IYNC 2008 Interlaken, Switzerland, 20 – 26 September 2008
Paper No. 382
382.1
Thermal Hydraulic Analysis Of Thorium-Based Annular Fuel Assemblies
Kyu Hyun Han Korea Institute of Nuclear Safety,
19, Guseong-dong, Yuseong-gu, Daejeon, 305-338, Republic of Korea [email protected]
ABSTRACT
Thermal hydraulic characteristics of thorium-based fuel assemblies loaded with annular seed
pins have been analyzed using AMAP combined with MATRA, and compared with those of the
existing thorium-based assemblies. MATRA and AMAP showed good agreements for the pressure
drops at the internal subchannels. The pressure drop generally increased in the cases of the
assemblies loaded with annular seed pins due to the larger wetted perimeter, but an exception existed.
In the inner subchannels of the seed pins, mass fluxes were high due to the grid form losses in the
outer subchannels. About 43% of the heat generated from the seed pin flowed into the inner
subchannel and the rest into the outer subchannel, which implies the inner to outer wall heat flux ratio
was approximately 1.2. The maximum temperatures of the annular seed pins were slightly above
500°C. The MDNBRs of the assemblies loaded with annular seed pins were higher than those of the
existing assemblies. Due to the fact that interchannel mixing cannot occur in the inner subchannels,
temperatures and enthalpies were higher in the inner subchannels.
1. INTRODUCTION
The thorium-based fuel cycle has attracted attention because it promises a number of benefits
relative to the conventional uranium-based cycle for commercial reactors. There are two alternative
designs of thorium fuel assemblies. One of them is the Seed-Blanket Unit (SBU) [6] which is equal in
outer dimensions to the conventional pressurized water reactor (PWR) fuel assembly. The other
design is the Whole Assembly as Seed or Blanket (WASB) [1] where each type of fuel occupies a
whole PWR assembly. The main drawback of the two designs from a thermal hydraulic perspective is
the high power imbalance between the seed and the blanket region. To remedy this, the heat removal
in the seed region should be enhanced. Recently, the annular fuel pin was proposed by NERI [3] to be
implemented in current PWR cores to achieve a significant increase of core power density while
improving safety margins. It can be applied to the thorium fuel assemblies for the enhanced heat
removal in the seed region. Subchannel codes such as MATRA [2] capable of modeling the entire
Proceedings of the International Youth Nuclear Congress 2008
382.2
core are necessary to capture the benefits of mixing effects which improve DNBR in the hot channel.
MATRA does not have the capability to model both internally and externally cooled annular fuel pins.
Therefore, to analyze the thermal hydraulics of thorium fuel assemblies loaded with annular seed pins,
a subchannel code with capabilities to calculate the coolant flow distribution between internal and
external channels and heat flow split into individual channels is needed.
2. DEVELOPMENT OF AMAP
A search for a subchannel code with capabilities to model innovative internally and externally
cooled annular fuel pins has been in vain so far. Thus, this study is mainly focused on providing a
method to analyze fuel assemblies loaded with annular fuel pins laying special emphasis on coolant
and heat flow split into internal and external channels, combining it with MATRA, and comparing
thorium fuel assemblies loaded with annular seed pins of preliminary designs with those loaded with
cylindrical ones from a thermal hydraulic perspective.
2.1 Coolant Flow Split
The proposed annular fuel pin introduces a new variable that needs to be considered in the
calculation – partial coolant flow penetrating the annular pin in the axial direction. The coolant flow
must be distributed in the manner of equalizing pressure drops in all the subchannels. However,
MATRA offers channel inlet flows split option for equal pressure gradient across the first axial node
only. Therefore, the coolant flow distribution must be adjusted by an adequate pressure drop model.
The calculations of the pressure drop in a heated channel allowing for nonequilibrium conditions such
as nonequal velocity and nonsaturated phases are considered in this study. Essentially, four flow
regions may exist over the entire length of the subchannel [4]. They are regions of the single phase
liquid, subcooled boiling, bulk boiling and single phase vapor. However, only two of them, that is,
regions of the subcooled and bulk boiling, are considered here for simplicity, as shown in Figure 1. The
existence of these flow regions depends on the heat flux and the inlet conditions. The total pressure
drop can be obtained as the summation of the pressure drops over each axial region:
BBSCBtotal ppp ∆+∆=∆ (1)
where:
=∆ SCBp pressure drop in the subcooled boiling region
=∆ BBp pressure drop in the bulk boiling region
Three components of pressure drop, that is, elevation, acceleration and friction, over each
region are considered here. The total pressure drop without any form pressure losses is given by:
∑ ∫ ∫=
++=∆
+ ++
1
0
22
2
21 1
1
2)(
i
z
z
z
zef
mooz
z
f
mtot
i
i
i
i
i
idz
D
Gfr
Ggdzp
ρφ
ρρ ll (2)
where each numerical index corresponds to each transition point, including inlet and outlet.
Proceedings of the International Youth Nuclear Congress 2008
382.3
L
BulkBoiling
ZB
SubcooledBoiling
0
De
FLOW
3660 mm
q"
Figure 1: Subchannel flow regions
2.2 Heat Flow Split
Another new variable to be considered is the partial heat flow directed to the inner channel of
the annular pin. All current PWR cores employ fuel pins cooled at their external surface by an open
flow, hence all the energy generated within the pin is transferred to the flow stream along the fuel pin
array. However, in the annular fuel pin with an internal cooling hole, only part of the heat rate
generated in a fuel pellet will be transferred to the external coolant in the open fuel pin array and the
remaining part will be transferred to the internal coolant flowing through the hole. The current version
of MATRA is not capable of modeling fuels other than cylindrical and plate fuels. Therefore, the heat
flow split must be given by an adequate heat transfer model. For the heat transfer coefficient, in the
particular case of water, Weisman gave:
333.08.0
.. PrRe023.0)( =∞ tcNu (3)
0430.1/826.1 −= DPψ (4)
On the other hand, the wall temperatures of the fuel pins are given by the heat equation:
t
Tcq
z
Tk
z
Tk
rr
Tkr
rrp ∂∂
=+
∂∂
∂∂
+
∂∂
∂∂
+
∂∂
∂∂
ρφφ
&2
11 (5)
From the equality of heat transfer fraction:
2222 :: moimoi rrrrqq −−= (6)
where mr satisfies the equation:
0== mrr
dr
dT , (7)
the heat directed to the internal and external channels can be calculated by the relations,
respectively:
)( iwiiii TTAhq ∞−= (8)
)( owoooo TTAhq ∞−= (9)
Proceedings of the International Youth Nuclear Congress 2008
382.4
2.3 AMAP
Using the models described above, a program named AMAP (Assistant of MATRA for Annular
fuel Pin simulation) which can be attached to MATRA and calculate coolant and heat flow split in the
annular fuel pin has been developed. To begin with, additional isolated inner subchannels of the
annular seed pins are defined in the input data. Then MATRA is executed using the input. When
MATRA finishes the calculation, coolant temperature, mass flux, density, quality and void fraction of
each subchannel are collected. From the collected data, heat transfer coefficients of the coolant and
temperatures of inner and outer surfaces of the seed pins are calculated. Finally, pressure drop in
each inner subchannel and heat flow directed to the inner and outer subchannels are calculated from
the previous result. The next step is to check if the previously assumed mass flow distribution and
power fraction are within the allowable margin of error. If they are, the calculation stops, but if they are
not, different mass flow distribution and power fraction are assumed and MATRA is executed again.
This loop is repeated until the mass flow distribution and power fraction are within the error tolerance.
The flow chart of AMAP is given in Figure 2.
Start
Initial execution of MATRA
Get T∞, G, ρ, χ, α
Calculate hi, ho, Twi, Two
Calculate ∆pi, qi, qo
|∆pavg - ∆pm| ≤ ε1 ?|∆pi - ∆pim|/∆pi ≤ ε2 ?|qi/q - qim/q| ≤ ε3 ?|qo/q - qom/q| ≤ ε3 ?
End
Define isolated innersubchannels of seed pins
Execute MATRA
qim/q ← (qi/q + qim/q)/2qom/q ← (qo/q + qom/q)/2
∆pm > ∆pavg ?
Gj ← Gj - β1 Gj ← Gj + β2
Yes
Yes
No
No
Start
Initial execution of MATRA
Get T∞, G, ρ, χ, α
Calculate hi, ho, Twi, Two
Calculate ∆pi, qi, qo
|∆pavg - ∆pm| ≤ ε1 ?|∆pi - ∆pim|/∆pi ≤ ε2 ?|qi/q - qim/q| ≤ ε3 ?|qo/q - qom/q| ≤ ε3 ?
End
Define isolated innersubchannels of seed pins
Execute MATRA
qim/q ← (qi/q + qim/q)/2qom/q ← (qo/q + qom/q)/2
∆pm > ∆pavg ?
Gj ← Gj - β1 Gj ← Gj + β2
Yes
Yes
No
No
Figure 2: Flow chart of AMAP
2.4 Validation of AMAP
The initial MIT 15×15 annular fuel design (not optimized) was analyzed at a level of isolated unit
cell using RELAP5/MOD3.2 by KAERI. The KSNPP was used as the reference plant model for the
Proceedings of the International Youth Nuclear Congress 2008
382.5
core operating conditions. The dimensions of the annular fuel in the MIT design were derived from the
Westinghouse 17×17 reference design to preserve the fuel-to-moderator ratio and to have the same
enthalpy rise in the inner and outer channel. The annular pin from 15×15 fuel assemblies is shown on
Figure 3. Table 1 gives the operating parameters of the core and the main design features of the
annular fuel.
6.62 mm
5.99
4.00
3.37
Internal
coolingExternal
cooling
Figure 1: Geometries in the annular fuel layers
Table 1: 15×15 unit cell parameters
3.568 m2Total
2.2824 m2Outer
1.2856 m2InnerCoolant flow
area
6.6225 mmrout
3.3665 mmrinClad
44.83 kW/mq’maxHot rod
28.92 kW/mq’max
20.5 kW/mq’coreAverage rod
36,108No. of fuel rods
15,454 kg/secCore flow rate
0.215 mAssembly pitch
3.81 mActive core length
177No. of assembly
2,815 MWthTotal core thermal power
15×15Assembly type
3.568 m2Total
2.2824 m2Outer
1.2856 m2InnerCoolant flow
area
6.6225 mmrout
3.3665 mmrinClad
44.83 kW/mq’maxHot rod
28.92 kW/mq’max
20.5 kW/mq’coreAverage rod
36,108No. of fuel rods
15,454 kg/secCore flow rate
0.215 mAssembly pitch
3.81 mActive core length
177No. of assembly
2,815 MWthTotal core thermal power
15×15Assembly type
The available data which could be compared with the calculation result of MATRA/AMAP were
heat flow split and DNBR profiles. Figure 4 compares the heat transfer fractions calculated by AMAP
and RELAP. Here, the pressure drop in the core is set as 0.145MPa. As can be seen from the
chopped cosine power shape, AMAP calculation gives more heat toward the outer subchannel than
RELAP does, resulting in less heat directed to the inner subchannel. Because, this calculation is done
about the hottest fuel pin, both the I/O heat flux ratio and the inner subchannel mass flux are the
lowest among the pins in the core. Along with MIT result, DNBR comparison of the RELAP and AMAP
calculation using W-3 CHF correlation is given in Figure 5. In the lower part of the fuel pin, AMAP
Proceedings of the International Youth Nuclear Congress 2008
382.6
result agrees well with the MIT result and is rather higher than the RELAP result, while in the upper
part, deviation becomes evident. Relatively lower DNBR of the AMAP is due to the approximation of
axial heat flux distribution. In the region close to the exit, the shape used in the RELAP gives nearly
zero heat flux. However, MATRA requires exact value of heat flux both at the bottom and top regions.
That’s why AMAP’s heat flux shape is a completely symmetric chopped cosine. Table 2 summarizes
the comparison.
0.E+00
1.E+05
2.E+05
3.E+05
4.E+05
5.E+05
6.E+05
7.E+05
8.E+05
9.E+05
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Relative axial position
Heat
flu
x (W
/m2 )
AMAP_in
AMAP_out
RELAP_in
RELAP_out
Figure 4: Comparison of axial heat flux distributions
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0 0.5 1 1.5 2 2.5 3 3.5 4
Axial location (m)
DN
BR
RELAP_in
AMAP_in
MIT_in
Figure 5: Comparison of DNBR profiles in the inner subchannels
Table 2: Comparison of annular fuel calculation
−432.07Pellet peak
temperature(oC)
1.26911.2261Heat flux ratio
42.3%57.7%38.4%61.6%Heat transfer
split
−−4684.243387.01G (kg/sec-m2)
Inner channelOuter channelInner channelOuter channel
RELAPAMAP
−432.07Pellet peak
temperature(oC)
1.26911.2261Heat flux ratio
42.3%57.7%38.4%61.6%Heat transfer
split
−−4684.243387.01G (kg/sec-m2)
Inner channelOuter channelInner channelOuter channel
RELAPAMAP
3. THORIUM BASED ANNULAR FUEL ASSEMBLIES
The preliminary designs of annular seed pins for thorium fuel assemblies have been done
Proceedings of the International Youth Nuclear Congress 2008
382.7
based on the dimensions of the existing thorium fuel assemblies. The thicknesses of the annular fuel
pellet and the gas gap are 0.96 mm and 0.085 mm, respectively, which are the same as those of the
WASB-B seed pin. The cladding thickness is 0.4 mm for all three kinds of the seed pin as before. The
three thorium fuel assemblies loaded with annular seed pins are named SBU_A, WASB-A_A and
WASB-B_A respectively, where the ‘_A’ implies ‘annulus’. Also, the seed pins of the SBU_A and the
WASB-A_A are identical as before. The core radial and axial power distributions were taken from the
SBU MOC results [1] in order to analyze and compare the different alternative designs as before. In
the case of the SBU_A, one whole unit is analyzed, however, in the case of the WASB_B, the selected
modeling region, as shown in Figure 6, was taken as the symmetric volume composed of one quarter
each of two seed assemblies and one quarter each of two blanket assemblies. The relative pin power
distributions for the SBU_A, WASB-A_A and WASB-B_A were available at an assembly level.
Subchannels and rods were also defined in a similar way as was done for the existing thorium fuel
assemblies. An example for WASB-B_A is shown in Figure 7.
Figure 6: Selected modeling region
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
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137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153
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273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289
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315 319318317316
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119
120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136
137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153
154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187
188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204
205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221
222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238
239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255
256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272
273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289
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305 307 309 310 311 312 313306
315 319318317316
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353 354 355 361360359358357356
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119
120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136
137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153
154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187
188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204
205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221
222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238
239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255
256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272
273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289
336335334
290 291 295293292
297296 298
308
300 301 302
294
304
305 307 309 310 311 312 313306
315 319318317316
323
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320 322 328327326325324
332
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337 343
351
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299
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353 354 355 361360359358357356
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433432428 430 431
426 427425
415
423422421
429
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408404 405 406 407
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Figure 7: WASB-B_A subchannel identification
Proceedings of the International Youth Nuclear Congress 2008
382.8
4. THERMAL HYDRAULIC ANALYSIS
Assuming that the operating parameters of the thorium-based reactors loaded with annular
seed pins are the same as those of a typical Westinghouse 4-loop PWR, as shown in Table 3, thermal
hydraulic analyses have been performed using MATRA and AMAP.
Table 3: Operating parameters of a typical Westinghouse 4-loop PWR
Parameter Value
Core Heat Output [MWth] 3400
System Pressure [MPa] 15.5
Effective Flow Rate [Mg/s] 17.7
Active Fuel Height [cm] 366
Number of Assemblies 193
Inlet Coolant Temperature [°C] 289
The calculations for the existing assemblies are done using MATRA. The assemblies loaded
with annular seed pins cause higher pressure drop than the existing ones because they have larger
wetted perimeter due to the additional cladding volume. However, in the case of WASB-B_A, pressure
drop decreased compared with WASB-B, which might be explained by ‘offset effect’ by high MDNBR.
Figure 8 shows hottest cell pressure drop of the WASB-B_A. It is clear from the Figure that relatively
higher coolant temperature in the inner subchannel brings about pressure drop which is equal to the
outer subchannel pressure drop mainly caused by the grid spacers.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 1000 2000 3000 4000
Axial distance, mm
Pre
ssure
dro
p, M
Pa
Inner ch.
Outer ch.
Figure 8: Hottest cell axial pressure drop profiles for the WASB-B_A
In the cases of the assemblies loaded with annular seed pins, as the outer diameter of the
seed pin is larger than that of the blanket pin, mass fluxes in the outer subchannels of the seed pins
are low, as shown in Figures 9 for WASB-B_A. In the inner subchannels of the seed pins, mass fluxes
are high due to the grid form losses in the outer subchannels. Figure 10 gives power fractions of the
Proceedings of the International Youth Nuclear Congress 2008
382.9
annular seed pins. About 43% of the heat generated from the seed pin flows into the inner subchannel
and the rest into the outer subchannel, which implies the inner to outer wall heat flux ratio is
approximately 1.2. Figure 11 shows radial temperature profiles at the hottest axial positions in the
hottest annular seed pins. For the fuel-clad gap, a constant conductance of 1000 Btu/hr-ft2-°F, which is
typical for PWR fuel, was assumed. The maximum temperatures of the seed pins are approximately
501°C, 513°C and 515°C for the SBU_A, WASB-A_A and WASB-B_A respectively. The MDNBR
profiles are given in Figure 12, which clearly identifies higher thermal margins of the assemblies
loaded with annular seed pins compared with the existing ones. As significant different power levels
can be found in the seed region compared with the blanket region, the analysis must be done at the
hottest spot in the fuel. In this case, the hottest subchannel shows the higher temperature found in the
fuel.
2500
2600
2700
2800
2900
3000
3100
3200
3300
3400
3500
G,
kg/m
2 s
3400-3500
3300-3400
3200-3300
3100-3200
3000-3100
2900-3000
2800-2900
2700-2800
2600-2700
2500-2600
3000
3100
3200
3300
3400
3500
3600
3700
3800
3900
4000
G,
kg/m
2 s
3900-4000
3800-3900
3700-3800
3600-3700
3500-3600
3400-3500
3300-3400
3200-3300
3100-3200
3000-3100
Figure 9: Exit mass flux distributions of the WASB-B_A
Proceedings of the International Youth Nuclear Congress 2008
382.10
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100
Seed pin numberPow
er fractio
n
Inner ch.
Outer ch.
Figure 10: Power fractions of the annular seed pins
320
340
360
380
400
420
440
460
480
500
520
2.2 3.2 4.2 5.2 6.2
Radial position, mm
Tem
pera
ture
, oC
SBU_A
WASB-A_A
WASB-B_A
Figure 11: Radial temperature profiles at the hottest axial positions in the hottest annular seed
pins
0
1
2
3
4
5
6
7
8
9
10
0 1000 2000 3000 4000
Axial distance, mm
MDNBR
SBU
WASB-A
WASB-BSBU_A
WASB-A_A
WASB-B_A
Figure 12: MDNBR profiles
Proceedings of the International Youth Nuclear Congress 2008
382.11
1250
1300
1350
1400
1450
1500
1550
0 1000 2000 3000 4000
Axial distance, mmEnt
halp
y, k
J/kg
SBU
WASB-A
WASB-B
SBU_A
WASB-A_A
WASB-B_A
Figure 13: Average enthalpy profiles
1250
1300
1350
1400
1450
1500
1550
1600
1650
1700
0 1000 2000 3000 4000
Axial distance, mm
Ent
halp
y, k
J/kg
SBU
WASB-A
WASB-B
SBU_A
WASB-A_A
WASB-B_A
Figure 14: Hottest subchannel enthalpy profiles
The average enthalpy profiles given in Figure 13 together with the hottest subchannel profiles
given in Figure 14 reveal that heat transfer to the coolant is heavily biased toward some hot
subchannels in the cases of the assemblies loaded with annular seed pins. The enthalpies in the inner
subchannels are higher than those in the outer subchannels owing to the fact that interchannel mixing
cannot occur in the inner subchannels. It is desirable to achieve approximately the same coolant
enthalpy rise in both of the outer and inner subchannels. On the whole, the assemblies loaded with
annular seed pins show better thermal hydraulic performances than the existing assemblies.
5. CONCLUSIONS
The most important challenge for all of the analyzed designs loaded with annular seed pins
was to deal with the coolant and heat flow split into internal and external channels. The power fraction
tolerance was set at 0.1%, the tolerance of the pressure drops among subchannels 0.005 MPa, and
the tolerance between MATRA’s and AMAP’s pressure drop results at internal subchannels 5%. The
calculation results are summarized as follows:
Proceedings of the International Youth Nuclear Congress 2008
382.12
(1) The pressure drop generally increases in the cases of the assemblies loaded with annular
seed pins due to the larger wetted perimeter, but an exception exists.
(2) In the inner subchannels of the seed pins, mass fluxes are high due to the grid form losses
in the outer subchannels.
(3) About 43% of the heat generated from the seed pin flows into the inner subchannel and the
rest into the outer subchannel, which implies the inner to outer wall heat flux ratio is
approximately 1.2.
(4) The maximum temperatures of the annular seed pins are slightly above 500°C.
(5) The MDNBRs of the assemblies loaded with annular seed pins are higher than those of the
existing assemblies.
(6) Due to the fact that interchannel mixing cannot occur in the inner subchannels, enthalpies
are higher in the inner subchannels.
ACKNOWLEDGEMENTS
The participation of IYNC2008 is supported by Korean Nuclear Society.
REFERENCES
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