoolant heated in the core passes the long riser and flows intothe annular space through the four hot legs. These elbow-shapedhot legs are equipped with flowmeters to measure the naturalcirculation flow rate. The once-through heat exchanger, whoseeffective length is 1.205 m, comprises 12 helical tubes arranged into3 columns. The pressurizer vessel is connected to the top of the RTFthrough a long, narrow pipe. Three parameters, i.e. system pressure,heater power and secondary feedwater flow rate, are controlled inthe tests.

6.2.1. Steady-state natural circulation testsThe steady-state mass flow rate produced by natural circula-

tion in the primary loop is simulated at 2.0 MPa. In the tests, themass flow rate and coolant temperatures are recorded at variouscore powers while the primary system pressure is kept constant byregulating the power of the heaters equipped inside the pressur-izer. In all cases, secondary feedwater at 20 ◦C and 1 bar is sent intothe helical coil at a rate of 4.5 LPM per tube. The heat loss to thesurrounding environment is estimated to be less than 5%.

In the simulations of the TAPINS, a total of 37 nodes consti-tute the primary circuit of the RTF; nodes for the core (5), riser(5), upper head including hot legs (8), S/G (14), downcomer (3),and lower plenum (2) establish the RCS of the RTF as illustrated inFig. 11. In particular, fine nodalization is prepared for the helical-coil S/G section in an attempt to assure the precise prediction of theheat transfer with coolant. Minor losses due to an abrupt changein flow area are calculated from the relevant empirical correlations(Todreas and Kazimi, 1990a). We clarify that there is no manip-ulation of these loss coefficients to fit the results to the test databetween cases. Only when the heat removal rate from the S/G isthe same as the input power do the thermal–hydraulic variablesconverge to their fully stabilized values.

The simulation results produced by the TAPINS for the steady-state mass flow rate are compared with experimental data fromsix tests performed using different core powers, as shown inFig. 12. Undoubtedly, the higher the power generated by thecore, the greater the natural circulation flow, since a high inputpower increases the temperature gradient of the coolant, andsubsequently, the buoyancy force that arises due to the densitydifferences. It is observed that, even though the difference in mid-plane elevations between the core and the S/G is almost 2.5 m, themass flow rate is less than 0.5 kg/s for the power range used inthis study. This low natural circulation flow of the RTF is attributed

374 Y.-G. Lee et al. / Nuclear Engineering and Design 249 (2012) 364– 378

0 test

eat

W

w

R

Fbe1ctatR(itsea

i

ried out at SNU. As the RTF is designed basically for steady-statetests on the natural circulation, not many parameters are control-lable in these experiments. However, since the core power and thefeedwater flow rate can be easily regulated, three transient tests

Table 4Steady-state coolant temperature in the RTF at various core power.

Power (kW) Core inlet (◦C) Core outlet (◦C) Feedwateroutlet (◦C)

RTF data TAPINS RTF data TAPINS RTF data TAPINS

70.55 50.63 49.77 106.95 106.78 37.49 38.8299.70 60.47 59.60 128.21 128.29 45.56 46.57

Fig. 9. REX-1

xperimental results; the maximum deviation is at most 3.9%. Annalytical expression for the natural circulation flow is derived inhe form (Lewis, 1977):

nc =[

2 �2gˇP

cR(zSG − zcore)

]1/3

(32)

here the overall flow resistance around the loop is defined by:

=∑

k

fkLk

DhkA2

k

+∑

j

Kj

A2j

(33)

This analytic function is also plotted versus the core power inig. 12 to provide comprehensive estimates of the steady-stateehavior of the RTF. All parameters appearing in Eq. (32) arevaluated using the stabilized conditions for an experiment at41.55 kW. It is shown that the predictions of the TAPINS are verylose not only to the experimental data but also to the results ofhe analytical calculation. The deviation from the curve observedt powers lower than 100 kW results from the dependence ofhe overall flow resistance and thermophysical properties on theeynolds number and the temperature, respectively. In fact, Eq.32) tells us that the mass flow rate is proportional to the total heatnput to the power of 1/3, assuming that the flow resistance andemperature profile of the primary system are constant. In reality, aubstantial inaccuracy in this calculation may be induced unless the

xact distributions of the flow velocity and the fluid temperaturere utilized in each case.

The simulation results for coolant temperatures are listedn Table 4, along with the measured values from the tests.

facility (RTF).

Compared to the experimental data, the maximum deviation isless than 4 ◦C. The equilibrium temperature distribution in theRCS is closely associated with the cooling capability of the heatexchangers. For example, if the calculated heat transfer rate fromthe primary system to the S/G tubes is lower than the core power,the overall coolant temperatures will gradually increase until heatbalance equilibrium is established. Therefore, the results presentedin Table 4 demonstrate that the incorporated S/G model works verywell for predicting the shell-side and tube-side heat transfers acrossthe helical tubes.

6.2.2. Changes in the core powerUsing the RTF, several transient experiments were also car-

141.55 74.15 72.75 157.98 155.46 56.90 57.70145.75 75.14 74.01 159.97 158.05 58.44 58.81170.10 83.31 81.29 174.36 172.26 65.04 65.29172.45 82.95 81.94 176.89 173.31 65.64 65.90

Y.-G. Lee et al. / Nuclear Engineering and Design 249 (2012) 364– 378 375

Fig. 10. Primary side configuration of RTF.

Fig. 11. TAPINS nodalization diagram for RTF experiments.

0 50 100 150 200

0.0

0.1

0.2

0.3

0.4

0.5

RTF experiment

Analytical calculation

TAPIR

Ma

ss F

low

Ra

te (

kg

/s)

Core Power (kW)

Eq. (32) evaluated at 141.55 kW

Fig. 12. Steady-state natural circulation flow rate in the RTF.

0 500 100 0 150 0 200 0 250 0 3000

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

Mass F

low

Ra

te (

kg/s

) RTF experi men t

TAPI NS

Time (sec)

Fig. 13. Transient coolant flow rates in response to a reduction in core power.

investigating changes in these factors are presented in this paper:an increase in core power, a reduction in core power, and a reduc-tion in feedwater flow. Through comparison with the transient dataobtained by RERI, assessments of the predictive capability of theTAPINS can be conducted.

Figs. 13 and 14 show the variation of the coolant flow rate andtemperatures when the core power abruptly dropped by half froma stabilized state. At 200 s, the core power is reduced from 138.6 kWto 71.2 kW in a ramp type drop for 40 s. One has to remember thatthe heat transport between the fluid and the internal structuresis not trivial in this kind of scaled-down test rig, especially when adramatic temperature change occurs in the fluid. The stored energyin the structural wall may serve as a heat source during transients,or the relatively cooler internals may absorb a lot of heat from thefluid. In particular, the thermal–hydraulic behavior of the RTF ischaracterized by a low flow rate and a large temperature rise, andthus the heat transfer with the structural wall has to be modeled.For transient simulations of the TAPINS, the heat exchange with thereactor internals is modeled using a lumped approach as follows:

dTs

Mscsdt

= −˛As(Ts − T∞) (34)

The outer surfaces of the walls are assumed to be adiabatic, andthe same heat transfer correlations are used as in the core heat

376 Y.-G. Lee et al. / Nuclear Engineering and Design 249 (2012) 364– 378

0 500 100 0 150 0 200 0 250 0 3000

40

80

120

160

200

Coo

lan

t T

em

pe

ratu

re (

oC

)

RTF data: core inle t

RTF data: core exit

TAPINS: core inle t

TAPINS: core exit

F

tcpatt

aiierlatawtpS

iit

0 500 1000 1500 2000 2500 3000

0.28

0.32

0.36

0.40

0.44

Ma

ss F

low

Ra

te (

kg

/s)

RTF Experim ent

TA PINS

Time (sec)

ig. 14. Transient coolant temperatures in response to a reduction in core power.

ransfer models. The sensitivity study revealed that the modeledoolant flow underwent premature changes in flow rate and tem-eratures unless the effect of the structural wall was taken intoccount. In simulations of the reduction in core power, the heatransfer rate from the wall instantaneously reached 12% of theime-dependent core power.

In this transient, the reduction in core power is followed by rapid drop of the natural circulation flow. As the flow veloc-ty is lowered, the temperature rise across the core is somewhatncreased, causing a slight overshoot in the coolant flow rate bynhancing the driving force of the free convection. Then the flowate and the temperatures slowly decrease until a new stabi-ized state is established. The TAPINS succeeds in predicting theforementioned flow pattern setup by natural circulation and theransient behavior of the coolant temperatures with fine accuracy,s shown in Figs. 13 and 14. The outlet temperature of the feed-ater is also plotted in Fig. 15. Since it is a direct indication of

ime-dependent heat transport to the secondary system, Fig. 15roves that the TAPINS predicts the heat transfer in the helical-coil/G fairly well.

As a similar transient case, the simulation results of an increasen core power are plotted in Figs. 16 and 17 along with correspond-ng experimental data. Over 40 s, the core power rose from 69.5 kWo 142.75 kW at 200 s. Immediately after the sudden increase in

300025002000150010005000

35

40

45

50

55

60

65

Power reduction: RTF data

Power reduction: TAPINS

Feedwater reduction: RTF data

Feedwater reduction: TAPINS

Tem

pera

ture

(oC

)

Time (sec)

Fig. 15. Variation in the outlet temperature of feedwater.

Time (sec)

Fig. 16. Transient coolant flow rate in response to an increase in core power.

heat input, even though the up-and-down behavior of the flow rateis more conspicuous in the simulation result, the analysis capabilityof the TAPINS seems quite acceptable.

6.2.3. Reduction in feedwater flow rateThe remaining transient is initiated by reducing the feedwa-

ter flow rate into the helical tubes. The ball valves located at theentrance of the helical coils are partially closed so that the flow ratein each tube is reduced from 4.5 LPM to 2.7 LPM. The experimentaldata and the simulation results are plotted in Figs. 18 and 19. Asthe reduction in feedwater flow rate causes a slight decline of theheat transfer in the tube-side, the heat input from the core takesa while to be completely removed from the S/G. According to thesimulation by the TAPINS, the cooling rate at the shell-side of thehelical tubes is reduced to a minimum of 85% of the core power. Inthe meantime, the average temperature of the RCS gradually goesup due to the power-cooling mismatch. While the heat removalreturns to its normal level, the outlet temperature of the feedwateralso increases until it reaches a new steady-state.

Compared to the previous transients caused by the changes in

the core power, it is noted that the effect of the feedwater flow rateis relatively insignificant in this transient. In fact, Eq. (32) describescases for which the total input power is equal to the amount of heatremoved, and the details of the heat transport to the heat sink are

0 500 1000 1500 2000 2500 3000

40

60

80

100

120

140

160

RTF d ata: cor e i nlet

RTF d ata: cor e exi t

TAPINS: core inlet

TAPINS: core exi t

Co

ola

nt T

em

pe

ratu

re (

oC

)

Time (sec)

Fig. 17. Transient coolant temperatures in response to an increase in core power.

Y.-G. Lee et al. / Nuclear Engineering a

0 500 1000 15 00 200 0 2500 3000

0.30

0.32

0.34

0.36

0.38

0.40

Mass F

low

Ra

te (

kg/s

)

Time (sec)

RT F experimen t

TAPINS

Fig. 18. Transient coolant flow rate in response to a reduction in feedwater flowrate.

0 500 1000 1500 20 00 25 00 3000

40

60

80

100

120

140

160

Co

ola

nt T

em

pera

ture

(oC

)

Time (se c)

RT F da ta: core in let

RTF da ta: core exi t

TAPI NS: core inl et

TAPI NS: core exit

Ffl

nits

cCsstsstcfalt

7

a

ig. 19. Transient coolant temperatures in response to a reduction in feedwaterow rate.

ot so predominant in determining the free convective flow raten the transients. Nevertheless, the TAPINS effectively estimateshe qualitative behavior of the primary system in the transient, ashown in Figs. 18 and 19.

The computing times for the above three transients were alsohecked to confirm the fast-running capability of the TAPINS. ThePU time spent in completing the transient calculation is mea-ured on a PC equipped with a 2.8 GHz i7 CPU. When the time-stepize is set to 0.01 s, it takes about 668 s in CPU time to finish theransient computation of 3000 s. This indicates that the computingpeed of the TAPINS is more than four times the speed of the realystem, and thus the TAPINS can easily carry out real-time calcula-ions. With an identical time-step size, there is little difference inomputing time between the transient cases. From the results, theast-running capability of the TAPINS is quantitatively proved. As andditional remark, the transient simulations with various time-stepead to almost identical results unless the time-step size exceedshe numerical limitation.

. Conclusions

On the basis of the one-dimensional momentum integral model, thermal–hydraulic system code named TAPINS is developed at

nd Design 249 (2012) 364– 378 377

SNU. Requiring a simple pre-process setup, the TAPINS incorporatesrelevant models for the system components of integral reactors. Inparticular, a dynamic model for the steam–gas pressurizer is newlyproposed so that the effect of non-condensable gas on the pres-sure transient can be taken into account. This paper is the firstfundamental publication on the TAPINS to prove the validity ofthe incorporated hydrodynamic and component models from thevalidation results.

For a comprehensive assessment of the developed systemcode, a SET of the insurge transients in the pressurizer and anIET of the natural circulation in a scaled-down version of theapparatus are simulated using the TAPINS. Through comparisonwith experimental data, it is revealed that the TAPINS can pro-vide reliable predictions for an integral reactor system operatingon natural circulation, even though a few simplifying assump-tions and the undemanding solution method are employed to thethermal–hydraulic model to facilitate solutions for transients. Thefast-running capability of the TAPINS is also proved in simulations.The TAPINS adequately can be used to confirm the design basisof an integral reactor and investigate its RCS response to the var-ious non-LOCA transients. The contents of this paper deal merelywith the issue of validation of the incorporated models, while theresults of analyses to assess the design decisions and to simulatethe transient responses of REX-10 are expected to be reported in asucceeding publication.

To perform advanced safety analyses of anticipated accidentsthat could accompany the two-phase phenomena in REX-10, werequire a more elaborate hydrodynamic model of the balances ofthe two-phase flows. At SNU, as a second version of TAPINS, a subse-quent thermal–hydraulic system code is currently under design anddevelopment on the basis of the drift-flux model. In future works,more in-depth analyses will be performed with the support of addi-tional data regarding plausible accidents in the RTF and simulationsusing other reliable system codes.

Acknowledgments

This work was supported by Basic Research Program, whichis funded by the Ministry of Education, Science and Technology(MEST) of Korea.

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