benchmarkingcomsolmultiphysicssingle-subchannel thermal...
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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
4 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 5
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
6 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 7
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)
Fuel (25degC)In clad (25degC)Out clad (25degC)Outlet (25degC)
(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)
0 5 10 15 20 25 30Fuel element power (kW)
(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
8 Science and Technology of Nuclear Installations
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)
COMSOL modelRELAP5MOD33 model
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)
COMSOL modelRELAP5MOD33 model
60
80
100
120
140
160
0 5 10 15 20 25 30Fuel element power (kW)
T = 1132degC
(a)
Max
out
er cl
ad te
mpe
ratu
re (deg
C)
COMSOL modelRELAP5MOD33 model
B C D E F GGSTR ring
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
Science and Technology of Nuclear Installations 9
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)
Fuel element power (kW)
COMSOL modelRELAP5MOD33 model
(a)
Aver
age o
utle
t tem
pera
ture
(degC)
COMSOL modelRELAP5MOD33 model
60
65
70
75
80
85
B C D E F GGSTR ring
(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)
B C D E F GGSTR ring
RELAP5MOD33 modelCOMSOL model
Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring
10 Science and Technology of Nuclear Installations
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
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The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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
4 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 5
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
6 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 7
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)
Fuel (25degC)In clad (25degC)Out clad (25degC)Outlet (25degC)
(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)
0 5 10 15 20 25 30Fuel element power (kW)
(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
8 Science and Technology of Nuclear Installations
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)
COMSOL modelRELAP5MOD33 model
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)
COMSOL modelRELAP5MOD33 model
60
80
100
120
140
160
0 5 10 15 20 25 30Fuel element power (kW)
T = 1132degC
(a)
Max
out
er cl
ad te
mpe
ratu
re (deg
C)
COMSOL modelRELAP5MOD33 model
B C D E F GGSTR ring
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
Science and Technology of Nuclear Installations 9
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)
Fuel element power (kW)
COMSOL modelRELAP5MOD33 model
(a)
Aver
age o
utle
t tem
pera
ture
(degC)
COMSOL modelRELAP5MOD33 model
60
65
70
75
80
85
B C D E F GGSTR ring
(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)
B C D E F GGSTR ring
RELAP5MOD33 modelCOMSOL model
Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring
10 Science and Technology of Nuclear Installations
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
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Nuclear InstallationsScience and Technology of
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The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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
4 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 5
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
6 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 7
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)
Fuel (25degC)In clad (25degC)Out clad (25degC)Outlet (25degC)
(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)
0 5 10 15 20 25 30Fuel element power (kW)
(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
8 Science and Technology of Nuclear Installations
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)
COMSOL modelRELAP5MOD33 model
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)
COMSOL modelRELAP5MOD33 model
60
80
100
120
140
160
0 5 10 15 20 25 30Fuel element power (kW)
T = 1132degC
(a)
Max
out
er cl
ad te
mpe
ratu
re (deg
C)
COMSOL modelRELAP5MOD33 model
B C D E F GGSTR ring
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
Science and Technology of Nuclear Installations 9
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)
Fuel element power (kW)
COMSOL modelRELAP5MOD33 model
(a)
Aver
age o
utle
t tem
pera
ture
(degC)
COMSOL modelRELAP5MOD33 model
60
65
70
75
80
85
B C D E F GGSTR ring
(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)
B C D E F GGSTR ring
RELAP5MOD33 modelCOMSOL model
Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring
10 Science and Technology of Nuclear Installations
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
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Submit your manuscripts atwwwhindawicom
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
4 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 5
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
6 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 7
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)
Fuel (25degC)In clad (25degC)Out clad (25degC)Outlet (25degC)
(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)
0 5 10 15 20 25 30Fuel element power (kW)
(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
8 Science and Technology of Nuclear Installations
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)
COMSOL modelRELAP5MOD33 model
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)
COMSOL modelRELAP5MOD33 model
60
80
100
120
140
160
0 5 10 15 20 25 30Fuel element power (kW)
T = 1132degC
(a)
Max
out
er cl
ad te
mpe
ratu
re (deg
C)
COMSOL modelRELAP5MOD33 model
B C D E F GGSTR ring
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
Science and Technology of Nuclear Installations 9
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)
Fuel element power (kW)
COMSOL modelRELAP5MOD33 model
(a)
Aver
age o
utle
t tem
pera
ture
(degC)
COMSOL modelRELAP5MOD33 model
60
65
70
75
80
85
B C D E F GGSTR ring
(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)
B C D E F GGSTR ring
RELAP5MOD33 modelCOMSOL model
Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring
10 Science and Technology of Nuclear Installations
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
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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
Science and Technology of Nuclear Installations 5
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
6 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 7
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)
Fuel (25degC)In clad (25degC)Out clad (25degC)Outlet (25degC)
(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)
0 5 10 15 20 25 30Fuel element power (kW)
(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
8 Science and Technology of Nuclear Installations
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)
COMSOL modelRELAP5MOD33 model
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)
COMSOL modelRELAP5MOD33 model
60
80
100
120
140
160
0 5 10 15 20 25 30Fuel element power (kW)
T = 1132degC
(a)
Max
out
er cl
ad te
mpe
ratu
re (deg
C)
COMSOL modelRELAP5MOD33 model
B C D E F GGSTR ring
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
Science and Technology of Nuclear Installations 9
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)
Fuel element power (kW)
COMSOL modelRELAP5MOD33 model
(a)
Aver
age o
utle
t tem
pera
ture
(degC)
COMSOL modelRELAP5MOD33 model
60
65
70
75
80
85
B C D E F GGSTR ring
(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)
B C D E F GGSTR ring
RELAP5MOD33 modelCOMSOL model
Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring
10 Science and Technology of Nuclear Installations
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
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Nuclear InstallationsScience and Technology of
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The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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
6 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 7
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)
Fuel (25degC)In clad (25degC)Out clad (25degC)Outlet (25degC)
(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)
0 5 10 15 20 25 30Fuel element power (kW)
(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
8 Science and Technology of Nuclear Installations
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)
COMSOL modelRELAP5MOD33 model
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)
COMSOL modelRELAP5MOD33 model
60
80
100
120
140
160
0 5 10 15 20 25 30Fuel element power (kW)
T = 1132degC
(a)
Max
out
er cl
ad te
mpe
ratu
re (deg
C)
COMSOL modelRELAP5MOD33 model
B C D E F GGSTR ring
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
Science and Technology of Nuclear Installations 9
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)
Fuel element power (kW)
COMSOL modelRELAP5MOD33 model
(a)
Aver
age o
utle
t tem
pera
ture
(degC)
COMSOL modelRELAP5MOD33 model
60
65
70
75
80
85
B C D E F GGSTR ring
(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)
B C D E F GGSTR ring
RELAP5MOD33 modelCOMSOL model
Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring
10 Science and Technology of Nuclear Installations
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
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The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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
Science and Technology of Nuclear Installations 7
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)
Fuel (25degC)In clad (25degC)Out clad (25degC)Outlet (25degC)
(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)
0 5 10 15 20 25 30Fuel element power (kW)
(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
8 Science and Technology of Nuclear Installations
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)
COMSOL modelRELAP5MOD33 model
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)
COMSOL modelRELAP5MOD33 model
60
80
100
120
140
160
0 5 10 15 20 25 30Fuel element power (kW)
T = 1132degC
(a)
Max
out
er cl
ad te
mpe
ratu
re (deg
C)
COMSOL modelRELAP5MOD33 model
B C D E F GGSTR ring
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
Science and Technology of Nuclear Installations 9
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)
Fuel element power (kW)
COMSOL modelRELAP5MOD33 model
(a)
Aver
age o
utle
t tem
pera
ture
(degC)
COMSOL modelRELAP5MOD33 model
60
65
70
75
80
85
B C D E F GGSTR ring
(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)
B C D E F GGSTR ring
RELAP5MOD33 modelCOMSOL model
Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring
10 Science and Technology of Nuclear Installations
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
Hindawiwwwhindawicom Volume 2018
Nuclear InstallationsScience and Technology of
TribologyAdvances in
Hindawiwwwhindawicom Volume 2018
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
OpticsInternational Journal of
Hindawiwwwhindawicom Volume 2018
Antennas andPropagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Power ElectronicsHindawiwwwhindawicom Volume 2018
Advances in
CombustionJournal of
Hindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Renewable Energy
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
Hindawiwwwhindawicom Volume 2018
International Journal ofInternational Journal ofPhotoenergy
Hindawiwwwhindawicom Volume 2018
Solar EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Advances in Condensed Matter Physics
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
High Energy PhysicsAdvances in
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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)
Fuel (25degC)In clad (25degC)Out clad (25degC)Outlet (25degC)
(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)
0 5 10 15 20 25 30Fuel element power (kW)
(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
8 Science and Technology of Nuclear Installations
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)
COMSOL modelRELAP5MOD33 model
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)
COMSOL modelRELAP5MOD33 model
60
80
100
120
140
160
0 5 10 15 20 25 30Fuel element power (kW)
T = 1132degC
(a)
Max
out
er cl
ad te
mpe
ratu
re (deg
C)
COMSOL modelRELAP5MOD33 model
B C D E F GGSTR ring
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
Science and Technology of Nuclear Installations 9
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)
Fuel element power (kW)
COMSOL modelRELAP5MOD33 model
(a)
Aver
age o
utle
t tem
pera
ture
(degC)
COMSOL modelRELAP5MOD33 model
60
65
70
75
80
85
B C D E F GGSTR ring
(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)
B C D E F GGSTR ring
RELAP5MOD33 modelCOMSOL model
Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring
10 Science and Technology of Nuclear Installations
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
Hindawiwwwhindawicom Volume 2018
Nuclear InstallationsScience and Technology of
TribologyAdvances in
Hindawiwwwhindawicom Volume 2018
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
OpticsInternational Journal of
Hindawiwwwhindawicom Volume 2018
Antennas andPropagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Power ElectronicsHindawiwwwhindawicom Volume 2018
Advances in
CombustionJournal of
Hindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Renewable Energy
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
Hindawiwwwhindawicom Volume 2018
International Journal ofInternational Journal ofPhotoenergy
Hindawiwwwhindawicom Volume 2018
Solar EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Advances in Condensed Matter Physics
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
High Energy PhysicsAdvances in
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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)
COMSOL modelRELAP5MOD33 model
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)
COMSOL modelRELAP5MOD33 model
60
80
100
120
140
160
0 5 10 15 20 25 30Fuel element power (kW)
T = 1132degC
(a)
Max
out
er cl
ad te
mpe
ratu
re (deg
C)
COMSOL modelRELAP5MOD33 model
B C D E F GGSTR ring
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
Science and Technology of Nuclear Installations 9
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)
Fuel element power (kW)
COMSOL modelRELAP5MOD33 model
(a)
Aver
age o
utle
t tem
pera
ture
(degC)
COMSOL modelRELAP5MOD33 model
60
65
70
75
80
85
B C D E F GGSTR ring
(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)
B C D E F GGSTR ring
RELAP5MOD33 modelCOMSOL model
Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring
10 Science and Technology of Nuclear Installations
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
Hindawiwwwhindawicom Volume 2018
Nuclear InstallationsScience and Technology of
TribologyAdvances in
Hindawiwwwhindawicom Volume 2018
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
OpticsInternational Journal of
Hindawiwwwhindawicom Volume 2018
Antennas andPropagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Power ElectronicsHindawiwwwhindawicom Volume 2018
Advances in
CombustionJournal of
Hindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Renewable Energy
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
Hindawiwwwhindawicom Volume 2018
International Journal ofInternational Journal ofPhotoenergy
Hindawiwwwhindawicom Volume 2018
Solar EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Advances in Condensed Matter Physics
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
High Energy PhysicsAdvances in
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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)
Fuel element power (kW)
COMSOL modelRELAP5MOD33 model
(a)
Aver
age o
utle
t tem
pera
ture
(degC)
COMSOL modelRELAP5MOD33 model
60
65
70
75
80
85
B C D E F GGSTR ring
(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)
B C D E F GGSTR ring
RELAP5MOD33 modelCOMSOL model
Figure 15 Average mass flow rate calculated by the single-subchannel models at each GSTR ring
10 Science and Technology of Nuclear Installations
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
Hindawiwwwhindawicom Volume 2018
Nuclear InstallationsScience and Technology of
TribologyAdvances in
Hindawiwwwhindawicom Volume 2018
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
OpticsInternational Journal of
Hindawiwwwhindawicom Volume 2018
Antennas andPropagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Power ElectronicsHindawiwwwhindawicom Volume 2018
Advances in
CombustionJournal of
Hindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Renewable Energy
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
Hindawiwwwhindawicom Volume 2018
International Journal ofInternational Journal ofPhotoenergy
Hindawiwwwhindawicom Volume 2018
Solar EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Advances in Condensed Matter Physics
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
High Energy PhysicsAdvances in
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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)
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
60
70
80
90
100
110
(b)
Aver
age o
utle
t tem
pera
ture
(degC)
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
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
Science and Technology of Nuclear Installations 11
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
Hindawiwwwhindawicom Volume 2018
Nuclear InstallationsScience and Technology of
TribologyAdvances in
Hindawiwwwhindawicom Volume 2018
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
OpticsInternational Journal of
Hindawiwwwhindawicom Volume 2018
Antennas andPropagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Power ElectronicsHindawiwwwhindawicom Volume 2018
Advances in
CombustionJournal of
Hindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Renewable Energy
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
Hindawiwwwhindawicom Volume 2018
International Journal ofInternational Journal ofPhotoenergy
Hindawiwwwhindawicom Volume 2018
Solar EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Advances in Condensed Matter Physics
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
High Energy PhysicsAdvances in
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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
data and benchmark the COMSOL Multiphysics single-subchannel thermal-hydraulic evaluation of a TRIGA Re-actor with RELAP5 results and experimental data
+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
12 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
Hindawiwwwhindawicom Volume 2018
Nuclear InstallationsScience and Technology of
TribologyAdvances in
Hindawiwwwhindawicom Volume 2018
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
OpticsInternational Journal of
Hindawiwwwhindawicom Volume 2018
Antennas andPropagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Power ElectronicsHindawiwwwhindawicom Volume 2018
Advances in
CombustionJournal of
Hindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Renewable Energy
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
Hindawiwwwhindawicom Volume 2018
International Journal ofInternational Journal ofPhotoenergy
Hindawiwwwhindawicom Volume 2018
Solar EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Advances in Condensed Matter Physics
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
High Energy PhysicsAdvances in
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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
Science and Technology of Nuclear Installations 13
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
14 Science and Technology of Nuclear Installations
Hindawiwwwhindawicom Volume 2018
Nuclear InstallationsScience and Technology of
TribologyAdvances in
Hindawiwwwhindawicom Volume 2018
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
OpticsInternational Journal of
Hindawiwwwhindawicom Volume 2018
Antennas andPropagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Power ElectronicsHindawiwwwhindawicom Volume 2018
Advances in
CombustionJournal of
Hindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Renewable Energy
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
Hindawiwwwhindawicom Volume 2018
International Journal ofInternational Journal ofPhotoenergy
Hindawiwwwhindawicom Volume 2018
Solar EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Advances in Condensed Matter Physics
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
High Energy PhysicsAdvances in
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
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
14 Science and Technology of Nuclear Installations
Hindawiwwwhindawicom Volume 2018
Nuclear InstallationsScience and Technology of
TribologyAdvances in
Hindawiwwwhindawicom Volume 2018
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
OpticsInternational Journal of
Hindawiwwwhindawicom Volume 2018
Antennas andPropagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Power ElectronicsHindawiwwwhindawicom Volume 2018
Advances in
CombustionJournal of
Hindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Renewable Energy
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
Hindawiwwwhindawicom Volume 2018
International Journal ofInternational Journal ofPhotoenergy
Hindawiwwwhindawicom Volume 2018
Solar EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Advances in Condensed Matter Physics
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
High Energy PhysicsAdvances in
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom
Hindawiwwwhindawicom Volume 2018
Nuclear InstallationsScience and Technology of
TribologyAdvances in
Hindawiwwwhindawicom Volume 2018
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
OpticsInternational Journal of
Hindawiwwwhindawicom Volume 2018
Antennas andPropagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Power ElectronicsHindawiwwwhindawicom Volume 2018
Advances in
CombustionJournal of
Hindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Renewable Energy
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
Hindawiwwwhindawicom Volume 2018
International Journal ofInternational Journal ofPhotoenergy
Hindawiwwwhindawicom Volume 2018
Solar EnergyJournal of
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Advances in Condensed Matter Physics
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
High Energy PhysicsAdvances in
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Submit your manuscripts atwwwhindawicom