subchannel analysis of candu-scwr fuel
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Progress in Nuclear Energy 51 (2009) 799–804
Contents lists avai
Progress in Nuclear Energy
journal homepage: www.elsevier .com/locate/pnucene
Subchannel analysis of CANDU-SCWR fuel
Changying Li a,b, Jianqiang Shan a,*, Laurence K.H. Leung c
a State Key Laboratories of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an Shaanxi 710049, Chinab China Nuclear Power Technology Research Institute, Guangdong Shenzhen 518026, Chinac Chalk River Laboratories, Atomic Energy of Canada Limited, Chalk River, Ontario, Canada K0J 1J0
Keywords:SubchannelCANDU-SCWRATHASCANFLEX
* Corresponding author. Tel.: þ86 29 82663769; faxE-mail address: [email protected] (J. Shan).
1 CANDU – Canada Deuterium Uranium (a registere
0149-1970/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.pnucene.2009.05.004
a b s t r a c t
A cooperative study has been initiated at Xi’an Jiaotong University (XJTU) with Atomic Energy of CanadaLimited (AECL) to develop a subchannel code ATHAS for preliminary analyses of flow and enthalpydistributions and cladding temperatures in CANDU fuel at super-critical water conditions. The code isapplicable for transient and steady-state calculations. Then the paper uses the ATHAS code to analyzeCANDU-SCWR which is operating at 25.0 MPa pressure. The results show that the maximum cladding-surface temperature of CANFLEX bundle is 804.1 �C, which is below the limit of design, and it is appropriatefor use in the CANDU super-critical water-cooled reactor (SCWR) based on heat-transfer analysis.
� 2009 Elsevier Ltd. All rights reserved.
1. Introduction
The super-critical water-cooled reactor (SCWR) is essentiallya pressurized water reactor operating above the thermodynamiccritical point of water (Tc¼ 647.096 K, Pc¼ 22.064 MPa). It isconsidered as one of the most promising Generation IV reactorsbecause of its simplicity, high thermal efficiency, and nearly fiftyyears of industrial experience from thermal-power stations witha SCW cycle(Buongiorno, 2003). Evolving from the existing designs,there are currently two types of SCWR concepts: (a) a large reactorpressure vessel containing the reactor core (fuelled) heat source,analogous to conventional PWRs and BWRs, and (b) distributedpressure tubes or channels containing fuel bundles, analogous toconventional CANDU1 and RBMK nuclear reactors. The design ofCANDU-SCWR aims at cost reduction and improved safety, ascompared to the existing fleet of CANDU reactors.
A relatively large amount of research studies in Japan andEuropean Union have been focusing on the pressure-vessel type ofSCWR design. Oka (Oka, 2000) summarized design concepts ofSCWR and proposed the concept of once-through cycle, super-critical pressure, light-water-cooled reactors (Oka and Koshizuka,2000; Yamaji et al., 2005) Heusener et al.(Heusener et al., 2000)proposed a different conceptual design of the SCWR. Both conceptsof Oka and Heusener are thermal reactor; Yoo et al. (Yoo et al.,2005) introduced a separate concept based on the fast reactordesign.
: þ86 29 82667802.
d trademark of AECL).
All rights reserved.
Russia and Canada have been focusing on the pressure-tubedesign of the SCWR (Duffey et al., 2005). The pressure-tube designeliminates the need of a thick wall vessel. In principle, this designhas the four key features for improving safety and performance:passive heat removal, multi-pass reactor flow, flexible fuellingstrategy, and flat power and temperature distributions in the core.
1.1. Features of pressure-tube type of SCWR design
The separation of coolant and moderator allows the introduc-tion of a passive heat-removal system to mitigate consequencesduring accident scenarios where active cooling may not be avail-able. Decay heat is removed through radiation and convection fromdistributed channels during accidents, and consequently prevent-ing fuel melting in the core. Therefore, this design is potentially aninherently safe system.
The use of multi-pass reactor flows facilitates the inclusion ofreheat and superheat features in the design (without overheatingthe pressure tube). These features allow the production of processheat on demand and improve the thermal efficiency.
A distributed fuel-channel system allows the introduction ofoptimized fuel bundles into each channel tailoring appropriate fuelcycle, cladding temperature, and flow and power distributionsindependently. This ensures stable and predictable performance ofthe reactor and allows the flexibility to design specific reactor sizeand thermal power from 300 MW to 1400 MW (by changing thenumber of fuel channels in the core) to meet the customerrequirements on site, financing and product mix.
The separation of coolant and moderator provides, to someextents, the flexibility to adjust the lattice pitch of channels and fuel
Start
Initialize (t=0)
Lateral Momentum
Set boundary condition
Axial Momentum
Mass conservation
Energy Balance
Continuity iteration
Outer iteration
Next step
Update W
Update F
Update P F W
N
Y
update h
Read input:geometry
Convergence
Stop
Fig. 1. Evaluation scheme of ATHAS subchannel code.
C. Li et al. / Progress in Nuclear Energy 51 (2009) 799–804800
enrichment for requirements of negative void, and power andtemperature coefficients of reactivity. In addition, the power andtemperature distributions in the core can be flattened (due tointerlacing the flow directions of neighboring channels) to ensureinherently safe operational and performance characteristics.
1.2. Previous subchannel analyses in support of SCWR fuel design
The super-critical water coolant remains in single phase at alloperating conditions of the SCWR. Therefore, the traditionallimiting criteria based on either the dryout or the burnoutphenomenon is not applicable. In turn, maximum cladding-surfacetemperature (MCST) and peak fuel centerline temperature havebeen adopted as design criteria for the SCWR. The highly hetero-geneous SCWR reactor core in radial and axial directions limits theapplication of the traditional single-channel thermal-hydraulicanalyses to predict accurately the maximum cladding-surfacetemperature in support of the fuel and core designs. Preliminaryanalyses of the cladding temperature of bundles in a fuel channelhave been performed using subchannel codes. Mukohara (Muko-hara et al., 2000) developed a subchannel analysis code to supportthe SCWR design in Japan. Cheng (Cheng et al., 2003) applied thesubchannel code ‘‘STAFAS’’ to investigate the thermal-hydraulicbehavior of a fuel assembly for the high performance light-waterreactor (HPLWR). Oriani and Kucukboyaci (Oriani and Kucukboyaci,2004) analyzed the subchannel conditions with the revised VIPREcode in USA.
Most subchannel analyses applied the uniform cladding-surfacetemperature assumption because flow conditions in subchannelsaround the rod are almost constant prior to CHF occurrences, andhence the azimuthal conduction around the cladding is notimportant at subcritical conditions. On the other hand, flowconditions in subchannels around the rod differ considerably atsuper-critical conditions (Oka and Koshizuka, 2000; Duffey et al.,2005), leading to a sharp variation in cladding-surface temperature.The uniform-temperature assumption would lead to under-prediction of the maximum cladding-surface temperature, and anazimuthal conduction model is required to provide a realisticprediction.
1.3. Objectives of the current study
A cooperative study has been initiated at Xi’an JiaotongUniversity (XJTU) with Atomic Energy of Canada Limited (AECL) todevelop a subchannel code for preliminary analyses of flow andenthalpy distributions and fuel cladding temperature at super-critical water conditions. This study focuses on the development ofa new subchannel code (ATHAS, Advanced Thermal-HydraulicsAnalysis-Subchannel) for fuel bundle analysis with super-criticalwater flow. The code is applicable for transient and steady-statecalculations.
Objectives of this paper are to provide a description of theATHAS subchannel code, predictions of cladding temperature in the43-rod bundle.
2. Subchannel analysis code ATHAS
The subchannel code ‘ATHAS’ has been developed by Xi’anJiaotong University. Fig. 1 illustrates the evaluation scheme of thecode. After the initialisation of all parameters, the code reads in thesubchannel configuration of the bundle, initial and boundaryconditions (i.e., pressure, mass flow rate, coolant inlet temperature,and power), and power distributions. And then the calculationstarts with the outer iteration to solve the momentum, mass, andenergy based on assumed flows in all subchannels. Separate
iterations are required to solve the mass and energy equations(referred as inner iteration in Fig. 1). The outer iteration is consid-ered complete after both the axial flow and energy convergence.Calculated results are outputted and the calculation terminates insteady-state analyses or proceeds to the next time step in transientanalyses.
The code is developed on the basis of mass, energy, andmomentum (lateral and axial directions) conservative equations.Besides, closure relationships are required to facilitate the calcu-lations. These relationships capture the heat transfer and hydraulicresistance between the super-critical fluid and cladding surfaces,and turbulent mixing between subchannels.
3. Subchannel analysis of a CANFLEX bundle
The preliminary design of the CANDU-SCWR fuel has beeninitiated, but the bundle geometry and fuel composition have notbeen established. Therefore, the current CANDU 43-rod bundle hasbeen adopted to facilitate the current analysis.
3.1. Fuel assembly configuration
Fig. 2 illustrates the CANDU 43-rod fuel bundle configurationincluding the rod and subchannel identifications. The rods arearranged in 4 rings in the channel. The outside and inside two ringshave an outer diameter of 11.52 mm, 13.53 mm, respectively. Asa simplification, the heated length of the element is assumed thesame as the overall length and appendages are not simulated in thisstudy. The inner diameter of the pressure tube is assumed as
1
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56
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23 24
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43
1
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131415
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343536
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53
54
55
56
57
58
5960
61
62
63
64
65
66
67
68
69
70
Fig. 2. Subchannel identification in a CANDU 43-rod fuel bundle.
Table 2Reactor operation parameters in Current Analysis.
Parameters Values
Coolant inlet pressure 25 MPaCoolant inlet temperature 350 �CCoolant exit temperature 625 �CAverage coolant mass flux 890.3 kg m�2$s�1
Average heat flux 0.978 MW m�2
Limit of cladding-surface temperature 850 �C
646.494
672.445
698.396
724.347
750.298
776.249
802.2
1
2
3
47
8
910
11
12
1318
19
20
2122
23 2425
26
27
28
2938
39
40
41
4243
1
2
34
5
6
7
8
9
10
11
1216
17
18
19
20
21
22
2324
2526
27
28
2941
42
43
4445
4647
4849
5051
52
53
54
5565
66
67
68
6970
C. Li et al. / Progress in Nuclear Energy 51 (2009) 799–804 801
104.1 mm. Table 1 lists dimensions of the bundle and the calculatedflow area.
Table 2 lists flow conditions employed in the current analysis.These flow conditions have been introduced to test the code anddiffer from those proposed for the CANDU-SCWR (Duffey et al.,2005). Relevant flow conditions will be applied in subsequentphases. The average surface heat flux of the bundle is also listed inthe table.
The bundle exhibits a symmetric cosine axial-power profile anda non-uniform radial power profile. Local-to-average power ratiosare 0.90969, 0.95095, 0.90164 and 1.08982 for the centre, innerring, middle ring, and outer-ring elements, respectively.
3.2. Options of the analysis case
A reference case has been established to analyze the subchannelcharacteristics of the CANDU 43-rod bundle under super-criticalconditions. It is based on the following options:
1. Heat-transfer correlation: Bishop 1964 correlation;
Nux ¼ 0:0069 Re0:9x Pr0:66
x
�rw
rb
�0:43
x
�1þ 2:4
Dx
�(1)
2. Turbulent mixing model: Rowe and Angle model for the gap-to-diameter ratio of 0.149.
Table 1Fuel assembly geometry parameters.
Parameters Values
Element diameter 13.53/11.52 mmElement length 643.9 cmElement heated length 643.9 cmPressure-tube diameter 104.1 mmOverall flow area 37.09 cm2
Because gap-to-diameter ratio of CANDU-SCWR 43-rod isaround 0.137, Rowe and Angle model is selected to calculateturbulent mixing coefficient;
b ¼ 0:021$Re�0:1 (2)
3. Flow resistance correlation: Blasius equation
The below Blasius equation is used to calculate the frictionalcoefficient.
f ¼ 0:3164$Re�0:25 (3)
4. Three dimensional fuel rod heat conduction model is includedin the calculation of cladding temperature.
These options assure that the analysis case can obtain a conser-vative result.
3.3. Results of analysis case
Fig. 3 illustrates the coolant temperature and maximum clad-ding-temperature distributions at the outlet of the fuel bundle. Thelocation of maximum cladding temperature, however, is just afterthe axially central position (due to the non-uniform axial-powerprofile). The highest coolant temperature is 696.26 �C at sub-channel 35, while the lowest is 542.96 �C at both subchannels 55and 65.
542.69
568.641
594.592
620.54356
141516
17 30
31
323334
35
36
37 131415
30
31
3233
343536
3738
39
4056
57
58
5960
61
62
63
64
Fig. 3. Distributions of coolant and maximum cladding-surface temperatures at theoutlet of the CANDU 43-rod fuel string at super-critical pressure.
0 1 2 3 4 5 60.9
1.0
1.1
1.2
1.3
1.4
Mass flu
x / M
g/(m
2s
)
sc(7)sc(15)sc(18)sc(35)sc(43)sc(49)sc(60)sc(65)sc(70)
Axial location /m
Fig. 4. Subchannel coolant mass-flux distribution along axial nodes.
C. Li et al. / Progress in Nuclear Energy 51 (2009) 799–804802
Circumferential temperature distributions are relatively small atrods in the inner and middle rings, but increase at outer-ring rods.Temperature differences at outer-ring rods are due to the assumedcold pressure-tube temperature, reducing the coolant temperaturein subchannels.
Fig. 4 shows axial variations of predicted mass flux at varioussubchannels along the bundle. The variation of mass flux in sub-channels at each node is attributed to differences in hydraulicdiameters. The axial mass-flux variation is relatively drastic in thesesubchannels. This is attributed to the drastic variations of densityand viscosity leading to sharp changes in pressure drop as the bulktemperature in the subchannel reaches the pseudo-criticaltemperature. The mass flux redistributes after the pseudo-criticalpoint when the bulk-temperature difference increases.
0 1 2 3350
400
450
500
550
600
650
700sc(7)sc(15)sc(18)sc(35)sc(43)sc(49)sc(60)sc(65)sc(70)
Co
olan
t tem
peratu
re /°C
Axial l
Fig. 5. Subchannel coolant temperatu
Fig. 5 shows the coolant temperature distribution of typicalsubchannels along the axial nodes. The subchannel temperaturedistribution is almost uniform prior to the pseudo-criticaltemperature. Beyond this point, the temperature differencebetween the cool and hot subchannels increases reachinga maximum of 153.57 �C.
Fig. 6 illustrates cladding-surface temperature distributions attypical subchannels along the bundle. The surface temperatureincreases generally along the bundle, reaching a maximum atlocations close to the downstream end, and decreases afterward.This maximum temperature location corresponds mainly to thepower and flow variations. The maximum predicted surfacetemperature is 802.2 �C at Rod 33 facing subchannel 60. These rodsare located in the outer ring of the bundle (where the local power is
4 5 6ocation /m
re distribution along axial nodes.
0 1 2 3 4 5 6350
400
450
500
550
600
650
700
750
800
Clad
din
g su
rface tem
peratu
re /°C
Axial location /m
1-7
6-15
8-18
15-35
20-43
22-49
33-60
38-65
43-70
Fig. 6. Cladding-surface temperature of typical locations along axial nodes (1–7 denotes the fragment of rod 1 that facing subchannel 7).
0 1 2 3 4 5 6
5000
10000
15000
20000
25000
30000
35000
Axial location /m
1-7
6-15
8-18
15-35
20-43
22-49
33-60
38-65
43-70
Heat tran
sfer co
efficien
t / W
/(m
2K
)
Fig. 7. Heat-transfer coefficient of typical locations along the axial nodes.
C. Li et al. / Progress in Nuclear Energy 51 (2009) 799–804 803
the highest) while the subchannel 60 has a relative highertemperature than other channels.
Fig. 7 shows corresponding variations of heat-transfer coeffi-cient along the bundle. The heat-transfer coefficient increasesgradually at the inlet end and sharply as the temperatureapproaches the pseudo-critical point. It reaches the maximum atthe pseudo-critical point, and decreases sharply afterward. Thissharp variation is attributed to the properties change at the pseudo-critical point. Beyond the maximum point, the heat-transfer coef-ficient decreases gradually towards the end of the bundle andreaches the minimum point corresponding to the maximumsurface temperature locations in Fig. 6.
4. Conclusions
A subchannel code ‘‘ATHAS’’ has been developed in support of fueldesign for the pressure-tube type of SCWR. And the code has beenapplied to the analysis of the CANDU-type SCWR fuel. The result hasshown that (1) from the heat-transfer point of view, a CANDU 43-rodbundle is appropriate for use in the CANDU-SCWR. The MCST 802.2 �Cof the case is below the design limit of cladding-surface temperature850 �C. The assessment result from this study signifies the urgentneed of reliable experimental data on crucial parameters for corre-lation development and code validation. This would minimize the riskand maximize the performance of the SCWR design.
C. Li et al. / Progress in Nuclear Energy 51 (2009) 799–804804
Acknowledgments
The authors would like to express their appreciation to AtomicEnergy of Canada Limited and Xi’an Jiaotong University for theirfinancial support.
Nomenclature
D hydraulic diameter/mF axial flow rate/kg s�1
f frictional coefficienth enthalpy/kJ kg�1
Nu nusselt NumberP pressure/MPaPr prandtl numberW lateral flow rate/kg s�1
Re renault numbert time/sx axial location/mr density/kg m�3
b turbulent mixing coefficient
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