NUREG/IA-0468 

International 

 Agreement Report

Validation of RELAP5 Model of Ringhals 4 

Against a Load Step Test at Uprated Power

 

 

 

 Prepared by: 

J. Bánáti and A. Stathis

Chalmers University of Technology 

Department of Applied Physics 

Division of Nuclear Engineering 

SE – 41 296 Gothenburg, Sweden

K. Tien, NRC Project Manager 

 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: December 2015

Date Published: September 2016

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

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

Published by

U.S. Nuclear Regulatory Commission

NUREG/IA-0468 

International 

 Agreement Report

Validation of RELAP5 Model of Ringhals 4 

Against a Load Step Test at Uprated Power

 

 

 

 Prepared by: 

J. Bánáti and A. Stathis

Chalmers University of Technology 

Department of Applied Physics 

Division of Nuclear Engineering 

SE – 41 296 Gothenburg, Sweden

K. Tien, NRC Project Manager 

 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: December 2015

Date Published: September 2016

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

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

Published by

U.S. Nuclear Regulatory Commission

iii

ABSTRACT

After finishing the large component replacement project of the steam generators and the 

pressurizer, the Unit 4 of the Ringhals Nuclear Power Plant was operated in test mode between 

2011 and 2014. In order to reach the ultimate goal of power uprate, and obtain a license for 

operation at the new nominal conditions, a series of tests had to be accomplished.

The R4-QP-101 maneuverability test was performed on March 3, 2015. The test was focusing on 

evaluation of the system responses for ± 10 % perturbances in the load. The data collected during 

test provided a good opportunity for verification of the full plant model, which is being developed 

for the RELAP5/Mod3.3 Patch04 computer code, with incorporation of the new component 

models.

The present International Agreement Report introduces the test procedure and shows an 

overview on the key parameters that are utilized. There is a brief summary given on the 

applicability field of the computer code. Preparation of the input deck and the nodalization of the 

primary and secondary sides are touched upon.

Strategies applied for achievement of steady-state conditions are addressed in the document. 

The steady-state results are presented in plotted format, demonstrating how the control system 

brought the entire unit to stable conditions. The calculated steady-state parameters were very 

close to the measured plant data, before the transient initiation.

A chapter summarizes the results of the validation study using the transient data to simulate the 

startup test. Quantification of simulation accuracy has proven that the stand-alone RELAP5 

thermal-hydraulic model is capable of reproduction of the key features and events of the test. 

Sufficiently good agreement between the measured and simulated data resulted in a successful 

verification of the plant model. The Ringhals 4 model is suitable for analysis of other types of 

transients already in its current state of development. Nevertheless, further refinement in the input 

is planned as soon as new test data will be available.

Keywords: Ringhals 4, Load Step, RELAP5, code validation

v

FOREWORD

The present International Agreement Report was prepared with the intention to provide feedback 

to the developers and the user community of the NRC computer codes in order to demonstrate 

the capabilities of RELAP5/Mod3.3 Patch 4. The authors made intensive efforts to build an up-todate model of the recently uprated Ringhals 4 unit for analyses of transients using best estimate 

methods. As the results reveal in the current document, the code has successfully been validated 

against a start-up and maneuverability test conducted at relevant NPP.

I am convinced that the modeling strategies and main conclusions in this study will contribute to 

better understanding of a number of key thermal-hydraulic phenomena and will broaden the 

knowledge-base of safety authorities, as well as that of the code users worldwide.

Prof. Imre Pázsit

Division of Nuclear Engineering

Chalmers University of Technology

Gothenburg, Sweden

vii

CONTENTS

Page

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

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

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

TABLES ....................................................................................................................................xi

ACKNOWLEDGMENTS..........................................................................................................xiii

ABBREVIATIONS ....................................................................................................................xv

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

 1.1 Power Uprates ......................................................................................................... 1-1

 1.2 Plant Modernizations at Ringhals ............................................................................. 1-1

 1.3 Objectives of the Test............................................................................................... 1-3

 1.4 Motivations for the Model Verification....................................................................... 1-3

2. PROCEDURE OF THE TEST ........................................................................................... 2-1

 2.1 Test Phases .............................................................................................................. 2-1

 2.1.1 Part A: Steady-State....................................................................................... 2-1

 2.1.2 Part B: Power Decrease................................................................................. 2-1

 2.1.3 Part C: Operation at Reduced Power ............................................................. 2-1

 2.1.4 Part D: Power Increase .................................................................................. 2-1

 2.1.5 Part E: Restored Power Level ........................................................................ 2-1

 2.2 Test Results.............................................................................................................. 2-1

 2.2.1 Database of Measured Quantities .................................................................. 2-1

 2.2.2 Plots of the Measured Parameters ................................................................. 2-1

3. DESCRIPTION OF THE CODE AND THE MODEL .......................................................... 3-1

 3.1 The RELAP5 Code as an Analytical Tool.................................................................. 3-1

 3.2 Development of the R4 Model................................................................................... 3-1

 3.2.1 The R3 Model as a Starting Point................................................................... 3-1

 3.2.2 Status of the Current R4 Model ...................................................................... 3-1

 3.3 Description of the Primary Side................................................................................. 3-2

 3.3.1 The Reactor Pressure Vessel Internals .......................................................... 3-3

 3.3.2 Heat Structures in the Fuel............................................................................. 3-7

 3.3.3 Axial Power Distribution.................................................................................. 3-7

 3.3.4 The Main Circulation Pump Model.................................................................. 3-8

 3.3.5 The Safety Systems ....................................................................................... 3-8

 3.3.6 Primary Side of the Steam Generators ........................................................... 3-8

 3.4 Description of the Secondary Side ............................................................................ 3-9

 3.4.1 Secondary Side of the Steam Generators ...................................................... 3-9

 3.4.2 The Feedwater and Steam Lines.................................................................... 3-9
viii

4. STEADY-STATE RESULTS ............................................................................................. 4-1

 4.1 Energy and Mass Balance Calculation...................................................................... 4-1

 4.1.1 Balance Equations of the Secondary Side...................................................... 4-1

 4.1.2 Balance Equations of the Primary Side .......................................................... 4-2

 4.1.3 Strategies to Reach Steady-State .................................................................. 4-2

 4.2 Plots of the Steady-State Convergence..................................................................... 4-4

5. ANALYSIS OF THE TRANSIENT..................................................................................... 5-1

 5.1 Boundary Conditions................................................................................................. 5-1

 5.1.1 Heat Source Boundary Condition ................................................................... 5-1

 5.1.2 Turbine Pressure Boundary Condition............................................................ 5-1

 5.1.3 Turbine Control Valve Opening Boundary Condition ...................................... 5-1

 5.1.4 Feedwater Temperature Boundary Condition................................................. 5-1

 5.2 Discussion of the Transient Results .......................................................................... 5-4

 5.3 Plots of the Transient Calculation.............................................................................. 5-6

 5.4 Modeling Problems with the PRZ Level and the Charging Flow .............................. 5-12

 5.5 Run Statistics.......................................................................................................... 5-14

6. QUANTIFICATION OF SIMULATION ACCURACY.......................................................... 6-1

 6.1 Fast Fourier Transform Based Method (FFTBM) Analysis......................................... 6-1

 6.1.1 Average Amplitude......................................................................................... 6-1

 6.1.2 Additional Measures for Accuracy Quantification............................................ 6-2

 6.1.3 Signal Mirroring .............................................................................................. 6-2

 6.1.4 FFTBM Analysis Methodology........................................................................ 6-2

 6.2 Results of the FFTBM Analysis ................................................................................. 6-3

7. CONCLUSIONS................................................................................................................ 7-1

8. REFERENCES.................................................................................................................. 8-1
ix

FIGURES

Page

Figure 1 Aerial View of the Four Units at Ringhals.............................................................. 1-1

Figure 2 Ringhals 2, 3, and 4 – Similar Type of 3-Loop Westinghouse-Design Reactor...... 1-2

Figure 3 Timeline of the Ringhals 4 Power Uprate.............................................................. 1-2

Figure 4 Electric Power from the 2 Generators ................................................................... 2-2

Figure 5 Pressure in the Impulse Chamber......................................................................... 2-2

Figure 6 Position of Control Rod Bank D ............................................................................ 2-3

Figure 7 Neutronic Power ................................................................................................... 2-3

Figure 8 Cold Leg Temperature.......................................................................................... 2-4

Figure 9 Hot Leg Temperature............................................................................................ 2-4

Figure 10 Loop Average Temperature .................................................................................. 2-5

Figure 11 Loop Flowrate....................................................................................................... 2-5

Figure 12 Drainage Flowrate ................................................................................................ 2-6

Figure 13 Charging Flowrate for PRZ Level Control.............................................................. 2-6

Figure 14 Pressure in the Pressurizer................................................................................... 2-7

Figure 15 Output Signal for PRZ Pressure Control ............................................................... 2-7

Figure 16 PRZ Proportional Heater Control Signal................................................................ 2-8

Figure 17 Control Signal for PRZ Spray Valve ...................................................................... 2-8

Figure 18 Level in the PRZ ................................................................................................... 2-9

Figure 19 Output Signal for PRZ Level Control ..................................................................... 2-9

Figure 20 Pressure in the SG Steam Dome........................................................................ 2-10

Figure 21 Temperature of Feedwater.................................................................................. 2-10

Figure 22 Turbine Control Valve Position............................................................................ 2-11

Figure 23 Feedwater Flowrate ............................................................................................ 2-11

Figure 24 Steam Flowrate................................................................................................... 2-12

Figure 25 Narrow Range Level in the SG ........................................................................... 2-12

Figure 26 Process of model Development for Ringhals 4...................................................... 3-2

Figure 27 Internal Structure of a Westinghouse-Type PWR Pressure Vessel ....................... 3-3

Figure 28 Numbering Scheme of the Radial Nodalization..................................................... 3-4

Figure 29 Nodalization of the RPV Internals ......................................................................... 3-5

Figure 30 Nodalization of the Entire Primary Side................................................................. 3-6

Figure 31 Geometry of the Fuel Rods with Radial Mesh Points ............................................ 3-7

Figure 32 Power Distribution in the 8 Axial Nodes ................................................................ 3-8

Figure 33 Nodalization Scheme of SG 1............................................................................. 3-10

Figure 34 Nodalization Scheme of the Entire Secondary Side ............................................ 3-11

Figure 35 Fluid Conditions in the SG by the SNAP Visualization Vool ................................ 3-12

Figure 36 Void Fractions in the SG by the SNAP Visualization Tool ................................... 3-13

Figure 37 Pressure in the Pressurizer................................................................................... 4-4

Figure 38 Collapsed Level in the Pressurizer........................................................................ 4-4

Figure 39 PRZ Pressure Control Signal................................................................................ 4-5

Figure 40 PRZ Proportional Heater Signal............................................................................ 4-5

Figure 41 Charging Flowrate of the PRZ............................................................................... 4-6

Figure 42 Average Temperature in the Loop......................................................................... 4-6

Figure 43 Temperature in the Hot Leg .................................................................................. 4-7

Figure 44 Temperature in the Cold Leg ................................................................................ 4-7

Figure 45 Feedwater Flowrate to the SG .............................................................................. 4-8

Figure 46 Steam Flowrate from SG ...................................................................................... 4-8

Figure 47 Narrow Range Level in the SG ............................................................................. 4-9
x

Figure 48 Pressure in the SG................................................................................................ 4-9

Figure 49 Temperature Difference in the Loop...................................................................... 5-2

Figure 50 Normalized Thermal Power as a Boundary Condition........................................... 5-2

Figure 51 Turbine Pressure as a Boundary Condition........................................................... 5-3

Figure 52 Turbine Control Valve Position as a Boundary Condition ...................................... 5-3

Figure 53 Feedwater Temperature as a Boundary Condition................................................ 5-4

Figure 54 Pressure in the PRZ.............................................................................................. 5-6

Figure 55 PRZ Pressure Control Signal................................................................................ 5-6

Figure 56 PRZ Proportional Heater Signal............................................................................ 5-7

Figure 57 PRZ Spray Valve Lift with Zooming on a Large Peak at ~345 s ............................ 5-7

Figure 58 Level in the PRZ ................................................................................................... 5-8

Figure 59 PRZ Charging Flowrate ........................................................................................ 5-8

Figure 60 Loop Average Temperature .................................................................................. 5-9

Figure 61 Hot Leg Temperature............................................................................................ 5-9

Figure 62 Cold Leg Temperature........................................................................................ 5-10

Figure 63 Pressure in the SG.............................................................................................. 5-10

Figure 64 Feedwater Flowrate ............................................................................................ 5-11

Figure 65 Steam Flowrate................................................................................................... 5-11

Figure 66 Narrow Range Level in the SG ........................................................................... 5-12

Figure 67 Actual and Desired Levels in the PRZ................................................................. 5-13

Figure 68 Measured Levels and the Setpoint vs. Loop Average Temperature .................... 5-13

Figure 69 Actual and Courant Limit Time Steps.................................................................. 5-14

Figure 70 AA of Feedwater Flowrate..................................................................................... 6-5

Figure 71 AA of Steam Flowrate........................................................................................... 6-5

Figure 72 AA of SG Pressure................................................................................................ 6-5

Figure 73 AA of SG Level ..................................................................................................... 6-5

Figure 74 AA of PRZ Pressure.............................................................................................. 6-5

Figure 75 AA of PRZ Level ................................................................................................... 6-5

Figure 76 AA of Average Temperature ................................................................................. 6-5

Figure 77 AA of PRZ Prop. Heater Signal............................................................................. 6-5

Figure 78 AA of PRZ Spray Signal........................................................................................ 6-6

Figure 79 AA of Charging Flow............................................................................................. 6-6

Figure 80 Total Average Accuracy........................................................................................ 6-6
xi

TABLES

Page

Table 1 Parameters at the End of the Steady-State Run ................................................... 4-3

Table 2 Variables, Weighting Factors and Results of the 0-4500 s Interval........................ 6-3

xiii

ACKNOWLEDGMENTS

The present study has been prepared within a project in close collaboration between Chalmers 

University of Technology and the Swedish Radiation Safety Authority. SSM is kindly 

acknowledged for providing financial support for this project. The Document Number of the 

Contract is SSM2015-686-3 and the Activity Number is 2030076-00.

The authors wish to thank Magnus Holmgren at Vattenfall Ringhals AB for providing the measured 

test data, as well as for his personal communication on the operation of the control systems.

Last but not least, special thanks are due to Dr. Andrej Prošek at the Institute “Jožef Stefan” in 

Ljubljana, Slovenia. He has given valuable information and generous help on application of 

FFTBM methodology for quantification of simulation accuracy.

xv

ABBREVIATIONS

AA Average Amplitude

BC Boundary Condition

BWR Boiling Water Reactor

CAMP Code Applications and Maintenance Program

CL Cold Leg

CVCS Chemical and Volume Control System

DC Downcomer

DFT Discrete Fourier Transformation

ECCS Emergency Core Cooling System

FA Fuel Assembly

FCV Feed Control Valve

FFT Fast Fourier Transform

FFTBM Fast Fourier Transform Based Method

FSAR Final Safety Analysis Report

FW Feed Water

HL Hot Leg

HS Heat Structure

INEL Idaho National Engineering Laboratory

JSI Jožef Stefan Institute

LB-LOCA Large Break Loss of Coolant Accident

LOCA Loss of Coolant Accident

LP Lower Plenum

MCP Main Circulation Pump

MSIV Main Steam Isolation Valve

NPP Nuclear Power Plant

NRC Nuclear Regulatory Commission

NSSS Nuclear Steam Supply System

PARCS Purdue Advanced Reactor Core Simulator

PI Proportional Integral

PLS Precautions, Limitations, and Setpoints

PRZ Pressurizer

PWR Pressurized Water Reactor

RCP Reactor Coolant Pump

RCS Reactor Coolant System

RAB Ringhals AB

RPV Reactor Pressure Vessel

RELAP Reactor Excursion and Leakage Analysis Program

RTA Relevant Thermal-hydraulic Aspects

R3 Ringhals Unit 3

R4 Ringhals Unit 4

SB-LOCA Small Break Loss of Coolant Accident

SG Steam Generator

SL Steam Line

SNAP Symbolic Nuclear Analysis Package

SSM Swedish Radiation Safety Authority

TCV Turbine Control Valve

WH Westinghouse Electric Company

1-1

1. INTRODUCTION

1.1 Power Uprates

During the last decades, power utilities made enormous efforts into modernization of their plants 

in order to increase the amount of produced electricity in a more cost-effective and competitive 

way. The process of increasing the licensed power level of a commercial nuclear power plant is 

called a power uprate [1]. Power uprates are generally categorized based on the magnitude and 

the methods used to achieve the power increase. Power uprates have been implemented at a 

number of nuclear power plants (NPPs) in many countries. Currently, there are also a significant 

number of NPPs that have plans for larger or smaller power uprates. The increase in the electricity 

produced at an NPP can be achieved in several ways:

• Increase the thermal power in the reactor;

• Improve the thermal conversion efficiency in the secondary side of the power plant by 

refurbishing or replacing the steam generators (SGs), the high pressure or low 

pressure turbine units, or by a combination of these actions.

1.2 Plant Modernizations at Ringhals

The Ringhals NPP (Figure 1) is situated at the Swedish West Coast and it comprises four units: 

one boiling water reactor (BWR) and three Westinghouse-type (Figure 2) pressurized water 

reactors (PWRs). The latest-built Unit 4 was commissioned for commercial operation in 1983. It 

went through a number of extensive modifications and modernizations in 2011. Within the project 

of “QUATTRO/R4”, the SGs, the pressurizer (PRZ), and large parts of the turbine plant have been 

replaced. Refurbishment of these components affected also the relevant control and protection 

systems. The new nominal (100 %) thermal power of the unit is 3300 MWth in the current upgraded 

state. However, the permitted maximal power was still limited to 2773 MWth after the component 

replacement and a test operational mode was maintained between 2011 and 2014. Finally, the 

Swedish Radiation Safety Authority (SSM) permitted to increase the power and issued the license 

for the upgrade during the spring of 2015. Figure 3 shows a timeline of the power uprate process.

Figure 1 Aerial View of the Four Units at Ringhals
1-2

Figure 2 Ringhals 2, 3, and 4 – Similar Type of 3-Loop Westinghouse-Design Reactor

Figure 3 Timeline of the Ringhals 4 Power Uprate
1-3

1.3 Objectives of the Test

To ensure the continued safe operation of the plant, several tests, such as a load step, a full 

scram, and a load rejection test have successfully been conducted after installation of the new 

components but still operating at the ordinary power (2773 MWth). When the license was obtained 

for operation at the uprated power (~3000 MWth), a new series of tests were repeated. One of 

them was a ± 10 % load step test (R4 – QP-101-b), which is the object of the present study. The 

main purpose of the current maneuverability test was to verify that the unit, including the recently 

installed components with the automations and control systems, are able to handle a perturbation 

of the power in a satisfactory manner.

Specifically, two key issues were highlighted in the investigations:

• Checking the ability of the rod control system to adapt the reactor power according to the 

turbine power needs, without activation of the steam dump.

• Collecting data on the PRZ level changes due to the temperature variations in the 

reactor coolant system (RCS).

The magnitude of the power step was carefully set to remain within a ±10 % margin because this 

change is large enough to generate a challenge for the control systems, but still it remains under 

the level, which would trigger safety of protection systems, such as a reactor scram or opening a 

safety valve.

1.4 Motivations for the Model Verification

A new stand-alone RELAP5 computer code model has been built in order to simulate the entire 

unit 4 at Ringhals by utilizing the experience gained with unit 3 modeling. Comprehensive 

descriptions of the full-plant models of R3 and R4 are published in [2] and [3], respectively. The 

new code input includes the replaced component models of the SGs and the PRZ models, which 

were prepared on the basis of technical details provided by manufacturer. The engineering 

database specified by the designer reflects the nominal parameters for 100 %, i.e. 3300 MW 

thermal power, and the model is built accordingly. However, the operation at a lower power 

needed some modifications and adaptations in the input.

The present validation study on a new load step test is a follow-up to the work, formerly published 

in a scientific report [4], which discussed a similar subject. Also, a conference paper [5]

summarized the results of a startup test performed at a lower power. This test gave the very first 

opportunity for verification of the model performance against a real plant transient. Within this 

progression, the current activity is a part of the process in which the ultimate goal is to provide a 

thoroughly verified, “multi-purpose” R4 model that is suitable for a wide scope of transient 

analyses. Quantification of simulation accuracy is investigated in Chapter 6, which has been 

prepared by the co-author of this Report, Athanasios Stathis. The topic is a part of his Master of 

Sciences Thesis [6].

Last but not least, sharing the knowledge and experiences with verification of the RELAP5 code 

can be an important feedback for the code developers, as well as essential information for the 

entire code user community. The work presented in the current study is a Swedish in-kind

contribution in a form of an International Agreement Report for the US Nuclear Regulatory 

Commission (US NRC).

2-1

2. PROCEDURE OF THE TEST

2.1 Test Phases

The R4 Load Step Test was performed on March 3, 2015. Preparation for the test began earlier 

but the data acquisition started at 09 h 25 m 43 s (0 s) and finished at 10 h 40 m 43 s (4500 s). 

This means that the length of the recorded data is one and a half hours. The test consist of 5 

distinct phases, as described in the followings.

2.1.1 Part A: Steady-State

The plant was operated in a steady-state. Obviously, this does not mean that the parameters are 

“mathematically” stable. Beyond the stochastic noise, most of the measured quantities reflect a 

continuously oscillating nature, partly due to the control systems. Between 0 s and 333 s, the 

electric generators T41 and T42 produced a steady value of 533.5 MW (Figure 4).

2.1.2 Part B: Power Decrease

The transient was initiated with an instant decrease of steam demand at 334 s. As a consequence, 

the generated electric power and the pressure of the turbine impulse chamber started to fall 

(Figure 5). In a short period of time, the control rod drive mechanism inserted the rods to the core 

with maximal speed (Figure 6). This is reflected also in decrease of the neutronic power, from 

90.5 % to approx. 82 % (Figure 7). During this transition period, as it can be observed on the 

plots, many parameters show large “undershoots” or “overshoots”, represented by huge peaks.

2.1.3 Part C: Operation at Reduced Power

It is difficult to determine the exact starting point when the plant reached a quasi-steady condition. 

Some kind of stabilization began at approx. 450 s. However, the rod control system continued 

moving the rods until 2100 s and the position was finally kept constant after that.

2.1.4 Part D: Power Increase

Up-step of the power started with a sudden increase of steam demand at ~3918 s. The control 

rods were pulled up, while the electric power was increasing to its original level. This transition 

period lasted until approx. 4000 s.

2.1.5 Part E: Restored Power Level

Despite the fact that the power was restored by 4000 s of transient time, most of the other 

parameters did not completely stabilize before the end of the data recording.

2.2 Test Results

2.2.1 Database of Measured Quantities

The test database was provided by Ringhals in a set of 533 ASCII files (1 file per measured 

channel). Frequency of the data sampling was 1 Hz. Due to different interpretation of the 

engineering units at the plant and in the code simulation, a MATLAB script was prepared for 

conversion between, for instance overpressure and absolute pressure (Pa), or deg. C and Kelvin.

2.2.2 Plots of the Measured Parameters
2-2

Figure 4 Electric Power from the 2 Generators

Figure 5 Pressure in the Impulse Chamber
2-3

Figure 6 Position of Control Rod Bank D

Figure 7 Neutronic Power
2-4

Figure 8 Cold Leg Temperature

Figure 9 Hot Leg Temperature
2-5

Figure 10 Loop Average Temperature

Figure 11 Loop Flowrate
2-6

Figure 12 Drainage Flowrate

Figure 13 Charging Flowrate for PRZ Level Control
2-7

Figure 14 Pressure in the Pressurizer

Figure 15 Output Signal for PRZ Pressure Control
2-8

Figure 16 PRZ Proportional Heater Control Signal

Figure 17 Control Signal for PRZ Spray Valve
2-9

Figure 18 Level in the PRZ

Figure 19 Output Signal for PRZ Level Control
2-10

Figure 20 Pressure in the SG Steam Dome

Figure 21 Temperature of Feedwater
2-11

Figure 22 Turbine Control Valve Position

Figure 23 Feedwater Flowrate
2-12

Figure 24 Steam Flowrate

Figure 25 Narrow Range Level in the SG
3-1

3. DESCRIPTION OF THE CODE AND THE MODEL

3.1 The RELAP5 Code as an Analytical Tool

In prior agreement with SSM, the RELAP5 code has been selected as the numerical tool for the 

transient analysis. It has been developed for best-estimate transient simulation of light water 

reactor coolant systems during postulated accidents. The code originates from the Idaho National 

Engineering Laboratory (INEL) and first it was created for the U.S. Nuclear Regulatory 

Commission (NRC). Code uses include analyses required to support rulemaking, licensing audit 

calculations, evaluation of accident mitigation strategies, evaluation of operator guidelines, and 

experiment planning analysis. RELAP5 has also been used as basis for a nuclear plant analyzer 

(NPA). The code models specific simulations of transients in LWR systems, e.g., the coupled 

behavior of the reactor coolant system and the core for loss-of-coolant accidents and, operational 

transients such as anticipated transient without scram, loss of offsite power, loss of feedwater, 

station blackout, turbine trip and, loss of flow. RELAP5 is a highly generic code that, in addition 

to calculating the behavior of a reactor coolant system during a transient, can be used for 

simulation of a wide variety of hydraulic and thermal transients in both nuclear and nonnuclear 

systems involving mixtures of steam, water, non-condensable, and solute. 

RELAP5/MOD3.3 Patch-04-jm was the latest installed version of the code [7] at the time of the 

analysis and it was used without any modification in the source code. RELAP5 is maintained 

jointly by the NRC and a consortium consisting of several countries and U.S. organizations that 

were members of the International Code Assessment and Applications Program (ICAP) and its

successor organization, Code Applications and Maintenance Program (CAMP). Sweden is a 

signatory member country of the CAMP Agreement.

The RELAP5/MOD3 code is based on a one-dimensional, nonhomogeneous and non-equilibrium 

six-equation hydrodynamic model for the two-phase systems. The mass, momentum and energy 

balance equations are solved by a fast, partially implicit numerical scheme to permit economical 

calculation of system transients. The objective of the RELAP5 development effort from the outset 

was to produce a code that included important first-order effects necessary for accurate prediction 

of system transients but that was sufficiently simple and cost effective so that parametric of 

sensitivity studies were possible. The code includes many generic component models from which 

general systems can be simulated. The component models include pumps, valves, and pipes, 

heat releasing or absorbing structures, reactor point kinetics, electric heaters, jet pumps, turbines, 

separators, accumulators, and control system components. In addition, special process models 

are included for effects such as form loss, flow at an abrupt area change, branching, choked flow, 

boron tracking, and non-condensable gas transport.

3.2 Development of the R4 Model

3.2.1 The R3 Model as a Starting Point

A very simplified RELAP5 model was created for R3/4 by J. Eriksson [8] at Studsvik EcoSafe in 

1994. About a decade later, Chalmers University of Technology took over the developmental 

efforts on the legacy input. The former coarse nodalization has been refined, thoroughly updated, 

extended, and a coupled neutron kinetic model has been prepared. A technical description of the 

coupled R3 model is summarized in [2]. Results of the validations have been published in a 

number of technical reports, international conferences, and scientific journals [9], [10], and [11].

3.2.2 Status of the Current R4 Model
3-2

The current RELAP5 model of the R4 was built on the basis of the R3 (Figure 26). Since the 

layouts of the R3 and the R4 units are similar, the main intention was to keep as many elements 

from the R3 model as possible. However, the steam generators and the pressurizer were replaced 

with the new AREVA-design components in 2011. The structures of these parts, especially the 

SGs are significantly different from those that are installed in R3. Consequently, building a new 

full-plant model became necessary.

Figure 26 Process of model Development for Ringhals 4

The current R4 model represents the “state-of-the-art” and the practical experiences that have 

been gained by the modeling efforts over the last few years. Quality assurance is guaranteed by 

the results of the extensive verification and validation tests that the Ringhals models have passed 

successfully. A number of startup and maneuverability tests were performed with using 2783 MWth

before the power uprate at the end of 2011. In particular, a transient with a stepwise change of 

load by ± 10 % was used for validation of the new components and the related control system 

responses to the perturbations. The results are summarized in a conference paper [5].

The plant parameters, details of the control system data, setpoints, technical specifications and 

operational data were obtained from the Precautions, Limitations, and Setpoints (PLS) document

of R4 [12].

3.3 Description of the Primary Side
3-3

3.3.1 The Reactor Pressure Vessel Internals

The complex structure of the reactor pressure vessel (RPV) internals of a Westinghouse-type 

PWR is shown in Figure 27 [13]. The core consists of 157 fuel assemblies. The fuel rods are 

arranged into a 17x17 matrix. The length of a fuel rod is 3.66 m.

Figure 27 Internal Structure of a Westinghouse-Type PWR Pressure Vessel

In the core region, each of the 157 fuel assemblies is modeled individually, both for the 

hydrodynamics and for the heat structures. Such a detailed nodalization has been chosen in order 

to allow 1:1 coupling between the thermal hydraulic and neutron kinetic calculations. 
3-4

It is assumed that a 1/3 radial section of the core of is connected to 1 loop out of 3 loops, marked 

with red, green, and blue colors, respectively in Figure 28. In principle, 52 and 1/3 assemblies 

belong to 1 loop. This means that, due to lacking triangular (120o

) symmetry, the assembly in the 

center (no. 364) is equally split between the 3 loops. In axial direction, the active core was 

discretized into eight levels.

Figure 28 Numbering Scheme of the Radial Nodalization

The core inlet and outlet needed special considerations due to a limitation in RELAP5, that a 

“branch” component may be connected to a maximum of 9 other volumes. To overcome this 

limitation, 6 branches per loop were inserted to the core inlet and outlet. (Components 171-176, 

271-276, 371-376 at the inlet, and 191-196, 291-296, 391-396 at the outlet on Figure 29).

It is essential that some specific phenomena, for instance an asymmetric behavior of the loops 

can be properly captured. For this reason, the downcomer (DC), the way as the core is split into 

three parallel channels in order to retain the 3-loop structure of the primary side even within the 

reactor pressure vessel.
3-5

Figure 29 Nodalization of the RPV Internals
3-6

Figure 30 Nodalization of the Entire Primary Side

It has to be underlined that the DC is modeled in a realistic manner, including the material 

properties and the wall thicknesses of metallic structures. Application of 6 axial nodes in an 
3-7

“annulus” component provides adequate resolution for level tracking and thermal stratification. 

Modeling of heat transfer between the fuel assemblies, the baffle, the barrel, the DC wall, the RPV 

wall, and the ambient assures that the DC-related thermal hydraulic phenomena are simulated 

with high fidelity.

It is also important to distinguish between the coolant flowing through the fuel assemblies while 

being heated, and the remaining part of the main loop flow. Thus, the core has been extended 

with altogether three bypass channels per loop in the following manner: 

• the first one is representing the baffle-barrel space, 

• the second one is modeling the open guide thimbles, and

• the third channel is created for the flow path at the core periphery. 

The flow resistances were set according to the plant data and therefore resulted in a realistic 

distribution of the pressure losses. Figure 30 shows the nodalization of the entire primary side.

3.3.2 Heat Structures in the Fuel

The radial description of the fuel rods consists of 3 materials:

• the pellet with UO2 fuel, 

• the gap with He gas, and 

• the cladding with zircaloy. 

Altogether 9 mesh points are defined in the heat structures accordingly (Figure 31). The radial 

coordinates of the mesh points are indicated as distances from the center line.

Figure 31 Geometry of the Fuel Rods with Radial Mesh Points

3.3.3 Axial Power Distribution

Distribution of the relative power in axial direction is shown in Figure 32. Altogether 8 axial nodes 
3-8

are used for the heat source in the active part of the core, which is the same number as of the 

corresponding hydrodynamic cells.

Figure 32 Power Distribution in the 8 Axial Nodes

3.3.4 The Main Circulation Pump Model

The MCPs are modeled with “pump” components available in RELAP5. The homologous curves, 

torque and head data were obtained from plant documentation. The model was adopted from R3 

input without any modification in the updated version of the R4 input deck. Maintaining the primary 

side loop flowrate is achieved with controlling the velocity of the pump. A dedicated control 

variable (cntrlvar-180) stores the deviation of the actual loop flowrate from the setpoint value of 

the desired loop flowrate in kg/s. A PI controller (cntrlvar-181) determines the pump velocity in 

order to approach the setpoint value as close as possible.

3.3.5 The Safety Systems

One hydro-accumulator component (901, 903, and 905) is connected to each loop of the primary 

system through an emergency core cooling mixer component (x86). X denotes here the number 

of loop, i.e. 1, 2, or 3. These ECC mixers are operating in tandem with the other mixers (x85) that 

may inject water either from the boron tank (916) or from the residual heat removal system (930 

and 940).

The primary side model is extended with a time dependent junction (498) simulating the normal 

letdown, and a charging line (450) and the corresponding charging valve (451).

3.3.6 Primary Side of the Steam Generators

The coolant enters to the inlet plenum (120) from the hot leg (Figure 33). The inverted U-shaped 

heat exchanger tubes are modeled with a single channel (130). The tube bundle model has 

altogether 22 cells. The cells from 130-01 to 130-10 are vertical and upwards directed. The cells 
3-9

130-11 and 130-12 are simulating the U-turn of the tubes with tilted volumes at the top. The cells 

between 130-13 and 130-22 are again vertical but pointing downwards on the cold leg side. The 

outlet plenum is modeled with a branch component (140).

3.4 Description of the Secondary Side

3.4.1 Secondary Side of the Steam Generators

The feedwater is injected through the distributor, and enters to the top volume of the inner DC

(505-01). The flow is downwards directed in the channel and reaches the connection junction 

(508) at the tube plate. It turns upwards at cold side of the riser (510). The boiler section starts 

with a component (530) having 4 internal cells above the divider plate. The evaporator has 2 

components (535 and 538). Phase separation takes place in the separator (540).

The water droplets are diverted from the separator to the upper part of the DC, which is connected 

to the inlet of cell 545-04. The volume (554) is a downwards directed channel, ending in a junction 

(548), which connects to the outer DC component (550). The fluid is recirculated in this volume 

and fed into the hot side of the riser (520) at the bottom of the SG. The volume (520) is thermally 

associated with the hot leg side of the heat exchanger tube bundle, and also with the cold side of 

the riser through the divider plate. In those secondary volumes where the heat exchanger tubes 

are led through (510, 520, and 530) the “bundle friction” option is applied. The steam drum, the 

dryer, and the steam dome are modeled with 2 volumes (560 and 570) at the top of the SG. In 

fact, (570) is a branch component and its exit junction is connected to steam line. The upper part 

of the outer DC (545) appears both on the left and right sides of the nodalization.

3.4.2 The Feedwater and Steam Lines

The nodalization scheme of the entire secondary side is shown in Figure 34. The boundary 

conditions for the normal FW are set in a time dependent volume (581). Distribution of the FW 

takes place in a branch component (854). The normal FW line consists of a control valve (862, 

872, and 882) and an isolation valve (864, 874, and 884), respectively in each loop. The auxiliary 

FW is taken from the boundary volumes (891, 893, and 895). The flowrate of the injected auxiliary 

FW is controlled by time dependent junctions (892, 894, and 896).

The steam line is split into 2 parts (x85 and x95), each partitioned to 10 volumes. “X” is again 

associated with the loop number, i.e. x = 5, 6, and 7 mean loops 1, 2, and 3, respectively. The 

main steam isolation valve (x94) is connecting the 2 parts together. Relatively high resolution of 

meshing was chosen in order to capture propagation of pressure pulses along the steam lines. 

Altogether 6 safety valves (x86...x91) and a relief valve (x92) are connected to the steam line, in 

parallel with each other. The steam lines are merging at a branch component (800). The Ringhals4 unit has 2 turbines and 4 turbine dumps. These components are modeled in a simplified way in 

the current RELAP5 model. Turbine 1 and 2, and their control valves are simulated with time 

dependent junctions (814 and 824) and motor valves (813 and 823), respectively.
3-10

Figure 33 Nodalization Scheme of SG 1
3-11

Figure 34 Nodalization Scheme of the Entire Secondary Side
3-12

Figure 35 Fluid Conditions in the SG by the SNAP Visualization Vool
3-13

Figure 36 Void Fractions in the SG by the SNAP Visualization Tool

4-1

4. STEADY-STATE RESULTS

It is essentially important that a numerical simulation should reach perfect steady-state before 

initiating a transient calculation. However, looking at the measured plant data, this goal seems to 

be theoretical because even in the most stable and normal operation of a plant, in fact, it is in a 

“quasi-steady-state” condition. Consequently, the term “steady” can mean minor oscillations 

around a setpoint value.

4.1 Energy and Mass Balance Calculation

Exact calorimetric details of the thermal power were not available from the plant at the time of the 

simulations. One of the possible approaches to determine a consistent dataset is to make an 

estimate, using averaged data over the measured stable period of time. This “hand-calculated” 

dataset can satisfy the energy and mass balance equations, which will be entered to the RELAP5 

input as initial conditions.

The balance calculations help also to determine those parameters that are not directly available 

from the measure database. For instance, the primary loop flowrate is recorded as percentage of 

the nominal flow but the reference (i.e. 100 %) value is not known. Still, it is necessary to enter 

the flowrate data in SI units (kg/s) into the RELAP5 input.

Knowing the flowrate mFW , temperature TFW , and pressure pFW of the feedwater, the enthalpy

hFW can be determined. With assumption of saturated steam (xsteam = 1) the enthalpy of the steam 

hsteam can also be determined. With neglecting the small amount of blowdown steam and 

averaging of the flowrates, the thermal energy QSG,sec of the steam generators can be calculated.

By taking into account the considerations above, the following, reasonably simplified balance 

equations can be set up:

4.1.1 Balance Equations of the Secondary Side

6

6

,sec

3

,sec,

1

524.57 kg/s

T 480.92 K

70.0 bar

h 0.889723 10 J/kg

518.17 kg/s

64.31 bar

x 1

h 2.7797 10 J/kg

521.37 kg/s 2

( ) 985.377 MW

3

FW

FW

FW

FW

steam

steam

steam

steam

FW steam

SG steam FW

SG i

i

m

p

m

p

h

m m

m

Q mh h

Q N

=

=

=

=

= ⋅

=

=

=

= = ⋅ ′′

+ = =

= −=

∑ = ⋅





  



SG = 2956.132 MW
4-2

4.1.2 Balance Equations of the Primary Side

With assumption of the PRZ pressure pPRZ to be the primary system pressure, and knowing the 

temperatures of the hot leg THL and of the cold leg TCL, the enthalpy difference Δh can be 

determined. Neglecting the losses of heat transfer between the primary and secondary sides, as 

well as the additional heat generated by the main circulation pumps, we can calculate the loop 

flowrate mloop from the SG thermal energy QSG, according to the following simplified equations:

6

6

6

,

6

, ,sec

6

,

6

154.99 bar

593.68 K

556.51 K

1.45632 10 J/kg

1.24997 10 J/kg

0.20635 10 J/kg

385.377 10 W

985.377 10 W

0.20635 10 J/kg

477

PRZ

HL

CL

HL

CL

HL CL

SG prim loop

SG prim SG

SG prim

loop

loop

p

T

T

h

h

hh h

Q mh

Q Q

Q

m

h

m

=

=

=

= ⋅

= ⋅

∆= − = ⋅

= ∆

= = ⋅

⋅ = = ∆ ⋅

=





3

,

1

5.27 kg/s

3 14 325.81 kg/s total loop i loop

i

mm m =

  = =⋅ = ∑

4.1.3 Strategies to Reach Steady-State

As in any numerical plant analysis, the basic assumption is that the unit is operating under steadystate before moving out from stable conditions. Therefore, it is essential to provide a set of proper 

initial conditions prior to the transient initiation. This aim can be achieved by running the code 

long enough, while the control systems are actuated and converging the system to a sufficiently 

stable condition. This method is in accordance with the procedure suggested by the code User 

Guidelines, instead of using the “steady-state” option of the input, which may result in premature 

termination of the run.

The following strategies have been applied:

• The core heating power (2956.1 MW) is kept constant by the user-given heat source data 

in a fuel bundle. Control variable 001 specifies this boundary condition (BC).

• For maintaining the primary system pressure (Figure 37) close to the setpoint value, the 

PRZ pressure control system is driven by a control signal (Figure 39), the same way as in 

the plant: i.e. by spraying of coolant taken from the cold legs or heating the system up by 

the proportional heaters (Figure 40).

• The desired primary side level (Figure 38) is achieved by controlling the PRZ level control 

system. Charging of the coolant (Figure 41) is provided from the chemical and volume 

control system (CVCS). The PRZ level program is always a function of the actual average 

loop temperature (Figure 42).

• The temperatures in the hot leg (Figure 43) and cold leg (Figure 44) are not controlled. 

These are derived quantities in the code calculation.

• Concerning the primary side loop flowrate, the pump speed is controlled by monitoring the 
4-3

difference between the actual loop flowrate and the prescribed value. The pump rotation 

is adjusted by a PI controller accordingly.

• On the secondary side, the SG level control system is regulating the feedwater flowrate 

(Figure 45) and steam flowrate (Figure 46) in order to keep the SG level (Figure 47) at the 

necessary elevation. Deviations between the feedwater flows and the steam flows are 

sensed, and the level is compared to the actual setpoint value, which is a function of the 

reactor power. The feedwater control valve (FCV) is then actuated by modifying its crosssectional area for injection of the appropriate amount of feedwater.

• The secondary side pressure (Figure 48) is given by a constant boundary condition. The 

turbine model is a simplified time dependent volume with a pressure boundary.

The parameters of the steady-state case are summarized in Table 1. Deviations of the achieved

values from the desired ones are very small. Therefore, it can be concluded that the plant 

parameters have converged to a stable condition, which satisfies the expected heat balance 

between the primary and secondary sides.

Plots of the initial search run are shown in Figure 37 ... Figure 48. 

Table 1 Parameters at the End of the Steady-State Run

Parameter Unit Desired Achieved

Diff.

[%]

Parameter

in RELAP

Reactor power MWth 2956.1 2956.1 0.0000 cntrlvar-001 (BC)

Primary pressure bar 154.99 154.998 0.0052 p-435120000

PRZ level % 41.94 42.33 0.9213 cntrlvar-430

PRZ charging flow kg/s 5.6011 5.5981 0.0536 mflowj-451000000

PRZ prop. heater % 53.14 54.02 1.6560 cntrlvar-411

Hot leg temperature K 593.68 593.67 0.0017 tempf-120010000

Cold leg temperature K 556.51 556.42 0.0162 tempf-140010000

Average temperature oC 301.94 301.98 0.0132 cntrlvar-434

Loop mass flowrate kg/s 4775.27 4772.56 0.0568 mflowj-180010000

Feedwater flowrate kg/s 521.37 519.32 0.3932 mflowj-868000000

Steam flowrate kg/s 521.37 519.39 0.3798 mflowj-594000000

SG level % 66.71 66.71 0.0000 cntrlvar-502

SG pressure bar 64.31 64.40 0.1399 p-570010000
4-4

4.2 Plots of the Steady-State Convergence

Figure 37 Pressure in the Pressurizer

Figure 38 Collapsed Level in the Pressurizer
4-5

Figure 39 PRZ Pressure Control Signal

Figure 40 PRZ Proportional Heater Signal
4-6

Figure 41 Charging Flowrate of the PRZ

Figure 42 Average Temperature in the Loop
4-7

Figure 43 Temperature in the Hot Leg

Figure 44 Temperature in the Cold Leg
4-8

Figure 45 Feedwater Flowrate to the SG

Figure 46 Steam Flowrate from SG
4-9

Figure 47 Narrow Range Level in the SG

Figure 48 Pressure in the SG

5-1

5. ANALYSIS OF THE TRANSIENT

5.1 Boundary Conditions

In many computer code calculations attempting to simulate full-plant transients it is obvious that 

some parameters are not available due to lacking measurement, documentation, or inaccessible 

information. In some cases, this shortcoming can be bypassed with derivation of the missing data 

from other known variables. In a few calculations, it is enough to approximate unavailable data 

with constants or simple functions. Applications of boundary conditions are natural parts of the 

transient simulations, and this approach is discussed in the following paragraphs.

5.1.1 Heat Source Boundary Condition

It is important to emphasize that the simulation in the current study used a so called stand-alone

model of Ringhals 4. It means that only the thermal-hydraulic features of RELAP5 were applied, 

without any internal neutronic feedback or without coupling to an external neutronic code, such 

as PARCS. (There are intentions to prepare a neutron kinetic model of Unit 4 in the future). This 

fact has put some limitation on the present analysis because it was not possible to take the minor 

power changes into account, which were originating from control rod movements. Note that with 

changing coolant temperatures, the density, the moderation, and the power are also changing. 

These effects were interacting with the power control and the rod drive mechanism, which was 

not modeled in this stand-alone simulation. Nevertheless, the core heating power is also in strong 

correlation with the temperature difference (ΔT) of the loop (Figure 49), and both the hot leg 

temperature and cold leg temperature were measured quantities. Consequently, the thermal 

power was approximated with a user-given input, based on the loop ΔT, as an estimation. The 

normalized heat source is shown in Figure 50, with respect to 2956.13 MW.

5.1.2 Turbine Pressure Boundary Condition

As it has been mentioned before, the secondary side model of Ringhals 4 is not a closed loop as 

it is in the plant. A real turbine is far too complex to model in the present analysis. Therefore, the 

components between the turbine and the feedwater pump are modeled in a simplified manner. 

The turbine is replaced with a pressure boundary condition, assuming saturated steam and 

pressure, according to the curve in Figure 51.

5.1.3 Turbine Control Valve Opening Boundary Condition

Features of the turbine control valve (TCV), such as opening vs. stem position, are not known. In 

fact, throttling of the turbine is driven by a very sophisticated mechanism. Adequate modeling of 

the TCV and the related controls are beyond the scope of the present study. For achievement of 

proper conditions, position of the TCV was assumed according to the curve in Figure 52.

5.1.4 Feedwater Temperature Boundary Condition

Temperature of the feedwater is always a function of the actual load. Due to the simplifications 

mentioned before, the turbine discharges and the feedwater pre-heaters are not part of the current 

model. Consequently, temperature of the feedwater is provided for the input with a boundary 

condition. The time function of the temperature is depicted in Figure 53.
5-2

Figure 49 Temperature Difference in the Loop

Figure 50 Normalized Thermal Power as a Boundary Condition
5-3

Figure 51 Turbine Pressure as a Boundary Condition

Figure 52 Turbine Control Valve Position as a Boundary Condition
5-4

Figure 53 Feedwater Temperature as a Boundary Condition

5.2 Discussion of the Transient Results

Calculation of the transient began with restarting the simulation from the end point of the steadystate run. In the transient input, the “reset” option was used on card number 100 and restart 

number of “-1” was given on card number 103. The SSDTT flag was set to “00032” on card 201.

The main characteristic periods of the transient can be observed in the calculation, namely:

1. Stable operation at high power

2. Power reduction

3. Operation at reduced power

4. Power increase

5. Operation at restored power

The first period of stable operation is basically an extension of steady-state. At approx. 333 s, the 

instant power reduction resulted in a large peak, followed by a sudden fall of the PRZ pressure 

(Figure 54). The control system of the PRZ generates a signal from the setpoint deviation. The 

signal shown in Figure 55 drives the opening of pressurizer spray valve, the power of the 

proportional heaters, and the on/off heaters. The magnitude of pressure changes first deactivated 

the PRZ proportional heaters (Figure 56) temporarily reaching zero power. Soon after that, the 

sudden pressure increase triggered the PRZ spray system (Figure 57) for a few seconds. 

Simultaneously, the proportional heaters became powered at their maximal capacity. A peak was 

experienced in the PRZ level (Figure 58) during the power reduction. While the primary system

level was modeled with good accuracy, the charging flowrate (Figure 59) showed larger deviations

limited to the period of power changes. This discrepancy is discussed further in section 5.4.

Concerning the coolant temperatures, a similar behavior can be observed. The loop average 

temperature (Figure 60, note in [

o

C]) and the cold leg temperature (Figure 62) show higher peaks, 
5-5

while the hot leg temperature (Figure 61) increase is almost negligible. With respect to the fluid 

temperatures, a general trend of slow decrease characterizes the quasi-steady period at reduced 

power.

When the power was suddenly restored, the PRZ parameters reacted the opposite way, 

compared to the up-step. A large negative peak was followed by a surge in the pressure within a 

few tens of seconds. Just before 4000 s of transient time, the low PRZ pressure required 

energizing of the proportional heaters. This had an immediate effect on the primary side pressure 

and activation of the spray system became necessary. Injection of cold water by the spray system 

was maintained for ~250 s, which brought the PRZ pressure constantly down until the end of the 

transient.

On the secondary side, the pressures measured in the SG steam dome (Figure 63) and in the 

steam line are very well simulated by the code, though the latter is somewhat underestimated. 

This indicates that sources of pressure losses (such as the flow restrictor or the main steam 

isolation valve) have to be carefully examined and adjusted.

While the feedwater flowrate (Figure 64) is almost perfectly calculated, the corresponding steam 

flowrate (Figure 65) is a bit higher than the measured value. This can be explained by the fact 

that the “missing” few kg/s is nearly the same amount as a blow-down, which is extracted from 

the secondary system for purification. Since the blow-down discharge is not part of the model, the

real mass flows are accurately calculated by the code. 

Large peaks are often present in many numerical simulations. In some cases these are not 

realistic, or at least their sources are unknown. Such peaks can be observed both in the calculated 

flowrates of feedwater and steam. This phenomenon may be a consequence of a sudden closure 

or opening of a valve. Alternatively, it can be attributed to the derivative component of the modeled 

SG feed control system, which is reacting to large instant changes in such a way. Further 

investigations are necessary on this issue.

Another parameter, the SG level (Figure 66) is a good indicator for good simulation of the mass 

balance in the secondary side. The simulated narrow range SG level follows very well the 

dynamical changes of measured level. This is an evidence for properly designed and wellfunctioning model of the SG level control system.

It has to be noted that most of the measured signals contained high level of noise, making the 

comparison very difficult. For reduction of the measurement noise in the previous plots, the 

Savitzky-Golay filtering algorithm was applied with using MATLAB. The unfiltered, raw test data 

were plotted in Chapter 2 of this document.
5-6

5.3 Plots of the Transient Calculation

Figure 54 Pressure in the PRZ

Figure 55 PRZ Pressure Control Signal
5-7

Figure 56 PRZ Proportional Heater Signal

Figure 57 PRZ Spray Valve Lift with Zooming on a Large Peak at ~345 s
5-8

Figure 58 Level in the PRZ

Figure 59 PRZ Charging Flowrate
5-9

Figure 60 Loop Average Temperature

Figure 61 Hot Leg Temperature
5-10

Figure 62 Cold Leg Temperature

Figure 63 Pressure in the SG
5-11

Figure 64 Feedwater Flowrate

Figure 65 Steam Flowrate
5-12

Figure 66 Narrow Range Level in the SG

5.4 Modeling Problems with the PRZ Level and the Charging Flow

As it was shown in Figure 58, the code managed to simulate the PRZ level with a good accuracy. 

However, this was achieved with much lower charging flowrate during the down-step of the power 

and on the contrary, with overestimated charging flow during the power up-step (Figure 59). No 

explanation has been found, yet for such a behavior. In particular, it is interesting that the 

necessary charging flow is simulated quite well in the other periods of the transient.

Another mismatch was detected in connection to the PRZ. As it can be clearly recognized in 

Figure 67, the actual measured levels are scattered within a bounding range of more than 1.5 %. 

Most likely, these signals (40313LT-459, 40313LT-460, and 40313LT-461) were calibrated 

purposely in such a way. However, the signal of the desired setpoint level (i.e. the “level program”, 

which is a function of the loop average temperature) is always out of measured bounding range. 

The value determined by the level program is practically less than the lowest measured signal of 

40313LT-460. This phenomenon caused difficulties in proper modeling of the PRZ level.

Mismatching between the level setpoint and the actual levels is further confirmed in Figure 68. It 

can be observed that the lowest measured level signal (40313LT-460) shows the strongest 

correlation with the setpoint value documented in the PLS. However, even this relatively good 

correlation is limited to a small range of loop average temperatures. Consequently, the modeled 

control system may struggle to find the correct level setpoint for the PRZ. This is affecting the 

amount of charging water to be injected into the primary system. As a future activity, this 

phenomenon will be investigated and improved at a later stage of the R4 RELAP5 model 

development.
5-13

Figure 67 Actual and Desired Levels in the PRZ

Figure 68 Measured Levels and the Setpoint vs. Loop Average Temperature
5-14

5.5 Run Statistics

In a numerical simulation of a transient, it is always important to have information about the 

stability and smoothness of the calculation. The two plots in Figure 69 describe the relationship 

between the actual time step and the Courant-limit time step. The former one is practically 

constant (0.025 s), which is the same as the requested time step. The latter one is nearly constant, 

and it is just slightly higher than the actual time step. The fact, that the actually used time step is 

never reduced, it indicates that the calculation is running smoothly. On the other hand, the two 

time steps values were very close to each other. Consequently, the calculation was performed 

quite “economically” because the requested time step was set to just 0.002 s less than the value 

allowed by the Courant-limit. The initial reduction of the time step is due to resetting from the endpoint of the steady-state. The final reduction is a consequence of the requested termination of the 

run exactly at 4500 s, resulting in a shortened time step.

Figure 69 Actual and Courant Limit Time Steps

The calculations were performed on a computer with a 3.5 GHz 4 cores Intel i7 4770K processor

and 32 GB RAM running Ubuntu version of Linux. The total consumed CPU time was 3167 s for 

altogether 300121 attempted advancements. The ratio between the CPU time and the transient 

time is 3167 s / 4500 s = 0.7038.
6-1

6. QUANTIFICATION OF SIMULATION ACCURACY

6.1 Fast Fourier Transform Based Method (FFTBM) Analysis

Fast Fourier Transform Based Method (FFTBM) is a method used for the quantification of 

“goodness” both for a particular variable prediction and overall model predictions. The basis of 

FFTBM is the calculation of the relative error between calculated and measured (test) data in the 

frequency domain. Thus, FFTBM can become a very useful aid on the search of discrepancy 

sources. In addition it can be used as an aid to tackle practical issues related with the models 

used, such as the fidelity of the nodalization needed, margin for simplifications or further 

improvements, etc. [14].

For the FFTBM analysis JSI FFTBM Add-in 2007 is used. It is an Excel-2007 add-in developed 

by Jožef Stefan Institute in Ljubljana by Dr. Andrej Prošek.

6.1.1 Average Amplitude

Average Amplitude (AAAA) is the basic measure used for FFTBM analysis. Supposing that the 

difference between the calculated FFcccccc(tt) signal and the experimental one FFeeeeee(tt) reads in the 

time domain as:

ΔΔFF = FFcccccc(tt) − FFeeeeee(tt),

then the average amplitude AAAA is calculated as:

AAAA = ∑ |ΔΔ̃FF(ffnn)| 2mm

nn=0

∑ |FF�

eeeeee(ffnn)| 2mm

nn=0

,

where ΔΔ̃FF(ffnn) and FF�

eeeeee(ffnn) the discrete Fourier transformation of ΔΔFF and FFeeeeee as calculated by 

FFT algorithm respectively. Average amplitude could be interpreted as an integral measure that 

keeps track of the relative magnitude of the discrepancy between the experimental and calculated 

variable over a time interval.

The following statements can be made for variables predictions based on average amplitude:

• AAAA ≤ 0.3 corresponds to very good variable prediction.

• 0.3 < AAAA ≤ 0.5 corresponds to good variable prediction.

• 0.5 < AAAA ≤ 0.7 corresponds to poor variable prediction.

• AAAA > 0.7 corresponds to very poor variable prediction.

This criterion refers to one variable. However, it is often needed to assess the overall prediction 

capability of a model based on NNvv vv number of variables. Thus, the total average amplitude AAAAtttttt

for all of the variables of interest can be computed as:

AAAAtttttt = �(wwff)ii · AAAAii

NNvvvvvv

ii=1

,
6-2

where (wwff)ii the (normalized) weighting factor of the ii − tth variable of interest. The selection of 

weighting factors is a matter of subjective engineering judgment and should be specified for the 

transient of interest. The AAAA criterion mentioned above can be applied for AAAAtttttt to assess the 

overall prediction “goodness” of the model.

6.1.2 Additional Measures for Accuracy Quantification

The following additional measures can assist the accuracy quantification within the FFTBM 

context:

• variable accuracy VV ii, ii = 1, 2, ... , NNvv vv

• minimal and maximal variable accuracy VV mm and VV mm

• number of discrepancies NNNN

Variable accuracy VV ii of the ii − tth variable of interest shows what the total average amplitude 

AAAAtttttt would be if the rest of the chosen variables all have the same weighting factor (wwff)ii and 

average amplitude AAAAii. Therefore, it is designated as:

VV ii = AAAAii ∙ (wwff)ii ∙ NNvv vv

It should be mentioned that the criterion for AAAA is applicable for VV ii too. Minimal variable accuracy 

VV mm and maximal variable accuracy VV mm indicate the minimum and the maximum variable 

accuracy among the accuracy amplitudes AAAAii, ii = 1, ... , NNvv vv of the NNvv vv chosen variables. 

Consequently, they are defined as:

VV mm = max{VV ii}, ii = 1, ... , NNvv vv

and

VV mm = min{VV ii}, ii = 1, ... , NNvv vv.

Minimal variable accuracy VV mm is used to define the number of discrepancies NN . It is accepted 

that the acceptability limit for a calculation is 0.4 and thus, AAAAtttttt < 0.4. Hence, the number of 

discrepancies NNNN is equal with the number of variables for which VV ii > 0.4. It is obvious that 

NNNN = 0 when VV mm < 0.4. It should be mentioned that a prerequisite for the application of 

FFTBM is that the average amplitude of the primary pressure is AAAA < 0.1 due to the significant 

influence of this variable in the system.

6.1.3 Signal Mirroring

Discrete calculated and discrete experimental signals are mirrored in the time domain in order to 

avoid an inherent weakness of the original FFTBM method that produced unphysical AAAA results 

[15]. AAAA ( AAAAii oooo AAAAtttttt) should exhibit an overall increasing monotonous trend with increasing 

time window, since it is an integral discrepancy measure throughout the increasing time window 

interval. Consequently as time window increases, addition of discrepancies of the newly added 

time slots occur, which is why AAAA should monotonically increase. However this does not happen 

when the last and the first point of the discrete signal differ significantly. FFT multiplies the discrete 

signal so as to create a periodic infinite signal. As a result, any difference between the first sample 

of each period with the last sample of the previous period increases the frequency content of AAAA, 

distorting it significantly.

6.1.4 FFTBM Analysis Methodology

The transient is divided in phenomenological windows for which the relevant thermal-hydraulic 
6-3

aspects (RTA) are identified. Variables that best describe the RTA are chosen. Then the weighting 

factors of the variables are set. Average amplitude AAAAii for each of the chosen variables as well 

as the total average amplitude AAAAtttttt are calculated using the increasing time window approach. 

In increasing time window approach the transient is divided in equal and successive time slots. 

Increasing time windows are then constructed by addition of successive time slots so that the first 

time window corresponds to the first time slot, the second time window to the addition of the two 

first time slots etc. Hence, the last time window corresponds to the whole duration of the transient. 

AAAAii for ii = 1, ... , NNvv and AAAAtttttt are calculated for each time window and plotted as function of

time [16]. This time window approach allows better tracking of the evolution of AAAAii or AAAAtttttt, 

especially for transients with few phenomenological windows.

The transient is separated in five phenomenological windows same as it was described in the 

previous sections. Since the purpose of the Load Step Test is, among others, to check the ability 

of the control systems to mitigate the transient, selection of variables and their weighting factors 

takes place accordingly. Hence, 20 variables were chosen (Table 2) that are descriptive also for

the most important RTAs. Most of them appear as inputs or outputs in the modelled PRZ level 

and pressure controllers, as well as in SG level controller. 

Concerning the selection of weighting factors, a scale between 0 and 4 is used to assess the 

importance of the selected variables. Input variables of the controllers are assigned to a 

significance factor of 4. Variables appearing as controller outputs are assigned to a significance 

factor of 3 and the rest of the selected variables to a significance factor of 2. Then the significance 

factors are normalized (so that their summation equals one). For the FFTBM calculations 15 

increasing time windows are considered with 300 s increments.

6.2 Results of the FFTBM Analysis

Evolution of each variable of average amplitude as function of time and in addition, of the total 

average amplitude, are presented in the following figures. The average amplitude and variable 

accuracy results for the last time window, 0 - 4500 s, representative of the whole transient, are 

presented in Table 2.

It can be observed in Figure 71 - Figure 79 that jumps of average amplitudes occur in most of the 

variables, as well as in total average amplitude, during the second increasing time window of 

0 – 600 s. This time window includes the sudden power decrease phase of the transient. 

However, such a significant average amplitude variations could not be observed in the increasing 

time window including the power increase phase. Thus, it seems that the model performs better 

after the step of power reduction.

As Table 2 and Figure 80 indicate, the total average amplitude is below 0.3. Consequently, the 

overall model predictions can be characterized as “very good”. Furthermore, it can be seen that 

the first 14 variables have average amplitude below 0.3 and their predictions can be marked as 

“very good”. Among those 14 variables, 11 are static quantities, such as pressures, temperatures 

and PRZ/SG collapsed levels, which have average amplitude equal or below 0.1. This

demonstrates an excellent ability of the code to predict static variables. For the rest of the 

variables, comprising of steam mass flowrates, charging flowrate and spraying control signal, the 

average amplitudes remain under the acceptability limit 0.4, and their predictions can be marked 

as “good”, except the charging flowrate.

Table 2 Variables, Weighting Factors and Results of the 0-4500 s Interval

No. Variable 0 – 4500 s

wf AA VA
6-4

1 Primary pressure 0.06 0.017848 0.019831

2 Level in PRZ 0.06 0.090816 0.100907

3 Pressure in SG-1 0.03 0.024022 0.013345

4 Pressure in SG-2 0.03 0.027866 0.015481

5 Pressure in SG-3 0.03 0.026025 0.014458

6 Level in SG-1 0.06 0.089762 0.099736

7 Level in SG-2 0.06 0.096436 0.107151

8 Level in SG-3 0.06 0.093780 0.104200

9 Average temp. in loop-1 0.06 0.007577 0.008419

10 Average temp. in loop-2 0.06 0.007702 0.008557

11 Average temp. in loop-3 0.06 0.007964 0.008849

12 Feedwater flow in SG-1 0.06 0.263144 0.292382

13 Feedwater flow in SG-2 0.06 0.250198 0.277998

14 Feedwater flow in SG-3 0.06 0.266469 0.296077

15 Spraying control signal 0.04 0.495459 0.412882

16 Steam line-1 flow-rate 0.06 0.316915 0.352128

17 Steam line-2 flow-rate 0.06 0.363501 0.403890

18 Steam line-3 flow-rate 0.06 0.335377 0.372641

19 Charging flow-rate 0.06 1.050899 1.167666

20 Proportional heaters capacity 0.04 0.356188 0.296824

Total 0.22

Charging flowrate is the only variable that is very poorly predicted which consolidates the 

suspicions about the PRZ level controller. The spraying output signal lies in the “good” prediction 

margin but above the acceptability limit. The level and the pressure in the PRZ and as a result 

the amount of spraying, are affected by the quantity of the water injected in the primary side and 

thus, by the PRZ level controller.

Looking at the VV data column of Table 2, it can be observed that the variable accuracies of 17 

among the 20 chosen variables have variable accuracies below the acceptability limit, 15 of which 

exhibit VV < 0.3. Thus it also reflects the good quality and maturity of the model. The number of 

discrepancies NNNN in most of increasing time windows is equal to 2, mostly due to charging flow 

and secondly due to the spraying control signal. In the time window of 0 - 3000 s and beyond,

NNNN = 3 due to the two variables mentioned above plus the steam flowrate in loop-2.

It is worth mentioning that the predictions of steam flows are considered “good” (AAAA < 0.4) but 

they can be further improved. The plant operators admit that the pressure losses in the steam line 

is greater than they expected. Thus, improvement of this factor should improve the agreement

between measured and calculated steam flows which will culminate in the steam flows average 

amplitudes to become less than 0.3.

To conclude, the overall code predictions are very good as indicated by the total average 

amplitude diagram (AAAAtttttt < 0.3 throughout the duration of the transient) and the code can be

characterized as very reliable and of high quality. Nonetheless, there is still a margin for 

improvements, especially regarding the modeled PRZ level controllers.
6-5

Figure 70 AA of Feedwater Flowrate Figure 71 AA of Steam Flowrate

Figure 72 AA of SG Pressure Figure 73 AA of SG Level

Figure 74 AA of PRZ Pressure Figure 75 AA of PRZ Level

Figure 76 AA of Average Temperature Figure 77 AA of PRZ Prop. Heater Signal
6-6

Figure 78 AA of PRZ Spray Signal Figure 79 AA of Charging Flow

Figure 80 Total Average Accuracy
7-1

7. CONCLUSIONS

An important stage of the R4 model development process has been summarized in the current 

study. Incorporation of the new components (i.e. the AREVA design SGs and the PRZ) into the 

full plant model was a challenging task and this was the second opportunity to validate the new 

model against a startup test. Prior experiences with the prototype geometries could be utilized in 

the present Report.

On the basis of the presented steady-state and transient results, it can be concluded that the 

over-all performance of the R4 RELAP5 model is good. The general trends during the 5 

distinguishable parts of the transient were well predicted by the code. Quantitative matching of 

the parameters was satisfactory, which resulted in a successful validation of the model, as well 

as the code. The primary to secondary side energy transfer was sufficiently well simulated. The 

Ringhals 4 model is suitable for analysis of other types of transients already in its current state of 

development.

However, as always, there is a margin for improvement. For instance, application of FFTBM tool 

has revealed that characteristics of some control valves need to be obtained and examined 

because this is a critical parameter, which is influencing the general behavior of the transients.

The calculated charging flow showed the largest deviations during the sudden power changes. 

This can be partly attributed to the problematic level program of the PRZ.

8-1

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NUREG/IA

-0468 Validation of RELAP5 Model of Ringhals 4 Against a Load Step 

Test at Uprated Power