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Analysis of NEA-NSC PWR Uncontrolled
Control Rod Withdrawal at Zero Power
Benchmark Cases with NODAL3 Code
Article in Science and Technology of Nuclear Installations · November 2017
DOI: 10.1155/2017/5151890

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Science and Technology of Nuclear Installations
Volume 2017, Article ID 5151890, 8 pages
https://doi.org/10.1155/2017/5151890

Research Article
Analysis of NEA-NSC PWR Uncontrolled
Control Rod Withdrawal at Zero Power Benchmark Cases withNODAL3 CodeTagor Malem Sembiring,1 Surian Pinem,1 and Peng Hong Liem2,31Center for Nuclear Reactor Technology and Safety, National Nuclear Energy Agency of Indonesia (BATAN), Kawasan Puspiptek,
Gd. No. 80, Serpong, Tangerang Selatan 15310, Indonesia
2
Nippon Advanced Information Service (NAIS Co., Inc.), 416 Muramatsu, Tokaimura, Ibaraki 319-1112, Japan
3
Cooperative Major in Nuclear Engineering, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan
Correspondence should be addressed to Tagor Malem Sembiring; tagorms@batan.go.id
Received 24 August 2017; Revised 26 October 2017; Accepted 6 November 2017; Published 23 November 2017
Academic Editor: Arkady Serikov
Copyright © 2017 Tagor Malem Sembiring et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The in-house coupled neutronic and thermal-hydraulic (N/T-H) code of BATAN (National Nuclear Energy Agency of Indonesia),
NODAL3, based on the few-group neutron diffusion equation in 3-dimensional geometry using the polynomial nodal method,has been verified with static and transient PWR benchmark cases. This paper reports the verification of NODAL3 code in the
NEA-NSC PWR uncontrolled control rods withdrawal at zero power benchmark. The objective of this paper is to determine theaccuracy of NODAL3 code in solving the continuously slow and fast reactivity insertions due to single and group of control rod bankwithdrawn while the power and temperature increment are limited by the Doppler coefficient. The benchmark is chosen since manyorganizations participated using various methods and approximations, so the calculation results of NODAL3 can be compared toother codes’ results. The calculated parameters are performed for the steady-state, transient core averaged, and transient hot pellet
results. The influence of radial and axial nodes number was investigated for all cases. The results of NODAL3 code are in very good
agreement with the reference solutions if the radial and axial nodes number is 2 × 2 and 2 × 18 (total axial layers), respectively.

1. Introduction
An in-house analytical tool for Pressurized Water Reactor (PWR) safety, NODAL3 code, has been developed by
National Nuclear Energy Agency of Indonesia (BATAN) [1].
The capability of developing analytical tool for neutronic
and thermal-hydraulic parameters of PWR is important tosupport the self-review of the proposed nuclear power plantin Indonesia. NODAL3 code is a coupled neutronic andthermal-hydraulic code based on the few-group nodal neutron diffusion equations in 3-dimensional (3-D) Cartesiangeometry for steady and time-dependent problems. The code
has been verified with the PWR static and transient benchmark cases [1–6]. The calculated results of NODAL3 codeshow very good agreement with the reference solutions [1, 5].
The PWR transient benchmark cases are reactivity initiatedaccident (RIA) [7, 8]. In those cases, the reactor is scrammed

after the power reaches the limit condition; however, in thereal operating condition, there is a delay time for the control
rods (CRs) to shut down after the neutron flux or power
reaches the limit condition.
The important reactivity insertion analysis in PWR besidethe RIA is the uncontrolled withdrawal of single or group CRs
at zero power. Fraikin and Finnemann proposed the PWR
benchmark cases for the uncontrolled safety withdrawal of
CRs at zero power accident [9]. In contrast to the RIA
benchmark, the reactor will be scrammed after a certain
delay time; it means the maximum power occurs before
the scram. The uncontrolled withdrawal of CRs accident
affects the reactivity and power distribution anomaly thatshould be postulated in the safety analysis of DBA (designbasis accident) [10]. Therefore, the proposed benchmark isvery useful to know the accuracy of an analytical tool insolving the PWR postulated initiating event of uncontrolled2
withdrawal of CRs at zero power. In addition, there weremany participated institutions using various methods andapproximation [11], including the reference solutions, so
the calculation results of NODAL3 code can be compareddirectly.
In the benchmark of uncontrolled control rod withdrawal
at zero power, the accidents are continuously slow andfast reactivity insertion, due to the single and the groupcontrol rod bank withdrawal, respectively. The power andtemperature increments are limited by the feedback reactivityof Doppler. The objective of this work is to determine
the accuracy of NODAL3 code in analyzing the transientparameters of continuous slow and fast reactivity accident
due to the uncontrolled control rod withdrawal at zero power
which is one important aspect in the DBA analysis of PWR.
This paper is organized as follows. In Section 2, a description of the NEA-NSC uncontrolled control rod withdrawal atzero power benchmark cases is given. Section 3 describes thecore calculation method of NODAL3 code. Section 4 presents
some results and discussion, followed by the conclusion ofthis work in Section 5.

2. NEA-NSC PWR 3D/1D Uncontrolled
Control Rods Withdrawal at Zero Power
Benchmark Cases
The NEA-NSC PWR uncontrolled CR withdrawal benchmark core is almost the same as the rod ejection benchmark
except the CR layout [12] and dynamic evolution [9]. There
are 157 fuel assemblies (FA) in the benchmark core, where 48
assemblies are with CR. As seen in Figure 1, there are 3 types ofenrichment for FAs, 2.1 w/o, 2.6 w/o, and 3.1 w/o, with 4 CRs
banks A, B, C, D, and one shutdown bank S. The banks of
B, C, D and S (type 1 absorbers) are located in 2.1 w/o FAs
and the bank of A (type 2 absorbers) is located in 3.1 w/o FAs[9]. The radial dimension is 21.606 cm × 21.606 cm while theactive core height is 367.3 cm with the upper and lower axialreflector thickness of 30.0 cm. Some FAs are with burnable
absorber rods (BA), such as 12 BAs, 16 BAs, and 20 BAs in the
2.6 w/o FAs, as well as 12 BAs and 16 BAs in the 3.1 w/o FAs.
Reference [7] shows some specifications of CR; total CR
length is 362.159 cm. The full insertion of CR is 37.7 cm fromthe bottom of the lower reflector, so the height of 401.183 cm
is the full withdrawal CR position. The CRs position for fully
insertion and withdrawal correspond to 0 and 228 in unit ofsteps, respectively. The detailed thermal-hydraulic data andthe macroscopic cross sections and derivatives are prescribedin [9].
In the uncontrolled CR withdrawal benchmark, there are
4 cases, Cases A, B, C and D; however, only three Cases, which
are Case A, Case B, and Case D, are considered in this work.
Case C is not considered since it is different from Case B onlyby the heat transfer coefficient between cladding and water
which is set constant of 30,000 W/m2 /K [9]. In addition, thereference results showed only small difference between Case
B and Case C [12]. In each case, the transient parameters

Science and Technology of Nuclear Installations

D

A
S
B

C
S

C

D

B

A
S

S
C

D

=2.1 w/o=3.1 w/o=2.6 w/o + 12 buranble absorber (BA) rods

=2.6 w/o + 20 BA=3.1 w/o + 12 BA=3.1 w/o + 16 BA=2.6 w/o + 16 BA=control element=reflector element

A, B, C, D, and S = bank CR

Figure 1: The NEA-NSC PWR uncontrolled CRs withdrawal benchmark core configuration [9].

are analyzed until 10 s after reactor trip signal occurred. The
calculated benchmark cases are as follows [9]:(i) Case A represents a single CRs bank withdrawal(bank D) and other CRs banks (C, B, A, and S) remain
fully withdrawn until scram.
(ii) Case B represents a group CRs bank withdrawal(banks B and C), CRs bank A and D remain fully
inserted, and other CRs banks S are fully withdrawn
until scram.
(iii) Case D represents group CRs bank withdrawal (banks
A and B), CRs banks C and D remain fully inserted,and other CRs banks S are fully withdrawn until
scram.

3. Benchmark Core Calculations
All calculation results of NODAL3 code will be comparedwith the reference solution, PANTHER code, as describedin [12]. Same as the previous works [1, 5], all transient cases
are calculated by adiabatic (AM) and improved quasistatic(IQM) methods. The detail numerical of those methods aredescribed in [1].
NODAL3 code used a 3D symmetrical quarter coreconfiguration as described in Figure 1 for the core calculation.
The core is divided into 18 layers axially, from bottom totop, 1 layer for lower reflector (30.0 cm thickness), 16 layers
for active core (7.7 cm, 11.0 cm, 15.0 cm, 30.0 cm (10 layers),
12.8 cm (2 layers), 8.0 cm), and 1 layer for upper reflector

Science and Technology of Nuclear Installations

3
cladding temperature, however the benchmark
result D7 is maximum outer cladding temperature.

=2.1 w/o=2.6 w/o=3.1 w/o=reflector element

Figure 2: A symmetrical core configuration for 2nd axial layer [9].

(30.0 cm). The active core configuration of 2nd layer frombottom (7.7 cm) is described in Figure 2, while the remaining
layers are configured as shown in Figure 1.
The calculation results of NODAL3 are compared with thereference solutions for [12]:(1) Steady-state results(i) Critical boron concentration, ppm (result B1)(ii) Axial power peak factor, 𝐹𝑧 (result B2)(iii) Radial power peak factor, 𝐹𝑥𝑦 (result B3)(iv) Global (3D) power peak factor, 𝐹𝑞 (𝑧) (result B6)
Note: 𝐹𝑧 values at 6th (result B4) and 13th (result
B5) axial layer are not available to be presented
since the NODAL3 code cannot give the output
for the those active layers.
(2) Transient core averaged results(i) Fission power relative to nominal, %, and timeof maximum power, s (result C1)(ii) Average coolant outlet temperature (maximum
value), 𝑇𝐶, ∘ C (result C3)(iii) Average core Doppler temperature (maximum
value), 𝑇𝐹 , ∘ C (result C4)
Note: NODAL3 code cannot give the output forresult C2, coolant heating.
(3) Transient hot pellet results(i) Maximum fuel centreline temperature, ∘ C(result D6)
Note: NODAL3 code cannot give the output
for result D1–D5 and D7. For information,
NODAL3 calculates the maximum inner

It is assumed that the CRs are withdrawn with the velocityof 72 steps/minute, while the CRs drop with constant velocityof 228 steps in 2.2 s. The CRs begin to drop 0.6 s after thefission power reaches 35% of nominal power (2,775 MW). It
is noted that the initial power is 10−13 of nominal power. The
moderator inlet conditions (flow, pressure, temperature, andboron concentration) are constant during the transient [9].
The NODAL3 calculations were carried out by using thefollowing input conditions: 2 × 2 radial nodes per FA, 1 × 18
axial nodes layers and the maximum time step of 5.5 ms. In
this work, the influence of the radial and axial node number
is investigated. We found in the previous research work thatthe number of nodes gives a significant influence in thecalculation results [5]. In order to be consistent with theprevious researches [1, 5], the NODAL3 results are comparedto the references in terms of their absolute value of relative
deviation (%) [1, 12].

4. Results and Discussion
4.1. Steady-State Results. Table 1 shows the steady-stateparameter results (B1, B2, B3, and B6) for Cases A, B, and C.
The calculation results of NODAL3 have the maximum deviations of 0.64% in the calculated 𝐹𝑥𝑦 and 𝐹𝑞 (𝑧) parameters forCase A, while the deviation of other calculated parameters
is less than 0.37% for all cases. The NODAL3 steady-statebenchmarks’ results show an excellent agreement with thereference’s results [12]. It is noted that the radial and axial
node number used in NODAL3 code is different with thereference, PANTHER code. Therefore, the effect of the radial
and axial node number is presented in Tables 2 and 3.
Tables 2 and 3 show the influence of the radial andaxial node number per FA, respectively. It is clear that theradial node number has significant influence compared withthe axial one, since the maximum deviation changes in therange of 0.64%–1.27% and 0.32%–0.64% for radial and axial
nodes, respectively. Among those parameters, the criticalboron concentration and the global (3D) power peak factor,
𝐹𝑞 (𝑧), are sensitive to the radial node number. Those results
show that the core configuration of Case A is sensitive tothe nodes number, probably because of the local effect of
the single CRs bank withdrawal. The calculation results of
NODAL3 codes become closer to the reference’s results if it
is used with the radial nodes number per FA of 2 × 2 andthe axial node numbers of 2 × 18. By using the recommended
node numbers, the deviation can be lowered to 50% or
the maximum deviation is to be 0.32%. However, a further
analysis needs to be carried out in the future to clarify which
the node number is optimum to obtain a satisfy calculation
results.
4.2. Transient Core Averaged Results. Table 4 and Figures
3–5 show the calculated transient core parameters by using
NODAL3 code for Cases A, B, and C. More than 10%
deviations occur in the fission power relative to nominal (𝑃)4Science and Technology of Nuclear Installations
Table 1: Steady-state results for Cases A, B, and D.

Parameters

Results

Critical boron concentration, ppm
Axial power peak factor, 𝐹𝑧
Radial power peak factor, 𝐹𝑥𝑦
Global (3D) power peak factor, 𝐹𝑞 (𝑧)

B1
B2
B3
B6

Critical boron concentration, ppm
Axial power peak factor, 𝐹𝑧
Radial power peak factor, 𝐹𝑥𝑦
Global (3D) power peak factor, 𝐹𝑞 (𝑧)

B1
B2
B3
B6

Critical boron concentration, ppm
Axial power peak factor, 𝐹𝑧
Radial power peak factor, 𝐹𝑥𝑦
Global (3D) power peak factor, 𝐹𝑞 (𝑧)

B1
B2
B3
B6

NODAL3

Reference
Case A
1262.7
1.513
1.242
1.880
Case B
793.6
1.507
1.912
2.886
Case D
793.6
1.507
1.912
2.886

AM

IQM

1266.5 (0.30%)∗
1.513 (0.00%)
1.234 (0.64%)
1.868 (0.64%)

1266.5 (0.30%)
1.513 (0.00%)
1.234 (0.64%)
1.868 (0.64%)

795.0 (0.18%)
1.508 (0.07%)
1.905 (0.37%)
2.877 (0.31%)

795.0 (0.18%)
1.508 (0.07%)
1.905 (0.37%)
2.877 (0.31%)

795.0 (0.18%)
1.508 (0.07%)
1.905 (0.37%)
2.877 (0.31%)

795.0 (0.18%)
1.508 (0.07%)
1.905 (0.37%)
2.877 (0.31%)

Note. ∗ Number in parentheses are the absolute value of relative deviation of NODAL3 with the reference.

Table 2: Effect of radial node number per FA for steady-state parameters in Cases A, B, and D.
Parameters

Results

Critical boron concentration, ppm
Axial power peak factor, 𝐹𝑧
Radial power peak factor, 𝐹𝑥𝑦
Global (3D) power peak factor, 𝐹𝑞 (𝑧)

B1
B2
B3
B6

Critical boron concentration, ppm
Axial power peak factor, 𝐹𝑧
Radial power peak factor, 𝐹𝑥𝑦
Global (3D) power peak factor, 𝐹𝑞 (𝑧)

B1
B2
B3
B6

Critical boron concentration, ppm
Axial power peak factor, 𝐹𝑧
Radial power peak factor, 𝐹𝑥𝑦
Global (3D) power peak factor, 𝐹𝑞 (𝑧)

B1
B2
B3
B6

Reference

1×1

Case A
1262.7
1.513
1.242
1.880
Case B
793.60
1.507
1.912
2.886
Case D
793.60
1.507
1.912
2.886

NODAL3 (node number per FA)∗
2×2

4×4

1278.7 (1.27%)∗∗1.515 (0.13%)
1.238 (0.32%)
1.877 (0.16%)

1266.5 (0.30%)
1.513 (0.00%)
1.234 (0.64%)
1.868 (0.64%)

1262.9 (0.02%)
1.515 (0.13%)
1.252 (0.81%)
1.897 (0.90%)

800.5 (0.87%)
1.508 (0.07%)
1.889 (1.20%)
2.852 (1.18%)

795.0 (0.18%)
1.508 (0.07%)
1.905 (0.37%)
2.877 (0.31%)

793.5 (0.01%)
1.508 (0.07%)
1.911 (0.05%)
2.885 (0.03%)

800.5 (0.87%)
1.508 (0.07%)
1.889 (1.20%)
2.852 (1.18%)

795.0 (0.18%)
1.508 (0.07%)
1.905 (0.37%)
2.877 (0.31%)

793.5 (0.01%)
1.508 (0.07%)
1.911 (0.05%)
2.885 (0.03%)

Note. ∗ The axial node number is 1 × 18 nodes per axial layer; ∗∗ number in parentheses are the absolute value of relative deviation of NODAL3 with the reference.

of Cases B and D, with the range of 12.78%–17.90%, while
the deviation range for Case A is < 0.48%. As noted in[12], the power increased rapidly because there is continuous
fast reactivity insertion, so those deviations are observed.
However, the deviation of NODAL3 is less than the standard
deviation of the benchmark participants’ results in previous
work [12], because their deviations are in the range of
21%–24.5%.
Table 4 shows that the deviation of time of maximum
fission power is about 1.22%–1.44% for all cases. The deviation
is equivalent to Δ𝑡 = 0.42 s–1.18 s difference; that is, 𝑃 of
NODAL3 occurs about 0.42 s–1.18 s later. Those are clearlyshown in Figures 3–5; however, the deviations of NODAL3
are still smaller than the benchmark participants’ results [12].
Tables 5 and 6 show effect of radial and axial nodes
number on the 𝑃 (fission power relative to nominal) andtime of maximum fission power parameters. It is clear thatthe calculated 𝑃 results are sensitive with the radial andaxial node number, since the deviation is in the range of
0.56%–17.90% and 0.48%–17.90% for radial and axial nodes
number, respectively. On the other hand, the calculated timeof maximum fission power results is not sensitive since thedeviation is in the range of 0.0%–2.59% and 0.0%–1.34% forradial and axial node number, respectively. It is noted that the

Science and Technology of Nuclear Installations

5

Table 3: Effect of axial node number per FA for steady-state parameters in Cases A, B, and D.
Parameters

Results

Reference

Critical boron concentration, ppm
Axial power peak factor, 𝐹𝑧
Radial power peak factor, 𝐹𝑥𝑦
Global (3D) power peak factor, 𝐹𝑞 (𝑧)

B1
B2
B3
B6

1262.7
1.513
1.242
1.880

Critical boron concentration, ppm
Axial power peak factor, 𝐹𝑧
Radial power peak factor, 𝐹𝑥𝑦
Global (3D) power peak factor, 𝐹𝑞 (𝑧)

B1
B2
B3
B6

793.60
1.507
1.912
2.886

Critical boron concentration, ppm
Axial power peak factor, 𝐹𝑧
Radial power peak factor, 𝐹𝑥𝑦
Global (3D) power peak factor, 𝐹𝑞 (𝑧)

B1
B2
B3
B6

793.60
1.507
1.912
2.886

NODAL3 (node number for a axial layer per FA)∗1 × 182 × 184 × 188 × 18
Case A
1266.5 (0.30%)∗∗1266.6 (0.31%)
1266.6 (0.31%)
1266.7 (0.32%)
1.513 (0.00%)
1.514 (0.07%)
1.514 (0.07%)
1.514 (0.07%)
1.234 (0.64%)
1.245 (0.24%)
1.245 (0.24%)
1.245 (0.24%)
1.868 (0.64%)
1.886 (0.32%)
1.886 (0.32%)
1.886 (0.32%)
Case B
795.0 (0.18%)
795.0 (0.18%)
795.0 (0.18%)
795.1 (0.19%)
1.508 (0.07%)
1.508 (0.07%)
1.508 (0.07%)
1.508 (0.07%)
1.905 (0.37%)
1.905 (0.37%)
1.905 (0.37%)
1.905 (0.37%)
2.877 (0.31%)
2.876 (0.35%)
2.876 (0.35%)
2.876 (0.35%)
Case D
795.0 (0.18%)
795.0 (0.18%)
795.0 (0.18%)
795.1 (0.19%)
1.508 (0.07%)
1.508 (0.07%)
1.508 (0.07%)
1.508 (0.07%)
1.905 (0.37%)
1.905 (0.37%)
1.905 (0.37%)
1.905 (0.37%)
2.877 (0.31%)
2.876 (0.35%)
2.876 (0.35%)
2.876 (0.35%)

Note. ∗ The radial node number is 2 × 2 nodes; ∗∗ number in parentheses are the absolute value of relative deviation of NODAL3 with the reference.

Table 4: Transient core averaged results for Cases A, B, and D.
Parameters

Results

NODAL3

Reference

AM

IQM

35.56
82.14
295.3
358.7

35.39 (0.48%)∗
83.24 (1.34%)
294.8 (0.17%)
359.5 (0.22%)

35.42 (0.39%)
83.32 (1.44%)
294.8 (0.17%)
359.8 (0.31%)

134.80
34.30
290.5
315.2

110.67 (17.90%)
34.71 (1.20%)
290.3 (0.07%)
313.6 (0.51 %)112.16 (16.80%)
34.74 (1.28%)
290.3 (0.07%)
313.8 (0.44%)

96.85
39.40
290.0
312.6

109.23 (12.78%)
39.91 (1.29%)
290.3 (0.10%)
313.7 (0.35%)

110.60 (14.20%)
39.93 (1.35%)
290.3 (0.10%)314.0 (0.45%)

Case A
Fission power relative to nominal (𝑃), %Time of maximum fission power, sAverage coolant outlet temperature (𝑇𝐶 ), ∘ C
Average core Doppler temperature (𝑇𝐹 ), ∘ C

C1
C3
C4
Case B

Fission power relative to nominal (𝑃), %Time of maximum fission power, sAverage coolant outlet temperature (𝑇𝐶 ), ∘ C
Average core Doppler temperature (𝑇𝐹 ), ∘ C

C1
C3
C4
Case D

Fission power relative to nominal (𝑃), %Time of maximum fission power, sAverage coolant outlet temperature (𝑇𝐶 ), ∘ C
Average core Doppler temperature (𝑇𝐹 ), ∘ C

C1
C3
C4

Note. ∗ Number in parentheses are the absolute value of relative deviation of NODAL3 with the reference.

Table 5: Effect of radial node number per FA for fission power and time of peak fission power in Cases A, B, and D.
Parameters

Results

Fission power relative to nominal (𝑃), %Time of maximum fission power, s

C1

Fission power relative to nominal (𝑃), %Time of maximum fission power, s

C1

Fission power relative to nominal (𝑃), %Time of maximum fission power, s

C1

Reference
Case A
35.56
82.14
Case B
134.8034.30
Case D
96.85
39.40

1×1

NODAL3 (node number per FA)∗
2×2

4×4

35.31 (0.70%)∗∗84.27 (2.59%)

35.39 (0.48%)
83.24 (1.34%)

35.39 (0.48%)
82.81 (0.82%)

113.77 (15.60%)
34.70 (1.17%)

110.67 (17.90%)
34.71 (1.20%)

110.11 (18.32%)
34.68 (1.11%)

112.10 (15.75%)
39.40 (0.00%)

109.23 (12.78%)
39.91 (1.29%)

108.81 (12.35%)
40.01 (1.55%)

Note. ∗ The axial node number is 1 × 18 nodes per axial layer; ∗∗ number in parentheses are the absolute value of relative deviation of NODAL3 with the reference.

6

Science and Technology of Nuclear Installations
Table 6: Effect of axial node number per FA for fission power and time of peak fission power in Cases A, B, and D.

Parameters

Results

Reference

Fission power relative to nominal (P), %Time of maximum fission power, s

C1

35.56
82.14

Fission power relative to nominal (P), %Time of maximum fission power, sC1

134.8034.30

Fission power relative to nominal (P), %Time of maximum fission power, s

C1

96.85
39.40

NODAL3 (node number for a axial layer per FA)∗1 × 182 × 184 × 188 × 18
Case A
35.39 (0.48%)
83.24 (1.34%)
Case B
110.67 (17.90%)
34.71 (1.20%)
Case D109.23 (12.78%)
39.91 (1.29%)

35.37 (0.53%)
83.07 (1.13%)

35.32 (0.67%)
83.07 (1.13%)

35.36 (0.56%)
83.10 (1.17%)

133.10 (1.26%)
34.43 (0.38%)

128.86 (4.41%)
34.30 (0.00%)

129.63 (3.84%)
34.31 (0.03%)

93.56 (3.40%)
39.32 (0.20%)

96.13 (0.74%)
39.33 (0.18%)

97.94 (1.13%)
39.33 (0.18%)

Power/2775 MW

0.4

400

0.3
360
0.2
320

0.1
0

280
65

70

75

80

85

90

1.2

375

1
350
0.8
0.6

325

0.4
300
0.2
0

275
38

95

39

TF reference
TF AM
TF IQM

P reference
P AM
P IQM

1.4

340

Power/2775 MW

1.2
1

320

0.8
0.6
300

0.4
0.2

280

0
33

34

35

36

37

38

39

40

Maximum fuel Doppler temperature (∘ C)

Figure 3: Fission power (𝑃) and average core Doppler temperature(𝑇𝐹 ) distributions for Case A.

32

Time (s)P reference
P AM
P IQM

41

42

Time (s)Time (s)P reference
P AM
P IQM

40

Maximum fuel Doppler temperature (∘ C)

440

Power/2775 MW

0.5

Maximum fuel Doppler temperature (∘ C)

Note. ∗ The radial node number is 2 × 2 nodes; ∗∗ number in parentheses are the absolute value of relative deviation of NODAL3 with the reference.

TF reference
TF AM
TF IQM

Figure 4: Fission power (𝑃) and average core Doppler temperature(𝑇𝐹 ) distributions for Case B.

TF reference
TF AM
TF IQM

Figure 5: Fission power (𝑃) and average core Doppler temperature(𝑇𝐹 ) distributions for Case D.

reference, PANTHER code, used the 3 × 3 nodes and 48 nodes
for radial and axial, respectively [12], so the increment of axial
nodes in NODAL3 calculations, 18 nodes (1 × 18) to 36 nodes(2 × 18), give closer result to the reference.
4.3. Transient Hot Pellet Results. Table 7 shows that thedeviation of >1% occurs in Cases B and D, while the deviationin Case A is < 1%, except IQM method. The maximum
deviation of fuel centerline temperature is 3.62% (Case B
with AM method) or equivalent to Δ𝑇 = 17.3∘ C (lower).
However, the maximum deviation of NODAL3 is less than thestandard deviation of the benchmark participants’ results inprevious work [12], because their deviations are in the rangeof 19∘ C–30.8∘ C.
Tables 8 and 9 indicate that the maximum fuel temperature is more sensitive to the axial node number than the radial
node number, since the results vary with the case. It is clear inCase B, since the deviation is in the range of 0.73%–3.62% and3.53%–3.85% for axial and radial node number, respectively.

Science and Technology of Nuclear Installations

7

Table 7: Transient fuel pellet results for Cases A, B, and D.
Parameters

Results
Case A
D6
Case B
D6
Case D
D6

Maximum fuel temperature at hot pellet centerline, ∘ C
Maximum fuel temperature at hot pellet centerline, ∘ C
Maximum fuel temperature at hot pellet centerline, ∘ C

NODAL3

Reference

AM

IQM

631.8

632.9 (0.17%)

639.4 (1.20%)

478.2

460.9 (3.62%)

462.8 (3.22%)

451.4

457.8 (1.42%)

458.8 (1.64%)∗

Note. Number in parentheses are the absolute value of relative deviation of NODAL3 with the reference.

Table 8: Effect of radial node number per FA for transient hot pellet results in Cases A, B, and D.
Parameters

Results

NODAL3 (node number per FA)∗
1×1
2×2
4×4

Reference
Case A

Maximum fuel temperature at hot pellet centerline, ∘ C

D6

631.8

629.2 (0.41%)∗∗632.9 (0.17%)

632.9 (0.17%)

Maximum fuel temperature at hot pellet centerline, ∘ C

D6

478.2
Case D
D6
451.4

459.8 (3.85%)

460.9 (3.62%)

461.3 (3.53%)

459.8 (1.86%)

457.8 (1.42%)

458.2 (1.51%)

Case B

Maximum fuel temperature at hot pellet centerline, ∘ C

Note. ∗ The axial node number is 1 × 18 nodes per axial layer; ∗∗ number in parentheses are the absolute value of relative deviation of NODAL3 with the reference.

Table 9: Effect of axial nodes number per FA for transient hot pellet results in Cases A, B, and D.
Parameters

Results Reference

Maximum fuel temperature at hot pellet centerline, ∘ C

D6

Maximum fuel temperature at hot pellet centerline, ∘ C

D6

Maximum fuel temperature at hot pellet centerline, ∘ C

B1Case A
631.8
Case B
478.2
Case D
451.4

NODAL3 (node number for a axial layer per FA)∗1 × 182 × 184 × 188 × 18632.9 (0.17%)∗∗ 632.3 (0.08%) 633.0 (0.19%) 633.0 (0.19%)
460.9 (3.62%)

474.7 (0.73%) 472.4 (1.21%)

472.9 (1.11%)

457.8 (1.42%)

446.8 (1.02%) 448.8 (0.58%) 450.0 (0.31%)

Note. ∗ The radial node number is 2 × 2 nodes; ∗∗ number in parentheses are the absolute value of relative deviation of NODAL3 with the reference.

By using some axial node numbers, the deviation can belowered to 79.8% (2 × 18 nodes), 66.6% (4 × 18 nodes), and69.3% (8 × 18 nodes).

Conflicts of Interest

5. Conclusions and Future Works

Acknowledgments

The in-house coupled neutronic and thermal-hydraulic codeof BATAN, NODAL3, based on the few-group neutron
diffusion equation in 3-dimensional geometry using thepolynomial nodal method, has been verified with the NEANSC PWR uncontrolled control rods withdrawal at zero
power benchmark. The results of NODAL3 code show very
good agreement with the reference solutions, especially withthe 2 × 2 of radial nodes and 2 nodes per axial layer (total 18
layers).
As future works, the NODAL3 code will be used toanalyze the real experimental data of PWR such as describedin the IAEA-TECDOC-815 [13], as well as transient analysisof an advanced PWR type reactor, such as AP1000 reactor.

This work has been partially supported by the IAEA ResearchContract no. 18731/R0 and the Finance Ministry of Indonesia(DIPA) for fiscal years of 2015-2016.

The authors declare that they have no conflicts of interest.

References[1] S. Pinem, T. M. Sembiring, and P. H. Liem, “The verification of
coupled neutronics thermal-hydraulics code NODAL3 in the
PWR rod ejection benchmark,” Science and Technology of
Nuclear Installations, vol. 2014, Article ID 845832, 9 pages, 2014.
[2] T. M. Sembiring and S. Pinem, “Valdation of NODAL3 code on
the PWR NEACRP Benchmark Core,” in Proceedings of theProceeding of 14th National Seminar on NPP Safety Technology
and Nuclear Facility, pp. 172–178, Bandung, 2009.

8[3] T. M. Sembiring and S. Pinem, “The validation of the NODAL3
code for static cases of the PWR benchmark core,” Journal of
Nuclear Science and Technology Ganendra, vol. 15, no. 2, pp. 82–
92, 2012.
[4] T. M. Sembiring, S. Pinem, and P. H. Liem, “Validation of fullcore geometry model of the NODAL3 code in the PWR transient benchmark problems,” Journal Teknologi Reaktor Nuklir
Tri Dasa Mega, vol. 17, no. 3, pp. 141–148, 2015.
[5] S. Pinem, T. M. Sembiring, and P. H. Liem, “NODAL3 Sensitivity Analysis for NEACRP 3D LWR Core Transient Benchmark(PWR),” Science and Technology of Nuclear Installations, vol.
2016, Article ID 7538681, 2016.
[6] P. H. Liem, S. Pinem, T. M. Sembiring, and H. Tran, “Status ondevelopment and verification of reactivity initiated accident
analysis code for PWR (NODAL3),” Nucl. Sci. Technol, vol. 6,
no. 1, pp. 1–13, 2016.
[7] H. Finnemann and A. Galati, “NEACRP 3-D LWR Core
Transient Benchmark - Final Specifications,” in NEACRP-L-335(Revision 1), 1992.
[8] H. Finnemann, H. Bauer, A. Galati, and R. Martinelli, “Resultsof LWR core transient benchmark,” NEA/NSC/DOC 25,
Nuclear Energy Agency of the OECD (NEA), Paris, France,
1993.
[9] R. Fraikin and H. Finnemann, “NEA-NSC 3-D/1-D PWR coretransient benchmark uncontrolled withdrawal of control rods
at zero power,” NEA/NSC 9, 1993.
[10] Internatinal Atomic Energy Agency, Considerations on theapplication of the IAEA safety requirements for the design of
nuclear power plants, IAEA-TECDOC-1791, IAEA, Vienna,
Austria, 2016.
[11] S. Aoki, T. Suemura, J. Ogawa, and T. Takeda, “The verificationof 3 dimensional nodal kinetics code ANCK using transient
benchmark problems,” Journal of Nuclear Science and Technology, vol. 44, no. 6, pp. 862–868, 2007.
[12] R. Fraikin, “PWR benchmark on uncontrolled rods withdrawal
at zero power,” NEA Nuclear Science Committee 20, Tractebel
Energy Engineering, Brussels, Belgium, 1997.
[13] “International Atomic Energy Agency, In-core fuel management code package validation forPWRs, IAEA-TECDOC-815,
IAEA, Vienna, Austria, 1995”.

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