NUREG/IA-0175

NSI RRC KI90-12/1-3-00 

IPSN/00 - 13 

International 

Agreement Report 

Analysis of 

Pin-by-Pin Effects for 

LWR Rod Ejection Accident 

Prepared by 

A. Avvakumov, V. Malofeev, V Sidorov 

Nuclear Safety Institute 

Russian Research Centre 

"Kurchatov Institute" 

Kurchatov Square 1 

Moscow 123182 

Russia 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

March 2000 

Prepared for 

U.S. Nuclear Regulatory Commission, Institute for Protection and Nuclear Safety (France), 

and Ministry of Science and Technologies of the Russian Federation 

Published by 

U.S. Nuclear Regulatory Commission
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NUREG/IA-0175

NSI RRC KM90-12/1-3-00 

IPSN/00-13 

International 

Agreement Report 

Analysis of 

Pin-by-Pin Effects for 

LWR Rod Ejection Accident 

Prepared by 

A. Avvakumov, V. Malofeev, V. Sidorov 

Nuclear Safety Institute 

Russian Research Centre 

"Kurchatov Institute" 

Kurchatov Square 1 

Moscow 123182 

Russia 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

March 2000 

Prepared for 

U.S. Nuclear Regulatory Commission, Institute for Protection and Nuclear Safety (France), 

and Ministry of Science and Technologies of the Russian Federation 

Published by 

U.S. Nuclear Regulatory Commission
NUREG/IA-0175 has been 

reproduced from the best available copy.
ABSTRACT

This study was undertaken to demonstrate capabilities of the pin-by-pin model used 

by the BARS code and to understand various effects of intra-assembly pin-by-pin 

representation of fuel power, bumup and temperature in calculational analysis of 

light water reactor rod ejection accidents (LWR REAs). Effects of pin-by-pin fuel 

power and bumup representation were investigated on the basis of calculations for 

the peripheral control rod ejection in VVER-1000 of the South Ukrainian NPP Unit 1. 

Comparative analysis of the REA in pressurized water reactor (PWR) of Three Mile 

Island Unit 1 using the BARS code with the diffusion nodal codes PARCS and 

CRONOS2 was done. The important differences in obtained results and effects of 

pin-by-pin fuel temperature representation are discussed in the report.

iii
TABLE OF CONTENTS 

Page 

A B S T R A C T ................................................................................................................. ii 

LIST OF FIGURES ................................................................................................ vii 

LIST OF TABLES .................................................................................................. ix 

ACKNOWLEDGMENTS ............................................................................................. xi 

1. INTRODUCTION ................................................................................................ 1 

2. ADVANCED HETEROGENEOUS METHOD FOR LWR PIN-BY-PIN 

CALCULATIONS ............................................................................................... 5 

3. REVIEW OF VALIDATION RESULTS ............................................................... 7 

3.1. Reactivity Coefficients ................................................................................ 7 

3.2. Pin-by-Pin Power Distribution .................................................................... 9 

3.3. Power Pulse Transient ............................................................................. 15 

4. RELAP - BARS PLANT DYNAMIC MODEL .................................................... 19 

4.1. Description of the Coupled Model ............................................................ 19 

4.2. Reconstruction of the Pin-by-Pin Fuel Temperature Distribution .............. 22 

5. BARS PIN-BY-PIN FUEL CYCLE MODEL ...................................................... 25 

5.1. Calculation of Fuel Nuclide Composition and Database Generation ...... 27 

5.2. Fuel Cycle Calculation with the Precalculated Database .......................... 28 

6. FUEL CYCLE MODELING IN VVER. VALIDATION RESULTS ...................... 29 

6.1. Validation of Calculational Model to Predict Fuel Nuclide Composition in 

V V E R ....................................................................................................... . . 29 

6.1.1. CB2 Calculational Benchmark ............................................................. 30 

6.1.2. Experimental Data for Spent Fuel of VVER-440 and VVER-1 000 ..... 32 

6.2. Validation of Calculational Model for VVER-1 000 Fuel Cycle ................... 37 

7. CALCULATION OF A VVER-1000 REA. EFFECT OF PIN-BY-PIN FUEL 

POWER AND BURNUP REPRESENTATION .................................................. 45 

7.1. Initial Conditions of the Accident ............................................................... 46 

7.2. Analysis of Rod Ejection Accident Modeling ............................................. 46 

8. CALCULATION OF TMI-1 REA ....................................................................... 53 

8.1. Steady-State Calculations ......................................................................... 55

V
8.2. Intercomparison Between the Pin-by-Pin and Assembly-by-Assembly 

Models in a PW R REA ............................................................................. 60 

8.3. Validation of Fuel Temperature Reconstruction Method ........................... 65 

8.4. Effect of Detailed Intra-Assembly Fuel Temperature Representation ..... 65 

9. CONCLUSIONS ............................................................................................... 71 

10. REFERENCES ............................................................................................... 75

vi
LIST OF FIGURES

Page 

Figure 3.1 Critical Assembly ZR-6. Loading Pattern 244/244 ....................................... 11 

Figure 3.2 Comparison of Calculational and Experimental Data for Assembly 

244/244 ....................................................................................................... . . 11 

Figure 3.3 Critical Assembly ZR-6. Loading pattem 113/113 ....................................... 12 

Figure 3.4 Comparison of Calculational and Experimental Data for Assembly 

113/113 ....................................................................................................... . . 12 

Figure 3.5 Critical Assembly ZR-6. Loading Pattern 103/103 ....................................... 13 

Figure 3.6 Comparison of Calculational and Experimental Data for Assembly 

103/103 ....................................................................................................... . . 13 

Figure 3.7 Critical Assembly ZR-6. Loading pattern 144/144 ........................................ 14 

Figure 3.8 Comparison of Calculational and Experimental Data for Assembly 

144/144 ....................................................................................................... . . 14 

Figure 3.9 Cross-Sectional Layout of IGR Reactor ....................................................... 17 

Figure 3.10 Comparison of Calculational and Experimental Data for the Pulse with 

Inserted Reactivity of 1.8 PB at IGR Reactor ................................................... 18 

Figure 4.1 Scheme of RELAP - BARS Coupling .......................................................... 21 

Figure 5.1 Structure of the BARS Fuel Cycle Model ..................................................... 26 

Figure 6.1 Layout of the Fuel Assembly of the Novovoronezh NPP Unit 5 .................. 33 

Figure 6.2 Reactor Power During First 3 Cycles .......................................................... 39 

Figure 6.3 Boron Concentration in the Coolant During the First Cycle ......................... 40 

Figure 6.4 Boron Concentration in the Coolant During the Second Cycle .................... 41 

Figure 6.5 Boron Concentration in the Coolant During the Third Cycle ....................... 42 

Figure 7.1 Control Rod Pattern in the VVER-1 000 Core Before REA .......................... 47 

Figure 7.2 Reactor Power and Reactivity During REA ................................................. 50 

Figure 7.3 Fuel Enthalpy Increment and Its Relative Deviation During REA ................ 51 

Figure 7.4 Pin-by-Pin Power Distribution After Rod Ejection ......................................... 52 

Figure 8.1 One-Eight Core Layout ............................................................................... 54 

Figure 8.2 Layout of Assembly H9 ............................................................................... 56

vii
Figure 8.3 Power Distribution at Initial Conditions ........................................................ 58 

Figure 8.4 Power Distribution After Withdrawal of Rod N12 ......................................... 61 

Figure 8.5 Power Distribution at Initial Conditions After Reflector Model Correction ....... 62 

Figure 8.6 Fuel Temperature Increment in the Hottest Fuel Pellet vs. Time ................ 66 

Figure 8.7 Reactor Power vs. Time ............................................................................. 67 

Figure 8.8 Enthalpy Increment for the Hottest Fuel Pellet vs. Time .............................. 68

viii
LIST OF TABLES

Page 

Table 3.1 Calculational Results for the Doppler Coefficient in PWR Fresh Fuel Cells ........ 7 

Table 3.2 Calculational Results for the Doppler Coefficient in BWR Fuel Cells .............. 8 

Table 3.3 Calculational Results for the Void Coefficient in BWR Fuel Cells ................... 8 

Table 3.4 Calculational Results for the Moderator Temperature Coefficient in BWR 

Fuel C ells ..................................................................................................... . . 8 

Table 3.5 BARS Calculational Results for ZR-6 Assemblies ........................................ 10 

Table 6.1 Comparison of the Calculational Results from HELIOS and BARS-TRIFON .... 31 

Table 6.2 Comparison of the Calculational and Measured Data (kg/tU) for the Fuel 

Samples with Initial Enrichment of 4.4 wt% (Novovoronezh NPP Unit 5 

VV ER-1 000) .................................................................................................. 35 

Table 6.3 Comparison of the Calculational and Measured Data (kg/tU) for the Fuel 

Samples with Initial Enrichment of 3.6 wt% (Novovoronezh NPP Unit 5 

VV ER-1 000) .................................................................................................. 35 

Table 6.4 Comparison of the Calculational and Measured Data (kg/tU) for the Fuel 

Sample with Initial Enrichment of 4.4 wt% (Kola NPP Unit 3 VVER-440) ....... 36 

Table 6.5 Lengths (FPD) of First 3 Cycles in the Kozloduy NPP Unit 5 ........................ 38 

Table 7.1 Comparison of the REA Calculational Results for Pin-by-Pin (Case 1) and 

Average (Case 2) Bumup Models ................................................................. 48 

Table 8.1 Steady-State Parameters ............................................................................. 57 

Table 8.2 Radial Peaking Factors in Pin-by-Pin Power Distribution .............................. 59 

Table 8.3 Steady-State Parameters After Reflector Model Correction .......................... 63 

Tab!e 8.4 Parameters of the REA .................................................................................. 64

ix
ACKNOWLEDGMENTS

The authors would like to thank Drs. V. Asmolov (RRC KI, Russia) who was the 

initiator and coordinator of this work, R. 0. Meyer, D. D. Ebert (US NRC) and 

J. Papin (IPSN, France) for their supervision and support of this project. 

The authors pay a high tribute to untimely deceased Dr. Franz Schmitz for his 

special contribution into this project. 

The authors would also like to acknowledge the contributions of Drs. S. Pylev (RRC 

KI, Russia) who assisted during the coupling of the neutronic and thermal-hydraulic 

models, A. Dukhovensky (RRC KI, Russia) who provided the data on VVERs, 

A. Aronson (BNL, USA), T. J. Downar and H. G. Joo (Purdue University, USA) who 

provided the input deck for PWR calculations. 

Special acknowledgement is given to Dr. D. J. Diamond (BNL, USA) for his many 

suggestions and comments during this work. 

Finally, the authors wish to thank Mr. G. Abyshov for his help in preparing the final 

report.

xi
1. INTRODUCTION

Large deformations of the power distribution in the core accompany the course of 

certain reactivity initiated accidents (RIAs) such as rod ejection (REA), steam line 

break and boron dilution in a pressurized water reactor (PWR). At present 3 D best

estimate neutronic models are widely used for the analysis of these accidents 

instead of very conservative 1 D - 2 D methodologies. Best-estimate methods are 

available to calculate maximum fuel pellet enthalpy that expresses acceptance 

criteria for RIAs, but it is important to determine the uncertainty in the calculated fuel 

enthalpy. 

Practically in all modem best-estimate neutronic codes the fuel assembly is 

represented as homogenized region (an assembly-by-assembly approach). As 

indicated in Reference 1 such a code could underestimate fuel enthalpy for the rod 

drop accident in a boiling water reactor by approximately 100%. The main sources of 

the underestimation in the calculated fuel enthalpy for this accident were an 

uncertainty in control rod worth and an systematic error due to intra-assembly power 

peaking. If the code calculates only an assembly averaged power distribution the 

latter error could be considerable. To eliminate this systematic error methods for a 

pin-by-pin reconstruction of the power distribution within the assembly are begun to 

apply in dynamic calculations. However, the reconstruction approaches require a 

special validation for transients. In this manner one of the important problem is to 

understand whether it is necessary to take into account feedbacks due to detailed 

intra-assembly power distribution. 

Since a best-estimate dynamic code is meant to calculate events that have not been 

observed in actual plants a comparison with other codes is made to validate one for 

the events of interest. However, the comparison for codes of the similar neutronic 

nature (the assembly-by-assembly diffusion approach) does not allow to clarify 

understanding the uncertainty in the calculated results for a number of the key 

parameters. To improve this understanding the comparison should be done with the 

qualitatively different code with more rigorous neutronic model.

1
Recently in Russian Research Centre "Kurchatov Institute" a plant dynamic model for 

VVER and PWR RIA calculation has been developed. The model is based on the 

coupling of the RELAP5/MOD3.2 thermal hydraulic code with the BARS 3 D detailed 

neutronic code and is intended to calculate a wide range of RIAs in light water 

reactors (LWRs) including control rod ejection, boron dilution and steam line break 

(Refs. 2, 3, and 4). The BARS code performs the reactor calculation in framework of 

full-scale pin-by-pin neutronic model with an explicit representation of each fuel pin 

(up to 80,000 calculational cells). This model is based on an advanced method of 

heterogeneous reactor theory that is more rigorous than widely used homogeneous 

diffusion approach and is appropriated to direct pin-by-pin calculations. 

In previous studies a validation of the heterogeneous method for LWRs was made 

for large variety of calculational and experimental benchmarks (Refs. 4-7). It was 

shown that the BARS code predicts multiplication factor (Keff) and pin-by-pin power 

distribution in complicated configurations of the critical assembly not worse than 

precise Monte Carlo and transport codes. It was also demonstrated the RELAP

BARS code capabilities for VVER REA modeling. 

The main objective of this study was to assess the effect of a detailed intra-assembly 

representation of the power, fuel temperature, and bumup on the course of LWR 

REAs. An analysis of this effect allows to improve the understanding of the 

uncertainty in best-estimate REA calculations. 

The effect of the pin-by-pin power representation was demonstrated by the RELAP

BARS calculation of the VVER-1000 REA and by comparison of the RELAP-BARS 

results with the PARCS and CRONOS2 best-estimate calculations for the TMI-1 

PWR REA benchmark (Refs. 8-10). To analyze the effect of the fuel rod temperature 

non-uniformity a special method for pin-by-pin fuel temperature reconstruction was 

developed and validated. The effect was assessed for the TMI-1 PWR REA 

benchmark. To analyze the effect of the detailed fuel bumup representation a 3 D 

pin-by-pin fuel cycle model was developed and validated. The assessment of this 

effect was made for the VVER-1 000 REA.

2
Section 2 expounds features of the heterogeneous method. Section 3 contains a 

review of the validation results of the heterogeneous model for LWR pin-by-pin 

neutronic calculations. The results include a validation of reactivity coefficients, a pin

by-pin power distribution, and a power pulse transient. Section 4 focuses on the 

RELAP-BARS LWR plant dynamic model. It also consists in a description of the 

method for the intra-assembly reconstruction of the pin-by-pin fuel temperature 

distribution. Section 5 describes the BARS pin-by-pin fuel cycle model. Section 6 

contains the validation results for the VVER-1000 pin-by-pin calculations of fuel 

burnup and fuel cycle. Section 7 assesses the effect of the pin-by-pin fuel power and 

bumup representation on the course of the VVER-1 000 REA. Section 8 analyzes the 

effect of a detailed intra-assembly representation of the power and fuel temperature 

on the course of the TMI-1 PWR REA. The conclusions are drawn concerning the 

importance of the pin-by-pin representations.

3
2. ADVANCED HETEROGENEOUS METHOD FOR LWR PIN-BY-PIN 

CALCULATIONS 

The BARS code was developed on the basis of the advanced method of 

heterogeneous reactor theory. The heterogeneous method is based on analytical 

representation of the neutron flux distribution in the form of Green's functions 

superposition. For LWR applications this method allows directly to take into account 

detailed structure of the core by explicit representation of fuel pins, absorber rods, 

etc. The Green's function is derived from a solution of a few group diffusion equation 

for an infinite uniform media with a singular source at the cell axis. The intensities of 

the singular sources are determined in such a way that relationship between neutron 

flux and current at the boundary of each reactor cell coincides with that obtained 

from the precise transport calculation of a single cell. The latter relationship is 

defined by means of a boundary condition matrix (A-matrix). This matrix is 

determined as a result of a set of neutron transport calculations for the cell with 

varying neutron currents at the cell boundary (Ref. 11). In comparison with few group 

neutron cross sections A-matrices provide for the same accuracy of the reactor 

calculation by smaller number of energy groups. 

An axial dependence of the neutron flux is found by Fourier series expansion. As a 

result of the solution of the original differential equations, a set of linear algebraic 

equations is obtained. These general heterogeneous equations connect all pairs of 

the reactor cells. It leads to unresolved computation problem in reactor calculations 

because the reactors with only small number of cells could be calculated by using 

even modem computers. To produce equations to connect only neighboring cells a 

difference approximation of the Green's functions is performed (Ref. 12). 

To calculate fast transients, the heterogeneous method uses "time absorption" 

matrices instead of the traditional neutron velocities (Ref. 3). The spatial-time 

neutron flux distribution within a time step is represented in a form of a product of a 

time-dependent amplitude function and a spatial-dependent form-function (quasi

static approach). The amplitude function is determined by solving point kinetic 

equations. Parameters of the reactor point kinetics are found using a perturbation

5
theory method. The form-function is determined by solving linear equations system 

with a delayed neutron source. To reduce the number of 3 D calculations during the 

transient a special term describing the reactivity dependence due to reactor energy 

release feedback is included into the point kinetic equations. 

It should be noted that the heterogeneous theory does not require the validity of the 

diffusion approximation over the reactor. The diffusion equations are used only to 

determine Green's function shape that weakly influences the reactor calculation 

accuracy. It is very important for pin-by-pin calculation of LWRs with heterogeneous 

structure of modem fuel assemblies. It should be also noted that unlike a 

homogenized assembly LWR calculation a pin-by-pin one requires a rather large 

number of energy groups because of a small size of cells. As the BARS validation 

results showed, A-matrix approach allows to make pin-by-pin LWR calculations with 

reasonable accuracy using only 4-5 groups. 

The neutron data base of BARS (A-matrices) is calculated by the TRIFON code (Ref. 

11). TRIFON solves the multigroup neutron transport equation in various reactor 

cells using the collision probability method taking into account detailed structure of 

resonant cross sections. Strong resonances are calculated explicitly by an additional 

division of the basic energy mesh within the resonance. Weak resonances are taken 

into account approximately in framework of the effective resonance level model (Ref. 

13). This approach allowed to reduce significantly a required total number of groups. 

The neutron database of TRIFON was generated by the NJOY code on the basis of 

ENDF/B-VI library (Refs. 14 and 15). The TRIFON basic energy mesh consists of 89 

groups (24 in fast neutron region and 65 in thermal one). The major resonance of 

234U, 236U, 24°Pu, 242pu and 11 most strong resonances of 2

3U are calculated 

explicitly. The resonances of 23 8U above 210 eV are calculated by 6 effective 

resonance levels. The total number of energy groups is about 350. This resonant 

treatment was validated by comparison with calculational results obtained by the 

UNK code, which uses very fine energy mesh with 7,000 energy groups (Refs. 16 

and 5).

6
3. REVIEW OF VALIDATION RESULTS

To demonstrate the capability of the BARS pin-by-pin calculations to predict LWR 

neutronic parameters some results of previous studies are presented. These results 

refer to a validation of most important parameters - reactivity coefficients, a pin-by

pin power distribution, and a power pulse transient. 

3.1. Reactivity Coefficients 

Accuracy in prediction of the reactivity coefficients is a key factor in the analysis of 

LWR transients, especially for RIA conditions. To analyze uncertainties in prediction 

of the reactivity coefficients, a number of PWR and BWR benchmark fuel cells were 

calculated by the TRIFON code. All the benchmark calculations were performed 

using Monte Carlo codes MCNP-3A (with data library based on ENDF/B-V) and 

MCNP-4A (ENDF/B-VI) (Refs. 17-19). 

Table 3.1 presents the calculational results for the Doppler coefficient in PWR fresh 

fuel cells as compared with Monte Carlo benchmark calculations for different fuel 

enrichment (c,). Monte Carlo result is given with a single standard deviation (a) from 

the mean as an uncertainty; e is relative deviation in TRIFON result in comparison 

with MCNP-3A (e3) and MCNP-4A (Q). Comparison of the presented data shows that 

almost all the TRIFON results are in excellent agreement with the MCNP 

calculations. 

Table 3.1 Calculational Results for the Doppler Coefficient in PWR Fresh Fuel Cells 

F-f MCNP-3A MCNP-4A TRIFON 

(%) cD a -Y(%) aD C3(%) 

0.7 - 5.429 ± 0.760 - 5.468 ± 0.323 - 5.52531 1.77 1.04 

1.6 - 3.558 0.310 - 3.388 0.207 -3.43951 -3.34 1.51 

2.4 - 2.715 0.277 - 2.754 ±_0.157 -2.82679 4.11 2.64 

3.1 - 2.584 ± 0.225 - 2.789 ± 0.137 - 2.51830 - 2.53 - 9.69 

3.9 - 2.370 0.187 - 2.534 0.155 -2.40529 1.49 -5.08

7
MCNP-4A (ENDF/B-VI) benchmark calculations for BWR fuel cells were carried out 

for a wide range of fuel enrichment, fuel and moderator temperatures, moderator 

void fraction and the fuel bumup. The total number of calculated fuel cells (except for 

cells with Gd) is 77. Tables 3.2 - 3.4 present a summary of the TRIFON calculational 

results for the Doppler coefficient, the void coefficient and the moderator 

temperature coefficient as compared with Monte Carlo calculations depending on 

fuel burnup.

Table 3.2 Calculational Results for the Doppler Coefficient in BWR Fuel Cells 

Bumup Nos. of Deviation from MCNP-4A (%) 

(GWd/ST) calculations Max RMS 

0 13 6.8 4.3 

10 12 7.1 3.4 

35 12 11.6 7.3 

Table 3.3 Calculational Results for the Void Coefficient in BWR Fuel Cells 

Bumup Nos. of Deviation from MCNP-4A (%) 

(GWd/ST) calculations Max RMS 

0 6 2.0 1.1 

10 6 2.2 1.3 

35 6 3.5 2.2 

Table 3.4 Calculational Results for the Moderator Temperature Coefficient in BWR 

Fuel Cells 

Burnup Nos. of Deviation from MCNP-4A (%) 

(GWd/ST) calculations Max RMS 

0 4 5.5 2.8 

10 3 6.4 4.3 

35 3 13.2 7.7

8
The results show the following. The TRIFON calculations of the Doppler coefficient 

give very good results for the fresh and slightly bumup fuel: the root mean square 

(RMS) deviation is 3-4 %; as for cells with fuel bumup of 35 GWd/ST this value is 

7 % (this is quite satisfactory result). Calculational accuracy to predict the void effect 

is very high: the TRIFON and MCNP results are in agreement of no more than 4 %. 

As for the moderator temperature coefficient, almost all the TRIFON results are 

within 3a of the MCNP results. 

3.2. Pin-by-Pin Power Distribution 

To validate the LWR pin-by-pin model, experimental results obtained at ZR-6 critical 

assembly were used (Ref. 20). These results include measurements of a water 

critical level and the pin-by-pin distribution of fuel activation. ZR-6 assembly consists 

of shortened VVER fuel rods with fuel enrichment of 1.6, 3.6, 4.4%, absorber rods of 

a different type and water cells. The moderator temperature was 20, 80 and 1300C. 

Boric acid concentration in the moderator was up to 8 g/l. The total number of critical 

configurations with a fuel lattice of 12.7 mm (lattice of VVER-1000 type) selected for 

a validation of the LWR pin-by-pin model is 107. 

All assemblies may be divided into the following types according to their 

configurations: 

"* uniform configurations (single-zone and double-zone); 

"* Xn type configurations with absorbers or water holes in each n-th lattice position; 

"* K91 "fuel assembly" type configurations (19 "fuel assemblies", each having 91 

cells); 

"* K271 "fuel assembly" type configurations (7 "fuel assemblies", each having 271 

cells); 

"* K331 "fuel assembly" type configurations (1 "fuel assembly" with 331 cells). 

All of the calculations were performed by using the BARS code with 5-group neutron 

data bases prepared by the TRIFON code with ENDF/B-VI.

9
In Figures 3.1 - 3.8 core loading patterns and a radial distribution of the fuel 

activation (both calculated and measured) are presented for some configurations. 

The calculated data were normalized to the mean value over experimental data. 

Radial distributions of the fuel activation are given in directions, pointed at the core 

loading pattern: experimental data - by symbols and calculated ones - by curves. 

Table 3.5 presents the BARS calculational results for the multiplication factor and the 

calculational accuracy in prediction of the pin-by-pin fuel activation distribution. All 

data in Table 3.5 were averaged on each type of assemblies and for all assemblies. 

Each Keff value is given together with the corresponding mean square deviation for 

the assemblies of this type. For a comparison corresponding results for the KENO-V 

Monte Carlo code and the HELIOS transport code are presented (Refs. 21 and 22). 

Table 3.5 BARS Calculational Results for ZR-6 Assemblies 

Code assembly Type of assmbl asembies Nos. of Mean value of Keff RMS (%) assemblies 

BARS Uniform 33 0.99494 ± 0.00165 1.33 

BARS Xn 39 0.99706 ± 0.00275 1.65 

BARS K91 11 0.99731 ± 0.00199 1.91 

BARS K271 12 0.99487 ± 0.00155 

BARS K331 12 0.99614 ± 0.00166 1.29 

BARS All types 107 0.99608 ± 0.00207 1.49 

KENO-V All types 107 0.99480 ± 0.00360 

HELLOS - 34 1.00244 ± 0.00368 1.44 

The calculational results show that the BARS code with rather high accuracy predicts 

the multiplication factor and the spatial distribution of the fuel activation for the cores 

of a complex geometry with rather strong local deformations in the neutron flux due 

to various types of the perturbation (the water cells, the absorbers, the water gap or 

even the trap). It should be mentioned that the BARS calculational accuracy for ZR-6 

assemblies is not worse in comparison with KENO-V and HELIOS for a precise 

calculation of fuel assemblies.

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3.3. Power Pulse Transient 

To validate the BARS pin-by-pin transient model, experimental results of the power 

dynamic behavior obtained at the pulsed graphite reactor IGR were used. IGR is 

intended to test reactor fuel rods under RIA conditions. 

The basic feature of such transients is the fact that the power rise is initiated by a 

control rod withdrawal and is suppressed by the negative temperature feedback: the 

increase in the graphite temperature leads to the increase in the thermal neutron 

leakage and, as a result, to a large negative reactivity insertion. Such experiments 

that model the control rod ejection accident in LWR with temperature feedback are 

unknown. 

The reactor core (see Figure 3.9) consists of graphite columns impregnated with 

highly enriched uranium. In the core center there is a central experimental channel 

where the capsule containing test fuel rod samples is to be loaded. The core is 

surrounded by a graphite reflector, a thermal shield and a water tank. To control 

reactor operations 16 Gd rods in the core and in the reflector are used. The time 

dependence of the reactor power was measured by means of a set of out-core 

ionization chambers in the water tank and in-core detectors located near the 

experimental capsule. 

The dynamic behavior of IGR in pulse experiments is characterized by: sharp 

changes in the reactor power; significant deformations of the neutron flux; strong 

heterogeneity in the core graphite temperature distribution; effects of the control rod 

interference and the graphite heating up on the control rod worth; a strong 

dependence of the prompt neutron lifetime and the feedback coefficient on the 

reactor core temperature. 

The validation of the BARS transient module was performed on the basis of 

experiments carried out at IGR with inserted reactivity within 0.9 - 1.8 0 (03 - delayed 

neutron fraction). The IGR power time profile was recorded by 6 ionization chambers 

and 3 in-core detectors. Figure 3.10 shows the comparison of the calculational and

15
experimental results for the test with inserted reactivity of 1.8 P. As shown in the 

figure, calculated and measured power time profiles are in an excellent agreement.

16
1 - central experimental channel; 

2 - control rod channel; 

3 - shim rod channel; 

4 - lateral experimental channel; 

5 - internal part of the core; 

6 - external part of the core; 

7 - graphite reflector. 

Figure 3.9 Cross-Sectional Layout of IGR Reactor 

17
1.2

1.0 

(a 0.8 

0.6 

••20.6 

a) 

0.2

oI

1

I U 1 U

2 3 4 5 

Time (sec)

6 7 8

Figure 3.10 Comparison of Calculational and Experimental Data for the Pulse with 

Inserted Reactivity of 1.8 J3 at IGR Reactor.

18

Ionization 

chambers: 

o IC-2 

K> IC-4 

L IC-5 

o IC-6 

v 10-7 

SIC-14 

In-core detectors: 

@ D-1 

SD-1911 

[ D-1916 

-- Calculation 

(reactor power) I

OWWOMMOMij N lký I
4. RELAP - BARS PLANT DYNAMIC MODEL

4.1. Description of the Coupled Model 

A specific feature of the RELAP - BARS coupling is a large computational cost per 

one time step of the BARS code in comparison with RELAP5/MOD3 code. 

Mentioned above feature of the BARS kinetic method allows to choose time step for 

whole reactor calculations depending only on degree of variations in power shape, in 

spite of variations in total reactor power, thermal hydraulic parameters and 

feedbacks. In virtue of it, the BARS time step, as a rule, is much larger than the 

RELAP one, with the exception of time periods of a fast reactivity insertion (a control 

rod ejection). For this reason, the neutronic calculation in each time step is divided 

into the following stages: 

1. The calculation of the neutron flux spatial-energy form-function and the delayed 

neutron precursor distributions. It requires the largest computational time. 

2. The calculation of point kinetic parameters, the amplitude function and the 

determination of the pin-by-pin power distribution. This stage requires a much 

smaller computational time compared with a single step calculation by RELAP. 

The first stage calculations are performed rather seldom depending on the reactor 

power distribution changes. The second stage calculations are carried out at each 

time step determined by RELAP. 

The RELAP-BARS coupling is based on certain options of the RELAP5/MOD3 code 

that allows to tabulate the reactor power distribution as a function of spatial 

coordinates and time, and to connect an additional subroutine to the RELAP code. In 

the framework of the RELAP model, the BARS neutronic calculation can be 

considered as determination of the core power distribution as a function of spatial 

coordinates and time for the RELAP next time step taking into account thermal 

hydraulic feedbacks. In this case the BARS code can be considered as a subroutine 

of the RELAP code, while preserving the logic of thermal hydraulic calculations.

19
To provide the data exchange between the RELAP and BARS codes, the COTT 

interface code is used. This code calculates also pin-by-pin fuel temperature 

distribution by the reconstruction method and some additional thermal hydraulic 

parameters, which are not calculated by RELAP. Besides, the COTT code contains 

simplified thermal hydraulic option based on 1 D single- or two-phase homogeneous 

flow with a slip ration. This option is used for thermal-hydraulic calculation of the core 

during slow transients such as fuel cycle modeling. 

The reconstruction procedure is described below. 

Before the transient modeling, the plant initial steady state is calculated. The 

neutronic calculation of the reactor steady state is performed by the BARS steady

state option, which solves the non-linear eigenvalue problem. During the coupled 

neutronic - thermal hydraulic calculation the core initial conditions can be 

automatically adjusted. 

The following adjustment possibilities are available: 

"* to change the neutron generation rate, 

"* to change the axial position of some control rods or control rod banks, 

"* to change the boric acid concentration in the coolant. 

Unlike the dynamic calculation of the plant initial steady-state, the adjusted steady

state calculation allows rather quickly to balance neutronic and thermal hydraulic 

processes without a variation in the reactor power. 

The plant initial steady-state calculation by the RELAP - BARS code is performed in 

two stages: 

"* the RELAP steady-state calculation without using the BARS code at a 

predetermined reactor power, 

" the iterative calculation of the plant steady-state by the RELAP - BARS code. 

Then the dynamic calculation is performed. The transient neutronic calculation is 

carried out by the BARS time-dependent option, and the thermal hydraulic 

calculation - by the RELAP dynamic option. Figure 4.1 shows the scheme of the 

sequence of the RELAP - BARS calculations.

20
INTERFACE

Transformation of Formats Power Distribution 

for Power Distribution: Calculation and 

BARS -4 RELAP Generation of Signals

Transformation of Control 

and Protection Signals: 

BARS -4 RELAP Coordination and 

Correction of At

Preparation of 

BARS Input Data

Transformation of Control 

and Protection Signals: 

RELAP -4 BARS

Format Transformation of 

Thermal-Hydraulic Data: 

RELAP -4 BARS

Figure 4.1 Scheme of RELAP - BARS Coupling

21

Yes

BARS RELAP
4.2. Reconstruction of the Pin-by-Pin Fuel Temperature Distribution 

In practice the RELAP5/MOD3.2 code could not be used for full-scale pin-by-pin core 

thermal hydraulic calculations because of the input deck restriction and an extremely 

large running time. That is why a new method to reconstruct a 3 D pin-by-pin fuel 

temperature distribution was developed. Since a number of the hottest fuel pins can 

be calculated by RELAP directly, the pin-by-pin fuel temperature representation is 

needed only to take into account the effect of the intra-assembly fuel temperature 

distribution on the Doppler feedback, and since this effect is not expected to be 

large, a very high accuracy for the pin-by-pin fuel temperature reconstruction is not 

required. From the other side the reconstruction procedure has to be a fast-running 

one because of total number of the fuel pins within the LWR core is typically about 

50,000. Therefore, the reconstruction method that leads to a simple analytical 

expression for the fuel temperature was proposed. 

The method is based on a representation of the radial averaged fuel rod temperature 

for any axial node by sum of two terms: 

Tk(t) = T(t) + 0k(t) 

where 

Tk(t) is the radial averaged fuel rod temperature, 

T(t) is the radial averaged fuel temperature for the rod with averaged power, 

calculated by RELAP, 

Ok(t) is the deviation of the radial averaged fuel rod temperature from T, 

k is the index of the rod within the fuel assembly. 

To obtain the expression for Ok(t), the following approximations are used: 

"* the heat transfer coefficient, the coolant temperature, and the fuel and cladding 

volumetric heat capacities and conductivities are identical for all rods within the 

assembly; 

"* the fuel thermal conductivity and volumetric heat capacity are determined by T;

22
" a radial dependence of the deviation of the fuel rod temperature from the fuel 

temperature for the rod with averaged power, calculated by RELAP, is described 

by a parabola; 

"* a radial dependence of the deviation of the cladding temperature from the 

cladding temperature for the rod with averaged power is linear. 

Within any RELAP time step these approximations allow to formulate the linear 

Fourier equations for the radial dependence of the fuel and cladding temperature 

deviations. Integrating and summing these equations over the radial direction, the 

heat balance equation for the rod is obtained. It contains a heat flux at the cladding 

surface. To exclude the heat flux from the heat balance equation, the boundary 

condition at the cladding surface and the approximations for the fuel and cladding 

temperature deviations are used. As a result the following equation for Ok(t) is 

obtained: 

c dek(t)/dt = qk - (2/r) OC Ok(t) , t1-1 < t < tj 

with the initial condition 

0k(to) = 0 k 

where 

c is the fuel volumetric heat capacity, 

qk = Qk(t) -Q(t), 

Qk(t) is the fuel rod volumetric heat source, 

Q(t) is the assembly average volumetric heat source, 

r is the fuel pellet radius, 

j is the RELAP time step index, 

1/a = 1/af +1/%g +1/Ic +1/as, 

af is the fuel thermal conductivity,

23
%~ is the gas gap thermal conductivity,

occ is the cladding thermal conductivity, 

(Xj is the cladding - coolant thermal conductivity. 

This differential equation has a simple analytical solution that can be given for any 

RELAP time step with index "j" as below: 

0k(tj) = (qk/cz) (1 - exp(-a/cAtj) + Ok(tj-1) exp(-W/cAtj)), Atj = tj- tj-l. 

Thus, the determination of the pin-by-pin fuel temperature distribution consists of two 

stages: 

"* an assembly-by-assembly fuel temperature calculation by the RELAP code using 

an assembly averaged power distribution, calculated by the BARS code; 

"* pin-by-pin fuel temperature reconstruction within each assembly by the COTT 

code used as an interface code between RELAP and BARS.

24
5. BARS PIN-BY-PIN FUEL CYCLE MODEL

The solution of a problem of modeling of a LWR fuel cycle concerns a wide spectrum 

of neutronic and thermal-hydraulic phenomena taking place in the reactor core and 

other plant systems. To take into account all of these phenomena in details is rather 

problematic, but the pin-by-pin approach allows modeling the fuel cycle in more 

realistic manner. 

The main goal in such a calculation is to predict a fuel nuclide composition as a 

function of the cycle time. Fuel cycle codes, based on an assembly-by-assembly 

representation of the core, used consequently assembly averaged fuel bumup. Such 

approximation may lead to an uncertainty in safety analysis of the high bumup core. 

In this Section, the BARS pin-by-pin fuel cycle model is briefly described from the 

point of view of its advantages compared with an assembly-by-assembly method. 

The pin-by-pin approach used in BARS allows, in principle, to create a fuel cycle 

model in which fuel depletion equations could be solved directly for each 

calculational node according to neutronic and thermal-hydraulic parameters 

calculated for this node. A database of such a "direct" model will include A-matrices 

for each node recalculated by the TRIFON code after the routine BARS calculational 

step. The reasons why this model was not realized were as follows: 

"* number of the calculational nodes is 1,000,000 (50,000 pins x 20 axial layers); 

"* the TRIFON running time to calculate 1 node is about 10-12 s. 

Thus, a total time to generate the database for a single bumup step is equal to about 

120 days. That is why a fuel cycle model with the database calculated in advance 

(instead of "direct" calculations during the cycle) has been developed. 

The fuel cycle model implemented in the BARS code is based on the following 

approaches: 

"* calculation of a fuel nuclide composition and generation of the database; 

"* calculation of the fuel cycle with the precalculated database. 

Figure 5.1 gives a schematic structure of the BARS fuel cycle model.

25
BARS-TRIFON Bumup 

Interface Code 

Calculation of Nuclide 

Composition for 

Next Time Moment

NoI e 

I Yes

Figure 5.1 Structure of the BARS Fuel Cycle Model

26

Input

BARS 

Calculation of Process 

Rates for All Nuclides in 

Each Fuel Pin

TRIFON 

Calculation of Database 

With New Nuclide 

Composition in FA

TRIFON 

Forming of the Global Database 

To Calculate Fuel Cycle

W

-J Output
5.1. Calculation of Fuel Nuclide Composition and Database Generation 

This stage may be considered as two independent steps. 

The first step includes calculation of the nuclide composition in fuel rods within a 

single fuel assembly calculated by the BARS code. The criticality is kept up by 

varying the neutron current at the assembly outer boundary. Initial database for the 

BARS code is calculated by the TRIFON code for the fresh fuel. For each fuel rod 

the BARS code calculates neutron absorption and generation rates which are used 

as coefficients in a set of depletion equations solved by a special interface routine. 

This interface code uses nuclide transformation scheme taking into account 24 

heavy nuclides, 49 explicit fission products and 4 lumped fission products (Reference 

23). Fuel rods nuclide compositions determined at each bumup step are used as 

input data for the TRIFON code for the next recalculation of the BARS database. 

Calculations are carried out at fixed thermal-hydraulic parameters with given 

dependencies of power and boron concentration in the coolant on time up to the 

maximum value of fuel bumup. The number of such calculations with different 

thermal-hydraulic parameters depends on demands for the global database 

generation. 

The second step consists in collection and processing of the calculated data on fuel 

nuclide composition. Obtained nuclide compositions for all fuel rods as functions of 

exposure are averaged for several sets of selected rods having the similar history of 

exposure. The total amount of such sets does not exceed 5-7. As a rule, fuel rods of 

any set are selected according to their position in the fuel assembly (near the control 

rod guide, near the water gap between assemblies, etc.) The global database for the 

BARS fuel cycle modeling is generated by the TRIFON code for several fuel rods 

types differing by initial fuel enrichment, the exposure history, thermal-hydraulic 

parameters, etc. In practice of calculations it is enough to have no more than 50-60 

types.

27
As a result, the global database contains several sets of A-matrices in the form of 

table functions of several parameters: fuel bumup, fuel temperature, moderator 

density, xenon concentration, and boron poisoning in the coolant and so on. 

It should be noted that a nuclide composition prediction in burnable poison rods is a 

separate problem and is not considered in the present study. 

5.2. Fuel Cycle Calculation with the Precalculated Database 

This stage includes an LWR fuel cycle calculation by the BARS code using the 

global database precalculated by the TRIFON code. The core thermal-hydraulic 

calculations are carried out by the COTT code used as a coupled subroutine within 

the BARS code. Thermal-hydraulic parameters are calculated in the framework of 

assembly-by-assembly representation. (There is also a possibility to use pin-by-pin 

thermal hydraulics.) An iterative procedure for critical boron concentration in the 

coolant is used. At each bumup step, fuel bumup and xenon concentration are 

recalculated for each calculational node. The reactor power, inlet coolant 

temperature, initial boron concentration and control bank position are the input 

parameters in the BARS calculation.

28
6. FUEL CYCLE MODELING IN VVER. VALIDATION RESULTS 

As it was mentioned, the pin-by-pin LWR fuel cycle model consists in two 

independent steps. For this reason a validation procedure was split into two stages; 

each of them may be considered as separate procedure and corresponding 

validation results may be of interest in other areas (for instance, a prediction of the 

nuclide composition in the high burnup fuel). 

First stage dealt with the problem of prediction of nuclide composition in the fuel rods 

of a VVER under various operational conditions including geometrical and thermal

hydraulic effects on neutron spectrum in the fuel irradiated up to 60 MWd/kgU. 

Second stage involved the modeling of the VVER-1 000 fuel cycle itself by the BARS 

code using a neutron database prepared by the TRIFON code. The BARS input deck 

included available operational information on the fuel reloading scheme, soluble 

boron concentrations in the moderator during the fuel cycle, the reactor power 

history, axial positions of regulating banks of control rods, etc. 

6.1. Validation of Calculational Model to Predict Fuel Nuclide Composition in 

VVER 

Unfortunately, the experimental data on the VVER spent fuel nuclide composition 

available in literature are rather poor. As a rule, they include the data only for major 

actinides without any information on fission products playing an important role in the 

fuel cycle. Thus, these data do not allow validating a depletion code as a whole from 

the point of view of calculational accuracy in prediction of fission products 

composition. In this case it was worth to use calculational benchmarks aimed to 

compare capabilities of different depletion codes with various neutron data libraries. 

Another reason to use them was a possibility to analyze uncertainties due to different 

factors: neutronic and depletion models, libraries, etc.

29
As a result, it has been chosen the following validation database: 

"* VVER-440 burnup credit calculational benchmark CB2 (Ref. 24); 

"* a set of measured data for the nuclide composition of the high bumup spent fuel 

for VVER-440 and VVER-1 000 reactors (Refs. 25 and 26). 

6.1.1. CB2 Calculational Benchmark 

This benchmark has been prepared in 1997 in the collaboration with the 

OECD/NEA/NSC Bumup Credit Criticality Benchmarks Working Group (Ref. 24). 

Reference 24 gives a detailed specification of this benchmark and contains 10 

calculational sets obtained from 9 institutes of 7 countries. These data were 

calculated using modern depletion codes, such as CASMO-4, SCALE 4.3, WIMS7, 

HELIOS, etc. Depletion calculations for VVER-440 fuel pin cell were carried out for 

two burnup values: 30 and 40 MWd/kgU. Total number of nuclides which 

concentrations are given is 26 including 15 fission products. 

In our study the calculational set obtained by the HELIOS (version 1.5) code was 

chosen as a reference one for validation because of the neutron library used by 

HELIOS was based on the same ENDF/B-VI file used also in the TRIFON code 

library. This fact allowed us to minimize the calculational uncertainty due to 

differences in the neutron libraries used by both codes. 

The BARS-TRIFON results were calculated under the following conditions: 

"* number of energy groups in BARS: 5; 

"* number of energy groups in TRIFON: 260; 

"* numbers of bumup steps (recalculations of database) : 30 (for 30 MWd/kgU) and 

40 (40 MWd/kgU). 

The BARS-TRIFON code calculated the nuclide composition (except for l'Ru that is 

not included in bumup chains) for each fuel rod within the fuel assembly and then the 

averaged data for selected nuclides were compared with the HELIOS results. The 

averaged results and the relative deviations (6) are presented in Table 6.1.

30
Table 6.1 Comparison of the Calculational Results from HELIOS and BARS-TRIFON 

Burnup = 30 MWd/kgU Burnup = 40 MWd/kgU 

Nuclide 

HELIOS BARS E (%) HELIOS BARS c (%) 

235u 2.894-4* 2.887-4 -0.2 1.931-4 1.929-4 -0.1 

2 36 U 9.378-5 9.402-5 0.3 1.065-4 1.073-4 0.7 

238u 2.158-2 2.157-2 -0.01 2.139-2 2.138-2 -0.01 

237Np 8.540-6 7.714-6 -9.7 1.213-5 1.087-5 -10.4 

23Pu 2.541-6 2.363-6 -7.0 5.055-6 4.641-6 -8.2 

239pu 1.362-4 1.386-4 1.8 1.420-4 1.456-4 2.5 

240pu 4.475-5 4.822-5 7.7 5.734-5 6.243-5 8.9 

241Pu 2.829-5 2.775-5 -1.9 3.691-5 3.653-5 -1.0 

242Pu 7.231-6 7.194-6 -0.5 1.351-5 1.353-5 0.1 

241

Am 8.653-7 8.307-7 -4.0 1.358-6 1.306-6 -3.8 

243Am 1.389-6 1.339-6 -3.6 3.362-6 3.255-6 -3.2 

95Mo 3.402-5 3.440-5 1.1 4.537-5 4.569-5 0.7 

99Tc 3.980-5 3.936-5 -1.1 5.134-5 4.998-5 -2.6 

1

0 3

Rh 2.096-5 2.159-5 3.0 2.669-5 2.729-5 2.2 

1°9Ag 3.175-6 3.053-6 -3.9 4.745-6 4.508-6 -5.0 

133Cs 4.310-5 4.203-5 -2.5 5.533-5 5.308-5 -4.0 

143Nd 2.931-5 2.947-5 0.5 3.497-5 3.504-5 0.2 

145

Nd 2.328-5 2.353-5 1.0 2.930-5 2.947-5 0.6 

147Sm 2.595-6 2.554-6 -1.6 3.603-6 3.470-6 -3.7 

149 Sm 1.046-7 1.067-7 2.0 1.018-7 1.037-7 1.8 

1

iSm 9.347-6 9.188-6 -1.7 1.256-5 1.223-5 -2.6 

1

5 1

sm 5.037-7 5.340-7 6.0 5.649-7 6.022-7 6.6 

152 Sm 3.705-6 3.982-6 7.5 4.535-6 4.921-6 8.5 

1

•Eu 3.550-6 3.702-6 4.3 5.108-6 5.354-6 4.8 

1

55

Gd 1.61 9-9 1.504-9 -7.1 2.579-9 2.491-9 -3.4 

*Read as 2.894 .10-4

31
Based on the comparison of these data the following conclusions could be given: 

"* the deviations for major fissionable nuclides did not exceed 0.2% (for 235U), 2.5% 

(for 239pu), 1.9% (for 241Pu) and 0.01% (for 23U); 

"* the maximum deviations for actinides were observed for 237Np (10%), 24°Pu (9%) 

and 238pu (8%); 

" the mean deviations for fission products did not exceed 4% (except for 5' 5 Sm, 

152Sm and 15 5

Gd) and the maximum deviation was 8.5% for 1

5 2

Sm. 

It should be noted that the comparison with some other results from Reference 24 

indicated more significant deviations (especially, for 1

55Gd), that may be explained to 

some extend by using different calculational approaches or neutron libraries. 

6.1.2. Experimental Data for Spent Fuel of VVER-440 and VVER-1000 

The experimental data for the VVER spent fuel nuclide composition consisted in 5 

sets for fuel samples from the Novovoronezh NPP Unit 5 VVER-1000 and 1 set for a 

fuel sample from the Kola NPP Unit 3 VVER-440. Initial enrichment of the fuel 

samples was 3.6 or 4.4 wt.%. The fuel bumups were in the range of 44 to 60 

MWd/kgU. The reason why the data for such high bumup fuel were chosen in this 

validation was to specify the code capabilities in prediction of long-duration fuel 

cycles in VVERs. 

The tested samples of the VVER-1000 belonged to 4 fuel rods of the same fuel 

assembly irradiated during 3 fuel cycles. Non-symmetrical arrangement of the fuel 

rods and control rod guide tubes in the fuel assembly for Novovoronezh NPP Unit 5 

VVER-1 000 differs from that for a standard VVER-1000. It can be seen in Figure 6.1 

where the considered fuel rods are indicated using accepted for VVER notation. The 

assembly contained fuel rods with initial enrichment of 4.4 wt.% except for peripheral 

row with enrichment of 3.6 wt.%.

32
00000000000 000000000000 0000000000000 000000000000,00 000000000000000 0000000000000000 000000®OOO®OOOOOO 000000000000000000 00000000®0000000000 00000000000000000000 00000000®0000000000000 00000000000000000000 

00000®0000000000000 000000000000000000 000000®0000000000 0000000000000000 

00000000000000 0000000000000 000000000000 ®oooooooooe 

0 -fuel rod 

0 - control rod guide tube 

0 - experimental tube 

Figure 6.1 Layout of the Fuel Assembly of the Novovoronezh NPP Unit 5

33
The VVER-440 fuel assembly of the Kola NPP Unit 3 was irradiated during 5 fuel 

cycles. It consisted in 126 fuel rods and the central Zr-tube. The tested sample 

belonged to the fuel rod No.81 that was located at the outer row near the comer fuel 

rod. 

All of the samples were cut approximately from the central part of the fuel rod. 

References 25 and 26 contain the nuclide compositions of considered samples in 

terms of kilograms per tone of initial U (for high bumup fuel 1 MWd/kgU is equal to 

approximately 0.97 kg/tU.) 

Due to the evident non-physical discrepancy and poor accuracy, the data for 241

Am, 

242Cm and 2 44Cm were not considered in the comparison. 

The BARS-TRIFON results were calculated under the following conditions: 

"* number of energy groups in BARS: 5; 

"* number of energy groups in TRIFON: 280; 

"* number of bumup steps: 60 (for 60 MWd/kgU). 

Operational data on the primary coolant thermal hydraulics, the boric acid 

concentrations in the coolant and duration of the fuel cycles including downtime 

between cycles were taken into account. Cooling times before measurements were 

3.4 years for the VVER-1 000 fuel rods and 7.1 years for the VVER-440 fuel rod. 

Calculational results and the relative deviations (E) are presented in Tables 6.2 

through 6.4. Notation of the experimental samples was given accordingly to 

corresponding fuel rod numbers; two samples from the same fuel rod No.307 were 

indicated as 307a and 307b (the last sample was cut 70 cm below the middle point 

on the fuel rod active length). Experimental uncertainty is given in the brackets after 

the value as an error in the last digit.

34
Table 6.2 Comparison of the Calculational and Measured Data (kg/tU) for the Fuel 

Samples with Initial Enrichment of 4.4 wt% (Novovoronezh NPP Unit 5 VVER-1 000) 

Sample No.61 Sample No.257 

Nuclide 

Measured BARS - (%) Measured BARS E (%) 

235u 11.7 (1)* 10.8 -8.2 8.80 (7) 8.58 -2.5 

236u 5.33 (6) 5.67 6.4 6.23 (6) 5.94 -4.6 

238u 927(1) 927 0.0 924(1) 923 -0.1 

23Pu 0.27 (2) 0.20 -26. 0.32 (2) 0.26 -18. 

239pu 5.64 (6) 5.80 2.8 5.38 (7) 5.78 7.4 

2

4Pu 2.29 (3) 2.41 5.2 2.55 (3) 2.65 3.9 

241

Pu 1.51 (2) 1.42 -6.0 1.60(1) 1.52 -5.0 

242pu 0.56 (1) 0.60 7.1 0.79 (1) 0.77 -2.5 

243

Am 0.15(1) 0.14 -8.2 0.21 (1) 0.19 -7.2 

Burnup 45. (2) 45.0 - 50. (2) 50.5 

*Read as 11.7 ± 0.1 

Table 6.3 Comparison of the Calculational and Measured Data (kg/tU) for the Fuel 

Samples with Initial Enrichment of 3.6 wt% (Novovoronezh NPP Unit 5 VVER-1000) 

Sample No.307a Sample No.307b Sample No.317 

Nuclide 

Measured BARS (%) Measured BARS E (%) Measured BARS (%) 

235u 4.35 (3)* 4.16 -4.3 3.69 (2) 3.96 7.3 3.60 (4) 3.77 -4.7 

23u 4.92 (3) 4.98 1.2 5.38 (4) 4.99 -7.2 4.82 (3) 5.00 3.7 

23u 927 (1) 926 -0.1 927 (1) 926. -0.1 928 (1) 925 -0.3 

238Pu 0.31 (2) 0.29 -6.2 0.32 (2) 0.30 -6.2 0.31 (2) 0.31 0.1 

239Pu 5.00(5) 5.14 2.8 5.10(5) 5.12 0.4 5.18(4) 5.11 -1.4 

240pu 2.62 (3) 2.85 8.8 2.73 (2) 2.88 5.5 2.67 (3) 2.90 8.6 

241_pu 1.64(2) 1.50 -8.5 1.67(1) 1.50 -10. 1.72(2) 1.52 -11. 

2Pu 1.12(1) 1.05 -6.2 1.12(1) 1.08 -3.6 1.19(1) 1.12 -5.9 

243

Am 0.29(2) 0.28 -1.2 0.29(1) 0.30 1.7 0.31 (1) 0.31 0.1 

Burnup 52. (2) 52.4 - 53. (2) 53.1 - 54. (1) 54.0 

*Read as 4.35 ±_ 0.03

35
Table 6.4 Comparison of the Calculational and Measured Data (kg/tU) for the Fuel 

Sample with Initial Enrichment of 4.4 wt% (Kola NPP Unit 3 VVER-440) 

Sample No.81 

Nuclide 

Measured BARS S (%) 

23u 0.22 (2)* 0.17 -20. 

235

U 4.71 (4) 5.03 6.9 

2

3U 6.65 (5) 6.48 -2.6 

238u 915.4 (1) 914.7 -0.1 

238pu 0.57 (1) 0.43 -26. 

23 9

pu 5.75 (5) 5.89 2.4 

240pu 3.03 (3) 3.31 9.2 24 1 Pu 1.32 (2) 1.30 -2.3 

242

pu 1.27(2) 1.12 -11. 

Burnup 61. (1) 61.0 

*Read as 0.22 ± 0.02 

Based on the data for high burnup fuel presented in Tables 6.2 through 6.4, the 

following conclusions could be given: 

"* the mean deviations for major fissionable nuclides did not exceed 6% (for 235U), 

3% (for 239Pu), 7% (for 241 Pu) and 0.1% (for 238U); 

"• the maximum deviations for actinides were observed for 238pu (26%), 241Pu, 242Pu 

(11%) and 24°Pu (9%); 

"* all the deviations are greater compared with the calculational benchmark for the 

VVER-440 fuel irradiated to 30 and 40 MWd/kgU. 

Thus, it is safe to conclude that the BARS-TRIFON code models the nuclide 

composition of the VVER fuel with reasonable accuracy when compared with the 

measured data up to the fuel burnup of 60 MWd/kgU. The burnup chains model 

implemented in the code provides very good accuracy in prediction of the fission 

products in the VVER spent fuel.

36
6.2. Validation of Calculational Model for VVER-1 000 Fuel Cycle 

Below the BARS calculational results for modeling of first 3 fuel cycles in the 

Kozloduy NPP Unit 5 are presented. This unit has a VVER-1 000 reactor operated in 

2-year cycle regime since 1988. Initial loading of the core consisted in the fuel of 3 

different enrichments: 2% (79 assemblies), 3% (42 assemblies) and 3.3% (36 

assemblies, among them 6 assemblies with 3%-fuel at the periphery). After the first 2 

cycles 2%- and 3%-fuel assemblies were charged and replaced by the 3.3%-fuel 

assemblies (except for a few assemblies with 3%-fuel at the periphery). 

Reference 27 contains a brief description of operational parameters for first 3 cycles: 

effective lengths of the cycles, fuel reload maps, the tables of thermal-hydraulic (the 

coolant inlet temperature and flow) and operational (core power, boron poisoning 

and positions of the regulating banks in the core) data. Thermal-hydraulic 

parameters were more or less stable during the cycles. The coolant flow was 

approximately (66.5 ± 0.5) kilotons per hour. The mean values for the coolant inlet 

temperature (with deviation of 20C during the cycles) were: 

"* 2860C in the first cycle (at the last 6 days of this cycle the temperature was 

reduced by 4-50C); 

"* 2820C in the second cycle; 

"* 2840C in the third cycle. 

Unfortunately, all the tables were given as a function of effective power days (not 

calendar days). For this reason it was impossible to model the cycles using detailed 

data on core power and regulating banks positions. Another reason was a very 

complicated behavior of core power (Figure 6.2) with frequent changes in regulating 

banks position (several regulating banks were used). 

In this study it was assumed that the reactor was operated during all the cycles at 

rated power of 3000 MW with partly inserted 6 control rods of regulating bank No.10 

located at the central part of the core. According to the rated power, axial location for 

these control rods was chosen as 260-270 cm from the bottom of the core.

37
The coolant inlet temperature and flow were constant during each cycle (the 

reduction in inlet temperature at the end of the first cycle was effectively taken into 

account as additional full power days due to negative temperature feedback). The 

burnup calculational step was 20 days in all calculations. The boric acid 

concentration in the coolant was a key parameter in this validation and the length of 

the fuel cycle was determined as a time period from the beginning of the cycle up to 

a time moment when the boric acid concentration reached the zero level. 

BARS calculational parameters were as follow: 

"* number of energy groups: 5; 

"* number of axial fuel zones with different properties: 15; 

"* number of axial harmonics: 16. 

Figure 6.3 through 6.5 illustrate the boron concentration behavior during the cycles. 

The measured data are given as circles and the calculational results - as bold 

curves. As it can be seen from Figure 6.4, the most spread of the measured data 

was observed for the first quarter of the second cycle. The calculational dependence 

was practically linear during the cycles. 

Table 6.5 gives the comparison between the operational and calculational cycle 

lengths in terms of full power days (FPD). 

Table 6.5 Lengths (FPD) of First 3 Cycles in the Kozloduy NPP Unit 5 

Cycle No. Operation Calculation Deviation 

1 296.7 294.3 -2.4 

2 324.5 317.7 -6.8 

3 317.8 320.3 2.5

38
0 100 200 300 400 500 600 700 800 900 1000 

Cycle time (FPD) 

Figure 6.2 Reactor Power During First 3 Cycles

39

3000

2500 

S2000 

ao 

0 

a

1500 

0 

co 1000 a) 

500 

0
1.2

0.9o 0 . • i- irst t-uel uycle. 

C .r_ 

o 0.6 

0. 

C 

0 

c 

m 

0.3 

0.0 . . . . . . . 

0 50 100 150 200 250 300 

Cycle time (FPD) 

Figure 6.3 Boron Concentration in the Coolant During the First Cycle

40
1.5

1.2 Secon Fuel Cycle. 

0o 

0 

C o. 

0o 

"c 0.6 

0 

0.0 

0 50 100 150 200 250 300 350 

Cycle time (FPD) 

Figure 6.4 Boron Concentration in the Coolant During the Second Cycle

41
1.5

1.2 0 

0 0)0 

0.9 0.. 

0 0 

M 

0 c 2 0.6 

0.0 

0 50 100 150 200 250 300 350 

Cycle time (FPD) 

Figure 6.5 Boron Concentration in the Coolant During the Third Cycle.

42
For the first cycle the calculational value was effectively increased by 6.5 FPD due to 

the moderator temperature effect. This increment Ar was estimated accordingly to 

the following simple formula: 

Ax = AT at / aB / CB', 

where 

AT is the moderator temperature decrement, 

at is the moderator temperature coefficient of reactivity, 

aB is the boron coefficient of reactivity, 

CB/ is the derivative of the boron concentration as a function of FPD. 

Substitution of AT = 4.5 K and the corresponding EOC parameters (at = -61 pcm/K; 

aB = -0.11 1/(g/kg); cB'= 0.0038 (g/kg)/FPD) gave Ax = 6.5 FPD. 

From the presented comparison of the calculational and operational data on the 

cycle lengths, the following conclusions may be derived: 

"* a good agreement was obtained for the cycle lengths; the mean deviation over 3 

cycles did not exceed 4 FPD; 

" the boron concentration behavior during the cycles agreed with the operational 

data, though it was difficult to give quantitative estimate of this agreement 

because of the very complicated history of the reactor power; 

Nevertheless, it is clear that the comprehensive validation has to include the detailed 

modeling of the fuel cycle with corresponding changes in such parameters as inlet 

coolant temperature, reactor power, control banks position, etc. Such calculations, of 

course, are very expensive because they demand a lot of calculational steps.

43
7. CALCULATION OF A VVER-1 000 REA. EFFECT OF PIN-BY-PIN 

FUEL POWER AND BURNUP REPRESENTATION 

In recent calculational studies of power excursions in VVER-1000 core containing 

only fresh fuel, a number of interesting results was found (Ref. 28). Among them the 

following ones may be pointed out: 

"* ejection of a peripheral control rod resulted in a very complicated pin-by-pin 

power distribution in assemblies directly adjacent to the accident one; 

"* the hottest fuel rod did not necessarily belong to assembly with peak power; 

"* fuel assemblies, adjacent to the accident one from the one side and to the 

reflector from the other, with relatively low power contained fuel rods with power 

exceeded maximum value for fuel rods in assembly with peak power. 

This Section describes an analogous study of a VVER-1000 but with bumup core. 

Two comparative calculations were carried out by the RELAP5-BARS coupling code 

for the South Ukrainian NPP Unit 1 VVER-1 000 at the end of the third fuel cycle. The 

main difference between these calculations was in fuel bumup representation. Two 

types of the core were considered: one with pin-by-pin bumup distribution and 

another - with assembly averaged bumup when all nodes of any axial layer within 

any fuel assembly were of the same bumup. Main goal of this comparison was to 

understand how the burnup representation could influence the consequences of the 

VVER REA from the point of view of the peak fuel enthalpy. 

The South Ukrainian NPP Unit 1 was operated in 2-year cycle regime without any 

burnable poison rods in the core. Calculational procedure and main results for the 

first 3 cycles were identical to those described in previous Section. Calculational 

average burnup of the core at the end of the cycle was 21 MWd/kgU with peak 

bumup of 37.5 MWd/kgU for the calculational node in the central part of the core. 

Neutronic calculations by the BARS code were carried out using 4 energy groups, 6 

groups of delayed neutron precursors and 16 axial harmonics. The thermal-hydraulic 

model of the core used by the RELAP5 code was identical to that described in 

Reference 28 with selected the hottest fuel pin as separate heat structure.

45
7.1. Initial Conditions of the Accident

The initial thermal-hydraulic conditions in the reactor corresponded to hot zero power 

(HZP) startup. The reactor power was 10-6 of the rated power, and the coolant inlet 

temperature and flow rate were 2870C and 17 t/s respectively. 

A key factor in REA analysis is the worth of ejected control rod. At normal operational 

conditions the worth of any rod does not exceed 1$. Because the goal of this study 

was to analyze consequences of a REA at conservative initial reactor conditions with 

the ejected control rod worth of 1.2$, the initial control rod pattern was changed. 

There are 61 control rods grouped in 10 different banks in the VVER-1000 core. In 

this study it was assumed that 18 control rods of 3 banks in the central part of the 

core and 18 control rods (including the accident rod) of 3 peripheral banks were fully 

inserted. Figure 7.1 presents location of inserted control rods before the accident. As 

shown in the figure, the control rod pattern was non-symmetrical because one 

control rod located near the ejected one was assumed as stuck out. This asymmetry 

resulted in required worth of the ejected control rod. It should be mentioned that such 

an approach is more realistic compared with artificial adjustment of neutron cross 

sections for this region to reach the desired value of the control rod worth. 

7.2. Analysis of Rod Ejection Accident Modeling 

As it was above mentioned, two identical calculations were done. Case 1 - with the 

pin-by-pin burnup distribution and Case 2 - with the assembly averaged one. Thus, 

the RELAP-BARS input decks for both variants differed only by the initial burnup 

distributions. 

First of all, two calculations of HZP steady state were performed. Comparison of the 

results gave the following maximum deviations in the neutronic parameters: 

"* assembly-by-assembly power distribution: 4%; 

"* control rods banks worth: 4%; 

"* worth of a single control rod: 7%; 

"* delayed neutron fraction: 0.2%; 

"* prompt neutron life time: 0.2%.

46
rod

Figure 7.1 Control Rod Pattern in the VVER-1000 Core Before REA

47
The deviation in the worth of the ejected rod was found as no more than 0.2%. Thus, 

uncertainties in REA calculational results due to that deviation were expected as 

minimal. 

The accident was initiated at time zero with the peripheral control rod ejection at a 

speed of 35.4 m/s (thus, the control rod was ejected during 0.1 s). The maximum 

value of reactivity of approximately 1.21$ was reached practically just after the full 

withdrawal of the control rods at about 0.2 s. The reactor power reached a peak 

value at 0.4 s, after that, due to the large negative Doppler feedback, the power 

excursion was terminated. During the transient no scram was assumed. Total 

duration of the calculated transient was chosen as 3 s. 

Calculational results for both cases were found as very close each other. Table 7.1 

presents a comparison of some neutronic and thermal-hydraulic parameters for both 

cases during the transient. 

Table 7.1 Comparison of the REA Calculational Results for Pin-by-Pin (Case 1) and 

Average (Case 2) Burnup Models 

Parameter of transient Case 1 Case 2 Deviation 

Maximum reactivity ($) 1.2102 1.2076 - 0.2 % 

Peak power (% of rated power) 113.5 112.2 - 1.1 % 

Time of power peak (ms) 402 403 1 ms 

Pulse width (ms) 85.3 85.9 0.7 % 

Prompt neutron life time for peak power (ms) 0.0281 0.0280 - 0.4 % 

Delayed neutron fraction for peak power (%) 0.5810 0.5822 0.2 % 

Power at t=3 s (% of rated power) 6.02 6.05 0.5 % 

Enthalpy increment for the hottest pin (cal/g) 22.1 21.9 - 1.1 % 

Fuel temperature for the hottest pin (K) 861 858 - 3 K

48
Figure 7.2 shows the reactor power and the reactivity as functions of the time of the 

transient. Deviations of these parameters decreased by the end of transient 

(Table 7.1). 

Fuel enthalpy increment (pellet radial average for any axial layer) which is a key 

factor in RIA analysis is shown in Figure 7.3. This figure shows also a relative 

deviation in the fuel enthalpy increment between both cases. 

The pin-by-pin power distribution (one-half part of the core) is presented in 

Figure 7.4. As the figure shows this distribution is very complicated, especially near 

the ejected rod. In this region, each assembly adjacent to the reflector has a very 

large distortion in the power across the assembly. Average power of such 

assemblies was relatively small, but they contained the pins with more high power 

compared to those in the assembly with peak power (the accident assembly). This 

effect is a matter of principle in the comparison of two approaches: assembly-by

assembly and pin-by-pin. 

From the data presented in Table 7.1 and Figures 7.2 and 7.3, the following major 

conclusion may be given: the deviations in the neutronic and thermal-hydraulic 

parameters due to different bumup representation model are rather small. As the 

possible reasons of such result, the following may be considered. In this study, the 

VVER-1000 core with very low average burnup (21 MWd/kgU) was analyzed. 

Besides, a VVER-1000 reactor operated in 2-year cycle regime does not contain 

burnable poison rods in the core.

49
1.2 2

S 0.9 1.5 

=a: 

-0 

C 0.3 o 0.5 

0 0.5 1 1.5 2 2.5 3 

Time (s) 

Figure 7.2 Reactor Power and Reactivity During REA

50
30 i-I-- rrrr -rrrr I r- I-r -rIrI-I -rrrr 6 

25 4 

~20 2 FO 

,, C E 02 

2> 

15 0 

-0. ------- - -* 

S10 

5 -4 

0 0.5 1 1.5 2 2.5 3 

Time (s) 

Figure 7.3 Fuel Enthalpy Increment and Its Relative Deviation During REA

51
Location of ejected rod 

Location of stuck rod

01

Figure 7.4 Pin-by-Pin Power Distribution After Rod Ejection
8. CALCULATION OF TMI-1 REA

This Section describes recent RELAP-BARS calculational efforts aimed to 

understand the uncertainty in analysis of the effect of the detailed intra-assembly fuel 

power and temperature representation on neutronic and thermal-hydraulic 

parameters during a PWR REA. The effect of the pin-by-pin power representation 

was studied by comparison of the RELAP-BARS results with the PARCS and 

CRONOS2 calculations. Analysis of the effect of intra-assembly fuel temperature 

representation was made using two different approaches in the calculation of the fuel 

temperature: assembly-by-assembly (Case 1) and pin-by-pin (Case 2). The last 

model is based on the fuel temperature reconstruction method described in Section 

4. Both models used the same pin-by-pin power calculational approach. The major 

difference between two models was the representation of the fuel temperature within 

any assembly. In Case 1 the single axial distribution of the fuel temperature of the 

pin with averaged power was used for all pins within the assembly. While in Case 2 

each fuel pin has its own axial fuel temperature distribution calculated using the 

corresponding power distribution. 

The reactor model used in the RELAP-BARS calculations was based on the PWR of 

Three Mile Island Unit 1 that was chosen as an international benchmark (Ref. 29). 

The reactor core having one-eight symmetry contains fuel assemblies with fuel 

bumup ranged from 23 up to 58 GWd/t (at the end of the cycle). To generate neutron 

database for BARS, fuel nuclide compositions averaged over each assembly in each 

axial layer were used. This information was received from U.S. partners. Thus, fuel 

pins within each assembly in each axial layers had the same set of A-matrices. 

Initial conditions were hot zero power (HZP) with 20 control rods of 3 regulating 

banks fully inserted in the core as shown on Figure 8.1. This figure indicates that all 

inserted control rods are located at assemblies with high bumup fuel. It is obvious 

that after withdrawal of one of them, peak power will be observed in any neighboring 

assembly having relatively low bumup. For instance, after withdrawal of peripheral 

rod N12 of Bank 7, peak power will be in assembly N13 with fuel bumup of 24 

GWd/t.

53
8 9 10 11 12 13 14 15

52.86 H 

Bank 7 

K

57.94

L

56.25 30.85 49.53 28.11 53.86 55.78 

Bank 7 Bank 6

30.80

57.57 

Bank 6

M

55.43 29.83 53.95 

Bank 5

25.55 1 49.17

.3 .3 V 3 .3

30.22 54.40 27.86 23.30 1 47.30

9 9 3 9

49.71 

Bank 5

N

28.85 52.85 40.94

I9

48.75 

Bank 7

0

23.86

37.34

41.45

52.86 - fuel burnup (GWd/t) 

Bank 7 - No. of regulating Bank 

- the hottest fuel assembly 

Figure 8.1 One-Eight Core Layout

54
In basis case, considered as a REA, after ejection of central rod H8, power (both 

assembly averaged and pin-by-pin) reaches its peak value in assembly H9. This 

unrodded assembly with average bumup of 30 GWd/t contains two hottest pins 

located near the water gap between both assemblies as shown on Figure 8.2. 

8.1. Steady-State Calculations 

Before REA modeling, a number of steady-state calculations were carried out using 

RELAP-BARS coupled code. Below a comparison of the different neutronic 

approaches concerning REA modeling is presented. There were two models: the pin

by-pin one (BARS) and assembly-by-assembly one (PARCS and CRONOS2). 

The goal of such an intercomparison was to specify major differences in some 

neutronic and thermal-hydraulic parameters (power distribution, worth of the ejected 

control rod, the Doppler and moderator temperature coefficients of reactivity) which 

could effect on consequences of the REA. 

It should be noted that PARCS and CRONOS2 used the same two-group cross 

sections generated with the CASMO-3 code (Ref. 10). As a result, steady state 

calculational data were very close for both codes. For this reason only the PARCS 

results were used in this intercomparison. 

BARS calculational parameters were as follow: 

"* number of energy groups: 4; 

"* number of axial fuel zones with different properties: 24; 

"* number of axial harmonics: 20. 

Table 8.1 summarizes basic steady state parameters calculated by BARS and 

PARCS with corresponding deviation of the BARS value from the PARCS one. 

Together with worth of regulating banks and single rods of Bank 7, this table contains 

data on axial peaking factors and reactivity coefficients: the Doppler one and the 

isothermal temperature coefficient (ITC).

55
L - the hottest fuel pins 

R] - control rod guide tube 

I- - instrumentation tube 

Figure 8.2 Layout of Assembly H9

56
Table 8.1 Steady-State Parameters 

Parameter PARCS BARS Deviation (%) 

Worth of Bank 5 (pcm) 1423 1548 8.8 

Worth of Bank 6 (pcm) 849 859 1.2 

Worth of Bank 7 (pcm) 1050 1105 5.2 

Worth of rod H8 (pcm) 347 338 -2.6 

Worth of rod H12 (pcm) 188 202 7.4 

Worth of rod N12 (pcm) 344 543 58 

Axial peaking factor 2.65 3.10 17 

Doppler coefficient (pcm/K) -2.8* -2.8 

ITC (pcm/K) -47.9 -46.8 2.3 

* - Calculated by CRONOS2 

Figure 8.3 presents a comparison of the assembly power distributions calculated by 

PARCS and BARS at initial conditions. 

Comparison of the steady-state results obtained by using different methods, allows 

to give the following conclusions: 

"* a good agreement was found for worth of regulating banks and single rods H8 

and H12 as well as for the temperature coefficients of reactivity; 

"* the BARS model overestimated worth of single peripheral rod N12 approximately 

by 60% (it is important to note that such an overestimation in rod worth may result 

in the increase in local peak enthalpy increment by a factor of 2 or even more); 

"* the BARS model overestimate the average peaking factor for an axial power 

distribution by 17%; 

"* maximum difference in the assembly power distributions was about 13% for the 

assemblies adjacent to the radial reflector.

57
0.921 1.875 1.576 1.598 0.665 0.846 0.386 0.284 

0.826 1.713 1.457 1.501 0.624 0.806 0.382 0.291 

-10.3 -8.6 -7.6 -6.1 -6.2 -4.7 -1.0 2.5

1.519 

1.389 

-8.6

0.613 

0.610 

-0.5

-7.3 -5.5 -2.7 -0.5 4.3 6.2

0.820 

0.757 

-7.7

+ 4-

1.324 

1.272 

-3.9

1.100 

1.150 

4.5

1.314 

1.376 

4.7

1.107 

1.191 

7.6

0.400 

0.451 

12.7

0.676 

0.654 

-3.3

1.244 

1.257 

1.0

0.726 

0.725 

0.1

1.055 

1.103 

4.5

1.144 

1.210 

5.8

0.660 

0.748 

13.3

0.790 

0.871 

10.2

0.536 

0.604 

12.7

Figure 8.3 Power Distribution at Initial Conditions

58

PARCS 

BARS 

E ,%

1.723 

1.597 

-7.3

1.281 

1.211 

-5.5

1.250 

1.216 

-2.7

0.929 

0.969 

4.3

0.386 

0.410 

6.2
Note that the maximum deviation in the assembly power distribution was observed in 

peripheral assemblies with two facets adjacent to the radial reflector, This fact may 

be partly explained by different approaches of preparation of the neutron databases 

for the fuel and reflector regions. In the assembly-by-assembly model, neutron cross 

sections for fuel assembly are generated under the assumption that this assembly is 

surrounded by similar assemblies with specified boundary conditions for neutron 

current at its facets. It is clear, that such a model is not adequate in case when the 

considered assembly in the core is surrounded also by the reflector region. This 

disparity will be larger for assemblies surrounded by the reflector from two sides. The 

pin-by-pin model, as the ZR-6 validation results showed, successfully overcomes 

such troubles. Nevertheless, this problem deserves comprehensive investigation 

using precise codes to model LWR core-reflector interface. 

It should be paid attention to a significant difference in worth of control rod N12 

compared with one of control rod H12. Calculational results show that when one or 

other control rod is withdrawn, a distortion in the fuel pin power distribution takes 

place. Withdrawal of the most peripheral rod results in the largest distortion in the 

power distribution. To characterize a degree of a power distortion Table 8.2 shows 

radial peaking factors (RPFs) in pin-by-pin power distributions calculated by the 

BARS code for initial conditions and when one of the rods was withdrawn. The third 

column of the table contains RPF in power distributions averaged on each assembly. 

Table 8.2 Radial Peaking Factors in Pin-by-Pin Power Distribution 

Type of calculation Pin-by-pin RPF Averaged RPF 

Initial conditions (Banks 5-7 in) 1.85 1.71 

Withdrawal of rod H8 2.80 2.59 

Withdrawal of rod H12 2.55 2.39 

Withdrawal of rod N12 6.22 5.07

59
When a power distribution is rather smooth over the core, the averaged RPF may be 

considered as analogous to RPF calculated by the assembly-by-assembly model. In 

this case boundary conditions for neutron current between fuel assemblies are more 

or less equivalent to those used during generation of cross sections. 

But in case of a large power distortion in the local area of the core, the model of 

generation of assembly average cross sections may be not adequate due to intra

assembly effects. Especially, these effects are displayed for assemblies adjacent to 

the accident one. 

Comparison of RPFs for withdrawal of rods H8 and H12 shows that the power 

deviations are not so large in these cases. That is why the results from different 

codes are well agreed (see Table 8.1). On the contrary, in case with withdrawal of 

rod N12, the pin-by-pin RPF becomes a factor of 3.4 higher compared with the 

unperturbed case. In the vicinity of assembly N12 (this area included also 4 

neighboring assemblies) a very large distortion in pin-by-pin power distribution arose 

(Figure 8.4). Correct description of such distortion in the framework of the assembly

by-assembly model is problematic. This is a question of principal in REA analysis by 

the pin-by-pin and the assembly-by-assembly models. 

8.2. Intercomparison Between the Pin-by-Pin and Assembly-by-Assembly 

Models in a PWR REA 

It is obvious that observed differences in the steady-state parameters could result in 

significant uncertainties in REA consequences (especially when the peripheral rod is 

ejected) and it would be difficult to do reasonable comparison of REA calculations 

from different methods. For this reason, to provide initial steady-state conditions as 

close as possible, the radial reflector neutronic model in the BARS code was 

changed by artificial increase in the neutron absorption by boron poisoning of 1000 

ppm. As for axial reflectors, the data for the bottom one were used for both 

reflectors. After such corrections in the BARS reflector model, the maximum 

deviation in a power distribution became no more than 6% (Figure 8.5). Table 8.3 

gives major steady-state parameters after the correction.

60
0.152 0.143 

0.404 0.343 

0.484 0.230 

0.437 0.504 

0.532 0.557 

0.353 0.816 

0.776

4 5 6 7 8 9 10 11 12 13 14 15

Figure 8.4 Power Distribution After Withdrawal of Rod N12 

61

0.241

0.196 

0.396 

0.244

0.289 

0.373 

0.445 

0.250

0.111 

0.150 

0.336 

0.287 

0.756 

0.809 

1.063 

0.598

0.171 

0.415 

0.275 

0.596 

0.649 

0.969 

0.987 

1.441 

1.355

0.196 

0.529 

0.643 

0.581 

0.717 

0.512 

1.291 

1.393 

1.837 

1.110

H 

K

0.295 

0.622 

0.413

0.404 

0.536 

0.661 

0.403 

0.939 

1.059 

1.635 

1.732 

2.448 

1.767

L

0.411 

0.730 

0.745 

1.048 

0.573 

1.124 

1.233 

3.512 

3.607 

5.068 

3.200

0.379 

0.611 

0.937 

0.917 

0.566 

2.059 

2.974 

2.615 

2.198

0.369 

0.401 

0.437 

0.859 

1.085

M 

N 

0

0.826 

0.868 

1.101 

0.779 

2.140 

2.717 

4.252 

4.501
0.921 1.875 

0.869 1.790 

-5.6 -4.5 

1.519 

1.447 

-4.7

1.576 1.598 

1.515 1.557 

-3.9 -2.5 

1.723 1.281 

1.662 1.250 

-3.5 -2.4 

0.820 1.324 

0.787 1.307 

-4.0 -1.3 

0.676 

0.668 

-1.2

0.665 

0.647 

-2.7 

1.250 

1.247 

-0.2 

1.100 

1.165 

5.9 

1.244 

1.255 

0.9 

0.726 

0.709

0.846 

0.820 

-3.1 

0.613 

0.618 

0.8 

1.314 

1.371 

4.3 

1.055 

1.078 

2.2 

1.144 

1.155 

1 n -2 .. PARCS 0.660 

BARS 0.667 

F ,% 1.1 

Figure 8.5 Power Distribution at Initial Conditions After Reflector Model Correction

0.386 

0.383 

-0.8 

0.929 

0.961 

3.4 

1.107 

1.162 

5.0 

0.790 

0.816 

3.3 

0.536 

0.538 

n A

0.284 

0.274 

-3.5 

0.386 

0.390 

1.0 

0.400 

0.411 

2.7

62
Table 8.3 Steady-State Parameters After Reflector Model Correction 

Parameter PARCS BARS Deviation (%) 

Worth of Bank 5 (pcm) 1423 1532 7.6 

Worth of Bank 6 (pcm) 849 856 0.8 

Worth of Bank 7 (pcm) 1050 1083 3.1 

Worth of rod H8 (pcm) 347 349 0.6 

Worth of rod H12 (pcm) 188 204 8.5 

Worth of rod N12 (pcm) 344 473 38 

Axial peaking factor 2.65 2.68 1.1 

As shown from the table, differences in the worth of regulating banks became 

smaller, but as before the correction the rod N12 worth differs significantly from the 

PARCS one. Thus, despite all corrections in the reflector model, a large difference in 

the worth of peripheral rod N12 still exists. The most probable explanation of this 

phenomenon is intra-assembly effects when a large distortion in the power 

distribution occurs at a local area of the core near the reflector. 

Below the results of REA calculations with different codes are presented. The basic 

scenario was a fast ejection of the central control rod with fixed worth of 1.2$ (with 

the delayed neutron fraction of 521 pcm). To provide the last value (instead of 0.67$ 

in reality) some modifications were done in each code. 

BARS and PARCS used the same thermal-hydraulic code (RELAP5) with the similar 

input decks, while CRONOS2 was coupled with the FLICA4 thermal-hydraulic code. 

Table 8.4 presents some parameters of the REA. The agreement is very good 

between all codes. Local fuel enthalpy reaches its peak value at the same assembly 

H9 and the same axial node at the top of the core. The maximum increment in fuel 

enthalpy in assembly H9 was about 19 cal/g (BARS) and 17 caVg (PARCS).

63
Table 8.4 Parameters of the REA 

Parameter RELAP- RELAP- FLICA4 PARCS BARS CRONOS2 

Control rod worth ($) 1.206 1.209 1.196 

Peak power (GW) 10.89 10.69 10.37 

Time of peak power (ms) 360 338 360 

Power pulse width (ms) 65 63 69 

Another direction in the intercomparison was to compare the intra-assembly power 

distribution in the hottest assembly (H9) calculated "directly" by BARS and 

reconstructed by a special procedure used together with the PARCS code. (Note, 

that this procedure is used as independent part of calculations and does not 

influence the calculational routine.) This comparison for the initial time moment and 

the time when reactor power reaches peak value, is presented in Reference 10. The 

agreement of the data is rather good. Both methods indicate the same location of the 

hottest pins (Figure 8.2). Local peaking factors in assembly H9 were 1.27 (BARS) 

and 1.25 (PARCS) for the initial time moment and 1.08 (BARS) and 1.07 (PARCS) 

for peak power. 

It is important to emphasize that the intercomparison of such a kind for the accident 

with the peripheral rod ejection could be of the most interest because of more 

dramatic consequences. Such transient (under the assumption of stuck rod near the 

accident one) does not require any artificial modification in worth of the ejected rod. 

Next part of this REA study concerns intra-assembly representation of fuel 

temperature during the transient. As before mentioned, two cases for the fuel 

temperature representation were considered in the REA calculation: 

"* Case 1 - the assembly-by-assembly model; 

"* Case 2 - the pin-by-pin model.

64
8.3. Validation of Fuel Temperature Reconstruction Method

The validation of the reconstruction method for the intra-assembly fuel temperature 

distribution within any assembly was done directly in the framework of the REA 

calculation. For this reason a number of fuel pins of interest were considered as 

separate heat structures in the RELAP input deck. This allowed comparing fuel 

temperatures in selected fuel pins calculated "directly" by RELAP and by 

"approximate" reconstruction method. 

Figure 8.6 shows fuel temperature increment for the hottest fuel pellet calculated 

"directly" (solid curve) and relative deviation between "approximate" and "direct" 

calculations (dashed curve) as a function of the time of the accident. As it was shown 

in the figure, the relative uncertainty of the reconstruction method for the hottest fuel 

pin compared with "direct" calculation did not exceed 1.5% during the transient (this 

resulted in the temperature deviation of no more than 1.5 K at the time of the peak 

power). 

Thus, the following conclusion can be done: the reconstruction method allows to 

calculate the fuel temperature distribution within any assembly during a REA with a 

reasonable accuracy. 

8.4. Effect of Detailed Intra-Assembly Fuel Temperature Representation 

Figures 8.7 and 8.8 show reactor power and enthalpy increment for the hottest fuel 

pellet as functions of the time of the transient. These dependencies are given as 

solid curves calculated for Case 2. Here the relative deviations between Case 2 and 

Case 1 are indicated as dashed curves. As the figures show, the relative difference 

in calculations of the reactor power and the fuel enthalpy by two methods did not 

exceed 2.5% with decreasing to 1% at the end of the transient. 

Table 8.5 presents major parameters of the transient calculated by both models. The 

last column gives relative deviation between Case 2 and Case 1.

65
300 3

C E 200 2 

0 C 

C 

0)D 

----------------------------------------------

0 0 E 100 • 

- i 

LI0 8 

0 0 0 0.5 1 1.5 2 2.5 

Time (s) 

Figure 8.6 Fuel Temperature Increment in the Hottest Fuel Pellet vs. Time

66
-4

3 i -3 

S-2 

0 I' -.- -------------------------- 1 

0 0 

0 0.5 1 1.5 2 2.5 

Time (s) 

Figure 8.7 Reactor Power vs. Time

67

4
25 -5

S20 -4 

E-1 Q 

E 15 

2 

CC 

" 10 -2• 

",,u. 5 -1 

0 0 

0 0.5 1 1.5 2 2.5 

Time (s) 

Figure 8.8 Enthalpy Increment for the Hottest Fuel Pellet vs. Time

68
As the Figure 8.7 shows, the reactor power reached the peak value at 0.34 s when 

the maximum increase in fuel temperature for the hottest assembly was about 100 K 

(see Figure 8.6). At the same time the maximum difference in fuel temperature 

across this assembly was less than 10 K. Such relatively low fuel temperature non

uniformity and not great fuel temperature increment during the transient were key 

factors which allow to understand why all parameters calculated in both cases are 

well agreed. 

Table 8.5 Main Parameters of the REA with Different Fuel Temperature Models 

Parameter of transient Case 1 Case 2 Deviation 

Peak power of the core (GW) 10.69 10.51 -1.7% 

Peak power of the fuel pin (kW) 835 821 -1.7% 

Maximum temperature in fuel pin (K) 834.6 834.5 -0.1K 

Maximum increment in fuel enthalpy (caVg) 20.6 20.3 -1.4% 

Comparison of the results shown that calculation with assembly-by-assembly fuel 

temperature representation gave slightly conservative results in key parameters of 

the transients in the comparison with the pin-by-pin one.

69
9. CONCLUSIONS

The major goal of this study was to analyze effects of the pin-by-pin representation 

of fuel power, bumup and temperature on the course of LWR RIAs. The pin-by-pin 

model, based on the heterogeneous reactor theory, was implemented in the BARS 

code. A coupling of BARS with RELAP5/MOD3 and some interface codes allow by 

now to solve a wide range of problems of interest for various types of reactors: 

"* steady states at different conditions (including determination of reactivity effects); 

"* slow transients (including modeling of LWR fuel cycle); 

"* fast transients (including LWR RIAs such as control rod ejection and steam line 

break). 

Unlike nodal diffusion models used the assembly-by-assembly approach, the pin-by

pin model opens qualitatively different opportunities in the analysis of the intra

assembly effects of fuel power, bumup and temperature on consequences of LWR 

RIAs. 

Validation results obtained for critical assembly ZR-6, demonstrate capabilities of the 

BARS code to predict fine pin-by-pin power effects near fuel-reflector boundary and 

in the vicinity of any perturbation in the core. Similar effects in the pin-by-pin power 

distribution were found in the RELAP-BARS modeling of the peripheral control rod 

ejection in VVER-1000 of the South Ukrainian NPP Unit 1 with core bumup of about 

21 MWd/kgU. The REA analysis showed that: 

"* ejection of a peripheral control rod resulted in very complicated pin-by-pin power 

distribution in assemblies directly adjacent to the accident one; 

"* fuel assemblies with relatively low power contained fuel rods with power 

exceeded maximum value for fuel rods in assembly with peak power; 

"* the hottest fuel rod did not necessarily belong to assembly with peak power; for 

this reason an assembly-by-assembly model may result in underestimation of the 

local peak enthalpy, because of a flux reconstruction method is used, as a rule, 

only for the assembly with peak power.

71
Effects of the pin-by-pin burnup representation compared with the assembly

averaged model were found as rather small for such slightly burnt-out cores. 

Intercomparison of calculational results for TMI-1 obtained with different neutronic 

models: the pin-by-pin one (BARS) and the assembly-by-assembly (PARCS and 

CRONOS2), displayed a number of problems which are very important in reactor 

safety analysis. There were noticeable differences in the radial and axial power 

distributions. Besides, the BARS value for the worth of single peripheral control rod 

was approximately 60% higher. This fact can play a major role in safety analysis of 

such a REA. A supposition about significant influence of a large power distortion 

(intra-assembly effect) in a local area of the core on neutronic parameters was put 

forward. 

On the contrary, worths of the regulating banks and central control rod were in a 

rather good agreement. Comparison of the calculational results for the accident with 

ejection of the central control rod with fixed worth of 1.2$ and adjusted reflector 

model in the BARS code, show also a very good agreement between different codes. 

Besides, in this case the procedure of neutron flux reconstruction used together with 

PARCS gives quite satisfactory results for the pin-by-pin restoration of the power 

distribution within the assembly adjacent to the accident one. 

Another intra-assembly effect considered in this study was the effect of the pin-by

pin fuel temperature representation. As the RELAP-BARS calculations of the TMI-1 

REA shows this effect is rather small. The calculation using assembly-by-assembly 

fuel temperature distribution gave slightly conservative results in key parameters of 

the REA. 

Summarizing the results of this study, the following general conclusion may be 

submitted. No doubt, intra-assembly effects play significant role in prediction of many 

important parameters of reactor safety such as worth of ejected control rod and local 

fuel enthalpy. It is evident that comprehensive analysis of the RIA with a large 

distortion of the power distribution demands to use the pin-by-pin model.

72
In the future work, main efforts should be applied to further calculational 

investigations of the problems, which were pointed out in this report, namely: 

"* validation of the fuel cycle model for long duration cycles in VVER and PWR with 

cores containing burnable absorbers; 

"* analysis of effects of bumup representation for REA in a VVER with high bumup 

core; 

" study of effects of the LWR fuel-reflector interface and worth of control rods on 

the basic safety parameters by comparison with precise codes; 

"* analysis of above mentioned effects for the accident with the peripheral control 

rod ejection or other RIA, such as, for example, boron dilution accident in a VVER 

or a PWR.

73
10. REFERENCES

1. D. Diamond and L. Neymotin, "Sensitivity Studies for the BWR Rod Drop 

Accident," Letter Report FIN W6382, October 31, 1996. 

2. "RELAP5/MOD3.2 Code Manual," NUREG/CR-5535, INEL-95/0174, 1995. 

3. A. Awakumov and V. Malofeev, "Three-Dimensional Simulation of Delayed 

Neutron Transients in a Heterogeneous Reactor," At. Energy, 70 (1), 1991. 

4. A. Awakumov and V. Malofeev, "An Advanced 3 D Pin-by-Pin Neutronic Model 

for the LWR RIA Analysis: Features, Advantages and Validation," Report No. 90

12/1-8-97, Nuclear Safety Institute of Russian Research Centre "Kurchatov 

Institute", 1997. 

5. A. Awakumov, et al., "Validation of the BARS Code Package with ENDF/B Based 

Data Library," Report No. 90-12/1-4-98, Nuclear Safety Institute of Russian 

Research Centre "Kurchatov Institute", 1998. 

6. A. Awakumov and V. Malofeev, "Validation of an Advanced Heterogeneous 

Model for LWR Detailed Pin-by-Pin Calculations," Proceedings of the 

International Conference on the Physics of Nuclear Science and Technology, 

Long Island, NY, October 1998. 

7. A. Awakumov and V. Malofeev, "Validation of a Pin-by-Pin Neutron Kinetics 

Method for LWRs," Proceedings of the International Twenty-Sixth Water Reactor 

Safety Information Meeting, Bethesda, Maryland, October 1998. 

8. H.G. Joo, et al., "PARCS: A Multi-Dimensional Two-Group Reactor Kinetics Code 

Based on the Nonlinear Analytic Nodal Method," PU/NE-98-26, Purdue 

University, September 1998. 

9. J.J. Lautard, S. Loubiere, C. Fedon-Magnaud, "CRONOS, A Modular 

Computational System for Neutronic Core Calculations,"Proc. IAEA Specialist 

Mtg. on Advanced Calculational Methods for Power Reactors, Cadarache, 

France, September 1990.

75
10.D.J. Diamond, et al., "Intercomparison of Results for a PWR Rod Ejection 

Accident," Proceedings of the International Twenty-Seventh Water Reactor 

Safety Information Meeting, Bethesda, Maryland, October 1999. 

11.A. Kwaratzhely and B. Kochurov, "A Method for Calculation of Neutronic 

Parameters in a Heterogeneous Reactor Cell," At. Energy, 58 (2), 1985. 

12. B. Kochurov and V. Malofeev, "A Difference Approach to the Solution of 

Heterogeneous Reactor Equations," Annals of Nuclear Energy, 4, 21, 1977. 

13. B. Kochurov, "Effective Resonance Levels," At. Energy, 60 (3), 1986. 

14.R.E. McFarlane, "NJOY91.91: A Code System for Producing Pointwise and 

Multigroup Neutron and Photon Cross Sections from ENDF/B Evaluated Nuclear 

Data," ORNL PSR-171, Oak Ridge National Laboratory, 1993. 

15."ENDF/B Summary Documentation," BNL-NCS-17541 (ENDF-201), 4e ed. 

(ENDF/B-VI), P. F. Rose, Ed., Brookhaven National Laboratory (Oct. 1991; 

Release-2, 1993; Release-3, 1996). 

16.V. Davidenko and V. Tsybulsky, "Detailed Calculation of Neutron Spectrum in a 

Cell of a Nuclear Reactor," Proceedings of the International Conference on the 

Physics of Nuclear Science and Technology, Long Island, NY, October 1998. 

17.R.D. Mosteller, et al., "Benchmark Calculations for the Doppler Coefficient of 

Reactivity," Nuclear Science and Engineering, 107, 265, 1991. 

18. F. Rahnema and H.N.M. Gheorghiu, "ENDF/B-VI Benchmark Calculations for the 

Doppler Coefficient of Reactivity," Annals of Nuclear Energy, 23, 12, 1996. 

19.F. Rahnema, D. Ilas, and S. Sitaraman, "Boiling Water Reactor Benchmark 

Calculations," Nuclear Technology, 117, 184, 1997. 

20. "Experimental Investigations of the Physical Properties of VVER-type Uranium

Water Lattices," Final Report of TIC, Budapest, Akademiai Kiado, 1 (1985), 3 

(1991).

76
21."The VVER Experiments: Regular and Perturbed Hexagonal Lattices of Low

Enriched U0 2 Fuel Rods in Light Water," Report LEU-COMP-THERM-015, vol. 

IV, KFKI, Budapest, 1996. 

22.S.P. Szabo and R.J. Stammler, "HELIOS: Benchmarking Against Hexagonal TIC 

Experiments," Proceedings of the International Conference on the Physics of 

Nuclear Science and Technology, Long Island, NY, October 1998. 

23.A.D. Galanin, "Revision of Scheme for the Major Fission Products with Weak 

Effective Fission Product," Preprint ITEP-1 35, 1989 (Rus). 

24.L. Markova, "CB2 Result Evaluation (VVER-440 Bumup Credit Benchmark)," 9th 

AER Symposium on VVER Reactor Physics and Reactor Safety, Slovakia, 

October 4-8, 1999. 

25."Post-Irradiation Examinations of Fuel Assembly No. 4436001114 Irradiated at 

NV NPP Unit 5 During 3 Fuel Cycles up to Bumup of 44.7 MWd/kgU," 0-4011, 

RIAR, Dimitrovgrad, 1991 (Rus). 

26."Post-Irradiation Examinations of Fuel Assemblies Nos. 14422198 and 14422222 

Irradiated at Kola NPP Unit 3 up to Burnups of 46.22 and 48.18 MWd/kgU," 0

4326, RIAR, Dimitrovgrad, 1994 (Rus). 

27."In-Core Fuel Management Code Package Validation for WWERs," IAEA

TECDOC-847, November, 1995. 

28.A. Awakumov, et al., "3 D Pin-by-Pin Modeling of Rod Ejection RIA in VVER

1000," Report No. 90-12/1-33-97, Nuclear Safety Institute of Russian Research 

Centre "Kurchatov Institute", 1997. 

29. K.N. Ivanov et al., "Pressurized water Reactor Main Steam Line Break (MSLB) 

Benchmark; Volume I: Final Specifications," NEAINSC/DOC(99)8, U.S. Nuclear 

Regulatory Commission and OECD Nuclear Energy Agency, April 1999.

77
:FORM 336 

110Z 

1,3202

US. NUCLEAR REGULATORY COMMISSION 

BIBUOGRAPHIC DATA SHEET I•a,nf,,,b f•• n Si LA 'anwe)e

NRC 

3201 

2.1

Analysis of Pin-by-Pin Effects for LWR Rod Ejection Accident 

5. AUTHOR(S) 

A. Awakumov, V. Malofeev, V. Sidorov

p I1. REPORT NUMBER I

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (i NRC, provide Division- Oftea RRo-, US Ncý%---ReguiCy ,,,Commnissio, and melting addres•; if con•racl, 

prov-de name nd meing address.) 

Nuclear Safety Institute of Russian Research Centre 

"Kurchatov Institute" 

Moscow, Russia 

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (/Ft'RC, WWe 'Same as above'^ conbucb provide NRC Division, Office a Rf, US Nuclear~ tu.t.Y Com.miss ion. 

end -ef addreess) 

Division of Systems Analysis and Regulatory Effectiveness 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

10. SUPPLEMENTARY NOTES 

11. ABSTRACT (200 words or e1) 

This study was undertaken to demonstrate the capabilities of the pin-by-pin model used by the BARS code and to understand the 

various effects of intra-assembly pin-by-pin representation of fuel power, burnup and temperature in calculational analysis of light 

water reactor rod ejection accidents (LWR REAs). Effects of pin-by-pin fuel power and burnup representation were investigated 

on the basis of calculations for the peripheral control rod ejection in a VVER-1 000 of the South Ukrainian NPP Unit 1. 

Comparative analysis of the REA in the Three Mile Island pressurized water reactor using the BARS code with the diffusion nodal 

codes PARCS and CRONOS2 was undertaken. Important differences between the three kinetics codes and the effects of the 

pin-by-pin fuel temperature representation are discussed.

12. KEY WORDS/DESCRIPTORS (List wads rph see that wiN assist reseache" in ocating thepors-t) 

BARS, PARCS, CRONOS2, transient analysis, safety analysis, 3D kinetics, coupled 

thermal-hyrdualic-neutronic computer codes, fuel pin power

13. AVAILASILIIY STATEMENT 

unlimited 

14. SECURITY CLASSIFICATION 

(This Pae) 

unclassified 

(This "apa0 

unclassified 

15. NUMBER OF PAGES 

16. PRICE

NRC FORM 335 (2-89)

nTLE AND SUBTITLE

I

I

1 .REPORT (Assigned by NUMBER NRC, Add Vot., Supp., Rev., 

and Addendum Numbers, If any.) 

NUREGAIA-0175 

NSI RRC K190-12/1-3-00 

IPSNI00-13 

3. DATE REPORT PUBLISHED 

MONTH-I YEAR 

February 2000 

4. FIN OR GRANT NUMBER 

W6500 

6. TYPE OF REPORT 

Technical 

7. PERIOD COVERED gnciusive Dtes-)

I

I
Federal Recycling Program
NUREG/IA- 0175

UNITED STATES 

NUCLEAR REGULATORY COMMISSION 

WASHINGTON, D.C. 20555-0001

ANALYSIS OF PIN-BY-PIN EFFECTS FOR LWR ROD EJECTION ACCIDENT

SPECIAL STANDARD MAIL 

POSTAGE AND FEES PAID 

USNRC 

PERMIT NO. G-67

MARCH 2000