A Combined Method for Predicting the Boron Deposited Mass ...ScienceandTechnologyofNuclearInstallations Relative Power Factor 0.8 0.6 0.4 0.2 0 No Crud Layer hin Crud Layer hick Crud

Research ArticleA Combined Method for Predicting the Boron Deposited Massand the CIPS Risk

Shengzhe Li Dongmei Yang Tengfei Zhang and Xiaojing Liu

School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China

Correspondence should be addressed to Xiaojing Liu xiaojingliusjtueducn

Received 26 December 2018 Accepted 12 February 2019 Published 26 March 2019

Academic Editor Arkady Serikov

Copyright copy 2019 Shengzhe Li et al This 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

CIPS is a shift in the axial power towards the bottom half of the core also known as axial offset anomaly (AOA) which resultsfrom the deposited of corrosion products during an operation The main reason of CIPS is the solute particles especially boroncompounds concentrated inside the porous deposit The impact of CIPS is that the axial power distribution control may be moredifficult and the shutdown margin can be decreased simultaneously Besides it also requires estimated critical condition (ECC)calculations to account for the effects of AOA In this article thermal-hydraulic subchannel code and boron deposit model havebeen combined to analyze the CIPS risk The neutronics codes deal with the generation of homogenized neutron cross section aswell as the calculation of local power factor A simple rod assembly is analyzed with this combined method and simulation resultsare presented Simulation results provide the boron hideout amount inside crud deposits and power shapes The obtained resultsclearly show the power shape suppression in regions where crud deposits exist which is a clear indication of CIPS phenomenonAnd the CIPS effects on CHF have also been investigated Result shows a margin of DNBR decrease in the crud case

1 Introduction

It is universally acknowledged that axial offset anomaly(AOA) also known as crud induced power shift (CIPS) cansuppress the neutron flux at the upper half of the core Themost famous AOA occurred in the late 1990s when Callawayexperienced a severe AOA during Cycle 9 [1] In order torecover shutdown margin Callaway had to reduce its powerto 70 Itmust be noted that AOA results from a combinationof multiple physical phenomena One of the main reasonsis crud which is referred to be the deposition of corrosionproducts onto fuel cladding releasing from reactor coolantsystem surfaces The porous crud is formed as a consequenceof sub-cooled nucleate boiling (SNB) in the upper part of theassemblies As the deposits are formed boron concentrateswithin the crud while SNB is proceeding Because a largeamount of boron accumulates in the crud layer the axialpower distribution of nuclear core shift due to boron-10 has ahigh absorption cross section Hence neutron flux and theburnup peaking factor shift from top half to bottom halfInterestingly near the end of cycle (EOC) excess burnup inthe bottom of the core and reduced boron concentration in

the primary system cause the power shape shift to reversepartially restoring the burnup distribution The appearanceof CIPS makes the control of power distribution especiallyaxial more difficult Therefore under the background of theobjective of prolonged core life as well as the improvement ofNPPrsquos safety and economy it is essential to assess the CIPSrisk of the core

The CIPS phenomenon involves the thermal hydraulicthe formation and deposition of crud boron advectionand diffusion inside crud deposits and neutron transportBoth the single mechanism and the coupling effects shouldbe understood to perform a reasonable CIPS predictionThe relationship between evaporation and deposition hasbeen studied in the past years presenting the experimentalevidences of deposits formed during boiling [2 3] Theprocess of heat and mass transfer within crud deposits is aself-multi-physics mechanism including a special capillary-derived boiling phenomenon which is referred to as wick-boiling [4] Water is absorbed into the deposit by capillarysuction evaporates into steam at the ldquomouthrdquo of the chimneyand finally disappears in the coolant as steam bubbles Uponthe recent years researchers have built upon this concept and

HindawiScience and Technology of Nuclear InstallationsVolume 2019 Article ID 9537421 8 pageshttpsdoiorg10115520199537421

2 Science and Technology of Nuclear Installations

developed it into different crud calculation models [5ndash11] Inthe experimental research scientists observed the fractallineproperties of PWR fuel crud [12] and then found that asystematic theory of fractal porous media [13] can be used torefine some parameters and assumptions in the crud model

Simulations between crud deposition models andthermal-hydraulic codes have also been investigated suchas the coupled solution between STAR-CCM+ and the crudmodel [14] the coupled simulation between COBRA-IV andthe crud model [15] and the coupled calculation betweenCTF and the crud model which models deposits growtherosion and thermal feedback [16] In nuclear simulatedcircumstances the neutronics and thermal-hydraulicscoupling are the most classical combination to resolve corephysical phenomena By adding the crud prediction modelmulti-coupling the simulation between STAR-CCM+ crudmodel and neutronics code DeCART is also investigated[17ndash19] In fact although STAR-CCM+ is a very powerfulCFD tool it is still time-consuming whereas subchannelcodes are much more economical and acceptable for CIPSrisk assessment and prediction BOA 30 [20] a tool for CIPSrisk assessment [21] which is codeveloped by WestinghouseElectric Company and the Electric Power Research Institute(EPRI) adopted the VIPRE-01 [22] subchannel code as thethermal hydraulic code

The effort of this paper is to implement the crud andthermal hydraulic subchannel code together to simulateboron-accumulated amount along the assembly The boroninventory can act as an input to the neutronics code whichcould offer the power shape distribution along the assemblyIn the following section the combined methodology ispresented in detail The methodology consists of three partsa boron deposit model based on Cohenrsquos model [5] thesubchannel code COBRA-IV which is a sophisticated codefor reactor core simulation and the neutronics calculationcodesDRAGON[23] and SKETCH-N [24] Section 3 demon-strates the simulation results and shows the CIPS effect ona 3times3 fuel pin assembly Additionally the effect of variouscrud thicknesses is discussed And the effects on CHF aresimulated and discussed Section 4 concludes this paper

2 Methodology

21 Overview of the Framework The present methodology inthis paper provides a combined framework for modeling theCIPS phenomenon This framework includes three modules(TH crud and neutron) and the simulation is processed insequence Firstly an initial power distribution along axial fuelpin is calculated in the SKETCH-N code In this stage thefuel pellets are arranged uniformly along the axial height So acosine-shape power distribution can be solved and the powerfactor at each axial node is known This power distributionshape is up-down symmetric and is also used for valuing thepower shift at the end of stage Secondly coupled calculationbetween the thermal-hydraulic code and the crud modelbegins While COBRA-IV code sweeping is at the axial levelchannel sweeping and rod sweeping are the subcycles of theaxial sweeping Fluid temperature is solved in the channelsweeping cycle and the deposit location is determined by

the SNB criterion in the rod sweeping cycle If the criterionindicates the sign of deposit the crud module solves theboron deposit amount on the local nodal Lastly the neutronabsorption cross section is solved in the DRAGON code andthen axial power distribution shape can be solved in theSKETCH-N code The power shape diagram can be plottedwhich could be regarded as an indication of CIPS risk Thiscalculation sequence is shown in Figure 1

Due to the difference in solution meshes the thermalhydraulic results are channel-centered while the crud solu-tion domain is rod-centered Because the rod sweeping cycleactivates after the channel sweeping cycle it is important toapproximate the spatial transform from COBRA-IV code tothe crud model Here volume-averaged density and mass-weighted temperature of the surrounding channels (north-west northeast southwest southeast) are used as coolantinformation for crud model simulation The schematic dia-gram is shown in Figure 2

22 Module Descriptions In the present work the subchan-nel analysis code COBRA-IV is chosen for the thermal-hydraulic analysis The main objective of this module is tocalculate the fluid temperature and the cladding temperatureThe fluid temperature serves as the simulating boundaryof the crud model whereas the cladding temperature iscalculated to identify the subcooled nucleate boiling regionThis paper proposes a conservative assumption that crud willonly occur in the SNB locations Corrosion products sourcefrom corrosion surfaces or from previously deposited crudback to the bulk coolant The deposition rate of the crudcaused by SNB is much higher than the nonboiling surfacesand it is assumed that the deposits have uniform thicknessin the SNB region because this framework does not includedeposited dynamics for now

The subchannel code COBRA-IV uses Levy model [25]to calculate the subcooled void fraction and then predictsthe outer cladding temperature and the local heat transfercoefficient by Thom correlation [26] (see (1)) The subcoolednucleate boiling occurs when the predicted outer claddingtemperature is just above the saturated temperature TheThom correlation is suitable for up to about 20MPa underconditions where the nucleate boiling contribution domainsover forced convection The correlation is used for estimatetemperature difference when the local heat flux is given

119879119904119886119905 = 225 ∙ 11990205 exp (minus 11987587) (1)

where 119879119904119886119905 is the wall temperature elevation above thesaturation temperature K q isthe heat flux MWm2 and Pis the pressure of water MPa

It is assumed that the soluble metal ions only exist inliquid phase so if bubbles evaporate from the surface of fuelpin solute particles will precipitate and then coat on theboiling surfaceThedeposit has specialmorphologyThe areaalways filled with vapor during wick boiling phenomenais called chimney Microscopic exanimation of the depositsshows the existence of steam chimneys The chimneys areacross the deposit thickness orientation and point toward the

Science and Technology of Nuclear Installations 3

Start

Fuel Power Factor

Cladding Temperature Calculation

T_cgtT_sat

Boron Deposit Calculation

The original power distributionis provided by SKETCH-N

Axial Sweeping

SNB == true

SNB == falseCross-section Calculation

Channel Sweeping

Fluid Temperature Calculation

Rod Sweeping

Finish

Power Shape Crud-coolantheat transfercoefficient h

COBRA-IV

crud module

DRAGON

SKETCH-N

Figure 1 Calculation sequence for CIPS prediction

Figure 2 Schematic diagram of the TH crud modules transforming volume averaged COBRA-IV channel information for crud modelcalculation

coolant Crud can grow to 10-100120583m thick with the averagepore size rangingwithin 01-1120583m porosity range 40-50 [27]The chimney population represents the number of chimneyspermm2 2000-5000 typically and eachwith a diameter of 2-6120583m

The model used in this study calculates temperature andboron species concentration distributions in the crud depositThe simulation unit cell consists of one steam chimney and itssurrounding porous shell Heat transfer is assumed to occurin the porous shell media Conduction and convection takeplace in the medium while evaporation and condensationoccur at the chimney boundary Flow of liquid is modeled as

diffusive flowwhile velocities are related to pressure gradientsaccording to Darcyrsquos law

119906 = minus120581120583998810119875 (2)

where 119906 is the Darcy velocity ms 120581 is permeability the heatflux MWm2 120583 is dynamic viscosity Pasdots and 998810P is thepressure gradient vector of water Pam

And solute species are modeled by equilibrium betweenadvective current and diffusive current

119869 = minus119863nabla119862 + 119906119862 (3)


R

Z

CRUD

Symmetry

Coolant

Chimney

CLAD q

core radius

Thickness

CRUD radius

Fuel rod clad

Liquid flow (containing solutes)

Vapor flow

Steam chimney

Figure 3 Chimney-centred wick boiling sketmatic (a) a diagram of boundarys (b) a diagram of heat transfer process

where 119869 is the net solute flux 119863 is diffusive coefficient m2sand C is boron concentration moldm3

A schematic diagram is shown in Figure 3 display-ing a two-dimensional cylindrical simulation unit and itsboundaries The above equations are discreted by upwinddifferencing finite-volume approach and iteratively solveduntil convergence Temperature and pressure fields are solvedseparately and the results affect the concentration solutionsThe solution process is couple-solved This iteratively solvedmodel is introduced by Haq et al [6] and Short et al [11] andhas been reproduced by Li and Liu [15]

Obviously deposit layer is established between fuel pincladding and coolantTherefore there are two nature bound-aries of a single simulation unit which are referred to ascoolant boundary and cladding boundary The boundaryconditions vary among different rods and various coolantconditions such as rod powers at different rods and axial lev-els or coolant temperatures and concentrations in differentchannels and various rod-coolant heat transfer coefficientIt should be noted that the origin COBRA-IV missed theboron transport calculation ability In our previous research[28] the boron transport simulation capacity has beenimplemented in the COBRA-IV code After the bound-aries are all determined boron hideout amount of anyrodassembly could be calculatedThe boron hideout amountis proportional to deposit thickness local heat flux bulkconcentration and some porous characters due to somesensitive researches [9 15 29]

Theprecipitation of lithiummetaborate1198711198941198611198742 in the crudlayer is considered to be a root cause of CIPSThe equilibriumequation of this reaction is [7]

1198711198941198611198742 (119904) + 1198672119874 +119867+ 999445999468 119871119894+ + 119861 (119874119867)3 (4)

The neutron-kinetics codes DRAGON and SKETCH-Nare selected as the neutron solver for the neutron-physicalcalculation In order to calculate neutron cross sections itis necessary to identify the compositions in the deposit Themajority compositions in the crud solid structure are Fe3O4

Figure 4 Top view schematic drawing of the 9-rod geometry

NiO NiFe2O4 and ZrO2 [27] Both water and concentratedsolutes are in the pore region After providing the compositedelement the DRAGON code would interpolate the absorp-tion cross section which is supplied by standard librariesThecross sections of the crud layer are divided into seven groupsand each group correspond to a range of energy Finally theSKETCH-N module would use these cross sections to printthe shifted power shape diagram

3 Numerical Results

In this section a 3times3 fuel rods assembly with square latticeis solved under this combined method and the results arepresented A top view of the assembly geometry is schemedin Figure 4 Typical geometry parameters are listed in Table 1Due to the symmetric geometry of the assembly one-eighthof the assembly can represent the flow and heat transfer fieldof the whole assembly Channel can be identified as cornerside and center channel respectively

As the COBRA-IV input the 36576mm-height fuel rod isdivided into 36 equal axial levels each with 1016mm heightChannel exit pressure is set equal to 155Mpa and inlet mass


Table 1 Fuel rod specification [30]

Input ValueInner clad diameter 836mmOuter clad diameter 95mmRod pitch 126mmFuel stack height 36576mmPellet material UO2Clad material Zircaloy-4

Table 2 Volume fractions of crud solid structure assumed in thisstudy [11]

Materials Volume fractionNiO 015Fe3O4 010NiFe2O4 075

velocity is 3600kg(m2∙s) with a temperature of 270∘C (54315K) A cosine shape axial power distribution with the averageheat flux value of 1000kwm2 is used In addition the coolantboron concentration is set equal to 1200ppm

According to the preceding part of the content someparameters should be determined as the input of the crud cal-culation module First uniform deposit thickness is assumedat each location where SNB takes place Then the statisticalmajority number [27] the porosity is set equal to 06chimney population is set to 2000 per square millimeterchimney diameter is set to 4 120583m and the other porousmedium character values are calculated based on fractallineporous medium concept In order to compare differentdeposit thickness effects on boron hideout inventory twocases are calculated in this work one case with the thicknessof 30 120583m representing thin deposit and the other case withthe thickness of 50 120583m representing a thick one

The corrosion source in primary system mainly comesfrom SG tubes Crud solid almost consists of nickel iron andthere oxide Table 2 shows the volume fractions of crud solidwhich are assumed in this study Crud is mainly composed ofnickel ferrate whose density varies slightly with temperatureAt 600k the density is 39 gcm3 [31] Each compoundelement in the crud and the boron amount is transferred intomass fraction A pin geometry with crud layer which is also aschematic drawing for SKETCH-N is shown in Figure 5Thegeometry is the same as the thermal hydraulic input Becauseof the radial symmetry of the component the fuel assemblyis treated as a fuel pin with crud and coolant layer around itThe axial active zone is of 36576mm-height and it is dividedinto 18 levels Reflect boundary layers are arranged at both thetop and the bottom of the fuel pin

31 SNB Region and Boron Hideout Amount After com-pletely sweeping the axial levels along the fuel assemblythe calculation of combined TH-crud module is finishedBoron hideout mass along the assembly is figured out It isfound that boron inventory distributes relative uniform in theradial direction due to the high symmetric of fuel pin the

crud

Figure 5 Schematic drawing of crud position

1

08

06

04

02

00 2 4 6 8 10

(mgm)Liner Boron Hideout Density

Thin Crud LayerThick Crud Layer

Rela

tive A

xial

Lev

el(x

Ｒ0)

Figure 6 Boron hideout amount along assembly

axial distribution is more uniformThe axially boron hideoutmass result is drawn in Figure 6 This figure also indicatesthe locations where SNB takes place SNB takes place fromthe middle upper part of the assembly and ends before thechannel exit The SNB could not be maintained at the end ofchannel because of the decreased local heat flux

32 CIPS Prediction and AO Value The axial power dis-tribution shown in Figure 7 indicates a signal of CIPSphenomenon Local power reduces as a result of neutron fluxsuppression Also because of the power constant in the wholereactor the suppression of power in the crud pin region leadsto an increased power at the nondeposit region Therefore


Relative Power Factor

08

06

04

02

0

No Crud LayerThin Crud LayerThick Crud Layer

0 05 1

1

15 2

Rela

tive A

xial

leve

l(x

Ｒ0)

Figure 7 Axial power shift indicates the CIPS

it results in a downward shift in the axial power distributionMoreover it can be found that thick crudwill bringmore axialpower shift than thin crud

The axial offset anomaly value is defined byWestinghouseCompany [1] AO difference indicates the power differencebetween top half and bottom half of core

119860119874 = 119875119905119900119901 minus 119875119887119900119905119905119900119898119875119905119900119901 + 119875119887119900119905119905119900119898 (5)

where119875119905119900119901 is power integration for the top half of the core and119875119887119900119905119905119900119898 is power integration for the bottom half of the coreIf AO is negative power shift will occur in the core The

AO differences can indicate AOA levels of the power plantThese levels can be divided into ldquomoderate AOArdquo with adifference of -5 and ldquosevere AOArdquo with a difference of -10 In this simulated case AO value is equal to -104 forthin crud and -148 for thick crud Both of them achieve theldquosevere AOArdquo difference Typically core design has sufficientexcess shutdownmargin to come out against moderate AOAhowever severe AOA may treat the full power operation ofthe plant

33 CIPS Effects on CHF The shifted axial power shape willnot only change the heat source along the rod but alsoaffect the thermal properties of the heat transfer mechanismSubchannel codes are always adopted to calculate the critical

50

40

30

20

10

00 02 04 06 08 1

Relative Axial levelNo Crud LayerThin Crud LayerThick Crud Layer

(ＲＲ0)

DN

BR W

3-co

rrel

atio

n

Figure 8 The DNBR distribution along the assembly


(ＲＲ0)

DN

BR W

3-co

rrel

atio

n

6

55

5

45

4

35

3

25

204 045 05 055 06 065 07 075 08 085

Figure 9 The DNBR distribution along the assembly (zoom in)

heat flux (CHF) in the reactor design The Westinghouse-3 (W-3) CHF correlation [32] is widely used for PWRconditions where departure from nucleate boiling (DNB) isthe dominant CHFmechanismThe departure from nucleateboiling ratio (DNBR) is a local value which varies along therod height The minimum value of the DNBR (MDNBR) isa significant parameter to identify the worst location and itsdangerous level In this section theDNBR are calculated bothin the normal cosine power shape and in the shifted cosinepower shape Different thickness effects are also considered

The results of the DNBR distribution along the assemblyare presented in Figures 8 and 9 Curves clearly show theMDNBR location is changed and the value is also decreasedin the shifted power cases In the ldquono crudrdquo case MDNBRoccurs at relative location of about 07 with the value of 332In the ldquothin crudrdquo case MDNBR occurs at relative location ofabout 064 with the value of 311 And in the ldquothick crudrdquo caseMDNBR occurs at relative location of about 061 with the


value of 30 The distribution trend of MDBNR is the same asthat of CIPS towards the bottom of the core And the thickerdeposit worsens this situation

4 Conclusion

In this study a combination of thermal-hydraulic crud andneutronics modules is described The aim of this frameworkis to predict the CIPS phenomena A 3times3 fuel pin assemblyis solved by this combined work and the axial power shapeis given The results clearly show the power is suppressedin the crud-existing region and rises in the normal regionwhich is a clear sign of axial power shift Thick crud inducesmore power shift than thin crud According to the AO valuedefinition the calculated case in this study achieves the severeAOA levelThe CHF calculation results show the CIPS effectson thermal-hydraulic design CIPS will cause the locationof MDNBR to change and reduces the margin Howeverthis combined work is based on several assumptions suchas equal thickness deposit in SNB region and neglecting theredistribution effect caused by spacer grid and mixing vaneAdvanced CHF correlation is also important because thesurface of crud is rough and hydrophilic Andmore efforts areneeded to improve the simulation ability especially validationand verification

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors have declared that no conflicts of interest exist

References

[1] J Deshon PWR Axial Offset Anomaly (AOA) Guidelines Revi-sion 1 EPRI Palo Alto CalifUSA 2004

[2] N B Hospeti and R B Mesler ldquoDeposits formed beneathbubbles during nucleate boiling of radioactive calcium sulfatesolutionsrdquo AIChE Journal vol 11 no 4 pp 662ndash665 1965

[3] E P Partridge and A H White ldquoMechanism of formation ofcalcium sulfate boiler scalerdquo Industrial amp Engineering Chem-istry vol 21 no 9 pp 834ndash838 1929

[4] R V Macbeth ldquoBoiling on surfaces overlayed with a porousdeposit heat transfer rates obtainable by capillary actionrdquoAtomic Energy Establishment AEEW-Rndash711 Winfrith Eng-land 1971

[5] P Cohen ldquoHeat andmass transfer for boiling in porous depositswith chimneysrdquo in Proceedings of the in AICHE Symposiumseries 70 pp 71ndash80 American Institute of Chemical Engineers1974

[6] I U Haq N Cinosi M Bluck G Hewitt and S WalkerldquoModelling heat transfer and dissolved species concentrationswithin PWR crudrdquoNuclear Engineering andDesign vol 241 no1 pp 155ndash162 2011

[7] J Henshaw J C McGurk H E Sims A Tuson S Dickinsonand J Deshon ldquoAmodel of chemistry and thermal hydraulics in

PWR fuel crud depositsrdquo Journal of Nuclear Materials vol 353no 1-2 pp 1ndash11 2006

[8] M Jin and M Short ldquoMultiphysics modeling of two-phasefilm boiling within porous corrosion depositsrdquo Journal ofComputational Physics vol 316 pp 504ndash518 2016

[9] C Pan B G Jones and A J Machiels ldquoConcentration levelsof solutes in porous deposits with chimneys under wick boilingconditionsrdquo Nuclear Engineering and Design vol 99 no C pp317ndash327 1987

[10] C Pan B G Jones and A J Machiels ldquoWick boiling perfor-mance in porous deposits with chimneysrdquo in Proceedings ofthe ASME National Heat Transfer Conference Symposium onMultiphase flow and Heat Transfer 1985

[11] M P Short D Hussey B K Kendrick T M Besmann C RStanek and S Yip ldquoMultiphysics modeling of porous CRUDdeposits in nuclear reactorsrdquo Journal of Nuclear Materials vol443 no 1-3 pp 579ndash587 2013

[12] I Dumnernchanvanit V K Mishra N Q Zhang et al ldquoThefractalline properties of experimentally simulated PWR fuelcrudrdquo Journal of Nuclear Materials vol 499 pp 294ndash300 2018

[13] B M Yu ldquoAnalysis of flow in fractal porous mediardquo AppliedMechanics Reviews vol 61 no 5 Article ID 050801 2008

[14] V Petrov B K Kendrick D Walter A Manera and J SeckerldquoPrediction of CRUD deposition on PWR fuel using a state-of-the-art CFD-based multi-physics computational toolrdquo NuclearEngineering and Design vol 299 pp 95ndash104 2016

[15] S Li and X Liu ldquoDevelopment of boron tracking andboron hideout (CRUD) model based on subchannel approachrdquoNuclear Engineering and Design vol 338 pp 166ndash175 2018

[16] R Salko et al ldquoDevelopment of COBRA-TF for modelingfull-core reactor operating cyclesrdquo Advances in Nuclear FuelManagement V (ANFM 2015) 2015

[17] D JWalter B K Kendrick V Petrov AManera B Collins andT Downar ldquoProof-of-principle of high-fidelity coupled CRUDdeposition and cycle depletion simulationrdquo Annals of NuclearEnergy vol 85 pp 1152ndash1166 2015

[18] D J Walter and A Manera ldquoCRUD boron and burnableabsorber layer 2-Dmodeling requirements usingMOCneutrontransportrdquo Annals of Nuclear Energy vol 87 pp 388ndash399 2016

[19] L Zou H Zhang J Gehin and B Kochunas ldquoCoupledthermal-hydraulicneutronicscrud framework in prediction ofcrud-induced power shift phenomenonrdquo Nuclear Technologyvol 183 no 3 pp 535ndash542 2013

[20] Boron-Induced Offset Anomaly Risk Assessment Tool Version 30EPRI Palo Alto Calif USA 2010

[21] J Deshon D Hussey B Kendrick J McGurk J Secker and MShort ldquoPressurized water reactor fuel crud and corrosion mod-elingrdquo JOM e Journal of e Minerals Metals amp MaterialsSociety (TMS) vol 63 no 8 pp 64ndash72 2011

[22] C W Stewart ldquoVIPRE-01 a thermal-hydraulic code for reactorcoresrdquo Tech Rep Electric Power Research Institute PacificNorthwest Laboratory Palo Alto Calif USA Richland Wash-ington USA

[23] G Marleau A Hebert and R Roy ldquoA user guide for DRAGON306rdquo Rep IGE-174 Rev 7 vol 7 2008

[24] V G Zimin SKETCH-N A Nodal Neutron Diffusion Codefor Solving Steady-State and Kinetics Problems JAERI ReportTokyo Japan 2011

[25] S Levy ldquoForced convection subcooled boiling-prediction ofvapor volumetric fractionrdquo International Journal of Heat andMass Transfer vol 10 no 7 pp 951ndash965 1967


[26] WM Rohsenow J P Hartnett and Y I ChoHandbook of HeatTransfer McGraw-Hill New York NY USA 1998

[27] J Buongiorno ldquoCan corrosion and CRUD actually improvesafety margins in LWRsrdquo Annals of Nuclear Energy vol 63 pp9ndash21 2014

[28] S Z Li X J Liu and X Cheng ldquoDevelopment of Borontransport model based on subchannel approachrdquo in Proceedingsof the 11th International Topical Meeting on Nuclear Reac-tor ermal-Hydraulics Operation and Safety (NUTHOS-11)Gyeongju Korea 9 October 2016

[29] D J Walter A High Fidelity Multiphysics Framework forModeling CRUD Deposition on PWR Fuel Rods University ofMichigan 2016

[30] A T Godfrey ldquoVERA Core Physics Benchmark ProgressionProblem Specificationsrdquo CASL-U-2012-0131-004 p 189 2014

[31] A T Nelson J T White D A Andersson et al ldquoThermalexpansion heat capacity and thermal conductivity of nickelferrite (NiFe2O4)rdquo Journal of the American Ceramic Society vol97 no 5 pp 1559ndash1565 2014

[32] L S Tong ldquoPrediction of departure fromnucleate boiling for anaxially non-uniform heat flux distributionrdquo Journal of NuclearEnergy vol 21 no 3 pp 241ndash248 1967

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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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developed it into different crud calculation models [5ndash11] Inthe experimental research scientists observed the fractallineproperties of PWR fuel crud [12] and then found that asystematic theory of fractal porous media [13] can be used torefine some parameters and assumptions in the crud model

Simulations between crud deposition models andthermal-hydraulic codes have also been investigated suchas the coupled solution between STAR-CCM+ and the crudmodel [14] the coupled simulation between COBRA-IV andthe crud model [15] and the coupled calculation betweenCTF and the crud model which models deposits growtherosion and thermal feedback [16] In nuclear simulatedcircumstances the neutronics and thermal-hydraulicscoupling are the most classical combination to resolve corephysical phenomena By adding the crud prediction modelmulti-coupling the simulation between STAR-CCM+ crudmodel and neutronics code DeCART is also investigated[17ndash19] In fact although STAR-CCM+ is a very powerfulCFD tool it is still time-consuming whereas subchannelcodes are much more economical and acceptable for CIPSrisk assessment and prediction BOA 30 [20] a tool for CIPSrisk assessment [21] which is codeveloped by WestinghouseElectric Company and the Electric Power Research Institute(EPRI) adopted the VIPRE-01 [22] subchannel code as thethermal hydraulic code

The effort of this paper is to implement the crud andthermal hydraulic subchannel code together to simulateboron-accumulated amount along the assembly The boroninventory can act as an input to the neutronics code whichcould offer the power shape distribution along the assemblyIn the following section the combined methodology ispresented in detail The methodology consists of three partsa boron deposit model based on Cohenrsquos model [5] thesubchannel code COBRA-IV which is a sophisticated codefor reactor core simulation and the neutronics calculationcodesDRAGON[23] and SKETCH-N [24] Section 3 demon-strates the simulation results and shows the CIPS effect ona 3times3 fuel pin assembly Additionally the effect of variouscrud thicknesses is discussed And the effects on CHF aresimulated and discussed Section 4 concludes this paper

2 Methodology

21 Overview of the Framework The present methodology inthis paper provides a combined framework for modeling theCIPS phenomenon This framework includes three modules(TH crud and neutron) and the simulation is processed insequence Firstly an initial power distribution along axial fuelpin is calculated in the SKETCH-N code In this stage thefuel pellets are arranged uniformly along the axial height So acosine-shape power distribution can be solved and the powerfactor at each axial node is known This power distributionshape is up-down symmetric and is also used for valuing thepower shift at the end of stage Secondly coupled calculationbetween the thermal-hydraulic code and the crud modelbegins While COBRA-IV code sweeping is at the axial levelchannel sweeping and rod sweeping are the subcycles of theaxial sweeping Fluid temperature is solved in the channelsweeping cycle and the deposit location is determined by

the SNB criterion in the rod sweeping cycle If the criterionindicates the sign of deposit the crud module solves theboron deposit amount on the local nodal Lastly the neutronabsorption cross section is solved in the DRAGON code andthen axial power distribution shape can be solved in theSKETCH-N code The power shape diagram can be plottedwhich could be regarded as an indication of CIPS risk Thiscalculation sequence is shown in Figure 1

Due to the difference in solution meshes the thermalhydraulic results are channel-centered while the crud solu-tion domain is rod-centered Because the rod sweeping cycleactivates after the channel sweeping cycle it is important toapproximate the spatial transform from COBRA-IV code tothe crud model Here volume-averaged density and mass-weighted temperature of the surrounding channels (north-west northeast southwest southeast) are used as coolantinformation for crud model simulation The schematic dia-gram is shown in Figure 2

22 Module Descriptions In the present work the subchan-nel analysis code COBRA-IV is chosen for the thermal-hydraulic analysis The main objective of this module is tocalculate the fluid temperature and the cladding temperatureThe fluid temperature serves as the simulating boundaryof the crud model whereas the cladding temperature iscalculated to identify the subcooled nucleate boiling regionThis paper proposes a conservative assumption that crud willonly occur in the SNB locations Corrosion products sourcefrom corrosion surfaces or from previously deposited crudback to the bulk coolant The deposition rate of the crudcaused by SNB is much higher than the nonboiling surfacesand it is assumed that the deposits have uniform thicknessin the SNB region because this framework does not includedeposited dynamics for now

The subchannel code COBRA-IV uses Levy model [25]to calculate the subcooled void fraction and then predictsthe outer cladding temperature and the local heat transfercoefficient by Thom correlation [26] (see (1)) The subcoolednucleate boiling occurs when the predicted outer claddingtemperature is just above the saturated temperature TheThom correlation is suitable for up to about 20MPa underconditions where the nucleate boiling contribution domainsover forced convection The correlation is used for estimatetemperature difference when the local heat flux is given

119879119904119886119905 = 225 ∙ 11990205 exp (minus 11987587) (1)

where 119879119904119886119905 is the wall temperature elevation above thesaturation temperature K q isthe heat flux MWm2 and Pis the pressure of water MPa

It is assumed that the soluble metal ions only exist inliquid phase so if bubbles evaporate from the surface of fuelpin solute particles will precipitate and then coat on theboiling surfaceThedeposit has specialmorphologyThe areaalways filled with vapor during wick boiling phenomenais called chimney Microscopic exanimation of the depositsshows the existence of steam chimneys The chimneys areacross the deposit thickness orientation and point toward the


Start

Fuel Power Factor


T_cgtT_sat



Axial Sweeping

SNB == true


Channel Sweeping


Rod Sweeping

Finish


COBRA-IV

crud module

DRAGON

SKETCH-N






119906 = minus120581120583998810119875 (2)



119869 = minus119863nabla119862 + 119906119862 (3)


R

Z

CRUD

Symmetry

Coolant

Chimney

CLAD q

core radius

Thickness

CRUD radius

Fuel rod clad


Vapor flow

Steam chimney






1198711198941198611198742 (119904) + 1198672119874 +119867+ 999445999468 119871119894+ + 119861 (119874119867)3 (4)




3 Numerical Results












crud


1

08

06

04

02

00 2 4 6 8 10



Rela

tive A

xial

Lev

el(x

Ｒ0)






08

06

04

02

0


0 05 1

1

15 2

Rela

tive A

xial

leve

l(x

Ｒ0)




119860119874 = 119875119905119900119901 minus 119875119887119900119905119905119900119898119875119905119900119901 + 119875119887119900119905119905119900119898 (5)




50

40

30

20

10

00 02 04 06 08 1


(ＲＲ0)

DN

BR W

3-co

rrel

atio

n



(ＲＲ0)

DN

BR W

3-co

rrel

atio

n

6

55

5

45

4

35

3

25

204 045 05 055 06 065 07 075 08 085






4 Conclusion


Data Availability




References















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



Start

Fuel Power Factor


T_cgtT_sat



Axial Sweeping

SNB == true


Channel Sweeping


Rod Sweeping

Finish


COBRA-IV

crud module

DRAGON

SKETCH-N






119906 = minus120581120583998810119875 (2)



119869 = minus119863nabla119862 + 119906119862 (3)


R

Z

CRUD

Symmetry

Coolant

Chimney

CLAD q

core radius

Thickness

CRUD radius

Fuel rod clad


Vapor flow

Steam chimney






1198711198941198611198742 (119904) + 1198672119874 +119867+ 999445999468 119871119894+ + 119861 (119874119867)3 (4)




3 Numerical Results












crud


1

08

06

04

02

00 2 4 6 8 10



Rela

tive A

xial

Lev

el(x

Ｒ0)






08

06

04

02

0


0 05 1

1

15 2

Rela

tive A

xial

leve

l(x

Ｒ0)




119860119874 = 119875119905119900119901 minus 119875119887119900119905119905119900119898119875119905119900119901 + 119875119887119900119905119905119900119898 (5)




50

40

30

20

10

00 02 04 06 08 1


(ＲＲ0)

DN

BR W

3-co

rrel

atio

n



(ＲＲ0)

DN

BR W

3-co

rrel

atio

n

6

55

5

45

4

35

3

25

204 045 05 055 06 065 07 075 08 085






4 Conclusion


Data Availability




References















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



R

Z

CRUD

Symmetry

Coolant

Chimney

CLAD q

core radius

Thickness

CRUD radius

Fuel rod clad


Vapor flow

Steam chimney






1198711198941198611198742 (119904) + 1198672119874 +119867+ 999445999468 119871119894+ + 119861 (119874119867)3 (4)




3 Numerical Results












crud


1

08

06

04

02

00 2 4 6 8 10



Rela

tive A

xial

Lev

el(x

Ｒ0)






08

06

04

02

0


0 05 1

1

15 2

Rela

tive A

xial

leve

l(x

Ｒ0)




119860119874 = 119875119905119900119901 minus 119875119887119900119905119905119900119898119875119905119900119901 + 119875119887119900119905119905119900119898 (5)




50

40

30

20

10

00 02 04 06 08 1


(ＲＲ0)

DN

BR W

3-co

rrel

atio

n



(ＲＲ0)

DN

BR W

3-co

rrel

atio

n

6

55

5

45

4

35

3

25

204 045 05 055 06 065 07 075 08 085






4 Conclusion


Data Availability




References















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018











crud


1

08

06

04

02

00 2 4 6 8 10



Rela

tive A

xial

Lev

el(x

Ｒ0)






08

06

04

02

0


0 05 1

1

15 2

Rela

tive A

xial

leve

l(x

Ｒ0)




119860119874 = 119875119905119900119901 minus 119875119887119900119905119905119900119898119875119905119900119901 + 119875119887119900119905119905119900119898 (5)




50

40

30

20

10

00 02 04 06 08 1


(ＲＲ0)

DN

BR W

3-co

rrel

atio

n



(ＲＲ0)

DN

BR W

3-co

rrel

atio

n

6

55

5

45

4

35

3

25

204 045 05 055 06 065 07 075 08 085






4 Conclusion


Data Availability




References















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018




08

06

04

02

0


0 05 1

1

15 2

Rela

tive A

xial

leve

l(x

Ｒ0)




119860119874 = 119875119905119900119901 minus 119875119887119900119905119905119900119898119875119905119900119901 + 119875119887119900119905119905119900119898 (5)




50

40

30

20

10

00 02 04 06 08 1


(ＲＲ0)

DN

BR W

3-co

rrel

atio

n



(ＲＲ0)

DN

BR W

3-co

rrel

atio

n

6

55

5

45

4

35

3

25

204 045 05 055 06 065 07 075 08 085






4 Conclusion


Data Availability




References















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018




4 Conclusion


Data Availability




References















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018






















Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018














Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018


Documents

A Combined Method for Predicting the Boron Deposited Mass ...ScienceandTechnologyofNuclearInstallations Relative Power Factor 0.8 0.6 0.4 0.2 0 No Crud Layer hin Crud Layer hick Crud