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A subchannel analysis code MATRA-LMR for wire wrapped LMR subassembly Won-Seok Kim, Young-Gyun Kim*, Young-Jin Kim Korea Atomic Energy Research Institute, PO Box 105, Yusong, Taejon 305-600, Korea Received 7 September 2000; accepted 2 April 2001 Abstract In sodium cooled liquid metal reactors design limits are imposed on the maximum tem- peratures of the cladding and fuel pins. Thus an accurate prediction of the core coolant/fuel temperature distribution is essential to LMR core thermal hydraulic design. The detailed subchannel thermal hydraulic analysis code MATRA-LMR is being developed for LMFBR core design and analysis based on COBRA-IV-I and MATRA. The major modifications and improvements implemented in MATRA-LMR are as follows: sodium property calculation subprogram, sodium coolant heat transfer correlations, and most recent pressure drop corre- lations. To assess the development status of this code, benchmark calculations were per- formed with the ORNL 19 pin tests and EBR-II seven-assembly SLTHEN calculation results. The calculation results of MATRA-LMR were compared to the measurements and to the SABRE4 and SLTHEN code calculation results, respectively. Finally, the major technical results of the conceptual design for the KALIMER U-10%Zr binary alloy fueled core have been compared with the calculations of the MATRA-LMR, SABRE4 and SLTHEN codes. # 2001 Published by Elsevier Science Ltd. 1. Introduction The design of liquid metal reactor cores requires accurate prediction of the peak temperatures of the rod and coolant to ensure that certain economic and safety considerations will be met. Thus, to achieve a safe and economical design, it is necessary to use reasonably, rather than extremely, conservative design limits. Many of these relate to fuel, cladding, and coolant outlet temperatures for steady-state and Annals of Nuclear Energy 29 (2002) 303–321 www.elsevier.com/locate/anucene 0306-4549/02/$ - see front matter # 2001 Published by Elsevier Science Ltd. PII: S0306-4549(01)00041-X * Corresponding author. Fax: +82-42-868-8256. E-mail address: [email protected] (Y.-G. Kim).

A subchannel analysis code MATRA-LMR for wire wrapped LMR subassembly

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Page 1: A subchannel analysis code MATRA-LMR for wire wrapped LMR subassembly

A subchannel analysis code MATRA-LMRfor wire wrapped LMR subassembly

Won-Seok Kim, Young-Gyun Kim*, Young-Jin Kim

Korea Atomic Energy Research Institute, PO Box 105, Yusong, Taejon 305-600, Korea

Received 7 September 2000; accepted 2 April 2001

Abstract

In sodium cooled liquid metal reactors design limits are imposed on the maximum tem-peratures of the cladding and fuel pins. Thus an accurate prediction of the core coolant/fueltemperature distribution is essential to LMR core thermal hydraulic design. The detailed

subchannel thermal hydraulic analysis code MATRA-LMR is being developed for LMFBRcore design and analysis based on COBRA-IV-I and MATRA. The major modifications andimprovements implemented in MATRA-LMR are as follows: sodium property calculation

subprogram, sodium coolant heat transfer correlations, and most recent pressure drop corre-lations. To assess the development status of this code, benchmark calculations were per-formed with the ORNL 19 pin tests and EBR-II seven-assembly SLTHEN calculation results.

The calculation results of MATRA-LMR were compared to the measurements and to theSABRE4 and SLTHEN code calculation results, respectively. Finally, the major technicalresults of the conceptual design for the KALIMER U-10%Zr binary alloy fueled core havebeen compared with the calculations of the MATRA-LMR, SABRE4 and SLTHEN codes.

# 2001 Published by Elsevier Science Ltd.

1. Introduction

The design of liquid metal reactor cores requires accurate prediction of the peaktemperatures of the rod and coolant to ensure that certain economic and safetyconsiderations will be met. Thus, to achieve a safe and economical design, it isnecessary to use reasonably, rather than extremely, conservative design limits. Manyof these relate to fuel, cladding, and coolant outlet temperatures for steady-state and

Annals of Nuclear Energy 29 (2002) 303–321

www.elsevier.com/locate/anucene

0306-4549/02/$ - see front matter # 2001 Published by Elsevier Science Ltd.

PI I : S0306-4549(01 )00041 -X

* Corresponding author. Fax: +82-42-868-8256.

E-mail address: [email protected] (Y.-G. Kim).

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transient conditions. For instance, no significant fuel melting is allowed in the fuel;the cladding temperature must also be consistent with corrosion considerations; thecore assembly mixed mean outlet coolant temperature and the difference in themixed mean coolant temperature at the exit of adjacent assemblies must be withinallowable limits to ensure structural integrity of the upper internal structures duringthe prescribed lifetime; the sodium temperature must not exceed its boiling point(Tang et al., 1978; Waltar and Reynolds, 1981).Since a typical liquid metal reactor core is comprised of several thousands of fuel

pins clustered in groups of several hundreds of pins per assembly, a complete ther-mal hydraulic analysis requires the knowledge of coolant distributions and pressurelosses throughout the core. Fluid flow and heat transfer in the rod bundles are com-plex phenomena, and the basic understanding of these phenomena is essential toachieving optimum design performance during normal operation conditions andmaintaining structural integrity during off-normal operations. In order to ensure thatthese design bases are satisfied, in past years much effort has been made to develop thebundle thermal hydraulic subchannel analysis codes that yield detailed coolant tem-peratures for all the subchannels in the bundle. At present, COBRA-IV-I (Wheeler etal., 1976; Stewart et al., 1977) and SUPERENERGY-2 (Basehore and Todreas,1980; Yang and Yacourt, 1995) have been developed and used as subchannel codesin the USA, and SABRE4 (MacDougall and Lillington, 1984; Dobson and O’Neill,1992) in the UK. Most of the subchannel codes currently used in the design of anuclear reactor core were developed long ago and their applicable ranges are limited.Therefore, requests for the development of a subchannel code for best-estimatedesigns are raised based on various experimental and theoretical results that havebeen accumulated to date. This necessity led us to develop MATRA-LMR (multi-channel analyzer for transient and steady-state in rod array for liquid metal reactor),a detailed subchannel thermal hydraulic analysis code for liquid metal reactors,based on COBRA-IV-I and MATRA (Yoo and Hwang, 1997).The accuracy and proper coding of MATRA-LMR have been confirmed by a

benchmark analysis with the ORNL 19 pin tests and EBR-II 7-assembly SLTHENcalculation results. The major technical results of the conceptual design for theKALIMER U-10%Zr binary alloy fueled core have been compared with the calcu-lation of the MATRA-LMR, SABRE4 and SLTHEN codes. KALIMER (Koreaadvanced liquid metal reactor) is a sodium cooled pool-type reactor with a thermaloutput of 392.0 MW (electric power of 150.0 MW), and is a prototype reactor (Park,1998). It is currently in the conceptual optimization stage at KAERI.

2. MATRA-LMR code

The detailed subchannel analysis code MATRA-LMR, an LMR version ofMATRA, was developed specifically for LMR analysis. MATRA is a thermalhydraulic analysis code, which was developed at KAERI based on the subchannelapproach for calculating the enthalpy and flow distribution in nuclear fuel rodbundle elements for both steady-state and transient conditions. While the existing

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COBRA-IV-I, the reference code of MATRA (Yoo and Hwang, 1997), runs on aCDCCYBERmainframe computer,MATRA runs on an IBMPC orHPWS to give amore convenient computing environment. MATRA was provided with an improvedstructure and functions to give a more convenient user interface and working envir-onment, and an increased code accuracy by various methods. Whereas MATRA isdesigned to handle a wide variety of single and two phase flow problems for PWRs,MATRA-LMR is intended for LMR applications. In this respect, MATRA-LMR is amodified version of MATRA with three major features. First, sodium property cor-relations are built in the code as a subprogram. Second, correlations of heat transfercoefficients are changed for sodium coolant. Third, MATRA-LMR has additionalmodels for pressure drop correlations such as Novendstern, Chiu-Rohsenow-Todreas and Cheng-Todreas which were developed for the flow field induced by wirewraps. Fig. 1 shows the MATRA-LMR code development procedure. The followingdescribes the modified features of the MATRA-LMR code in detail.

Fig. 1. MATRA-LMR code development procedure.

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2.1. Sodium properties and heat transfer coefficients

In recent years, the COBRA-IV-I code, with its various versions, has been widelyused in analyzing the thermal hydraulic performance of nuclear reactor cores.However, COBRA-IV-I cannot be directly used for LMR cores, because it does notmodel sodium coolant. MATRA-LMR was developed for the analysis of sodiumcooled LMRs. MATRA-LMR has sodium properties tables in the code as a defaultsubprogram (Golden and Tokar, 1967).An LMR has the advantage of a tight arrangement of thin fuel pins because of the

high heat transfer coolant. Heat transfer coefficients are higher for liquid metalsthan for other fluids because of their high thermal conductivity compared to otherfluids. High thermal conductivity allows heat to be transported far out into the fluidwith relatively little resistance. The consequences of these differences are in the heattransfer correlation for the Nusselt number. The behavior of the Nusselt number(Nu) for liquid metals follows the relation:

Nu ¼ A þ B Peð ÞC

ð1Þ

Where Pe is the Peclet number, i.e. Pe=Re Pr. In the MATRA-LMR code, theswitch for selecting the heat transfer coefficient which is sensitive to boundary con-ditions and channel shapes, such as Lyon-Martinelli (Lyon, 1951), Westinghouseand Schad-Modified (Carelli and Kazimi, 1976) correlations, has been implemented.

2.2. Pressure drop

In MATRA-LMR, basic equations, which describe the properly averaged valuesof pressure, enthalpy, and velocity fields for each computational cell, can be derivedfrom the governing equations just like in COBRA-IV-I. The subchannel codesrequire some input parameters that must eventually be supplied through physicallybased empirical correlations. This is especially true when attempting to model com-plex geometry LMR subassemblies that have helical-wrapped fuel pins (Stordeur,1961). Because of the complex geometry caused by the wire wraps, simple equivalentdiameter techniques are not sufficient to accurately predict the pressure drop in thefuel pin region of the reactor. An accurate prediction of the pressure drop is neededso that plant parameters may be optimized. Because testing of all possible config-urations is not practical and the pressure drop in the pin bundle is a substantialportion of the total plant pressure loss, a method to predict the pressure drop moreaccurately in fuel assemblies utilizing wire wrap spacing is required.COBRA-IV-I has a pressure drop model for smooth pipes with equivalent dia-

meter techniques. This model is very simple and out of date. In the case of wire wrapspacing rods, the flow area in a central subchannels is the area surrounded by threerods excluding the area taken up by the wires. Only 50% of the wire area are onaverage in that subchannel. Similarly, the wetted perimeter is the sum of the peri-meters of the three rods in the subchannel plus 50% of the wire perimeters. Based onthis idea, new techniques have been developed to improve accuracy from the

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experimental work. The following three pressure drop models have been imple-mented in MATRA-LMR.

2.2.1. Novendstern modelNovendstern’s analysis (Novendstern, 1972) took advantage of all the previous

methods, together with experimental data. In this model the wire wrap is accountedfor by means of an effective friction factor. Using the flow conditions for the centralsubchannel, the pressure drop is determined by,

�P ¼ M fsmooth L=Deð Þ � V2=2� �

ð2Þ

The multiplication factor, M, is used to get the effective value from the pressuredrop calculated with the smooth tube friction factor. It primarily accounts for thewire lead and fuel pin pitch to diameter ratio,

M ¼1:034

P=Dð Þ0:124

þ29:7 P=Dð Þ

6:94 Reð Þ0:086

H=Dð Þ2:239

� �0:885ð3Þ

The Blasius relation for the friction factor, fsmooth, is applicable for the flow con-ditions in an LMR, hence,

fsmooth ¼ 0:316=Re0:25 ð4Þ

2.2.2. Chiu–Rohsenow–Todreas (CRT) modelThe CRT model (Chiu et al., 1978) represents an improvement over the Novend-

stern model. The principal difference is that the CRT model divides the pressuredrop across the channel into two components, one due to friction losses and one dueto form losses from flow perpendicular to the wire wrap. The CRT model treats themechanisms responsible for the pressure drop in greater detail. In the CRT model,as shown in Fig. 2, pressure drop parameters are derived for channel type 1 (inter-ior) and 2 (edge) only. The values for the corner channels (channel type 3) areassumed to be the same as for the edge channels since the corner channels have littleinfluence on the flow.The resulting pressure drops for channel types 1 and 2 are shown below,

�P1 ¼ fs1L

De1

�V212

1þ C1Ar1

A1

De1

H

P2

�Pð Þ2þH2

� �ð5Þ

�P2 ¼ fs2L

De2

�V222

C3 1þ C2 nVT

V2

� �gap

" #28<:

9=;1:375

ð6Þ

W.-S. Kim et al. / Annals of Nuclear Energy 29 (2002) 303–321 307

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2.2.3. Cheng–Todreas (CT) modelThis correlation (Cheng and Todreas, 1986) based on the model for the sub-

channel friction factor and mixing parameters are calibrated by the available data.

�Pi ¼ fi L=Deið Þ � V2i =2� �

ð7Þ

-Interior f1 ¼1

Rem1

C0f1

P0w1

Pw1

� �þ Wd

3Ar1

A1

� �De1

H

� �De1

Dw

� �m� �ð8Þ

-Edge f2 ¼C0

f2

Rem2

1þ WsAr2

A2

� �tan2�

� � 3�mð Þ

2

ð9Þ

-Corner f3 ¼C0

f3

Rem3

1þ WsAr3

A3

� �tan2�

� � 3�mð Þ

2

ð10Þ

3. Benchmark calculations

3.1. Brief descriptions of the benchmark codes

3.1.1. SABRE4 codeSABRE4 (subchannel analysis of blockage in reactor elements) is a 3-D subchannel

code designed to calculate the thermal hydraulics of a fast reactor subassembly. TheSABRE4 code permits the calculation of steady-state or transient, single or two phaseflows and the geometrical options include general representation of grids, wirewraps, multiple blockages and bowed pins, etc. Transient flows may be calculatedusing semi-implicit or fully implicit time solution methods and the temperature

Fig. 2. Geometry of subchannels and wire wrap.

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distributions within the fuel pins are determined as well as the velocity and tem-perature of the coolant. General inlet boundary conditions are available, includingpressure, velocity and total mass flow, and the outlet boundary condition is taken asa constant pressure. The wire wrap model introduces resistance with its principalaxes along and perpendicular to the wire, resulting in very satisfactory modeling ofthe inducement of swirl (MacDougall and Lillington, 1984). A more detaileddescription for the wire wrap model is given below.

3.1.1.1. Wire wrap model. Experimental observations of the flow in wire wrappedbundles indicate that the wire wraps have two main effects. Firstly, they increase theoverall pressure drop in the bundle and secondly, they divert the flow locally in thedirection of the wraps. The model used in SABRE4 is based on the assumption thatthe effects of a wire wrap can be represented solely by its direction and resistancecharacteristics. Thus the model does not take any direct account of the geometricaldifferences in cross-sectional area due to the presence of the wire wrap. The differencesin area and perimeter are however included in the derivation of the wrap resistancecoefficients, which are referred to the velocities in the superficial areas of the bundle.The effects of the wire wraps on the flow in a wire wrapped bundle are represented byresistance terms in the axial and lateral momentum equations for the subchannels.However, the actual subchannel flow areas are not modified as they are in MATRA-LMR (Davies, 1981).The flow components parallel and perpendicular to a wire wrap are analyzed

independently. Parallel flow depends on the pressure gradient in this direction, andperpendicular flow depends on the pressure difference across the wrap.

-Tangenital pressure gradient �@p

@s¼ Ks � v2s ð11Þ

-Normal pressure gradient �@p

@n¼ Kn � vn vnj j ð12Þ

Where s and n are the distances measured in the tangential and normal directions,Ks and Kn are resistance coefficients in these directions, and vs and vn are the com-ponents of the flow velocity v in these directions. These equations yield the axial andlateral pressure gradients due to the wire wraps. The pressure drop characteristicsare added to the subchannels where the wire wraps pass.

3.1.2. SLTHEN codeThe above two codes use sophisticated physical modeling processes to simulate the

crossflow between subchannels. They couple the momentum equations with energyequations by solving the velocity distributions from the momentum equations andthen by using these velocities in the energy equations. They also use iterative proce-dures for the finite difference equations to obtain convergent solutions. Because ofthese characteristics, it requires a large amount of computer time to solve the flowequations for every channel in a bundle using the conventional subchannel analysis

W.-S. Kim et al. / Annals of Nuclear Energy 29 (2002) 303–321 309

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model. In order to enhance computational efficiency, the simplified energy equationmixing model called ENERGY was developed in the mid 1970s specifically forLMRs. These approximations enable the momentum equations to be decoupledfrom the energy equations. Once the flow is split, the temperatures and the pressuredrops are calculated along the axial noding with the finite difference equations.These simplifications enable a significant reduction in storage space and the runningtime required for computation (Khan et al., 1975).The wire wrapped rods are packed in an array that is enclosed by a duct. In the

central region the mean flow oscillates around each rod as it progresses in axialdirection. In the outer region near the wall the flow field is quite different. The dif-ference in the flow pattern in the outer and inner regions of the assembly suggeststhat the bundle flow be divided into two regions. As shown in Fig. 3, region I is theinner region where the wire wrap mixing effect can be modeled by an effective eddydiffusivity, ". Region II is the outer region which can be additionally modeled by anaverage circumferential swirl flow due to the unidirectional wire wrap in that area.The SLTHEN (steady-state LMR core thermal hydraulics analysis code based on

ENERGY model) code is a modified version of the SUPERENERGY2 code, whichis a multi-assembly, steady state subchannel analysis code based on the above sim-plified energy equation mixing model. This code improves the numerical schemes ofSUPERENERGY2 to accommodate the axial convection due to the interassemblygap flow and to enhance the computational efficiency by adopting the ymethod. Fueland cladding temperature calculation models are also developed, and the recentcorrelations for the flow split and mixing parameters are incorporated (Yang, 1997).

3.2. ORNL 19 pin test

ORNL 19 pin tests were performed in the fuel failure mockup (FFM), a large hightemperature sodium facility built specifically for testing simulated LMR fuel rodbundles at design power, flow and temperature (Fontana et al., 1974). The fuel wassimulated by electric cartridge heaters fabricated to duplicate the reactor fuel rodconfiguration and heat flux. Rod bundle 2A, which had 19 simulated fuel rods in ahexagonal duct, was the second bundle operated in the FFM. The rods were 5.84

Fig. 3. Flow field in the two regions of the ENERGY model.

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mm in diameter, and the wire wrap spacers were 1.42 mm in diameter and werewrapped around the fuel rod on a 30.48 cm pitch. The FFM bundle 2A fuel rod hada 53.34 cm heated length that started 40.64 cm from the bottom. The total length ofthe fuel rod was 101.6 cm. Both the axial and radial power profile were uniform, andliquid sodium was used as coolant. The primary purpose of the tests was to measurethe temperature distributions within the rod bundle at the duct wall and exit. Thedetailed input data for the 19 pin tests are shown in Table 1.Several runs were performed during the course of experimentation with bundle 2A

with varying flow and power. Simulations in this paper, however, were done for twocases: one is the high power/flow case which has 16975 W/rod and 3.038 kg/s andthe other is the low power/flow case which has 263 W/rod and 4.087E-2 kg/s. Fig. 4shows the subchannel numbering scheme for the MATRA-LMR and SABRE4 coderespectively.First, to see the effect of the number of axial nodes on the calculated temperature,

calculations were repeated for the high power/flow case with an increasing numberof nodes. Fig. 5 shows the peak temperature of subchannel 1 and the bundle averagetemperature according to the number of axial nodes such as 40, 80 and 120. Thereare the same bundle average temperatures for the different node cases. For peaktemperature, the 40 node case showed a slightly lower temperature than the othersthat had almost the same temperatures. Considering the computing time and com-

Table 1

Input parameters for ORNL FFM-2A 19 pin test

Input parameter Value

Rod information Rod diameter (m) 5.84E-3

Rod pitch (m) 7.26E-3

Wire wrap diameter (m) 1.42E-3

Wire wrap pitch (m) 0.3048

Rod pitch/rod diameter 1.243

Duct inside flat-to-flat distance (m) 3.41E-2

Total length (m) 1.016

Initial conditions System pressure (Pa) 1.0132E5

Inlet temperature (�C) 315

Inlet mass flow (kg/s) (high/low) 3.0378 / 4.087E-2

Average rod power (W) (high/low) 16975 / 263

Axial power distribution Uniform

Radial power distribution Uniform

Calculation parameters Wire pitch fraction (�) 0.0417

Turbulent mixing factor () 0.01

Conduction shape factor (Gk) 0.5

Number of axial nodes 80 (MATRA-LMR)

20 (SABRE4)

Correlations Pressure drop model

Novendstern, CRT 0.316Re�0.25

CT Re�0.18

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puter storage, however, the 80 node case is supposed to be and adopted as a rea-sonable case for the MATRA-LMR code calculations of the ORNL 19 pin tests.Fig. 6 shows the comparisons for the pressure drop models used in the MATRA-

LMR code with the ORNL 19 pin high power/flow case. The accuracy of the pres-sure drop data was the important parameter for predicting the temperatures in thefuel bundle. The three models used have similar trends to the experimental results asshown in Fig. 6. But the Novendstern model generally predicted high and inaccuratetemperatures, especially for the interior subchannels. One possible reason is that theNovendstern model does not take into account the form loss induced by the wiresand it uses the same pressure drop correlation for the interior and the edge sub-channels which have differences in geometry and flow behavior. The CRT modelwas more accurate, though it predicted a slightly higher temperature than theexperimental results. On the contrary, the CT model predicted a slightly lower tem-perature than the experimental results. Based on the above comparisons, the CRTmodel was adopted to use for reasonable results.Fig. 7 shows the normalized temperatures at the end of the heated length for the

high power/flow case. The temperature profiles are plotted in Fig. 7 for the calcula-tions with the MATRA-LMR, SABRE4 and SLTHEN codes and compared with

Fig. 4. Subchannel numbering schemes.

Fig. 5. Temperatures according to the number of axial nodes (MATRA-LMR).

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the experimental results at the same axial location. MATRA-LMR predicted theexperiment within a 15% maximum, but the other two codes showed much differentbehavior from the experiment. SABRE4 greatly underpredicted at the outer region,i.e. the edge and corner sides. Although it predicted well the temperatures of theinterior subchannels, it failed to predict the temperatures of the peripheral sub-channels. The difference between the MATRA-LMR and SABRE4 calculationscomes partly from the modeling of the pressure drop induced by wire wraps. Forinstance, the wire wrap model in SABRE4 assumes that the effects of the wraps canbe represented as specified resistance coefficients tangential and perpendicular to thewire wraps. Geometrical differences in area and wetted perimeter are included in thederivation of these coefficients, while actual subchannel flow areas are modified inMATRA-LMR. On the other hand, SLTHEN overpredicted the temperatures in theinterior side. Unlike the above two codes, SLTHEN uses a relatively simple modelto reduce the computing time. According to the simple model, there are only twovelocity fields for the inner and the outer regions respectively, and the same sub-channel velocity is maintained in each region while the other two codes have differ-ent velocities corresponding to the heat source in each subchannel.

Fig. 6. Normalized temperatures at the end of the heated length.

Fig. 7. Normalized temperatures at the end of the heated length.

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Fig. 8 shows the axial temperature profiles in the interior (channel 1) and the edge(channel 32) subchannels for the high power/flow case with the MATRA-LMR andSABRE4 codes. As discussed above, both codes show excellent agreement with theexperimental results in interior subchannel 1. But in edge subchannel 32, SABRE4underpredicted the temperatures more than MATRA-LMR. The following figuresshow more detailed reasons for it.Figs. 9, 10 and 11 show the subchannel crossflow velocities in the internal gap,

outer gap, and edge gap for the high power/flow case, respectively. The values of theimportant wire wrap diversion parameters are as follows: firstly, the model used inSABRE4 requires that the axial mesh in the problem shall be chosen so that a wirewrap traverses one axial mesh length at the same time as it traverses one subchannel.That means the axial mesh length must be set equal to one-sixth of the wire wrappitch. As a result, the number of axial nodes in SABRE4 is 20 for the ORNL 19 pintests. Secondly, the resistance coefficients required by the wire wrap for the maincontrol volume (ks=0.1789, kn=0.7599) and for the lateral control volume

Fig. 8. Axial temperature profiles in the interior edge subchannels.

Fig. 9. Subchannel crossflow velocities in the internal gap (channels 1–6).

314 W.-S. Kim et al. / Annals of Nuclear Energy 29 (2002) 303–321

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(ks=0.1909, kn=8.8835) were used in SABRE4. Subchannel crossflow velocities inthe internal gap between the channels 1 and 6 show that the two codes predictedalmost the same, i.e. 0.25 m/s, as shown in Fig. 9. Fig. 10 shows the crossflow velo-cities as a function of axial position for the outer gap between the interior and theedge, channels 9 and 26. Compared to the case of the internal gap as shown in Fig. 9,the magnitudes of the crossflow velocities were larger, but the two predictions werestill in good agreement.On the contrary, for the crossflow velocities in the edge gap between channels 25

and 26, the two code predictions show different behavior as shown in Fig. 11. Thereis one circumferential swirl flow due to the unidirectional wire wrap in the edgesubchannels, that is, the summation effect of swirl forces by wire wraps passingthrough adjacent edge gaps near the duct wall. MATRA-LMR predicted larger cross-flow velocities than SABRE4. In this calculation, the axial average velocity was pre-dicted as about 7.5 m/s and the crossflow velocity about 1.5 m/s by MATRA-LMR.

Fig. 10. Subchannel crossflow velocities in the outer gap (channels 9–26).

Fig. 11. Subchannel crossflow velocities in the edge gap (channels 25–26).

W.-S. Kim et al. / Annals of Nuclear Energy 29 (2002) 303–321 315

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The above behavior on the edge side might cause the temperature underpredictionswith SABRE4 at the outer regions.Fig. 12 shows the normalized temperatures at the end of the heated length for the

low power/flow case of 4.087E-2 kg/s and 263 W/rod. In this case, the SABRE4calculations are in reasonably good agreement with the experiment, while theMATRA-LMR calculations are higher in the internal region and the results of bothcodes are slightly lower in the outer region than the experimental results. As shownby the results, the conductive heat transfer has more important influences on thetemperature distributions throughout the bundle at the lower power/flow case. Inthis low power/flow case, the Reynolds number is 1000, while it is 77400 for the highpower/flow case. The calculation conditions were out of application for theSLTHEN code because of its basic models.

3.3. EBR-II 91 pin test

The EBR-II experiment that is used in this paper is a seven assembly problem.This seven assembly problem is composed of one 7 pin assembly, two 61 pinassemblies, and four 91 pin assemblies as shown in Fig. 13. The power and flow ratesof each assembly are also shown in the figure. Two 91 pin assemblies are calculatedfor comparison: a high power/flow assembly of 0.63 MW and 3.889 kg/s and a lowpower/flow assembly of 0.37 MW and 3.076 kg/s.Table 2 gives the comparisons of the above three codes on the average exit and

peak subchannel temperatures. It was observed that MATRA-LMR predictedslightly different temperatures from the other two codes by as much as 3% higher inthe average exit and lower in the peak subchannel temperatures. The computingtime of MATRA-LMR is 75% less than SABRE4, but it is considerably larger thanSLTHEN. Based on the results, MATRA-LMR that is being developed for pre-dicting the temperature distributions in wire wrapped LMR fuel rod bundles mat-ches the available data with the same precision as the complicated or simplifiedsubchannel analysis codes which are used now.

Fig. 12. Normalized temperatures at the end of the heated length (low power/flow).

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3.4. Application to KALIMER core design

The Korea advanced liquid metal reactor (KALIMER), a 150 MWe pool typesodium cooled prototype reactor, is currently in the conceptual design and optimi-zation stage. An initial design concept was also proposed through the feasibilitystudy of various innovative design features. Based on the insight and results fromprevious work, the KALIMER program plan was updated to call for completion ofthe basic design and supporting R&D work by 2006.The KALIMER core system is designed to generate 392.2 MWth of power. The

reference core utilizes a homogeneous core configuration in the radial direction withtwo driver fuel enrichment zones, surrounded by a layer of blanket assemblies. Thereference core has an active core height of 100 cm and a radial equivalent diameterof 172 cm, and the height-to-diameter ratio for the active core becomes 0.581. Thephysically outermost core diameter of all assemblies is 344.7 cm. The major designparameters and geometric characteristics of the assembly are given in Table 3.

Fig. 13. Layout of the EBR-II seven assembly problem.

Table 2

Calculation results for the EBR-II 91 pin test

Parameters MATRA-LMR SABRE4 SLTHEN

High power/flow case

Avg exit temperature, �C 512.9 498.0 495.1

Peak subchannel T, �C 560.6 574.6 571.0

Computing time, s 330 1440 0.78

Low power/flow case

Avg exit temperature, �C 475.2 465.0 462.0

Peak subchannel T, �C 510.4 520.1 512.3

Computing time, s 378 1440 0.78

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A KALIMER inner core, outer core, and radial blanket assemblies were chosen tocalculate the temperature distributions with the MATRA-LMR code, and to com-pare the results with the SABRE4 and SLTHEN codes. Fig. 14 shows the sub-channel numbers where the temperatures are compared across the radial blanket

Table 3

Input parameters for KALIMER U-10%Zr binary alloy fueled core design

Core Core thermal output (MWth) 392.2

Core electric power (MWe) 150.0

Core inlet / outlet temperature (�C) 386.2 / 530.0

Total flow rate (kg/s) 2143

Active core height (mm) 1000

Core diameter (mm) 3447.3

Core configuration Radial homogeneous

Pins per fuel assembly (driver/radial blanket) 271 / 127

271 / 127 pin Total axial height (mm) 3163.0

Rod outer diameter (driver/radial blanket) (mm) 7.67/12

Rod pitch (driver/radial blanket) (mm) 8.95/13

Wire wrap diameter (driver/radial blanket) (mm) 1.2/0.95

Wire wrap lead (driver/radial blanket) (mm) 208.5/300

Cladding thickness (driver/radial blanket) (mm) 0.53/0.54

Duct wall thickness (mm) 3.7

Duct inside flat-to-flat distance (mm) 149.8

Nominal linear pin power (IF/OF/RB) (W/cm) 148/159/35

Assembly nominal flowrate (IF/OF/RB) (kg/s) 21.6/23.7/4.59

Assembly coolant inlet temperature (�C) 386.2

Number of axial nodes 250 (MATRA-LMR)

64 (SABRE4)

Radial power distribution Uniform

Fig. 14. MATRA-LMR 127 pins subchannel numbering scheme.

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assembly. As shown in Figs. 15–17, the three code results are in good agreement inthe inner region, though SABRE4 predicted a slightly higher temperature. In thesecalculations, they showed similar mixing behavior induced by wire wraps in theinner region, because the radial power profile is assumed to be uniform.

Fig. 15. Temperatures at the end of the heated length (KALIMER radial blanket assembly).

Fig. 16. Temperatures at the end of the heated length (KALIMER inner core assembly).

Fig. 17. Temperatures at the end of the heated length (KALIMER outer core assembly).

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On the other hand, in the outer region where the peripheral swirl flow occurred, asillustrated in the figures, MATRA-LMR predicted higher temperatures than theother two codes, because MATRA-LMR generated a larger swirl flow. As shown infigures, the calculation results of SABRE4 in the outer region show more under-prediction than the other two codes according to the flow and increasing power.Based on the calculation results for the high power/flow case of the ORNL 19 pin testmentioned above, it might be concluded that the MATRA-LMR gives more precisepredictions than the other two codes for both regions of the bundle. All the calcu-lations were performed on an HP J200 workstation. The required computing timefor the radial blanket was 1758, 2400 and 1.38 s for the MATRA-LMR, SABRE4and SLTHEN codes, respectively.

4. Conclusions

The development status of the detailed subchannel analysis code MATRA-LMRwas assessed from benchmark calculations with the SABRE4 and SLTHEN codes.The MATRA-LMR calculations for the ORNL 19-pin assembly tests and EBR-II91-pin experiments were compared to the measurements, and to SABRE4 andSLTHEN code calculation results.The comparison results for the ORNL 19 pin tests showed that there was good

agreement between the MATRA-LMR calculations and the experimental data asshown in the normalized temperatures at the end of the heated length. Also theaccuracy of the pressure drop models was compared for the ORNL 19-pin assemblytests. The results indicated that the CRT model predictions were in good agreementwith the experimental results better than the other models. SABRE4 underestimatedthe temperatures on the edge side and the SLTHEN results showed higher tem-peratures in the internal region. One of the main reasons for the differences amongthe three code results is the pressure drop induced by wire wraps. In comparisons forthe EBR-II seven assembly problem calculations, it was observed that MATRA-LMR predicted slightly different temperatures from the other two codes by as muchas 3% higher in the average exit and lower in the peak subchannel temperatures.The computing time of MATRA-LMR is 75% less than SABRE4, but it is con-siderably larger than SLTHEN. In the application for KALIMER design, MATRA-LMR predicted as well as the other two codes.From all the benchmark calculations, it can be concluded that the MATRA-LMR

code could be used as a reliable analysis tool for LMR subassembly design and perfor-mance analysis. The current version of MATRA-LMR is used only for a single sub-assembly analysis, but it is planned to extend for multi-assembly whole core calculations.

Acknowledgements

The authors are grateful to their colleagues for their help and useful discussionson the subject. This work was supported by the Nuclear R&D Long-Term

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Development Program, the Ministry of Science and Technology, Republic ofKorea.

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