Development and Verification of a Transient Analysis Tool ...downloads.hindawi.com/journals/stni/2018/6801736.pdf · 16.03.2018 · KALIMER- STAR-LM SSTAR Developing-KAIST SNL MIT

Research ArticleDevelopment and Verification of a TransientAnalysis Tool for Reactor System Using Supercritical CO2Brayton Cycle as Power Conversion System

PanWu Chuntian Gao and Jianqiang Shan

School of Nuclear Science and Technology Xirsquoan Jiaotong University 28 Xianning West Road Xirsquoan Shanxi China

Correspondence should be addressed to Pan Wu wupan2015mailxjtueducn and Jianqiang Shan jqshanmailxjtueducn

Received 16 March 2018 Revised 3 July 2018 Accepted 30 July 2018 Published 2 September 2018

Academic Editor Arkady Serikov

Copyright copy 2018 PanWu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Supercritical CO2 Brayton cycle is a good choice of thermal-to-electric energy conversion systemwhich owns a high cycle efficiencyand a compact cycle configuration It can be used in many power-generation applications such as nuclear power concentratedsolar thermal fossil fuel boilers and shipboard propulsion system Transient analysis code for Supercritical CO2 Brayton cycle isa necessity in the areas of transient analyses control strategy study and accident analyses In this paper a transient analysis codeSCTRANCO2 is developed for Supercritical CO2 Brayton Loop based on a homogenous model Heat conduction model pointneutron power model (which is developed for nuclear power application) turbomachinery model for gas turbine compressorand shaft model and PCHE type recuperator model are all included in this transient analysis code The initial verifications wereperformed for components and constitutivemodels like heat transfermodel frictionmodel and compressormodelTheverificationof integrated system transient was also conducted through making comparison with experiment data of SCO2EP of KAIST Thecomparison results show that SCTRANCO2owns the ability to simulate transient process for S-CO2Brayton cycle SCTRANCO2will become an important tool for further study of Supercritical CO2 Bryton cycle-based nuclear reactor concepts

1 Introduction

Supercritical CO2(s-CO2) Brayton cycle is a promising powerconversion technology which has advantages like compactsystem configuration compared to steam generation systemhigher efficiency and less need of water consumption Ithas aroused great interests among industry and academia ofdifferent energy types especially in nuclear and solar energy[1 2]

Many researchers studied the feasibility of using s-CO2Brayton cycle as power conversion system for nuclear appli-cations One option is to use s-CO2 Brayton cycle to coolthe reactor core directly Figure 1 shows the coolant flowand heat transfer in the nuclear reactor system couplingwith s-CO2 Brayton cycle The s-CO2 entering the reactorcore is heated to high temperature by the thermal energyreleased in the core Then high-temperature s-CO2 flowsinto the gas turbine and drives the shaft to rotate Thegenerator connected with the shaft can produce electricity

After the expansion process through the turbine s-CO2depressurized to a lower pressure which is usually slightlyover the critical pressureThe high-temperature low pressures-CO2 enters the recuperator to heat the s-CO2 to requiredinlet temperature for the reactor at the high pressure sideAfter transferring energy to the high pressure side thelow pressure side s-CO2 is then cooled to be close to thecritical temperature of s-CO2 by secondary water flow inthe precooler The s-CO2 flow rejects heat in the precoolerand makes sure that the high density s-CO2 is compressedby the compressor High pressure leaving the compressoris heated by the low pressure side coolant and enters thereactor core as described before In the development of thistype of reactor concepts the concept of reactor core cooledby s-CO2 should be developed as well as the configurationof s-CO2 Brayton cycle As the only successfully operatedCO2 cooled reactor Advanced Gas Reactor (AGR) uses CO2coolant at 433MPa and bundled fuel pins formed by oxidefuel and stainless-steel cladding [3] Even though operating

HindawiScience and Technology of Nuclear InstallationsVolume 2018 Article ID 6801736 14 pageshttpsdoiorg10115520186801736

2 Science and Technology of Nuclear Installations

Reactor

Recuperator

Precooler

Water side

Compressor TurbineGenerator

S-CO2 flow

Figure 1 Schematicmap of nuclear reactor system cooled by s-CO2Brayton cycle

pressure and the neutronic spectrum are different from thatof S-CO2 cooled fast reactor the operational characteristicssafety issues and behavior of the fuel cladding and coolantcould provide great reference for S-CO2 cooled fast reactorcore design Pope [4] from MIT has proposed a 4-loop2400MWth direct S-CO2 cooled fast reactor concept coupledwith recompression S-CO2 Brayton cycle This concept ownsa core design with Tube in Duct (TID) assemblies andadvanced shielding material advanced cladding materials forhigh burn-up fuel and high temperature Oxide fuel wasselected as the fuel form for its chemical compatibility withCO2 Accident analysis and safety design have been carriedout for this concept [5] A relatively small fast reactor conceptwhich is cooled with CO2 at pressure of 20MPa is proposedby Parma et al from Sandia National Laboratories [6] Thereactor concept applied bundled fuel assemblies which refersfrom that of AdvancedGasReactor (AGR) [3] A supercriticalCO2-cooledMicroModular Reactor (MMR)with 362MWthpower is developed by [7] Transportability is one of theMMRrsquos features which is achieved by the compact cycleconfiguration and modularized reactor design

Another option to apply S-CO2 Brayton cycle workingas the power conversion system of existing Gen IV reactorconcept which tries to take advantages of large amount ofRampD work of these new concepts and improve the cycleefficiency at the same time Feasibility of S-CO2 Braytoncoupled to sodium fast reactor concept KALIMER-600 [8]lead fast reactor concept STAR-LM [9] and SSTAR [10] S-CO2 Brayton cycle configuration as well as the transientperformance and control strategy of these concepts has beencarried out which shows great potential for applying S-CO2Brayton cycle on these new reactor concepts A summary ofthe core design and Brayton cycle design of the above nuclearapplications is listed in Table 1

Transient analysis code is a necessity for study of controlstrategy dynamic characteristic and safety analysis for S-CO2Brayton cycle direct or indirect cooled reactors According tothe features of Brayton cycle coupled reactor applications thetransient analysis code should possess the ability to simulatereactor core precooler recuperator and turbomachineryincluding compressor gas turbine and rotating shaft model

Different transient analysis codes have been developed tosatisfy the demand for control strategy and accident study

for s-CO2 Brayton cycle direct or indirect cooled reactors Atransient analysis codeMMS-LMRwas developed to simulatethe system transient and evaluate control logics for sodium-cooled fast reactor KALIMER-600 [8]The code can simulatecoolant of Sodium and CO2 and modules like reactor pipeNa-CO2 heat exchanger recuperator and compressor CodeMARS has been applied to carry out up-power and down-power transient simulation for the Supercritical CO2 IntegralExperimental Loop (SCIEL) [11] A modified GAMMA+code was developed and applied for the analysis of KAISTMicro Modular Reactor (MMR) for simulation of loss ofload and loss of coolant accidents [12] Accurate CO2 prop-erties near critical point and turbomachinery performancemap were incorporated into the original GAMMA+ whichwas previously a transient analysis code for Very High-Temperature Reactor (VHTR) system developed by KAERIThe performance map for GAMMA+ is produced by KAIST-TMD which is an in-house code to design the turbomachin-ery GAMMA+ code simulation ability near critical pointhas been validated with comparing with the experimentdata from SCO2PE [13] RELAP5-3D has s-CO2 propertiesand compressor and turbine models which could help tosimulate the s-CO2 Brayton cycle It has been used to analyzethe safety performance for s-CO2 cooled fast reactors withpassive safety system under loss of coolant accident andloss of generator load accident [4 5] A plant dynamicscomputer code named Plant Dynamics Code (PDC) has beendeveloped by ANL [14] The PDC solves time-dependentmass momentum and energy conservation equations for s-CO2 fluid plus the turbomachinery shaft dynamics equationThis code has been applied to various applications such astransient and control strategies analysis of s-CO2 Braytoncycle coupled to lead-cooled fast reactor [9] autonomousload following for an SFR by coupling with SAS4ASASYSYS-1 to determine the core side [15] simulation of s-CO2Integrated System Test [16] and off-design behavior analysisfor s-CO2 Brayton cycle coupled to sodium-cooled fastreactor [17] Validation work has been done by comparingPDC compressor model with SNLBNI compressor test data[18] TRACE source code was modified by adding new fluid(s-CO2) as well as Brayton turbomachinery componentsto enhance its ability to simulate s-CO2 Brayton cycle [1920] Cycle design and control features during startup andoperation have been carried out [21] GAS-PASS is a dynamicsimulation and control code for gas-cooled Brayton cyclereactor power conversion system It has been modified todeal with the use of s-CO2 Brayton cycle [22] The controlstrategies have been studied [23]

Through the overview of the current transient analysiscode development for nuclear application related Braytoncycle we can find most of the codes are developed basedon existing transient analysis codes with incorporating CO2property turbomachinery models and PCHE models Thevalidation work is based on experimental data produced by s-CO2 Brayton cycle experimental platforms such as 100 kWes-CO2 power cycle system facility constructed by the cooper-ation of Knolls Atomic Power Laboratory (KAPL) and BettisAtomic Energy Laboratory (BAEL) in 2012 [24] 10MWebasic s-CO2 Brayton cycle established by Sadia National

Science and Technology of Nuclear Installations 3

Table1Overviewof

currentstudy

onS-CO2Braytoncyclestudy

workingas

powe

rcon

versionsyste

mon

nucleara

pplications

Con

cept

Nam

e-

MMR

SC-G

FR-

KALIMER

-600

STAR-LM

SSTA

RDevelop

ing

-KA

IST

SNL

MIT

KAER

IArgon

neNational

Labo

ratory

Argon

neNational

Labo

ratory

Institutio

nBraytoncycle

-direct

direct

direct

indirect

indirect

indirect

coup

ledmetho

d

CoreP

art

thermalpo

wer(MW)

362

200

2400

15289

400

45Pressure

(MPa)

2020

2001

01

01

Fueltype

UCfuel

UO2

UO2B

eOU-TRU

-10

ZrTR

U-N

Enric

hed

toN15

Nitridefuel

Cladding

type

Stainlesssteel

HighNi

ODSMA956

Mod

HT9

Co-extrud

ed

-Stainlesssteel

Si-enh

anced

FM

stainless

steelwith

FM

substrate

Coreo

utlettem

perature

550

650

650

5453

578

5658

Massfl

owrate(kgs)

180

920

11708

77313

19708

2125

Coo

lant

CO2

CO2

CO2

Sodium

PbPb

Powe

rCon

version

Syste

m

Braytoncycletype

simplec

ycle

nospecificd

esign

recompressio

ncycle

recompressio

ncycle

recompressio

ncycle

recompressio

ncycle

Cyclem

assfl

owrate

(kgs)

180

-2927

80766

2276

2393

TPof

compressor

Inlet(∘ CM

Pa)

60880

-32769

312574

312574

312574

TPof

compressoro

utlet

(∘ CM

Pa)

1422200

-60

920

848200

85200

849200

TPof

recompressio

ncompressorinlet

(∘ CM

Pa)

--

709771

912746

863740

5909740

1

TPof

recompressio

ncompressoro

utlet

(∘ CM

Pa)

--

1591

200

1894

1998

18381998

1898

20

TPof

turbineinlet

(∘ CM

Pa)

5501993

-6501945

50801974

54001988

5414

1999

TPof

turbineo

utlet

(∘ CM

Pa)

44075816

-5299

793

394276

426977

1342017435

Reference

-[7]

[6]

[4]

[8]

[9]

[10]


laboratory(SNL) [25] and the s-CO2 integral experimentloop (SCIEL) constructed by Korea Atomic Energy ResearchInstitute (KAERI) [26] Component performance and cycletransient characteristics of these experiment facility are vitalfor validating the newly developed code

As China is also launching projects into s-CO2 Braytoncycle development for concentrated solar thermal fossil fuelboilers and nuclear power transient analysis code for S-CO2 Brayton cycle is urgently needed to help in predesigningof experimental facility as well as the new Brayton cycle-based reactor concept development The development of atransient analysis code is presented in this paper SCTRAN[27] which originally is a safety analysis code for SCWR isselected to be upgraded to simulate the S-CO2 Brayton cycleby adding accurate thermal property and constitutive modelfor CO2 turbomachinery models (including compressor gasturbine and shaft) Due to the lack of experiment datathe current validation strategy is to make simple validationwith limited experiment data and code-to-code comparisonwith other codes like GAMMA+ The initial verification forSCTRANCO2rsquos ability to do component model simulationand cycle simulation is carried out

2 Code Development

21 Introduction of SCTRAN SCTRAN is a one-dimensionalsafety analysis code for SCWRs which applies homogeneousmodel to simulate the fluid flow The homogeneous modelassumes the two phases of coolant are in thermal equilibriumstate and the velocity difference of the two phases is zeroCompared to drift model and two-phase model this modelneeds less constitutive correlations and is easy to be solvednumerically For most of the transient or accident case in s-CO2 Brayton cycle the coolant will stay in gas state That isthe reason why homogeneous model is adopted to developthe transient analysis code for s-CO2 Brayton cycle Theconservative equations of mass momentum and energy areas follows

Mass conservative equation is

120597120597119905120588119860 + 120597

120597119911119882 = 0 (1)

Momentum conservative equation is

120597120597119905119882 + 120597

120597119911119882119881 = minus119860120597119901120597119911 minus 2119860120588119881 |119881|

119863ℎ 119891119905119901 + 120588119860119892119911 (2)

The first item in the right hand of the equation denotespressure drop the second item denotes fanning frictionpressure drop and the last item denotes the pressure dropcaused by gravity

Energy conservative equation is

119889119889119905119880 = minus12

119871119860

119889119889119905 (

1198822120588 ) minussum

119895

(119882119892ℎ119892 +119882119897ℎ119897)

+ 12 (119882119892119881119892119881119892 +119882119897119881119897119881119897) +119882119892 (119911 minus 119911119895) + 119876

(3)

Thefirst item in the right hand of the equation denotes kineticenergy change rate the second item denotes energy transfercaused by fluid flow and the last item denotes energy transfercaused by heat transfer and inner heat source

Based on staggered grid method control volume balancemethod and one-order upwind difference scheme applyingto the time derivative related items a numerical procedureis developed with which the mass and energy of the controlvolumes and the mass flow of the junctions can be obtainedconveniently

In order to calculate the core power and its reactivityfeedback effects SCTRAN applies the fission decay heatequation and point neutron kinetics equation with six groupsof delayed neutron to calculate the core power

1V120597120601 (119903 119905)

120597119905 = 119863nabla2120601 (119903 119905) minus Σ119886120601 (119903 119905)

+ (1 minus 120573) 119896infinΣ119886120601 (119903 119905) +6sum119894=1

120582119894119862119894 (119903 119905)(4)

The item in the left hand of the equation denotes the neutronflux variation with time the first item in the right hand ofthe equation denotes the neutron leakage rate the seconditem denotes the neutron absorption rate and the third andfourth item separately represent the neutron production rateof prompt neutron and delayed neutron

SCTRANrsquos ability to simulate the transients and accidentsof SCWR has been verified by comparing with APROS codeand RELAP5-3D code [27] respectively It has been widelyused in transient and accident analysis for supercritical waterreactor [28 29]

In order to make SCTRAN suitable for s-CO2 Braytoncycle-based reactor system accurate CO2 property packageand heat transfer and friction models for carbon dioxide andturbomachinery models including gas turbine compressorand rotating shaft should be developed

22 Compressor Model Development

221 Basic Model of Compressor The goal of compressormodel is to calculate the flow condition inside the compressorand at the compressor outlet A quasistatic status is assumedfor flow inside compressor under which situation the perfor-mance map could be used to evaluate the efficiency and pres-sure ratio of compressor The solution of compressor modelshould include pressure rise which could be used for fluidmomentum conservation equation enthalpy increase whichwas needed in fluid energy conservation equation and torquewhich is needed for shaft model to simulate rotating speed

Figure 2 shows the fluid enthalpy and entropy variationduring ideal and realistic compression process The idealcompression process is regarded as an isentropic process andthe realistic compression process needs a factor of compressoradiabatic efficiency to account for the additional enthalpyincrease compared to that of the ideal processThe definitionof adiabatic total to total efficiency is as follows

120578119886119889 = Isentropic workActual work

= ℎ11987921015840 minus ℎ1198791ℎ1198792 minus ℎ1198791 (5)


h

S

Ｂ02

Ｂ2Ｍ

Ｂ01

０02

０2

０01

０1

Figure 2 Ideal and realistic compression process inside compressor

Therefore the actual outlet enthalpy of compressor can beobtained with ideal outlet enthalpy and adiabatic efficiencythrough (5) The ideal enthalpy increase could be obtainedthrough the integration of equation DH=vlowastDP

The pressure rise and adiabatic efficiency through thecompressor are obtained from the performance map whichis specially produced for the targeted compressor by otherspecific codes As the compressor pressure ratio is regarded tobe obtained from compressor performance map according tothe rotating speed and coolant flow rate the pressure increasethrough compressor can be obtained

Δ119875 = 1198751198791 (119877119901 minus 1) (6)

where Rp denotes the compressor pressure ratio and 1198751119879denotes the compressor inlet total pressure The kineticchange of the fluid is included in the item of total pressurein (6)

Assuming that no heat dissipated in the compressionprocess the compressor power acting on the fluid is

119882119888V = ∙119898 (ℎ1198792 minus ℎ1198791 ) = ∙119898 (ℎ11987921015840 minus ℎ1198791 ) + ∙119898 (ℎ1198792 minus ℎ11987921015840)= Ws +Wd

(7)

where ℎ1198792 is the real enthalpy at the compressor outlet ℎ11987921015840 isthe ideal enthalpy at the compressor outlet 119882119904 is the powerproduced by compressor during the isentropic process and119882119889 is the dissipated power in the compression process

In the ideal compression process the ideal work producedby compressor equals the energy increase of s-CO2 flowingthrough the compressor

120591119904 =∙119898120596 (ℎ11987921015840 minus ℎ1198791 ) (8)

The dissipated torque can be calculated using the followingequation

120591d =∙1198981205961 minus 120578119886119889120578119886119889 (ℎ11987921015840 minus ℎ1198791 ) (9)

Summing up (8) and (9) the total torque of the compressoris obtained

120591t = 120591119904 + 120591d =∙119898120596

1120578119886119889 (ℎ

11987921015840 minus ℎ1198791 ) (10)

h

SCompression

Ｂ02

Ｂ2Ｍ

Ｂ01

０02

０2

０01

０1

Figure 3 Ideal and realistic expansion process inside gas turbine

Therefore through (5) (6) and (10) the enthalpy increasepressure increase of fluid through the compressor and totaltorque of the compressor can be obtained

222 Incorporation of Compressor Model to Code SCTRANThe compressor component will be regarded as a normaljunction and volume when incorporating into SCTRANThepressure rise calculated by compressor model will be addedto the momentum conservation equation of the representedjunction and the enthalpy change calculated by compressormodel will be added to the energy conservation equation ofthe represented volume

23 Gas Turbine Model Development Figure 3 shows theideal and realistic expansion process inside gas turbinemodel The process of turbine acting is inverse process ofcompressor acting Thus the same theory was applied to gasturbine model and the following correlations are obtained

For fluid enthalpy increase

Δℎ = ℎ11987921015840 minus ℎ1198791120578119886119889 (11)

For pressure drop

Δ119875 = 1198751 (119877119901 minus 1) (12)

For total torque of gas turbine

120591t = 120591119904 + 120591d =∙119898 120578119886119889120596 (ℎ11987921015840 minus ℎ1198791 ) (13)

24 Shaft Model Development In the Brayton cycle thereare many turbomachineries connected to the shaft whichinclude gas turbine compressor generator and control sys-tem The shaft model for evaluation shaft rotating speed is asfollows

sum119894

119868119894119889120596119889119905 = sum119894

120591119894 minussum119894

119891119894120596 + 120591119888 (14)

The first item on right hand of (14) denotes the torquesproduced by compressor turbine or generator The seconditem denotes the torques produced by friction while the thirditem denotes the torque produced by control system


Table 2 Relative prediction error of the developed CO2 property package compared to NIST REFPROP 90

CO2 Property Symbol Regions Relative errorSaturated liquid enthalpy hf - plusmn0015Saturated vapor enthalpy hg - plusmn0009Temperature T

subcooled area -005 to 01 99 of which is within relative errors of plusmn005superheated region 1 plusmn02 99 of which is within relative errors of plusmn01superheated region 2 -01 to 025 99 of which is within relative errors of plusmn005

Specific volume vsubcooled area -05 to 1 99 of which is within relative errors of plusmn0 5

superheated region 1 -1 to 4 99 of which is within relative errors of plusmn1superheated region 2 -05 to 01 95 of which is within relative errors of plusmn01

Dynamic viscosity 120583 - -15 to 05 99 of which is within plusmn05

25 Constitutive Model Incorporation

251 Properties of Carbon Dioxide An independent andaccurate thermal property model for carbon dioxide over alarge parameter range is needed to be incorporated into codeSCTRAN Generally there are three methods to calculate thefluid thermal property in thermal hydraulic analysis codeswhich include property lookup tables or figures solutionof fluid state equations and direct calculation of fittingcorrelation In method of property tables or figures the fluidthermal property is plotted in figures or tabulated in tableswhich is easy for users to find property for certain stateHowever the calculation efficiency of this method is lowwhich makes it hard to be applied in large thermal analysiscodes which needs to calculate the fluid property repeatedlyThe solution of fluid state equation is based on strict theoret-ical and experimental study Thus this method can producefluid property with high accuracy However these basic fluidstate equations are complex and time-consuming becauseiterations are needed to get the final results The methodof fitting correlation is to get a mathematical correlationwith certain prediction accuracy for fluid property basedon the existing thermal property data The mathematicalcorrelation can be polynomial expression or some othertype This method with the merits of small computationaleffort and high prediction accuracy can be convenientlyprogrammed into thermal analysis codes It has been widelyused in thermal analysis codes Thus the method of fittingpolynomial correlation was applied in this paper to developthe CO2 property package

The based thermal property data which is used forfitting correlations comes from NIST REFPROP The ther-mal property package covers pressure range of 01sim20MPaand temperature range of 0sim991∘C Parameters includingsaturated liquid and vapor enthalpy temperature specificvolume and dynamic viscosity have been obtained throughthe pressure and enthalpyThe property calculation is dividedinto three regions based on pressure and enthalpy which aresubcooled area superheated region 1 (enthalpy over 360 kJkgbut below 600 kJkg) and superheated region 2 (enthalpyover 600 kJkg) Table 2 shows the relative prediction errorbetween the developed CO2 property and NIST REFPROP90 It seems that the developed package can predict CO2

property very well in most property range with a relativeerror lower than 05 However for property near criticalpoint very large prediction error exists The predictionperformance of the developed CO2 property package atnear critical point area should be improved in the futurework

252Heat Transfer Correlation For the straight semicircularflow channels in PCHE correlation Gnielinski is applied([30]) This correlation is suitable for application range of Rebetween 2300 and 5times106 and Pr between 05 and 2000

119873119906 = ℎ119863119890120582 = (1198918) (Re minus 1000) Pr1 + 127radic(1198918) (Pr23 minus 1) (15)

where

119891 = 1(18 log (Re) minus 15)2 (16)

The correlations for other Reynolds number and otherstructure of flow channel are not included in code Furtherstudy should be carried out in this area to expand the codeapplication range For the heat transfer of coolant flowingthrough fuel buddle inside the core correlation Gnielinskiis currently used There are still problems in clarifying theuncertainty produced by applying Gnielinski correlation toevaluate core heat transferHowever several published papers[4 31] applied Gnielinski to calculate the heat transfer insidethe core without explaining the uncertainty

253 Friction Correlation The friction is evaluated bycorrelation Zigrang-Sylvester which is an approximateexplicit correlation of Colebrook-White correlation [30] TheZigrang-Sylvester is suitable for situation ofwhichRenumberis larger than 3400 The correlation is listed as follows

1radic119891 = minus2 log 120576

37119863119890+ 251

Re[114 minus 2 log( 120576

119863119890 +2125Re09

)](17)


experiment data(relative roughness0005)SCTRANCO2(relative roughness0005)experiment data(relative roughness0015)SCTRANCO2(relative roughness0015)experiment data(relative roughness0025)SCTRANCO2(relative roughness0025)

001

01

1

Dar

cy fr

ictio

n fa

ctor

f

1000 10000 100000 1000000100Re

Figure 4 Comparison for friction coefficient of various roughnessbetween experimental data and SCTRANCO2 prediction

When Re is lower than 2300 the friction model for laminarflow is used

119891 = 64Re

(18)

When Re number is between 2300 and 3400 a linearinterpolation is needed

3 Initial Verification for ComponentModel in SCTRANCO2

31 Friction Model Verification Wang et al [32] has attainedfriction coefficients of supercritical carbon dioxide withvarious pressures and temperatures in pipes through exper-iments The measured pipeline in the experiment has alength of 75m and variable diameters of 30mm 10mmand 6mm The variable diameter enables the study of tuberoughness effect on friction coefficient without changing thetubematerial The temperature range of the experiment is 30-150∘C the pressure range is 35-40MPa theReynolds numberrange is 200-20times106 and surface relative roughness (ratio ofroughness over tube diameter) is 0005 0015 and 0025Thesystem pressure and coolant flow Reynolds number cover theoperation and transient conditions in s-CO2 Brayton cycleThe temperature range is a little bit narrow compared to thatof s-CO2 Brayton cycle So the experiment data in [32] isapplied to verify the friction model in code SCTRANCO2As concluded in [32] Reynolds number can reflect vari-ation of physical property parameter comprehensively soa horizontal tube is modeled by SCTRANCO2 with 20nodes The coolant flow Re number is adjusted by changingthe inlet coolant flow rate Figure 4 illustrates the friction

coefficient comparison between the experiment data andSCTRANCO2 predicted result Reynolds number variesfrom 200 to 20times106 From the figure we can find that theprediction results in laminar flow area and turbulent flow areafit well with the experiment data

32 Heat Transfer Model Verification

321 Evaluation of Gnielinski Correlation on PCHE HeatTransfer Experimental Data A heat transfer experimentabout PCHE which use s-CO2 and water as the heat transfermedia in conditions relevant to the precooler in the s-CO2Brayton cycle is conducted by [33] Different experimentcases as well as CFD simulation with small and largetemperature differences across the PCHE have been carriedout The heat transfer data produced by experiment andnumerical simulation is used in this paper to evaluate theprediction performance of Gnielinski correlation on PCHEheat transfer The schematic maps of the experimental loopare shown in Figure 5 The experiment loop is made up ofa water loop and a closed s-CO2 loop The heat exchangehappens in the PCHE which has overall dimensions of120times200times1200mmThe s-CO2 inlet temperature of the PCHEcould be controlled by adjusting the power supply Somelarge temperature difference tests are carried out to simulatethe working conditions of the precooler in the Braytoncycle

Several large temperature difference tests are simulatedby SCTRANCO2 to verify that if correlation Gnielinski iscapable of simulating the working conditions of precoolerThe nodalization of SCTRANCO2 is shown in Figure 6 Asthere is no technique to measure the coolant temperatureinside PCHE flow channel only PCHE outlet temperaturecan be compared between the result of SCTRANCO2 andthe experimental data to evaluate the overall heat transfercoefficient Amesh size sensitivity is carried out to investigatethe proper nodalization for evaluating PCHE heat transferAs shown in Figure 7 with the increase of node number theoutlet temperature at s-CO2 and water side for case 6 pre-dicted by SCTRANCO2 becomes closer to the experimentdata Considering the balance between prediction accuracyand calculation time 20 nodes are selected to simulate thePCHE

Table 3 lists the experimental conditions of the caseswhich are used to verify the heat transfer model in theSCTRANCO2 code In these cases for the CO2 side theoperation pressure is about 8 MPa and the s-CO2 inlettemperature is held constant at 88∘C with mass flow rate of100 200 300 400 and 500 kghr For the water side the massflow rate is set to 700 kghr and the water inlet temperaturesvaried to achieve the desired S-CO2 outlet temperature Fortest B6simB10 the target S-CO2 outlet temperature is 36∘C andfor test B11simB15 the target S-CO2 outlet temperature is 38∘C

Figure 8 shows the temperature distribution along thechannel length from SCTRANCO2 Due to the fact thatonly the PCHE inlet and outlet temperature data is availableaccording to the experiment it is not possible to verify theaccuracy of the temperature distributions calculated by thecodeHowever the simulated temperature distribution agrees


FILTERCOLDLEG

COLDLEG

CORIOLISFLOWMETER

LEVELDETECTOR

EXHAUST

PRESSURIZERGEARPUMP

DIELECTRICUNION

HOTLEG

HOTLEG

HEATRIC HX

FILTER

P

P

P

=

=

=

=

=

ABSOLUTE PRESSURE

DIFFERENTIAL PRESSURE

FLUID TEMPERATURE

WALL TEMPERATURE

RELIEF VALVE

Water

S-CO2

CO2

CO2

Δ０

Δ０

Δ０

４

４７

４

４４４

４７４７４７４７

４

４

４

４

0-60 VAC

440 VAC 770 A

POWER SUPPLY

5000 A

４

Figure 5 Schematic diagram of the experiment loop [33]

1 2 i-1 i i+1 N+1NInlet of cold side Outlet of cold side

Outlet of hot side Inlet of hot side

Figure 6 SCTRANCO2 nodalization for PCHE

Observed s-CO2 temperature

Observed water temperature

35

36

37

38

39

40

41

42

Tem

pera

ture

(∘C)

10 20 30 40 500Node number

Outlet temperature of s-CO2 sideOutlet temperature of water side

Figure 7 Mesh size sensitivity on outlet temperature prediction forPCHE in case 6

with typical counter-flow heat exchanger temperature distri-butions in physical aspect Figure 9 shows the comparisonbetween experimental data and simulation result on s-CO2outlet temperature The square dots represent the simula-tion result using 2D-FLUENT by [33] and the solid circlerepresents the simulation result using SCTRANCO2 with

30

40

50

60

70

80

90

Tem

pera

ture

(∘C)

400 800 12000Length (mm)

Cold side(Water)Hot side(CO2)

Figure 8 Temperature distribution of water and s-CO2 sidepredicted by SCTRANCO2 for test B6

Gnielinski correlation and the dash line shows the 3 errorband From the figure we can see that prediction errors ofthe outlet temperature of the precooler for SCTRANCO2 arelarger in the cases which aim to achieve an outlet temperatureof 36∘C than that in the cases which aim to achieve anoutlet temperature of 38∘C However the prediction errors ofSCTRANCO2 for all the experimental conditions are in the3 error bandwhich indicateGnielinski correlation is able topredict the heat transfer conditions for precooler By the waythe 2D-FLUENT result shows large prediction errors due tothe setting of unchanged water property by [33]


Table 3 Details of the experimental conditions

TEST NO Ph mCO2 Th in Th out mH20 Tc in

MPa Kghr ∘C ∘C kghr ∘CB6 8003 10053 8863 3607 70159 3563B7 8001 20077 8810 3598 69978 3511B8 7972 29714 8936 3620 7018 3505B9 8003 40101 8792 3605 70177 3328B10 7995 50061 8793 3590 70009 3128B11 8003 10003 8768 3794 69780 3768B12 8005 19973 8885 3797 69780 3753B13 7998 30131 8817 3803 69986 3748B14 8020 40429 8897 3829 70162 3758B15 7998 50179 8809 3801 70225 3683

Fluent-2DSCTRANCO2

36 38 40 42 44 4634Hot Side Exit Experimental Temperature (

∘C)

34

36

38

40

42

44

46

Hot

Sid

e Exi

t Sim

ulat

ion

Tem

pera

ture

(∘C)

Figure 9 The comparison for S-CO2 outlet temperature betweenexperimental data and simulation result

33 Compressor Model Verification Due to lack of designand experiment data on compressor performance the ver-ification of compressor model is carried out through code-to-code compressor with RELAP5-3D code on compressorconsuming power and GAMMA+ on the outlet temperatureprediction in the open literature

331 Comparison with Code RELAP5-3D on Compres-sor Consuming Power Fisher and Davis [34] presented adetailed information of compressor model in RELAP5-3Dand carried out a comparison between RELAP5-3D and theoperation result of recompressing compressor designed byMIT The same operation condition will be simulated bySCTRANCO2 in this part to verify its ability to calculate theconsuming power needed for compressor operation

Figure 10 depicts the nodalization of the recompressingcompressor simulation Control volumes 341 and 382 are theinlet and outlet boundaries of this simple model which aresimulated by time-dependent volume in SCTRANCO2 and

382

380

350

346 345

341

compressorTime dependentjunction

Time dependent volume

Figure 10 Nodalization of the recompressing compressor

RELAP5-3DThe pressure of control volume 341 is 908MPaand the temperature is 363K which will keep constant in thesimulation Control volume 350 represents the compressorThe compressor rotating speed and inlet mass flow ratewill be changed to evaluate the compressor performance atdifferent conditions A series of steady-state calculation werecarried out to study the performance of the compressor underrelative compressor rotating speed of 05 08 and 10 aswell as relative s-CO2 flow rate between 04 and 10 Theperformance map of the compressor in [34] was adopted forSCTRANCO2 simulation

Figure 11 showed the result comparison betweenSCTRANCO2 and RELAP5-3D The results predictedby SCTRANCO2 were in excellent agreement with theRELAP5-3D predicted result At relative speed ratio of10 the largest relative error the consuming power is 12while at relative speed ratio of 08 the largest relativeerror the consuming power is 147 When the relativespeed ratio comes to 05 the largest relative error is 81which is much higher than those This larger error maybe produced in the process of assembling data from thepaper not due to the compressor model The performanceof SCTRANCO2 compressor model verified its ability topredict the compressor consuming power


Table 4 Experiment data from SCO2PE and predicted result from SCTRANCO2 and GAMMA+ on the compressor outlet temperature

Experiment(SCO2PE data) GAMMA SCTRANCO2

Compressor outlet temperature∘C case 1 383 422(+39) 4055(+225)case 2 458 465(+07) 4667(+087)

Compressor outlet pressureMPa case 1 865 865 865case 2 912 912 915

compressor efficiency case 1 586 586 586case 2 361 361 361

relative speed=05relative speed=08

relative speed=10

0

10

20

30

40

50

60

70

80

90

100Po

wer

cons

umed

by

com

pres

sor (

MW

)

025 050 075 100 125 150000Relative corrected flow

RELAP5-3DSCTRANCO2

Figure 11 Predicted compressor consuming power by SCTRANCO2 and RELAP5-3D

10 15

20

25 30Time dependent volumeTime dependent junction Compressor

Figure 12 Nodalization of GAMMA code [13]

332 Comparison with Experiment Data and CodeGAMMA+ on Compressor Outlet Temperature PredictionBae et al [13] carried out experimental and numericalinvestigation of s-CO2 test loop (SCO2PE) near critical pointoperation Two different compressor operation conditionsnear the critical point are designed to verify the GAMMA+predicted result for the compressor outlet temperatureFigure 12 shows the nodalization of code GAMMA+ forthe compressor part of SCO2PE Control volumes 15 20and 25 denote the compressor part and control volume100 is a time-dependent junction which can adjust theinlet flow rate and temperature for the compressor Controlvolume 30 is the outlet boundary which is also simulatedby time-dependent volume The same model was built bySCTRANCO2 Two different operation conditions aresimulated In case 1 the compressor flow rate is 286kgsand the fluid temperature is 325∘C and the compressor

inlet pressure is 744MPa In case 2 the compressor flowrate is 200kgs and the fluid temperature is 399∘C andcompressor inlet pressure is 829MPa In order to focuson the verification of outlet temperature prediction thepressure ratio and efficiency of the compressor and theinlet condition of the compressor are set to be the same asthose in SCTRANCO2 model GAMMA+ model and theexperimental conditions Table 4 shows the experimentaldata from SCO2PE and predicted result from SCTRANCO2and GAMMA+ on the compressor outlet temperature Incase 1 the compressor operation condition is closer to thecritical point the prediction errors of both codes are largerthan those in case 2 In case 1 SCTRANCO2 predicteda smaller outlet temperature bias of 225∘C compared totemperature bias of 39∘C predicted by GAMMA+ In case2 outlet temperature predicted by these two codes is closeto each other which is also close to the experiment data


Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa

Experiment T Experiment P MPa

GAMMA T GAMMA P MPa

SCTRANCO2 T SCTRANCO2 P MPaC

C

C

C

C

C

C

C

C

C

C

C

Figure 13 Nodalization of SCTRANCO2model and steady-state result at each node

However large experiment data uncertainty exists when theoperation condition is close to critical point

333 Summary According to the two verifications forcompressor model the compressor model in code SCTRANCO2 can predict reasonable compressor consuming powerand outlet temperature The prediction accuracy of codeSCTRANCO2 is close to those of RELAP5-3D andGAMMA+ as well as the experiment data produced bySCO2PE facility However if the quasisteady compressormodel is suitable for transient performance prediction isstill uncertain The reason for not carrying out transientson analysis of compressor turbine or shaft is that nocorresponding experimental or numerical data is foundin the open literature More transient experiments oncompressor and turbine performance should be establishedto validate turbomachinery model in SCTRANCO2 in thefuture

4 Initial Verification for Cycle Simulationwith SCTRANCO2

SCO2PE (Supercritical CO2 Pressurizing Experiment) is as-CO2 compressor test facility which aims to collect CO2compressor operation and performance data [13] It is mainlymade up of two systems which is a primary CO2 and a sec-ondary water systemThe CO2 loop includes a canned motortype compressor a heat exchanger an expansion valve andpipesThe s-CO2 flow through the compressor is pressurizedand heated Then it is depressurized through the expansionvalve with an isentropic process The s-CO2 flow leavingthe expansion valve will enter the heat exchanger and becooled by the secondary water flow The schematic diagramof the SCO2PE loop is shown in Figure 13 The pressureratio of SCO2PE is relatively low compared to that in the

s-CO2 Brayton cycle used for nuclear application Howeverthe steady and transient experiment data obtained from thisfacility could be used to validate steady performance of thecompressor and the transient behavior of closed compressorloop

The nodalization of SCTRANCO2 is shown in Figure 13Compared to the GAMMA+ model described in [13]SCTRANCO2 made some minor modification in its modelSCTRANCO2 applies a heat flux boundary to simulatethe heat exchanger for simplicity The pressure ratio andefficiency is assumed to keep constant in the steady andtransient simulation Figure 13 shows the nodalization ofSCTRANCO2model and the predicted steady-state result ateach node The steady-state fluid temperature and pressureis very close to the experiment data and the result ofGAMMA+

A reduction in water cooling transient is initialized byreducing the water flow rate from 025 kgs to 017 kgsin 50 seconds The water cooling reduction transient isone of the accidents anticipated in Brayton cycle coolednuclear application The transient simulation by SCTRAN isillustrated in Figure 14 Only the result for the first 180s iscompared At 60s the water flow rate decreased from normalflow rate of 025 kgs to 017 kgs in 50 seconds When thewater flow rate starts to decrease the average temperatureof s-CO2 in the loop increases which further results inthe loop pressure rise Figure 14 shows the inlet and outpressure and the inlet and out temperature of the compressorIn the comparison code SCTRANCO2 predicted the rightparameter variation and the results are very close to theexperiment data and GAMMA+ result Compared to theexperiment data the relative error of compressor inlet andoutlet pressure is within 1 while the relative error of thecompressor inlet and outlet temperature is within 5 Thecomparison result showed that code SCTRANCO2 is able tosimulate the transient process of s-CO2 closed loop


Compressor Inlet(SCTRANCO2)Compressor Outlet(SCTRANCO2)Compressor Inlet(Experiment data)Compressor Outlet(Experiment data)Compressor Inlet(GAMMA code)Compressor Outlet(GAMMA code)

Compressor Inlet(SCTRANCO2)Compressor Outlet(SCTRANCO2)Compressor Inlet(Experiment data)Compressor Outlet(Experiment data)Compressor Inlet(GAMMA)Compressor Outlet(GAMMA)

30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)

Figure 14 Pressure and temperature variation during the cooling reduction transient

5 Present Scope of Validation and FurtherWork to Be Done for the Overall Validation

SCTRAN is originally a transient analysis code for super-critical water reactor (SCWR) It has been applied to carryout accident analysis and safety system design for differenttypes of SCWR [28 29] Thus it is easy for SCTRAN to beupdated for s-CO2 cooled nuclear application A lot of workson numerical algorithms computational time step controland convergent criteria have been studied when SCTRAN isused for supercritical water reactorThenumerical algorithmsbetween SCTRANCO2 and SCTRAN are all the same Thatis the reason why this part is not included in the paperHowever the time step and the mesh size should be carefullyselected after sensitivity analysis For the s-CO2 Brayton cyclepart the transient turbomachinery model is developed andverification of transient analysis of closed s-CO2 loop inSection 4 indicates that SCTRANCO2 owns the ability todo closed loop transient For now SCTRANCO2 could beused to do transient analysis and control strategy analysisfor s-CO2 Brayton cycle in any type due to the fact thatthe compressor turbine and shaft component are modeledseparatelyThe performance of the closed Brayton cycle couldbe evaluated qualitatively not quantitatively For furthervalidation of SCTRANCO2 a large amount of experimentdata on transient turbomachinery performance and transientcycle operation is still in urgent need For further applicationin accident analysis for s-CO2 cooled reactor SCTRANCO2needs to incorporate an overall heat transfer package fora wide operation parameter ranging from supercritical tosubcritical pressure and high to lowmass flow rate for the fuelbuddle inside the core as well as the micro flow channels ofthe PCHE Only with the overall validation on these aspects

SCTRANCO2 could be further used for accident analysissafety system and control system design for s-CO2 Braytoncycle

6 Conclusion

A transient analysis code SCTRANCO2 was developedthrough incorporating accurate thermal property heat trans-fer model and friction model for CO2 and turbomachinerymodel including compressor gas turbine and rotating shaftThe initial verification work on friction model with tubeexperimental data and compressor model with results ofRELAP5-3D was carried out to testify the code program-ing The verification work on heat transfer correlation andcompressor model with experimental data is to validatetheir applicability on s-CO2 applications The results of cyclesimulation indicate that SCTRANCO2 owns the ability tosimulate transient conditions for closed s-CO2 Brayton cycleThe following conclusions can be made

(1) The friction model in SCTRANCO2 was able to pre-dict the right friction coefficient in a wide Reynoldsnumber of 200-106

(2) The Gnielinski correlation in code SCTRANCO2could predict a reasonable outlet temperature of theheat exchanger which works under the operationconditions of the precooler

(3) The compressor model of SCTRANCO2 could pre-dict accurate compressor consuming power and out-let temperature which indicate that it can be used forBrayton cycle simulation

(4) Transient simulation of SCO2PE indicates thatSCTRANCO2 owns the ability to conduct transient


simulations for s-CO2 Brayton cycle Howeveraccurate turbomachinery performance map shouldbe developed and incorporated into the code in thefuture for simple and recompression Brayton cycleanalysis

Nomenclature

119860 Aream2119862119901 Specific heat capacityJsdot(kgsdotK)minus1119863ℎ Hydrodynamic diameterm119891119905119901 Friction coefficient119892119911 Gravitational accelerationm2 sdotsminus1119877119890 Reynolds number119905 Times119881 Fluid velocitymsdotsminus1119882 Mass flow ratekgsdotsminus1119892 Gravity acceleration msdotsminus2ℎ EnthalpyJsdotkgminus1ℎ119897 Specific saturated liquid enthalpyJsdotkgminus1ℎ119892 Specific saturated gas enthalpyJsdotkgminus1119877119901 Pressure ratio119901 PressureMPa119902 Heat fluxWsdotmminus2119904 Specific entropyJsdot(kgsdotK)minus1119911 Lengthm119880 Internal energyJsdotkgminus1119876 Heat source Jsdotkgminus1Greek Letters

120601 Neutron flux120578 Efficiency120591 Torque Nsdotm120583 Dynamic viscosity Nsdotssdotmminus2120588 Densitykgsdotmminus3 Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors would like to express their special thanks for thefinancial support from National Natural Science Foundationof China (Grant no 11605132) and Nuclear Power Institute ofChina

References

[1] Y Ahn S J Bae M Kim et al ldquoReview of supercritical CO2power cycle technology and current status of research and

developmentrdquo Nuclear Engineering and Technology vol 47 no6 pp 647ndash661 2015

[2] M-J Li H-H Zhu J-Q Guo K Wang and W-Q Tao ldquoThedevelopment technology and applications of supercritical CO2power cycle in nuclear energy solar energy and other energyindustriesrdquo Applied Thermal Engineering vol 126 pp 255ndash2752017

[3] D E Shropshire ldquoLessons Learned From GEN I Carbon Diox-ide Cooled Reactorsrdquo in Proceedings of the 12th InternationalConference onNuclear Engineering pp 1ndash11 Arlington VaUSA2004

[4] M A Pope Thermal Hydraulic Design of a 2400MWthDirest Supercritical CO2-Cooled Fast Reactor [Phd thesis] Mas-sachusetts Institute of Technology 2006

[5] M A Pope J I Lee P Hejzlar and M J Driscoll ldquoThermalhydraulic challenges of Gas Cooled Fast Reactors with passivesafety featuresrdquo Nuclear Engineering and Design vol 239 no 5pp 840ndash854 2009

[6] E J Parma S A Wright M E Vernon D Darryn et alSandiarsquos Supercritical CO2 Direct Cycle Gas Fast Reactor (SC-GFR) Concept Sandia National Laboratories 2011

[7] B S Oh Y H Ahn H Yu et al ldquoSafety evaluation ofsupercritical CO2 cooled micro modular reactorrdquo Annals ofNuclear Energy vol 110 pp 1202ndash1216 2017

[8] J-E Cha T-H O Lee J-H Eoh et al ldquoDevelopment of asupercritical co2 brayton energy conversion system coupledwith a sodium cooled fast reactorrdquo Nuclear Engineering andTechnology vol 41 no 8 pp 1025ndash1044 2009

[9] A Moisseytsev and J J Sienicki ldquoTransient accident analysis ofa supercritical carbon dioxide Brayton cycle energy convertercoupled to an autonomous lead-cooled fast reactorrdquo NuclearEngineering and Design vol 238 no 8 pp 2094ndash2105 2008

[10] J J Sienicki M A Smith A V Moisseytsev et al ldquoA SmallSecure Transportable Autonomous Lead-Cooled Fast Reactorfor Deployment at Remote Sitesrdquo in Proceedings of the AmericasNuclear Energy Symposium 2004

[11] J-H Park H S Park T Kim and J G Kwon ldquoTransientAnalysis of Supercritical Carbon Dioxide Brayton Cycle Loopfor System Operation and Controlrdquo NUTHOS-11 1ndash9 2016

[12] B S Oh J I Lee S G Kim et al ldquoTransient Analyses of sCO 2CooledKAIST-MicroModular Reactor withGAMMA+Coderdquoin Proccedings of the 5th International Symposium - SupercriticalCO2 Power Cycles vol 2 pp 1ndash18 2016

[13] S J Bae Y Ahn J Lee S G Kim S Baik and J I Lee ldquoExper-imental and numerical investigation of supercritical CO2 testloop transient behavior near the critical point operationrdquoAppliedThermal Engineering vol 99 pp 572ndash582 2016

[14] A Moisseytsev and J J Sienicki ldquoDevelopment of a PlantDynamics Computer Code for Analysis of a SupercriticalCarbon Dioxide Brayton Cycle Energy Converter Coupledto a Natural Circulation Lead-Cooled Fast Reactorrdquo Reportnumber ANL-0627 2006

[15] A Moisseytsev and J J Sienicki ldquoInvestigation of plant controlstrategies for the supercritical CO2 Brayton cycle for a sodium-cooled fast reactor using the plant dynamics coderdquo Reportnumber ANL-GenIV-147 2010

[16] A Moisseytsev and J J Sienicki ldquoSimulation of S-CO2 Inte-grated System Test With Anl Plant Dynamics Coderdquo in Pro-ceedings of the 5th International Symposium - Supercritical CO2Power Cycles pp 1ndash19 San Antonio Tex USA 2016


[17] J Floyd N Alpy A Moisseytsev et al ldquoA numerical investi-gation of the sCO2 recompression cycle off-design behaviourcoupled to a sodium cooled fast reactor for seasonal variationin the heat sink temperaturerdquoNuclear Engineering and Designvol 260 pp 78ndash92 2013

[18] A Moisseytsev and J J Sienicki ldquoValidation of the ANLPlant Dynamics Code Compressor Model with SNL BNICompressor Test Datardquo in Proceedings of the Supercritical CO2Power Cycle Symposium Boulder Colo USA 2011

[19] M J Hexemer H T Hoang K D Rahner BW Siebert and GD Wahl ldquoIntegrated Systems Test (IST) S-CO2 Brayton LoopTransientModel Description and Initial Resultsrdquo in Proceedingsof the S-CO2 Power Cycle Symposium pp 1ndash172 2009

[20] M J Hexemer ldquoSupercritical CO2 Brayton Cycle IntegratedSystem Test (IST) TRACE Model and Control System Designrdquoin Proceedings of the Supercritical CO2 Power Cycle Symposiumpp 1ndash58 2011

[21] M J Hexemer ldquoSupercritical Co2 brayton recompression cycledesign and control features to support startup and operationrdquoin Proceedings of the 4th International Symposium - SupercriticalCO2 Power Cycles pp 1ndash9 2014

[22] N A Carstens P Hejzlar and M J Driscoll ldquoControl SystemStrategies and Dynamic Response for Supercritical CO2 PowerConversion Cyclesrdquo Report number MIT-GFR-038 2006

[23] N A Carstens Control Strategies for Supercritical CarbonDioxide Power Conversion Systems [PhD thesis] 2007

[24] K J Kimball and EM Clementoni ldquoSupercritical carbon diox-ide brayton power cycle development overviewrdquo in Proceedingsof the ASME Turbo Expo 2012 Turbine Technical Conference andExposition pp 931ndash940 Denmark June 2012

[25] T Conboy S Wright J Pasch D Fleming G Rochau and RFuller ldquoPerformance Characteristics of an Operating Supercrit-ical CO2Brayton Cyclerdquo Journal of Engineering for Gas Turbinesand Power vol 134 no 11 2012

[26] Y Ahn J Lee S G Kim J I Lee J E Cha and S-W LeeldquoDesign consideration of supercritical CO2 power cycle integralexperiment looprdquo Energy vol 86 pp 115ndash127 2015

[27] P Wu J Gou J Shan Y Jiang J Yang and B ZhangldquoSafety analysis code SCTRAN development for SCWR and itsapplication to CGNPC SCWRrdquo Annals of Nuclear Energy vol56 pp 122ndash135 2013

[28] P Wu J Gou J Shan B Zhang and X Li ldquoPreliminary safetyevaluation for CSR1000 with passive safety systemrdquo Annals ofNuclear Energy vol 65 pp 390ndash401 2014

[29] P Wu J Shan J Gou L K H Leung B Zhang and B ZhangldquoHeat transfer effectiveness for cooling of Canadian SCWR fuelassembly under the LOCALOECC scenariordquoAnnals of NuclearEnergy vol 81 pp 306ndash319 2015

[30] V Dostal A Supercritical Carbon Dioxide Cycle for next Gener-ation Nuclear Reactors [PhD thesis] 2004

[31] B Liu L Cao H Wu X Yuan and K Wang ldquoPre-conceptualcore design of a small modular fast reactor cooled by supercriti-cal CO2rdquoNuclearEngineering andDesign vol 300 pp 339ndash3482016

[32] Z Wang B Sun J Wang and L Hou ldquoExperimental study onthe friction coefficient of supercritical carbon dioxide in pipesrdquoInternational Journal of Greenhouse Gas Control vol 25 pp 151ndash161 2014

[33] J V Meter Experimental Investigation of a Printed Circuit HeatExchanger Using Supercritical Carbon Dioxide and Water AsHeat Transfer Media [master thesis] Kansas State University2006

[34] J E Fisher and B D Cliff ldquoRELAP5-3D CompressorModelrdquo inProceedings of the Space Nuclear Conference ANS Meeting pp5ndash8 San Diego Calif USA June 2005

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Active and Passive Electronic Components

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Submit your manuscripts atwwwhindawicom


Reactor

Recuperator

Precooler

Water side

Compressor TurbineGenerator

S-CO2 flow

Figure 1 Schematicmap of nuclear reactor system cooled by s-CO2Brayton cycle

pressure and the neutronic spectrum are different from thatof S-CO2 cooled fast reactor the operational characteristicssafety issues and behavior of the fuel cladding and coolantcould provide great reference for S-CO2 cooled fast reactorcore design Pope [4] from MIT has proposed a 4-loop2400MWth direct S-CO2 cooled fast reactor concept coupledwith recompression S-CO2 Brayton cycle This concept ownsa core design with Tube in Duct (TID) assemblies andadvanced shielding material advanced cladding materials forhigh burn-up fuel and high temperature Oxide fuel wasselected as the fuel form for its chemical compatibility withCO2 Accident analysis and safety design have been carriedout for this concept [5] A relatively small fast reactor conceptwhich is cooled with CO2 at pressure of 20MPa is proposedby Parma et al from Sandia National Laboratories [6] Thereactor concept applied bundled fuel assemblies which refersfrom that of AdvancedGasReactor (AGR) [3] A supercriticalCO2-cooledMicroModular Reactor (MMR)with 362MWthpower is developed by [7] Transportability is one of theMMRrsquos features which is achieved by the compact cycleconfiguration and modularized reactor design

Another option to apply S-CO2 Brayton cycle workingas the power conversion system of existing Gen IV reactorconcept which tries to take advantages of large amount ofRampD work of these new concepts and improve the cycleefficiency at the same time Feasibility of S-CO2 Braytoncoupled to sodium fast reactor concept KALIMER-600 [8]lead fast reactor concept STAR-LM [9] and SSTAR [10] S-CO2 Brayton cycle configuration as well as the transientperformance and control strategy of these concepts has beencarried out which shows great potential for applying S-CO2Brayton cycle on these new reactor concepts A summary ofthe core design and Brayton cycle design of the above nuclearapplications is listed in Table 1

Transient analysis code is a necessity for study of controlstrategy dynamic characteristic and safety analysis for S-CO2Brayton cycle direct or indirect cooled reactors According tothe features of Brayton cycle coupled reactor applications thetransient analysis code should possess the ability to simulatereactor core precooler recuperator and turbomachineryincluding compressor gas turbine and rotating shaft model

Different transient analysis codes have been developed tosatisfy the demand for control strategy and accident study

for s-CO2 Brayton cycle direct or indirect cooled reactors Atransient analysis codeMMS-LMRwas developed to simulatethe system transient and evaluate control logics for sodium-cooled fast reactor KALIMER-600 [8]The code can simulatecoolant of Sodium and CO2 and modules like reactor pipeNa-CO2 heat exchanger recuperator and compressor CodeMARS has been applied to carry out up-power and down-power transient simulation for the Supercritical CO2 IntegralExperimental Loop (SCIEL) [11] A modified GAMMA+code was developed and applied for the analysis of KAISTMicro Modular Reactor (MMR) for simulation of loss ofload and loss of coolant accidents [12] Accurate CO2 prop-erties near critical point and turbomachinery performancemap were incorporated into the original GAMMA+ whichwas previously a transient analysis code for Very High-Temperature Reactor (VHTR) system developed by KAERIThe performance map for GAMMA+ is produced by KAIST-TMD which is an in-house code to design the turbomachin-ery GAMMA+ code simulation ability near critical pointhas been validated with comparing with the experimentdata from SCO2PE [13] RELAP5-3D has s-CO2 propertiesand compressor and turbine models which could help tosimulate the s-CO2 Brayton cycle It has been used to analyzethe safety performance for s-CO2 cooled fast reactors withpassive safety system under loss of coolant accident andloss of generator load accident [4 5] A plant dynamicscomputer code named Plant Dynamics Code (PDC) has beendeveloped by ANL [14] The PDC solves time-dependentmass momentum and energy conservation equations for s-CO2 fluid plus the turbomachinery shaft dynamics equationThis code has been applied to various applications such astransient and control strategies analysis of s-CO2 Braytoncycle coupled to lead-cooled fast reactor [9] autonomousload following for an SFR by coupling with SAS4ASASYSYS-1 to determine the core side [15] simulation of s-CO2Integrated System Test [16] and off-design behavior analysisfor s-CO2 Brayton cycle coupled to sodium-cooled fastreactor [17] Validation work has been done by comparingPDC compressor model with SNLBNI compressor test data[18] TRACE source code was modified by adding new fluid(s-CO2) as well as Brayton turbomachinery componentsto enhance its ability to simulate s-CO2 Brayton cycle [1920] Cycle design and control features during startup andoperation have been carried out [21] GAS-PASS is a dynamicsimulation and control code for gas-cooled Brayton cyclereactor power conversion system It has been modified todeal with the use of s-CO2 Brayton cycle [22] The controlstrategies have been studied [23]

Through the overview of the current transient analysiscode development for nuclear application related Braytoncycle we can find most of the codes are developed basedon existing transient analysis codes with incorporating CO2property turbomachinery models and PCHE models Thevalidation work is based on experimental data produced by s-CO2 Brayton cycle experimental platforms such as 100 kWes-CO2 power cycle system facility constructed by the cooper-ation of Knolls Atomic Power Laboratory (KAPL) and BettisAtomic Energy Laboratory (BAEL) in 2012 [24] 10MWebasic s-CO2 Brayton cycle established by Sadia National


Table1Overviewof

currentstudy


workingas

powe

rcon

versionsyste

mon

nucleara

pplications

Con

cept

Nam

e-

MMR

SC-G

FR-

KALIMER

-600

STAR-LM

SSTA

RDevelop

ing

-KA

IST

SNL

MIT

KAER

IArgon

neNational

Labo

ratory

Argon

neNational

Labo

ratory

Institutio

nBraytoncycle

-direct

direct

direct

indirect

indirect

indirect

coup

ledmetho

d

CoreP

art

thermalpo

wer(MW)

362

200

2400

15289

400

45Pressure

(MPa)

2020

2001

01

01

Fueltype

UCfuel

UO2

UO2B

eOU-TRU

-10

ZrTR

U-N

Enric

hed

toN15

Nitridefuel

Cladding

type

Stainlesssteel

HighNi

ODSMA956

Mod

HT9

Co-extrud

ed

-Stainlesssteel

Si-enh

anced

FM

stainless

steelwith

FM

substrate

Coreo

utlettem

perature

550

650

650

5453

578

5658

Massfl

owrate(kgs)

180

920

11708

77313

19708

2125

Coo

lant

CO2

CO2

CO2

Sodium

PbPb

Powe

rCon

version

Syste

m

Braytoncycletype

simplec

ycle

nospecificd

esign

recompressio

ncycle

recompressio

ncycle

recompressio

ncycle

recompressio

ncycle

Cyclem

assfl

owrate

(kgs)

180

-2927

80766

2276

2393

TPof

compressor

Inlet(∘ CM

Pa)

60880

-32769

312574

312574

312574

TPof

compressoro

utlet

(∘ CM

Pa)

1422200

-60

920

848200

85200

849200

TPof

recompressio

ncompressorinlet

(∘ CM

Pa)

--

709771

912746

863740

5909740

1

TPof

recompressio

ncompressoro

utlet

(∘ CM

Pa)

--

1591

200

1894

1998

18381998

1898

20

TPof

turbineinlet

(∘ CM

Pa)

5501993

-6501945

50801974

54001988

5414

1999

TPof

turbineo

utlet

(∘ CM

Pa)

44075816

-5299

793

394276

426977

1342017435

Reference

-[7]

[6]

[4]

[8]

[9]

[10]




2 Code Development



120597120597119905120588119860 + 120597

120597119911119882 = 0 (1)


120597120597119905119882 + 120597

120597119911119882119881 = minus119860120597119901120597119911 minus 2119860120588119881 |119881|

119863ℎ 119891119905119901 + 120588119860119892119911 (2)



119889119889119905119880 = minus12

119871119860

119889119889119905 (

1198822120588 ) minussum

119895

(119882119892ℎ119892 +119882119897ℎ119897)

+ 12 (119882119892119881119892119881119892 +119882119897119881119897119881119897) +119882119892 (119911 minus 119911119895) + 119876

(3)




1V120597120601 (119903 119905)

120597119905 = 119863nabla2120601 (119903 119905) minus Σ119886120601 (119903 119905)

+ (1 minus 120573) 119896infinΣ119886120601 (119903 119905) +6sum119894=1

120582119894119862119894 (119903 119905)(4)








= ℎ11987921015840 minus ℎ1198791ℎ1198792 minus ℎ1198791 (5)


h

S

Ｂ02

Ｂ2Ｍ

Ｂ01

０02

０2

０01

０1




Δ119875 = 1198751198791 (119877119901 minus 1) (6)




(7)



120591119904 =∙119898120596 (ℎ11987921015840 minus ℎ1198791 ) (8)


120591d =∙1198981205961 minus 120578119886119889120578119886119889 (ℎ11987921015840 minus ℎ1198791 ) (9)


120591t = 120591119904 + 120591d =∙119898120596

1120578119886119889 (ℎ

11987921015840 minus ℎ1198791 ) (10)

h

SCompression

Ｂ02

Ｂ2Ｍ

Ｂ01

０02

０2

０01

０1






Δℎ = ℎ11987921015840 minus ℎ1198791120578119886119889 (11)

For pressure drop

Δ119875 = 1198751 (119877119901 minus 1) (12)


120591t = 120591119904 + 120591d =∙119898 120578119886119889120596 (ℎ11987921015840 minus ℎ1198791 ) (13)


sum119894

119868119894119889120596119889119905 = sum119894

120591119894 minussum119894

119891119894120596 + 120591119888 (14)















where

119891 = 1(18 log (Re) minus 15)2 (16)




37119863119890+ 251

Re[114 minus 2 log( 120576

119863119890 +2125Re09

)](17)



001

01

1

Dar

cy fr

ictio

n fa

ctor

f

1000 10000 100000 1000000100Re



119891 = 64Re

(18)











FILTERCOLDLEG

COLDLEG

CORIOLISFLOWMETER

LEVELDETECTOR

EXHAUST

PRESSURIZERGEARPUMP

DIELECTRICUNION

HOTLEG

HOTLEG

HEATRIC HX

FILTER

P

P

P

=

=

=

=

=

ABSOLUTE PRESSURE


FLUID TEMPERATURE

WALL TEMPERATURE

RELIEF VALVE

Water

S-CO2

CO2

CO2

Δ０

Δ０

Δ０

４

４７

４

４４４

４７４７４７４７

４

４

４

４

0-60 VAC

440 VAC 770 A

POWER SUPPLY

5000 A

４







35

36

37

38

39

40

41

42

Tem

pera

ture

(∘C)

10 20 30 40 500Node number




30

40

50

60

70

80

90

Tem

pera

ture

(∘C)

400 800 12000Length (mm)








Fluent-2DSCTRANCO2


∘C)

34

36

38

40

42

44

46

Hot

Sid

e Exi

t Sim

ulat

ion

Tem

pera

ture

(∘C)





382

380

350

346 345

341













relative speed=10

0

10

20

30

40

50

60

70

80

90

100Po

wer

cons

umed

by

com

pres

sor (

MW

)


RELAP5-3DSCTRANCO2


10 15

20






Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa


GAMMA T GAMMA P MPa


C

C

C

C

C

C

C

C

C

C

C












30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



Table1Overviewof

currentstudy


workingas

powe

rcon

versionsyste

mon

nucleara

pplications

Con

cept

Nam

e-

MMR

SC-G

FR-

KALIMER

-600

STAR-LM

SSTA

RDevelop

ing

-KA

IST

SNL

MIT

KAER

IArgon

neNational

Labo

ratory

Argon

neNational

Labo

ratory

Institutio

nBraytoncycle

-direct

direct

direct

indirect

indirect

indirect

coup

ledmetho

d

CoreP

art

thermalpo

wer(MW)

362

200

2400

15289

400

45Pressure

(MPa)

2020

2001

01

01

Fueltype

UCfuel

UO2

UO2B

eOU-TRU

-10

ZrTR

U-N

Enric

hed

toN15

Nitridefuel

Cladding

type

Stainlesssteel

HighNi

ODSMA956

Mod

HT9

Co-extrud

ed

-Stainlesssteel

Si-enh

anced

FM

stainless

steelwith

FM

substrate

Coreo

utlettem

perature

550

650

650

5453

578

5658

Massfl

owrate(kgs)

180

920

11708

77313

19708

2125

Coo

lant

CO2

CO2

CO2

Sodium

PbPb

Powe

rCon

version

Syste

m

Braytoncycletype

simplec

ycle

nospecificd

esign

recompressio

ncycle

recompressio

ncycle

recompressio

ncycle

recompressio

ncycle

Cyclem

assfl

owrate

(kgs)

180

-2927

80766

2276

2393

TPof

compressor

Inlet(∘ CM

Pa)

60880

-32769

312574

312574

312574

TPof

compressoro

utlet

(∘ CM

Pa)

1422200

-60

920

848200

85200

849200

TPof

recompressio

ncompressorinlet

(∘ CM

Pa)

--

709771

912746

863740

5909740

1

TPof

recompressio

ncompressoro

utlet

(∘ CM

Pa)

--

1591

200

1894

1998

18381998

1898

20

TPof

turbineinlet

(∘ CM

Pa)

5501993

-6501945

50801974

54001988

5414

1999

TPof

turbineo

utlet

(∘ CM

Pa)

44075816

-5299

793

394276

426977

1342017435

Reference

-[7]

[6]

[4]

[8]

[9]

[10]




2 Code Development



120597120597119905120588119860 + 120597

120597119911119882 = 0 (1)


120597120597119905119882 + 120597

120597119911119882119881 = minus119860120597119901120597119911 minus 2119860120588119881 |119881|

119863ℎ 119891119905119901 + 120588119860119892119911 (2)



119889119889119905119880 = minus12

119871119860

119889119889119905 (

1198822120588 ) minussum

119895

(119882119892ℎ119892 +119882119897ℎ119897)

+ 12 (119882119892119881119892119881119892 +119882119897119881119897119881119897) +119882119892 (119911 minus 119911119895) + 119876

(3)




1V120597120601 (119903 119905)

120597119905 = 119863nabla2120601 (119903 119905) minus Σ119886120601 (119903 119905)

+ (1 minus 120573) 119896infinΣ119886120601 (119903 119905) +6sum119894=1

120582119894119862119894 (119903 119905)(4)








= ℎ11987921015840 minus ℎ1198791ℎ1198792 minus ℎ1198791 (5)


h

S

Ｂ02

Ｂ2Ｍ

Ｂ01

０02

０2

０01

０1




Δ119875 = 1198751198791 (119877119901 minus 1) (6)




(7)



120591119904 =∙119898120596 (ℎ11987921015840 minus ℎ1198791 ) (8)


120591d =∙1198981205961 minus 120578119886119889120578119886119889 (ℎ11987921015840 minus ℎ1198791 ) (9)


120591t = 120591119904 + 120591d =∙119898120596

1120578119886119889 (ℎ

11987921015840 minus ℎ1198791 ) (10)

h

SCompression

Ｂ02

Ｂ2Ｍ

Ｂ01

０02

０2

０01

０1






Δℎ = ℎ11987921015840 minus ℎ1198791120578119886119889 (11)

For pressure drop

Δ119875 = 1198751 (119877119901 minus 1) (12)


120591t = 120591119904 + 120591d =∙119898 120578119886119889120596 (ℎ11987921015840 minus ℎ1198791 ) (13)


sum119894

119868119894119889120596119889119905 = sum119894

120591119894 minussum119894

119891119894120596 + 120591119888 (14)















where

119891 = 1(18 log (Re) minus 15)2 (16)




37119863119890+ 251

Re[114 minus 2 log( 120576

119863119890 +2125Re09

)](17)



001

01

1

Dar

cy fr

ictio

n fa

ctor

f

1000 10000 100000 1000000100Re



119891 = 64Re

(18)











FILTERCOLDLEG

COLDLEG

CORIOLISFLOWMETER

LEVELDETECTOR

EXHAUST

PRESSURIZERGEARPUMP

DIELECTRICUNION

HOTLEG

HOTLEG

HEATRIC HX

FILTER

P

P

P

=

=

=

=

=

ABSOLUTE PRESSURE


FLUID TEMPERATURE

WALL TEMPERATURE

RELIEF VALVE

Water

S-CO2

CO2

CO2

Δ０

Δ０

Δ０

４

４７

４

４４４

４７４７４７４７

４

４

４

４

0-60 VAC

440 VAC 770 A

POWER SUPPLY

5000 A

４







35

36

37

38

39

40

41

42

Tem

pera

ture

(∘C)

10 20 30 40 500Node number




30

40

50

60

70

80

90

Tem

pera

ture

(∘C)

400 800 12000Length (mm)








Fluent-2DSCTRANCO2


∘C)

34

36

38

40

42

44

46

Hot

Sid

e Exi

t Sim

ulat

ion

Tem

pera

ture

(∘C)





382

380

350

346 345

341













relative speed=10

0

10

20

30

40

50

60

70

80

90

100Po

wer

cons

umed

by

com

pres

sor (

MW

)


RELAP5-3DSCTRANCO2


10 15

20






Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa


GAMMA T GAMMA P MPa


C

C

C

C

C

C

C

C

C

C

C












30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018





2 Code Development



120597120597119905120588119860 + 120597

120597119911119882 = 0 (1)


120597120597119905119882 + 120597

120597119911119882119881 = minus119860120597119901120597119911 minus 2119860120588119881 |119881|

119863ℎ 119891119905119901 + 120588119860119892119911 (2)



119889119889119905119880 = minus12

119871119860

119889119889119905 (

1198822120588 ) minussum

119895

(119882119892ℎ119892 +119882119897ℎ119897)

+ 12 (119882119892119881119892119881119892 +119882119897119881119897119881119897) +119882119892 (119911 minus 119911119895) + 119876

(3)




1V120597120601 (119903 119905)

120597119905 = 119863nabla2120601 (119903 119905) minus Σ119886120601 (119903 119905)

+ (1 minus 120573) 119896infinΣ119886120601 (119903 119905) +6sum119894=1

120582119894119862119894 (119903 119905)(4)








= ℎ11987921015840 minus ℎ1198791ℎ1198792 minus ℎ1198791 (5)


h

S

Ｂ02

Ｂ2Ｍ

Ｂ01

０02

０2

０01

０1




Δ119875 = 1198751198791 (119877119901 minus 1) (6)




(7)



120591119904 =∙119898120596 (ℎ11987921015840 minus ℎ1198791 ) (8)


120591d =∙1198981205961 minus 120578119886119889120578119886119889 (ℎ11987921015840 minus ℎ1198791 ) (9)


120591t = 120591119904 + 120591d =∙119898120596

1120578119886119889 (ℎ

11987921015840 minus ℎ1198791 ) (10)

h

SCompression

Ｂ02

Ｂ2Ｍ

Ｂ01

０02

０2

０01

０1






Δℎ = ℎ11987921015840 minus ℎ1198791120578119886119889 (11)

For pressure drop

Δ119875 = 1198751 (119877119901 minus 1) (12)


120591t = 120591119904 + 120591d =∙119898 120578119886119889120596 (ℎ11987921015840 minus ℎ1198791 ) (13)


sum119894

119868119894119889120596119889119905 = sum119894

120591119894 minussum119894

119891119894120596 + 120591119888 (14)















where

119891 = 1(18 log (Re) minus 15)2 (16)




37119863119890+ 251

Re[114 minus 2 log( 120576

119863119890 +2125Re09

)](17)



001

01

1

Dar

cy fr

ictio

n fa

ctor

f

1000 10000 100000 1000000100Re



119891 = 64Re

(18)











FILTERCOLDLEG

COLDLEG

CORIOLISFLOWMETER

LEVELDETECTOR

EXHAUST

PRESSURIZERGEARPUMP

DIELECTRICUNION

HOTLEG

HOTLEG

HEATRIC HX

FILTER

P

P

P

=

=

=

=

=

ABSOLUTE PRESSURE


FLUID TEMPERATURE

WALL TEMPERATURE

RELIEF VALVE

Water

S-CO2

CO2

CO2

Δ０

Δ０

Δ０

４

４７

４

４４４

４７４７４７４７

４

４

４

４

0-60 VAC

440 VAC 770 A

POWER SUPPLY

5000 A

４







35

36

37

38

39

40

41

42

Tem

pera

ture

(∘C)

10 20 30 40 500Node number




30

40

50

60

70

80

90

Tem

pera

ture

(∘C)

400 800 12000Length (mm)








Fluent-2DSCTRANCO2


∘C)

34

36

38

40

42

44

46

Hot

Sid

e Exi

t Sim

ulat

ion

Tem

pera

ture

(∘C)





382

380

350

346 345

341













relative speed=10

0

10

20

30

40

50

60

70

80

90

100Po

wer

cons

umed

by

com

pres

sor (

MW

)


RELAP5-3DSCTRANCO2


10 15

20






Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa


GAMMA T GAMMA P MPa


C

C

C

C

C

C

C

C

C

C

C












30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



h

S

Ｂ02

Ｂ2Ｍ

Ｂ01

０02

０2

０01

０1




Δ119875 = 1198751198791 (119877119901 minus 1) (6)




(7)



120591119904 =∙119898120596 (ℎ11987921015840 minus ℎ1198791 ) (8)


120591d =∙1198981205961 minus 120578119886119889120578119886119889 (ℎ11987921015840 minus ℎ1198791 ) (9)


120591t = 120591119904 + 120591d =∙119898120596

1120578119886119889 (ℎ

11987921015840 minus ℎ1198791 ) (10)

h

SCompression

Ｂ02

Ｂ2Ｍ

Ｂ01

０02

０2

０01

０1






Δℎ = ℎ11987921015840 minus ℎ1198791120578119886119889 (11)

For pressure drop

Δ119875 = 1198751 (119877119901 minus 1) (12)


120591t = 120591119904 + 120591d =∙119898 120578119886119889120596 (ℎ11987921015840 minus ℎ1198791 ) (13)


sum119894

119868119894119889120596119889119905 = sum119894

120591119894 minussum119894

119891119894120596 + 120591119888 (14)















where

119891 = 1(18 log (Re) minus 15)2 (16)




37119863119890+ 251

Re[114 minus 2 log( 120576

119863119890 +2125Re09

)](17)



001

01

1

Dar

cy fr

ictio

n fa

ctor

f

1000 10000 100000 1000000100Re



119891 = 64Re

(18)











FILTERCOLDLEG

COLDLEG

CORIOLISFLOWMETER

LEVELDETECTOR

EXHAUST

PRESSURIZERGEARPUMP

DIELECTRICUNION

HOTLEG

HOTLEG

HEATRIC HX

FILTER

P

P

P

=

=

=

=

=

ABSOLUTE PRESSURE


FLUID TEMPERATURE

WALL TEMPERATURE

RELIEF VALVE

Water

S-CO2

CO2

CO2

Δ０

Δ０

Δ０

４

４７

４

４４４

４７４７４７４７

４

４

４

４

0-60 VAC

440 VAC 770 A

POWER SUPPLY

5000 A

４







35

36

37

38

39

40

41

42

Tem

pera

ture

(∘C)

10 20 30 40 500Node number




30

40

50

60

70

80

90

Tem

pera

ture

(∘C)

400 800 12000Length (mm)








Fluent-2DSCTRANCO2


∘C)

34

36

38

40

42

44

46

Hot

Sid

e Exi

t Sim

ulat

ion

Tem

pera

ture

(∘C)





382

380

350

346 345

341













relative speed=10

0

10

20

30

40

50

60

70

80

90

100Po

wer

cons

umed

by

com

pres

sor (

MW

)


RELAP5-3DSCTRANCO2


10 15

20






Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa


GAMMA T GAMMA P MPa


C

C

C

C

C

C

C

C

C

C

C












30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018















where

119891 = 1(18 log (Re) minus 15)2 (16)




37119863119890+ 251

Re[114 minus 2 log( 120576

119863119890 +2125Re09

)](17)



001

01

1

Dar

cy fr

ictio

n fa

ctor

f

1000 10000 100000 1000000100Re



119891 = 64Re

(18)











FILTERCOLDLEG

COLDLEG

CORIOLISFLOWMETER

LEVELDETECTOR

EXHAUST

PRESSURIZERGEARPUMP

DIELECTRICUNION

HOTLEG

HOTLEG

HEATRIC HX

FILTER

P

P

P

=

=

=

=

=

ABSOLUTE PRESSURE


FLUID TEMPERATURE

WALL TEMPERATURE

RELIEF VALVE

Water

S-CO2

CO2

CO2

Δ０

Δ０

Δ０

４

４７

４

４４４

４７４７４７４７

４

４

４

４

0-60 VAC

440 VAC 770 A

POWER SUPPLY

5000 A

４







35

36

37

38

39

40

41

42

Tem

pera

ture

(∘C)

10 20 30 40 500Node number




30

40

50

60

70

80

90

Tem

pera

ture

(∘C)

400 800 12000Length (mm)








Fluent-2DSCTRANCO2


∘C)

34

36

38

40

42

44

46

Hot

Sid

e Exi

t Sim

ulat

ion

Tem

pera

ture

(∘C)





382

380

350

346 345

341













relative speed=10

0

10

20

30

40

50

60

70

80

90

100Po

wer

cons

umed

by

com

pres

sor (

MW

)


RELAP5-3DSCTRANCO2


10 15

20






Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa


GAMMA T GAMMA P MPa


C

C

C

C

C

C

C

C

C

C

C












30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018




001

01

1

Dar

cy fr

ictio

n fa

ctor

f

1000 10000 100000 1000000100Re



119891 = 64Re

(18)











FILTERCOLDLEG

COLDLEG

CORIOLISFLOWMETER

LEVELDETECTOR

EXHAUST

PRESSURIZERGEARPUMP

DIELECTRICUNION

HOTLEG

HOTLEG

HEATRIC HX

FILTER

P

P

P

=

=

=

=

=

ABSOLUTE PRESSURE


FLUID TEMPERATURE

WALL TEMPERATURE

RELIEF VALVE

Water

S-CO2

CO2

CO2

Δ０

Δ０

Δ０

４

４７

４

４４４

４７４７４７４７

４

４

４

４

0-60 VAC

440 VAC 770 A

POWER SUPPLY

5000 A

４







35

36

37

38

39

40

41

42

Tem

pera

ture

(∘C)

10 20 30 40 500Node number




30

40

50

60

70

80

90

Tem

pera

ture

(∘C)

400 800 12000Length (mm)








Fluent-2DSCTRANCO2


∘C)

34

36

38

40

42

44

46

Hot

Sid

e Exi

t Sim

ulat

ion

Tem

pera

ture

(∘C)





382

380

350

346 345

341













relative speed=10

0

10

20

30

40

50

60

70

80

90

100Po

wer

cons

umed

by

com

pres

sor (

MW

)


RELAP5-3DSCTRANCO2


10 15

20






Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa


GAMMA T GAMMA P MPa


C

C

C

C

C

C

C

C

C

C

C












30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



FILTERCOLDLEG

COLDLEG

CORIOLISFLOWMETER

LEVELDETECTOR

EXHAUST

PRESSURIZERGEARPUMP

DIELECTRICUNION

HOTLEG

HOTLEG

HEATRIC HX

FILTER

P

P

P

=

=

=

=

=

ABSOLUTE PRESSURE


FLUID TEMPERATURE

WALL TEMPERATURE

RELIEF VALVE

Water

S-CO2

CO2

CO2

Δ０

Δ０

Δ０

４

４７

４

４４４

４７４７４７４７

４

４

４

４

0-60 VAC

440 VAC 770 A

POWER SUPPLY

5000 A

４







35

36

37

38

39

40

41

42

Tem

pera

ture

(∘C)

10 20 30 40 500Node number




30

40

50

60

70

80

90

Tem

pera

ture

(∘C)

400 800 12000Length (mm)








Fluent-2DSCTRANCO2


∘C)

34

36

38

40

42

44

46

Hot

Sid

e Exi

t Sim

ulat

ion

Tem

pera

ture

(∘C)





382

380

350

346 345

341













relative speed=10

0

10

20

30

40

50

60

70

80

90

100Po

wer

cons

umed

by

com

pres

sor (

MW

)


RELAP5-3DSCTRANCO2


10 15

20






Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa


GAMMA T GAMMA P MPa


C

C

C

C

C

C

C

C

C

C

C












30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018






Fluent-2DSCTRANCO2


∘C)

34

36

38

40

42

44

46

Hot

Sid

e Exi

t Sim

ulat

ion

Tem

pera

ture

(∘C)





382

380

350

346 345

341













relative speed=10

0

10

20

30

40

50

60

70

80

90

100Po

wer

cons

umed

by

com

pres

sor (

MW

)


RELAP5-3DSCTRANCO2


10 15

20






Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa


GAMMA T GAMMA P MPa


C

C

C

C

C

C

C

C

C

C

C












30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018









relative speed=10

0

10

20

30

40

50

60

70

80

90

100Po

wer

cons

umed

by

com

pres

sor (

MW

)


RELAP5-3DSCTRANCO2


10 15

20






Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa


GAMMA T GAMMA P MPa


C

C

C

C

C

C

C

C

C

C

C












30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



Expansion valve

123

4

6

11

10

5

987

Compressor

Heat exchanger

S-CO2 closed loop

318 741 MPa

318 741 MPa

319 746 MPa

354

357

353

789MPa

790MPa

789MPa

331

328

323 751 MPa

751 MPa

751 MPa


GAMMA T GAMMA P MPa


C

C

C

C

C

C

C

C

C

C

C












30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018





30

32

34

36

38

40

42

S-

2Te

mpe

ratu

re(∘

C)

20 40 60 80 100 120 140 160 1800Time (s)

20 40 60 80 100 120 140 160 1800Time (s)

74

76

78

80

82

84

86

88Pr

essu

re (M

Pa)





6 Conclusion








Nomenclature






Acknowledgments


References

















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018




Nomenclature






Acknowledgments


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

Development and Verification of a Transient Analysis Tool ...downloads.hindawi.com/journals/stni/2018/6801736.pdf · 16.03.2018 · KALIMER- STAR-LM SSTAR Developing-KAIST SNL MIT