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 mensa@kins.re.kr

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

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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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