NUREG/IA-0455 

International 

 Agreement Report

Analysis of the Control Rod Drop 

Accident (CRDA) for Lungmen ABWR

 

 

 

 Prepared by: 

Chunkuan Shih*, Ai-Ling Ho*, Jong-Rong Wang*, Hao-Tzu Lin, Show-Chyuan Chiang**, 

Chia-Chuan Liu**

Institute of Nuclear Energy Research, Atomic Energy Council, R.O.C.

1000, Wenhua Rd., Chiaan Village, Lungtan, Taoyuan, 325, Taiwan

*Institute of Nuclear Engineering and Science, National Tsing Hua University

101 Section 2, Kuang Fu Rd., HsinChu, Taiwan

**Department of Nuclear Safety, Taiwan Power Company

242, Section 3, Roosevelt Rd., Zhongzheng District, Taipei, Taiwan

K. Tien, NRC Project Manager 

 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: April 2015

Date Published: August 2015

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission
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NUREG/IA-0455 

International 

 Agreement Report

Analysis of the Control Rod Drop 

Accident (CRDA) for Lungmen ABWR

 

 

 

 Prepared by: 

Chunkuan Shih*, Ai-Ling Ho*, Jong-Rong Wang*, Hao-Tzu Lin, Show-Chyuan Chiang**, 

Chia-Chuan Liu**

Institute of Nuclear Energy Research, Atomic Energy Council, R.O.C.

1000, Wenhua Rd., Chiaan Village, Lungtan, Taoyuan, 325, Taiwan

*Institute of Nuclear Engineering and Science, National Tsing Hua University

101 Section 2, Kuang Fu Rd., HsinChu, Taiwan

**Department of Nuclear Safety, Taiwan Power Company

242, Section 3, Roosevelt Rd., Zhongzheng District, Taipei, Taiwan

K. Tien, NRC Project Manager 

 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: April 2015

Date Published: August 2015

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission

iii

ABSTRACT

The purpose of this report is to understand the realistic behavior in Lungmen ABWR (Advanced 

Boiling Water Reactor) during a control rod drop accident (CRDA) transient. The CRDA transient 

would lead the reactor through an extremely fast and localized power excursion, requiring an 

accurate core modeling. The CRDA analysis for Lungmen ABWR was performed by coupling the 

3D neutron kinetic code, PARCS, and two-phase thermal-hydraulic (T-H) code, TRACE. After 

TRACE/PARCS coupling calculation, the output data from TRACE/PARCS would be putted into 

FRAPTRAN code as boundaries, such as a function of time-dependent fuel rod power and coolant 

boundary conditions, to calculate the fuel damage. The CRDA analysis for Lungmen ABWR was 

performed for two conditions: a) case1: hot-full-power (HFP) at beginning of cycle (BOC); b) 

case2: hot-zero-power (HZP) at BOC. Under these conditions, the damage mechanisms of fuel 

rod are: 1) cladding ballooning and burst; 2) embrittlement and failure by high-temperature 

oxidation; 3) melting of cladding and/or fuel pellets. And the relevant quantities for fuel 

performance are the maximum fuel enthalpy and the melting temperatures of cladding and fuel 

pellet. The results of CRDA analysis show that a) case1: no fuel failure occurs under HFP 

condition at BOC; b) case2: the fuel rod nearby the dropped control rod failed under HZP condition 

at BOC, and the FRAPTRAN data exposes that the main reason of rod failure is the cladding high 

temperature.
iv 
v

FOREWORD

The US NRC (United States Nuclear Regulatory Commission) is developing an advanced thermal 

hydraulic code named TRACE for nuclear power plant safety analysis. The development of 

TRACE is based on TRAC, integrating RELAP5 and other programs. NRC has determined that 

in the future, TRACE will be the main code used in thermal hydraulic safety analysis, and no 

further development of other thermal hydraulic codes such as RELAP5 and TRAC will be 

continued. A graphic user interface program, SNAP (Symbolic Nuclear Analysis Program) which 

processes inputs and outputs for TRACE is also under development. One of the features of 

TRACE is its capacity to model the reactor vessel with 3-D geometry. It can support a more 

accurate and detailed safety analysis of nuclear power plants. TRACE usually used in the nuclear 

power plants analysis. This report showed TRACE can also do the calculation of small system 

such as dry-storage cask.

Taiwan and the United States have signed an agreement on CAMP (Code Applications and 

Maintenance Program) which includes the development and maintenance of TRACE. INER 

(Institute of Nuclear Energy Research, Atomic Energy Council, R.O.C.) is the organization in 

Taiwan responsible for the application of TRACE in thermal hydraulic safety analysis, for 

recording user’s experiences of it, and providing suggestions for its development. To meet this 

responsibility, the TRACE/PARCS/FRAPTRAN model of Lungmen NPP has been built. In this 

report, the TRACE/PARCS/FRAPTRAN model of Lungmen NPP was used to evaluate the 

Lungmen CRDA transient.

vii

CONTENTS

Page

ABSTRACT ............................................................................................................................. iii

FOREWORD............................................................................................................................. v 

CONTENTS ............................................................................................................................ vii

FIGURES ................................................................................................................................. ix 

TABLES................................................................................................................................... ix 

EXECUTIVE SUMMARY........................................................................................................ xi 

ABBREVIATIONS................................................................................................................. xiii

1. INTRODUCTION..............................................................................................................1-1

2. MODELS OF LUNGMEN ABWR ..................................................................................2-1

2.1 Lungmen TRACE Model............................................................................................2-1 

2.2 Lungmen PARCS Model............................................................................................2-3 

2.3 Lungmen TRACE/PARCS Coupling Model................................................................2-6 

2.4 Lungmen TRACE/PARCS/FRAPTRAN Model...........................................................2-7 

3. INITIAL CONDITIONS AND RESULTS........................................................................3-1

3.1 Case1-HFP Condition at BOC ...................................................................................3-3 

3.2 Case2-HZP Condition at BOC ...................................................................................3-8 

4. CONCLUSIONS ..............................................................................................................4-1

5. REFERENCES ................................................................................................................5-1
viii 
ix

FIGURES

Page

Figure 1 Lungmen TRACE model ......................................................................................2-2

Figure 2 Core pattern for Lungmen PARCS model. ...........................................................2-3

Figure 3 Control rod pattern for case1-HFP .......................................................................2-4

Figure 4 Control rod pattern for case2-HZP .......................................................................2-4

Figure 5 Core averaged axial power shape at (a) HFP and (b) HZP condition ...................2-5

Figure 6 The procedure of TRACE/PARCS coupling calculation........................................2-6

Figure 7 Schematic of fuel rod geometry in FRAPTRAN....................................................2-8

Figure 8 Flowchart of combining TRACE/PARCS and FRAPTRAN codes.........................2-9

Figure 9 Inserted reactivity due to control rod drop at various rod position.........................3-2

Figure 10 Reactivity components evolution in case1............................................................3-3

Figure 11 Reactor thermal power evolution in case1 ...........................................................3-4

Figure 12 Fuel centerline temperature at each node from bottom to top of fuel 

in case1 ..............................................................................................................3-4

Figure 13 Cladding Inside temperature at each node from bottom to top of fuel 

in case1 ..............................................................................................................3-5

Figure 14 Average fuel enthalpy at each node from bottom to top of fuel in case1...............3-5 

Figure 15 Fuel surface hoop strain in case1 ........................................................................3-6

Figure 16 Cladding hoop strain in case1 ..............................................................................3-6

Figure 17 Structural radial gap in case1 ...............................................................................3-7

Figure 18 Gap heat transfer coefficient in case1 ..................................................................3-7

Figure 19 Reactivity components evolution in case2............................................................3-9

Figure 20 Reactor thermal power evolution in case2 ......................................................... 3-10

Figure 21 Local void fraction around the dropped control rod in case2 .............................. 3-10

Figure 22 Fuel centerline temperature at each node form bottom to top of fuel 

in case2 ............................................................................................................ 3-11

Figure 23 Cladding inside temperature at each node form bottom to top of fuel 

in case2 ............................................................................................................ 3-11

Figure 24 Average fuel enthalpy at each node form bottom to top of fuel in case2............. 3-12

Figure 25 Fuel surface hoop strain in case2 ...................................................................... 3-12

Figure 26 Cladding hoop strain in case2............................................................................ 3-13

Figure 27 Structural radial gap in case2............................................................................. 3-13

Figure 28 Gap heat transfer coefficient in case2................................................................ 3-14

TABLES

Page

Table 1 Core initial conditions for two CRDA cases ...........................................................3-1
x
xi

EXECUTIVE SUMMARY

An agreement in 2004 which includes the development and maintenance of TRACE has been 

signed between Taiwan and USA on CAMP. INER is the organization in Taiwan responsible for

applying TRACE to thermal hydraulic safety analysis in order to provide users’ experiences and 

development suggestions. To fulfill this responsibility, the TRACE/PARCS model of Lungmen 

NPP is developed by INER. 

According to the user manual, TRACE is the product of a long term effort to combine the 

capabilities of the NRC’s four main systems codes (TRAC-P, TRAC-B, RELAP5 and RAMONA) 

into one modernized computational tool. NRC has ensured that TRACE will be the main code 

used in thermal hydraulic safety analysis in the future without further development of other thermal 

hydraulic codes, such as RELAP5 and TRAC. Besides, the 3-D geometry model of reactor vessel, 

which is one of the representative features of TRACE, can support a more accurate and detailed 

safety analysis of NPPs. On the whole TRACE provides greater simulation capability than the 

previous codes, especially for events like LOCA. 

PARCS is a multi-dimensional reactor core simulator which involves a 3-D calculation model for 

the realistic representation of the physical reactor while 1-D modeling features are also available. 

PARCS is capable of coupling the thermal-hydraulics system codes such as TRACE directly, 

which provide the temperature and flow field data for PARCS during the calculations.

Lungmen NPP is the fourth NPP in Taiwan. It has two identical units of ABWRs with 3,926 MWt 

rated thermal power each, consisted of 872 GE14 assemblies with 205 control rods. The steam 

flow is 7.64×106 Kg/h at rated power condition. The designed rated core flow is 52.2×106 Kg/h. 

Compared with BWRs, ABWR replaced the recirculation loop by 10 RIPs (reactor internal pumps), 

eliminating the probability of large break LOCA. 10 RIPs could provide 111% rated core flow at 

the nominal operating speed of 151.84 rad/sec.

The initiating event for CRDA is the separation of a control rod blade from its driving mechanism. 

And the control rod is removed from core due to gravity and drops in a free fall. The CRDA can 

occur at any reactor operating condition. As control rod drops, the ability of neutron absorption 

decreases, causing an increase in fission rate and reactor power. This power excursion may lead 

to failure of the fuel rod and integrity of the reactor core, and in very severe case, even lead to 

disruption of the reactor.

The CRDA is the design-basis reactivity-initiated accident (RIA) in BWR. Historically, the point 

kinetics model or one dimensional kinetics model using core wide coefficients having a significant 

conservatism has been employed for the safety assessment of RIA [1]. This approach is 

insufficient to calculate an extremely fast and localized power excursion induced by CRDA. In 

order to understand the realistic reactor and fuel behavior in Lungmen ABWR, in this report, 

CRDA transient is performed by coupling the 3D neutron kinetic code, PARCS, and two-phase TH code, TRACE. After TRACE/PARCS coupling calculation, the output data from TRACE/PARCS 

would be inputted into FRAPTRAN code as a function of time-dependent fuel rod power and 

coolant boundary conditions to calculate the fuel damage. And there are two cases to discuss: a) 

case1: HFP condition at BOC; b) case2: HZP condition at BOC.
xii
xiii

ABBREVIATIONS

BOC Beginning Of Cycle

CRDA Control Rod Drop Accident

CPR Critical Power Ratio

DNBR Departure From Nuclear Boiling Ratio

GDC-28 General Design Criterion 28

HFP Hot-Full-Power

HZP Hot-Zero-Power

LOCA Loss Of Coolant Accidents

PCMI Pellet-Clad Mechanical Interaction

RG Regulatory Guide

RIPs Reactor Internal Pumps

SRVs Safety Relief Valves

TCVs Turbine Control Valves

TBV Turbine Bypass Valve
xiv
1-1 

1. INTRODUCTION

The purpose of this report is to understand the realistic behaviour in Lungmen ABWR during 

CRDA transient. The analysis of CRDA for Lungmen ABWR was performed by using TRACE v5.0 

p2, PARCS V3.0, and FRAPTRAN 1.4 under SNAP Configuration 2.0.6. 

The fuel rod behaviour under CRDA is affected by the characteristic of the power pulse, core 

coolant conditions, burn-up-dependent state of fuel rod, and fuel rod design [2]. There are four 

potential failure modes for the fuel rod, one at low temperature: 

 by pellet-clad mechanical interaction (PCMI) under the early heat-up stage,

and three at high temperature:

 by cladding ballooning and burst,

 by disruption of the cladding upon quenching from high temperature,

 by melting the cladding and/or fuel pellets.

Low-temperature PCMI-induced cladding failure is defined by the initial fuel enthalpy increase, 

which may occur in high-burn-up fuel rod, but not in fresh fuel rod. Thus, for the zero-burn-up fuel 

rod, high-temperature failures are its limiting failure modes. Cladding ballooning and burst occurs, 

if clad-to-coolant heat transfer is impaired by a boiling crisis (film-boiling) and the fuel rod internal 

gas pressure exceeds the coolant pressure (rod internal overpressure). Fuel rod disruption under 

quenching is due to cladding embrittlement by high temperature oxidation under the film-boiling 

phase. High-temperature failure is defined by the total radial average fuel enthalpy as a function 

of pressure difference between internal and external pressure of fuel rod [3].

Acceptance criteria for CRDA events are based on 10CFR50 Appendix A, General Design 

Criterion 28 (GDC-28) requirements detailed within Regulatory Guide (RG) 1.77 and NUREG0800 Standard Review Plan. For CRDA with zero-burn-up fuel rod at HFP and HZP, the following 

criteria are listed [4][5][6]:

 Fuel cladding failure criteria: for zero power conditions, a peak radial average fuel enthalpy

can not be greater than 170cal/g for fuel rods with an internal rod pressure at or below system

pressure and 150cal/g for fuel rods with an internal rod pressure exceeding system pressure;

for intermediate and full power conditions, fuel cladding failure is presumed if local heat flux

exceeds thermal design limits (e.g. DNBR and CPR).

 Coolable core geometry criteria: peak radial average fuel enthalpy must remain below

230cal/g; peak fuel temperature must remain below incipient fuel melting conditions (fuel

centerline temperature < 3078.15K); peak cladding temperature must remain below incipient

cladding melting conditions (< 1473.15K).

There are two cases to discuss: a) case1: HFP condition at BOC; b) case2: HZP condition at 

BOC. And the results show that a) case1: no fuel failure occurs under HFP condition at BOC; b) 

case2: the fuel rod nearby the dropped control rod failed under HZP condition at BOC, and the 

FRAPTRAN data exposes that the main reason of rod failure is the cladding high temperature.
1
2-1 

2. MODELS OF LUNGMEN ABWR

2.1 Lungmen TRACE Model

The analysis of CRDA for Lungmen ABWR was performed by using TRACE v5.0 p2. The 

preliminary Lungmen TRACE model is established based on the relevant documents, as shown 

in Figure 1 [7]~[10]. There are three major control systems implemented in Lungmen TRACE 

model: feedwater control system, pressure control system, and RIP control system. The core 

region was modeled by 22 thermal-hydraulic channels to simulate the T-H behavior of 872 fuel 

assemblies. In the region around the dropped rod, each channel represented a single assembly 

in order to reflect accurately the T-H reactivity feedback effects following a control rod drop. In 

other region, each channel represented several fuel assemblies. The number of axial nodes in 

each channel is 11. According to the assemblies in the real reactor, the vessel was divided into 

eleven axial levels, four radial rings, and six azimuthal sectors. The six azimuthal sectors are 

orientated in 36 ゚, 36 ゚, 108 ゚, 36 ゚, 36 ゚, 108 ゚, 36 ゚apart, and each azimuthal sector is 

connected with the feed water line inlet (six feedwater lines). There are four main steam lines 

connected to the 36 ゚azimuthal sector of vessel and ten RIPs connected to six azimuthal sectors, 

one for every 36 ゚. The ten RIPs were separated into three groups, four RIPs not connect to M/G 

sets (RIP3) and six RIPs connect to M/G sets (RIP1 and RIP2, thee for each). There are four sets 

of valves included in this model. The MSIVs and Turbine control valves (TCVs) are normally 

opened. The turbine bypass valve (TBV) and six groups of safety relief valves (SRVs), simulating 

eighteen SRVs distributed at the four main steam lines with different setpoints, are normally 

closed. In addition, the Moody choke flow model was adopted for limiting the maximum SRVs’ 

flow.

In addition, the steady state plant parameters from Lungmen TRACE model had been 

successfully verified with those from FSAR and RETRAN02. The verified results reveal that there 

is respectable accuracy in the Lungmen TRACE model [11][12].
2-2 

Figure 1 Lungmen TRACE model
2-3 

2.2 Lungmen PARCS Model

The analysis of CRDA for Lungmen ABWR was performed by using PARCS V3.0. PARCS 

involves 3D reactor core simulator for the realistic representation of physical reactor, and it can 

solve steady-state and time-dependent, multi-group neutron diffusion and SP3 transport 

equations in orthogonal and hexagonal core geometries. Figure 2 shows the core pattern for 

Lungmen PARCS model. For radial mesh, there are 1012 nodes in Lungmen PARCS model: 872 

nodes model 872 fuel assemblies (yellow square); 140 nodes model the reflector outside the core 

(blue square). And the number of axial planes is 25 in the effective fuel region. The cross-section 

data used in PARCS calculation is provided by PMAXS file which is generated by GenPMAXS 

program from the macroscopic cross-section libraries and the results of lattice code, CASMO [13].

The preliminary Lungmen PARCS model is established by our laboratory colleagues, Chen [14] 

and Chang [15]. The kinf calculated from PARCS had been verified by that from SIMULATE. 

The result shows the respectable accuracy in Lungmen PARCS model that the error bar is smaller

than 10-5. 

Figure 3 shows a control rod pattern in Lungmen ABWR under reactor normal operation condition. 

Figure 4 shows the control rod pattern at HZP condition. Normally, the 205 control rod were

divided into 19 groups, each group has different initial step. For analysis with CRDA, an additional

control rod group was added to control the selected control rod. Figure 5 shows the core averaged 

axial power shape at (a) HFP and (b) HZP condition.

Figure 2 Core pattern for Lungmen PARCS model
2-4 

Figure 3 Control rod pattern for case1-HFP

Figure 4 Control rod pattern for case2-HZP
2-5 

(a) HFP (b) HZP

Figure 5 Core averaged axial power shape at (a) HFP and (b) HZP condition
2-6 

2.3 Lungmen TRACE/PARCS Coupling Model

Note that the case ARI and FMCRD run-in was performed by TRACE/PARCS coupling model, 

but in case SLCS initiation we substituted PARCS for point kinetics because Lungmen PMAXS 

file used in core power calculation has problems in boron reactivity calculation.

Figure 6 displays the flowchart of TRACE/PARCS coupling model. During the transient 

calculation, PARCS determines the core power distribution by using T-H conditions provided by 

TRACE. The power information is then transferred back to TRACE to calculate the new T-H 

conditions for PARCS. Thus the TRACE/PARCS coupling model gives the actual core power and 

T-H distribution at any time point.

Based on this preliminary Lungmen TRACE/PARCS coupling model, Feng et al. [16] analyzed 

the loss feed water heater transient and compared the results with plant vender data. It shows 

that the Lungmen TRACE/PARCS coupling model has an ability of transient simulation of 

Lungmen NPP.

Figure 6 The procedure of TRACE/PARCS coupling calculation [17] PARCS TRACE Lattice

CASMO-4 GenPMAXS PMAXS

Thermal-hydraulic 

Calculation Code

Node-wise 

Cross Section

Node-wise 

Power

History for 

each Region

Cross Section 

Module

Neutronics 

Calculation

Depletion 

Module

Temperature and Flow 

Information
2-7 

2.4 Lungmen TRACE/PARCS/FRAPTRAN Model

The analysis of CRDA for Lungmen ABWR was performed by using FRAPTRAN 1.4. FRAPTRAN 

is a computer code for analyzing the thermo-mechanical behavior of light water reactor (LWR) 

fuel rod under transients and accidents, such as LOCAs and RIAs [18]. Figure 7 illustrates the 

schematic of fuel rod in FRAPTRAN model. The axial fuel length from bottom to top was divided 

into 12 nodes, and the fuel radial direction was divided into 17 nodes, including 15 nodes in the 

pellet and 2 nodes in the cladding. Although different numbers of axial node were used in these 

codes, important physical parameters could be obtained by simple linear interpolation.

Figure 8 shows the flowchart of combining FRAPTRAN and TRACE/PARCS. The input file of 

FRAPTRAN mainly composes of three parts to define the transient problems: a) Fuel rod 

geometry (Figure 7); b) Power history, including axial pin power shape and pin power history; c)

Coolant boundary conditions, including coolant temperature, coolant pressure, and claddingcoolant heat transfer coefficient. In FRAPTRAN code, there are two modes we can choose to 

input the coolant boundary condition: COOLANT mode and HEAT mode. In this report, HEAT 

mode was chosen because the coolant boundary condition can be defined certainly from 

TRACE/PARCS output data. In addition, the reference temperature used in the calculation of fuel 

and clad enthalpy was defined at 298.15K.

The mechanical model used in FRAPTRAN for calculating the mechanical response of the fuel 

and cladding is the FRACAS-I model. This model does not account for stress-induced deformation 

of the fuel and therefore is called the rigid pellet model. This model includes the effects of thermal 

expansion of the fuel pellet; rod internal gas pressure; and thermal expansion, plasticity, and hightemperature creep of the cladding. After the cladding strain has been calculated by the 

mechanical model, the strain is compared with the value of an instability strain obtained from 

MATPRO (Hagrman et al., 1981). If the cladding effective plastic strain is greater than the cladding 

instability strain, then the cladding cannot maintain a cylindrical shape and local ballooning 

occurs. And the ballooning model, BALON2, is used to calculate the localized, nonuniform 

straining of the cladding. For the local region at which instability is predicted, a large deformation 

ballooning analysis is performed. No further strain is calculated for non-ballooning nodes. 

Modification of local heat transfer coefficients is calculated as the cladding ballooning progresses 

and additional surface area is presented to the coolant. 
2-8 

Figure 7 Schematic of fuel rod geometry in FRAPTRAN
2-9 

Figure 8 Flowchart of combining TRACE/PARCS and FRAPTRAN codes

3-1 

3. INITIAL CONDITIONS AND RESULTS

The initiating event for CRDA is the separation of a control rod blade from its driving mechanism. 

And the control rod is removed from core due to gravity and drops in a free fall. The CRDA event 

can occur at any reactor operating condition. Two conditions were performed for CRDA analysis

of Lungmen ABWR: a) case1: HFP condition at BOC; b) case2: HZP condition at BOC. The initial 

core conditions and parameters used in the analysis for each case were shown in Table 1. And 

the initial control rod patterns for these two cases were shown in Figure 3 and Figure 4, 

respectively. Figure 9 shows the inserted reactivity due to a control rod drop at various controlrod-drop-distances from reactor core center, indicating that the inserted reactivity of the dropped 

control rod located in the periphery of core is larger than that located in the center of core. Thus, 

in the following two cases, the CRDA analyses were performed with choosing the dropped control 

rod located in the periphery of core. In addition, the reactor would be scrammed if the reactor 

power level reaches 115% rated power (4514.9MWt). 

Reactivity is a fundamental quantity, expressing the departure of a nuclear reactor from criticality 

as the control rod drops and describing the feedback effects of fuel and moderator during the 

transient. There are four important factors: control rod position, fuel temperature (Doppler), 

moderator temperature, and moderator void fraction. Hence, the reactivity rate of change may be 

written [16]:

ρρ̇ = ρρCCCĊ +

∂∂

∂∂TTff

TṪ

ff + ∂∂ρρ

∂∂TTmm

TṪ

mm +

∂∂

∂∂ααmm

αα̇mm = ρρCCCĊ + ρρTTTṪ + ρρDDDḊ

where ρCṘ , ρTḞ , and ρDṀ are the reactivity rate of change induced by control rod, fuel 

temperature, and moderator density. Ṫ

f and Ṫm are the rate of temperature change for fuel and 

moderator, and α̇m is the rate of change for the moderator void fraction. 

Table 1 Core initial conditions for two CRDA cases

Core condition/Parameter Value/Assumption

Case1 Case2

Initial power level (MW) 3926

(rated power)

3.926E-3 

(1E-6 rated power)

Dome pressure (MPa) 7.17 6.62

Coolant temperature (K) 560.61 547.5

Core flow (%) 100% 35%

Control rod drop speed (m/s) 0.7
3-2 

Figure 9 Inserted reactivity due to control rod drop at various rod position
3-3 

3.1 Case1-HFP Condition at BOC

At 500sec, the selected control rod starts to fall. Figure 10 shows the trend of the different 

reactivity feedback components during the transient. As control rod drops, the reactivity raises. 

The positive reactivity leads the reactor power to increase, as shown in Figure 11, increasing the 

fuel temperature immediately (Figure 12). The increase of fuel temperature feedbacks a negative 

reactivity to system, called Doppler effect. At the same time, the moderator void fraction increases 

immediately when fuel temperature increases. The time lag for fuel-to-cladding-to-coolant transfer 

does not show an obvious effect in case1. And the increase of moderator void fraction also gives 

a negative feedback-reactivity. The negative feedback-reactivity from fuel and moderator 

suppresses the reactivity increase and lets the reactor back to criticality at higher power level. 

During the whole transient, the maximum value of power is 4267MWt (about 109% rated power) 

at 517.2sec. No reactor scram occurs. Figure 13 and Figure 14 show the average cladding 

temperature and average fuel enthalpy at each node form bottom to top of fuel. The maximum 

value of fuel centerline temperature, cladding inside temperature, and average fuel enthalpy are 

1347.2K, 587.4K, and 2.085×105

J/kg (49.83cal/g), respectively, which all occurs at node 5 

(elevations~1.43m) where the fuel rod is more reactive at HFP condition, as shown in Figure 5 

(a). In addition, the fuel temperature, cladding temperature, and maximum fuel enthalpy are well 

below the limitation of criteria, indicating that no fuel failure occurs in case1. And it is not 

necessary to discuss the high-temperature failures in fuel rod.

Figure 10 Reactivity components evolution in case1
3-4 

Figure 11 Reactor thermal power evolution in case1

Figure 12 Fuel centerline temperature at each node from bottom to top of fuel in case1
3-5 

Figure 13 Cladding Inside temperature at each node from bottom to top of fuel in case1

Figure 14 Average fuel enthalpy at each node from bottom to top of fuel in case1
3-6 

Figure 15 Fuel surface hoop strain in case1 

Figure 16 Cladding hoop strain in case1
3-7 

Figure 17 Structural radial gap in case1 

Figure 18 Gap heat transfer coefficient in case1
3-8 

3.2 Case2-HZP Condition at BOC

At 200sec, the selected control rod starts to fall. Figure 15 shows the trend of the different 

reactivity feedback components during the transient. As control rod drops, the reactivity raises. 

Because of the low fuel temperature and subcooled moderator under HZP condition, compared 

with HFP condition, the effects of fuel and moderator feedback in reactivity are delayed, and the 

power level increases obviously about 3.3sec after transient starts, as shown in Figure 16. Figure 

17 shows that the local boiling around the dropped control occurs at 203.4sec. At the same time, 

the moderator density starts to affect the reactivity. Compared with the effect of fuel temperature 

(starting at 202.5sec), T-H feedback seems to need a longer time, for fuel-to-cladding-to-coolant 

transfer, to be effective than at HFP condition. The negative feedback-reactivity from fuel and 

moderator suppresses the reactivity increase and lets the reactor drop below prompt critical, 

terminating the power excursion. The maximum value of power is 22646MWt (about 577% rated 

power) at 203.5sec. Finally, the reactor power is significantly reduced by reactor scram.

Figure 18, Figure 19, and Figure 20 show the fuel centerline temperature, average cladding 

temperature and average fuel enthalpy at each node form bottom to top of fuel. The maximum

value of fuel centerline temperature, cladding inside temperature, and average fuel enthalpy are

3113.2K (at node 10; elevations~3.02m), 1405.7K (at node 8; elevations~2.38m), and 

1.053×106

J/kg (251.67cal/g at node 9; elevations~2.70m), respectively, which occurs at where 

the fuel rod is more reactive at HZP condition, as shown in Figure 5 (b). 

The fuel temperature, cladding temperature, and maximum fuel enthalpy all reached the limitation

of criteria, indicating that the fuel rod nearby the dropped control rod failed in case2. Figure 21 

and Figure 22 show that both pellets and cladding expand during the transient, but the expansion 

of pellets is faster than that of cladding. Thus, the gas gap, between the pellets and cladding, is 

decreased, as shown in Figure 23. Figure 24 shows the gap heat transfer coefficient. As the gap 

is shortened, the heat transfer becomes better and has maximum value when the pellet touches

the cladding inner-surface. Finally, the cladding melts due to high temperature (>1473.15K). In 

addition, the fuel centerline temperature also exceeds the criteria (3078.15K), indicating that there 

is pellet melting in the center of fuel.
3-9 

Figure 19 Reactivity components evolution in case2
3-10

Figure 20 Reactor thermal power evolution in case2

Figure 21 Local void fraction around the dropped control rod in case2
3-11

Figure 22 Fuel centerline temperature at each node form bottom to top of fuel in case2

Figure 23 Cladding inside temperature at each node form bottom to top of fuel in case2
3-12

Figure 24 Average fuel enthalpy at each node form bottom to top of fuel in case2

Figure 25 Fuel surface hoop strain in case2
3-13

Figure 26 Cladding hoop strain in case2

Figure 27 Structural radial gap in case2
3-14

Figure 28 Gap heat transfer coefficient in case2
4-1

4. CONCLUSIONS

The purpose of this report is to understand the realistic behavior in Lungmen ABWR during a 

CRDA transient. The control rod drop inserts a positive reactivity, leading the reactor power to 

rise. Conversely, the increase of fuel temperature and decrease of moderator density feedback a 

negative reactivity to suppress the reactivity increase and to let the reactor drop below prompt 

critical, terminating the power excursion. In case2, because of the low fuel temperature and 

subcooled moderator under HZP condition, compared with HFP condition, the effects of fuel and 

moderator feedback in reactivity are delayed, and the power level increases obviously about 

3.3sec after transient starts. Moreover, T-H feedback seems to need a longer time, for fuel-tocladding-to-coolant transfer, to be effective at HZP condition than at HFP condition. 

In case1, the fuel temperature, cladding temperature, and maximum fuel enthalpy are well below 

the limitation of criteria, indicating that no fuel failure occurs under HFP condition at BOC. In case2, 

the fuel rod nearby the dropped control rod was found to fail in CRDA analysis. And the 

FRAPTRAN data exposes that the main reason of rod failure is the cladding high temperature. 
 
5-1 

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NUREG/IA-0455 Analysis of the Control Rod Drop Accident (CRDA) for Lungmen ABWR