Konvoi PWR Core Model with TRACE and

“Learn to solve every problem that has been solved.”

Richard Feynman

´ UNIVERSIDAD POLITECNICA DE MADRID

Abstract Konvoi PWR Core Model with TRACE and SUBCHANFLOW. Coupling Analysis ´ ndez by Iván Ferna

The analysis of the thermal hydraulic core behaviour of PWR is traditionally performed with one dimensional or three-dimensional best-estimate system codes like RELAP5, ATHLET or CATHARE-3D and TRACE, respectively. These codes use either 1D or 3D coarse spatial meshes to represent the flow conditions within the core. The analysed PWR core consists of 193 fuel assemblies where each fuel assembly represents a group of around 300 fuel rods (pin arrangement 18×18−24) that are located one close to another. Under certain flow conditions e.g. non-symmetrical thermal hydraulic core behaviour, the cross-flow between the fuel assemblies can be considerable. Contrary to system codes, subchannel codes such as SUBCHANFLOW (SCF ), COBRA-TF, FLICA, etc. are able to describe the axial flow but also the transversal flow under steady-state and transient conditions using physical sound models.

Hence, the coupling of system codes with subchannel codes is a necessary step to increase the prediction capability of the flow conditions within the core (subchannel code) taking into account the whole plant behaviour (system code). Such multi-scale thermal hydraulic solutions for nuclear power plants are being developed worldwide; also devoted to the coupling of CFD and with subchannel or system codes. For the time being, CFD simulations of PWR core at fuel rod level that facilitate the prediction of local safety parameters are too CPU-intensive and hence they are considered only in a long term perspective.

To assess the possibility of the coupling of TRACE with SCF, a PWR core will be analysed with these two codes and the obtained results compared to each other. The familiarization with these numerical tools, their numerical methods and programming structure will help to prospect their coupling as well as to identify the way of coupling.

SUBCHANFLOW, TRACE, PWR, coupling

Acknowledgements Muchas gracias a César Queral por aceptar ser mi tutor en este trabajo y guiarlo para que tenga un final feliz. A Javier Jiménez y Victor Hugo Sánchez por tratarme tan bien durante mi estancia en el KIT y ayudarme con los problemas que encontré en el modelado los inputs. A mi empresa NFQ Solutions, que me ha dado la posibilidad de realizar este master y disponer de tiempo para estudiar y, a mi compa˜ nero Javier Magán, por su ayuda con el manejo de SNAP.

iii

Contents Abstract

ii

Acknowledgements

iii

Contents

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List of Figures

vii

List of Tables

viii

Abbreviations

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1 Introduction 1.1 Thesis goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 3

2 TRACE and SUBCHANFLOW Overview 2.1 TRACE . . . . . . . . . . . . . . . . . . . . 2.1.1 Calculus Flow . . . . . . . . . . . . . 2.1.2 Solution Methods . . . . . . . . . . . 2.2 SUBCHANFLOW . . . . . . . . . . . . . . 2.2.1 Basic Conservation Equations . . . . 2.2.2 Numerical Solution Procedure . . . . 2.2.3 SCF Calculus Flow . . . . . . . . . .

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3 Reactor Description 10 3.1 General Reactor Information . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1.1 Fuel assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.2 Point Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4 Reactor Core Design 4.1 TRACE Model . . . . . . . . . . . . . . 4.1.1 PIPE Component . . . . . . . . 4.1.1.1 Friction Equations . . . 4.1.2 POWER Component . . . . . . . 4.1.2.1 Point-Reactor Kinetics 4.1.3 FILL Component . . . . . . . . . 4.1.4 BREAK Component . . . . . . . iv

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15 16 17 17 19 20 22 22

Contents

4.2

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4.1.5 Heat Structure HTSTR Component 4.1.6 Inlet and Outlet PIPE . . . . . . . . SUBCHANFLOW Model . . . . . . . . . . 4.2.1 Reactor Data . . . . . . . . . . . . 4.2.1.1 Correlations . . . . . . . . 4.2.2 Channel Layout . . . . . . . . . . . . 4.2.3 Rod layout . . . . . . . . . . . . . . 4.2.4 Point Kinetics . . . . . . . . . . . .

5 TRACE-SCF Model Comparison 5.1 Steady State . . . . . . . . . . . . . . . . . 5.1.1 SUBCHANFLOW . . . . . . . . . . 5.1.2 TRACE . . . . . . . . . . . . . . . . 5.1.3 Comparison . . . . . . . . . . . . . 5.2 Transients . . . . . . . . . . . . . . . . . . . 5.2.1 Decrease in Reactor Coolant Flow . 5.2.2 Reactor Coolant Temperature Drop 6 Coupling Overview 6.1 Previous Plant Code - Subchannel coupling 6.1.1 COBRA/TRAC . . . . . . . . . . . 6.1.2 MARS . . . . . . . . . . . . . . . . . 6.2 Coupling paradigms . . . . . . . . . . . . . 6.3 SUBCHANFLOW Coupling . . . . . . . . . 6.4 TRACE Coupling . . . . . . . . . . . . . . . 7 SCF-ECI-TRACE 7.1 TRACE 5 Patch 3 . . . . . . . . . . . . . 7.2 TRACE 5.0 ECI . . . . . . . . . . . . . . 7.2.1 Daemon . . . . . . . . . . . . . . . 7.3 A cuasi explicit option . . . . . . . . . . . 7.4 Benchmark model . . . . . . . . . . . . . 7.4.1 Results . . . . . . . . . . . . . . . 7.5 ECI . . . . . . . . . . . . . . . . . . . . . 7.5.1 Data needed . . . . . . . . . . . . 7.5.2 Calculus Flow . . . . . . . . . . . . 7.5.3 ECI Modules . . . . . . . . . . . . 7.5.4 ECI Process . . . . . . . . . . . . . 7.5.5 Mapping Variables TRACE - SCF 7.5.6 Mapping Variables SCF - TRACE 7.6 SCF-ECI Outlook . . . . . . . . . . . . . 7.6.1 Road Map . . . . . . . . . . . . . . 7.6.2 Main goals . . . . . . . . . . . . . 7.6.3 Limitations . . . . . . . . . . . . .

A TRACE Steady State

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57 57 58 59 59 61 62 62 63 65 67 69 70 78 80 81 83 83

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Contents

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B SCF Steady State Input

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C Mail NRC. Bug TRACE 5 Patch 3

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Bibliography

122

List of Figures 2.1 2.2

TRACE Calculus Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cooling Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1 3.2

GKN II Core Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Fuel Assembly Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1 4.2 4.3 4.4 4.5 4.6 4.7

Snap Core Representarion . . . . . . . . . . . . . . . . . . . . . . . Moody Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . Axial Power Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . Fuel rod radial nodalization . . . . . . . . . . . . . . . . . . . . . . Gnielinski and Dittus-Boelter correlations versus heat transfer data CASMO & HELIOS Linear Power . . . . . . . . . . . . . . . . . . PWR Coolant Reactivity Coefficient Curves . . . . . . . . . . . . .

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17 18 20 24 28 32 34

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14

Salome and SCF Representarion . . . . . . . . . . . . . . . Pressure Drop. Steady State . . . . . . . . . . . . . . . . . Axial Temperature. Steady State . . . . . . . . . . . . . . . Axial Coolant Velocity. Steady State . . . . . . . . . . . . . Coolant Flow Drop . . . . . . . . . . . . . . . . . . . . . . . Power during Coolant Flow Transient . . . . . . . . . . . . Reactivity during Flow Transient . . . . . . . . . . . . . . . Maximun Fuel Temperature during Flow Transient . . . . . Maximun Inner Rod Temperature during Flow Transient . . SCF Axial Void Fraction. Flow Transient . . . . . . . . . . Temperature Transient . . . . . . . . . . . . . . . . . . . . . Power during Temperature Transient . . . . . . . . . . . . . Reactivity during Temperature Transient . . . . . . . . . . Maximum Fuel Temperature during Temperature Transient

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39 40 40 41 42 43 43 44 44 45 46 46 47 47

6.1 6.2 6.3 6.4

Initial and Boundary Conditions Coupling Coupling Schemes . . . . . . . . . . . . . SCF-MCNP Explicit Coupling Scheme . SCF-DYNSUB Library Coupling . . . . .

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7.1 7.2 7.3 7.4

Slave Task Boundary Conditions . . . . . . . . . . TRACE Standalone vs. TRACE Two Tasks . . . ECI Data Transfer Scheme . . . . . . . . . . . . . SCF-ECI and TRACE-ECI basic schema . . . . . .

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5 8

List of Tables 3.1 3.2 3.3 3.4 3.5 3.6

General reactor data . . . Benchmark Specifications Fuel Assembly data . . . . Fuel Assembly Features . Doppler Coefficients . . . Feedback Coefficient . . .

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4.1 4.2 4.3

Core Flow Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Delayed-Neutron Constants . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Rod Geometrical Fuel Info . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.1 5.2 5.3

SCF Steady State Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 TRACE Steady State Results . . . . . . . . . . . . . . . . . . . . . . . . . 39 SCF vs. TRACE Steady Results . . . . . . . . . . . . . . . . . . . . . . . 40

7.1 7.2 7.3 7.4 7.6 7.7 7.8 7.9 7.10 7.5 7.11 7.12

ECI Input Transfers . . . . . . . . ECI Init Transfers . . . . . . . . . ECI Old Time Transfers . . . . . . ECI Control Transfers . . . . . . . ECI SemiEdg Transfers . . . . . . ECI SemiSave Transfers . . . . . . ECI Conduct Transfers . . . . . . . ECI StbVsave Transfers . . . . . . ECI End Step Transfers . . . . . . ECI StbVset Transfers . . . . . . . Global ECI Info Mapping . . . . . SCF Boundary conditions Mapping

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viii

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71 71 74 74 76 76 77 77 77 78 79 80

Abbreviations BWR

Boiling Water Reactor

CAMP

Code Applications and Maintenance Program

cDp

Coefficient of the Pressure difference at a defined junction

CFD

Computational Fluid Dynamics

CHF

Critical Heat Flux

CSN

Consejo de Seguridad Nuclear

DNB

Departure from Nucleate Boiling

ECI

External Component Interface

EOS

Equation-Of-State

FA

Fuel Assembly

FSAR

Final Safety Analysis Report

GCSM

General Control Simulation Module

HTSTR

Heat Structure

IAPWS-97

The International Association for the Properties of Water and Steam

INR

Institute for Neutron Physics and Reactor Technology

KAERI

Korea Advanced Energy Research Institute

KIT

Karlsruhe Institute of Technology

KWU

Kraftwerk Union

LBLOCA

Large Break Loss of Coolant Accident

LOCA

Loss of Coolant Accident

LWR

Light Water Reactor

MCNP

Monte Carlo Neutron Particle

NCG

Non Condensable Gas

NPP

Nuclear Power Plant

NRC

US Nuclear Regulatory Commission ix

Abbreviations

x

pcm

Percent millirho

PWR

Pressurized Water Reactor

SAFDL

Specified Acceptable Fuel Design Limit

SCAIS

System Code for an Integrated Safety Assessment

SCF

SUBCHANFLOW

SCFR

Supercritical Fast Reactor

SETS

stability-enhancing two-step method

SOR

successive over relaxation

Chapter 1

Introduction TRACE and SCF are codes with different goals, but both can be used to model a reactor core as the one selected during this research. Both codes are presented with its main capabilities and also some of the improvements that each one can add to the other in a full reactor application that is beyond this master project. During Chapter 3, the German PWR Konvoi Reactor “Neckarwestheim” (GKN II) is presented as the selected plant to perform the core model design. All data found needed to develop the inputs is added to a section of this work and ordered in the proper manner to deal with it as TRACE and SCF input data. Some of the information was provided due to previous work at Karlsruhe Institute of Technology KIT with GKN II, but most data was found while desktop research on the Internet. The documents with the information used are referenced in the bibliography at the end of this thesis. How to model a PWR core with a thermal hydraulic code as TRACE and with the subchannel code SCF is deeply explained during Chapter 4. The models have been developed making a comparison of the approaches used by each one, trying to use the same equations if possible in order to analyse the results in an easier way. Once both models are ready, the Steady State is compared and the results validated. The last step of the analysis is to simulate two transients;

• A Coolant Mass Flow Transient. A drop flow of 1/3rd of the inlet Mass Flow is considered and can be shown as a lose of one Feedback Pump.

1

Chapter 1. Introduction

2

• A Primary Coolant Temperature Transient. A 30K drop as the one simulated can happen for example in an inadvertent opening of a Steam Generator valve.

The results are shown to analyse how both codes behave with those typical transient. At this point of the work it is clear why coupling SCF to a plant model is needed, since otherwise, SCF only can simulate a transient at boundary conditions level losing the very valuable info of realimentation with a Plant Code. Also TRACE can take advantage of a detailed core model with an easier development and lower computational time as well as crossed flow between channels. However, the most important feaure that SCF includes is the posibility to describe not only the axial flow but also the transversal flow under Steady State and Transient conditions. The second part of the project (Chapters 6 and 7) is an analysis of the coupling between TRACE and SCF. It starts with an overview of the coupling capabilities of both codes and the different approaches that can be selected while coupling codes. Implicit, semiimplicit and explicit code coupling are discussed. The benefits of each type of coupling and also its limitations are presented, leading us to the best coupling paradigm needed to TRACE-SCF. The External Coupling Interface ECI of TRACE is introduced as the best option to couple it to SCF, due to its low level coupling capabilities in semi-implicit paradigm. Both codes were coupled by different techniques to other codes in order to develop methodologies studying a broad accident without taking care of the mapping of information needed between this codes, reduce uncertainties or errors associated with interface transfer and to improve the accuracy of calculation. During this research, a suitable benchmark model was designed and analysed both SCF and TRACE in standalone simulations to be the test case for a future coupling. This model is simple but real enough to evaluate the coupled capabilities. Results shown that both codes can simulate the phenomenology of a full reactor core at the modeled level, but the multiphysics of coupling will give us a system able to study a broader problem that neither TRACE nor SCF in standalone could represent.

Chapter 1. Introduction

1.1

3

Thesis goals

The objectives of this work are mainly;

• Develop TRACE and SCF input deck core models to the German PWR Konvoi Reactor Neckarwestheim (GKN II ), analyze its results for the Steady State calculation and after that, study both codes behaviour to realistic but simplified transients. • Coupling analysis of TRACE and SCF. The different types and dimensions of code coupling are reviewed and a proper strategy is designed. A simplified model has been developed and tested with TRACE-ECI and it is ready to be coupled to the future SCF-ECI. The road map agenda is also provided to estimate the work needed to accomplish the tasks.

Chapter 2

TRACE and SUBCHANFLOW Overview During this chapter, TRACE and SCF, the codes that this research is related, are presented. TRACE source code is available at KIT, through CAMP agreement with the U.S. Nuclear Regulatory Commission US NRC, making it accessible and modifiable. SCF was developed by the INR.

2.1

TRACE

TRACE is a reactor system code developed by the NRC for analysing plant behaviour in Light Water Reactors LWR. Its goal is to be the reference NRC code to Best Estimate Analysis. It merges four systems codes (TRAC-P, TRAC-B, RELAP5 and RAMONA) into one computational tool [1]. TRACE was designed to perform best-estimate analyses of loss-of-coolant accidents (LOCAs), operational transients, and other accident scenarios in pressurized light-water reactors. It can also model phenomena occurring in experimental facilities designed to simulate transients in reactor systems. Models used include multidimensional two-phase flow, nonequilibrium thermodynamics, generalized heat transfer, reflood, level tracking, and reactor kinetics.

4

Chapter 2. Overview

2.1.1

5

Calculus Flow

The fluid field equations used by TRACE to model two-phase flow, and the numerical approximations made to solve these equations starts with single phase Navier-Stokes equations in each phase, and jump conditions between the phases. Time averaging is applied to this combination of equations to obtain a useful set of two-fluid, two-phase conservation equations. TRACE uses this flow model in both one and three dimensions. The basic two-fluid, two-phase field equation set consists of separate mass, energy, and momentum conservations for the liquid and gas fields. This gives a starting point of six partial differential equations to model steam/water flows [1]. The solution of this equations and the approaches and assumptions are the basis of most thermal hydraulic codes and in the case of TRACE are broadly tested around the world due CAMP agreements between NRC and other institutions.

Figure 2.1: TRACE Calculus Flow

Chapter 2. Overview

2.1.2

6

Solution Methods

The two solution methods approximating the flow equations are based in semi-implicit and SETS ( 6.2) solutions. SETS solution allows the code to exceed the Courant Limit, and this fact makes TRACE the option to use smaller time steps than a semi-implicit one. The different approaches are detailed in Chapter 6. At first it solves the 1D Stabilizer Motion Equations solving a matrix to find the velocities. In the next step it solves the SETS Semi-Implicit, that is equivalent to the pure semi-implicit solution for velocities, mass and energy. During the final step the new-time velocities are calculated and can be treated as constants in the equation solutions. Solving the stabilizer mass and energy equations provides new values only for macroscopic densities and macroscopic energy densities. During code modernisation, TRACE was rewritten in Fortran 90 language. This change was absolutely necessary to achieve an extensible and modular code, since the old Fortran 77 cannot handle with dynamic data structures. Also developers though that in the future, there will be needs to couple TRACE with codes simulating other components or improving its models to simulate a multiphysic model. For this reason, TRACE calculus flow was structured to be able to interchange information with other components in some determined points. The Exterior Communication Interface ECI [2] is a set of modules that belongs to TRACE kernel, designed to communicate with external codes, but also thought as a generic flow connection driver transferring data at SETS synchronization points. The message passing is carried out by sockets or shared memory if process is split using the ECI. This interface seems to be the most natural way to couple TRACE with SCF, and during this work, this coupling, as well as other options, will be analysed.

2.2

SUBCHANFLOW

SCF [3] [4] is a computer code to analyze thermal-hydraulic phenomena in the core of PWR, BWR and innovative reactors operated with gas or liquid metal as coolant. It can handle both rectangular and hexagonal fuel bundles and core geometries. As boundary conditions, the total flow rate or a channel-dependent flow rate can be selected.

Chapter 2. Overview

7

It is possible to distribute the flow automatically to the parallel channels depending on the friction at the bundle inlet. In addition, a pure top-bottom pressure difference boundary can be applied for steady-state calculations. Fluid temperature at the inlet and pressure at the outlet are always needed as its boundary conditions. Modern coolant properties and state functions are implemented for water using the IAPWS-97 formulation. Also property functions for liquid metals (sodium and lead) and gases (helium and air) are available. An iterative steady-state numerical procedure is available to determine the power at which critical heat flux conditions appear during the simulation. SCF uses many empirical correlations for pressure drop, heat transfer coefficients, void generation, etc. The ones selected during this Thesis, as well as others available in the code, are explained during Chapter 4. A three-equation two-phase flow model that is a mixture equation for mass, momentum, and energy balance is implemented. The constitutive relations are expressed as mixture equations for wall friction and wall heat flux as well as a slip velocity relation. In addition, user defined empirical correlations can be implemented.

2.2.1

Basic Conservation Equations

In subchannel codes, a channel consists of a finite fraction of the total cross-sectional area of the nuclear reactor core region. The smallest possible channel would be the size of a subchannel surrounded by the fuel rods. 2.2 Transport of mass, momentum, and energy is possible along the axial direction and between the neighboring channels through the gap formed by the fuel rods. The basic transport equations are based on the Euler approach including friction at solid surfaces. In the lateral momentum equation, the convective transport of lateral momentum is neglected because the friction term dominates the cross-flow. In the energy equation, the heat flux from the rod surfaces is the main source term. For transient conditions, a combination between vapor and liquid is taken into account in the enthalpy time derivative. Turbulent transport of momentum and energy between neighboring channels is described by a simple empirical mixing model.

Chapter 2. Overview

8

Figure 2.2: Cooling Channels

2.2.2

Numerical Solution Procedure

The conservation equations along with the constitutive equations represent the system of equations of the mixture two-phase flow model. The basic flow variables are calculated in each time step axially layer by layer. For each axial layer, the coolant enthalpies are calculated first from the energy conservation equations. The axial pressure gradients are calculated from the combined axial and transverse momentum equation. The mass flow rates in the lateral directions are calculated from the transverse momentum equation, knowing the axial pressure gradients. The axial mass flow rates are deduced from the mass continuity equation. From the enthalpy of each computational cell, the steam quality and then, through the quality/void correlation, the steam volume fraction and hence the coolant density are computed. This procedure is repeated several times during each time step resulting in a fully implicit scheme. For steady-state calculations, the time step is set to a very large value. The sketched solution algorithm is limited to cases with axial flow rates which always keep positive. The linear equation system built up by the energy equations in each layer is solved by the SOR method. The equation system for the pressure gradients can be solved by a direct scheme or by the SOR method that needs less computer storage.

Chapter 2. Overview

9

The fuel rod temperatures are calculated in each iteration step depending on power release and cladding to coolant heat transfer. For each axial layer, the rod is divided into a number of radial rings to solve the heat conduction equation in radial direction by a finite volume method.

2.2.3

SCF Calculus Flow

The whole process of calculus flow of SCF is not cumbersome. In this paragraph the main time step loop with its calculus is presented in a schematical way.

• Reads input data with subroutine setup. • Time step loop begins. – Takes the initial values of maximum and minimum for departure from nucleate boiling superheating and critical heat flux. – The old time step values for transient are set – Establishes channel boundary conditions and forcing function values – Calculate power distribution – Calculate burnup – Calls solution scheme and executes (actually this is the important loop) ∗ Beginning of external iterations ∗ Beginning of axial sweep · Set conditions at start of channel · Calculate parameters to be saved from previous axial node · Calculate pressure gradient and lateral flow · Calculate axial flow and check for convergence ∗ End of axial sweep ∗ End of external iterations • End time step loop

Chapter 3

Reactor Description The German 4-Loop PWR Neckarwestheim (GKN II ) type KONVOI is the reactor selected to the analysis, it belongs to the Kraftwerk Union (KWU). The Framatom Benchmark specifications are used [5] to fed the models, the fuel type is selected to be FOCUS-X5. GKN II core contains 193 fuel assemblies FA with a thermal power of 3850M W and an electric power of 1350M W . The FA are of three different types, depending on its material constitution, with 103t of uranium 3.2% enrichment and 61 control rods. Water serves as a coolant and as a moderator at a pressure of 158bar with 291◦ C inlet temperature and 326◦ C outlet temperature. The outlet temperature is one of the key values to validate the correct behaviour of SCF and TRACE. The active height of the core is 3.9m and the radial diameter 3.45m along a main axis.

3.1

General Reactor Information

The general information about the reactor is shown in Table 3.1. The information related to the assembly and fuel was found in documents [5] [6]. The first document is concerned with the specifications of the PWR FA, U O2 (4w/o

235 U )

18 × 18–24, for code Comparisons. The second work is a study with libraries of twogroup diffusion for calculating several data of the KWU Convoy reactor with the Reactor Dynamics Program DYN3D.

10

Chapter 3. Reactor Description

11

Figure 3.1: PWR core of a KONVOI plant Table 3.1: General reactor data

3.1.1

Parameter

Value

Units

Power Mass flow rate Mass flow rate in core (94%) T inlet T outlet Avg. FA-power Avg. rod power Linear rod power

3850 19874 18682 291 326 19.95 71.56 14824

MW kg/s kg/s ◦C ◦C MW kW W/m

Fuel assembly

The data specification is valid to what is called cold geometry. The Temperature of measurements is 20◦ C. The core contains 193 FA and 61 control rods. There are three types of FA in the core, distributed as shows Figure 3.2.


12

Table 3.2: Benchmark Specifications

Parameter

Value

Units

Boron concentration Reference pressure Moderator temperature Fuel temperature Cladding temperature Specific rod power Core radius Active core length

500 15.8 1310 500 332.8 17.05 1.725 3.90

ppm MPa ◦C ◦C ◦C KW/m m m

Table 3.3: Fuel Assembly data

Parameter

Value

Units

Heavy metal-Nominal mass FA side length including water gap Fuel rod pitch

5.379E +05 23.00 1.27

kgHM cm cm

The FA geometry information of Table 3.3 was provided from previous work at KIT with GKN II. The information related to the fuel data was found in a magazzine where Framatome published some of the main features of it. [7] Despite the differences of fuel material composition, the Table 3.4 shows that the number of rods per FA makes FA type 1 and 2 very different from MOX Assemblies. Table 3.4: Fuel Assembly features

FA Type FOCUS-X5 Parameter

16x16 − (20)

No of rods per assembly Fuelled Unfuelled Overall assembly length (m) Overall assembly width (m) Rod length (m) Rod outside diameter (m) Pellet length (m) Pellet outside diameter (m) Pellet density (g/cm3 or TD) Clad material Clad thickness (m)

256 236 20 4.83E +00 2.30E −01 4.40E +00 1.08E −02 1.10E −02 9.11E −03 10.45 Zry4 7.25E −04

18x18 − (24) 324 300 24 4.83E +00 2.30E −01 4.40E +00 9.50E −03 9.80E −03 8.05E −03 10.45 Zry4 6.40E −04

To meet the requirements of compatibility of MOX-FA with the other FA in the core, MOX -fuel rods and assemblies follow the same thermo-hydraulic, thermal and mechanical design limits as uranium fuel.


13

It was chosen a typical design of a PWR MOX-FA, type 16 × 16 − 20. As it is shown in Table 3.4, the FA side length is the same for the three types of fuel, but MOX type has less pins than the others. This affects the calculation of the main thermal-hydraulic parameters.

Figure 3.2: Fuel Assembly Distribution

The FA composition ;

1. 81 FA1. Heavy metal enrichment of 4.6% of

234 U ,

and 2.6% of

235 U

2. 48 FA2. Contains two types of pins: • 4.6%wt of

238 U

• 2.6%wt of

235 U

with 5% of Gadolinium oxide

3. 64 MOX. 2%wt of P uO2

In our case, both SCF and TRACE consider generic U O2 and MOX enrichment for the calculus. At this point SCF presents an important advantage because you can include at input level the spacial location of each FA, and also you can add the information of the rods


14

inside the FA. The goals of this Master Thesis does not include model at low level but compare TRACE and SCF to typical transients and get TRACE model ready to a future coupling.

3.1.2

Point Kinetics

Also information about kinetics is known and was added to both TRACE and SCF codes in order to have more accurate simulation results. Table 3.5: Doppler Coefficient

◦C

Siemens Value pcm/◦ C

50 200 291 400 500 600 800 1200

−3.89 −3.47 −3.25 −3.02 −2.84 −2.67 −2.41 −2.06

The values of the Feedback Coefficients used to feed the models are the ones provided tothe benchmark and are shown in Table 3.6. Table 3.6: Feedback Coefficient

Feedback Coefficient Doppler (≈ 773k) Coolant (≈ 560k) Boron Void

pcm/◦ C −2.84 −39.3 −2.32 −1234.5(pcm/%)

Boron coefficient is irrelevant to the transients performed during this work, since no variation of Boron concentration occurs. The void coefficient value provided to the benchmark is a very large value and, for this reason we cannot think it would be negligible. Anyway, SCF and TRACE models have to be feed with those values, and the benchmark values were added.

Chapter 4

Reactor Core Design During this chapter TRACE and SCF input deck development will be broadly detailed. The correlations selected to perform a realistic and also equivalent simulation of the Konvoi PWR Core with the Collection Data and some needed assumptions are also discussed. TRACE model, was selected as the ideal case to perform the coupling benchmark analysis of SCF and TRACE, since it is simple but also realistic enough to behave as the actual coresystem. The future coupling between both codes is focused on multiphysic methodologies, to perform broad safety analysis adding the particular features of each one. The work made to model the reactor core with both codes shows that SCF has less versatility related to the correlations and input options, but on the other hand is able to model channels and also rods at pin level adding a very detailed study with much less human and computation effort than TRACE. The goal at Steady State level is to obtain similar pressure drop, outlet temperature and equivalent fuel rod temperatures as SCF and also equivalent to the actual core behaviour. In a second step the goal is to analyze the behaviour of both codes at transient level, and analyze the benefits that each code can add to the other. Also an important part of the analysis is the comparison of Point Kinetics added in both codes.

15

Chapter 4. Core Design

4.1

16

TRACE Model

The model designed to simulate the reactor thermal hydraulic core behaviour with TRACE includes some of the most important components of the code. Three heat structures HTSTR modelling the three types of FA, with its rods inside, inlet and outlet modeled with PIPE components, FILL and BREAK as boundary conditions, the core simulated also with a PIPE and a POWER component to add the energy generation and the Point Kinetics. The simplicity of the model can help comparing results and also to detect any problem that could rise while analysing results. TRACE version used during this work is the 5.0 because, as will be addressed in this work, TRACE 5 Patch 3 (the latest version while KIT working period) has its external interface ECI broken, and no tests would be possible to perform with it during the second part of this thesis with TRACE used in multiprocess behaviour. At the starting point of the research the use of the newest version was thought as the test version to the coupling, and some efforts were made in this direction that are discussed in Chapter 7. The model represents the core boundary conditions, the inlet and outlet and the core itself. (Appendix A ) The TRACE components to develop this model are;

• A PIPE component representing the vessel. • A POWER component to provide the power to three heat structure components. • HTSTR 10 20 and 30 that model the fuel assemblies that are inside of the core.( 81 Fuel assemblies of type 1, 48 fuel types and 64 fuel assemblies) • Inlet (PIPE 31) and outlet (PIPE 41). • The boundary conditions represented by FILL 1 (inlet boundary conditions) and BREAK 3 (outlet boundary conditions).

The main features of each component related to the model are discused below. The flow area, hydraulic diameter and wetted perimeter are known with simple calculations from the Collection Data and are some important geometrical parameters needed


17

to fed TRACE input. It is remarkable that the heated perimeter is calculated with the addition of each rod, and is the reason of the a priori big number. Table 4.1: Core Flow Information

4.1.1

Parameter

Value

Flow Area Hydraulic Diameter Heated Perimeter

0.0286 0.012 8.953

Units m2 m m

PIPE Component

During PIPE modeling, the most important question was to determine the value of friction factor, since this is likely the unknown parameter that makes the simulation results vary most. And has to agree with the one used by SCF if a proper comparison is desired.

Figure 4.1: Snap Core Representation.

The friction model used by TRACE in single phase [1] is controlled by two values in the input deck. NFF and fric. In the following, NFF is set to zero and the friction factor is selected with the insight of the first simulations performed with SCF.

4.1.1.1

Friction Equations

Two types of frictional pressure losses are modeled in TRACE [1]:


18

• Wall Drag. Models the fluid-wall deformation using a friction factor approach. • Form Drag. Models geometry specific pressure losses through user specification of additive loss coefficients due to abrupt flow area changes.

In our test we have single phase problem and wall drag coefficient is the one selected. TRACE defines it by: k Cwk = fwk D4h 12 ρk = fwk 2ρ Dh

where the subscript k indicates the fluid phase ( liquid or gas ) and fw is the Fanning friction factor.

Figure 4.2: Representation of the Moody Diagram using the Churchill friction factor formula [8]

The Churchill formula [9] for the friction factor is used in TRACE because it applies to all three flow regimes; laminar, transition, and turbulent. The Churchill friction factor formula is given by:

2

8 12 Re

+

1 (a+b)3/2

1

12

The first test performed with SCF arose values for the Reynolds Number of ≈ 5E +05, then following Moody Diagram 4.2, we see that is a smooth pipe with a friction factor that can be modeled in TRACE with a value approximated to 0.012.


19

The PIPE component models coolant flow in 1D tube. It has the potential to model coolant flow-area changes, wall heat sources, and heat transfer between the wall inner and outer surfaces. The wall can be modeled with a large number of material types to calculate the conduction heat-transfer. The model includes three pipes modeling the distinct types of FA of KONVOI core. TRACE needs several input parameters related to the geometry to solve the fluid dynamic problem as; dimensions of the core, fuel assemblies and pin rods. In addition, to solve the heat conduction within the fuel rods, further data is required as for example the material of the fuel, the gap and the cladding together with the temperature dependent thermo-physical properties such as heat conductivity, heat capacity or density. The ICHF tag is also important, since is the responsible of the Critical Heat Flux Calculation. Is set to 2 to use Biasi Correlation which consists of two equations: one for low-quality CHF and one for high-quality CHF. The CHF is defined as the maximum of the two equations.

4.1.2

POWER Component

Supplies the Power to the Heat Structures. Some of its input values are directly extracted from collection data, but some other need some approaches and others a guess. Let we see most of the values added to the input component;

• CPOWR array is normalized such that; Pn 1

(CP OW R(n)rdx(n)) =

Pn 1

rdx(n)

cpowr1 = 14400/53804 = 0.2676; cpowr2 = 0.4517; cpwr3 = 0.2807 Is the percentage of the Power that comes for each HTSTR. • RDPWR input is for the radial power distribution across a fuel pellet and is also normalized in the same way aas the power coefficient. Pn 1

(RDP W R(i)vol(i)) = vol(i) As the radius of the pellet has been defined to be

equal volumes for each node (See RADRD variable of HTSTR component), the variable RDPWR is 1.0 for each node.


20

The values for the axial power were defined with the same shape to SCF and TRACE based on a typical distribution at the beginning of fuel cycle.

Figure 4.3: Axial Power Profile.

4.1.2.1

Point-Reactor Kinetics

The power of the model can be added by two ways; 1. Specifying it in the input as a constant and the evolution set in a table where the points between the provided ones are calculated by interpolation. You have to know the response of the Power to the transient, that is quite complicated. 2. From the solution of the Point-Reactor-Kinetic equations. The Point Kinetics is the most common model to solve the reactor Power in thermal hydraulic and subchannel codes. There are different approaches depending on the number of delayed neutron groups considered. The Point Kinetics model used for both SCF and TRACE decompose the contribution of delayed neutrons into six groups with their corresponding percentages and time constants. This approach is not valid to real cases but is useful for academic purposes. The point-reactor-kinetics equations specify the time behavior of the core power level with neutronic reactivity as the driving parameter. Feedback reactivity based on changes in the core-averaged fuel temperature, coolant temperature, gas volume fraction, and boron concentration is calculated by TRACE. The point-reactor-kinetics equations are a coupled set of (I + 1) first-order differential equations defining the total fission power P and the delayed-neutron precursor concentrations Ci as a function of time. These equations are given by;


21 dP dt

=

+

PI

dCi dt

= −λi Ci +

βi P Λ

R−β Λ P

i=1 λi Ci

+

S Λ(1−R)

and;

for i = 1, 2, ..., I

where; P = thermal power (W) that results from fission occurring at time t, t =time (s), R = neutronic reactivity, k =effective neutron multiplication constant, β = total fraction of delayed neutrons, βi = fraction of delayed neutrons in group i, Λ = effective prompt-neutron lifetime (s), λi = decay constant for the delayed-neutron precursors in group i, Ci = power of the delayed-neutron precursor concentration in group i (W), I = number of delayed-neutron groups and S = thermal power (W) from an external source of neutrons in the reactor cores that are producing fission. The Kaganove Method is used to solve these equations in TRACE. It approximates the time dependence of P and kex = k–1 = R/(1–R) over each integration time step by second-order polynomials and assumes Λ(t) = `/(1 + Kex (t) where ` is a constant. For TRACE, it is more appropriate to approximate the time dependence of P by a second-order polynomial, R by a first-order polynomial, and Λ by a constant because TRACE linearly extrapolates its estimate of R(t) over the fluid-dynamics time step to be evaluated and because the weak time dependence of Λ generally is unknown. Table 4.2: Delayed-Neutron Constants [1]

Group i

Decay Constant λi (s–1 )

1 2 3 4 5 6

3.87 1.40 0.311 0.115 0.0317 0.0127

Neutron Fraction βi 0.000169 0.000832 0.00264 0.00122 0.00138 0.000247


22

More details of Feedback Coefficients are provided during SCF input deck design. The info needed to fill the reactor model kinetics, includes de Doppler Coefficient (or fuel temperature coefficient of reactivity), moderator reactivity coefficient and also boron and void coefficient. For our purpose, the important ones are Doppler and Moderator Coefficients, since the transients to be studied have no deppendence with the boron and, as the reactor is a PWR, the void fraction coefficient importance will be negligible.

4.1.3

FILL Component

The FILL component is used to impose boundary conditions at any 1D hydraulic component junction. It does not model a physical component itself. The FILL component added to the model imposes a mass flow boundary condition at the junction that is transmitted to its adjacent component. The fluid pressure, void fraction, fluid temperatures, non condensable gas partial pressure, and solute concentration that are specified for the FILL define the properties of the fluid convected into the adjacent component if an inflow condition occurs. IF T Y = 2 Constant Mass FLow During the Steady State calculation the Mass Flow remains constant. It will be the component in charge of transient modelling, since has the option to add tables and/or control block as input.

4.1.4

BREAK Component

The BREAK component specifies boundary conditions that induce time dependent behavior. The boundary conditions are established by specifying the fluid conditions leaving or entering the system. Observation: The point that was found during the model execution and testing, is that TRACE considers the BREAK component to be the correct value to the pressure, since its value is the one considered, and the FILL value is modified to fulfill the problem considerations.


4.1.5

23

Heat Structure HTSTR Component

The HTSTR component evaluates the dynamics of conduction, convection, and gap-gas radiation heat transfer in a fuel-rod or structure element. The pipe walls modeled by other components are also evaluated by the HTSTR component. All fluid components that include input for a pipe wall, internally spawn one or more HTSTR components, that calculate the conduction and convection from the pipe wall to the fluid. The heat-transfer in a HTSTR-component can be in either cylindrical, cartesian (x, z) or spherical geometry. The model includes three HTSTR to represent the heat generated in the core due to Fuel burning. The most relevant input parameters that helps TRACE to simulate the model are;

• PDRAT Pitch-to-diameter ratio for rod bundles. It is calculated directly from data collection. • HGAPO Gap-gas properties are calculated only when the dynamic fuel-claddinggap HTC option is used (NFC = 1). Also, while all properties include an emissivity for doing a radiative heat-transfer calculation, the calculation is only done in connection with the gap conductivity calculation. (in our case NFC=0). The element gas-gap HT C = 5670W/(m2K) that is a value of the Helium heat transfer coefficient. • RDX is the number of rods in the heat structure; – RDX1 = F A × Rod = 81 × 300 = 24300 – RDX2 = 48 × 300 = 14400 – RDX3 = 64 × 236 = 15104 • RADRD. Rod radii (m, f t) from the inside surface at no power cold conditions. In this model 8 radial nodes were considered. The distribution was made to have equal volume in each fuel pellet ring (this makes easier the power density distribution). With the clad rings, the same consideration was done. The values can be read in the input decks.


24

• ICHF. Is the flag responsible of the Critical Heat Flux Calculation. Is set to 2 to use Biasi Correlation which consists of two equations: one for low-quality CHF and one for high-quality CHF. The critical heat flux is defined as the maximum of the two equations.

Figure 4.4: Fuel rod radial nodalization.

4.1.6

Inlet and Outlet PIPE

The inlet and outlet pipes are only designed as a flow transfer component to simulate somehow the upper and lower plenum of a PWR reactor. This model can help us during the process of showing how to connect SCF to TRACE.

So far the considerations about TRACE input deck. During Chapter 5, some issues concerning to results will be discused, mainly related to Point Kinetics Method.

4.2

SUBCHANFLOW Model

During this section, the SCF input deck model (Appendix B) will be explained in detail. The models selected during input development, were the same as TRACE ones if possible, or the most appropriated if not exists this calculus. This methodology, tries to help us during the results analysis, making them clearer and more accurated.

4.2.1

Reactor Data

SCF input sections have to be filled with all the info related to the Reactor Core Geometry, the known boundary conditions, the operating conditions, the calculation control data as well as the maximum changes allowed to the Temperature at Cladding, Fuel and Coolant.

Chapter 4. Core Design 4.2.1.1

25

Correlations

• As GKN II is a PWR, the IAPWS 97 water properties are set. • The true vapor quality due to sub-cooled boiling can be calculated by SCF with different models found in literature.[9] – Levy [9] calculates the liquid subcooling at the point of the bubble departure; also calculates the local vapor void fraction from the thermal equilibrium value and a correlation to calculate the void fraction in subcooled boiling. – Bowring Model [10], based on bubble detachment and calculation of steam voidage in a subcooled region of a heated channel. It is used to identify the beginning of the fully developed boiling region. – Saha an Zuber Model [10] is used to identify the point where a significant void flow is occurred and the non equilibrium quality. – Unal presented semi-empirical correlations for prediction of maximum bubbledeparture diameter and maximum bubble growth time based on a heat transfer controlled bubble model for subcooled nucleate flow boiling of water. set_subcooled_void_levy = off set_subcooled_void_saha_zuber = on set_subcooled_void_unal = off set_subcooled_void_bowring = off • For homogeneous boiling no slip for the vapor is used. For the slipcase three correlations are available: 1. A modified Armand model. 2. The Smith combined ratio correlation based on equal velocity heads of a homogeneous mixture center and an annular liquid phase. 3. The Chexal-Lellouch model.[11] The correlation is continuous and does not depend on flow regime maps or spline fitting. set_boiling_void_homogeneous = off set_boiling_void_armand_mod = on set_boiling_void_smith = off set_boiling_void_chexal_lellouche = off


26

• The fluid two phase wall friction multiplier can be described with a pure homogeneous model, the Armand correlation or the Lockhart-Martinelli model. – Armand correlation is valid for two phase flows in macro sized tubes. – The method of Lockhart and Martinelli (1949) [12] is the original method that predicted the two-phase frictional pressure drop based on a two-phase multiplier for the liquid-phase, or the vapor-phase, respectively. Presented void fraction data as a function of Xn on two-phase/two-component adiabatic flows near atmospheric conditions. set_two_phase_friction_homogeneous = off set_two_phase_friction_armand = on set_two_phase_friction_lockhart = off • The turbulent friction can be calculated with several correlations: The Blasius single phase friction correlation is also defined in a SCF data card. It can be replaced by the Rehme correlation for wire wraps in triangular rod arrays. Heinrich Blasius in 1911 shows that the resistance to flow through smooth pipes could be expressed in terms of the Reynolds number for both laminar and turbulent flow [11]. Fx − iFy =

iρ 2

H C

dω 2 dz dz

First law of Blasius for turbulent fanning friction factor: f /2 = 0.039Re−0.26 Second law of Blasius for turbulent fanning friction factor: f /2 = 0.023Re−0.26 A further option is the Rehme correlation for triangular rod arrays with or without grid spacer. The Churchill correlation needs as additional input the surface roughness of the fuel rods and is the one selected for both codes. set_turbulent_friction_blasius = off set_turbulent_friction_rehme_wire = off set_turbulent_friction_rehme_grid = off set_turbulent_friction_churchill = on


27

• Single Phase Heat Transfer includees three options[5]. – The Dittus-B´’olter correlation (1930) is a common and particularly simple correlation useful for many applications. This correlation is applicable when forced convection is the only mode of heat transfer; i.e., there is no boiling, condensation, significant radiation, etc. The accuracy of this correlation is anticipated to be ±15%. – The Gnièlinski correlation used in the TRACE code. – For liquid metals the Subbotin correlation can be used. It needs the global rod diameter and pitch. set_heat_transfer_dittus_boelter = off set_heat_transfer_gnielinski = on set_heat_transfer_subbotin = off A comparison of the Gnielinski correlation to the classic correlation of DittusBoelter is given in Figure 4.5, but the important for us is that in our case both correlations should be equivalent, since converge to high Reynolds values. To be consistent with the models, Gnielinski is used in both codes. • For the critical Heat Flux in the water boiling curve several correlations are offered. set_chf_barnett+b&w = off set_chf_biasi = on set_chf_okb = off set_chf_w3 = off set_chf_levitan = off set_chf_epri = off The calculated critical heat flux can be corrected with the axial rod power profile. A correction is not necessary for the EPRI-CHF correlation which already includes a power shape correction. Using the EPRI correlation the shape correction correlation is set to none by the code automatically. The Appendix K of 10CF R50 suggested correlation is the B&W Barnett and Hugges (modified Barnett) that covers the Presure range of interest for Blowdown. [13]


28

Figure 4.5: Comparison of the Gnièlinski and Dittus-Boelter correlations versus heat transfer data for air in a long heated tube. [1]

In our case, the selected correlation is the Biasi ones, since TRACE has also the same correlation and is suitable for our simplified transients to be studied.

set_shape_chf_none = on set_shape_chf_cobra4i = off set_shape_chf_tong = off set_shape_chf_w3 = off set_shape_chf_smolin = off • Blasius and Reynolds factors. The Blasius single phase friction correlation is defined by coefficients given by the next keywords. It can be replaced by the Rehme correlation for wire wraps in triangular rod arrays. A further option is the Rehme correlation for triangular rod arrays with or without grid spacer. For the Rehme correlations the input of the keyword group special correlations is used. The Churchill correlation needs as additional input the surface roughness of the fuel rods.

! single phase friction factor = aa * reynolds**bb + cc


29

! for blasius only ! ! laminar blasius_laminar_prefactor = 64.0 (aaL) blasius_laminar_reynolds_exponent = -1.0 (bbl) blasius_laminar_constant = 0.0 (ccl) ! turbulent blasius_turbulent_prefactor = 0.316 (aat) blasius_turbulent_reynolds_exponent = -0.25 (bbt) blasius_turbulent_constant = 0.0 (cct) ! roughness = 1.5e-5 In the previous slice of SCF input are difined the values that help us to calculate the laminar and turbulent Blasius friction factor are calculated from the coefficients as: aal × Rebbl + ccl The turbulent Blasius friction factor is calculated from the coefficients as; aat × Rebbt + cct In the code the maximum of laminar and turbulent friction is taken for the Blasius and the Rehme correlations. The Churchill formula includes turbulent and laminar friction. In the first iteration of the problem, the Blasius friction factors to laminar and turbulent were used, but once viewed that Reynolds numbers were about 10+05 , that is a value when a laminar boundary layer will become unstable and turbulent (See Moddy’s Diagram 4.2), the Churchill correlation was set. Two reasons made this change needed: 1. Blasius correlations predict a very low value for friction what makes that our model underestimate the pressure drop. The range Blasius formula validation is for Reynold’s number less than 10+05 , then is not suitable for this model, since the simulation computes Reynolds values around 5E+05 during testing.


30

2. To be consistent with TRACE, that always uses Churchill correlation. The surface roughness of the fuel rods is used in the Churchill correlation, the value set in this case is for a smooth pipe, since the roughness is very low. The values for TRACE and SCF agree with Moody diagram using the Churchill friction factor formula.

4.2.2

Channel Layout

The heat flux selected to this case is shown in 4.3, and is a typical flow at the beginning of a lot of fuel cycles. The channel layout needs the geometrical info of each fuel assembly. Three types of assemblies to complete the 193 that compose the GKN II Konvoi core; 1. Uranium Oxide 2. Uranium Oxide with Gadolinium 3. MOX The composition and number of each type is described in Chapter 3. The boundary is filled by reflector, and is not taken into account by SCF neither by TRACE. To determine the location of each fuel assembly, only the radius and mesh nodalization (15×15) is needed. The numbering starts from the bottom left. Core radius is 1.725m and the assembly width (gap included) 0.23m. With this considerations, for example the rod number one is located in (−0.69, −1.61). Next info needed is the neighborhood of each channel. To fill it you need well defined the numbering and to know the gap spacing (4E − 04m) and the centroid-to-centroid distance (2.2996E − 01m). Only the neighbours with code greater than yours are needed if your assembly ids are growing. To SCF is possible to calculate the thermal connection between two channels (only for single phase flow) if the thermal wall properties are known. – The wall heat capacity times wall thickness (ρ × cp × thick) J/m2 /K – The width of the wall (width × axial node length = heat exchange area) m – Identification number of the first channel adjacent to the wall


31

– Conductive resistance of the wall associated with the first channel m2 K/W – Identification number of the second channel adjacent to the wall – Conductive resistance of the wall associated with the second channel m2 K/W This table is not filled in our case since we have no info about the conductive resistance. The channel area variation input is given in the first part by a keyword to insert gradually the area variation during Steady State iterations. In our case only one iteration is calculated.

4.2.3

Rod layout

To start filling this section of SCF input several values have to be set. No burn-up is considered because is only for long transients. The number of fuel nodes is set to 10. The pin radial heat conduction solution method has to be select. The simple TWIGL method of COBRA-EN calculates the rod center temperature, the fuel surface temperature and the inner and outer cladding surface temperatures in Steady State. The TWIGL model cannot be used for hollow pellets and should not be used for temperature dependent material properties. A more detailed method is a finite volume method using the SOR iteration procedure with several temperature nodes inside the fuel. A direct solution method is taken from COBRA-EN. For the dynamic fuel cladding gap conductance model a minimum value has to be given due to numerical reasons. (Tested with very different numbers without output effect in our case) Value of 5000 was selected. Table 4.3 is filled with info of the rod material type that composes the assembly, the outer diameter of the rods and the power fraction relative to average power of an assembly. Table 4.3: Rod Geometrical Fuel Information

Rod Data m2

wetted perimeter m

heated perimeter m

0.0285 0.02859 0.02891

9.882 9.882 8.7443

8.953 8.953 7.970

channel area FA1 U O2 FA2 U O2 Galium FA3 M OX


32

To calculate this point, we know from the total Power that the average power of an Assembly is 19.95M W . In [5] the fuel rod performance was calculated with DYN3D with CASMOS and HELIOS libraries to GKN II Reactor. The figure 4.6 shows the middle value for all fuel elements. The maximum relative deviation between the two versions can be found on the edge of the reactor core, where lower power densities occur. We take arbitrarily for our work the CASMO values. To find the power fraction relative to average power of an assembly, we multiply for the rods in each bundle and for the active length of the core. The average result of this simple calculus is 18.80M W per assembly, but as we are interested in the fraction of each one, we do not care about this error, but we use it as the “average” power to calculate the fraction in order to have it normalised.

Figure 4.6: CASMO & HELIOS Linear Power (kW/m) data

The following table to fill in SCF is related to the number of rods belonging to the assembly or channel. One rod can have till six neighbours. In our case all rods belong to the same assembly.


33

The material input card only needs to say the type, if those are included in the code material types (U O2 , U O2 , P uO2 in our case) rest of values are not needed. More info about materials is known from Framatome Data [7]. Values of Pressure and Volume of gas gap are unknown, and generic values are used for it. The conductivity of the gap was set with the same value as TRACE.

4.2.4

Point Kinetics

SCF adds the feature when the target set point kinetics is set to on.

&pointkinetics set_pointkinetics_power = on pointkinetics_max_time_step = 1.0e-6 prompt_neutron_lifetime = 2.0e-6 power_weighting_exponent = 2.0

fraction_delayed_neutrons_group_1 = 0.000247 fraction_delayed_neutrons_group_2 = 0.00138 fraction_delayed_neutrons_group_3 = 0.00122 fraction_delayed_neutrons_group_4 = 0.00264 fraction_delayed_neutrons_group_5 = 0.000832 fraction_delayed_neutrons_group_6 = 0.000169

decay_constant_group_1 = 0.0127 decay_constant_group_2 = 0.0317 decay_constant_group_3 = 0.1150 decay_constant_group_4 = 0.3110 decay_constant_group_5 = 1.4000 decay_constant_group_6 = 3.8700

doppler_coefficient = -2.84e-5 coolant_temperature_coefficient = -3.93e-4 void_coefficient = -0.12345 boron_coefficient = -2.32e-5


34

The reactivity units are by default in ∆K/K but as alternative units can be pcm percent millirho and the conversion is 1pcm = 10−05 ∆K/K The void coefficient is a number that can be used to estimate how much the reactivity of a nuclear reactor changes as voids (typically steam bubbles) form in the reactor moderator or coolant. The Point Kinetics system of equations is solved in SCF by a simple explicit EulerForward Method. [14]. The solution at the nth time-step is given by yn . The step size h is then given by h = tn − tn−1 . Given (tn , yn ), the Forward Euler Method computes yn+1 as;

yn+1 = yn + hf (yn , tn ), (Explicit) Forward Euler Method.

For the equation abobe we see that is a firs order aproach where the maximum time step has to be small compared to the prompt neutron lifetime divided by the sum of the fraction of delayed neutrons.

1.0E −06 = pointkinetics max time step

P6 1

prompt neutron lif etime f raction delayed neutrons group

Figure 4.7: PWR Coolant Reactivity Curves

' 3.1E −04


35

The Power weighting exponent is used in the averaging procedure to calculate the whole core variables like coolant and fuel temperature used in the feedback calculation. The appropriate value to use for the exponent will depend on the fuel-loading distribution in the reactor core. It should be set to 2.0 for the case where the core enrichment is radially constant. A value of 1.0 may be more appropriate for the case where the radial-power distribution is constant across the reactor core [3]. Figure 4.7 shows diferent curves of moderator coefficient deppending on the available boron concentration for a typical PWR. This curves are not uniques but deppend on the reactor, however allow us to verify that the values given for GKN II are reasonable. TRACE allows you to add Doppler, moderator, boro and void coefficients as a dependant curve related to the temperature. On the other hand SCF only allows one value to be added to each coefficient. This is an important advantage of TRACE, since during a transient, those coefficients can change very much. To be able to compare the results, the values are set constant to TRACE and the same values are set to SCF.

Chapter 5

TRACE-SCF Model Comparison The purpose of this chapter is to analize the behaviour of TRACE and SCF and compare its results with typical transients. As a first step, the Steady State of both models will be executed and its results compared. Once this results are checked and validated, the following transients will be analized:

1. A Coolant Mass Flow transient i.e due to a Pump Trip , causing a 33% drop of Mass Flow entering the core. 2. A Primary Temperature Drop transient. i.e due to inadvertent opening of a Steam Generator valve that triggers a 30K temperature drop.

The phenomenology of both transients will be briefly exposed. However, in our case no Safety Systems are introduced and only short transients (30s) without any system actuation is considered.

5.1

Steady State

During the analysis of the results, first the Steady State of both codes is simulated to compare the developed input deck models to test them in transient conditions. The first feeling while creating the inputs is that TRACE has a very broad range of options to modelate an accurate core, with many more parameters and time-tables than SCF. 36

Chapter 5. TRACE vs. SCF

37

On the other hand, all this options make the use of the code more difficult, the error management has several limitations, and create a full core as SCF allows is a very complex task. Trace model has one pipe, modelling the different types of FA as HTSTR components, but has no information about the geometrical location of each one. SCF can modelate each rod inside the assembly, adding low level info to the model. This detailed model is beyond our consideration to this work but is important to remark the options that a subchannel code adds to Plant codes. The results of both codes are presented in this section. A simple comparison of average values is carried out. No more detailed comparison can be performed since TRACE model was developed without FA detail, but groups of same FA type. The most important value is the drop pressure, since it drives other values and will be also the most important value to achieve convergence at the end of each time step. Also velocities, Fuel and Rod temperatures and Reynolds Number are evaluated.

5.1.1

SUBCHANFLOW

SCF main results are shown in Table 5.1. The simulation was also performed in SALOME [15] platform. SALOME is an opensource software that provides a generic platform for Pre and Post-Processing for numerical simulation. At the end of the simulation, you can generate a .med file that allows you to create a 3D view of the outputs. Several kind of views depending on the desired study can be drawn. The graphic view can help you to have a very good understanding of the represented variable in only a glance. To create the view as is shown, both mesh and nodes have to be added to the panel. In this case, the fuel surface temperature (◦ C) was selected as the variable to be printed. Figure 5.1 is a cut over the Z axis at level 8 with a transversal cut to see the Surface Fuel temperature distribution with SALOME of SCF model outputs. SCF results shown that GNK II Reactor is in a turbulent regime (Reynolds 5E +05) in its core and achieves convergence with a pressure drop of 8.48E +03P a. Maximum Center Pin Fuel Temperature is 1938K. The Critical Heat Flux is about 2.7E +16 (W/m2 )


38

Table 5.1: SCF Steady State Results

Dist. m

∆p pa

Enthalpy j/kg

Tem. K

t sat ◦C

Density Kg/m3

Qual. −

Vel. m/s

Reynolds −

0 0.195 0.39 0.585 0.78 0.975 1.17 1.365 1.56 1.755 1.95 2.145 2.34 2.535 2.73 2.925 3.12 3.315 3.51 3.705 3.9

8.48E + 04 8.07E +04 7.66E +04 7.24E +04 6.83E +04 6.41E +04 5.99E +04 5.57E +04 5.15E +04 4.72E +04 4.30E +04 3.87E +04 3.44E +04 3.01E +04 2.58E +04 2.15E +04 1.72E +04 1.29E +04 8.58E +03 4.29E +03 0.00E +00

1.29E +06 1.30E +06 1.30E +06 1.31E +06 1.32E +06 1.33E +06 1.34E +06 1.36E +06 1.37E +06 1.39E +06 1.40E +06 1.41E +06 1.43E +06 1.44E +06 1.45E +06 1.46E +06 1.47E +06 1.48E +06 1.49E +06 1.49E +06 1.50E +06

564.1 565.6 566.9 568.5 570.2 572.2 574.4 576.8 579.2 581.7 584.2 586.6 588.9 591.1 593.0 594.8 596.3 597.6 598.7 599.6 599.9

346.7 346.7 346.7 346.7 346.6 346.6 346.6 346.6 346.5 346.5 346.5 346.5 346.5 346.4 346.4 346.4 346.4 346.3 346.3 346.3 346.34

744.95 742.04 739.49 736.47 732.96 728.92 724.36 719.38 714.08 708.46 702.61 696.78 691.08 685.54 680.3 675.53 671.26 667.49 664.25 661.62 660.47

−0.38 −0.37 −0.36 −0.35 −0.34 −0.33 −0.32 −0.30 −0.29 −0.27 −0.26 −0.24 −0.23 −0.21 −0.20 −0.19 −0.18 −0.17 −0.16 −0.16 −0.15

4.53 4.54 4.56 4.58 4.60 4.63 4.66 4.69 4.72 4.76 4.80 4.84 4.88 4.92 4.96 4.99 5.02 5.05 5.08 5.10 5.11

4.41E +05 4.43E +05 4.46E +05 4.48E +05 4.52E +05 4.55E +05 4.60E +05 4.64E +05 4.69E +05 4.75E +05 4.80E +05 4.86E +05 4.92E +05 4.97E +05 5.02E +05 5.07E +05 5.12E +05 5.16E +05 5.19E +05 5.22E +05 5.24E +05

Values are compared to TRACE Reactor Core Model.

5.1.2

TRACE

To validate the results, we have to verify that the outputs we can compare with data, are correct.

Core average rod power =

7.1556E+04 W

The value of the average rod power calculated is the same as input data. A similar Table 5.2 to SCF is found in the output values;


39

Figure 5.1: Salome and SCF Representation Table 5.2: TRACE Steady State Results

node 1 2 3 4 5 6 7 8 9 10

5.1.3

Pressure cell 1.59435E +07 1.59347E +07 1.59258E +07 1.59168E +07 1.59078E +07 1.58986E +07 1.58894E +07 1.58801E +07 1.58708E +07 1.58614E +07

T. Sat k 620.2 620.1 620.1 620.0 620.0 619.9 619.9 619.9 619.8 619.8

T. Liq. k 565.9 568.9 572.8 577.8 583.5 588.7 593.1 596.3 598.8 600.1

T Gas k 620.2 620.1 620.1 620.0 620.0 619.9 619.9 619.9 619.8 619.8

ρ liq. kg/m3 741.0 734.9 726.7 716.2 703.9 691.5 680.0 670.9 663.6 6.594

ρ vap. kg/m3 106.8 106.7 106.6 106.5 106.4 106.3 106.2 106.1 106.0 105.8

v liq. m/s 4.530 4.552 4.590 4.642 4.710 4.792 4.878 4.961 5.028 5.083

v. gas m/s 4.551 4.567 4.605 4.657 4.725 4.807 4.893 4.976 5.043 5.098

Comparison

Some of the most important values to compare and validate the behaviour of both codes are present in this section. Table 5.3 includes the maximum and minimum Reynolds value that help us to know the flow regime of the reactor.


40

Table 5.3: SCF vs TRACE Steady Results

Variable Pressure Drop (P a) Max Center Pin Fuel T (K) Minimum Reynolds Maximum Reynolds

SCF 84800 1938.03 4.23E +05 6.31E +05

TRACE 82000 1960 4.27E +05 5.51E +05

Deviation (%) 3.28 1.38 0.083 12.61

Figure 5.2: Pressure Drop Comparison

Both codes agree in a Pressure drop with a small error between them. This is the reference variable to know if models are good enough. The result shows a reasonable values for both codes with less than a 5% of differences between them.

Figure 5.3: Axial Temperature. Steady State Comparison

The temperature follows a similar curve 5.3 for both codes finding almost the same value at core outlet of 600K, as the reference value.


41

Next image 5.4 shows the Coolant Velocity at axial level. Both codes show a similar behaviour and its outlet velocity is ≈ 5.1m/s.

Figure 5.4: Axial Coolant Velocity. Steady State Comparison

The outputs of both models show that both codes arrose equivalent results to this simplified core model. The results support that input deck design with SCF and TRACE was correctly performed. The advantage of SCF while studying a reactor core model is that with a quite simple model we have the geometrical information of each 193 fuel assemblies while with TRACE, to model such input would require a huge human and computational effort.

5.2

Transients

Western reactors have to satisfy its Design Criteria of Intrinsic Safety. The reactor core and the Cooling System have to compensate the quick reactivity changes. The meaning of this criteria related to Point Kinetics is that the Power Coefficient has to be negative in any case. As said previously, the transients simulated to compare SCF and TRACE behaviour do not considere Scram, nor any other safety system. Then we want to analize the new ”state” of the reactor when the transient conditions arrive to its new value.


42

This study allows us to compare both codes related to tipical transients broadly studied without adding extra complications, but we have to understand that are only for academic purposes.

5.2.1

Decrease in Reactor Coolant Flow

A drop in the Primary Coolant Flow can be a threat to core overheating because the cooling can be insufficient to remove the fuel heat generated. During the transient, the increase of coolant temperature triggers a negative realimentation that makes the Power decrease. If such a Power drop is not enough to fuel cooling, clad failure can occur. This transient is not a problem to Boiling Water Reactors BWR due to the void coef-

Figure 5.5: Coolant Flow Transient

ficient of reactivity that makes the Reactor Power decrease much than PWR’s. Due to this big difference between both types of reactors, BWR’s does not have Scram trips to those transients. Our transient model represents a Pump Trip, the 33% of the inlet flow drops quickly Figure 5.5 shows the Primary Flow during the transient. The typical analysis of this transient includes a Scram Trip due to Low Primary System flow at 87% of the nominal value. Our analysis does not include Scram nor any other safety action and the goal is to compare the final state for both SCF and TRACE.


43

Figure 5.6: Core Power

Figure 5.7: Reactivity during transient

The diferent behaviour of TRACE and SCF in the Power calculation can be explained by the methods used by both codes. While TRACE solves the Kinetic Equations by Kaganove method, SCF uses a first order explicit Euler-Forward method.

Figure 5.7 shows the curves of reactivity during the transient. The total reactivity is


44

Figure 5.8: Maximun Fuel Temperature during Flow Transient

negative as is expected in any transient simmulation of a LWR. The value calculated to TRACE is the sum of Coolant and Fuel reactivity values, but for SCF incorporates also the contribution of Void reactivity since, as it was pointed in Section 3.1.2 the value provided is very large, and even a small bubble contribution (Figure 5.10) can add a non negligible reactivity contribution. At the end, we can see the agreement of both codes calculating the total reactivity.

Figure 5.9: Maximun Inner Rod Temperature during Flow Transient

SCF output files are not easy to manage graphically, moreover each fuel rod includes a lot of information each time step in different output files. To make the comparison of Figure 5.8 the information of all SCF Rod outputs was processed to select the maximun


45

Rod Temperature at each time step.

The result shows a very acurated agreement between both codes.

Figure 5.10: SCF Axial Void Fraction at the end of the transient

The cladding Temperature and the saturation temperature remain almost constant during the transient 5.9, being the saturation temperature less than the cladding one. This means than no DNB is expected during the transient. One important difference found in the behaviour of both codes is the void fraction found at the end of the transient, while TRACE does not considere a representative value, SCF has about 3%. See Figure 5.10.

5.2.2

Reactor Coolant Temperature Drop

During a Coolant Temperature Drop Transient, the primary System can decrease its temperature due to different accidents of heat extraction increase through the Secondary System. The studied cases covering this accident in the FSAR are;

1. Decrease in the Feed Water Temperature. 2. Feed Water Flow Rising. 3. Pressure regulator failure causing vapour flow rising.


46

4. Inadvertent opening of a Steam Generator valve. 5. Steam Pipe Breaks

Figure 5.11: Temperature Transient.

In the transient simulated, the temperature Drop is 30K in 20s in a linear curve simulating for example and opening of a Steam Generator valve and follows the Figure 5.11. Its important to take into account the different units of SCF and TRACE related to temperatures. The result of this transients depends on the temperature coefficient sign. In our case

Figure 5.12: Power Comparison.

is a negative value αm < 0. Then, we know that the core temperature drop causes a positive reactivity. It causes a reactor Power increase and then the fuel temperature rises. The increase in fuel temperature triggers a Doppler reactivity [16] that stabilize the Reactor at a higher Power.


47

See Figure 5.12 Figure 5.13 represents SCF and TRACE reactivities. During this transient, only

Figure 5.13: Reactivity during transient

Figure 5.14: Maximum Fuel Temperature

Coolant and Fuel Reactivities are important to SCF and the Void and Boron reactivities are negligibles.


48

Also the maximum fuel temperature has been extracted from SCF finding the hoter temperatures arround the core. The values for both TRACE and SCF are very acurated (Figure 5.14), what shows the calculation agreement for this type of transient.

Chapter 6

Coupling Overview The interest of coupling Subchannel Codes with Plant Codes has a broad history during the last 20 years. Reviewing the literature we can find several works in this direction. The coupling of COBRA/TRAC [17] is likely the best documented. Next paragraph is a short review of two of the most important coupling between plant codes and subchannel codes, only to show the historical importance of them and its applications. Also this chapter will try to shed some light on the coupling paradigms and its main features in the second section. After that, SCF coupling cases and its paradigms are reviewed. TRACE coupling overview starts also with a short description of conections to other codes but quickly is focused on the review of ECI as the best option to perform SCF coupling.

6.1

Previous Plant Code - Subchannel coupling

Some efforts coupling Subchannel and Plant Codes were developed so far. The most documented is likely the COBRA/TRAC system. It is the result from the integration of COBRA-TF in TRAC-PD2.

6.1.1

COBRA/TRAC

COBRA-TF is based on three dimensional two-fluid, three-field formulation and was developed especially for the reflood thermal hydraulics of LBLOCA. 49

Chapter 6. Coupling Overview

50

The three fields are, continuous vapor, continuous liquid and entrained liquid drops. The conservation equations are solved using a semi-implicit finite-difference numerical technique on an Eulerian Mesh. TRAC-PD2 is a systems code designed to model the behavior of the entire reactor Primary System. It is part of the broad TRAC family codes. It include special models for each component in the system (accumulators, pumps, valves, pipes, pressurizers, steam generators and the reactor vessel). Unless the reactor vessel, the thermal-hydraulic response of the components to transients is treated with a five-equation drift flux representation of two-phase flow. The TRAC vessel component is restricted in the geometries modeled and cannot treat the liquid drops from the continuous liquid phase directly. The conection was performed removing the TRAC vessel module, and COBRA-TF implemented as the new vessel component. The resulting code is COBRA/TRAC. The vessel component in COBRA/TRAC has both the extended capabilities provided by the three-field representation of two-phase flow and the flexible nodalization. The code was assessed against a variety of two-phase flow data from experiments conducted to simulate important phenomena anticipated during postulated accidents and transients in light water reactors.

6.1.2

MARS

KAERI developed MARS [18] code with the main objective of producing a state-ofthe-art realistic thermal hydraulic system analysis code with multi-dimensional analysis capability. MARS achieves this objective by very tightly integrating the one dimensional RELAP5/MOD3 with the multi-dimensional COBRA-TF code. RELAP5 is a Plant Code based on one-dimensional two-fluid formulation, and includes many generic component and special process models. The method of integration of the two codes is based on the dynamic link library techniques, and the system pressure equation matrices of both codes are implicitly integrated and solved simultaneously. In addition, the EOS for the Light Water was unified by replacing the EOS of COBRA-TF by that of the RELAP5.


51

RELAP5 and COBRA-TF were coupled by different techniques, since some instabilities arose from the implicit coupling of both codes.[19]

Both cases related have been implicitly coupled, solving the problem merging its numerics resulting in a new code that cannot be split and has only one executable. The integration coupling of plant codes such as TRAC and RELAP to subchannel codes is a very difficult technical task, since you have to solve a full matrix that integrate the solver. Also much time constraints have to be added to avoid instabilities. This makes the integrated code to have a short range of applicability. Other great problem is that the new code can not be up to date with the evolution of the integrating codes.

6.2

Coupling paradigms

Different types of coupling can be used for coupled simulations. There are different dimensions in the classification of coupling paradigms: • Boundary vs Initial Conditions Coupling [20]. In boundary coupling, some of the output variables obtained during time step cycle in one of the codes are passed to other points of the time step cycle in the other code, overwriting the time dependent tables that define the boundary conditions of a synchronization point. In the Initial Conditions Coupling the execution of the first code is suspended, the second code is spawned, and proper initial conditions are transferred before the second code initialization. See Figure 6.1 • Time step choosing. Depending of the equations to solve, it is needed to select; – Synchronous Coupling, where the simulation codes use the same time step sizes and perform the same advancement at the same time or; – Asynchronous Coupling, the simulation codes are free to choose their own time step sizes subject to the restart and data exchange interval restrictions. • The mathematical solution algorithm[21] used by the coupled simulation. Solution algorithms are classified as explicit, semi-implicit, and fully implicit. The Figure 6.2 shows how it works in a clear scheme. Some types of solution algorithms are inherently synchronous like the semi-implicit and fully implicit solution


52

algorithms while others such as an explicit solution algorithm may be either synchronous or asynchronous.

The Initial Conditions Coupling can be used when a certain code is getting out of its scope of applicability, and new models available from other codes are necessary. A typical example of this type of coupling is the transition from conventional TH codes to severe accident codes, once degraded core conditions are detected. Our interest in this research is focused in Boundary Conditions Coupling, where time step interaction is needed, the time step choosing will be mostly synchronous, but some kind of asynchronous loops are not discarded in order to achieve convergence in several flux calculations where interaction is not needed.

Figure 6.1: Typical coupling scheme. A) Initial Conditions Coupling. B) Boundary Conditions Coupling

Explicit coupling is characterized by data that has been computed by one simulation code in a particular time advancement being used by another simulation code in subsequent advancements. For example one code may compute the Pressure in a volume and the other code will use that Pressure as a Boundary Condition during its time advancements. Easily speaking, explicit coupling means that the value remains constant while being used by the other code. The main problem of fully explicit codes to hydrodynamics is that the time step has to


53

be to short to achieve convergence, using the Sonic Courant Limit . None of the current two phase flow programs employs this technique. In thermal-hydraulic coupling, pressure boundary conditions may be exchanged between the codes and then both codes compute the flow rates of mass and energy across the boundaries. Each code has all of the information needed to advance its solution, however, there is nothing to ensure that the flow rates computed by the two simulation codes at the same physical location will have the same value. This implies that the amount of mass or energy that leaves one code will not be the same as the amount of mass or energy that enters the adjacent code.

Figure 6.2: The image shows the different solutions in boundary conditions coupling

Semi-implicit coupling is characterized by data being computed by one simulation code during an advancement and that data being used by another simulation code during the same advancement being shared introducing several loops during its evaluation. The time step size is limited by Material Courant Limit, and a stable solution is much more easier to find than in explicit cases (but, for sure the implementation of the solution is more difficult). As said previously TRACE includes its own semi-implicit calculus flow called SETS [22] stability-enhancing two-step method for fluid flow calculations. The SETS method is a two-step technique that uses the basic semi-implicit equation set with the addition of a stabilizing set of equations. The improvement of this method is that Material Courant Limit can be exceeded without introducing numerical instabilities. There are several criteria to be considered selecting the hydrodynamic coupling paradigm. The most important is that the system must conserve Mass and Energy, and also a desirable feature is that the coupled system would have the same stability limits than its constitutives.


6.3

54

SUBCHANFLOW Coupling

MCNP5/SUBCHANFLOW [23] coupled system makes possible a deep FA analysis of BWR, PWR or SCFR reactors. Key issues in such a coupled system are; the way in which thermal-hydraulic/neutronic feedbacks; the accuracy of the Monte Carlo solutions and; the observation of convergence during the iterative solution. In coupling codes describing neutronics and thermal hydraulics, the spatial discretization of both domains has to be mapped to each other so that the exchange of information can be carried out in a consistent manner. In addition, how the iteration loop is initiated is also important. Furthermore, one has to make sure that a converged solution is obtained after running reasonable number of coupled iterations.

Figure 6.3: SCF-MCNP Explicit Coupling Scheme

As we can see from the image 6.3, the connection of MCNP and SCF is an Initial Conditions Coupling, that is the natural way of coupling with a Monte Carlo code (statistical code) where time is not defined, but talis of each neutron. Due to the iterative coupling approach between both domains, a large number of iteration may be needed to get a converged solution. The coupling implements a relaxation method to speed-up the convergence behavior with the Fuel Temperature (due to its large oscillations during the coupled runs), as a convergence parameter.


55

Other SCF coupling was performed against a Reactor Dynamic Code, DYN3D-SP3 [24] able to solve the diffusion equation or even the transport equation considering feedback parameters coming from the thermalhydraulic core behavior. These codes usually contain a 1D two phase flow thermalhydraulic model capable to pass them assembly averaged feedback parameters. The product of this coupling was called DYNSUB [25] and is a pin by pin coupling. In the Figure 6.4, the two-way coupling scheme implemented in the new code DYNSUB is illustrated for a FA. The pin power distribution is calculated with DYN3D-SP3 for every node in the geometry. The calculated pin power is passed over to the thermal hydraulic part, where it is allocated in each axial node of the rods and of the subchannels considered in the SCF fuel assembly representation. The main problem of this type of coupling is that SCF mesh usually has a different refinement compared with the neutronic one.

Figure 6.4: The new code DYNSUB has DYN3D as master code and SCF is added as a library and acts as a slave in the simulation.

The second coupling step added a fixed point iteration [24], that is the basis of the semi-implicit calculations, since an iteration loop is added to obtain convergent values and agreement of both codes. Time step selection is based on the convergence of the thermal hydraulics parameters and global power but not on the local fluxes. A transient with a fast increase of neutron flux could be very challenging for such coupled system. Then, an algorithm that can select smaller time steps is added to DYNSUB. It is a kind of semi-implicit coupling but asynchronous, since several neutronic steps inside the thermal hydraulic step are allowed and the average value of the power densities at each neutronic step is estimated.


6.4

56

TRACE Coupling

TRACE is one of the most used Plant Codes to Best Estimate analysis. It has been coupled to many different codes during the last years. It has been coupled to Neutronic Codes (PARCS ), Subchannel Codes COBRA/TRAC or even CFD codes (TRACEANSYS CFX [26]). TRACE code incorporate its own interface of coupling codes (allowing even self coupling), ECI, than can manage explicit, semi-implicit or SETS coupling. This interface was developed during the modernisation of old TRAC-M code and carries out TRACE calculus flow. In addition it was developed as a proper coupling interface able to be connected to any kind of codes. So far no much work was done to couple codes through it. Only CONTAIN [2] and SCAIS [27] were coupled with ECI, but its important to remark that every code coupled to TRACE has to follow a very close flow as ECI does, since is TRACE flow itself. In 2009, in the framework of ISA code development, TRACE 5.0 was coupled to SCAIS following ECI Calculus Flow [28]. During this development, some issues related to ECI were corrected and a basic knowledge of the interface was achieved. TRACE5.0 ECI was tested by myself during SCAIS-TRACE coupling, and some bugs were found and repaired. The connection TRACE-SCAIS does not need the EXTERIOR component to the purposes we had, so no deep EXTERIOR test was made. SCAIS-TRACE coupling used only some of the capabilities of ECI but the basic interface shares the same structure and basic knowledge of ECI was achieved. The is that SCF-ECI has to deal with flow connections, that is the most complete information interchange. The effort has to be focused on the achievement of a convergence value in Pressure and Velocity without loss of Mass and Energy. The starting point is to verify the usability of EXTERIOR component with an easy model representing the Konvoi PWR core behavior in steady state conditions.

Chapter 7

SCF-ECI-TRACE The chapter begins with the problems found with TRACE Patch 3 dealing with ECI in order to simulate TRACE split in several process. Also an attempt to avoid non convergence in pressure is added as an easier way to perform a kind of semi-implicit coupling with actually an explicit one. This approach can solve the pressure drop convergence, but it can introduce Mass and Energy Loss, and should be considered only as an step in the coupling process, but surely not in the final solution.

7.1

TRACE 5 Patch 3

At the starting point of this work, TRACE5 Patch 3 was the code selected to test ECI and the connection to SCF. The first problem found with ECI is that in current TRACE release it does not work. During TRACE-ECI model testing, was found this problem. The problem arose testing ECI with the cases that were distributed with an old TRACE version (TRACE 4.160 ). All cases crash in the class SetImplicitM, during execution of subroutine GeometryIndices, where a structured matrix for a fully implicit flux calculation is being filled. The indexing of all possible unknown variables (volumes and edges) is created.

forrtl: severe (174): SIGSEGV, segmentation fault occurred Image

PC

Routine

Line

Source

tracep3_dev

0000000001815F97

setimplicit_mp_ge

602

SetImplicitM.f90

57

Chapter 7. SCF-ECI-TRACE

58

In this subroutine, the exterior component is not defined, and then the simulation arose an uncontrolled error. At the start of this research work, some efforts were put to try to fix this error, but after the fixing of this bug some others appear. After a couple of weeks understanding that the problem was bigger and the solution will be very difficult without specific knowledge about the code structure, a mail was sent to Chris Murray (one of the main developers) to ask about the future of ECI and bugs correction. As the question has been answered positively (Appendix C), the work continued in order to design an interface to SCF to be connected as an exterior component to TRACE. The version that has to be used during beta development is TRACE5.0, that is the last not broken ECI of TRACE.

7.2

TRACE 5.0 ECI

Once the current version of TRACE was discarded, the focus was to prepare our model with TRACE5.0, that was the last version with ECI working properly, to be a benchmark case to SCF-TRACE coupling validation. The model prepared to this benchmark is elementary, but some issues were found during the test, that showed ECI to be some limitations not addressed in its documentation. The main issue is that you have to define the EXTERIOR component as an hydraulic component with more than one cell. The reason is that otherwise, the code can not manage to create the EXTERIOR identificators and the code arise an unexpected error. The error was located in the class UtilM, in soubrutine EdgeInd that is in charge of describing a junction and returning what is beyond the junction edge, the velocity sign associated with outflow from the junction cell.

is = compSeg(ic)%seg1D(junCells(jj)%iSeg)%segInd

This problem was skipped by adding a second cell to pipes 31 and 41 modelling the core inlet and outlet. All TRACE models of this work, were changed to include this consideration, although is not relevant to the results of any simulation.


7.2.1

59

Daemon

In order to simulate TRACE coupled to other code (in this case itself) we need a socket ready to listen to the processes and send the information needed by each one. The port was changed since Linux does not work well with the default one, and also the size of the socket was increased since some cases were found where more buffer was needed to transmit the information.

//#define SOCKET_SIZE #define SOCKET_SIZE

200000 /* Size, in bytes, of socket queue */ 500000 // [email protected]

.... //const int PORT const int PORT

= 52182; = 22182;

// Base port used for sockets communication

// [email protected]

To understand how to work with multiprocess with ECI-TRACE a deep study of the only existing manual is a must. In this paragraph, only a rough outline is considered. If TRACE found a taskList file in the same directory as the rest of the inputs during initialization, it reads this file and starts the execution of as many processes as the taskList includes. Each input has the capability of ask to the socket what, when and where needs the information to perform its simulation and what info also it has that other process will need during the calculus flow transit. With those premises, the multiprocess is able to perform a parallelized simulation.

7.3

A cuasi explicit option

One of the starting points is to decide the coupling paradigm between TRACE and SCF. As discussed in previous chapter, explicit coupling between thermal hydraulics, implies oscillation and convergence problems due mainly to time step limits . A first approach can be an algorithm at the end step to “filter” this oscillations as U. Grundmann solved this problem coupling the thermohydraulics of ATHLETE and DYN3D [29]. ATHLETE and DYN3D coupled its thermal hydraulics with GCSM interface. It allows an explicit coupling and applies at the end of the time step a kind of low filter to agree


60

in the value of pressures and not having instability problems to allow convergence. In the simplest case of thermal hydraulics, they interchange six parameters. Three as Boundary conditions to interchange and the other three are calculated by it. The Pressure, the Enthalpy and the Mass Flow (TRACE needs many more values as will be shown during this work). ATHLET is a plant model and the reactor core is completely substituted by the DYN3D code model. The thermal-hydraulics of the whole NPP system is split into two parts; the thermal-hydraulics of the reactor core model and; the thermal-hydraulics of the rest of the NPP coolant system. The pressures, mass flow rates, enthalpies and boron acid concentrations are transferred at the interfaces. The exchange of these parameters is performed by GCSM. The use of large time steps can cause pressure oscillation over the core and mass flow rates in this type of coupling. These phenomena are damped by a low pass filter of first order. The numerical problems that were solved with the introduction of a low-pass filter passed to DYN3D as time-dependent boundary condition pressure difference be accessed via the core. The differential equation for a first order low pass filter is: y(t) + τ dy(t) dt = x(t) Were τ is the constant time of the filter, x(t) the input signal and y(t) is the output signal. The input signal is the calculated difference pressure of ATHLET across the core dP , and the output signal of DYN3D as boundary condition to be transferred pressure difference dP . With this considerations the value to the pressure is: dPnew + = dPAthlet With this low-pass filter numerically stable solutions are obtained with a time step of one second. The ECI can be adapted as a component interface to SCF to be coupled also with other codes, the key point is that once developed we can do an easy test connecting SCF with itself. It can open then a great range of options to SCF, to be coupled to other codes in the future.


7.4

61

Benchmark model

The model has been split in two different processes to test ECI component. The case is exactly the same as in the previous model but, in this case, the core and the heat structures are in one process and the boundary confitions are in another process.

Figure 7.1: Split Processes. Reactor Core and Boundary Conditions

To achieve multiprocess behaviour with TRACE, the EXTERIOR components have to be added to the inputs to tell the other process how many components are simulated in another process and where the connections between there have to be placed. EXTERIOR acts as a placeholder in a task’s local input for components that are actually modeled by other tasks. Figure 7.1 shows the two different models that build up the same model developed during Chapter 4. The master processs will be the inlet and outlet with boundary conditions and, the slave one will represent the core. SCF will act also as a slave process to TRACE in the future multiprocess simulation TRACE-SCF.

• From the master process viewpoint, only one component is exterior to it. The pipe representing the core, this exterior component has two junctions connecting to it.


62

• From slave viewpoint there are two exterior components. One is the inlet with one junction and the other the outlet with other junction.

The slave and master inputs have to be placed in different folders. To execute the whole system, TRACE executable is called from master folder, the taskList file has to be placed in the same folder and, the socket has to be listening to the information interchange. taskList file needed to execute TRACE in multiprocess with ECI :

# master #

taskname

slave #

Hostname

taskname

Working Directory /home/es1331/PROJECT/Inputs/LAST/ECI/boundary program name

arguments

/home/es1331/TRACEV5/Source-Install/bin/trace5.0 Hostname

inrsim04.inr.kit.edu

7.4.1

arguments

/home/es1331/TRACEV5/Source-Install/bin/trace5.0

inrsim04.inr.kit.edu #

program name

Working Directory /home/es1331/PROJECT/Inputs/LAST/ECI/core

Results

As it was expected the results in multiprocess are binary equal to TRACE standalone one’s. ECI deals with the information interchange and the daemon spawns the slave process and handles the whole process successfully. TRACE standalone vs TRACE-ECI Pressure comparison at top and bottom of PIPE 2. Figure 7.2. As it was expected, the results were identical as shown in , and the model is ready to study what variables, where and when have to be interchanged.

7.5

ECI

The ECI is a set of high level subroutines driving TRACE calculus flow with the option of parallelize process through a socket driver. Those routines allow the developer to refer to variables according to TRACE nomenclature, and to transfer the values at certain points in the flow diagram. The ECI is driven by a master process that spawns the other concurrent processes. The master process spawns the others according to the


63

Figure 7.2: Pressure Comparison. TRACE Standalone vs. TRACE Two Tasks

information provided in a file called taskList. Since the ECI is conceived to follow TRACE calculus, available synchronization points refer to stages of the SETS numerical method. The data transfer between the processes is shown in the Figure 7.3. There are three steps:

1. The first step fills the transfer table and exports the info. 2. During the second step the info is sent and the second process imports this info. 3. During the third step, the info is sent to the actual variable that uses this value during the time step cycle.

7.5.1

Data needed

During the development of SCF-ECI the interface rules have to be followed. It needs a very well structured data to succeed in the info scheduling. For each flow connection to other task, a given task sends to the master process:


64

Figure 7.3: ECI Data Transfer Scheme

• Identifier for the junction (must match in both tasks). • A flag indicating need to evaluate the momentum equation at the flow junction, setting the value to one means it is able to evaluate the momentum equation if necessary, or setting the value to two, declares that it must control the equation evaluation for proper implementation of its model. • An identifier of any flow variable evaluated at the center of the volume adjacent to the connecting surface (sent as 0 if the model holds that variable constant). • An identifier of any velocity evaluated at the edge adjacent to the connecting surface. • An identifier useful to extract information on the flow junction from its own data structure. • The component number.


7.5.2

65

Calculus Flow

The ECI is the kernel itself of TRACE calculus flow. As said previously it follows SETS calculus. Its synchronisation points are enumerated below. Not all steps need information interchange, but anyway have to be included in ECI-SCF :

1. Setup (a) Time step calculation. Calculate time step size based upon restrictions placed by conditions in the regions covered by each process. (b) Global Time Step. All time step limits are collected by the Central Process and a final step size sent back to the other processes. (c) Set old time values. Move new time results from the previous time step into the old time arrays. Generate basic old time only fluid properties such as viscosity, conductivity, and mean density. 2. Control System. All signal variables, trips, and control blocks are evaluated. Signal variables may reference state variables in regions modeled by another process. 3. Correlation Evaluation. Evaluate correlations for heat transfer and friction (wall and interfacial). This is separate from the basic time step setup because these correlations do involve basic fluid properties in adjacent components. Correlations may be component specific. This step also includes special component models such as pump momentum source terms and valve area calculations. 4. Stabilizer Momentum Equation (a) Evaluate Terms. Coefficients and right hand sides for the momentum equations are evaluated for each face in the system. These equations are linear equations with respect to the unknown stabilizer velocities. (b) Local Solution. Solution for velocities within this process in terms of unknown velocities in regions evaluated by other processes. (c) Central Solution. Final solution of the reduced velocity equations either on the central process or on a designated satellite process.


66

(d) Solution Storage. The global solution is stored in the local component data structures. 5. Semi-Implicit Equation Solution (a) Velocity Dependency Equation. Evaluate terms in the linear equations relating the new time velocities to the new time pressures. (b) Evaluate average quantities at volume edges for use in computation of mass and energy fluxes. (c) Evaluate Mass and Energy Equation Terms. Coefficients and right hand sides for the linearized mass and energy equations are evaluated for each volume in the system (d) Local Solution. Solution for pressure changes are obtained in terms of unknown pressure changes in regions evaluated by other processes. (e) Central Solution. Final solution of pressure equations either on the central process or on a designated satellite process. (f) Solution Storage. New time temperatures, air partial pressure and void fraction are computed based on the global pressure solution. These are used to update all dependent fluid state information. All new variables are stored in the local component data structures. (g) Local Convergence Checks. Each participating process checks changes in primary variables or residuals against local convergence limits to determine if the nonlinear equation solution is locally converged. (h) Global Convergence Check. This occurs automatically during the status check for data transfer at the end of step 5g. The central process surveys the local convergence checks from all processes. If all have declared convergence, the calculation moves on to the stabilizer mass and energy equations. If not the calculation branches back to step 5b for re-linearization of the equations and another iteration of the Newton solution method. If the maximum permitted iteration count is exceeded, or water packing is detected, this sends a message to trigger the appropriate time step backup. 6. Stabilizer Mass and Energy Equations. Coefficients and right hand sides for the stabilizer mass and energy equations are evaluated for each volume in


67

the system. These equations are linear in stabilizer macroscopic densities and macroscopic energy densities. (a) Evaluate Terms. (b) Local Solution. Solution for variables in terms of unknowns in regions evaluated by other processes. (c) Central Solution. Final solution of the reduced stabilizer equations either on the central process or on a designated satellite process. (d) Solution Storage. The global solution is stored in the local component data structures, and new time void fractions computed. Checks are made for excessive void fraction change that may trigger a time step backup. 7. Conduction Solution. Given boundary conditions from fluid components, and power from tables or kinetics calculations, the conduction equation is solved for metal temperatures in each heat structure in the system 8. Central Status Check. This occurs automatically during the status check for data transfer at the end of step 7. The central process checks to see if an excessive void fraction change or heat transfer energy error requires a backup. If not, information is transmitted on whether or not it is time for various edits. Satellite processes must respond to a request for a restart dump. 9. Time Step Wrap-up. Once all tests are cleared that might backup the time step. Some dependent variables are evaluated before cycling to the next step.

7.5.3

ECI Modules

ECI is mainly written in FORTRAN90 language, unless two classes written in C++ related to the socket communication. It needs several Modules without modification and other that have to be largely modified. A little review of each one is included in this chapter. • ExTransferM. High level driver subroutines for the exterior data transfer management. These subroutines are not dependent on the TRACE data structure, and should be used without modification for any other program using ECI data transfer interface.


68

Is in charge of many important tasks as accept the transmission, check the information, read it set it, send it or request the missing information to other process. • TaskDataM. Data structures supporting exterior transfer. • SpecExTransM. High level driver subroutines for the exterior data transfer. These subroutines are dependent on the calling program’s data structure, and must be modified for use in each specific program using this data transfer interface. This is one of the modules that needs more modifications in order to work coupled with TRACE. It requires specific knowledge of the code data structure to locate variables and components. • GenUtilM. Utility subprograms that are independent of the TRACE data structure. It should be used without modification for any other program using this data transfer interface, to provide access to the subroutines ReadNext, NextWord, and Search. • SyncPointsM. A list of synchronization points at which data transfers take place. • FluidVarListsM. This contains lists of fluid variables associated with flow junctions. It includes lists of cell edge variables, variables that require sign convention adjustments, translation tables for generic junction variable names, and lists of fluid variables required at each synchronization point. To use it in SUBCHANECI it has to be largely modified. • HSvarListsM. This contains lists of variables with information needed for transfer of heat to fluid at the surface of a heat conduction structure. It is also used by the TRACE internal data transfer service, for moving data between a heat structure and a fluid component. This module is TRACE specific, but could be useful to programmers of fluid flow or conduction programs, which use this interface to solve problems in conjunction with TRACE. It will remain as is in SCF-ECI component, since the Heat produced will not be transmitted out of the core. • IoM. This provides unit numbers for a message file (imout) and the terminal (itty). For SCF-ECI a revised version can be created with new definitions of the variables imout and itty.


69

• IntrTypeM. This provides Fortran 90 KIND definitions for REAL and INTEGER data types. • TableTransfersM. This provides derived types and subroutines used for table driven data transfers. • CFacesM. Is the interface to define the calls to C++ functions. • CIpcFunc. C++ functions implementing system specific setup and message passing calls. • CipcInclude. Definitions used by CIpcFunc. Some changes to the original code where already made in order to increase the socket size to deal with big buffers. It has been replaced both TRACE and SCF-ECI

In addition the ECI requires the files error and StopCode to print error messages and stop execution of the code respectively.

7.5.4

ECI Process

The process begins with the tasks setting, to initialize the interprocess communications, and provide information on all contributing tasks to each of the tasks involved in the system simulation. Whenever information is required that is not available in the process, it should be provided by other process. This builds a list of missing variables, their expected locations, and time of transfer. Once the program has set all of it’s internal initial conditions the components needed by each task but not present in that task, have to be located. During this exchange, a data structure is established to permit full solution of flow equations spanning multiple processes. To support this process, program specific implementations must be generated in the module SpecExtrans. If all components are found, then it is possible to request scheduling for information transfer. Transfer tables for each synchronization point are created then. With transfers scheduled, all that remains is to drive the actual transfers. The synchronization points described have to be filled with the info needed at each one.


70

Figure 7.4: SCF-ECI and TRACE-ECI basic schema

7.5.5

Mapping Variables TRACE - SCF

The strength of coupling SCF through ECI component to TRACE is that TRACE remains exactly as is, no modifications to source code are needed. We have to develop an ECI component to SCF and also add an “EXTERIOR” component, adding one input data card with the component number and junction Id’s. This SCF EXTERIOR component has to be generic enough to allow not only TRACE coupling, but also other simulation codes needing flow information. The boundary and initial conditions to be overwritten should be available in the users manual. Each coupled code receive from the other a single string variable, which allows to find a pointer to the memory address where the variable is placed. In addition to preparing for transfer of equation terms, we have to be ready to provide variables listed in the module FluidVarLists. Also the variables responsible of momentum equations have to be transferred. One important set of variables to note in programming fluid applications are the edge averages for flux terms (faArl, faArv, faArc, faAra, faArel, faArev, faLiqFr, and faVapFr). Direct use of these in mass and energy equations can significantly cut the chances of errors which will violate mass or energy conservation at the interprocess flow junction. At this point we are concerned only in TRACE direction mapping, since SCF will only need each time step to fill its boundary conditions. A list of variables needed by TRACE is in Table 7.1 , split at each synchronization point. It is remarkable that only geometrical info and values at the edge (junction) are needed to the connexion.

Chapter 7. SCF-ECI-TRACE Table 7.1: ECI Input Transfers

dx vol fa hd grav dh elev type vv vl vvn vln pn

Cell length flow direction Cell volume. Cell- Edge flow area Hydraulic Diameter Gravity Hydraulic Diameter Cell- Centered elevations Either ”import” or ”export” Old gas velocity Old liquid velocity New gas velocity New liquid velocity Pressure Table 7.2: ECI Init Transfers

wfmfl wfmfv faFrac ellFlag

faLiq faVap dpdx tfLev tfLevB noLT grav

dh modelFlg cosT vln vvn dx vol fa alp alpo anySideJ

1 is assigned to the other process 1 is assigned to the other process Flow area fraction is a special code variable that tells whether the cell across the junction has side junctions. This currently has an impact on the choice of momentum transport terms along the direction of the primary 1-D mesh. effective cell edge areas for liquid flow effective cell edge areas for gas flow axial pressure gradient two-phase water levels two-phase water levels below Level flag. noLT = 1 =⇒ Level Model is OF F . noLT = 0 =⇒ Level Model is ON Gravitation terms (cosine of the angle between the direction of increasing cell index and a vector directed vertically upwards). Hydraulic Diameter Flag for special flow model through side junction cosine of the angle between the side connection New liquid velocity New gas velocity Cell Length in flow direction Cell volume Flow Area. Old void fraction Void fraction at the start of the previous step variable to flag a cell which is host to side junctions

71


alp

Old void fraction

alpA

void fraction ABOVE a water level at current timestep

alpB

void fraction BELOW a water level at current timestep

alpE

void fraction at cell boundaries (0.0 or 1.0)

alpn

New void fraction

alpnE

prevailing void fraction at cell boundary when there is phase separation in either cell adjacent to the boundary, i.e. philn > 0.0 in cell j + 1 or philn < 0.0 in cell j − 1

alpo

Void fraction at the start of the previous step

ara

Old stabilizer value for Macroscopic noncondensible gas density

arel

old time product of liquid fraction, liquid density, specific liquid internal energy

arev

old time product of vapor fraction,vapor density, specific vapor internal energy

arl

Macroscopic liquid density

arv

Macroscopic vapor density (i.e. (1 − alp) × rol)

bit

component bit flag array, used to flag whether or not a velocity is large enough for a sign change to require re-evaluation of the cell edge averages

cl

Liquid conductivity

cv

Gas conductivity

dpbl

the pressure gradient at the immediate cell

gam

Old vapor generation rate per unit volume.

hgam

Contribution to phase change from subcooled boiling

hls

Liquid specific enthalpy evaluated at the total pressure

hvs

Steam specific enthalpy, evaluated at the steam partial pressure

72

Chapter 7. SCF-ECI-TRACE lvlXing

variable that flags the moving water level across a cell boundary. A positive value at the top cell boundary means that the level is leaving the cell. A negative value at the top cell boundary means that a level is coming into the cell from the cell above. Similarly, a positive value at the bottom cell boundary means that a level is coming into the cell from the cell below. A negative value at the top cell boundary means that a level is leaving the cell. The absolute value of this variable is the amount of time in which the water level is expected to reach the cell boundary

p

Old total pressure

pa

Old non-condensible gas partial pressure

phil

distance between a water level and the cell boundary at previous timestep

philn

distance between a water level and the cell boundary

pn

Pressure

roa

Old non-condensible gas density

rol

Old liquid density

roln

New liquid density

rom

Mixture density (old time level)

rov

Old gas density (steam plus non-condensible)

rovn

New gas density (steam plus non-condensible)

sig

Surface tension

tfLev

variable to flag the presence of a water level

tfLevB

variable to flag the presence of a water level at the previous time step

tlE

liquid temperature at the cell boundary in the presence of a water level

tln

New liquid temperature

tvE

gas temperature at the cell boundary in the presence of a water level

tvn

New gas temperature

visl

Liquid viscosity

73

Chapter 7. SCF-ECI-TRACE visv

Gas mixture viscosity

vl

Old liquid velocity

vLev

velocity of two-phase water level in a cell

vln

New liquid velocity

vlto

Old stabilizer liquid velocity

volFracA

fraction fluid volume ABOVE a water level

volFracB

fraction fluid volume BELOW a water level

vv

Old gas velocity

vvn

New gas velocity

vvto

Old stabilizer gas velocity

wpackE

an integer array (length nfaces) indicating if a water pack has occurred in this cell at any of the faces with coefficients in the cDp array

xg

Mass fraction for multi-species NCG gases

xl

Mass fraction for multi-species NCG liquids Table 7.3: ECI OldTime Transfers

Table 7.4: ECI Control Transfers

phil

vlto

distance between a water level and the cell boundary at previous timestep distance between a water level and the cell boundary prevailing void fraction at cell boundary when there is phase separation in either cell adjacent to the boundary, i.e. philn > 0.0 in cell j + 1 or philn < 0.0 in cell j − 1. correction to the liquid volume over timestep delt due to a phase separation interface crossing a boundary correction to the vapor volume over timestep delt due to a phase separation interface crossing a boundary Old stabilizer liquid velocity

vvn

New gas velocity.

vln

New liquid velocity.

philn alpnE

dVolLiq dVolVap

74

Chapter 7. SCF-ECI-TRACE dfldp

Derivative of liquid velocity with respect to adjacent pressure

dfvdp

Derivative of vapor velocity with respect to adjacent pressure

bitn

Iteration flags for current time step.

faWlIn

Product of the junction flow area and the weight factor used on the liquid variable in this junction cell to compute the junction face average

faWlOut

Product of the junction flow area and the weight factor used on the liquid variable across the junction from this junction cell to compute the junction face average

faWvIn

Product of the junction flow area and the weight factor used on the gas variable in this junction cell to compute the junction face average

faWvOut

Product of the junction flow area and the weight factor used on the gas variable across the junction from this junction cell to compute the junction face average

faLiq

Effective cell edge areas for liquid flow

faVap

Effective cell edge areas for gas flow

faLiqFr

Product of faLiq and the edge average liquid fraction

faVapFr

Product of faVap and the edge average gas fraction

faArv

Product of faVap and the edge average macroscopic gas density (void fraction times density of the mixed steam and noncondensible)

faArl

Product of faLiq and the edge average macroscopic liquid density (liquid fraction times liquid density)

faAra

product of faVap and the edge average macroscopic noncondensible density (void fraction times noncondensible density)

faArc

Product of faLiq and the edge average macroscopic solute density

75

Chapter 7. SCF-ECI-TRACE faArev

Product of faVap and the edge average macroscopic gas energy density (void fraction times density of the mixed steam and non-condensible)

faArel

Product of faLiq and the edge average macroscopic liquid energy density (liquid fraction times liquid density)

faArxg

Rate of faArv

faArxl

Rate of faArl

fa

Cell- Edge flow area. Table 7.6: ECI SemiEdg Transfers

vvn

New vapor velocity

vln

New liquid velocity

alpn

New void fraction

rovn

New vapor density

roln

New liquid density

pn

New total pressure

tvn

New gas temperature

tln

New liquid temperature

bitn

Iteration flags for current time step

eln

new time liquid specific internal energy

evn

new time vapor specific internal energy

wpackE

water packing testing still needs the flags in wpackE(1) or wpackE(2) Table 7.7: ECI SemiSave Transfers

alpn

New void fraction

76

Chapter 7. SCF-ECI-TRACE bitn

Iteration flags for current time step

arvn

New stabilizer value for αρ vapor

arln

New stabilizer value for αρ liquid

arEln

New stabilizer value for αρ liquid at Edge

arEvn

New stabilizer value for αρ vapor at Edge

aran

New stabilizer value for αρ Macroscopic noncondensible air density

concn

Solute concentration

xgn

Gas species mass fractions

xln

Liquid species mass fractions Table 7.8: ECI Conduct Transfers

dpdx

Pressure Gradient

wfhf

Weighting factor of horizontal stratified flow

alpn

New void fraction Table 7.9: ECI StbVsave Transfers

dpdx

Pressure Gradient Table 7.10: ECI End Step Transfers

77


78

Table 7.5: ECI StbVset Transfers

vvt vlt alp arv arl arev arel ara p vvn vln faVap faLiq fa vlt vvt

7.5.6

New stabilizer gas velocity New stabilizer liquid velocity Old void fraction Macroscopic liquid density Macroscopic vapor density (i.e. (1 − alp) × rol). old time product of vapor fraction, liquid density, specific liquid internal energy old time product of liquid fraction, liquid density, specific vapor internal energy Old stabilizer value for Macroscopic noncondensible gas density Old total pressure. New gas velocity. New liquid velocity. Effective cell edge areas for gas Flow Effective cell edge areas for Liquid Flow Cell- Edge Flow Area New stabilizer Liquid Velocity New stabilizer Vapor Velocity

Mapping Variables SCF - TRACE

SCF only will ask TRACE about the values of boundary conditions needed to calculate each time step and, of course, as slave process will ask for the global variables needed to carry out the simulation time steps. The master ECI (In our case TRACE ) deals with the global information, asking to all processes about the time step they need and some other stuff. Table 7.11 contains all SCF global info, and only some of this variables will apply to ECI.

dpdx

Pressure Gradient

actual time step

numstep

maximum number of time steps

nmaxdt

output message for time stepping (automatic,

step comment

limited) actual elapsed simulated time

etime

start simulation time

start time

stop simulation time

stop time


79

minimum time step, calculated by the code

dtmin

maximum time step, calculated by the code

dtmax

input time step, which is also the maximum

dtinput

timestep, if no transient table is used (see Table 7.1) actual time step length

dt

Maximum allowed change of cladding tempera-

deltem clad max

ture per time step Maximum allowed change of fuel center temper-

deltem center max

ature per time step Maximum allowed change of coolant tempera-

deltem coolant max

ture per time step Maximum allowed change of vapor void fraction

delvoid max

per time step Table 7.11: Global Info Mapping

SCF boundary conditions should also be modified at the beginning of each time step.

Total starting flow rate at inlet (sum of channel

flostart

flow rate) Steady state driving pressure drop as boundary

presdrop

condition Transient driving pressure drop as boundary

presdriv

condition Reference pressure at outlet

pref

Inlet enthalpy difference to saturation (inlet sub-

delta h sub

cooling) Average inlet enthalpy

hin

Average inlet temperature

tin

Average inlet boron cocentration

bin


80

Average inlet mass flux

gin

Average inlet mass flow rate

fin

Thermal power added

power added

Total enthalpy flow rate out

enth out

Total enthalpy flow rate in

enth in

Difference in enthalpy (out − (in + power))

enth diff

Total outlet mass flow rate

flow out

Total inlet mass flow rate

flow in

Flow rate difference

flow diff

Reference inlet mass flow rate per channel, basis

finlet ref(:)

for transient change Transient inlet flow multiplier per channel

flowfac(:)

Table 7.12: Boundary conditions Mapping

Not all but much of this information has to be transferred during the simulation of the coupled system. The mapping of this information in a proper way is one of the most challenging tasks of ECI-SCF development and will be the only specific part belonging to TRACE-SCF coupling not valid to any other SCF coupling through ECI. However, much information will be the same in any other coupling with flow connections and the work must be well documented to avoid unnecesary work in the future.

7.6

SCF-ECI Outlook

A core model of a German Nuclear Power Plant has been designed and analysed its result for both TRACE and SCF. The model is simple enough to be the prototype for a coupled system helping to understand the results and find any problem that could arise during the output analysis of the Coupled System. The model is not representative of the coupled benefits, since both codes can represent the physics underlying this problem, but the main reasons and benefits were exposed


81

during this research. The code coupling categories, advantages and limitations of the different approaches were also discussed.

7.6.1

Road Map

The road map to achieve the full semi-implicit coupling is described. The most important tasks and a first approach of its duration are added.

1. Study coupling paradigms with its advantages and limitations to select the best one to SCF-TRACE 2. Prepare a simple test case to probe the coupling, taking into account that the model has to represent the core physics of a German Konvoi PWR. 3. ECI Overview and Testing (TRACE -ECI -TRACE) 4. Mapping of variables that have to be interchanged during the coupling. The values we need are the ones to assure mass and energy conservation. (a) List of TRACE and SCF variables and its definitions. (b) Module to add the needed variables in SCF as derivatives of the current existing ones. Estimated task duration: 4 weeks 5. Add a new input target to SCF to “tell” TRACE SCF component number (the id that TRACE will use) and the junctions that will be connected to it. This new input will be the “EXTERIOR component” of SCF. Estimated task duration: 2 weeks 6. Integration of ECI subroutines to SCF. This will be one of the greatest tasks, and can be done during several stages, starting with an explicit coupling only synchronizing info in the oldTimeStep stage and performing a “low filtering” [29] of pressures to achieve a convergence. Estimated task duration: 12 weeks 7. At this point, it will be decided if further coupling is needed, depending on the level of convergence achieved so far. The semi-implicit coupling means that some other synchronization points will request information to be transmitted between the codes. Stage 5 of ECI flow process. Estimated task duration: 4 weeks


82

8. SCF will need to add a recalculation if convergence is not achieved to TRACE, and a new time step is selected. (if convergence is not achieved to our benchmark will be a constraint). This task should be an INR development. (Not added to timing valoration) 9. Also an important point is to track TRACE development, since as NRC developers told us, during 2014 autumn will try to fix ECI bugs. As has been told during this work, TRACE will remain “as is”, but several little differences are expected to ECI version and those will have to be integrated in SCF version. (This task can vary its order depending on the NRC ECI reparation advancement). Estimated task duration: 1 week 10. Extensive results verification of the simplified Benchmark Case. Comparison between stand alone and coupled results. Estimated task duration: 6 weeks 11. Full Benchmark case with a full PWR Konvoi model (TRACE ) - full core model (SCF ) coupling. Estimated task duration: 3 weeks 12. Developer manual. Estimated task duration: 1 week 13. User Manual. Estimated task duration: 1 week 14. Benchmark Report. Estimated task duration: 2 weeks

The above project description has several constraints that makes this proposal a useful but not full scope coupling connection, since several points are beyond the scope of the proposed work. (See ECI-SCF limitations). One of the main strengths of this work is that TRACE code remains without no modifications. This feature helps very much to reduce the developing time, however a deep understanding of its calculus flow and the ECI is needed in order to achieve the final goal of success coupling. Other expected ECI-SCF feature is the possibility of being coupled to other codes following the same calculus flow and interchanging variables with other codes as Neutronic codes [30] or fuel codes [31] The current research covers the first points of the whole project till 4.a and also the evaluation of the “to do” task list that has been reported in this section.


7.6.2

83

Main goals

The interface will be a qualitative leap in SCF development, since can be thought as a general connection interface to couple distinct types of codes. Development of SCF-ECI interface itself in FORTRAN 90 code with the C++ interconnection routines to deal with socket daemon. Self coupling. This has to be demonstrated by a simple case providing boundary conditions to ECI or splitting SCF core in two models and deal with both processes. It is a test to demonstrate that is enough general to allow not only TRACE connection but a broad connection interface. Ready to be coupled to TRACE5.0 and perform the benchmark analysis successfully. Complete developer and user guides as well as benchmark report. This task has to be done in parallel with interphase design and development, and with verification but is stated as a single task to better know the project timing. So far the time dedicated to this project includes; codes analysis, model development and testing, coupling analysis and Thesis writing is about 18 weeks of full dedication. The man power is valued in 36 weeks to fulfill the above tasks and have both codes coupled and the full benchmark tested.

7.6.3

Limitations

Some limitations beyond the proposed work are anticipated to be found with the use of ECI. To have a full scope connection between both codes is a hard task, since somehow SCF and TRACE would need some kind of 3D connection and also interchange two phase flow properties in each TRACE calculus flow. However ECI was thought to afford all this staff [2], but TRACE5.0 release is quite limited in the way of using it, and the following patches are an involution in ECI state. Good news are that NRC program still want to support ECI development Apendix C. Then the fixing of the bugs and also the improvement of ECI connection will be an important fact in future releases. The main limitations found so far will be;

1. The junction connection is a 1D connection, since the current state of ECI single junction connections does not allow two nor three dimensional coupling. A further


84

step in the SCF-ECI development would be to have several junctions connected to SCF, this will be the step to have somehow 2D connection between both codes. 2. BWR connection will need further work to allow data transfer, but is out of the scope of the desired coupling so far.

The most important risk that this project has to face is the convergence problem that could appear with the Pressure Drop agreement between codes. This problem has been studied during this research, and the semi-implicit coupling scheme described during this work should be enough to avoid this risk.

Appendix A

TRACE Steady State free format * ************* * main data * ************* * *

numtcr

ieos

inopt

nmat

id2o

1

0

1

0

0

dwr fuel assembly represented by pipes, htstr and power * * ***************** * namelist data * ***************** * &inopts cpuflg=1, dtstrt=-1.0, iadded=10, iconht=0, idiag=4, ikfac=0, ndia1=2, noair=1, nofat=.TRUE., nosets=0, nsdl=0,

85

Appendix A. TRACE Steady State

86

nsdu=5, nspl=0, nspu=5, usesjc=3, npower=1, nhtstr=3 &end * *************** * Model Flags * *************** * *

*

*

*

*

dstep

timet

0

0.0

stdyst

transi

ncomp

njun

ipak

1

0

9

4

1

epso

epss

1.0E-4

1.0E-4

oitmax

sitmax

isolut

ncontr

nccfl

10

10

0

0

0

ntsv

ntcb

ntcf

ntrp

ntcp

1

0

0

0

0

* ************************* * component-number data * ************************* * *

Component input order (IORDER)

*-- type ---- num ------------- name ----------------

+

jun1

* FILL

*

1 s * $1$liquid fill

+

10

* PIPE

*

2 s * UO2 PWR Fuel Assembly

+

80

* BREAK

*

3 s * $3$ break p = 1.58E7 pa

+

100

* HTSTR

*

10 s * $10$ heatstr for FA1

+

* HTSTR

*


+

* HTSTR

*


+

* PIPE

*

31 s * Core inlet Volume

+

10

80

* PIPE

*

41 s * Core outlet Volume

+

90

100

* POWER

*

100 e * $100$ PWR Core Power

+

* * **************************************************

jun2

90

jun3


87

* Starting Signal Variable Section of Model

*

************************************************** *n: TimeOf * *

idsv

isvn

ilcn

icn1

icn2

1

0

0

0

0

************************************************** * Finished Signal Variable Section of Model

*

************************************************** * * * * *******

type

num

userid

1

0

jun1

ifty

ioff

10

2

0

twtold

rfmx

concin

felv

0.0

1.0E20

0.0

0.0

dxin

volin

alpin

vlin

0.39

1.080015

fill *

*

*

*

component name

0.0

$1$liquid fill

tlin

0.0

564.15

pin

pain

flowin

vvin

tvin

1.58E7

0.0

1.8682E4

0.0

0.0

type

num

userid

2

0

ncells

nodes

jun1

jun2

epsw

10

0

80

90

4.5E-5

ichf

iconc

pipetype

ipow

npipes

2

0

0

0

1

radin

th

houtl

houtv

toutl

0.0

0.0

0.0

0.0

0.0

toutv

pwin

pwoff

rpwmx

pwscl

0.0

0.0

0.0

0.0

0.0

* * ******* pipe *

*

component name UO2 PWR Fuel Assembly

nsides 0

*

*

*

* dx

*

0.39

0.39

0.39

0.39s

* dx

*

0.39

0.39

0.39

0.39s

* dx

*

0.39

0.39e

* vol

*

2.1600303

2.1600303

2.1600303s

2.1600303

Appendix A. TRACE Steady State * vol

*

2.1600303

2.1600303

* vol

*

2.1600303

2.1600303e

* fa

*

5.538539

* fa

*

* fa

88 2.1600303

2.1600303s

5.538539

5.538539

5.538539s

5.538539

5.538539

5.538539

5.538539s

*

5.538539

5.538539

5.538539e

* fric

*

0.012

0.012

0.012

0.012s

* fric

*

0.012

0.012

0.012

0.012s

* fric

*

0.012

0.012

0.012e

* grav

*

1.0

1.0

1.0

1.0s

* grav

*

1.0

1.0

1.0

1.0s

* grav

*

1.0

1.0

1.0e

* hd

*

0.012076

0.012076

0.012076

0.012076s

* hd

*

0.012076

0.012076

0.012076

0.012076s

* hd

*

0.012076

0.012076

0.012076e

* hd-ht *

0.0

0.0133049

0.0133049

0.0133049s

* hd-ht *

0.0133049

0.0133049

0.0133049

0.0133049s

* hd-ht *

0.0133049

0.0133049

0.0133049e

* nff

*

1

0

0

0s

* nff

*

0

0

0

0s

* nff

*

0

0

0e

* alp

*

0.0

0.0

0.0

0.0s

* alp

*

0.0

0.0

0.0

0.0s

* alp

*

0.0

0.0e

* vl

*

5.0

4.0

4.0

4.0s

* vl

*

4.0

4.0

4.0

4.0s

* vl

*

4.0

4.0

4.0e

* vv

*

5.0

4.0

4.0

4.0s

* vv

*

4.0

4.0

4.0

4.0s

* vv

*

4.0

4.0

4.0e

* tl

*

564.15

564.15

564.15

564.15s

* tl

*

564.15

564.15

564.15

564.15s

* tl

*

564.15

564.15e

* tv

*

564.15

564.15

564.15

564.15s

* tv

*

564.15

564.15

564.15

564.15s

* tv

*

564.15

564.15e

* p

*

1.58E7

1.58E7

1.58E7

1.58E7s

* p

*

1.58E7

1.58E7

1.58E7

1.58E7s

* p

*

1.58E7

1.58E7e

* pa

*

0.0

0.0

0.0

0.0s

* pa

*

0.0

0.0

0.0

0.0s

* pa

*

0.0

0.0e


89

* * *******

type

num

userid

3

0

jun1

ibty

isat

ioff

adjpress

100

0

2

0

0

dxin

volin

alpin

tin

pin

0.4265

1.0

1.0

599.15

1.58E7

pain

concin

rbmx

poff

belv

0.0

0.0

1.0E20

0.0

0.0

type

num

userid

31

0

ncells

nodes

jun1

jun2

epsw

2

0

10

80

0.0

ichf

iconc

pipetype

ipow

npipes

1

0

0

0

1

radin

th

houtl

houtv

toutl

0.0

0.0

0.0

0.0

0.0

toutv

pwin

pwoff

rpwmx

pwscl

0.0

0.0

0.0

0.0

0.0

break *

*

*

component name $3$ break p = 1.58E7 pa

* * ******* pipe *

*

component name Core inlet Volume

nsides 0

*

*

*

* dx

*

0.195

0.195e

* vol

*

1.080015

1.080015e

* fa

*

5.538539

5.538539

* fric

*

0.012

0.012

* grav

*

1.0

1.0

1.0e

* hd

*

0.012076

0.012076

0.012076e

* hd-ht *

0.0

0.0

0.0e

1

1e

5.538539e 0.012e

* nff

*

1

* alp

*

0.0

0.0e

* vl

*

5.0

5.0

5.0e

* vv

*

5.0

5.0

5.0e

* tl

*

564.15

564.15e

* tv

*

564.15

564.15e

* p

*

1.58E7

1.58E7e

* pa

*

0.0

0.0e

* *

Appendix A. TRACE Steady State *******

type

num

userid

41

0

ncells

nodes

jun1

jun2

epsw

2

0

90

100

0.0

ichf

iconc

pipetype

ipow

npipes

1

0

0

0

1

radin

th

houtl

houtv

toutl

0.0

0.0

0.0

0.0

0.0

toutv

pwin

pwoff

rpwmx

pwscl

0.0

0.0

0.0

0.0

0.0

pipe *

*

90 component name Core outlet Volume

nsides 0

*

*

*

* dx

*

0.195

0.195e

* vol

*

1.080015

1.080015e

* fa

*

5.538539

5.538539

* fric

*

0.012

0.012

* grav

*

1.0

1.0

1.0e

* hd

*

0.012076

0.012076

0.012076e

* hd-ht *

0.0133049

0.0133049

0.0e

0

1e

5.538539e 0.012e

* nff

*

0

* alp

*

0.0

0.0e

* vl

*

4.0

4.0

5.0e

* vv

*

4.0

4.0

5.0e

* tl

*

599.15

599.15e

* tv

*

599.15

599.15e

* p

*

1.58E7

1.58E7e

* pa

*

0.0

0.0e

* * ******************************************** * Starting Heat Structure Section of Model * ******************************************** * *******

type

num

userid

10

1

nzhstr

ittc

hscyl

ichf

10

0

1

2

nofuelrod

plane

liqlev

iaxcnd

pdrat

0

1

0

0

1.33684

nmwrx

nfci

nfcil

hdri

hdro

0

0

0

0.0

0.0

htstr *

*

*

component name $10$ heatstr for FA1

Appendix A. TRACE Steady State *

*

91

nhot

nodes

fmon

nzmax

reflood

0

8

0

45

0

dtxht(1)

dtxht(2)

dznht

hgapo

0.0

0.0

0.01

5670.0

* *

idbcin *

0

0

0

0s

*

idbcin *

0

0

0

0s

*

idbcin *

0

0e

*

idbcon *

2

2

2

2s

*

idbcon *

2

2

2

2s

*

idbcon *

2

2e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

* hcomon2 *

2

1

0

0e

* hcomon2 *

2

2

0

0e

* hcomon2 *

2

3

0

0e

* hcomon2 *

2

4

0

0e

* hcomon2 *

2

5

0

0e

* hcomon2 *

2

6

0

0e

* hcomon2 *

2

7

0

0e

* hcomon2 *

2

8

0

0e

* hcomon2 *

2

9

0

0e

* hcomon2 *

2

10

0

0e

* dhtstrz *

0.39

0.39

0.39

0.39s

* dhtstrz *

0.39

0.39

0.39

0.39s

* dhtstrz *

0.39

0.39e

*

rdx

*

1.44E4e

*

radrd

*

0.0

2.01E-3

2.85E-3

*

radrd

*

4.11E-3

4.44E-3

4.75E-3e

*

matrd

*

1

1

1

*

matrd

*

3

2

2 e

*

nfax *

1

1

1

1s

*

nfax *

1

1

1

1s

3.49E-3

1 s

4.03E-3s


92

*

nfax *

1

1e

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95e

*

fpuo2 *

0.0e

*

ftd *

0.945e

*

gmix * f

0.0e

*

gmles *

0.0e

*

pgapt *

0.0e

*

plvol *

0.0 e

*

pslen *

0.0 e

*

clenn *

0.0 e

*

burn *

1.54E4

1.54E4

1.54E4

1.54E4s

*

burn *

1.54E4

1.54E4

1.54E4

1.54E4s

*

burn *

1.54E4

1.54E4e

* *******

type

num

userid

20

1

nzhstr

ittc

hscyl

ichf

10

0

1

2

nofuelrod

plane

liqlev

iaxcnd

pdrat

0

1

0

0

1.33684

nmwrx

nfci

nfcil

hdri

hdro

0

0

0

0.0

0.0

htstr *

*

*



*

93

nhot

nodes

fmon

nzmax

reflood

0

8

0

45

0

dtxht(1)

dtxht(2)

dznht

hgapo

0.0

0.0

0.01

5670.0

* *

idbcin *

0

0

0

0s

*

idbcin *

0

0

0

0s

*

idbcin *

0

0e

*

idbcon *

2

2

2

2s

*

idbcon *

2

2

2

2s

*

idbcon *

2

2e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

* hcomon2 *

2

1

0

0e

* hcomon2 *

2

2

0

0e

* hcomon2 *

2

3

0

0e

* hcomon2 *

2

4

0

0e

* hcomon2 *

2

5

0

0e

* hcomon2 *

2

6

0

0e

* hcomon2 *

2

7

0

0e

* hcomon2 *

2

8

0

0e

* hcomon2 *

2

9

0

0e

* hcomon2 *

2

10

0

0e

* dhtstrz *

0.39

0.39

0.39

0.39s

* dhtstrz *

0.39

0.39

0.39

0.39s

* dhtstrz *

0.39

0.39e

*

rdx

*

2.43E4e

*

radrd

*

0.0

2.01E-3

2.85E-3

*

radrd

*

4.11E-3

4.44E-3

4.75E-3e

*

matrd

*

1

1

1

*

matrd

*

3

2

2 e

*

nfax *

1

1

1

1s

*

nfax *

1

1

1

1s

3.49E-3

1 s

4.03E-3s


94

*

nfax *

1

1e

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95e

*

fpuo2 *

0.0e

*

ftd *

0.945e

*

gmix * f

0.0e

*

gmles *

0.0e

*

pgapt *

0.0e

*

plvol *

0.0 e

*

pslen *

0.0 e

*

clenn *

0.0 e

*

burn *

1.54E4

1.54E4

1.54E4

1.54E4s

*

burn *

1.54E4

1.54E4

1.54E4

1.54E4s

*

burn *

1.54E4

1.54E4e

* *******

type

num

userid

30

1

nzhstr

ittc

hscyl

ichf

10

0

1

2

nofuelrod

plane

liqlev

iaxcnd

pdrat

0

1

0

0

1.18139

nmwrx

nfci

nfcil

hdri

hdro

0

0

0

0.0

0.0

htstr *

*

*



*

95

nhot

nodes

fmon

nzmax

reflood

0

8

0

45

0

dtxht(1)

dtxht(2)

dznht

hgapo

0.0

0.0

0.01

5670.0

* *

idbcin *

0

0

0

0s

*

idbcin *

0

0

0

0s

*

idbcin *

0

0e

*

idbcon *

2

2

2

2s

*

idbcon *

2

2

2

2s

*

idbcon *

2

2e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

*qflxbco1 *

0.0e

* hcomon2 *

2

1

0

0e

* hcomon2 *

2

2

0

0e

* hcomon2 *

2

3

0

0e

* hcomon2 *

2

4

0

0e

* hcomon2 *

2

5

0

0e

* hcomon2 *

2

6

0

0e

* hcomon2 *

2

7

0

0e

* hcomon2 *

2

8

0

0e

* hcomon2 *

2

9

0

0e

* hcomon2 *

2

10

0

0e

* dhtstrz *

0.39

0.39

0.39

0.39s

* dhtstrz *

0.39

0.39

0.39

0.39s

* dhtstrz *

0.39

0.39e

*

rdx

*

1.5104E4e

*

radrd

*

0.0

2.28E-3

3.22E-3

*

radrd

*

4.65E-3

5.03E-3

5.38E-3e

*

matrd

*

1

1

1

*

matrd

*

3

2

2 e

*

nfax *

1

1

1

1s

*

nfax *

1

1

1

1s

3.94E-3

1 s

4.56E-3s


96

*

nfax *

1

1e

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95s

*

rftn *

605.95

605.95

605.95

605.95e

*

fpuo2 *

2.0e

*

ftd *

0.945e

*

gmix * f

0.0e

*

gmles *

0.0e

*

pgapt *

0.0e

*

plvol *

0.0 e

*

pslen *

0.0 e

*

clenn *

0.0 e

*

burn *

1.54E4

1.54E4

1.54E4

1.54E4s

*

burn *

1.54E4

1.54E4

1.54E4

1.54E4s

*

burn *

1.54E4

1.54E4e

******************************************** * Finished Heat Structure Section of Model * ******************************************** * * * * ***************************************** *

Starting Power Components

*


97

***************************************** * *******

type

power *

*

*

0

*

*

*

*

*

*

10

20

component name $100$ PWR Core Power

30 e

irpwty

ndgx

ndhx

nrts

nhist

11

6

71

10

1

q235

q239

q238

qavg

r239pf

200.0

200.0

200.0

200.0

0.8

fisphi

rans

fp235

fp238

2.3

1.0

1.0

0.0

izpwtr

izpwsv

nzpwtb

nzpwsv

nzpwrf

0

1

1

0

0

ipwrad

ipwdep

promheat

decaheat

wtbypass

0

0

0.0

0.0

0.0

nzpwz

nzpwi

nfbpwt

nrpwr

nrpwi

0

0

0

1

0

react

tneut

rpwoff

rrpwmx

rpwscl

0.0

0.0

0.0

1.0E10

1.0

rpowri

zpwin

zpwoff

rzpwmx

3.85E9

0.0

0.0

0.0

extsou

pldr

pdrat

fucrac

0.0

4.025E-3

1.3368

1.0

ircjtb 1,0

ircjtb 2,0

ircjtb 3,0

ircjtb 4,0

ibu 0

8

1

1

1

0

ircjtb 1,1

ircjtb 2,1

ircjtb 3,1

ircjtb 4,1

ibu 1

1

6

1

1

0

ircjtb 1,2

ircjtb 2,2

ircjtb 3,2

ircjtb 4,2

ibu 2

1

1

1

1

0

ircjtb 1,3

ircjtb 2,3

ircjtb 3,3

ircjtb 4,3

ibu 3

1

1

1

1

0

ircjfm1

ircjfm2

ircjfm3

ircjfm4

isnotb

0

0

0

0

0

powexp

bpp0

bpp1

bpp2

bpp3

2.0

0.0

0.0

0.0

0.0

*

*

0

3

*

*

100 chanpow

*

*

userid

numpwr

* htnum * *

num

* rdpwr1*

1.0

1.0

1.0

* rdpwr1*

0.0

0.0

0.0e

* rdpwr2*

1.0

1.0

1.0

* rdpwr2*

0.0

0.0

0.0e

1.0

1.0s

1.0

1.0s


98

* rdpwr3*

1.0

1.0

1.0

* rdpwr3*

0.0

0.0

0.0e

* cpowr *

0.2676

0.4516

0.2807e

1.0

1.0s

* zpwtb1*

0.0s

* zpwtb1*

0.4

0.69

0.94

1.22

1.4s

* zpwtb1*

1.34

1.16

0.88

0.7

0.4e

* zpwtb2*

0.0s

* zpwtb2*

0.4

0.69

0.94

1.22

1.4s

* zpwtb2*

1.34

1.16

0.88

0.7

0.4e

* zpwtb3*

0.0s

* zpwtb3*

0.4

0.69

0.94

1.22

1.4s

* zpwtb3*

1.34

1.16

0.88

0.7

0.4e

* rctf

*

323.0

473.0

564.0

673.0

773.0s

* rctf

*

873.0

1073.0

1473.0

0.0

0.0s

* rctf

*

0.0

-2.84e-5

-2.84e-5

-2.84E-5

-2.84e-5s

* rctf

*

-2.84e-5

-2.84e-5

-2.84e-5

-2.84e-5e

* rctc

*

0.0

323.0

473.0

523.0

564.0s

* rctc

*

573.3

603.0

0.0

0.0

-3.93e-4s

* rctc

*

-3.93e-4

-3.93e-4

-3.93e-4

-3.93e-4

-3.93e-4e

* rcal

*

0.0

0.0

0.0

0.0

-0.12345e

* rcbm

*

0.0

0.0

0.0

0.0

-2.321E-5e

* beta

*

1.69E-4

8.32E-4

2.64E-3

1.22E-3

1.38E-3s

* beta

*

2.47E-4e 1.4

0.311

0.115

0.0317s

* lamda *

3.87

* lamda *

0.0127e

***************************************** *

Finished Power Components

*

***************************************** * * * end * ***************** * Timestep Data * ***************** *

*

*

dtmin

dtmax

tend

rtwfp

1.0E-9

1.0E-3

100.0

1.0

edint

gfint

dmpint

sedint

50.0

1.0

1.0

10.0


endflag -1.0

99

Appendix B

SCF Steady State Input !-----------------------------------------------------------------------------&initialisation title = ’KONVOI Core Benchmark Ivan Fernandez’ !-------------------------------------------------------------!Rectangular_geometry = on ! !Fuel_assembly_base(nodal) = on !Pin_by_pin_base(local) = off !Hybrid_solution = off !structural_mesh = off !triangular_mesh = off ! !coolant_center_subchannels = off !mesh_displacement_in_x_cm = 160.64 !mesh_displacement_in_y_cm = 160.65 !mesh_displacement_in_z_cm = 0.0 !mesh_rotation_theta_degre = 0.0 ! !total_fuel_assemblies = 193 !total_hybrid_assemblies = 0 !fuel_assembly_pitch = 0.23116 !pin_pitch = 0.0127 !pin_boundary_pitch = 0.0127 !subchannels_in_x_for_one_FA = 17 !fuel_Doppler_lambda = 0.7 !power_normalization = 0 !time_interpolation = 0 ! !transient = off !printing = 20 !rod_no_start = 0 !rod_no_end = 0 !every = 0.05 ! !use_maps = off !columns = 17 !rows = 17 !file_location = ’/home/ivan/Documents/MAsterNuclear/Project/Inputs/SUBCHANFLOW’ !NK_map = nk_map_mox.txt !TH_map = th_map_mox.txt !-----------------------------------------------------------------------------&properties set_water = on

100

Appendix B. SCF Steady State Input set_lead_bismuth = off set_lead = off set_sodium = off set_helium = off set_air = off !-----------------------------------------------------------------------------&correlations set_subcooled_void_levy = off set_subcooled_void_saha_zuber = off set_subcooled_void_unal = off set_subcooled_void_bowring = on set_subcooled_void_none = off ! set_boiling_void_homogeneous = off set_boiling_void_armand_mod = on set_boiling_void_smith = off set_boiling_void_chexal_lellouche = off ! set_two_phase_friction_homogeneous = off set_two_phase_friction_armand = on set_two_phase_friction_lockhart = off ! set_turbulent_friction_blasius = off set_turbulent_friction_rehme_wire = off set_turbulent_friction_rehme_grid = off set_turbulent_friction_churchill = on ! set_heat_transfer_dittus_boelter = off set_heat_transfer_gnielinski = on set_heat_transfer_subbotin = off ! set_chf_barnett+b&w = off set_chf_biasi = on set_chf_okb = off set_chf_w3 = off set_chf_levitan = off set_chf_epri = off ! set_shape_chf_none = on set_shape_chf_cobra4i = off set_shape_chf_tong = off set_shape_chf_w3 = off set_shape_chf_smolin = off ! set_simple_fuel_cladding_gap = on set_transuranus_urgap_fuel_cladding_gap = off set_vver1000_benchmark_fuel_cladding_gap = off ! ! single phase friction factor = aa * reynolds**bb + cc ! for blasius only ! ! laminar blasius_laminar_prefactor = 64.0 blasius_laminar_reynolds_exponent = -1.0 blasius_laminar_constant = 0.0 ! turbulent blasius_turbulent_prefactor = 0.316 blasius_turbulent_reynolds_exponent = -0.25 blasius_turbulent_constant = 0.0 ! roughness = 1.5e-5 ! for churchill only (http://fluid.itcmp.pwr.wroc.pl/~znmp/dydaktyka/fundam_FM/Lecture11_12.pdf) ! ! heat transfer coefficient = (k/d)*(aa * reynolds**bb * prandtl**cc + dd) ! for dittus-boelter only !

101

Appendix B. SCF Steady State Input

102

dittus_boelter_prefactor = 0.023 dittus_boelter_reynolds_exponent = 0.8 dittus_boelter_prandtl_exponent = 0.4 dittus_boelter_constant = 0.0 ! effective_emissivity = 0.0 ! chf_multiplier = 1.0e10 !-----------------------------------------------------------------------------&special_parameters rod_pitch = 0.0127 rod_diameter = 0.95e-2 wire_wrap_pitch = 0.0 wire_wrap_diameter = 0.0 perimeter_ratio = 0.0 !-----------------------------------------------------------------------------&axial_heat_flux ! file = this_file ! relative_axial_location 0.000000

relative_heat_flux 0.40

0.020833

0.46

0.062500

0.58

0.104167

0.69

0.145833

0.79

0.187500

0.88

0.229167

0.99

0.270833

1.09

0.312500

1.22

0.354167

1.22

0.395833

1.34

0.437500

1.34

0.479167

1.40

0.520833

1.40

0.562500

1.34

0.604167

1.34

0.645833

1.22

0.687500

1.22

0.729167

1.09

0.770833

0.99

0.812500

0.88

0.854167

0.79

0.895833

0.69

0.937500

0.58

0.979167

0.46

1.000000

0.40

! !-----------------------------------------------------------------------------&channel_layout ! file = this_file ! channel_number

channel_area

wetted_perimeter

heated_perimeter

1

0.02859047

9.882445179

8.953539063

-0.69

-1.61

2

0.02859047

9.882445179

8.953539063

-0.46

-1.61

3

0.02859047

9.882445179

8.953539063

-0.23

4

0.02859047

9.882445179

8.953539063

0

5

0.02859047

9.882445179

8.953539063

0.23

-1.61

6

0.02859047

9.882445179

8.953539063

0.46

-1.61

7

0.02859047

9.882445179

8.953539063

0.69

-1.61

8

0.02859047

9.882445179

8.953539063

-1.15

-1.38

9

0.02859047

9.882445179

8.953539063

-0.92

-1.38

-1.61 -1.61

10

0.02859047

9.882445179

8.953539063

-0.69

-1.38

11

0.02859047

9.882445179

8.953539063

-0.46

-1.38

x_position

y_position


103

12

0.02859047

9.882445179

8.953539063

-0.23

13

0.02859047

9.882445179

8.953539063

0

14

0.02859047

9.882445179

8.953539063

0.23

-1.38

15

0.02859047

9.882445179

8.953539063

0.46

-1.38

16

0.02859047

9.882445179

8.953539063

0.69

-1.38

17

0.02859047

9.882445179

8.953539063

0.92

-1.38

18

0.02859047

9.882445179

8.953539063

1.15

-1.38

19

0.02859047

9.882445179

8.953539063

-1.38

-1.15

20

0.02859047

9.882445179

8.953539063

-1.15

-1.15

21

0.02859047

9.882445179

8.953539063

-0.92

22

0.028912

8.744308992

7.970220562

-0.69

-1.15

23

0.028912

8.744308992

7.970220562

-0.46

-1.15

24

0.02859047

25

0.028912

26

0.02859047

27

0.028912

8.744308992

7.970220562

0.46

-1.15

28

0.028912

8.744308992

7.970220562

0.69

-1.15

29

0.02859047

9.882445179

8.953539063

0.92

-1.15

30

0.02859047

9.882445179

8.953539063

1.15

-1.15

31

0.02859047

9.882445179

8.953539063

1.38

-1.15

32

0.02859047

9.882445179

8.953539063

-1.38

33

0.02859047

9.882445179

8.953539063

-1.15

34

0.028912

8.744308992

7.970220562

-0.92

-0.92

35

0.028912

8.744308992

7.970220562

-0.69

-0.92

36

0.02859047

37

0.028912

38

0.02859047

39

0.028912

40

0.02859047

41

0.028912

8.744308992

7.970220562

0.69

-0.92

42

0.028912

8.744308992

7.970220562

0.92

-0.92

43

0.02859047

9.882445179

8.953539063

1.15

-0.92

44

0.02859047

9.882445179

8.953539063

1.38

-0.92

45

0.02859047

9.882445179

8.953539063

-1.61

46

0.02859047

9.882445179

8.953539063

-1.38

47

0.028912

8.744308992

7.970220562

-1.15

-0.69

48

0.028912

8.744308992

7.970220562

-0.92

-0.69

49

0.02859047

50

0.028912

51

0.02859047

9.882445179

8.953539063

-0.23

52

0.02859047

9.882445179

8.953539063

0

53

0.02859047

54

0.028912

55

0.02859047

56

0.028912

8.744308992

7.970220562

0.92

-0.69

57

0.028912

8.744308992

7.970220562

1.15

-0.69

58

0.02859047

9.882445179

8.953539063

1.38

-0.69

59

0.02859047

9.882445179

8.953539063

1.61

-0.69

60

0.02859047

9.882445179

8.953539063

-1.61

61

0.02859047

9.882445179

8.953539063

-1.38

62

0.028912

63

0.02859047

64

0.028912

8.744308992

7.970220562

-0.69

-0.46

65

0.028912

8.744308992

7.970220562

-0.46

-0.46

66

0.028912

8.744308992

7.970220562

-0.23

67

0.02859047

68

0.028912

8.744308992

7.970220562

0.23

-0.46

69

0.028912

8.744308992

7.970220562

0.46

-0.46

70

0.028912

8.744308992

7.970220562

0.69

-0.46

71

0.02859047

72

0.028912

73

0.02859047

9.882445179

8.953539063

1.38

-0.46

74

0.02859047

9.882445179

8.953539063

1.61

-0.46

75

0.02859047

9.882445179

8.953539063

-1.61

-0.23

76

0.02859047

9.882445179

8.953539063

-1.38

-0.23

9.882445179 8.744308992 9.882445179

9.882445179 8.744308992 9.882445179 8.744308992 9.882445179

9.882445179 8.744308992

9.882445179 8.744308992 9.882445179

8.744308992 9.882445179

9.882445179

9.882445179 8.744308992

8.953539063 7.970220562 8.953539063

8.953539063 7.970220562 8.953539063 7.970220562 8.953539063

8.953539063 7.970220562

8.953539063 7.970220562 8.953539063

7.970220562 8.953539063

8.953539063

8.953539063 7.970220562

-1.38 -1.38

-1.15

-0.23 0

-1.15 -1.15

0.23

-0.46 -0.23 0 0.23 0.46

-0.69 -0.46

0.23 0.46 0.69

-1.15 -0.92

0

0.92 1.15

-1.15

-0.92 -0.92

-0.92 -0.92 -0.92 -0.92 -0.92

-0.69 -0.69

-0.69 -0.69 -0.69 -0.69 -0.69 -0.69 -0.69

-0.46 -0.46 -0.46 -0.46

-0.46 -0.46

-0.46 -0.46

Appendix B. SCF Steady State Input 9.882445179

77

0.02859047

78

0.028912

79

0.02859047

80

0.028912

8.744308992

7.970220562

-0.46

81

0.028912

8.744308992

7.970220562

-0.23

82

0.02859047

83

0.028912

8.744308992

7.970220562

0.23

-0.23

84

0.028912

8.744308992

7.970220562

0.46

-0.23

85

0.02859047

86

0.028912

87

0.02859047

9.882445179

8.953539063

1.15

-0.23

88

0.02859047

9.882445179

8.953539063

1.38

-0.23

89

0.02859047

9.882445179

8.953539063

1.61

-0.23

90

0.02859047

9.882445179

8.953539063

-1.61

91

0.02859047

9.882445179

8.953539063

-1.38

92

0.028912

93

0.02859047

9.882445179

8.953539063

-0.92

0

94

0.02859047

9.882445179

8.953539063

-0.69

0

95

0.02859047

9.882445179

8.953539063

-0.46

0

96

0.02859047

9.882445179

8.953539063

-0.23

97

0.02859047

9.882445179

8.953539063

0

98

0.02859047

9.882445179

8.953539063

0.23

0

99

0.02859047

9.882445179

8.953539063

0.46

0

8.744308992 9.882445179

9.882445179

9.882445179 8.744308992

8.744308992

8.953539063

104

7.970220562 8.953539063

8.953539063

8.953539063 7.970220562

7.970220562

-1.15

-0.23

-0.92

-0.23

-0.69

0

-0.23 -0.23 -0.23 -0.23

0.69

-0.23

0.92

-0.23

0 0

-1.15

0

0 0

100

0.02859047

9.882445179

8.953539063

0.69

101

0.02859047

9.882445179

8.953539063

0.92

102

0.028912

103

0.02859047

9.882445179

8.953539063

1.38

0

104

0.02859047

9.882445179

8.953539063

1.61

0

105

0.02859047

9.882445179

8.953539063

-1.61

0.23

106

0.02859047

9.882445179

8.953539063

-1.38

0.23

107

0.02859047

9.882445179

8.953539063

-1.15

108

0.028912

109

0.02859047

110

0.028912

8.744308992

7.970220562

-0.46

111

0.028912

8.744308992

7.970220562

-0.23

112

0.02859047

113

0.028912

8.744308992

7.970220562

0.23

0.23

114

0.028912

8.744308992

7.970220562

0.46

0.23

115

0.02859047

116

0.028912

117

0.02859047

9.882445179

8.953539063

1.15

0.23

118

0.02859047

9.882445179

8.953539063

1.38

0.23

119

0.02859047

9.882445179

8.953539063

1.61

0.23

120

0.02859047

9.882445179

8.953539063

-1.61

121

0.02859047

9.882445179

8.953539063

-1.38

122

0.028912

123

0.02859047

124

0.028912

8.744308992

7.970220562

-0.69

0.46

125

0.028912

8.744308992

7.970220562

-0.46

0.46

126

0.028912

8.744308992

7.970220562

-0.23

127

0.02859047

128

0.028912

8.744308992

7.970220562

0.23

0.46

129

0.028912

8.744308992

7.970220562

0.46

0.46

130

0.028912

8.744308992

7.970220562

0.69

0.46

131

0.02859047

132

0.028912

133

0.02859047

9.882445179

8.953539063

1.38

0.46

134

0.02859047

9.882445179

8.953539063

1.61

0.46

135

0.02859047

9.882445179

8.953539063

-1.61

136

0.02859047

9.882445179

8.953539063

-1.38

137

0.028912

8.744308992

7.970220562

-1.15

0.69

138

0.028912

8.744308992

7.970220562

-0.92

0.69

139

0.02859047

140

0.028912

141

0.02859047

8.744308992

8.744308992 9.882445179

9.882445179

9.882445179 8.744308992

8.744308992 9.882445179

9.882445179

9.882445179 8.744308992

9.882445179 8.744308992 9.882445179

7.970220562

7.970220562 8.953539063

8.953539063

8.953539063 7.970220562

7.970220562 8.953539063

8.953539063

8.953539063 7.970220562

8.953539063 7.970220562 8.953539063

1.15

-0.92

0 0 0

0.23 0.23

-0.69

0

0.69 0.92

-1.15

0.23 0.23 0.23 0.23

0.23 0.23

0.46 0.46 0.46

-0.92

0

0.92 1.15

-0.69 -0.46 -0.23

0.46

0.46 0.46

0.46 0.46

0.69 0.69

0.69 0.69 0.69


105

142

0.02859047

9.882445179

8.953539063

0

143

0.02859047

9.882445179

8.953539063

0.23

144

0.028912

145

0.02859047

146

0.028912

8.744308992

7.970220562

0.92

0.69

147

0.028912

8.744308992

7.970220562

1.15

0.69

148

0.02859047

9.882445179

8.953539063

1.38

0.69

149

0.02859047

9.882445179

8.953539063

1.61

0.69

150

0.02859047

9.882445179

8.953539063

-1.38

151

0.02859047

9.882445179

8.953539063

-1.15

152

0.028912

8.744308992

7.970220562

-0.92

0.92

153

0.028912

9.882445179

8.953539063

-0.69

0.92

154

0.02859047

155

0.028912

156

0.02859047

157

0.028912

158

0.02859047

159

0.028912

8.744308992

7.970220562

0.69

0.92

160

0.028912

8.744308992

7.970220562

0.92

0.92

161

0.02859047

9.882445179

8.953539063

1.15

0.92

162

0.02859047

9.882445179

8.953539063

1.38

0.92

163

0.02859047

9.882445179

8.953539063

-1.38

1.15

164

0.02859047

9.882445179

8.953539063

-1.15

1.15

165

0.02859047

9.882445179

8.953539063

-0.92

166

0.028912

8.744308992

7.970220562

-0.69

1.15

167

0.028912

8.744308992

7.970220562

-0.46

1.15

168

0.02859047

169

0.028912

170

0.02859047

171

0.028912

8.744308992

7.970220562

0.46

1.15

172

0.028912

8.744308992

7.970220562

0.69

1.15

173

0.02859047

9.882445179

8.953539063

0.92

1.15

174

0.02859047

9.882445179

8.953539063

1.15

1.15

175

0.02859047

9.882445179

8.953539063

1.38

1.15

176

0.02859047

9.882445179

8.953539063

-1.15

1.38

177

0.02859047

9.882445179

8.953539063

-0.92

1.38

178

0.02859047

9.882445179

8.953539063

-0.69

1.38

179

0.02859047

9.882445179

8.953539063

-0.46

1.38

180

0.02859047

9.882445179

8.953539063

-0.23

181

0.02859047

9.882445179

8.953539063

0

182

0.02859047

9.882445179

8.953539063

0.23

1.38

183

0.02859047

9.882445179

8.953539063

0.46

1.38

184

0.02859047

9.882445179

8.953539063

0.69

1.38

185

0.02859047

9.882445179

8.953539063

0.92

1.38

186

0.02859047

9.882445179

8.953539063

1.15

1.38

187

0.02859047

9.882445179

8.953539063

-0.69

1.61

188

0.02859047

9.882445179

8.953539063

-0.46

1.61

189

0.02859047

9.882445179

8.953539063

-0.23

190

0.02859047

9.882445179

8.953539063

0

191

0.02859047

9.882445179

8.953539063

0.23

1.61

192

0.02859047

9.882445179

8.953539063

0.46

1.61

193

0.02859047

9.882445179

8.953539063

0.69

1.61

8.744308992

7.970220562

9.882445179

8.953539063

9.882445179 8.744308992

0.46

8.953539063

9.882445179

8.744308992

0 0.23

8.953539063

7.970220562

0

8.953539063

0.23

! max_40_x_(neighbour+gap+distance)

1

2

4E-4

2.2996E-01

10

4E-4

2.2996E-01

/

2

3

4E-4

2.2996E-01

11

4E-4

2.2996E-01

/

3

4

4E-4

2.2996E-01

12

4E-4

2.2996E-01

/

4

5

4E-4

2.2996E-01

13

4E-4

2.2996E-01

/

5

6

4E-4

2.2996E-01

14

4E-4

2.2996E-01

/

6

7

4E-4

2.2996E-01

15

4E-4

2.2996E-01

/

7

0

0.0000000

8

9

4E-4

2.2996E-01

16

20

4E-4

4E-4

2.2996E-01

2.2996E-01

0.92 0.92 0.92

1.15

/

1.15 1.15

file = this_file

0.0000000

0.92 0.92

-0.23

!

channel

0.92

0.46

8.953539063

9.882445179

0.92

-0.23

8.953539063

9.882445179

0.69

-0.46

7.970220562

9.882445179

0.69 0.69

0.69

7.970220562

8.744308992

0.69

/

1.15

1.38 1.38

1.61 1.61


106

9

10

4E-4

2.2996E-01

21

4E-4

2.2996E-01

/

10

11

4E-4

2.2996E-01

22

4E-4

2.2996E-01

/

11

12

4E-4

2.2996E-01

23

4E-4

2.2996E-01

/

12

13

4E-4

2.2996E-01

24

4E-4

2.2996E-01

/

13

14

4E-4

2.2996E-01

25

4E-4

2.2996E-01

/

14

15

4E-4

2.2996E-01

26

4E-4

2.2996E-01

/

15

16

4E-4

2.2996E-01

27

4E-4

2.2996E-01

/

16

17

4E-4

2.2996E-01

28

4E-4

2.2996E-01

/

17

18

4E-4

2.2996E-01

29

4E-4

2.2996E-01

/

18

0

0.0000000

19

20

4E-4

2.2996E-01

32

4E-4

2.2996E-01

/

20

21

4E-4

2.2996E-01

33

4E-4

2.2996E-01

/

21

22

4E-4

2.2996E-01

34

4E-4

2.2996E-01

/

22

23

4E-4

2.2996E-01

35

4E-4

2.2996E-01

/

23

24

4E-4

2.2996E-01

36

4E-4

2.2996E-01

/

24

25

4E-4

2.2996E-01

37

4E-4

2.2996E-01

/

25

26

4E-4

2.2996E-01

38

4E-4

2.2996E-01

/

26

27

4E-4

2.2996E-01

39

4E-4

2.2996E-01

/

27

28

4E-4

2.2996E-01

40

4E-4

2.2996E-01

/

28

29

4E-4

2.2996E-01

41

4E-4

2.2996E-01

/

29

30

4E-4

2.2996E-01

42

4E-4

2.2996E-01

/

30

31

4E-4

2.2996E-01

43

4E-4

2.2996E-01

/

31

0

0.0000000

32

33

4E-4

2.2996E-01

46

4E-4

2.2996E-01

/

33

34

4E-4

2.2996E-01

47

4E-4

2.2996E-01

/

34

35

4E-4

2.2996E-01

48

4E-4

2.2996E-01

/

35

36

4E-4

2.2996E-01

49

4E-4

2.2996E-01

/

36

37

4E-4

2.2996E-01

50

4E-4

2.2996E-01

/

37

38

4E-4

2.2996E-01

51

4E-4

2.2996E-01

/

38

39

4E-4

2.2996E-01

52

4E-4

2.2996E-01

/

39

40

4E-4

2.2996E-01

53

4E-4

2.2996E-01

/

40

41

4E-4

2.2996E-01

54

4E-4

2.2996E-01

/

41

42

4E-4

2.2996E-01

55

4E-4

2.2996E-01

/

42

43

4E-4

2.2996E-01

56

4E-4

2.2996E-01

/

43

44

4E-4

2.2996E-01

57

4E-4

2.2996E-01

/

44

0

0.0000000

45

46

4E-4

2.2996E-01

60

4E-4

2.2996E-01

/

46

47

4E-4

2.2996E-01

61

4E-4

2.2996E-01

/

47

48

4E-4

2.2996E-01

62

4E-4

2.2996E-01

/

48

49

4E-4

2.2996E-01

63

4E-4

2.2996E-01

/

49

50

4E-4

2.2996E-01

64

4E-4

2.2996E-01

/

50

51

4E-4

2.2996E-01

65

4E-4

2.2996E-01

/

51

52

4E-4

2.2996E-01

66

4E-4

2.2996E-01

/

52

53

4E-4

2.2996E-01

67

4E-4

2.2996E-01

/

53

54

4E-4

2.2996E-01

68

4E-4

2.2996E-01

/

54

55

4E-4

2.2996E-01

69

4E-4

2.2996E-01

/

55

56

4E-4

2.2996E-01

70

4E-4

2.2996E-01

/

56

57

4E-4

2.2996E-01

71

4E-4

2.2996E-01

/

57

58

4E-4

2.2996E-01

72

4E-4

2.2996E-01

/

58

59

4E-4

2.2996E-01

73

4E-4

2.2996E-01

/

59

0

60

61

4E-4

2.2996E-01

75

4E-4

2.2996E-01

/

61

62

4E-4

2.2996E-01

76

4E-4

2.2996E-01

/

62

63

4E-4

2.2996E-01

77

4E-4

2.2996E-01

/

63

64

4E-4

2.2996E-01

78

4E-4

2.2996E-01

/

64

65

4E-4

2.2996E-01

79

4E-4

2.2996E-01

/

65

66

4E-4

2.2996E-01

80

4E-4

2.2996E-01

/

66

67

4E-4

2.2996E-01

81

4E-4

2.2996E-01

/

67

68

4E-4

2.2996E-01

82

4E-4

2.2996E-01

/

68

69

4E-4

2.2996E-01

83

4E-4

2.2996E-01

/

69

70

4E-4

2.2996E-01

84

4E-4

2.2996E-01

/

0.0000000

0.0000000

30

0.0000000

44

0.0000000

58

0.0000000

74

4E-4

4E-4

4E-4

4E-4

2.2996E-01

2.2996E-01

2.2996E-01

2.2996E-01

/

/

/

/


107

70

71

4E-4

2.2996E-01

85

4E-4

2.2996E-01

/

71

72

4E-4

2.2996E-01

86

4E-4

2.2996E-01

/

72

73

4E-4

2.2996E-01

87

4E-4

2.2996E-01

/

73

74

4E-4

2.2996E-01

88

4E-4

2.2996E-01

/

74

0

75

76

4E-4

2.2996E-01

90

4E-4

2.2996E-01

/

76

77

4E-4

2.2996E-01

91

4E-4

2.2996E-01

/

77

78

4E-4

2.2996E-01

92

4E-4

2.2996E-01

/

78

79

4E-4

2.2996E-01

93

4E-4

2.2996E-01

/

79

80

4E-4

2.2996E-01

94

4E-4

2.2996E-01

/

80

81

4E-4

2.2996E-01

95

4E-4

2.2996E-01

/

81

82

4E-4

2.2996E-01

96

4E-4

2.2996E-01

/

82

83

4E-4

2.2996E-01

97

4E-4

2.2996E-01

/

83

84

4E-4

2.2996E-01

98

4E-4

2.2996E-01

/

84

85

4E-4

2.2996E-01

99

4E-4

2.2996E-01

/

85

86

4E-4

2.2996E-01

100

4E-4

2.2996E-01

/

86

87

4E-4

2.2996E-01

101

4E-4

2.2996E-01

/

87

88

4E-4

2.2996E-01

102

4E-4

2.2996E-01

/

88

89

4E-4

2.2996E-01

103

4E-4

2.2996E-01

/

89

0

90

91

4E-4

2.2996E-01

105

4E-4

2.2996E-01

/

91

92

4E-4

2.2996E-01

106

4E-4

2.2996E-01

/

92

93

4E-4

2.2996E-01

107

4E-4

2.2996E-01

/

93

94

4E-4

2.2996E-01

108

4E-4

2.2996E-01

/

94

95

4E-4

2.2996E-01

109

4E-4

2.2996E-01

/

95

96

4E-4

2.2996E-01

110

4E-4

2.2996E-01

/

96

97

4E-4

2.2996E-01

111

4E-4

2.2996E-01

/

97

98

4E-4

2.2996E-01

112

4E-4

2.2996E-01

/

98

99

4E-4

2.2996E-01

113

4E-4

2.2996E-01

/

99

100

4E-4

2.2996E-01

114

4E-4

2.2996E-01

/

100

101

4E-4

2.2996E-01

115

4E-4

2.2996E-01

/

101

102

4E-4

2.2996E-01

116

4E-4

2.2996E-01

/

102

103

4E-4

2.2996E-01

117

4E-4

2.2996E-01

/

103

104

4E-4

2.2996E-01

118

4E-4

2.2996E-01

/

104

0

105

106

4E-4

2.2996E-01

120

4E-4

2.2996E-01

/

106

107

4E-4

2.2996E-01

121

4E-4

2.2996E-01

/

107

108

4E-4

2.2996E-01

122

4E-4

2.2996E-01

/

108

109

4E-4

2.2996E-01

123

4E-4

2.2996E-01

/

109

110

4E-4

2.2996E-01

124

4E-4

2.2996E-01

/

110

111

4E-4

2.2996E-01

125

4E-4

2.2996E-01

/

111

112

4E-4

2.2996E-01

126

4E-4

2.2996E-01

/

112

113

4E-4

2.2996E-01

127

4E-4

2.2996E-01

/

113

114

4E-4

2.2996E-01

128

4E-4

2.2996E-01

/

114

115

4E-4

2.2996E-01

129

4E-4

2.2996E-01

/

115

116

4E-4

2.2996E-01

130

4E-4

2.2996E-01

/

116

117

4E-4

2.2996E-01

131

4E-4

2.2996E-01

/

117

118

4E-4

2.2996E-01

132

4E-4

2.2996E-01

/

118

119

4E-4

2.2996E-01

133

4E-4

2.2996E-01

/

119

0

0.0000000

0.0000000

0.0000000

0.0000000

0.0000000

89

0.0000000

104

0.0000000

119

0.0000000

134

4E-4

4E-4

4E-4

4E-4

2.2996E-01

2.2996E-01

2.2996E-01

2.2996E-01

120

121

4E-4

2.2996E-01

135

4E-4

2.2996E-01

/

121

122

4E-4

2.2996E-01

136

4E-4

2.2996E-01

/

122

123

4E-4

2.2996E-01

137

4E-4

2.2996E-01

/

123

124

4E-4

2.2996E-01

138

4E-4

2.2996E-01

/

124

125

4E-4

2.2996E-01

139

4E-4

2.2996E-01

/

125

126

4E-4

2.2996E-01

140

4E-4

2.2996E-01

/

126

127

4E-4

2.2996E-01

141

4E-4

2.2996E-01

/

127

128

4E-4

2.2996E-01

142

4E-4

2.2996E-01

/

128

129

4E-4

2.2996E-01

143

4E-4

2.2996E-01

/

129

130

4E-4

2.2996E-01

144

4E-4

2.2996E-01

/

130

131

4E-4

2.2996E-01

145

4E-4

2.2996E-01

/

/

/

/

/


108

131

132

4E-4

2.2996E-01

146

4E-4

2.2996E-01

/

132

133

4E-4

2.2996E-01

147

4E-4

2.2996E-01

/

133

134

4E-4

2.2996E-01

148

4E-4

2.2996E-01

/

134

0

135

136

4E-4

2.2996E-01

0

0.0000000

136

137

4E-4

2.2996E-01

150

4E-4

2.2996E-01

/

137

138

4E-4

2.2996E-01

151

4E-4

2.2996E-01

/

138

139

4E-4

2.2996E-01

152

4E-4

2.2996E-01

/

139

140

4E-4

2.2996E-01

153

4E-4

2.2996E-01

/

140

141

4E-4

2.2996E-01

154

4E-4

2.2996E-01

/

141

142

4E-4

2.2996E-01

155

4E-4

2.2996E-01

/

142

143

4E-4

2.2996E-01

156

4E-4

2.2996E-01

/

143

144

4E-4

2.2996E-01

157

4E-4

2.2996E-01

/

144

145

4E-4

2.2996E-01

158

4E-4

2.2996E-01

/

145

146

4E-4

2.2996E-01

159

4E-4

2.2996E-01

/

146

147

4E-4

2.2996E-01

160

4E-4

2.2996E-01

/

147

148

4E-4

2.2996E-01

161

4E-4

2.2996E-01

/

148

149

4E-4

2.2996E-01

162

4E-4

2.2996E-01

/

149

0

150

151

4E-4

2.2996E-01

163

4E-4

2.2996E-01

/

151

152

4E-4

2.2996E-01

164

4E-4

2.2996E-01

/

152

153

4E-4

2.2996E-01

165

4E-4

2.2996E-01

/

153

154

4E-4

2.2996E-01

166

4E-4

2.2996E-01

/

154

155

4E-4

2.2996E-01

167

4E-4

2.2996E-01

/

155

156

4E-4

2.2996E-01

168

4E-4

2.2996E-01

/

156

157

4E-4

2.2996E-01

169

4E-4

2.2996E-01

/

157

158

4E-4

2.2996E-01

170

4E-4

2.2996E-01

/

158

159

4E-4

2.2996E-01

171

4E-4

2.2996E-01

/

159

160

4E-4

2.2996E-01

172

4E-4

2.2996E-01

/

160

161

4E-4

2.2996E-01

173

4E-4

2.2996E-01

/

161

162

4E-4

2.2996E-01

174

4E-4

2.2996E-01

/

162

0

163

164

4E-4

2.2996E-01

0

0.0000000

164

165

4E-4

2.2996E-01

176

4E-4

2.2996E-01

/

165

166

4E-4

2.2996E-01

177

4E-4

2.2996E-01

/

166

167

4E-4

2.2996E-01

178

4E-4

2.2996E-01

/

167

168

4E-4

2.2996E-01

179

4E-4

2.2996E-01

/

168

169

4E-4

2.2996E-01

180

4E-4

2.2996E-01

/

169

170

4E-4

2.2996E-01

181

4E-4

2.2996E-01

/

170

171

4E-4

2.2996E-01

182

4E-4

2.2996E-01

/

171

172

4E-4

2.2996E-01

183

4E-4

2.2996E-01

/

172

173

4E-4

2.2996E-01

184

4E-4

2.2996E-01

/

173

174

4E-4

2.2996E-01

185

4E-4

2.2996E-01

/

174

175

4E-4

2.2996E-01

186

4E-4

2.2996E-01

/

175

0

176

177

4E-4

2.2996E-01

0

0.0000000

0.0000000

/

177

178

4E-4

2.2996E-01

0

0.0000000

0.0000000

/

178

179

4E-4

2.2996E-01

187

4E-4

2.2996E-01

/

179

180

4E-4

2.2996E-01

188

4E-4

2.2996E-01

/

180

181

4E-4

2.2996E-01

189

4E-4

2.2996E-01

/

181

182

4E-4

2.2996E-01

190

4E-4

2.2996E-01

/

182

183

4E-4

2.2996E-01

191

4E-4

2.2996E-01

/

183

184

4E-4

2.2996E-01

192

4E-4

2.2996E-01

/

184

185

4E-4

2.2996E-01

193

4E-4

2.2996E-01

/

185

186

4E-4

2.2996E-01

0

0.0000000

186

0

187

188

4E-4

2.2996E-01

0

0.0000000

0.0000000

/

188

189

4E-4

2.2996E-01

0

0.0000000

0.0000000

/

189

190

4E-4

2.2996E-01

0

0.0000000

0.0000000

/

190

191

4E-4

2.2996E-01

0

0.0000000

0.0000000

/

0.0000000

0.0000000

0.0000000

0.0000000

0.0000000

0.0000000

149

0.0000000

0

0.0000000

175

0.0000000

0

0.0000000

0

4E-4

2.2996E-01

/

0.0000000

/

0.0000000

4E-4

0.0000000

2.2996E-01

/

0.0000000

/

0.0000000

0.0000000

0.0000000

0.0000000

/

/

/

0.0000000

/


109

191

192

4E-4

2.2996E-01

0

0.0000000

0.0000000

/

192

193

4E-4

2.2996E-01

0

0.0000000

0.0000000

/

193

0

0.0000000

0.0000000

0

0.0000000

0.0000000

/

! !-----------------------------------------------------------------------------&thermal_connection ! file = this_file connection_number

rho_cp_thickness

wall_width

first_channel

resistance

second_channel

! !-----------------------------------------------------------------------------&channel_area_variation ! gradual_insertion_iterations = 1 ! file = this_file channel_number

axial_location

channel_area

wetted_perimeter

heated_perimeter

! &gap_spacing_variation ! file = this_file gap_number

axial_location

gap_spacing

! !-----------------------------------------------------------------------------&rod_layout ! set_burnup_by_transient = off ! set_axial_conduction = off ! set_radial_twigl = off set_radial_sor = off set_radial_dir = on ! number_of_fuel_nodes = 10 ! next number is not taken into account, at last for this case tested from 50 to 5000 ... minimum_fuel_cladding_gap_conductance = 5000.0 ! file = this_file rod_number

material_type

outer_diameter

power_fraction -0.69

x_position

1

2

0.95e-2

0.362785402

2

2

0.95e-2

0.518976029

3

1

0.95e-2

0.5009301

4

2

0.95e-2

0.516486935

0

5

1

0.95e-2

0.496574186

0.23

-1.61

6

2

0.95e-2

0.518353756

0.46

-1.61

7

2

0.95e-2

0.363407675

0.69

-1.61

8

1

0.95e-2

0.305536247

-1.15

-1.38

9

2

0.95e-2

0.657120727

-0.92

-1.38

-0.46 -0.23

-1.61 -1.61 -1.61 -1.61

10

2

0.95e-2

0.927809663

-0.69

-1.38

11

2

0.95e-2

1.499678933

-0.46

-1.38

12

1

0.95e-2

1.510879854

-0.23

13

2

0.95e-2

1.023017496

0

14

1

0.95e-2

1.507768487

0.23

15

2

0.95e-2

1.498434386

0.46

16

2

0.95e-2

0.92905421

17

2

0.95e-2

0.658365274

18

1

0.95e-2

0.3042917

1.15

19

1

0.95e-2

0.3042917

-1.38

20

2

0.95e-2

0.758551294

-1.15

-1.15

21

2

0.95e-2

1.546349439

-0.92

-1.15

22

3

0.01075

1.220867254

-0.69

-1.15

23

3

0.01075

1.038765162

-0.46

-1.15

24

1

0.95e-2

0.998748833

-0.23

25

3

0.01075

1.021142379

0

0.69 0.92

-1.38 -1.38 -1.38 -1.38 -1.38 -1.38 -1.38 -1.15

-1.15 -1.15

y_position

resistance


110

26

1

0.95e-2

0.988170185

0.23

-1.15

27

3

0.01075

1.038765162

0.46

-1.15

28

3

0.01075

1.214503472

0.69

-1.15

29

2

0.95e-2

1.548838533

0.92

-1.15

30

2

0.95e-2

0.758551294

1.15

-1.15

31

1

0.95e-2

0.306158521

1.38

-1.15

32

2

0.95e-2

0.658987548

-1.38

-0.92

33

2

0.95e-2

1.548838533

-1.15

-0.92

34

3

0.01075

1.193943558

-0.92

-0.92

35

3

0.01075

1.054429858

-0.69

36

2

0.95e-2

1.32606465

37

3

0.01075

1.070584076

-0.23

38

2

0.95e-2

1.092089845

0

39

3

0.01075

1.068136467

40

2

0.95e-2

1.32606465

41

3

0.01075

1.070094554

0.69

-0.92

42

3

0.01075

1.193943558

0.92

-0.92

43

2

0.95e-2

1.546971712

1.15

-0.92

44

2

0.95e-2

0.658365274

1.38

-0.92

45

2

0.95e-2

0.364029948

-1.61

46

2

0.95e-2

0.92905421

47

3

0.01075

1.214503472

-1.15

-0.69

48

3

0.01075

1.070094554

-0.92

-0.69

49

2

0.95e-2

1.336021024

-0.69

-0.69

50

3

0.01075

0.939881768

-0.46

-0.69

51

1

0.95e-2

1.310507814

-0.23

52

1

0.95e-2

1.182941764

0

53

1

0.95e-2

1.309885541

0.23

-0.69

54

3

0.01075

0.927643724

0.46

-0.69

55

2

0.95e-2

1.336021024

0.69

-0.69

56

3

0.01075

1.053940336

0.92

-0.69

57

3

0.01075

1.211566341

1.15

-0.69

58

2

0.95e-2

0.928431937

1.38

-0.69

59

2

0.95e-2

0.364029948

1.61

-0.69

60

2

0.95e-2

0.518353756

-1.61

-0.46

61

2

0.95e-2

1.498434386

-1.38

-0.46

62

3

0.01075

1.038765162

-1.15

63

2

0.95e-2

1.32606465

64

3

0.01075

0.928133246

-0.69

-0.46

65

3

0.01075

1.080864033

-0.46

-0.46

66

3

0.01075

0.893866723

-0.23

67

2

0.95e-2

1.305529627

0

68

3

0.01075

0.893866723

0.23

-0.46

69

3

0.01075

1.080864033

0.46

-0.46

70

3

0.01075

0.940371289

0.69

71

2

0.95e-2

1.32606465

72

3

0.01075

1.038765162

1.15

-0.46

73

2

0.95e-2

1.500301206

1.38

-0.46

74

2

0.95e-2

0.518976029

1.61

-0.46

75

1

0.95e-2

0.496574186

-1.61

-0.23

76

1

0.95e-2

1.507768487

-1.38

-0.23

77

1

0.95e-2

0.988170185

-1.15

-0.23

78

3

0.01075

1.068136467

-0.92

-0.23

79

1

0.95e-2

1.309885541

-0.69

-0.23

80

3

0.01075

0.893866723

-0.46

-0.23

81

3

0.01075

1.091633511

-0.23

82

1

0.95e-2

1.085244838

0

83

3

0.01075

1.091633511

0.23

-0.23

84

3

0.01075

0.894356245

0.46

-0.23

85

1

0.95e-2

1.310507814

0.69

-0.23

86

3

0.01075

1.071073598

0.92

-0.23

87

1

0.95e-2

0.998126559

1.15

-0.23

88

1

0.95e-2

1.510879854

1.38

-0.23

89

1

0.95e-2

0.500307827

1.61

-0.23

90

2

0.95e-2

0.516486935

-1.61

-0.46

0.23 0.46

-1.38

-0.92

0.92

-0.92 -0.92 -0.92 -0.92 -0.92 -0.92

-0.69 -0.69

-0.69 -0.69

-0.46 -0.46

-0.46 -0.46

-0.46 -0.46

-0.23 -0.23

0


111

91

2

0.95e-2

1.023017496

-1.38

0

92

3

0.01075

1.021142379

-1.15

0

93

2

0.95e-2

1.092089845

-0.92

0

94

1

0.95e-2

1.182941764

-0.69

0

95

2

0.95e-2

1.305529627

-0.46

0

96

1

0.95e-2

1.085244838

-0.23

97

2

0.95e-2

0.875538696

0

98

1

0.95e-2

1.085244838

0.23

0

99

2

0.95e-2

1.305529627

0.46

0

0 0

100

1

0.95e-2

1.182941764

0.69

0

101

2

0.95e-2

1.091467572

0.92

0

102

3

0.01075

1.020652857

1.15

0

103

2

0.95e-2

1.023017496

1.38

0

104

2

0.95e-2

0.516486935

1.61

105

1

0.95e-2

0.5009301

106

1

0.95e-2

1.510879854

-1.38

0.23

107

1

0.95e-2

0.998748833

-1.15

0.23

108

3

0.01075

1.071073598

-0.92

0.23

109

1

0.95e-2

1.310507814

-0.69

0.23

110

3

0.01075

0.893866723

-0.46

0.23

111

3

0.01075

1.091633511

-0.23

112

1

0.95e-2

1.085244838

0

113

3

0.01075

1.091633511

0.23

0.23

114

3

0.01075

0.894356245

0.46

0.23

115

1

0.95e-2

1.310507814

0.69

0.23

116

3

0.01075

1.068625989

0.92

0.23

117

1

0.95e-2

0.988792458

1.15

0.23

118

1

0.95e-2

1.507768487

1.38

0.23

119

1

0.95e-2

0.496574186

1.61

0.23

120

2

0.95e-2

0.518976029

-1.61

0.46

121

2

0.95e-2

1.500301206

-1.38

0.46

122

3

0.01075

1.038765162

-1.15

123

2

0.95e-2

1.32606465

124

3

0.01075

0.939881768

-0.69

0.46

125

3

0.01075

1.080864033

-0.46

0.46

126

3

0.01075

0.893866723

-0.23

127

2

0.95e-2

1.305529627

0

128

3

0.01075

0.894356245

0.23

0.46

129

3

0.01075

1.080864033

0.46

0.46

130

3

0.01075

0.927643724

0.69

131

2

0.95e-2

1.32606465

132

3

0.01075

1.039254684

1.15

0.46

133

2

0.95e-2

1.499056659

1.38

0.46

134

2

0.95e-2

0.518353756

1.61

0.46

135

2

0.95e-2

0.364029948

-1.61

0.69

136

2

0.95e-2

0.928431937

-1.38

0.69

137

3

0.01075

1.211076819

-1.15

0.69

138

3

0.01075

1.053940336

-0.92

0.69

139

2

0.95e-2

1.336021024

-0.69

0.69

140

3

0.01075

0.927643724

-0.46

0.69

141

1

0.95e-2

1.310507814

-0.23

142

1

0.95e-2

1.182941764

0

143

1

0.95e-2

1.311130088

0.23

0.69

144

3

0.01075

0.940371289

0.46

0.69

145

2

0.95e-2

1.336021024

0.69

0.69

146

3

0.01075

1.070094554

0.92

0.69

147

3

0.01075

1.214992993

1.15

0.69

148

2

0.95e-2

0.929676484

1.38

0.69

149

2

0.95e-2

0.364652222

1.61

0.69

150

2

0.95e-2

0.658365274

-1.38

0.92

151

2

0.95e-2

1.546971712

-1.15

0.92

152

3

0.01075

1.193943558

-0.92

0.92

153

3

0.01075

1.070094554

-0.69

154

2

0.95e-2

1.32606465

155

3

0.01075

1.068625989

-1.61

-0.92

0.92

-0.46 -0.23

0 0.23

0.23 0.23

0.46 0.46

0.46 0.46

0.46 0.46

0.69 0.69

0.92 0.92 0.92


112

156

2

0.95e-2

1.091467572

0

157

3

0.01075

1.071073598

0.23

158

2

0.95e-2

1.32606465

159

3

0.01075

1.053940336

0.69

0.92

160

3

0.01075

1.193454036

0.92

0.92

161

2

0.95e-2

1.548838533

1.15

0.92

162

2

0.95e-2

0.658987548

1.38

0.92

163

1

0.95e-2

0.306158521

-1.38

1.15

164

2

0.95e-2

0.758551294

-1.15

1.15

165

2

0.95e-2

1.548838533

-0.92

1.15

166

3

0.01075

1.214503472

-0.69

1.15

167

3

0.01075

1.039254684

-0.46

1.15

168

1

0.95e-2

0.988170185

-0.23

169

3

0.01075

1.020652857

0

170

1

0.95e-2

0.998126559

0.23

1.15

171

3

0.01075

1.038765162

0.46

1.15

172

3

0.01075

1.211076819

0.69

1.15

173

2

0.95e-2

1.546349439

0.92

1.15

174

2

0.95e-2

0.759173568

1.15

1.15

175

1

0.95e-2

0.304913974

1.38

176

1

0.95e-2

0.3042917

177

2

0.95e-2

0.658365274

178

2

0.95e-2

0.92905421

179

2

0.95e-2

1.499056659

-0.46

180

1

0.95e-2

1.507768487

-0.23

181

2

0.95e-2

1.023017496

0

182

1

0.95e-2

1.510879854

0.23

1.38

183

2

0.95e-2

1.499678933

0.46

1.38

184

2

0.95e-2

0.927809663

0.69

1.38

185

2

0.95e-2

0.657743001

0.92

1.38

186

1

0.95e-2

0.305536247

1.15

1.38

187

2

0.95e-2

0.363407675

-0.69

1.61

188

2

0.95e-2

0.518353756

-0.46

1.61

189

1

0.95e-2

0.496574186

-0.23

190

2

0.95e-2

0.516486935

0

191

1

0.95e-2

0.500307827

0.23

1.61

192

2

0.95e-2

0.518976029

0.46

1.61

193

2

0.95e-2

0.362785402

0.69

1.61

! file = this_file rod

max_6_x_(channel+fraction)

1

1

300

/

2

2

300

/

3

3

300

/

4

4

300

/

5

5

300

/

6

6

300

/

7

7

300

/

8

8

300

/

9

9

300

/

10

10

300

/

11

11

300

/

12

12

300

/

13

13

300

/

14

14

300

/

15

15

300

/

16

16

300

/

17

17

300

/

18

18

300

/

19

19

300

/

20

20

300

/

21

21

300

/

22

22

236

/

23

23

236

/

24

24

300

/

0.46

-1.15

0.92 0.92 0.92

1.15 1.15

1.15 1.38

-0.92 -0.69

1.38 1.38 1.38 1.38 1.38

1.61 1.61

Appendix B. SCF Steady State Input 25

25

236

/

26

26

300

/

27

27

236

/

28

28

236

/

29

29

300

/

30

30

300

/

31

31

300

/

32

32

300

/

33

33

300

/

34

34

236

/

35

35

236

/

36

36

300

/

37

37

236

/

38

38

300

/

39

39

236

/

40

40

300

/

41

41

236

/

42

42

236

/

43

43

300

/

44

44

300

/

45

45

300

/

46

46

300

/

47

47

236

/

48

48

236

/

49

49

300

/

50

50

236

/

51

51

300

/

52

52

300

/

53

53

300

/

54

54

236

/

55

55

300

/

56

56

236

/

57

57

236

/

58

58

300

/

59

59

300

/

60

60

300

/

61

61

300

/

62

62

236

/

63

63

300

/

64

64

236

/

65

65

236

/

66

66

236

/

67

67

300

/

68

68

236

/

69

69

236

/

70

70

236

/

71

71

300

/

72

72

236

/

73

73

300

/

74

74

300

/

75

75

300

/

76

76

300

/

77

77

300

/

78

78

236

/

79

79

300

/

80

80

236

/

81

81

236

/

82

82

300

/

83

83

236

/

84

84

236

/

85

85

300

/

86

86

236

/

87

87

300

/

88

88

300

/

89

89

300

/

113


90

300

/

91

91

300

/

92

92

236

/

93

93

300

/

94

94

300

/

95

95

300

/

96

96

300

/

97

97

300

/

98

98

300

/

99

99

300

/

100

100

300

/

101

101

300

/

102

102

236

/

103

103

300

/

104

104

300

/

105

105

300

/

106

106

300

/

107

107

300

/

108

108

236

/

109

109

300

/

110

110

236

/

111

111

236

/

112

112

300

/

113

113

236

/

114

114

236

/

115

115

300

/

116

116

236

/

117

117

300

/

118

118

300

/

119

119

300

/

120

120

300

/

121

121

300

/

122

122

236

/

123

123

300

/

124

124

236

/

125

125

236

/

126

126

236

/

127

127

300

/

128

128

236

/

129

129

236

/

130

130

236

/

131

131

300

/

132

132

236

/

133

133

300

/

134

134

300

/

135

135

300

/

136

136

300

/

137

137

236

/

138

138

236

/

139

139

300

/

140

140

236

/

141

141

300

/

142

142

300

/

143

143

300

/

144

144

236

/

145

145

300

/

146

146

236

/

147

147

236

/

148

148

300

/

149

149

300

/

150

150

300

/

151

151

300

/

152

152

236

/

153

153

236

/

154

154

300

/

114


155

236

/

156

156

300

/

157

157

236

/

158

158

300

/

159

159

236

/

160

160

236

/

161

161

300

/

162

162

300

/

163

163

300

/

164

164

300

/

165

165

300

/

166

166

236

/

167

167

236

/

168

168

300

/

169

169

236

/

170

170

300

/

171

171

236

/

172

172

236

/

173

173

300

/

174

174

300

/

175

175

300

/

176

176

300

/

177

177

300

/

178

178

300

/

179

179

300

/

180

180

300

/

181

181

300

/

182

182

300

/

183

183

300

/

184

184

300

/

185

185

300

/

186

186

300

/

187

187

300

/

188

188

300

/

189

189

300

/

190

190

300

/

191

191

300

/

192

192

300

/

193

193

300

/

115

! ! Reference document of Thermal Properties ORNL/TM-2000/351 page 11 (fuel_density). 17 specific heat ! For material 2 y have no data. only aproached by hand ... file = this_file material 1

property uo2

2

uo2

3

uo2_puo2

fuel_conductivity

fuel_specific_heat

fuel_density

fuel_emissivity

fuel_thermal_expansion

3.46

292

10450

1.0

0.0

3.46

292

10450

1.0

0.0

3.46

298

10450

1.0

0.0

! ! Fuel roughness is the in fuel clad gap 8.5e-5 see also Sunderland page 28 file = this_file material

fuel_diameter

fuel_inner_radius

fraction_of_theoretical_density

fraction_of_puo2

fuel_roughness

1

8.05e-3

0.0

1.0

0.0

8.5e-5

2

8.05e-3

0.0

1.0

0.0

8.5e-5

3

9.11e-3

0.0

1.0

2.0

8.5e-5

! file = this_file material

property

clad_conductivity

clad_specific_heat

clad_density

clad_emissivity

clad_thermal_expansion

1

benpwr

22.34

242.672

6552

1.0

0.0

2

benpwr

22.34

242.672

6552

1.0

0.0

3

benpwr

22.34

242.672

6552

1.0

0.0

! file = this_file material

clad_thickness

gap_conductance

fill_gap

model_gap

clad_roughness

fill_gas_pressure

fill_gas_volume

1

0.64e-3

5670.00

off

off

1.0e-6

5.0e5

1.0d-5

2

0.64e-3

5670.00

off

off

1.0e-6

5.0e5

1.0d-5


0.725e-3

5670.00

off

116

off

1.0e-6

5.0e5

1.0d-5

! file = this_file configuration_type

number_of_zones

! file = this_file configuration_type

zone_number

zone_end_relative_axial_location

material

! file = this_file rod_number

relative_axial_location

burnup

0

0.0

0.0

0

1.0

0.0

! file = this_file rod_number

molar_fraction_he

0

molar_fraction_xe

1.0

0.0

molar_fraction_ar 0.0

molar_fraction_kr 0.0

molar_fraction_h 0.0

molar_fraction_n 0.0

!----------------------------------------------------------------------------------------------------------------------------------------&calculation_control ! set_sor_iteration = off set_gauss_elimination = off set_bicgstab_iteration = on ! ! set_boron_transport = off ! set_buoyancy = on set_critical_power_iteration = off ! ! start_time = 0.0 stop_time = 0.0 time_step = 0.0 number_of_time_steps = 0 ! maximum_cladding_temperature_change = 1.0 maximum_central_fuel_temperature_change = 5.0 maximum_coolant_temperature_change = 1.0 maximum_void_change = 0.02 ! print_timestep_every = 1 ! total_axial_length = 3.90 number_of_axial_nodes = 20 print_axial_level_every = 1 ! axial_flow_convergence = 1.0e-5 ! boundary_pressure_convergence = 1.0e-3 ! channel_orientation = 0.0 ! lateral_flow_damping = 0.7 axial_flow_damping = 0.7 sor_acceleration = 1.0 ! max_of_axial_flow_iterations = 200 min_of_axial_flow_iterations = 10 ! file = this_file time

time_step_size

! file = this_file cell_number cell_length !


117

!----------------------------------------------------------------------------------------------------------------------------------------&grid_spacer_wire_wrap set_wire_wrap

= off

set_grid_spacer = on set_both

= off

! gradual_insertion_iterations = 1 rod_diameter = 9.5e-3 wire_wrap_pitch = 0.0 wire_wrap_thickness = 0.0 ! file = this_file gap_number

effective_length

relative_crossing

relative_crossing

! file = this_file channel_number number_of_wire_wraps ! file = this_file channel_number


loss_coefficient

0

0.1200

0.0

0

0.2608

0.0

0

0.3989

0.0

0

0.5369

0.0

0

0.6750

0.0

0

0.8131

0.0

0

0.9512

0.0

! file = this_file gap_number


cross_flow_fraction

! !----------------------------------------------------------------------------------------------------------------------------------------&lateral_transport ! set_constant_mixing_coefficient = off set_rogers_tahir_rectangular = off set_rogers_tahir_triangular = off set_rogers_rosehart = on ! set_equal_mass_exchange = off set_equal_volume_exchange = on ! constant_mixing_coefficient = 0.0 void_drift_coefficient = 1.4 ! crossflow_resistance_coefficient = 0.5 lateral_conduction_factor = 0.0 ! !----------------------------------------------------------------------------------------------------------------------------------------&operating_conditions ! set_uniform_inlet_flux = on set_flow_split_first_axial = off set_flow_rate_fraction = off set_flux_fraction = off set_flow_rate = off set_flux = off ! set_pure_flow_condition = off set_unified_pressure_drop = on set_driving_pressure_condition = off ! set_transient_flow_rate_factor = on set_transient_flow_rate = off set_transient_flux = off !

Appendix B. SCF Steady State Input exit_pressure = 15.8e6 inlet_temperature = 291 ! inlet_boron_concentration = 500 inlet_flow_rate = 18682.0 inlet_mass_flux = 0.0 total_power = 3850.0e6 average_heat_flux = 0.0 pressure_drop = 0.0 heat_fraction_moderator = 0.019 ! ! ! file = this_file channel_number

inlet_temperature

! file = this_file channel_number

inlet_flow

! file = this_file time exit_pressure ! file = this_file time inlet_temperature ! file = this_file channel_number time inlet_temperature ! file = this_file time inlet_boron_concentration ! file = this_file channel_number time inlet_boron_concentration ! file = this_file time inlet_flow ! file = this_file channel_number time inlet_flow ! file = this_file time

heat_flux_factor

! file = this_file power_map_time ! file = this_file axial_cell_number

rod_number

power_map

! ! &pointkinetics

set_pointkinetics_power = on

pointkinetics_max_time_step = 1.0e-5

prompt_neutron_lifetime = 2.0e-5

power_weighting_exponent = 2.0

fraction_delayed_neutrons_group_1 = 0.000247 fraction_delayed_neutrons_group_2 = 0.00138 fraction_delayed_neutrons_group_3 = 0.00122 fraction_delayed_neutrons_group_4 = 0.00264

118


119

fraction_delayed_neutrons_group_5 = 0.000832 fraction_delayed_neutrons_group_6 = 0.000169

decay_constant_group_1 = 0.0127 decay_constant_group_2 = 0.0317 decay_constant_group_3 = 0.1150 decay_constant_group_4 = 0.3110 decay_constant_group_5 = 1.4000 decay_constant_group_6 = 3.8700

doppler_coefficient = -2.84e-5 coolant_temperature_coefficient = -3.93e-4 void_coefficient = -0.12345 boron_coefficient = -2.32e-5 ! !---------------------------------------------------------------------------------------------------------------------------------------&output_display ! delta_time = 0.0 ! file = this_file channel_number ! file = this_file rod_number ! file = this_file gap_number ! file = this_file axial_location

channel_or_rod_number

variable

!---------------------------------------------------------------------------------------------------------------------------------------end

Appendix C

Mail NRC. Bug TRACE 5 Patch 3 From: Fernandez Mora, Ivan (INR) [mailto:[email protected]] Sent: Tuesday, February 11, 2014 5:19 AM To: Murray, Christopher Subject: ECI problems

Dear Chris, My name is Ivan Fernandez, I wrote you some years ago since Spanish Nuclear Regulator, CSN, was connecting TRACE to its safety assessment code SCAIS through ECI and I was the main developer ([email protected]). You solved me my questions very quickly and SCAIS currently manages TRACE v5.0 control blocks and is able to simulate transients coupled through ECI . Currently I’m working at Karlsruhe Institute of Technology, KIT, analyzing the possibility of connecting TRACE to SubChanFlow (a subchannel code like Cobra, developed

at KIT) ).

The connection will need the Exterior Trace component, since it is a core replacement. I found that the ECI does not work with TRACEp3 to the basic inputs distributed in the original ECI version (of course modified to run alone with patch 3). My questions are; Are there any new samples working with ECI and TRACEp3? If not, will those bugs be repaired and ECI work again for future TRACE versions and the effort of developing an ECI interface to SubChanFlow is worthy? Sorry for the communication channel, since KIT is CAMP user, but I have not currently access to TRACE bugzilla. Thanks in advance Ivan Fernandez Mora

120

Appendix C. Mail NRC

121

From: Murray, Christopher [mailto:[email protected]] Sent: Tuesday, February 18, 2014 3:50 PM To: Fernandez Mora, Ivan (INR) Cc: Hoxie, Chris Subject: RE: ECI problems

Dear Ivan, We are aware that currently the ECI functionality is broken in current versions of TRACE (including patch 3).

Unfortunately, our code development priorities have been such that

fixing it has not been a priority for us.

I talked it over with my manager and we still

want to support it, so we are going to make some effort this Spring/Summer to get it working again.

Right now our focus is on getting Patch 4 of TRACE ready for release.

Because we have made so many significant changes to underlying TRACE architecture since the release of V5.0, fixing it may take some time.

I would estimate that it would not be

ready for use again until sometime in Fall of this year, assuming we are able to get one of our developers to start devoting some time to fixing it this Spring. Chris

Bibliography [1] Division of Safety Analysis. Office of Nuclear Regulatory Research. TRACE V5.0. THEORY MANUAL Field Equations, Solution Methods, and Physical Models. NRC, Washington, DC 20555-0001, 3 edition, 7 1993. An optional note. [2] John Mahaffy and Chris Murray. Communication between the consolidated code and other processes. Technical report, Penn State University Applied Research Laboratory, P.O. Box 30 State College, PA 16804, 1998. [3] Uwe Imke. Input Instructions for SUBCHANFLOW 2.5. Institute for Neutron Physics and Reactor Technology (INR), 8 2013. [4] Uwe Imke and Victor Hugo Sanchez. Validation of the subchannel code subchanflow using the nupec pwr tests (psbt). Hindawi Publishing Corporation Science and Technology of Nuclear Installations, 2012. [5] D. Porsch et al. Specifications of the pwr fuel assembly, uo2 (4 w/o u-235) 18 x 18 – 24, for code-to-code comparisons. 6 2004. [6] Siegfried Mittag. Erzeugung und Nutzung von Bibliotheken von Zwei-GruppenDiffusionsparametern zur Berechnung eines KWU-Konvoi-Reaktors mit dem Reaktordynamik-Programm DYN3D. Dresden : FZR, Wissenschaftlich-technische Berichte / Forschungszentrum Rossendorf, 2002.

Final Report, http://d-

nb.info/964776006. [7] Fuel design data, 2012. http://www.neimagazine.com. [8] S Beck and R Collins. Moody diagram. lines created using swami and jaine formula. University of Sheffield, 2008.

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Konvoi PWR Core Model with TRACE and

Konvoi PWR Core Model with TRACE and

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