Thermal Hydraulic and Neutronics Coupling Analysis for Plate …downloads.hindawi.com/journals/stni/2020/2562747.pdf · 2020. 8. 28. · ResearchArticle Thermal Hydraulic and Neutronics

Research ArticleThermal Hydraulic and Neutronics Coupling Analysis for PlateType Fuel in Nuclear Reactor Core

Linrong Ye1 Mingjun Wang 1 Xinrsquoan Wang1 Jian Deng 2 Yan Xiang3 Wenxi Tian1

Suizheng Qiu1 and G H Su1

1State Key Laboratory of Multiphase Flow in Power Engineering Department of Nuclear Science and TechnologyXirsquoan Jiaotong University Xirsquoan 710049 China2Science and Technology on Reactor System Design Technology Laboratory Nuclear Power Institute of China Chengdu China3Royal Institute of Technology (KTH) Stockholm 11428 Sweden

Correspondence should be addressed toMingjunWangwangmingjunmailxjtueducn and JianDeng dengjian_npic163com

Received 12 December 2019 Revised 10 June 2020 Accepted 29 June 2020 Published 28 August 2020

Academic Editor Fu Li

Copyright copy 2020 Linrong Ye et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e thermal hydraulic and neutronics coupling analysis is an important part of the high-fidelity simulation for nuclear reactorcore In this paper a thermal hydraulic and neutronics coupling method was proposed for the plate type fuel reactor core based onthe Fluent and Monte Carlo code e coupling interface module was developed using the User Defined Function (UDF) inFluent e three-dimensional thermal hydraulic model and reactor core physics model were established using Fluent and MonteCarlo code for a typical plate type fuel assembly respectively en the thermal hydraulic and neutronics coupling analysis wasperformed using the developed coupling code e simulation results with coupling and noncoupling analysis methods werecompared to demonstrate the feasibility of coupling code and it shows that the accuracy of the proposed coupling method ishigher than that of the traditional method Finally the fuel assembly blockage accident was studied based on the coupling codeUnder the inlet 30 blocked conditions the maximum coolant temperature would increase around 20degC while the maximum fueltemperature rises about 30degC e developed coupling method provides an effective way for the plate type fuel reactor core high-fidelity analysis

1 Introduction

e high-fidelity simulation for reactor core requires morephysics field coupling due to the strong feedback existing inthe nuclear reactor such as the reactivity interaction betweencore neutronics transport and thermal hydraulics e neu-tron flux distribution determines the core power distributionand further determines the temperature distributions of fueland coolant which would affect the neutron fission crosssections leading to the variation of core power distributionDue to the strong feedback effects the thermal hydraulics andneutronics research should be coupled together to achieve theaccurate performances of coolant and fuel assembly in nu-clear reactor core especially in some unexpected accidentconditions due to the large temperature variation In the earlyyears neutron transport was often calculated with simplified

point reactor neutron kinetics model due to the limitedcomputing capability and the results were usually conser-vative With the development of computational capability ithas been feasible to realize the multiphysics coupling analysisfor nuclear reactor high-fidelity simulations

Actually several thermal hydraulic and neutronics couplinganalyses have been performed in the past several decades Jiet al coupled Monte Carlo code MCNP5 and system codeRELAP5 to explore the feasibility of the pseudomaterialmethodfor Doppler feedback in the VHTGR In this study the crosssection libraries were interpolated to obtain the neutron crosssections at arbitrary temperature [1] Hu and Uddin developeda new explicit coupling scheme using User Defined Function(UDF) to couple MCNP5 and Fluent and some promisingresults were achieved [2] Cardoni realizedMCNP5 and STAR-CCM+ coupling to calculate 3D PWR fuel pin cell model and

HindawiScience and Technology of Nuclear InstallationsVolume 2020 Article ID 2562747 12 pageshttpsdoiorg10115520202562747

3times 3 model and obtained high-fidelity results of coolanttemperature and density fuel temperature and power distri-bution successfully demonstrating the coupling effects [3] Yanet al coupled STAR-CCM+ and deterministic codeDeCARTtocalculate PWR 3times 3 model with new mesh mapping methods[4] Hoogenboom et al built a flexible thermal hydraulic andneutronics coupling scheme with Python [5] Sjenitzer et alproposed a new method to perform transient coupling withMonte Carlo code [6] Ward et al used coupled system codeRELAP5 and 3D spatial kinetics code PARCS to simulate safetyperformance of the I2S-LWR plant during accident conditions[7] e thermal hydraulic and neutronics coupling algorithmin transient problems for the high-temperature gas-cooledreactor simulator TINTE was evaluated and developed [8]Results indicated that the proposed coupling algorithms Picardand JFNKwere better compared with the original semi-implicitcoupling algorithm in TINTE

In terms of plate type fuel reactor core analysis Tian et aldeveloped a thermal hydraulic analysis code for China Ad-vanced Research Reactor (CARR) e heat transfer and flowdistribution characteristics in the reactor core were studied[9] Gong et al found that all fuel and cladding temperatureswere below the design limits and remained safe with the inletvelocity ranging from 45ms to 75ms for the hottest as-sembly in 20MWplate type fuel reactor [10] Lu et al analyzedthe blockage accident of one assembly channel in 10MWplatetype fuel reactor and the results showed that the obstructedchannel causes temperature rise in adjacent channels Inaddition it was found that there was no boiling in obstructedchannel except for the hot channel because of lateral heatconduction of adjacent channels [11] Bousbia-Salah et alcalculated the neutron flux and power distribution of 10MWMTR usingMCNP5 code and it showed that theMCNP5 wasreliable for the plate type fuel core simulation and the cal-culation results were in good agreement with previous study[12] Xoubi et al investigated the impact of enrichment onneutron flux in the in-core facility of 10MW MTR withOpenMC and found the importance of flux trap calculationwhile considering the conversion of reactor core fromHEU toLEU [13] It also demonstrated the feasibility of the MonteCarlo method in analyzing plate type fuel reactor

It can be seen that most of the thermal hydraulic andneutronics coupling studies are performed for PWR rodbundle type fuel in the literatures while the couplinganalysis on plate type fuel reactor core is rare erefore aninnovative thermal hydraulic and neutronics couplingmethod was proposed based on the Fluent andMonte Carlocode through the UDF module for the plate type fuel re-actor core in this paper A typical plate type fuel assemblywas analyzed with the coupling code and the thermalhydraulic and neutronics features were studied and ana-lyzed in detail

2 Mathematic Model

e CFD method is widely utilized in the nuclear reactorthermal hydraulic analysis currently especially for the localdetailed three-dimensional flow and heat transfer processsuch as the coolant mixing in the reactor core [14] e basic

of CFD method is the fundamental governing equations offluid dynamics including the mass momentum and energyconservation equations For single-phase flow the mass andmomentum equations are given as follows

1p

zρzt

+ nabla middot u 0

ρDu

Dt ρF + nabla middot σ

(1)

where the u is the velocity ρ is the density F is the body forceper unit of fluid mass and σ is the stress tensor

For incompressible Newtonian fluid the NavierndashStokesequations are given as follows

nabla middot u 0 (2)

ρzρzt

+ u middot nablau1113888 1113889 ρF minus nabla middot p + nabla2u (3)

ρcP

zT

zt+ u middot nablau1113888 1113889 nabla middot (λnablaT) + q

rsquoprimersquo + ϕ (4)

where the T is temperature p is pressure cp is the specifichear capacity at constant pressure λ is thermal conductivityqrsquoprimersquo is volumetric heat source and ϕ is the dissipationfunction For the steady calculation in the paper the timederivative term is eliminated

For solid domains like fuel and cladding heat con-duction equation can be simplified from equation (4) asfollows

ρcP

zT

zt nabla middot (λnablaT) + q

rsquoprimersquo (5)

For fuel the volumetric heat source is fission heat or theheat generated by c-rays in cladding In this paper the heatin cladding is ignored and q

rsquoprimersquo is zero in cladding domaine direct numerical solution (DNS) method directly

solves NavierndashStokes equations and huge computing cost isrequired to simulate turbulence effect which is unfavorablein reactor scale simulation e computing cost could bedecreased by applying turbulence models For steady-statesimulation the Reynolds-averaged NavierndashStokes-based(RANS-based) models which describe time-averaged mo-tion of fluid flow are widely used in the engineering fieldse typical RANS-based models include the Reynolds stressmodel (RSM) and the models that introduce eddy viscosityhypothesis such as the k-ε model and k-ω model estandard k-ε model is the most common turbulence modelused in CFD and its equation is described below as anexample of RANS-based model [15]

ρDk

Dt

z

zxi

u +ut

σk

1113888 1113889zk

zxi

1113890 1113891 + Gk + Gb minus ρε

ρDεDt

z

zxi

u +ut

σε1113888 1113889

zεzxi

1113890 1113891 + C1εεk

Gk + C2εGb( 1113857 minus C2ερε2

k

(6)

2 Science and Technology of Nuclear Installations

where μt is turbulent viscosity and it is modelled asut ρCμ(ε2k) Gk is turbulent kinetic energy produced bylaminar velocity gradient Gb is turbulent kinetic energyproduced by buoyancy and C1ε C2ε Cμ σk and σε are modelconstants

e Monte Carlo method is a stochastic algorithm basedon probability statistics e neutron transport in nuclearreactor is random with certain statistical properties whichfits the scope of application of the Monte Carlo method wellFor the application of the Monte Carlo method in neutrontransport it simulates several histories of neutron fromgenerating to disappearing continuously instead of solvingneutron transport equations directly

With large numbers of neutron samples many averageparameters such as neutron flux distribution keff energyin the reactor and the confidence interval are obtainedaccording to central limit theory For critical problem inMonte Carlo code the fission source begins with a typicalhistory and is converged after enough neutrongenerations

3 Coupling Method

e coupling method between thermal hydraulic code andneutronics code is mainly divided into external couplingand internal coupling e internal coupling integrates thetwo codes together and the data transfer process is achievedinside the integrated code Although this method hasrelatively high accuracy and performs well in parallelism itrequires massive modification on the codes e externalcoupling is achieved through user interface module totransfer data between two codes without modification onthe codes erefore the two codes are able to remainindependent during external coupling process In thispaper the UDF which is a powerful user interface of Fluentfor secondary development [16] is compiled to coupleFluent and neutronics codes and realize the transfer databetween the two codes e Fluent meshes are mapped withMonte Carlo code cells through UDF module e MonteCarlo code provides heat source term to the Fluent mesheswhile the Fluent results renew the temperature and densityfor Monte Carlo code leading to the update of crosssections in the input file e detailed coupling scheme ispresented in Figure 1e fuel domain in Fluent is providedwith power distribution and the flow field is initialized andthen the CFD calculation begins When the residual ofcontinuity in Fluent is under 10minus4 the calculated tem-perature and density are extracted e Monte Carlo codeinput file is updated with the data and the cross sectionlibraries are renewed en the Monte Carlo code calcu-lation begins After Monte Carlo calculation the fissionenergy deposition in the output file is extracted andtransformed into power density in which case the Fluentsource term would be updated e coupling code finallydetermines whether the iteration converges by monitoringkeff

In this paper the geometry of plate type fuel assembly issimple and the one-to-one node mapping method

optimized for plate type fuel model is adopted during thecode coupling scheme e mapping scheme is achievedthrough UDF traversing the coordinates of models inFluent and Monte Carlo code and matching the cell IDwhich makes it available for mapping considerable numberof meshes providing high accuracy at the cost of a littlelonger time e mapping strategy also makes it convenientto modify the code to fit new plate type fuel model e heatsource term in Fluent is calculated by Monte Carlo codeand thus Monte Carlo code would not provide the powerdistribution directly e tally module in Monte Carlo codeis necessary for the fission energy deposition and it istransformed into power density according to the followingequation

qvi PDi

1113936ni1 Di middot Vi

(7)

where qvi is the power density of mesh i P is the total fuelpower Di is the average fission energy deposition in cell iand Vi is the volume of cell i

e initial heat source is provided by Monte Carlo codeand the new temperature and density are updated in theMonte Carlo code input file at each time step of Fluentcalculation convergenceen the cross section and thermalS (α β) libraries are updated according to new temperaturesere are mainly three methods to update the libraries (a)update the libraries corresponding to the exact tempera-tures (b) generate libraries with temperature interval of2sim5K with NJOY in advance and perform grouping ap-proximation based on the calculated temperature and (c)generate libraries with larger temperature interval andperform interpolation based on the calculated temperaturese calculation cost of method (a) is too high Method (b)costs less but still requires high memory Compared tomethod (a) the computing cost of method (c) is less and the

Initialize power distribution and flow field

Solve RANS

CFD converged

Update Monte Carlo code temperature and

density

Update cross section

libraries

Monte carlo calculation

Update power distribution

keff converged

Yes

No

Coupling done

No

Yes

Figure 1 e thermal hydraulic and neutronics coupling scheme

Science and Technology of Nuclear Installations 3

deviation of keff is just about 30 pcm and finally method (c)is selected e cross section libraries with 25degK temperatureinterval and thermal S (α β) libraries with 50degK temperatureinterval are generated using NJOY e cross section at anytemperature for each cell is obtained by interpolating thelibraries of adjacent temperature points e details of theinterpolation method are shown as follows

fL

TH

1113968minus

T

radic

TH

1113968minus

TL

1113968

Σ(T) fLΣ TL( 1113857 + 1 minus fL( 1113857Σ TH( 1113857

(8)

where TH is the highest temperature of selected interval TL isthe lowest one Σ is the macrosection and fL is the portion oflower temperature library

4 Thermal Hydraulic and NeutronicsCoupling Analysis

An active zone model of U3Si2-Al plate type fuel assembly ina typical reactor core is built in the paper e model

structure and cross sections are presented in Figure 2 edetailed parameters are presented in Table 1 and propertiesof fuel pellet and cladding are presented in Table 2 [17] evariations of density heat conduction coefficient andcoolant dynamic viscosity with temperatures are presentedas follows

Flow direction

FluidSolidNone

(a)74

76

616708

Coolant channel

22

06

136

(b)

Figure 2 e model of a typical plate type fuel assembly

Table 1 e fuel structure parameters

Parameters ValuesVolume (mmtimesmmtimesmm) 762times 762times1375Number of plates 21Fuel thickness (mm) 06Fuel width (mm) 850Fuel length (mm) 616Plate thickness (mm) 136Plate length (mm) 890Plate width (mm) 708Gap between plates (mm) 22Cladding thickness (mm) 038Roughness of surface 32times10minus6


ρ(T) 100068 minus 000351 times T minus 000461 times T2

+ 75898 times 10minus 6times T

3

(9)

λ(T) 05509 + 0002606 times T minus 1318 times 10minus 5times T

2 (10)

μ(T) 000177 minus 491 times T + 646 times 10minus 7times T

2

minus 313 times 10minus 9times T

3

(11)

e unit in equations (9) to (11) and Table 2 is K Allthe temperature-dependent parameters are hooked byUDF

Some reasonable assumptions are taken for simplifica-tions (a) symmetrical boundary conditions are set exceptthe inlet and outlet (b) the inlet and outlet planes areconstant pressure surface (c) no gap exists between fuelpellet and cladding and (d) the impact of oxidation film onthe fuel plate is ignored e operation pressure is0683MPa and the inlet temperature is 308K Prior to thecoupling analysis grid and turbulence model independentsensitivities are performed and the core neutronics model isvalidated

Totally five grid schemes are generated to perform theconstant power steady-state calculation e variations ofpressure drop and temperature at outlet with grid numbersare presented in Figure 3 It can be seen that the scheme with95256 meshes could be regarded as the grid-independentsolution

ree turbulence models realizable k-ε standard k-ωand RSM are selected for sensitivity analysis to determine themost suitable turbulence model e calculated coolanttemperature and pressure are presented in Figure 4 It can beseen that the turbulence model selection has very limitedinfluence on the calculation results and finally the realizablek-ε model is selected in the paper

e enrichment of 235U is 1975plusmn 020 and uraniumdensity in the fuel pellet is 43 gUcm3 Nuclei componentand design value of atomic density are presented in Table 3

e meshing model in Monte Carlo code and Fluent issimilar e inlet and outlet planes are set as the vacuumboundary and other boundaries are set as reflection Totally120 batches are run at one iteration and each batch has10000 neutron histories Before counting 20 neutronbatches are skipped for convergence of fission source toreduce the final deviation e libraries of neutron fissioncross sections in fuel and neutron scattering cross sections incoolant are shown in Tables 4 and 5

e reactivity coefficient calculation is performed tovalidate the feasibility of built neutronics model e eightgroups of calculations are carried out to determine the

coolant temperature coefficient and fuel temperature coef-ficient Group details are presented in Table 6 and the resultswith 95 confidence interval are presented in Table 7 eliner fitting is done after transforming keff to reactivitycoefficient as shown in Figures 5 and 6 e average fueltemperature coefficient is minus2086times10minus5 (K) and averagecoolant temperature coefficient is minus533times10minus5 (K) e twocoefficients documented in the literature are minus22745times10minus5

(K) and minus80734times10minus5 (K) and it can be seen that they areclose to the calculated value in this paper It demonstratesthat the neutronics model and cross section settings arereliable

41 Normal Operation Condition e coupling and non-coupling simulations were performed respectively and theresults are compared For noncoupling simulation cosinepower distribution is applied as the heat source In this casethe inlet velocity is set to 70ms and the total assemblypower is set to 785MW keff outlet temperature andpressure of each iteration are shown in Figure 7 It can beseen that after 5 iterations the calculation is generallyconverged

Figure 8 shows the coupled power density distribution inthe whole assembly e power distribution in a single platealong the thickness is treated as uniform distribution sinceits dimension is much smaller compared to that in the heightand width direction Figure 9 shows the comparison ofpower distribution in the middle plate between couplinganalysis and noncoupling analysis e calculated power

Table 2 e material properties

Position Material Density(kgmiddotmminus3)

Heat conduction coefficient(Wmiddotmminus1 Kminus1) Specific heat capacity (Jmiddotgminus1 Kminus1)

Fuel U3Si2-Al 6030 507 0892 + 000046Tminus 071times (0749 + 000038 T)

Cladding 6061-O aluminumalloy 2700 13125 + 833times10minus2 T 0897

Dev

iatio

n

Pressure dropOutlet temperature

00000

00005

00010

00015

00020

00025

00030

77616 95256 15699642336Number of meshes

Figure 3 Variations of coolant temperature and pressure dropwith different grid numbers


with coupling analysis code is larger near the edge in thewidth direction compared to that with noncoupling analysismethod due to the space self-shielding effect which enlargesthe fission rate near the edge Figure 10 shows the variationof power distribution with the iterations from the initialshape to the 5th iteration e powers increase at the bothends and power peak is lowered with the coupling analysisIt can be seen that the power is a little higher in the inlet sidewhile it is lower in the outlet side and the power peak movesto the inlet side after coupling It is because the coolanttemperature is lower and the density is higher in the inletside where the moderation effect is stronger than that in the

Cool

ant t

empe

ratu

re (K

)

k-epsilonw-omegaReynolds stress

305

310

315

320

325

330

335

02 04 06 08 1000Z (m)

(a)

k-epsilonk-omegaReynolds stress

Pres

sure

(Pa)

0

50000

100000

150000

200000

02 04 06 08 1000Z (m)

(b)

Figure 4 Results of coolant temperature and pressure drop with different turbulence models

Table 4 e variations of neutron fission cross-sections withtemperature in fuel

Temperature (K) ID extension300 010c325 011c350 012c375 013c400 014c425 015c450 016c475 017c500 018c525 019c550 020c575 021c600 022c625 023c650 024c675 025c

Table 3 Nuclide information for the fuel pellet

Nuclide Density (barn-cm)Al 31633eminus 2Si 72719eminus 3235U 21763eminus 3238U 87315eminus 3

Table 5 e variations of neutron scattering cross-sections withtemperature in coolant

Temperature (K) ID extension293 0032t323 0132t373 0232t423 0332t

Table 6 Group information

Number Tfuel (K) Twater (K) ρwater (g∙cmminus3)1 300 308 0994302 350 308 0994303 400 308 0994304 450 308 0994305 500 308 0994306 400 338 0980817 400 368 0962178 400 398 093926

Table 7 e keff results of each group

Number keffplusmn 95 CI1 159693plusmn 0001262 159539plusmn 0001123 159164plusmn 0001194 158958plusmn 0001315 158662plusmn 0001346 159010plusmn 0001057 158651plusmn 0001178 158463plusmn 000116


outlet side making the thermal neutron flux higher andfission rate greater e variation of power distributionsbefore and after coupling shows that the coupling codeintroduces the feedback effect between thermal hydraulicand neutronics and the feasibility of coupling code is proved

Figure 11 shows the comparison of coolant temperaturedistributions in the assembly before and after couplinganalysis Figure 12 provides the quantitative comparison of

temperatures of coolant cladding and fuel pellet betweenthe noncoupled and coupled analysis e temperature peakwith coupled analysis is lower than that with noncoupledanalysis indicating that cosine power distribution as-sumption is conservative Figure 13 shows the variation ofaverage heat transfer coefficient in the height direction Itincreases at the beginning rapidly and descends along theflow direction gradually

42 Blockage Condition Analysis For the plate type fuelreactor under certain accident conditions such as debrisflowing into reactor and fuel blistering the flow channelblockage will happen causing temperature to increasesharply inside the fuel plate and leading to large temperaturegradient along the plate whichmay induce structure ruptureof plates and cause severe consequences [18] e fuel as-sembly operation features under the blockage conditions areanalyzed with the coupling code in this section

Totally three positions at the inlet of assembly aremodelled as the solid partly to realize the fuel assemblyblockage conditions e cross sections of inlet blockagemodel are presented in Figure 14 and the 30 blockage of

Reac

tivity

Δkk

0370

0372

0374

400 500300Temperature (K)

Figure 5 Reactivity-fuel temperature

Reac

tivity

Δkk

0368

0370

0372

0374

320 340 360 380 400300Temperature (K)

Figure 6 Reactivity-coolant temperature

keffΔP

1585

1590

1595

1600

k eff

107900

107905

107910

107915

107920

107925

107930

107935

107940

ΔP

2 4 60Iteration

Figure 7 e variations of keff and pressure drop with iterations

Contour-1User memory 0

194e + 10185e + 10176e + 10167e + 10159e + 10150e + 10141e + 10132e + 10123e + 10114e + 10105e + 10959e + 09869e + 09780e + 09690e + 09601e + 09511e + 09422e + 09332e + 09243e + 09153e + 09

(a)



(b)

Figure 9 e power density contours in the middle plate (a)Noncoupled (b) Coupled



Figure 8 e power distribution in the whole assembly


channel is set e material is set as steel and the corre-sponding Monte Carlo code coolant cells are changed intosteel cells

Figure 15 presents the coolant temperature in the wholeassembly and Figure 16 shows the temperature contours atz 0285 just behind the obstructed location It can be seenthat blockage causes temperature rise in both coolant andfuel plates e temperatures of fuel plates along x minus0025are presented in Figure 17 e third blockage condition

causes higher temperature rise due to the reflective boundaryset in the Monte Carlo code Figure 18 shows the x-directiontemperature of fuel plates pointed with the black arrow inFigure 16 e large temperature gradient could be observedin all three conditions which would threaten the fuel me-chanical behaviors

As thermal hydraulic and neutronics coupling effect isintroduced in the calculation the effect of blockage on localheat transfer can be more accurately obtained e thermal

00 02 04 06 08 10000E + 000

540E + 009

108E + 010

162E + 010

216E + 010

Cosine distributionPower at iteration 1

Pow

er d

ensit

y (W

middotmndash3

)

Z (m)

ndash500E + 008

000E + 000

500E + 008

Power at iteration 5Power deviation aer coupling

Pow

er d

evia

tion

aer

coup

ling

(Wmiddotm

ndash3)

Figure 10 e average axial power profiles before and after coupling

z = 065m

[k]

Contour-1Static temperature

405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(a)

z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(b)

Figure 11 e coolant temperature contours (a) Noncoupled (b) Coupled


CoolantCladdingFuel

Coolant (aer coupling)Cladding (aer coupling)Fuel (aer coupling)

Tem

pera

ture

(K)

300320340360380400420440460480500520540

02225 04450 06675 0890000000Z (m)

Figure 12 e variations of temperature along Z direction before and after coupling

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2Kndash1

)

Before couplingAfter coupling

30000

32000

34000

36000

38000

40000

42000

44000

02 04 06 08 1000Z (m)

Figure 13 e variations of heat transfer coefficients along flow channels before and after coupling

(a) (b) (c)

Figure 14 e blockage condition setting at inlet (a) Blockage 1 (b) Blockage 2 (c) Blockage 3


Water-tStatic temperature

430004239041780411704056039950393403873038120375103690036290356803507034460338503324032630320203141030800

[k]

Figure 15 e assembly coolant temperatures under three inlet blockage conditions

X = ndash0025mX = ndash0025mX = ndash0025m

Y

XZ[k]


378493749637144367623643936087357343538235029346773432433972336203326732915325623221031857315053115230800

Figure 16 e temperature contours at z 00285m

Tem

pera

ture

(K)

Blockage 1Blockage 2Blockage 3

335340345350355360365370375380

ndash002 000 002 004ndash004y (m)

Figure 17 e fuel plate temperatures at z 00285m and x minus0025m


hydraulic parameters in highlighted position (as shown inFigure 19) are studied e local temperatures of fuel pelletcladding and coolant under three blockage conditions andnormal conditions are presented in Figure 20 For the 30blockage in one channel the coolant velocity decreasescausing local heat transfer coefficient to decrease greatly Asshown in Figure 21 the heat transfer coefficient generallydecreases by 5times103W(m2middotK) and the maximum decreaseis over 104W(m2middotK) leading to coolant temperature in-crease around 20degC at the outlet and fuel maximum tem-perature increase about 30degC

5 Conclusion

In this paper a thermal hydraulic and neutronics couplingscheme was proposed for plate type fuel reactor core ecoupling platform is based on the Fluent and Monte Carlocode through the UDF module en the thermal hydraulicand neutronics coupling analysis for the plate type fuelassembly was performed in detail e mesh-independentanalysis and turbulence model sensitivity analysis werecarried out to determine the number of meshes and tur-bulence model firstly Results show that the accuracy ofpower distribution is well improved and temperature dis-tributions of fuel pellet cladding and coolant are refined dueto the feedback effect introduction e power densitydistribution in the width direction is not uniform and thepower near the edge is higher than that at inner positionFollowing the normal operating condition study theblockage condition analysis with the coupling code wasperformed Under the conditions of 30 blockage in onechannel the heat transfer coefficient decreases obviouslye maximum coolant temperature would increase around20degC and the maximum fuel temperature rises about 30degCis work provides a promising analysis tool for the platetype nuclear reactor core high-fidelity simulation

Data Availability

e access to data is restricted due to the commercialconfidentiality


Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)

Figure 18 e variations of fuel plate temperatures along x-direction

Figure 19 e highlighted position

Blockage 1FuelCladdingCoolant



Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal

Figure 20 e variations of local temperatures in the heightdirection

Blockage 1Blockage 2

Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)

Figure 21 e variations of local heat transfer coefficients in theheight direction


Conflicts of Interest

e authors declare that there are no conflicts of interest

Acknowledgments

is research was supported by the National Natural ScienceFoundation of China (no 11705139)

References

[1] J Conlin W Ji J C Lee and W R Martin ldquoPseudo materialconstruct for coupled neutronic-thermal-hydraulic analysis ofVHTGRrdquo Germal Hydraulics of Next-Generation NuclearReactors vol 92 pp 225ndash227 2005

[2] J Hu and R Uddin ldquoCoupled neutronics and thermal-hy-draulics simulations using MCNP and FLUENTrdquo Transac-tions of the American Nuclear Society vol 98 pp 606ndash6082008

[3] J N Cardoni Nuclear Reactor Multi-Physics Simulations withCoupled MCNP5 and STAR-CCM+ University of IllinoisChampaign IL USA 2011

[4] J Yan B Kochunas M Hursin T Downar Z Karoutas andE Baglietto ldquoCoupled computational fluid dynamics andMOCneutronic simulations of Westinghouse PWR fuel assemblieswith grid spacersrdquo in Proceedings of the 14th InternationalTopical Meeting on Nuclear Reactor Germalhydraulics(NURETH-14) Toronto Canada September 2011

[5] J E Hoogenboom A Ivanov V Sanchez and C Diop ldquoAflexible coupling scheme for Monte Carlo and thermal-hy-draulics codesrdquo in Proceedings of the International Conferenceon Mathematics and Computational Methods Applied toNuclear Science And Engineering Rio de Janeiro Brazil May2011

[6] B L Sjenitzer J E Hoogenboom J Jimenez Escalante andV Sanchez Espinoza ldquoCoupling of dynamicMonte Carlo withthermal-hydraulic feedbackrdquo Annals of Nuclear Energyvol 76 pp 27ndash39 2015

[7] A M Ward M J Wang M D Neumann M MemmottA Manera and T J Downar ldquoA simulation of I2S-LWRselected transientsrdquo Annals of Nuclear Energy vol 145 2020

[8] H Zhang J Guo J Lu F Li Y Xu and T J Downar ldquoAnassessment of coupling algorithms in HTR simulator TINTErdquoNuclear Science and Engineering vol 190 no 3 pp 287ndash3092018

[9] W X Tian S Z Qiu Y Guo G H Su and D N JialdquoDevelopment of a thermal-hydraulic analysis code forCARRrdquo Annals of Nuclear Energy vol 32 no 3 pp 261ndash2792005

[10] D X Gong S F Huang G B Wang and K Wang ldquoHeattransfer calculation on plate-type fuel assembly of high fluxresearch reactorrdquo Science and Technology of Nuclear Instal-lations vol 2015 Article ID 198654 13 pages 2015

[11] Q Lu S Qiu and G H Su ldquoDevelopment of a thermal-hydraulic analysis code for research reactors with plate fuelsrdquoAnnals of Nuclear Energy vol 36 no 4 pp 433ndash447 2009

[12] A Bousbia-Salah H Benkharfia N KriangchaipornA Petruzzi F DrsquoAuria and N Ghazi ldquoMTR benchmark staticcalculations with MCNP5 coderdquo Annals of Nuclear Energyvol 35 no 5 pp 845ndash855 2008

[13] N Xoubi S A Darda A Y Soliman and T Abulfaraj ldquoAninvestigative study of enrichment reduction impact on theneutron flux in the in-core flux-trap facility of MTR researchreactorsrdquo Nuclear Engineering and Technology vol 52 2020

[14] H Ju M Wang C Chen et al ldquoNumerical study on theturbulent mixing in channel with Large Eddy Simulation(LES) using spectral element methodrdquo Nuclear Engineeringand Design vol 348 pp 169ndash176 2019

[15] V H Kaarle and M Weeratunge An Introduction to Com-putational Fluid Dynamics Ge Finite Volume MethodPearson Education London UK 2007

[16] X Zhao M Wang C Chen et al ldquoree-dimensional studyon the hydraulic characteristics under the steam generator(SG) tube plugging operations for AP1000rdquo Progress in Nu-clear Energy vol 112 pp 63ndash74 2019

[17] A M Zhang and Y L Kang ldquoDesign of U3Si2-Al plate-typefuel element for China advanced research reactorrdquo in Pro-ceedings Of the 18th International Conference On NuclearEngineering (ICONE18) Xirsquoan China May 2010

[18] L Li D Fang D Zhang et al ldquoFlow and heat transfercharacteristics in plate-type fuel channels after formation ofblisters on fuel elementsrdquo Annals of Nuclear Energy vol 134pp 284ndash298 2019


3times 3 model and obtained high-fidelity results of coolanttemperature and density fuel temperature and power distri-bution successfully demonstrating the coupling effects [3] Yanet al coupled STAR-CCM+ and deterministic codeDeCARTtocalculate PWR 3times 3 model with new mesh mapping methods[4] Hoogenboom et al built a flexible thermal hydraulic andneutronics coupling scheme with Python [5] Sjenitzer et alproposed a new method to perform transient coupling withMonte Carlo code [6] Ward et al used coupled system codeRELAP5 and 3D spatial kinetics code PARCS to simulate safetyperformance of the I2S-LWR plant during accident conditions[7] e thermal hydraulic and neutronics coupling algorithmin transient problems for the high-temperature gas-cooledreactor simulator TINTE was evaluated and developed [8]Results indicated that the proposed coupling algorithms Picardand JFNKwere better compared with the original semi-implicitcoupling algorithm in TINTE

In terms of plate type fuel reactor core analysis Tian et aldeveloped a thermal hydraulic analysis code for China Ad-vanced Research Reactor (CARR) e heat transfer and flowdistribution characteristics in the reactor core were studied[9] Gong et al found that all fuel and cladding temperatureswere below the design limits and remained safe with the inletvelocity ranging from 45ms to 75ms for the hottest as-sembly in 20MWplate type fuel reactor [10] Lu et al analyzedthe blockage accident of one assembly channel in 10MWplatetype fuel reactor and the results showed that the obstructedchannel causes temperature rise in adjacent channels Inaddition it was found that there was no boiling in obstructedchannel except for the hot channel because of lateral heatconduction of adjacent channels [11] Bousbia-Salah et alcalculated the neutron flux and power distribution of 10MWMTR usingMCNP5 code and it showed that theMCNP5 wasreliable for the plate type fuel core simulation and the cal-culation results were in good agreement with previous study[12] Xoubi et al investigated the impact of enrichment onneutron flux in the in-core facility of 10MW MTR withOpenMC and found the importance of flux trap calculationwhile considering the conversion of reactor core fromHEU toLEU [13] It also demonstrated the feasibility of the MonteCarlo method in analyzing plate type fuel reactor

It can be seen that most of the thermal hydraulic andneutronics coupling studies are performed for PWR rodbundle type fuel in the literatures while the couplinganalysis on plate type fuel reactor core is rare erefore aninnovative thermal hydraulic and neutronics couplingmethod was proposed based on the Fluent andMonte Carlocode through the UDF module for the plate type fuel re-actor core in this paper A typical plate type fuel assemblywas analyzed with the coupling code and the thermalhydraulic and neutronics features were studied and ana-lyzed in detail

2 Mathematic Model

e CFD method is widely utilized in the nuclear reactorthermal hydraulic analysis currently especially for the localdetailed three-dimensional flow and heat transfer processsuch as the coolant mixing in the reactor core [14] e basic

of CFD method is the fundamental governing equations offluid dynamics including the mass momentum and energyconservation equations For single-phase flow the mass andmomentum equations are given as follows

1p

zρzt

+ nabla middot u 0

ρDu

Dt ρF + nabla middot σ

(1)

where the u is the velocity ρ is the density F is the body forceper unit of fluid mass and σ is the stress tensor

For incompressible Newtonian fluid the NavierndashStokesequations are given as follows

nabla middot u 0 (2)

ρzρzt

+ u middot nablau1113888 1113889 ρF minus nabla middot p + nabla2u (3)

ρcP

zT

zt+ u middot nablau1113888 1113889 nabla middot (λnablaT) + q

rsquoprimersquo + ϕ (4)

where the T is temperature p is pressure cp is the specifichear capacity at constant pressure λ is thermal conductivityqrsquoprimersquo is volumetric heat source and ϕ is the dissipationfunction For the steady calculation in the paper the timederivative term is eliminated

For solid domains like fuel and cladding heat con-duction equation can be simplified from equation (4) asfollows

ρcP

zT

zt nabla middot (λnablaT) + q

rsquoprimersquo (5)

For fuel the volumetric heat source is fission heat or theheat generated by c-rays in cladding In this paper the heatin cladding is ignored and q

rsquoprimersquo is zero in cladding domaine direct numerical solution (DNS) method directly

solves NavierndashStokes equations and huge computing cost isrequired to simulate turbulence effect which is unfavorablein reactor scale simulation e computing cost could bedecreased by applying turbulence models For steady-statesimulation the Reynolds-averaged NavierndashStokes-based(RANS-based) models which describe time-averaged mo-tion of fluid flow are widely used in the engineering fieldse typical RANS-based models include the Reynolds stressmodel (RSM) and the models that introduce eddy viscosityhypothesis such as the k-ε model and k-ω model estandard k-ε model is the most common turbulence modelused in CFD and its equation is described below as anexample of RANS-based model [15]

ρDk

Dt

z

zxi

u +ut

σk

1113888 1113889zk

zxi

1113890 1113891 + Gk + Gb minus ρε

ρDεDt

z

zxi

u +ut

σε1113888 1113889

zεzxi

1113890 1113891 + C1εεk

Gk + C2εGb( 1113857 minus C2ερε2

k

(6)





3 Coupling Method




qvi PDi


(7)




Solve RANS

CFD converged


density


libraries



keff converged

Yes

No

Coupling done

No

Yes




fL

TH

1113968minus

T

radic

TH

1113968minus

TL

1113968


(8)





Flow direction

FluidSolidNone

(a)74

76

616708

Coolant channel

22

06

136

(b)







3

(9)


2 (10)


2


3

(11)

















Dev

iatio

n


00000

00005

00010

00015

00020

00025

00030

77616 95256 15699642336Number of meshes




Cool

ant t

empe

ratu

re (K

)


305

310

315

320

325

330

335

02 04 06 08 1000Z (m)

(a)


Pres

sure

(Pa)

0

50000

100000

150000

200000

02 04 06 08 1000Z (m)

(b)


















Reac

tivity

Δkk

0370

0372

0374



Reac

tivity

Δkk

0368

0370

0372

0374

320 340 360 380 400300Temperature (K)


keffΔP

1585

1590

1595

1600

k eff

107900

107905

107910

107915

107920

107925

107930

107935

107940

ΔP

2 4 60Iteration




(a)



(b)










00 02 04 06 08 10000E + 000

540E + 009

108E + 010

162E + 010

216E + 010


Pow

er d

ensit

y (W

middotmndash3

)

Z (m)

ndash500E + 008

000E + 000

500E + 008


Pow

er d

evia

tion

aer

coup

ling

(Wmiddotm

ndash3)


z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(a)

z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(b)



CoolantCladdingFuel


Tem

pera

ture

(K)

300320340360380400420440460480500520540

02225 04450 06675 0890000000Z (m)


Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2Kndash1

)


30000

32000

34000

36000

38000

40000

42000

44000

02 04 06 08 1000Z (m)


(a) (b) (c)




430004239041780411704056039950393403873038120375103690036290356803507034460338503324032630320203141030800

[k]



Y

XZ[k]


378493749637144367623643936087357343538235029346773432433972336203326732915325623221031857315053115230800


Tem

pera

ture

(K)


335340345350355360365370375380

ndash002 000 002 004ndash004y (m)




5 Conclusion


Data Availability



Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)






Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal



Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)





Acknowledgments


References























3 Coupling Method




qvi PDi


(7)




Solve RANS

CFD converged


density


libraries



keff converged

Yes

No

Coupling done

No

Yes




fL

TH

1113968minus

T

radic

TH

1113968minus

TL

1113968


(8)





Flow direction

FluidSolidNone

(a)74

76

616708

Coolant channel

22

06

136

(b)







3

(9)


2 (10)


2


3

(11)

















Dev

iatio

n


00000

00005

00010

00015

00020

00025

00030

77616 95256 15699642336Number of meshes




Cool

ant t

empe

ratu

re (K

)


305

310

315

320

325

330

335

02 04 06 08 1000Z (m)

(a)


Pres

sure

(Pa)

0

50000

100000

150000

200000

02 04 06 08 1000Z (m)

(b)


















Reac

tivity

Δkk

0370

0372

0374



Reac

tivity

Δkk

0368

0370

0372

0374

320 340 360 380 400300Temperature (K)


keffΔP

1585

1590

1595

1600

k eff

107900

107905

107910

107915

107920

107925

107930

107935

107940

ΔP

2 4 60Iteration




(a)



(b)










00 02 04 06 08 10000E + 000

540E + 009

108E + 010

162E + 010

216E + 010


Pow

er d

ensit

y (W

middotmndash3

)

Z (m)

ndash500E + 008

000E + 000

500E + 008


Pow

er d

evia

tion

aer

coup

ling

(Wmiddotm

ndash3)


z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(a)

z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(b)



CoolantCladdingFuel


Tem

pera

ture

(K)

300320340360380400420440460480500520540

02225 04450 06675 0890000000Z (m)


Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2Kndash1

)


30000

32000

34000

36000

38000

40000

42000

44000

02 04 06 08 1000Z (m)


(a) (b) (c)




430004239041780411704056039950393403873038120375103690036290356803507034460338503324032630320203141030800

[k]



Y

XZ[k]


378493749637144367623643936087357343538235029346773432433972336203326732915325623221031857315053115230800


Tem

pera

ture

(K)


335340345350355360365370375380

ndash002 000 002 004ndash004y (m)




5 Conclusion


Data Availability



Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)






Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal



Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)





Acknowledgments


References





















fL

TH

1113968minus

T

radic

TH

1113968minus

TL

1113968


(8)





Flow direction

FluidSolidNone

(a)74

76

616708

Coolant channel

22

06

136

(b)







3

(9)


2 (10)


2


3

(11)

















Dev

iatio

n


00000

00005

00010

00015

00020

00025

00030

77616 95256 15699642336Number of meshes




Cool

ant t

empe

ratu

re (K

)


305

310

315

320

325

330

335

02 04 06 08 1000Z (m)

(a)


Pres

sure

(Pa)

0

50000

100000

150000

200000

02 04 06 08 1000Z (m)

(b)


















Reac

tivity

Δkk

0370

0372

0374



Reac

tivity

Δkk

0368

0370

0372

0374

320 340 360 380 400300Temperature (K)


keffΔP

1585

1590

1595

1600

k eff

107900

107905

107910

107915

107920

107925

107930

107935

107940

ΔP

2 4 60Iteration




(a)



(b)










00 02 04 06 08 10000E + 000

540E + 009

108E + 010

162E + 010

216E + 010


Pow

er d

ensit

y (W

middotmndash3

)

Z (m)

ndash500E + 008

000E + 000

500E + 008


Pow

er d

evia

tion

aer

coup

ling

(Wmiddotm

ndash3)


z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(a)

z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(b)



CoolantCladdingFuel


Tem

pera

ture

(K)

300320340360380400420440460480500520540

02225 04450 06675 0890000000Z (m)


Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2Kndash1

)


30000

32000

34000

36000

38000

40000

42000

44000

02 04 06 08 1000Z (m)


(a) (b) (c)




430004239041780411704056039950393403873038120375103690036290356803507034460338503324032630320203141030800

[k]



Y

XZ[k]


378493749637144367623643936087357343538235029346773432433972336203326732915325623221031857315053115230800


Tem

pera

ture

(K)


335340345350355360365370375380

ndash002 000 002 004ndash004y (m)




5 Conclusion


Data Availability



Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)






Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal



Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)





Acknowledgments


References






















3

(9)


2 (10)


2


3

(11)

















Dev

iatio

n


00000

00005

00010

00015

00020

00025

00030

77616 95256 15699642336Number of meshes




Cool

ant t

empe

ratu

re (K

)


305

310

315

320

325

330

335

02 04 06 08 1000Z (m)

(a)


Pres

sure

(Pa)

0

50000

100000

150000

200000

02 04 06 08 1000Z (m)

(b)


















Reac

tivity

Δkk

0370

0372

0374



Reac

tivity

Δkk

0368

0370

0372

0374

320 340 360 380 400300Temperature (K)


keffΔP

1585

1590

1595

1600

k eff

107900

107905

107910

107915

107920

107925

107930

107935

107940

ΔP

2 4 60Iteration




(a)



(b)










00 02 04 06 08 10000E + 000

540E + 009

108E + 010

162E + 010

216E + 010


Pow

er d

ensit

y (W

middotmndash3

)

Z (m)

ndash500E + 008

000E + 000

500E + 008


Pow

er d

evia

tion

aer

coup

ling

(Wmiddotm

ndash3)


z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(a)

z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(b)



CoolantCladdingFuel


Tem

pera

ture

(K)

300320340360380400420440460480500520540

02225 04450 06675 0890000000Z (m)


Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2Kndash1

)


30000

32000

34000

36000

38000

40000

42000

44000

02 04 06 08 1000Z (m)


(a) (b) (c)




430004239041780411704056039950393403873038120375103690036290356803507034460338503324032630320203141030800

[k]



Y

XZ[k]


378493749637144367623643936087357343538235029346773432433972336203326732915325623221031857315053115230800


Tem

pera

ture

(K)


335340345350355360365370375380

ndash002 000 002 004ndash004y (m)




5 Conclusion


Data Availability



Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)






Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal



Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)





Acknowledgments


References





















Cool

ant t

empe

ratu

re (K

)


305

310

315

320

325

330

335

02 04 06 08 1000Z (m)

(a)


Pres

sure

(Pa)

0

50000

100000

150000

200000

02 04 06 08 1000Z (m)

(b)


















Reac

tivity

Δkk

0370

0372

0374



Reac

tivity

Δkk

0368

0370

0372

0374

320 340 360 380 400300Temperature (K)


keffΔP

1585

1590

1595

1600

k eff

107900

107905

107910

107915

107920

107925

107930

107935

107940

ΔP

2 4 60Iteration




(a)



(b)










00 02 04 06 08 10000E + 000

540E + 009

108E + 010

162E + 010

216E + 010


Pow

er d

ensit

y (W

middotmndash3

)

Z (m)

ndash500E + 008

000E + 000

500E + 008


Pow

er d

evia

tion

aer

coup

ling

(Wmiddotm

ndash3)


z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(a)

z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(b)



CoolantCladdingFuel


Tem

pera

ture

(K)

300320340360380400420440460480500520540

02225 04450 06675 0890000000Z (m)


Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2Kndash1

)


30000

32000

34000

36000

38000

40000

42000

44000

02 04 06 08 1000Z (m)


(a) (b) (c)




430004239041780411704056039950393403873038120375103690036290356803507034460338503324032630320203141030800

[k]



Y

XZ[k]


378493749637144367623643936087357343538235029346773432433972336203326732915325623221031857315053115230800


Tem

pera

ture

(K)


335340345350355360365370375380

ndash002 000 002 004ndash004y (m)




5 Conclusion


Data Availability



Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)






Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal



Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)





Acknowledgments


References

























Reac

tivity

Δkk

0370

0372

0374



Reac

tivity

Δkk

0368

0370

0372

0374

320 340 360 380 400300Temperature (K)


keffΔP

1585

1590

1595

1600

k eff

107900

107905

107910

107915

107920

107925

107930

107935

107940

ΔP

2 4 60Iteration




(a)



(b)










00 02 04 06 08 10000E + 000

540E + 009

108E + 010

162E + 010

216E + 010


Pow

er d

ensit

y (W

middotmndash3

)

Z (m)

ndash500E + 008

000E + 000

500E + 008


Pow

er d

evia

tion

aer

coup

ling

(Wmiddotm

ndash3)


z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(a)

z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(b)



CoolantCladdingFuel


Tem

pera

ture

(K)

300320340360380400420440460480500520540

02225 04450 06675 0890000000Z (m)


Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2Kndash1

)


30000

32000

34000

36000

38000

40000

42000

44000

02 04 06 08 1000Z (m)


(a) (b) (c)




430004239041780411704056039950393403873038120375103690036290356803507034460338503324032630320203141030800

[k]



Y

XZ[k]


378493749637144367623643936087357343538235029346773432433972336203326732915325623221031857315053115230800


Tem

pera

ture

(K)


335340345350355360365370375380

ndash002 000 002 004ndash004y (m)




5 Conclusion


Data Availability



Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)






Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal



Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)





Acknowledgments


References
























00 02 04 06 08 10000E + 000

540E + 009

108E + 010

162E + 010

216E + 010


Pow

er d

ensit

y (W

middotmndash3

)

Z (m)

ndash500E + 008

000E + 000

500E + 008


Pow

er d

evia

tion

aer

coup

ling

(Wmiddotm

ndash3)


z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(a)

z = 065m

[k]


405004001539530390453856038075375903710536620361353565035165346803419533710332253274032255317703128530800

(b)



CoolantCladdingFuel


Tem

pera

ture

(K)

300320340360380400420440460480500520540

02225 04450 06675 0890000000Z (m)


Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2Kndash1

)


30000

32000

34000

36000

38000

40000

42000

44000

02 04 06 08 1000Z (m)


(a) (b) (c)




430004239041780411704056039950393403873038120375103690036290356803507034460338503324032630320203141030800

[k]



Y

XZ[k]


378493749637144367623643936087357343538235029346773432433972336203326732915325623221031857315053115230800


Tem

pera

ture

(K)


335340345350355360365370375380

ndash002 000 002 004ndash004y (m)




5 Conclusion


Data Availability



Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)






Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal



Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)





Acknowledgments


References




















CoolantCladdingFuel


Tem

pera

ture

(K)

300320340360380400420440460480500520540

02225 04450 06675 0890000000Z (m)


Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2Kndash1

)


30000

32000

34000

36000

38000

40000

42000

44000

02 04 06 08 1000Z (m)


(a) (b) (c)




430004239041780411704056039950393403873038120375103690036290356803507034460338503324032630320203141030800

[k]



Y

XZ[k]


378493749637144367623643936087357343538235029346773432433972336203326732915325623221031857315053115230800


Tem

pera

ture

(K)


335340345350355360365370375380

ndash002 000 002 004ndash004y (m)




5 Conclusion


Data Availability



Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)






Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal



Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)





Acknowledgments


References





















430004239041780411704056039950393403873038120375103690036290356803507034460338503324032630320203141030800

[k]



Y

XZ[k]


378493749637144367623643936087357343538235029346773432433972336203326732915325623221031857315053115230800


Tem

pera

ture

(K)


335340345350355360365370375380

ndash002 000 002 004ndash004y (m)




5 Conclusion


Data Availability



Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)






Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal



Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)





Acknowledgments


References





















5 Conclusion


Data Availability



Tem

pera

ture

(K)

335340345350355360365370375380

ndash002 000 002 004ndash004x (m)






Tem

pera

ture

(K)

300

350

400

450

500

550

02 04 06 08 1000Z (m)

FuelCladdingCoolant

Normal



Blockage 3Normal

Hea

t tra

nsfe

r coe

ffici

ent (

Wmiddotm

ndash2middotK

ndash1)

20000

25000

30000

35000

40000

45000

50000

55000

02 04 06 08 1000Z (m)





Acknowledgments


References






















Acknowledgments


References




















Documents

Thermal Hydraulic and Neutronics Coupling Analysis for Plate …downloads.hindawi.com/journals/stni/2020/2562747.pdf · 2020. 8. 28. · ResearchArticle Thermal Hydraulic and Neutronics