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Study Thermohydraulic a Fixed Bed for Core of Nuclear ReactorJ. Almachi*1, J. Montenegro*1

1Escuela Politécnica Nacional, Quito, Pichincha, Ecuador*[email protected], [email protected]

Abstract: The fixed beds have the advantage oflarge heat transfer area, for they are used in somedesigns of innovative nuclear reactors as thereactor FBNR. Inside of study of fixed beds isimportant to define the following parameters:flow minimum and velocity profile of coolingfluid, temperature profile of cooling fluid and thefuel elements. In order to determine theparameters before described the SoftwareCOMSOL Multiphysics® was used, thegeometry was established in 3D for core ofnuclear reactor, and for termohydraulic studymodules used were heat transfer, conjugated heattransfer and flow. In this study was considered tonuclear fuel spheres as heat sources, the coolingfluid used in the simulation was water and thetype of study was stationary. The study oftermohydraulic parameters is important toestablish safe operating conditions to verify thatthe thermal limitations of the materials involvedin the reactor core are not exceeded.

Keywords: Fixed Bed, Heat Transfer, FBNR,Nuclear Reactor.

1. Introduction

Faced with the growing demand of energy ofworld population, nuclear energy capturesattention because is secure, competitive and doesnot produce greenhouse gases, there morecovered the 15 % of demand the electricityworldwide in 2015[1][2].

Since 2000 until today so as to potentiate theinclusion of nuclear energy in the energy matrix,are being developed new concepts of nuclearreactors, known as nuclear reactors of fourthgeneration, through which seeks to improve theefficiency of heat transfer in comparison withreactors of previous generations, therefore theimportance of thermohydraulics study of fixedbeds has like advantage their larger surface areaof heat transfer in the reactor core [3][4][5].Under this concept are being developed thereactor FBNR (Fixed Bed Nuclear Reactor).

1.1 Description of Nuclear Reactor FBNR

The fixed bed nuclear reactor, FBNR bases itsoperation in pressurized water reactors (PWR).Has a small size (2m in diameter and 6 m high)compared to PWRs, generates an output of 70MW, is modular in design, it does not requirerefueling site, since it can operate long periodswith fuel loaded in the factory building and hasan inherent safety system. All these featuresallow the reactor FBNR be part of the IAEA inthe INPRO program, because it meets therequirements set for nuclear reactors of fourthgeneration, security and economic profitability[6][7][8].

The FBNR reactor is a research proposal ofPhD. Farhang Sefidvash, fundamentals andtechnology of this reactor is public domain andis currently in the study phase.

The graphic representation of the FBNR can beseen in the Figure 1 [9].

Figure 1. Schematic Design of FBNR

In the design of FBNR are identified 3 modules,with a specific and independent function whichare: the core, the steam generator and the fuelchamber.

COMSOL Multiphysics and COMSOL are either registered trademarks or trademarks of COMSOL AB. Microsoft is a registeredtrademark of Microsoft Corporation in the United States and/or other countries.

Excerpt from the Proceedings of the 2016 COMSOL Conference in Boston

1.2 Core of Nuclear Reactor FBNR

According to the design proposed by SefidvashF., the reactor core is constituted by a cylinder1.71 m in diameter and 2 m high, the fuelspheres are inside forming a fixed bed, throughwhich pressurized water circulates, the water actsas cooling fluid, which also ensures that heatremoving the materials from which the fuelelements do not melt, the refrigerant ascendsthrough the core and is recirculated to operate ina closed circuit [10].

The fuel elements are based on HighTemperature Gas Cooled Reactor (HTGR)technology, in which the fuel elements arespherically shaped.Fuel spheres are made with CERMET, thismaterial is characterized by the high temperatureresistance.

The spherical CERMET fuel consists of coatedUO2 kernels embedded in a zirconium, orzirconium hydride, matrix which is thenovercoated with a protective outer fuel-free layer[11].

The Table 1. shows the values of the physicaland thermal properties CERMET material usedin the present study [12].

Table 1. CERMET properties

Properties Temperature 300°CThermal Conductivity 28.2 W/m°K

Specific Heat 431 J/kg.°KDensity 6940 kg/m3

2. Use of COMSOL Multiphysics®Software

In this section is described as COMSOLSoftware modules that were used, the requiredsteps to create the model for core of the reactorFBNR, the initial conditions and establishedconsiderations for simulation

2.1 Modules of COMSOL Software used inthe simulation2.1.1 Entrance to simulation interface Select the wizard modeling Select 3D Model

Select module conjugate heat transfer withinthis module select laminar flow section Select stationary study

2.1.2 Model Creation

Model creation is done in the geometry moduleby performing the following steps: Definition of material, choose the material(water) from the library of Software for thecooling fluid and create a new material for thespheres (CERMET) entering the thermophysicalproperties described in Table 1. In the CAD module, create the cylindricalcontainer of the bed and create the spheresplacing them in their respective coordinatesaccording to the required structure BCC andFCC

2.1.3 Multiphysics study

Select one of the circular faces of thecylinder and in the section laminar flow create acondition of entry that corresponds to theworkflow and temperature input, outputcondition corresponding to the output Select the spheres and in the section of heattransfer in solid, creating a heat source, whichshould indicate the overall transfer rate whichcorresponds to the value of the total power

2.1.4 Meshing

In the module meshing create a normal mesh In the study section place the value of 200iterations and an error range of 20

2.1.5 Results

In the results module select the data set Create lines and planes in the CAD model tolater extract data Select show graphics Import data from lines and planes created inTXT format.

2.2 Considerations for the simulation

The considerations for the simulation were:

Steady State Study Types of fixed bed structures: BCC and FCC


0.0 0.5 1.0 1.5 2.0

500

1000

1500

2000

2500

Temperature distribution,Flow 0.4[m/s]

Length [m]

Tem

pera

ture

[°K

]

T min=563.01 °K, T max=2173.89 °K

0.0 0.5 1.0 1.5 2.0

500

1000

1500

2000

2500


Length [m]

Tem

pera

ture

[°K

]

T min=563.01 °K, T max=2127.56°K

0.0 0.5 1.0 1.5 2.0

500

1000

1500

2000

2500


Length[m]

Tem

pera

ture

[°K

]

T min=563.01 °K, T max=2113.18 °K

0.0 0.5 1.0 1.5 2.0

500

1000

1500

2000

2500

Temperature distribution,Flow 1[m/s]

Length [m]

Tem

pera

ture

[°K

]

T min=563.01 °K, T max=2100.97 °K

Thermo physical properties of the materialsinvolved remain constant There is no phase change There uniform heat generation in the particlesthat make up the fixed bed

2.2 Initial Conditions

The initial conditions established by Sefidvash F.are shown in Table 2 [13].

Table 2. Initial conditions for simulation of core ofFBNR

Initial conditions ValueInlet temperature 290 °CHeat generation 134.4 W per sphereInlet Pressure 16 MPa

3. Experimental Results

3.1 BCC Configuration

The nuclear fuel in the form of spheres cansupport a maximum temperature of 3113 ° K.This fundamental parameter in the simulationbecause the critical temperature points arelocated in the central part of the fixed bed, asshown in Figure 2.

Figure 2. BCC configuration

3.1.1 Temperature of spheres

The critical area analysis is in the middle of thebed is therefore important to know what happensto each area along the bed length, the Figure 3shows the status of the spheres at different flow.

3.1.2 Temperature of fluid

Spheres transferred heat energy to the fluid, thisenters with a temperature of 563 ° K, the outlet

temperature of the fluid is important because thisis then studied for the design of the heatexchanger. The energy that wins the coolingfluid of the spheres is represented in the belowFigure 4.

Figure 3. Temperature of spheres in BCCconfiguration

0.0 0.5 1.0 1.5 2.0

560

580

600

620

640

660

680

700

Temperature ProfileFluent, BCC Arrangement

Length [m]

Tem

pera

ture

[°K

]

T=665.74 °K

T=631.55 °K

T=614.41 °K

T=604.09 °K

Fluid Speed0.4 m/s 0.6 m/s 0.8 m/s 1 m/s

Figure 4. Temperature of fluid in BCC configuration

3.1.3 Pressure

BCC arrangement has greater porosity becausein this type of bed more open spaces, thisparameter helps determine the pressure drop thatthe reactor core may have, the pressure curvesare shown in the following Figure 5.

3.2 FCC Configuration

FCC conditions mentioned in accordance BCCare valid in the FCC arrangement. The following


Figures 6, 7, 8, 9 helps visualize is happening inthe reactor core.

0.0 0.5 1.0 1.5 2.01575

0000

1585

0000

1595

0000

Different Pressures ProfileFlows, Arrangement BCC

length [m]

Pre

ssur

e [P

a]

Fluid Velocity0.4 m/s0.6 m/s0.8 m/s1 m/s

Figure 5. Pressure in BCC configuration

Figure 6. FCC configuration

0.0 0.5 1.0 1.5 2.0

500

1000

1500

2000

2500


Length [m]

Tem

pera

ture

[°K

]

T min=563.01 °K, T max=2281.9 °K

0.0 0.5 1.0 1.5 2.0

500

1000

1500

2000

2500


Length [m]

Tem

pera

ture

[°K

]

T min=563.01 °K, T max=2203.3 °K

0.0 0.5 1.0 1.5 2.0

500

1000

1500

2000

2500


Length [m]

Tem

pera

ture

[°K

]

T min=563.01 °K, T max=2164 °K

0.0 0.5 1.0 1.5 2.0

500

1000

1500

2000

2500

Temperature distribution,Flow 1[m/s]

Length [m]

Tem

pera

ture

[°K

]

T min=563.01 °K, T max=2140,3 °K

Figure 7. Temperature of spheres in FCCconfiguration

0.0 0.5 1.0 1.5 2.0

600

650

700

750

800

Temperature ProfileFluent, FCC Settlement

Length [m]

Tem

pera

ture

[°K]

T=750.94 °K

T=688.04 °K

T=656.48 °K

T=637.44 °K

Fluid Speed0.4 m/s 0.6 m/s 0.8 m/s 1 m/s

Figure 8. Temperature of fluid in FCC configuration

0.0 0.5 1.0 1.5 2.0

1450

0000

1500

0000

1550

0000

1600

0000

Different Pressures profileFlows, Arrangement FCC

Length [m]

Pre

ssur

e [P

a]

Fluid Velocity0.4 m/s0.6 m/s0.8 m/s1 m/s

Figure 9. Pressure in FCC configuration

4. Discussion

Figure 10 shows that there are points where thefluid stagnates and as a result those points higherconcentration generate heat this happens for bothFCC and BCC arrangement. Comparing Figure10 with Figure 2 and 3 must points having lowerspeed higher temperature acquired, this isbecause the convection coefficient at these pointsis small. This phenomenon helps determine untiltemperature can reach areas in all flowspresented the interior temperature of the areadoes not exceed the maximum working.

As shown in Figures 5 and 9 the pressure drop isvery small and increases with the fluid velocity.The ideal design parameter is 0.6 m / s because


pre hydraulic designs consent to be used a pumpwith features of 16000000 Pa and 0.6 m / s. Withthese parameters fluid temperatures and areasunder safe working parameters, shown in Figures3 , 4, 7, 8 decreased fluid velocity will cause thespheres acquire larger temperatures implyingincreased monitoring reactor core.

Figure 10. Graphic of velocity

As seen in Figure 11 the arrangement BCC haslower pressure drop and higher heatconcentration which is beneficial for the coolingfluid. Figures 3, 4, 7, 8 shows that thearrangement BCC is more stable and easier tocreate a traceability control each of the areasalong the bed, it benefits the periodicmaintenance and analysis and material controlnuclear which is operational. Create a BCCarrangement is less costly than an FCCarrangement.

5. Conclusions

BCC arrangement is more stable than theFCC arrangement has greater benefits to thecooling fluid, Traceability control of each of theareas of nuclear material increases compared theFCC. BCC configuration having higher porosityhas a lower pressure drop compared to the FCCstructure, this causes reduction of energy loss inthe operation of recirculation pumpspredesigned.

Figure 11. Pressure drop and Temperature for BCC and FCC configuration


Pressure parameters are initial conditions of thesimulation for determining the temperatureprofile both fluid and spheres.

In all cases both under FCC and BCC nuclearmaterial does not exceed the limit operatingtemperature as long as the fluid velocity isbetween 0.4 and 1 m / s, if the fluid velocitydecreases can raise the temperature of thespheres and creating an unstable and dangeroussystem.

This type of analysis by simulation withCOMSOL allows evaluate, correct and improvedesigns without creating highly costlyprototypes, simulation time in each of the caseshad an average of 5 hours, the interactiveinterface that COMSOL presents excellent sinceyou can see the convergence of the results in realtime and make the necessary corrections toimprove results

The data obtained in this paper will used toset the required parameters in the study ofneutronic in nuclear material present in the FixedBed Nuclear Reactor. Such studies can beperformed with other modules of COMSOLmultiphysic offers, remaining well as futurework to study this type of physical phenomenon.

The stability of treatment and dataacquisition COMSOL is robust, it allows linkingseveral physical phenomena in the same timeinterval thus reducing costs and post processingsimulation data. Whether the graphicpresentation and interactive design makes thissoftware unique when simulate geometries withdifferent metaphysical robust interactions.

6. References

1. IEA, Worl Energy Outlook 2015, 4-6 (2015)2. Perera J, Impulso a la innovación. BoletínIAEA 2004, 45-46 (2004)3. Diamonds P, Abundancia el futuro es mejor delo que piensas, 123-126. Antoni Bosh Editor S.A(2013)4. Nuclear Energy Agency. The Nuclear EnergyToday. 54. (2012)

5. Achenbach E, Heat and Flow Characteristicsof packed beds, Experimental thermal and fluidscience, 17-25 (1995)6. IAEA, Status report 72- Fixed Bed NuclearReactor (FBNR), 1-3 (2011)7. Gonzáles, L. Reactores Nucleares de CuartaGeneración,. 5, (2010)8. Sefidvash F, Thermal hydraulics of the fixedbed nuclear reactor concept, Kerntechnik, 12-18,(200699. Sefidvash F, Non-Proliferation Resistance andPhysical Protection of FBNR Nuclear Reactor,IAEA Technical Meeting, 5-7 (2010)10. Sefidvash F. Conceptual design of the fixedbed nuclear reactor (FBNR) Concept, IAEAReport, 123-125, (2005)11. Vatulin A, Stetsky Y et all, Developed ofCermet fuel, 1-18, (2005)12. Senor D, Painter C, et all, A new InnovativeSpherical Cermet Nuclear fuel Element toAchieve an Ultra Long Core Life for use in GridAppropiate LWRs, 3.14-3.15 (2007)13. Sefidvash F, Water Cooled FBNR NuclearReactor, IAEA-CN- 164, 1-10, (2008)

7. Acknowledgements

The authors are grateful to Prof. Angel PortillaHead of Heat Transfer Laboratory of theNational Polytechnic School, Ing. WilliamVenegas Teacher of the Finite Element of theNational Polytechnic School and the PhD.Farahng Sefidvash “Prometeo” Professor of theNational Polytechnic School, for providing thenecessary facilities for the preparation of thepaper.


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