BenchmarkingCOMSOLMultiphysicsSingle-Subchannel Thermal ...downloads.hindawi.com/journals/stni/2019/4375782.pdf · services such as ﬁssion track experiments, ... outer clad, andcoolant)

Research ArticleBenchmarking COMSOL Multiphysics Single-SubchannelThermal-Hydraulic Analysis of a TRIGA Reactor withRELAP5 Results and Experimental Data

Ahmed K Alkaabi 1 and Jeffrey C King2

1Khalifa University of Science and Technology Department of Nuclear Engineering PO Box 127788 Abu Dhabi UAE2Colorado School of Mines Nuclear Science and Engineering Program 1500 Illinois Street Golden CO 80401 USA

Correspondence should be addressed to Ahmed K Alkaabi ahmedalkaabikuacae

Received 27 May 2019 Accepted 28 July 2019 Published 20 August 2019

Academic Editor Tomasz Kozlowski

Copyright copy 2019 Ahmed K Alkaabi and Jeffrey C King +is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

COMSOL Multiphysics has been used to conduct thermal-hydraulic analysis in multiple nuclear applications +e aim of thisstudy is to benchmark the prediction accuracy of COMSOL Multiphysics in performing thermal-hydraulic analysis of TRIGA(Training Research Isotopes General Atomics) reactors such as the Geological Survey TRIGA Reactor (GSTR) by comparing itspredictions with RELAP5 (a widely used code in nuclear thermal-hydraulic analysis) results and experimental data +e GSTRtype is Mark I with a full thermal power of 1MW and it resides at the Denver Federal Center (DFC) in Colorado +e numericalinvestigation of the present work is carried out by developing single-subchannel thermal-hydraulic models of the GSTR utilizingRELAP5 and COMSOL codes +emodels estimate the temperatures (fuel outer clad and coolant) and water flow patterns in thecore as well as fuel element powers at which void starts to form within the coolant subchannels +en these modelsrsquo predictionsare quantitatively evaluated and compared with the measured data

1 Introduction

+e Geological Survey TRIGA Reactor (GSTR) situated inLakewood Colorado is a 1MW Mark I It is operated since1969 by the US Geological Survey (USGS) to provide manyservices such as fission track experiments neutron activa-tion analysis radioisotope production neutron irradiationneutron radiography and delayed neutron analysis [1] Tosafely operate in steady-state and transient modes the GSTRis fueled with uranium-zirconium hydride fuel that has aprompt negative temperature coefficient of reactivity Duringpulse mode operations this reactor can operate with a $3maximum insertion reactivity [2]

COMSOLMultiphysics has been utilized in many nuclearreactors investigations to perform multiphysics simulationssuch as thermal hydraulics +e aim of the present work isto study the prediction accuracy of COMSOL Multiphysicsin reactor cores with natural convection cooling such as

TRIGA reactors by benchmarking its predictions with theexperimental data as well as RELAP5 (extensively used forthermal-hydraulic evaluations of TRIGA reactors) resultsPreviously a detailed neutronic model of the GSTR core isdeveloped using MCNP5 in [3 4] which calculates theneutronic parameters of the GSTR core +en the models inthe present study use these neutronic parameters calculatedby the MCNP5 model to predict the temperatures and voidformation for the subchannel

+us the goal of this numerical and experimental studyis to develop single-subchannel thermal-hydraulic modelsusing a selection of applicable thermal-hydraulic codes suchas RELAP5 and COMSOL calculate the temperatures (fuelouter clad and coolant) and fluid flow direction with dif-ferent heat rates ranging from 5 to 30 kW conduct anexperiment to measure the water temperature in the fluxmonitor hole situated between B- and C-rings assess themodelsrsquo predictions and compare them with the measured

HindawiScience and Technology of Nuclear InstallationsVolume 2019 Article ID 4375782 14 pageshttpsdoiorg10115520194375782

data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data

2 Geological Survey TRIGA Reactor

+e GSTR situated in Lakewood Colorado is a 1MWMarkI TRIGA (Figure 1) +is reactor can operate with thermalpowers up to 1MW maximum in steady-state mode oper-ations and up to $3 maximum reactivity insertions duringpulse mode operations [2]+e GSTR core like other Mark ITRIGA reactors is composed of seven rings (labeled Athrough G) and situated at the bottom of a tank (234minner diameter and 750m high) +e water inside this tankyields effective radiation shielding [5]

+is reactor is fueled with uranium-zirconium hydride(U-ZrH) that has a prompt negative temperature coefficientof reactivity and lt20 concentration of U235 [6] +ecladding material of the GSTR fuel elements is made ofstainless steel (located in the B- C- D- E- and G-rings) oraluminum (located in the F- and G-rings) (Figure 2) [3] Tohold the fuel elements in their specified positions and invertical orientation the core top and bottom grid plates areused A detailed description of the GSTR including corecontrol rods fuel elements graphite reflector and coresupport grids can be retrieved from [7]

+e GSTR core is safely cooled by natural convectionwith steady-state thermal powers up to 1MW While op-erating in steady-state mode the NRC requires a continuousmonitoring of the pool temperature +e maximum al-lowable pool temperature is 60degC [8] thus tank cooling isneeded to run the reactor for long time at powers above100 kW As Mark I TRIGA reactors primary cooling looppump pulls out the water from the core to cool it down byremoving the heat using a heat exchanger+en water in thesecondary loop is cooled by a cooling tower which consistsof sprayers and fans to cool the water circulating through thesecondary cooling system [9] A schematic representation ofthe GSTR coolant circuit is illustrated in Figure 3

3 Numerical Methods

+is section presents a detailed overview of the single-sub-channel thermal-hydraulic models developed in this researchTo correctly compare between the results of these models thesame boundary and initial conditions described in detail inthe following paragraphs are incorporated within eachmodel

+e numerical simulations are carried out using a one- andthree-dimensional domains utilizing RELAP5 and COMSOLrespectively All thermodynamic properties for the water andfuel are prescribed as a function of temperature +e gravityterm is acting in the z direction as the flow is moving verticallyupward in this direction +e inlet and outlet are specified aspressure and temperature boundary conditions and the massflow and fluid directions of the coolant depend on the naturalconvection caused by the heat flux generated within the fuelelement +e remaining boundaries are as follows the sym-metry boundary at the connected adjacent subchannels andnonslip wall boundary with equivalent heat flux (see Figure 4

for the axial and radial power profiles of the fuel element) +egenerated power in the fuel elements depends on the fuelcladding material location and reactor-operating powerFigure 5 presents the power generated in each fuel element atreactor full power [3] Simulation are considered convergedwhen residuals fall below 10minus 6 threshold value Moreover anadditional check is also made to ensure that mass and energybalances are globally satisfied

+is research also calculates the average cross-sectionalarea of the coolant for each GSTR ring to anticipate thetemperatures and void development within coolant sub-channels at each ring (see Table 1 and Figure 6) +e cross-sectional areas and GSTR fuel elements pitches presented inTable 1 are computed utilizing the following equations

Atotal π R2o minus R

2i1113872 1113873 (1)

Acell Atotal

N Acoolant + Afuel (2)

Acoolant Acell minus π Rfuel( 11138572 (3)

Acoolant

2

3

radic

4P2

minusπ Rfuel( 1113857

2

2 (4)

P

2 Acoolant + π Rfuel( 11138572

1113872 11138733

radic

1113971

(5)

31 RELAP5MOD33 Model +e single-subchannel ther-mal-hydraulic model is developed utilizing RELAP5MOD33Patch 04 as this code has been widely used in the literature in[10ndash16] to do TRIGA Reactor thermal-hydraulic analysis+eRELAP5 model developed in the present research is con-sistent with the modeling approach used by these previousefforts +e RELAP5 model is composed of a cold leg hotsubchannel horizontal connector coolant source andcoolant sink (Figure 7) +e cold leg is included to impose thepressure differential between the cold coolant at the inlet andthe coolant passing through the heated subchannel +e coldleg has the same height and volume as the hot subchannel tocommunicate correctly to the hot subchannel +is modelingapproach is important to differentiate between the gravita-tional forces imposed on the cold leg versus that imposed onthe hot subchannel permitting for the method of cooling to beonly natural convection +e hot subchannel is the volumethat contains the heat structure (fuel element) +e horizontalconnector is a nonphysical connector to permit communi-cations between cold leg and hot subchannel volumes duringsimulation +e coolant source and sink (time dependentvolumes) are incorporated in the model to impose thetemperature and temporal pressure boundary conditionsduring the computational simulations

+e hot subchannel volume represents the coolant flowdue to the natural convection driven by the heat generated inthe fuel element +is volume is modeled to have 24 axialconnected volumes+us the flow in the pipe components is

2 Science and Technology of Nuclear Installations

driven solely by the density gradients resulting from vari-ations in temperature resulting from the input power +isapproach has been used in multiple previous models ofTRIGA-type reactors [3 10 11 13ndash15] +e heat structure atwo-dimensional component is represented with 24 radialmesh cells and 24 axial mesh cells to correctly model the fuelelement geometry and power profiles predicted by theMCNP5 model Figure 8 displays the two-dimensionalrepresentation of the heat structure in the model

32 COMSOL Multiphysics Model +is research also de-velops a three-dimensional single-subchannel thermal-hy-draulic model (shown in Figure 9) using COMSOL

Multiphysics code as this code has the capacity to modelfluid flow on heated volumes (fuel) in one- two- and three-dimensional domains +ree different meshes are generatedfor the COMSOL mesh convergence tests +e total numberof the quadrilateral control volumes for these meshes are4306584 2725000 and 1741360 for fine medium andcoarse meshes respectively +e temperature predictionsresults from different meshes show a satisfactory monotonicconvergence and the profiles obtained from these runs areoverlapping each other which means even the coarse meshis adequately refined for the present numerical simulationand no further improvement is to be anticipated by using themedium or finemeshes Hence the results obtained from thethree different meshes should give enough confidence that

Concrete

Tank liner

Top gridCoreGraphite

Bottom grid

234 m

77m

75m

06m

07m

(a)

B-ringC-ringD-ringE-ring

F-ringG-ring

Control rods

Graphite reflector

265 cm325 cm

(b)

Figure 1 (a) Side view and (b) top view of the core of the GSTR

Zirconium

Stainless steel cladding0051cm thickness

37cm OD

72cm

381

cm8

8cm

Top fitting

Graphite

Samarium trioxide disc

Fuel

Aluminum cladding008cm thickness

38cm OD

(a) (b)

72cm

356

cm10

cm

Bottom fitting

Figure 2 (a) Aluminum and (b) stainless steel cladded fuel elements of the GSTR

Science and Technology of Nuclear Installations 3

mesh convergence is satisfied and numerical predictions arereliable +erefore as no significant difference are noticedbetween the predictions of fine medium or coarse meshesthe coarse mesh is used to reduce the associated compu-tational cost +e gap and clad materials in the three-di-mensional COMSOL model are substituted with a singleeffective material to reduce the solution time and requirednumber of mesh cells (see Figure 10) +e effective thermalconductivity of the composite (gap and clad) is calculated asa function of the gap and clad thermal resistance as shown inthe following equation [17]

_q ΔT

Ltg tg + tc1113872 1113873kgAg1113872 11138731113872 1113873 + Ltc tg + tc1113872 1113873kcAc1113872 11138731113872 1113873 (6)

+e heat flux rate going through the gap and clad layersequals to the heat flux going through the homogenousmaterial with an effective thermal conductivity [17]

_q keffAeffΔT

L (7)

Equating equation (6) with equation (7) leads to [17]

Secondary loop

Primary loop

Forced circulation

Natural circulation

Coolant towerPump

PumpHeat exchanger

AirAir

Upward air flow

Water with concentrateddissolved solids

Figure 3 Schematic representation of the GSTR coolant circuit

0

02

04

06

08

1

12

14

16

0 10 20 30 40

Axi

al lo

catio

n-to

-ave

rage

pow

er ra

tio

Fuel element height (cm)

y = ndash00026x2 + 01027x + 04254

(a)

0 05 1 15 2Fuel element radius (cm)

y = 01886x2 ndash 01185x + 10016

0

02

04

06

08

1

12

14

16

Loca

tion-

to-a

vera

ge p

ower

ratio

(b)

Figure 4 (a) Axial and (b) radial power profiles of GSTR fuel element


ΔTLtg tg + tc1113872 1113873kgAg1113872 11138731113872 1113873 + Ltc tg + tc1113872 1113873kcAc1113872 11138731113872 1113873

keffAeffΔT

L

(8)

Solving for effective thermal conductivity in (equation(8)) results in [17]

keff tg

tg + tc1113872 1113873kg+

tc

tg + tc1113872 1113873kc

⎡⎢⎣ ⎤⎥⎦

minus 1

(9)

Mass of the homogenous material with effective densityequals to the mass of the gap and clad regions therefore thetotal mass of the composite equals [17]

M tg

tg + tc1113872 1113873LAgρg +

tc

tg + tc1113872 1113873LAcρc (10)

+e total mass of the homogenous material with effectivedensity is equal to

Total power = 915kWAll powers are given in kW

B-Shim 1 rodC-Shim 2 rod

A-Regulating rodFuel rodControl rod

786243

42

49

42

43

64

64

64

62 75

72

73

122

92 136

111101

134112

54C

92

Centralthimble

Transientrod

7590

93 8990

95

42 63

49

41

64

42

65

42 49 42

65

43

6564

63

42

50

65 43

4466

436477138

112

114

108 96 76

7910114137

9390 129

9481 67 52

44

46

6882

68838379

8465

6671

70

43

44

4452

44 46 45

7167

5345

96796442

51 63 78

91A

66

66

44

44

111112

104

104 94 78

7676 78 79

75

75

65 51

436677B

8514

Figure 5 Generated power in each fuel element at reactor full power

Table 1 GSTR fuel ring and flow cross-sectional areas

Ring Ring innerradius Ri (cm)

Ring outerradius Ro (cm)

Number of fuelelements (N)

Total ring areaAtotal (cm

2)Total cell area

Acell (cm2)

Cell flow areaAcoolant (cm

2)Fuel elementpitch (cm)

B 191 597 6 10051 1675 580 440C 597 996 12 19986 1666 571 439D 996 1393 18 29782 1655 560 437E 1393 1790 24 39715 1655 560 437F 1790 2187 30 49642 1655 560 437G 2187 2642 36 68899 1914 819 470


M LAeffρeff (11)

Setting equation (16) equal to equation (11) leads to

ρeff tg

tg + tc1113872 1113873ρg +

tc

tg + tc1113872 1113873ρc (12)

+e heat capacity of the homogenous material witheffective heat capacity equals to the heat capacity of the gapand clad regions therefore the total heat capacity of thecomposite equals [17]

C tg

tg + tc1113872 1113873LAgρgCg +

tc

tg + tc1113872 1113873LAcρcCc (13)

+e total heat capacity of the homogenous material witheffective heat capacity is equal to [17]

C LAeffρeffCeff (14)

Setting equation (13) equal to equation (14) and solvingfor effective heat capacity leads to [17]

Ceff tgρg

tg + tc1113872 1113873ρeffCg +

tcρctg + tc1113872 1113873ρeff

Cc (15)

4 Model Results and Discussion

+e single-subchannel thermal-hydraulic models that aredeveloped in this research predict the temperatures of thefuel outer clad and coolant to benchmark the COMSOLpredictions with RELAP5 results +ese temperatures arepredicted at normal inlet temperature (25degC) and maximumallowable inlet temperature (60degC) To study the effects ofchanging inlet temperature boundary condition on thetemperaturesrsquo predictions Figure 11(a) displays the tem-peratures predicted by the RELAP5 model versus the powergenerated by a fuel element located in the B-ring +eresulting temperatures consistently increase by 35degC as theinlet temperature increases from 25degC to 60degC as the impactof changing the inlet temperature is substantially linear (seeFigure 11(a)) As changing inlet temperature results inlargely linear change the temperatures can be predicted evenfor different inlet temperatures without needing to rerun themodels for the new inlet temperature In order to anticipatethe temperatures and void formations inside the core at themaximum allowable coolant temperature the remainingresults in this section are presented with an inlet temperatureof 60degC

+is research also studies the effects of changing the flowcross-sectional areas (Table 1) in these single-subchannelmodels on the temperaturesrsquo predictions Figure 11(b)presents these temperatures predicted by the RELAP5model versus the fuel element power for each GSTR ring atinlet temperatures of 60degC As demonstrated in Table 1 theflow cross-sectional areas from B- through F-rings differonly marginally thus the calculated temperatures in theserings are roughly identical for the same fuel element powersDifferently the G-ring flow cross-sectional area is higherand therefore results in different temperatures in this ringAs changing the flow cross-sectional areas of coolant in themodels to predict temperatures in the B- through F-ringsresults in extremely minor temperaturesrsquo differences thetemperatures in these rings versus the fuel element powercan be anticipated without needing to rerun the modelsmore than one time

41 Benchmarking with RELAP5MOD33 Results

411 Temperature Predictions Figure 12 presents themaximum fuel temperatures calculated by all of the modelsversus the fuel element power +e predicted temperaturesby these models are approximately the same with minordifferences +is present research also runs the models toproduce a graph that displays the maximum outer cladtemperatures versus the fuel element power (Figure 13) +e

Edge between B- and C-ringsEdge between C- and D-rings

Edge between D- and E-ringsEdge between E- and F-rings

Edge between F- and G-ringsEdge between G-ring and reflector

Figure 6 Fuel rings of the GSTR core

Coolantsource

Coolantsink

Horizontal connector

Cold leg Hot subchannel

Figure 7 RELAP5MOD33 model


results of these models are approximately similar +e outerclad temperatures calculated by the COMSOL model areapproximately the same as the temperatures predicted by theRELAP5 with slight differences +e COMSOL modelcorrectly calculates the outer clad temperature as the outerclad temperatures are affected by the heat transfer from theouter clad to coolant +e small differences in fuel and outerclad temperatures predicted by RELAP5 and COMSOLmodels in Figures 12 and 13 are due to the variations in theanalysis of flow behavior including field equation formu-lations numerical scheme order and geometry domain(one-dimensional for RELAP5 and three-dimensional forCOMSOL)

Due to the hydrostatic pressure discussed in Section 3the coolant boiling temperature inside the GSTR core in-creases to be in the range of 1132degC (top of the core) and1144degC (bottom of the core) due to the water column abovethe core Formation of void within the core starts at outer

clad temperatures higher than the saturation temperature(between 1132degC and 1144degC) as a result of the onset ofincipient boiling Based on this void-initiation temperaturethe COMSOL model anticipate that void developmenthappens in the GSTR core when the power generated by thefuel element is above 1790 kW as a result of outer cladtemperatures that are higher than the saturation tempera-ture +e COMSOL modelsrsquo predictions of the outer cladtemperatures are conservative as these models do not in-clude two-phase physics Lacking two-phase physics doesnot completely invalidate the COMSOLmodelsrsquo predictionsas convective heat transfer initially increases with the onsetof incipient boiling +is is considered in detail in [18] Toelaborate on void formation within the GSTR core and tocompare with the COMSOL model that lack two-phasephysics this paper runs the RELAP5 model to calculate thelocal maximum void fraction within the thermal-hydraulicsubchannels versus the fuel element power +e RELAP5model predicts that void starts to form within the thermal-hydraulic subchannels at fuel element powers more than1890 kW

Figure 14(a) shows the outlet temperatures calculated bythe RELAP5 and COMSOL models versus the fuel elementpower +e average coolant temperaturersquos predictions by theRELAP5 and COMSOL models differ slightly with maxi-mum plusmn15degC variations +ere is a maximum of 15degCdifferences between the COMSOL and RELAP5 results asshown in Figure 14(a) As explained in Section 31 thesubchannel flow volume in RELAP5 code is discretized byspecifying the subchannel cross-sectional flow area andsubchannel length +e subchannel length is discretized into24 nodes +e outlet temperature in RELAP5 model is thetemperature of the last node volume at the outlet of the

Top fittingGraphite

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 123456789

10111213141516171819

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 20Graphite

Bottom fitting

FuelZirconium Gap

Stainless steel clad

Cor

e act

ive z

one

Fuel Gap

Aluminum clad

Stainless steel-clad fuel element

Aluminum-clad fuel element

Figure 8 Two-dimensional representation of the heat structure in the RELAP5 model

Fuel element

Subchannel flow areaEffective material

substitutes gapand clad domains

Figure 9 Top view of the COMSOL model


subchannel On the contrary the outlet temperature in thethree-dimensional COMSOL model is calculated byselecting the outlet surface of the subchannel geometry andcomputing the average temperature of this surface usingpostprocessing tools within the COMSOL model Differentschemes of calculating outlet temperatures in RELAP5 andCOMSOL models lead to slightly different predicted outlettemperatures

Figure 14(b) presents the average coolant temperaturesfor each of the rings at reactor full power for fuel elementswith stainless steel cladding in the B- C- D- E- and G-ringsand with aluminum cladding in the F-ring +e highestoutlet temperatures happen in the B- and C-rings and this is

anticipated as the fuel elements in these rings generate thehighest power in the GSTR core As displayed inFigure 14(b) the average outlet temperature predicted by theRELAP5 and COMSOL has a big difference for the G-ring asthe subchannel flow area and fuel pitch in the G-ring ishigher than all other rings (see Table 1) due to space betweenthe graphite reflector that is surrounding the core and thefuel elements in the G-ring When incorporating this largerflow area in the three-dimensional COMSOL model itpredicts higher temperatures than the temperatures pre-dicted by the one-dimensional RELAP5 model Increasingthe flow cross-sectional area in the 24 axial nodes of thesubchannel in the RELAP5 model reduces the outlet

0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)

0 5 10 15 20 25 30Fuel element power (kW)

Fuel (60degC)In clad (60degC)Out clad (60degC)Outlet (60degC)


(a)

B- to F-ring fuelB- to F-ring inner cladB- to F-ring outer cladB- to F-ring outlet

G-ring fuelG-ring inner cladG-ring outer cladG-ring outlet

0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)


(b)

Figure 11 Temperatures versus the fuel element power for (a) each ring and (b) inlet temperatures of 25degC and 60degC

CladGap

tsteel = 0508mmtaluminum = 08mm

tg = 01mm

(a)

Effective material

teff = 0608mm for SS fuel elementsteff = 09 mm for Al fuel elements

(b)

Figure 10 +e thickness of (a) gap and clad in the fuel element and (b) effective material in the COMSOL model


temperature but the drop in outlet temperature is higherthan the drop in the COMSOL model +e RELAP5 modelpredicts higher mass flow rate in the G-ring when increasingthe cross-sectional flow area as shown in Figure 15 whichleads to lower predicted outlet temperature in the RELAP5model than outlet temperature predicted by the COMSOLmodel

+is work also generates three figures to predict tem-peratures of the GSTR including fuel (Figure 16(a)) outerclad (Figure 16(b) and average outlet (Figure 16(c)) tem-peratures at each GSTR ring versus the reactor power Toprepare these Figures graphs of fuel outer clad and outlettemperatures versus the fuel element power (similar toFigures 12(a) 13(a) and 14(a)) are generated for stainless

steel-clad (located in the B- C- D- E- and G-rings) andaluminum-clad (located in F- and G-rings) fuel elements Asshown in Figure 16 the hottest fuel elements in the GSTRcore are located in the B- and C- rings as these elementsgenerate the highest power [7]

412 Coolant Flow +e coolant flow and average massflow rate calculated by the single-subchannel models arepresented in this subsection In these single-subchannelmodels water (coolant) tends to flow axially from thebottom of the subchannel to the top of the subchannel dueto natural convection driven by the heat generated withinthe fuel element with no interaction with the neighboring

60

130

200

270

340

410

480

550

620

690

0 5 10 15 20 25 30

Max

imum

fuel

tem

pera

ture

(degC)

Fuel element power (kW)

COMSOL modelRELAP5MOD33 model

(a)

Max

imum

fuel

tem

pera

ture

(degC)


60

110

160

210

260

310

360

B C D E F GGSTR ring

(b)

Figure 12 Calculated maximum fuel temperatures in the fuel elements with stainless steel cladding versus the (a) fuel element power and(b) GSTR ring

Max

out

er cl

ad te

mpe

ratu

re (deg

C)


60

80

100

120

140

160


T = 1132degC

(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)



60

70

80

90

100

110

120T = 1132degC

(b)

Figure 13 Calculated outer clad temperatures in the fuel elements with stainless steel cladding versus the (a) fuel element power and(b) GSTR ring


subchannels Figure 17 presents the two-dimensionalcoolant flow direction predicted by the models

In the single-subchannel models the coolant subchannelis not connected to the neighboring thermal-hydraulicsubchannels In real sense the subchannels in the core of thereactor are interlinked thus the coolant could flow betweenneighboring subchannels based on variations of the coolantdensity in the core +is is particularly true within non-uniform power density cores for instance the GSTR Single-subchannel models restrict the flow directions as the heatproduced from neighboring fuel elements does not con-tribute to the buoyancy forces within the subchannel(coolant does not flow to or from the adjacent subchannels)which may limit the coolant flow rate and flow directions inthese models For instance driving forces in B- C- andD-rings which have the highest power density do notcontribute to the flow in the other subchannels Figure 15

displays the calculated average mass flow by the models ineach ring of the GSTR +is research verifies that the cal-culated power from equation (16) using the predicted av-erage mass flow rate (Figure 15) and the average inlet andoutlet temperatures (Figure 14) is the same as the inputtedheat flux in the models

P _mCpΔT (16)

42 Benchmarking with Experimental Data +is presentwork conducts an experiment to measure the coolanttemperature inside the core at five vertical positions (seeFigure 18) with reactor steady-state full power and an inlettemperature of 20degC (inlet temperature at the day of ex-periment) +is experiment was done by inserting thethermocouple (with 18m sheath to permit temperature

60

65

70

75

80

85

90

95

0 5 10 15 20 25 30

Aver

age o

utle

t tem

pera

ture

(degC)



(a)

Aver

age o

utle

t tem

pera

ture

(degC)


60

65

70

75

80

85


(b)

Figure 14 Calculated outlet temperatures in the fuel elements with stainless steel cladding versus the (a) fuel element power and (b) GSTRring

0

002

004

006

008

01

012

014

Aver

age m

ass f

low

rate

(kg

s)


RELAP5MOD33 modelCOMSOL model

Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring


measuring within the core) inside the flux monitor hole Asthe flux monitor hole is situated between the B- and C-rings(see Figure 19) average of the predicted coolant tempera-tures at B- and C-rings with an inlet temperature of 20degC(same as experiment) by the RELAP5 and COMSOL modelsis calculated and then compared it with the measuredcoolant temperatures

Figure 20 compares the measured coolant temperature atfive vertical locations inside flux monitor hole with thepredicted coolant axial temperatures by the RELAP5 andCOMSOLmodels+is experiment shows that the measuredtemperature increases versus the core height RELAP5 andCOMSOLmodels also predict that coolant temperature risesalong the core height with maximum temperature at thesubchannel outlet +e measured outlet temperature in theflux monitor hole equals to 417 plusmn 18degC while the

predicted outlet temperatures by the RELAP5 and COMSOLmodels are 441degC and 448degC respectively+ese differencesare due to the flow limitation of single-subchannel thermal-hydraulic models Within the single-subchannel models theflow of the coolant occurs directly from the subchannelrsquosbottom part to the subchannelrsquos top part due to naturalconvection caused by the heat generated within the fuelelement In real sense the subchannels in the core of thereactor are interlinked thus the coolant could flow betweenneighboring subchannels based on variations of the coolantdensity in the core +is is particularly true within non-uniform power density cores for instance the GSTR Tostudy the effects of flow patterns inside the core and improvethe temperatures predictions future research will develop adetailed computational fluid dynamics (CFD) multichannelthermal-hydraulic model

60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)

0 025 05 075 1Reactor power (MW)

B-ring SS-cladC-ring SS-cladD-ring SS-cladE-ring SS-clad

F-ring Al-cladG-ring SS-cladG-ring Al-clad

(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)

Figure 16 Predicted (a) fuel (b) outer clad and (c) outlet temperatures in each fuel ring versus the reactor power


5 Conclusions and Future Work

+e paper presents a numerical and experimental study todevelop single-subchannel thermal-hydraulic models usinga selection of applicable thermal-hydraulic codes such asRELAP5 and COMSOL calculate the fuel outer clad andcoolant temperatures and fluid flow direction with differentheat rates ranging from 5 to 30 kW conduct an experimentto measure the coolant temperature in flux monitor holesituated between B- and C-rings of the GSTR core assess themodelsrsquo predictions and compare them with the measured


+e temperatures and reactor powers at which voidstarts to form predicted by RELAP5 and COMSOL modelsare approximately similar with minor differences +e ex-periment to measure the coolant temperature inside theGSTR core at five vertical positions in the flux monitor hole(located between B- and C-rings) shows that the measuredtemperature increases as a function of core height RELAP5and COMSOL models in addition predict that coolant

Coolant flows axially in single-

subchannel models 650

cm

123456789

101112131415161718192021222324

(a) (b)

650

cm

Figure 17 Two-dimensional flow direction predicted by (a) RELAP5MOD33 and (b) COMSOL models

Bottom grid plate

650

cm

618

cm

Thermocouple

Experimentaxial locations

Top grid plate

Figure 18 Vertical positions of the experiment


temperature rises along the core height with maximumtemperature at the outlet +e measured outlet temperaturein the flux monitor hole equals to 417 plusmn 18degC while thepredicted outlet temperatures by the RELAP5 and COMSOLmodels are 441degC and 448degC respectively+ese differencesare due to the flow limitation of single-subchannel thermal-hydraulic models without taking into account the coolantcross flow between neighboring subchannels based onvariations of the coolant density in the core

+e next step of this research is to improve the tem-perature and void formation predictions by developingmultichannel thermal-hydraulic models as these models willincorporate the coolant cross flow between adjacent sub-channels depending on coolant density variations within theGSTR core +is will improve the modelsrsquo accuracy as theGSTR has a nonuniform power density core with multiplecoolant flow paths In contrast to the single-subchannelthermal-hydraulic models multichannel thermal-hydraulicmodels will consider the complex heat transfer and fluid flowpatterns within the core to more precisely predict thetemperatures and fluid flow paths A detailed experimental

verification of the temperature and flow conditions in theGSTR core will also improve the validation of the differentmodels +e results of both of these efforts will be presentedin future papers

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] T M DeBey B R Roy and S R Brady 8e US GeologicalSurveyrsquos TRIGA Reactor US Geological Survey Fact Sheet20123093 Denver CO USA 2012

[2] W Day License Amendment Request to Use Aluminum-Clad Fuelin the GSTR U S Nuclear Regulatory CommissionWashingtonDC USA 2004

[3] N E Shugart ldquoNeutronic and thermal hydraulic analysis ofthe geological survey TRIGA reactorrdquo Masterrsquos thesis Col-orado School of Mines Golden CO USA 2013

[4] N Shugart and J King ldquoNeutronic analysis of the geologicalsurvey TRIGA reactorrdquo Annals of Nuclear Energy vol 64pp 122ndash134 2014

[5] A K Alkaabi and J C King ldquoPrediction of coolant tem-peratures and fluid flow patterns within a TRIGA reactor coreusing RELAP5MOD33 and COMSOL codesrdquo in Proceedingsof the PHYSOR 2018 Conference pp 2394ndash2405 CancunMexico April 2018

[6] H Bock and M Villa TRIGA Reactor Characteristics AIAU-27306 Atomic Institute of the Austrian Universities WienAustria 2007

[7] A K Alkaabi 8ermal hydraulics modeling of the US geo-logical survey TRIGA reactor PhD thesis Colorado School ofMines Golden CO USA 2015

[8] US Geological Survey Revised Safety Analysis ReportTechnical Specifications and Environmental Report DocketNo 50ndash274 US Nuclear Regulatory Commission Wash-ington DC USA (2009)

[9] H Bock and M Villa TRIGA Reactor Main Systems AIAU-2730 Atomic Institute of the Austrian Universities WienAustria 2007

[10] W R Marcum T S Palmer B G Woods S T KellerS R Reese and M R Hartman ldquoA comparison of pulsingcharacteristics of the Oregon State University TRIGA reactorwith FLIP and LEU fuelrdquo Nuclear Science and Engineeringvol 171 no 2 pp 150ndash164 2012

[11] W R Marcum B G Woods and S R Reese ldquoExperimentaland theoretical comparison of fuel temperature and bulkcoolant characteristics in the Oregon State TRIGAreg reactorduring steady state operationrdquo Nuclear Engineering andDesign vol 240 no 1 pp 151ndash159 2010

[12] P A L Reis A L Costa C Pereira C A M SilvaM A F Veloso and A Z Mesquita ldquoSensitivity analysis to aRELAP5 nodalization developed for a typical TRIGA researchreactorrdquo Nuclear Engineering and Design vol 242 pp 300ndash306 2012

[13] A Bousbia-Salah A Jirapongmed T Hamidouche J WhiteF DrsquoAuria and M Adorni ldquoAssessment of RELAP5 model

Flux monitor hole

Control rods

G-ringF-ring

E-ringD-ringC-ringB-ring

265cm325cm

Figure 19 Flux monitor hole location

20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)

COMSOL ModelRELAP5MOD33 ModelB-ring experiment

Figure 20 Comparison of the measured and predicted coolanttemperatures versus the core height


for the University of Massachusetts Lowell research reactorrdquoNuclear Technology and Radiation Protection vol 21 no 1pp 3ndash12 2006

[14] A R Antariksawan M Q Huda T Liu J ZamitkovaC M Allison and J K Hohorst ldquoValidation of RELAPSCDAPSIMMOD34 for research reactor applicationsrdquo inProceedings of the13th International Conference on NuclearEngineering (ICONE13) Beijing China May 2005

[15] A L Costa P A L Reis C Pereira M A F VelosoA Z Mesquita and H V Soares ldquo+ermal hydraulic analysisof the IPR-R1 TRIGA research reactor using a RELAP5modelrdquo Nuclear Engineering and Design vol 240 no 6pp 1487ndash1494 2010

[16] S Chatzidakis A Ikonomopoulos and D Ridikas ldquoEvalua-tion of RELAP5MOD3 behavior against loss of flow exper-imental results from two research reactor facilitiesrdquo NuclearEngineering and Design vol 255 pp 321ndash329 2013

[17] G Nellis and S Klein Heat Transfer Cambridge UniversityPress New York NY USA 2009

[18] N E Todreas and M S Kazimi Nuclear Systems Volume I8ermal Hydraulic Fundamentals CRC Press Taylor ampFrancis Group LLC Boca Raton FL USA 2012


Hindawiwwwhindawicom Volume 2018

Nuclear InstallationsScience and Technology of

TribologyAdvances in


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

OpticsInternational Journal of


Antennas andPropagation



Power ElectronicsHindawiwwwhindawicom Volume 2018

Advances in

CombustionJournal of


Journal of


Renewable Energy

Acoustics and VibrationAdvances in


EnergyJournal of


Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018


International Journal ofInternational Journal ofPhotoenergy


Solar EnergyJournal of


Shock and Vibration


Advances in Condensed Matter Physics


RotatingMachinery



High Energy PhysicsAdvances in


Active and Passive Electronic Components

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Submit your manuscripts atwwwhindawicom


2 Geological Survey TRIGA Reactor

+e GSTR situated in Lakewood Colorado is a 1MWMarkI TRIGA (Figure 1) +is reactor can operate with thermalpowers up to 1MW maximum in steady-state mode oper-ations and up to $3 maximum reactivity insertions duringpulse mode operations [2]+e GSTR core like other Mark ITRIGA reactors is composed of seven rings (labeled Athrough G) and situated at the bottom of a tank (234minner diameter and 750m high) +e water inside this tankyields effective radiation shielding [5]

+is reactor is fueled with uranium-zirconium hydride(U-ZrH) that has a prompt negative temperature coefficientof reactivity and lt20 concentration of U235 [6] +ecladding material of the GSTR fuel elements is made ofstainless steel (located in the B- C- D- E- and G-rings) oraluminum (located in the F- and G-rings) (Figure 2) [3] Tohold the fuel elements in their specified positions and invertical orientation the core top and bottom grid plates areused A detailed description of the GSTR including corecontrol rods fuel elements graphite reflector and coresupport grids can be retrieved from [7]

+e GSTR core is safely cooled by natural convectionwith steady-state thermal powers up to 1MW While op-erating in steady-state mode the NRC requires a continuousmonitoring of the pool temperature +e maximum al-lowable pool temperature is 60degC [8] thus tank cooling isneeded to run the reactor for long time at powers above100 kW As Mark I TRIGA reactors primary cooling looppump pulls out the water from the core to cool it down byremoving the heat using a heat exchanger+en water in thesecondary loop is cooled by a cooling tower which consistsof sprayers and fans to cool the water circulating through thesecondary cooling system [9] A schematic representation ofthe GSTR coolant circuit is illustrated in Figure 3

3 Numerical Methods

+is section presents a detailed overview of the single-sub-channel thermal-hydraulic models developed in this researchTo correctly compare between the results of these models thesame boundary and initial conditions described in detail inthe following paragraphs are incorporated within eachmodel

+e numerical simulations are carried out using a one- andthree-dimensional domains utilizing RELAP5 and COMSOLrespectively All thermodynamic properties for the water andfuel are prescribed as a function of temperature +e gravityterm is acting in the z direction as the flow is moving verticallyupward in this direction +e inlet and outlet are specified aspressure and temperature boundary conditions and the massflow and fluid directions of the coolant depend on the naturalconvection caused by the heat flux generated within the fuelelement +e remaining boundaries are as follows the sym-metry boundary at the connected adjacent subchannels andnonslip wall boundary with equivalent heat flux (see Figure 4

for the axial and radial power profiles of the fuel element) +egenerated power in the fuel elements depends on the fuelcladding material location and reactor-operating powerFigure 5 presents the power generated in each fuel element atreactor full power [3] Simulation are considered convergedwhen residuals fall below 10minus 6 threshold value Moreover anadditional check is also made to ensure that mass and energybalances are globally satisfied

+is research also calculates the average cross-sectionalarea of the coolant for each GSTR ring to anticipate thetemperatures and void development within coolant sub-channels at each ring (see Table 1 and Figure 6) +e cross-sectional areas and GSTR fuel elements pitches presented inTable 1 are computed utilizing the following equations

Atotal π R2o minus R

2i1113872 1113873 (1)

Acell Atotal

N Acoolant + Afuel (2)

Acoolant Acell minus π Rfuel( 11138572 (3)

Acoolant

2

3

radic

4P2

minusπ Rfuel( 1113857

2

2 (4)

P

2 Acoolant + π Rfuel( 11138572

1113872 11138733

radic

1113971

(5)

31 RELAP5MOD33 Model +e single-subchannel ther-mal-hydraulic model is developed utilizing RELAP5MOD33Patch 04 as this code has been widely used in the literature in[10ndash16] to do TRIGA Reactor thermal-hydraulic analysis+eRELAP5 model developed in the present research is con-sistent with the modeling approach used by these previousefforts +e RELAP5 model is composed of a cold leg hotsubchannel horizontal connector coolant source andcoolant sink (Figure 7) +e cold leg is included to impose thepressure differential between the cold coolant at the inlet andthe coolant passing through the heated subchannel +e coldleg has the same height and volume as the hot subchannel tocommunicate correctly to the hot subchannel +is modelingapproach is important to differentiate between the gravita-tional forces imposed on the cold leg versus that imposed onthe hot subchannel permitting for the method of cooling to beonly natural convection +e hot subchannel is the volumethat contains the heat structure (fuel element) +e horizontalconnector is a nonphysical connector to permit communi-cations between cold leg and hot subchannel volumes duringsimulation +e coolant source and sink (time dependentvolumes) are incorporated in the model to impose thetemperature and temporal pressure boundary conditionsduring the computational simulations

+e hot subchannel volume represents the coolant flowdue to the natural convection driven by the heat generated inthe fuel element +is volume is modeled to have 24 axialconnected volumes+us the flow in the pipe components is





Concrete

Tank liner


Bottom grid

234 m

77m

75m

06m

07m

(a)


F-ringG-ring

Control rods

Graphite reflector

265 cm325 cm

(b)


Zirconium


37cm OD

72cm

381

cm8

8cm

Top fitting

Graphite


Fuel


38cm OD

(a) (b)

72cm

356

cm10

cm

Bottom fitting




_q ΔT



_q keffAeffΔT

L (7)


Secondary loop

Primary loop

Forced circulation

Natural circulation

Coolant towerPump

PumpHeat exchanger

AirAir

Upward air flow



0

02

04

06

08

1

12

14

16

0 10 20 30 40

Axi

al lo

catio

n-to

-ave

rage

pow

er ra

tio


y = ndash00026x2 + 01027x + 04254

(a)


y = 01886x2 ndash 01185x + 10016

0

02

04

06

08

1

12

14

16

Loca

tion-

to-a

vera

ge p

ower

ratio

(b)




keffAeffΔT

L

(8)


keff tg

tg + tc1113872 1113873kg+

tc

tg + tc1113872 1113873kc

⎡⎢⎣ ⎤⎥⎦

minus 1

(9)


M tg

tg + tc1113872 1113873LAgρg +

tc

tg + tc1113872 1113873LAcρc (10)





786243

42

49

42

43

64

64

64

62 75

72

73

122

92 136

111101

134112

54C

92

Centralthimble

Transientrod

7590

93 8990

95

42 63

49

41

64

42

65

42 49 42

65

43

6564

63

42

50

65 43

4466

436477138

112

114

108 96 76

7910114137

9390 129

9481 67 52

44

46

6882

68838379

8465

6671

70

43

44

4452

44 46 45

7167

5345

96796442

51 63 78

91A

66

66

44

44

111112

104

104 94 78

7676 78 79

75

75

65 51

436677B

8514







2)Total cell area

Acell (cm2)



B 191 597 6 10051 1675 580 440C 597 996 12 19986 1666 571 439D 996 1393 18 29782 1655 560 437E 1393 1790 24 39715 1655 560 437F 1790 2187 30 49642 1655 560 437G 2187 2642 36 68899 1914 819 470


M LAeffρeff (11)


ρeff tg

tg + tc1113872 1113873ρg +

tc

tg + tc1113872 1113873ρc (12)


C tg

tg + tc1113872 1113873LAgρgCg +

tc

tg + tc1113872 1113873LAcρcCc (13)




Ceff tgρg

tg + tc1113872 1113873ρeffCg +


Cc (15)










Coolantsource

Coolantsink









Top fittingGraphite

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 123456789

10111213141516171819

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 20Graphite

Bottom fitting

FuelZirconium Gap


Cor

e act

ive z

one

Fuel Gap

Aluminum clad




Fuel element








0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)




(a)



0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)


(b)


CladGap


tg = 01mm

(a)

Effective material


(b)







60

130

200

270

340

410

480

550

620

690

0 5 10 15 20 25 30

Max

imum

fuel

tem

pera

ture

(degC)



(a)

Max

imum

fuel

tem

pera

ture

(degC)


60

110

160

210

260

310

360


(b)


Max

out

er cl

ad te

mpe

ratu

re (deg

C)


60

80

100

120

140

160


T = 1132degC

(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)



60

70

80

90

100

110

120T = 1132degC

(b)






P _mCpΔT (16)


60

65

70

75

80

85

90

95

0 5 10 15 20 25 30

Aver

age o

utle

t tem

pera

ture

(degC)



(a)

Aver

age o

utle

t tem

pera

ture

(degC)


60

65

70

75

80

85


(b)


0

002

004

006

008

01

012

014

Aver

age m

ass f

low

rate

(kg

s)








60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)




(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)









cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018





Concrete

Tank liner


Bottom grid

234 m

77m

75m

06m

07m

(a)


F-ringG-ring

Control rods

Graphite reflector

265 cm325 cm

(b)


Zirconium


37cm OD

72cm

381

cm8

8cm

Top fitting

Graphite


Fuel


38cm OD

(a) (b)

72cm

356

cm10

cm

Bottom fitting




_q ΔT



_q keffAeffΔT

L (7)


Secondary loop

Primary loop

Forced circulation

Natural circulation

Coolant towerPump

PumpHeat exchanger

AirAir

Upward air flow



0

02

04

06

08

1

12

14

16

0 10 20 30 40

Axi

al lo

catio

n-to

-ave

rage

pow

er ra

tio


y = ndash00026x2 + 01027x + 04254

(a)


y = 01886x2 ndash 01185x + 10016

0

02

04

06

08

1

12

14

16

Loca

tion-

to-a

vera

ge p

ower

ratio

(b)




keffAeffΔT

L

(8)


keff tg

tg + tc1113872 1113873kg+

tc

tg + tc1113872 1113873kc

⎡⎢⎣ ⎤⎥⎦

minus 1

(9)


M tg

tg + tc1113872 1113873LAgρg +

tc

tg + tc1113872 1113873LAcρc (10)





786243

42

49

42

43

64

64

64

62 75

72

73

122

92 136

111101

134112

54C

92

Centralthimble

Transientrod

7590

93 8990

95

42 63

49

41

64

42

65

42 49 42

65

43

6564

63

42

50

65 43

4466

436477138

112

114

108 96 76

7910114137

9390 129

9481 67 52

44

46

6882

68838379

8465

6671

70

43

44

4452

44 46 45

7167

5345

96796442

51 63 78

91A

66

66

44

44

111112

104

104 94 78

7676 78 79

75

75

65 51

436677B

8514







2)Total cell area

Acell (cm2)



B 191 597 6 10051 1675 580 440C 597 996 12 19986 1666 571 439D 996 1393 18 29782 1655 560 437E 1393 1790 24 39715 1655 560 437F 1790 2187 30 49642 1655 560 437G 2187 2642 36 68899 1914 819 470


M LAeffρeff (11)


ρeff tg

tg + tc1113872 1113873ρg +

tc

tg + tc1113872 1113873ρc (12)


C tg

tg + tc1113872 1113873LAgρgCg +

tc

tg + tc1113872 1113873LAcρcCc (13)




Ceff tgρg

tg + tc1113872 1113873ρeffCg +


Cc (15)










Coolantsource

Coolantsink









Top fittingGraphite

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 123456789

10111213141516171819

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 20Graphite

Bottom fitting

FuelZirconium Gap


Cor

e act

ive z

one

Fuel Gap

Aluminum clad




Fuel element








0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)




(a)



0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)


(b)


CladGap


tg = 01mm

(a)

Effective material


(b)







60

130

200

270

340

410

480

550

620

690

0 5 10 15 20 25 30

Max

imum

fuel

tem

pera

ture

(degC)



(a)

Max

imum

fuel

tem

pera

ture

(degC)


60

110

160

210

260

310

360


(b)


Max

out

er cl

ad te

mpe

ratu

re (deg

C)


60

80

100

120

140

160


T = 1132degC

(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)



60

70

80

90

100

110

120T = 1132degC

(b)






P _mCpΔT (16)


60

65

70

75

80

85

90

95

0 5 10 15 20 25 30

Aver

age o

utle

t tem

pera

ture

(degC)



(a)

Aver

age o

utle

t tem

pera

ture

(degC)


60

65

70

75

80

85


(b)


0

002

004

006

008

01

012

014

Aver

age m

ass f

low

rate

(kg

s)








60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)




(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)









cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



_q ΔT



_q keffAeffΔT

L (7)


Secondary loop

Primary loop

Forced circulation

Natural circulation

Coolant towerPump

PumpHeat exchanger

AirAir

Upward air flow



0

02

04

06

08

1

12

14

16

0 10 20 30 40

Axi

al lo

catio

n-to

-ave

rage

pow

er ra

tio


y = ndash00026x2 + 01027x + 04254

(a)


y = 01886x2 ndash 01185x + 10016

0

02

04

06

08

1

12

14

16

Loca

tion-

to-a

vera

ge p

ower

ratio

(b)




keffAeffΔT

L

(8)


keff tg

tg + tc1113872 1113873kg+

tc

tg + tc1113872 1113873kc

⎡⎢⎣ ⎤⎥⎦

minus 1

(9)


M tg

tg + tc1113872 1113873LAgρg +

tc

tg + tc1113872 1113873LAcρc (10)





786243

42

49

42

43

64

64

64

62 75

72

73

122

92 136

111101

134112

54C

92

Centralthimble

Transientrod

7590

93 8990

95

42 63

49

41

64

42

65

42 49 42

65

43

6564

63

42

50

65 43

4466

436477138

112

114

108 96 76

7910114137

9390 129

9481 67 52

44

46

6882

68838379

8465

6671

70

43

44

4452

44 46 45

7167

5345

96796442

51 63 78

91A

66

66

44

44

111112

104

104 94 78

7676 78 79

75

75

65 51

436677B

8514







2)Total cell area

Acell (cm2)



B 191 597 6 10051 1675 580 440C 597 996 12 19986 1666 571 439D 996 1393 18 29782 1655 560 437E 1393 1790 24 39715 1655 560 437F 1790 2187 30 49642 1655 560 437G 2187 2642 36 68899 1914 819 470


M LAeffρeff (11)


ρeff tg

tg + tc1113872 1113873ρg +

tc

tg + tc1113872 1113873ρc (12)


C tg

tg + tc1113872 1113873LAgρgCg +

tc

tg + tc1113872 1113873LAcρcCc (13)




Ceff tgρg

tg + tc1113872 1113873ρeffCg +


Cc (15)










Coolantsource

Coolantsink









Top fittingGraphite

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 123456789

10111213141516171819

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 20Graphite

Bottom fitting

FuelZirconium Gap


Cor

e act

ive z

one

Fuel Gap

Aluminum clad




Fuel element








0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)




(a)



0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)


(b)


CladGap


tg = 01mm

(a)

Effective material


(b)







60

130

200

270

340

410

480

550

620

690

0 5 10 15 20 25 30

Max

imum

fuel

tem

pera

ture

(degC)



(a)

Max

imum

fuel

tem

pera

ture

(degC)


60

110

160

210

260

310

360


(b)


Max

out

er cl

ad te

mpe

ratu

re (deg

C)


60

80

100

120

140

160


T = 1132degC

(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)



60

70

80

90

100

110

120T = 1132degC

(b)






P _mCpΔT (16)


60

65

70

75

80

85

90

95

0 5 10 15 20 25 30

Aver

age o

utle

t tem

pera

ture

(degC)



(a)

Aver

age o

utle

t tem

pera

ture

(degC)


60

65

70

75

80

85


(b)


0

002

004

006

008

01

012

014

Aver

age m

ass f

low

rate

(kg

s)








60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)




(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)









cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



keffAeffΔT

L

(8)


keff tg

tg + tc1113872 1113873kg+

tc

tg + tc1113872 1113873kc

⎡⎢⎣ ⎤⎥⎦

minus 1

(9)


M tg

tg + tc1113872 1113873LAgρg +

tc

tg + tc1113872 1113873LAcρc (10)





786243

42

49

42

43

64

64

64

62 75

72

73

122

92 136

111101

134112

54C

92

Centralthimble

Transientrod

7590

93 8990

95

42 63

49

41

64

42

65

42 49 42

65

43

6564

63

42

50

65 43

4466

436477138

112

114

108 96 76

7910114137

9390 129

9481 67 52

44

46

6882

68838379

8465

6671

70

43

44

4452

44 46 45

7167

5345

96796442

51 63 78

91A

66

66

44

44

111112

104

104 94 78

7676 78 79

75

75

65 51

436677B

8514







2)Total cell area

Acell (cm2)



B 191 597 6 10051 1675 580 440C 597 996 12 19986 1666 571 439D 996 1393 18 29782 1655 560 437E 1393 1790 24 39715 1655 560 437F 1790 2187 30 49642 1655 560 437G 2187 2642 36 68899 1914 819 470


M LAeffρeff (11)


ρeff tg

tg + tc1113872 1113873ρg +

tc

tg + tc1113872 1113873ρc (12)


C tg

tg + tc1113872 1113873LAgρgCg +

tc

tg + tc1113872 1113873LAcρcCc (13)




Ceff tgρg

tg + tc1113872 1113873ρeffCg +


Cc (15)










Coolantsource

Coolantsink









Top fittingGraphite

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 123456789

10111213141516171819

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 20Graphite

Bottom fitting

FuelZirconium Gap


Cor

e act

ive z

one

Fuel Gap

Aluminum clad




Fuel element








0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)




(a)



0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)


(b)


CladGap


tg = 01mm

(a)

Effective material


(b)







60

130

200

270

340

410

480

550

620

690

0 5 10 15 20 25 30

Max

imum

fuel

tem

pera

ture

(degC)



(a)

Max

imum

fuel

tem

pera

ture

(degC)


60

110

160

210

260

310

360


(b)


Max

out

er cl

ad te

mpe

ratu

re (deg

C)


60

80

100

120

140

160


T = 1132degC

(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)



60

70

80

90

100

110

120T = 1132degC

(b)






P _mCpΔT (16)


60

65

70

75

80

85

90

95

0 5 10 15 20 25 30

Aver

age o

utle

t tem

pera

ture

(degC)



(a)

Aver

age o

utle

t tem

pera

ture

(degC)


60

65

70

75

80

85


(b)


0

002

004

006

008

01

012

014

Aver

age m

ass f

low

rate

(kg

s)








60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)




(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)









cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018


M LAeffρeff (11)


ρeff tg

tg + tc1113872 1113873ρg +

tc

tg + tc1113872 1113873ρc (12)


C tg

tg + tc1113872 1113873LAgρgCg +

tc

tg + tc1113872 1113873LAcρcCc (13)




Ceff tgρg

tg + tc1113872 1113873ρeffCg +


Cc (15)










Coolantsource

Coolantsink









Top fittingGraphite

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 123456789

10111213141516171819

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 20Graphite

Bottom fitting

FuelZirconium Gap


Cor

e act

ive z

one

Fuel Gap

Aluminum clad




Fuel element








0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)




(a)



0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)


(b)


CladGap


tg = 01mm

(a)

Effective material


(b)







60

130

200

270

340

410

480

550

620

690

0 5 10 15 20 25 30

Max

imum

fuel

tem

pera

ture

(degC)



(a)

Max

imum

fuel

tem

pera

ture

(degC)


60

110

160

210

260

310

360


(b)


Max

out

er cl

ad te

mpe

ratu

re (deg

C)


60

80

100

120

140

160


T = 1132degC

(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)



60

70

80

90

100

110

120T = 1132degC

(b)






P _mCpΔT (16)


60

65

70

75

80

85

90

95

0 5 10 15 20 25 30

Aver

age o

utle

t tem

pera

ture

(degC)



(a)

Aver

age o

utle

t tem

pera

ture

(degC)


60

65

70

75

80

85


(b)


0

002

004

006

008

01

012

014

Aver

age m

ass f

low

rate

(kg

s)








60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)




(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)









cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018






Top fittingGraphite

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 123456789

10111213141516171819

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 20Graphite

Bottom fitting

FuelZirconium Gap


Cor

e act

ive z

one

Fuel Gap

Aluminum clad




Fuel element








0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)




(a)



0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)


(b)


CladGap


tg = 01mm

(a)

Effective material


(b)







60

130

200

270

340

410

480

550

620

690

0 5 10 15 20 25 30

Max

imum

fuel

tem

pera

ture

(degC)



(a)

Max

imum

fuel

tem

pera

ture

(degC)


60

110

160

210

260

310

360


(b)


Max

out

er cl

ad te

mpe

ratu

re (deg

C)


60

80

100

120

140

160


T = 1132degC

(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)



60

70

80

90

100

110

120T = 1132degC

(b)






P _mCpΔT (16)


60

65

70

75

80

85

90

95

0 5 10 15 20 25 30

Aver

age o

utle

t tem

pera

ture

(degC)



(a)

Aver

age o

utle

t tem

pera

ture

(degC)


60

65

70

75

80

85


(b)


0

002

004

006

008

01

012

014

Aver

age m

ass f

low

rate

(kg

s)








60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)




(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)









cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018





0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)




(a)



0

100

200

300

400

500

600

700

Tem

pera

ture

(degC)


(b)


CladGap


tg = 01mm

(a)

Effective material


(b)







60

130

200

270

340

410

480

550

620

690

0 5 10 15 20 25 30

Max

imum

fuel

tem

pera

ture

(degC)



(a)

Max

imum

fuel

tem

pera

ture

(degC)


60

110

160

210

260

310

360


(b)


Max

out

er cl

ad te

mpe

ratu

re (deg

C)


60

80

100

120

140

160


T = 1132degC

(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)



60

70

80

90

100

110

120T = 1132degC

(b)






P _mCpΔT (16)


60

65

70

75

80

85

90

95

0 5 10 15 20 25 30

Aver

age o

utle

t tem

pera

ture

(degC)



(a)

Aver

age o

utle

t tem

pera

ture

(degC)


60

65

70

75

80

85


(b)


0

002

004

006

008

01

012

014

Aver

age m

ass f

low

rate

(kg

s)








60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)




(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)









cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018






60

130

200

270

340

410

480

550

620

690

0 5 10 15 20 25 30

Max

imum

fuel

tem

pera

ture

(degC)



(a)

Max

imum

fuel

tem

pera

ture

(degC)


60

110

160

210

260

310

360


(b)


Max

out

er cl

ad te

mpe

ratu

re (deg

C)


60

80

100

120

140

160


T = 1132degC

(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)



60

70

80

90

100

110

120T = 1132degC

(b)






P _mCpΔT (16)


60

65

70

75

80

85

90

95

0 5 10 15 20 25 30

Aver

age o

utle

t tem

pera

ture

(degC)



(a)

Aver

age o

utle

t tem

pera

ture

(degC)


60

65

70

75

80

85


(b)


0

002

004

006

008

01

012

014

Aver

age m

ass f

low

rate

(kg

s)








60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)




(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)









cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018





P _mCpΔT (16)


60

65

70

75

80

85

90

95

0 5 10 15 20 25 30

Aver

age o

utle

t tem

pera

ture

(degC)



(a)

Aver

age o

utle

t tem

pera

ture

(degC)


60

65

70

75

80

85


(b)


0

002

004

006

008

01

012

014

Aver

age m

ass f

low

rate

(kg

s)








60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)




(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)









cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018





60

110

160

210

260

310

360M

axim

um fu

el te

mpe

ratu

re (deg

C)




(a)

Max

out

er cl

ad te

mpe

ratu

re (deg

C)




60

70

80

90

100

110

(b)

Aver

age o

utle

t tem

pera

ture

(degC)




60

65

70

75

80

85

90

(c)









cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018








cm

123456789

101112131415161718192021222324

(a) (b)

650

cm


Bottom grid plate

650

cm

618

cm

Thermocouple


Top grid plate






Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018





Data Availability




References














Flux monitor hole

Control rods

G-ringF-ring


265cm325cm


20

30

40

50

0 02 04 06

Coo

lant

tem

pera

ture

(degC)

Core height (m)























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018





















Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018














Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018


Documents

BenchmarkingCOMSOLMultiphysicsSingle-Subchannel Thermal ...downloads.hindawi.com/journals/stni/2019/4375782.pdf · services such as ﬁssion track experiments, ... outer clad, andcoolant)