Nuclear Engineering and Design 238 (2008) 2678–2683

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Nuclear Engineering and Design

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Effects of wire-spacer shape in LMR on thermal–hydraulic performance

Wasim Raza, Kwang-Yong Kim ∗

Department of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-Gu, Incheon 402-751, Republic of Korea

a r t i c l e i n f o

Article history:Received 21 January 2008Received in revised form 23 April 2008Accepted 16 May 2008

a b s t r a c t

In this work, analyses of three-dimensional flow and convective heat transfer in wire-wrapped fuel assem-blies with different shaped wire-spacers have been carried out using Reynolds-averaged Navier–Stokesequations with shear stress transport turbulence model. Three cross-sectional shapes of wire-spacer, cir-cle, hexagon and rhombus have been tested. All the assemblies have been analyzed for single pitch ofwire-spacer with periodic boundary conditions applied at inlet and outlet of the calculation domain. It isfound that the assemblies exhibit the directional periodicity in radial gradients between the adjacent sub-

channels due to presence of wire-spacer. The overall pressure drop is highest in case of rhombus shapedwire-spacer assembly followed by hexagonal shaped. Although circular shaped wire-spacer gives lowestpeak temperature as well as lowest overall temperature difference in the assembly, the rhombus shaped

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. Introduction

Triangular arrayed wire-wrapped fuel pins within hexagonalucts are usually used in fuel assemblies of liquid metal fast breedereactors. The wire wound helically around each fuel pin providespacing between the fuel pins, produces secondary flow in thessembly to increase the coolant mixing between the subchannels,nd thereby reduces the peak temperature and temperature gradi-nt in the assembly. But, it also increases the pressure drop in thessembly.

Many experimental and numerical works have been per-ormed to analyze thermal–hydraulics of the wire-wrapped fuelssemblies. However, there is no analysis available with differ-nt cross-sectional shapes of wire-spacer to investigate the effectsn flow mixing and heat transfer. All of the previous works wereerformed with circular sectioned wire-spacer. Fontana (1973)btained the measurements of temperature distributions on theuct wall and at the exit of a 19-pin wire-spacer fuel assembly.oidt et al. (1980) investigated the hydraulic field inside a 217-pinire-spacer assembly. Chun and Seo (2001) performed an experi-ental evaluation of existing correlations for the pressure drop in19-pin wire-wrapped fuel assembly. Choi et al. (2003) carried

ut experimental work to measure the pressure drop in a 271-in fuel assembly and compared the available data with existingorrelations for friction factor. Fernandez and Carajilescov (2000)erformed an experimental investigation to obtain static pressure

∗ Corresponding author. Tel.: +82 32 872 3096; fax: +82 32 868 1716.E-mail address: kykim@inha.ac.kr (K.-Y. Kim).

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029-5493/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2008.05.003

hest Nusselt number on fuel rod surface.© 2008 Elsevier B.V. All rights reserved.

nd wall shear stress distributions in a 7-pin wire-wrapped assem-ly.

Most of the numerical analysis has been based on subchannelnalysis approach which poses a serious concern to the situationsith large flow disturbances (2006). SABRE-4 (Macdougall and

illington, 1984), COBRA-IV-I (Wheeler et al., 1976) and MATRA-MR (Kim et al., 2002) are some of the subchannel analysis codeseveloped so far. Recently, Ahmad and Kim (2006) analyzed pre-isely the three-dimensional turbulent flow and heat transfern a 7-pin wire-wrapped assembly based on Reynolds-averagedavier–Stokes (RANS) analysis. Raza and Kim (2008) performed theumerical optimization of 7-pin wire-wrapped assembly based onhree-dimensional RANS analysis.

This work presents the effects of wire-spacer shape onhermal–hydraulic performance of sodium coolant in a 7-pin wire-rapped fuel assembly. Three different cross-sectional shapes ofire-spacer, circle, hexagon, and rhombus, have been tested. The

esults have been analyzed in terms of pressure drop, peak tem-erature, temperature uniformity and heat transfer rate in the fuelssembly.

. Analysis methods

By using periodic boundary conditions, numerical analyses haveeen performed only for one period of the wire-spacer. To adopt

he periodic boundary conditions, source terms in the streamwise

omentum and energy equations have been modified so as toalibrate the gradual decrease and increase of pressure and temper-ture, respectively. These modified governing equations are sames those used by Ahmad and Kim (2006).

W. Raza, K.-Y. Kim / Nuclear Engineering a

Nomenclature

D diameter of the fuel rodDw diameter of the wire spacerDe equivalent diameter of the assemblyH wire wrap pitchk fluid thermal conductivityNu local Nusselt numberP fuel rod pitchPr Prandtl numberqo heat flux from the fuel rodRe Reynolds number (= UDe/�)T local temperatureTw fuel rod surface temperatureU averaged axial velocityW distance of the duct wall from fuel rod

Greek letters� kinematic viscosity� fluid density

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ftarethtpthe available resources. Hence, blending between the fuel rod andwire-spacer as has been used to obtain a good quality volume meshas shown in Fig. 2.

Fig. 1. Configuration and computational domain.

Fig. 1 shows the configuration of a 7-pin wire-wrapped fuelssembly. The analysis is performed for a single period of theire-spacer. The wire-wrap is mounted on the fuel rods in counter-

lockwise direction starting from 12-o’clock position. This figurelso shows the definition of geometric parameters of the testssembly. The specifications of the test assemblies and operatingonditions are shown in Table 1.

A commercial CFD code, ANSYS CFX 11.0 (2007), which employsn unstructured grid, has been used for the numerical analysis. Ahear stress transport (SST) model (Menter, 1994) with automaticall treatment is used as a turbulence closure. The SST model com-ines the advantages of the k–ε and k–ω models with a blending

able 1pecifications of the test assemblies and operating conditions

ire-spacer shape Circle Hexagon Rhombus

ead to diameter ratio, H/D 12.5 12.5 12.5itch to diameter ratio, P/D 1.262 1.262 1.262ire diameter to diameterratio, Dw/D

0.25 0.25a 0.25b

ass flow rate (kg/s) 1.7 1.7 1.7nlet temperature (K) 570.52 570.52 570.52oolant used Liquid sodium Liquid sodium Liquid sodium

a Ratio of diagonal of hexagon to diameter of fuel rod.b Ratio of diagonal of rhombus to diameter of fuel rod. F

nd Design 238 (2008) 2678–2683 2679

unction. The k–ω model is activated in the near-wall region, andhe k–ε model is used in the region far from the wall. Bardina etl. (1997) reported that the SST model efficiently captures sepa-ation under an adverse pressure gradient compared to the otherddy viscosity models. Thus, it accurately predicts the near-wallurbulence, which is critical to accurate prediction of the turbulenteat transfer. Wire-spacers and fuel rods are in point contact inwo dimensions and in line contact in three dimensions. It is notossible to obtain a volume mesh for this kind of geometry with

ig. 2. Mesh structures on the periodic surface for different wire-spacer shapes.

2680 W. Raza, K.-Y. Kim / Nuclear Engineering and Design 238 (2008) 2678–2683

ection

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Fig. 3. Streamlines on planes normal to flow dir

The fluid flows upward in the fuel assembly. To obtain a fullyeveloped turbulent flow at the inlet of the calculation domain,he periodic conditions are set at the inlet and outlet sections. Con-tant heat flux is imposed on the fuel rod surfaces while at theexagonal duct wall, adiabatic condition is used. All the simula-ions were conducted by means of a segregated method using theIMPLE scheme (Patankar, 1980) for pressure–velocity decoupling.

ominally second order-accurate scheme is selected for the dis-retization of the governing equations. A residual reduction factorf 10−6 for the mass conservation equation was used to monitor theonvergence of the iterative solution. Liquid sodium (Na) is used as

able 2emperature and pressure drop in the assembly

ire-spacer shape Tmax (K) Tmin (K) Pressure drop (Pa)

ircle 598.123 563.043 7092.48exagon 604.245 562.723 8258.08hombus 604.257 563.295 8445.76

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at axial locations, (a) H/4, (b) H/2 and (c) 3H/4.

coolant. Reynolds number based on the hydraulic diameter andean axial velocity is 60,000.

. Results and discussion

Grid system for circular shaped wire-spacer shown in Fig. 2 isame as those used by Raza and Kim (2008) for the optimization of-pin wire-wrapped fuel assembly. The optimum number of grids

s found to be 8.62 × 105 from the grid-dependency test performedy Raza and Kim (2008). The present analysis methods are exactlyame as those used by Ahmad and Kim (2006). They validatedhe numerical solutions for a 19 pin fuel assembly in comparisonith the experimental data (Chun and Seo, 2001). The accuracy ofumerical computation was acceptable.

In all the assemblies with different cross-sectional shapes, theow characteristics are found to be greatly influenced by theresence of wire-spacers, exhibiting radial direction periodicityepending on wire position. Fig. 3(a)–(c) shows the comparisonf surface streamlines on the plane normal to the flow direction

W. Raza, K.-Y. Kim / Nuclear Engineering and Design 238 (2008) 2678–2683 2681

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tdcImdconfirmed by Figs. 4–6, which show the temperature contours on

ig. 4. Temperature contours on plane normal to flow direction at axial location,H/4.

t the three axial locations for three cross-sectional shapes, circle,exagon, and rhombus. The surface streamline is defined as a lineverywhere tangent to the surface component of velocity vector.

he three different cross-sectional shapes show the macroscopicow structures similar to each other, but show some differences

n the extent and shape of secondary vortical motions. The flowtructure varies largely in axial direction depending on relative

aelf

Fig. 5. Temperature contours at the central fuel rods of the assembly.

ocation of wire-spacer. The overall pressure drop in cases of hexag-nal and rhombus shaped wire-spacers are found to be 16.4% and9.1% higher as compared to circular wire-spacer, respectively, ashown in Table 2.

Maximum temperature and temperature uniformity are impor-ant factors which should be considered in thermal–hydraulicesign of the liquid metal reactors. Therefore, it is necessary toompare qualitatively the thermal fields among these assemblies.n Table 2, the circular shaped wire-spacer shows the lowest maxi-

um temperature (Tmax), and also the lowest overall temperatureifference (Tmax − Tmin) among the three different shapes. This is

plane normal to the flow direction and on surfaces of central anddge fuel rods, respectively. However, the line averaged normalizedocal Nusselt numbers are minima for circular shape and maximaor rhombus shaped wire-spacer at all circumferential locations on

2682 W. Raza, K.-Y. Kim / Nuclear Engineering and Design 238 (2008) 2678–2683

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Fig. 6. Temperature contours at the edge fuel rods of the assembly.

uel rod surface as shown in Table 3, where the Nusselt numbersre averaged along the axial lines (points on this line exist wherehe line intersects with a mesh element face) at different angu-ar positions separated by 60◦ (starting from 12-o’clock position)round the central fuel rod surface. The normalized local Nus-

able 3ine averaged local Nusselt number at different circumferential locations on fuel rodurface

ire-spacer shape Line averaged (Nu/Nus) at different locations

A B C D E F

ircle 0.94 0.96 0.97 0.96 1.02 1.04exagon 1.15 1.10 1.05 0.99 1.09 1.17hombus 1.24 1.24 1.26 1.20 1.31 1.32

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ig. 7. Local Nusselt number variations in axial direction at location A on fuel rodurface.

elt number is defined as Nu/Nus, where Nu = q0De/k(Tw − T) andus = 4.82 + 0.0185Re0.827Pr0.827. Here, Nu, qo, De, k, T, Tw, Re, andr are local Nusselt number, heat flux, hydraulic diameter, ther-al conductivity, wall temperature, Reynolds number and Prandtl

umber. And, Nus is the Nusselt number obtained from the corre-ation (Incropera and Dewitt, 2002) which is for fully developedurbulent flow in circular tubes with constant surface heat fluxor liquid metals. Bulk temperature in the subchannel is used aseference fluid temperature.

Fig. 7 shows the local Nusselt number variations along the axialine at 0◦ (location A) on fuel rod surface. Here, Z is normalized dis-ance along the line. It is found that the nature of variations for allire-spacers is similar with two peaks at Z = 0.57 and Z = 0.83. Theseeaks are induced by separation and reattachment of the flow overhe wire-spacer, and thus the locations of these peaks are depen-ent on the location of wire on the fuel rod surface and also relatedo the temperature distribution shown in Figs. 5 and 6. Rhombusnd hexagonal shapes show similar distributions both qualitativelynd quantitatively while circular shape shows far small values. Thearge production of turbulent kinetic energy at sharp edges of the

ire-spacers seems to be the main reason for the heat-transfernhancement obtained by rhombus and hexagonal shapes. Sim-larity of thermal field between rhombus and hexagonal shaped

ire-spacers is also shown in Figs. 5 and 6.

. Conclusion

The comparative study on three-dimensional fluid structurend heat transfer among wire-wrapped fuel assemblies withhree different shaped wire-spacers has been carried out usingeynolds-averaged Navier–Stokes analysis for one period of wire-pacer. Circular, hexagonal and rhombus cross-sectional shapesf wire-spacer have been tested. Macroscopic flow structures inhe three tested assemblies with different shapes of wire-spacerre found to be similar to each other. But, there are some dif-erences in the thermal field and heat transfer. Circular shapef wire-spacer shows the obvious advantages in overall pressurerop, maximum temperature, and uniformity of temperature inhe assembly in comparison with the other two shapes. How-ver, in the aspect of heat transfer, rhombus and hexagonal

hapes show superiority to circular shape. Rhombus and hexag-nal shapes show almost same maximum temperature and overallemperature difference in the assembly. However, rhombus givesetter heat-transfer performance but higher pressure drop thanexagon.

ering a

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Roidt, R.M., Carelli, M.D., Markley, R.A., 1980. Experimental investigations of thehydraulic field in wire-wrapped LMFBR core assemblies. Nucl. Eng. Des. 62,

W. Raza, K.-Y. Kim / Nuclear Engine

cknowledgement

The authors would like to acknowledge the support from KOSEFnder 2006 Nuclear Energy Research Program (No. 2006-01397).

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